Time

[Parbat]

What does "time" really mean?
i really don't know that.

[ghwellsjr]

According to Richard Feynman, Time is what happens when nothing else is happening.

Actually, no one knows how to define time but we all know what it means. So that means you must know what it means. Why do you want to say that you really don't know what time is? You must be referring to some subtle aspect of it, like how can it be going slower for someone moving at a high speed? Is that what you are concerned about?

[Parbat]

i mean,how can we say "time" is a dimension?
& dimension means something that is required to explain any object,is that true?

[TheAlkemist]

Thanks for asking this question Parbat!!

How can time be a dimension? What I was taught in physics:
A dimension is "the least number of COORDINATES required to specify, uniquely, a point in a space."

So is a dimension the same as a coordinate?:confused: I thought dimensions were related to ARCHITECTURE, STRUCTURE and ORIENTATION (shape, geometry) and coordinates were used to specify the LOCATION of things.

In 3D space, the dimensions are LENGTH, WIDTH and HEIGHT, pointing outwards from the object. The coordinates are LONGITUDE, LATITUDE and ALTITUDE and they point inwards, towards the object because the specify location. The corresponding VECTORS would be DEPTH, BREADTH and ELEVATION which specify the mutually orthogonal DIRECTIONS the object moves. Dimensions and coordinates are static while vectors are dynamic. The only attributes common to these three concepts are direction and orthogonality which are QUALITATIVE attributes. That's it.

So how does time fit into this? How is time considered a dimension when it's routinely used--by mathematicians, as a NUMBER LINE--to QUANTIFY?

Time is a one-dimensional quantity used to sequence events, to quantify the durations of events and the intervals between them, and (used together with space) to quantify and measure the motions of objects.
http://en.wikipedia.org/wiki/Time

So if time is a QUANTIFIER of a sequence of events, where/how does the QUALITATIVE attribute of directionality orthogonality come in here? :confused: Or is this merely an attribute that mathematicians (or Einstein) added to create a model/manifold for doing the math? (Minkowski Space-time?):confused:

I don't get it. In science, don't we have to be objective and consistent with the terms (verbs, nouns, adverbs, adjectives) we use as per their definitions? Is't this required to maintain coherence and eliminate the ambiguity often encountered when metaphors are used? Isn't this what distinguishes science from other subjective forms of inquiry (like religion)?

I appologize for the lengthiness/dimension of this post. :tongue:

[bcrowell]

i mean,how can we say "time" is a dimension?
& dimension means something that is required to explain any object,is that true?

I don't understand what it would mean to explain an object.

In relativity, we have four coordinates that are used in order to specify an event. It doesn't make sense in relativity to treat a time coordinate differently from a spatial coordinate, because when one observer is in motion relative to another observer, each observer's measurements of time and distance are related to the other observer's measurements by equations that don't break apart cleanly into time and space equations.

[ghwellsjr]

Thanks for asking this question Parbat!!

How can time be a dimension? What I was taught in physics:
A dimension is "the least number of COORDINATES required to specify, uniquely, a point in a space."

So is a dimension the same as a coordinate?:confused: I thought dimensions were related to ARCHITECTURE, STRUCTURE and ORIENTATION (shape, geometry) and coordinates were used to specify the LOCATION of things.

In 3D space, the dimensions are LENGTH, WIDTH and HEIGHT, pointing outwards from the object. The coordinates are LONGITUDE, LATITUDE and ALTITUDE and they point inwards, towards the object because the specify location. The corresponding VECTORS would be DEPTH, BREADTH and ELEVATION which specify the mutually orthogonal DIRECTIONS the object moves. Dimensions and coordinates are static while vectors are dynamic. The only attributes common to these three concepts are direction and orthogonality which are QUALITATIVE attributes. That's it.

So how does time fit into this? How is time considered a dimension when it's routinely used--by mathematicians, as a NUMBER LINE--to QUANTIFY?

Time is a one-dimensional quantity used to sequence events, to quantify the durations of events and the intervals between them, and (used together with space) to quantify and measure the motions of objects.
http://en.wikipedia.org/wiki/Time

So if time is a QUANTIFIER of a sequence of events, where/how does the QUALITATIVE attribute of directionality orthogonality come in here? :confused: Or is this merely an attribute that mathematicians (or Einstein) added to create a model/manifold for doing the math? (Minkowski Space-time?):confused:

I don't get it. In science, don't we have to be objective and consistent with the terms (verbs, nouns, adverbs, adjectives) we use as per their definitions? Is't this required to maintain coherence and eliminate the ambiguity often encountered when metaphors are used? Isn't this what distinguishes science from other subjective forms of inquiry (like religion)?

I appologize for the lengthiness/dimension of this post. :tongue:

Everything you have said is excellent, but you stopped too soon. You should also have said that your choice of co-ordinate system should not make any difference in how you analyze a situation, don't you agree?

Well, that's the problem. When we try to define the distance between to events, widely separated in distance and time, we will get different answers for every co-ordinate system we use and that's no fun.

So to solve this problem we use a new kind of vector that includes both the normal three-component vector for space and the normal scalar for time, and we call it a four-vector. Then we invent (or discover) a way to calculate a new "distance" called "interval" that is always the same, no matter which co-ordinate system we use to describe, characterize, or analyze any situation.

Does that make sense to you?

[Time Machine]

So if time is a QUANTIFIER of a sequence of events, where/how does the QUALITATIVE attribute of directionality orthogonality come in here? :confused: Or is this merely an attribute that mathematicians (or Einstein) added to create a model/manifold for doing the math? (Minkowski Space-time?):confused:

I don't get it. In science, don't we have to be objective and consistent with the terms (verbs, nouns, adverbs, adjectives) we use as per their definitions? Is't this required to maintain coherence and eliminate the ambiguity often encountered when metaphors are used? Isn't this what distinguishes science from other subjective forms of inquiry (like religion)?


I'm not much keen on time as a dimension either. As time dilation is now being proved reactive to gravity, could time be thought of as a force? Perhaps "force" is the wrong termanology but "energy" doesn't quite cut it.

[TheAlkemist]

Everything you have said is excellent, but you stopped to soon. You should also have said that your choice of co-ordinate system should not make any difference in how you analyze a situation, don't you agree?What do you mean by "analyze a situation"? I'm going to assume that you mean how you describe an event occurring between (at least) two objects?

To analyze = qualify and quantify.

The coordinate system specifies the locations of the objects.
The dimension system specifies the shapes of the objects.
The vector system specifies the motion of the objects.
Coordinates and dimensions and vectors are all concepts used to qualify the situation. At this point, yes, it should make no difference how you analyze the situation if you stay consistent with these systems.

However...in order to quantify the situation we invented another abstract concept called numbers. Specifically number lines. And herein lies the mysterious merger of quantifying and qualifying concepts--numbers (quantifier) and lines (geometric qualifier) respectively. At which point numbers (with magnitude) have now inherited directionality. Vectors inherit magnitude, time inherits directionality.


Well, that's the problem. When we try to define the distance between to events, widely separated in distance and time, we will get different answers for every co-ordinate system we use and that's no fun.Why? If you don't muddle qualifiers and quantifiers there shouldn't be a problem. You should be able to objectively qualitatively define the distance between 2 objects in space by the relationship between their coordinates AND further define that distance relationship using a quantifying concept. My issue is in the packaging. When you start assigning attributes like directionality to abstract concepts like time. It's like talking about the direction of love, anger, or the color blue. these are all concepts which only have meaning in the context of the relationship between at least two objects. Eg., anger vs sadness, love vs hate, red vs blue, etc

This is not a trivial issue of semantics. When we use words in science, we must use them consistently as an objective criterion.


So to solve this problem we use a new kind of vector that includes both the normal three-component vector for space and the normal scalar for time, and we call it a four-vector. Then we invent (or discover) a way to calculate a new "distance" called "interval" that is always the same, no matter which co-ordinate system we use to describe, characterize, or analyze any situation.

Does that make sense to you?No. Sound like convenient mathematical magic to me. :frown: "Abra-kadabra!"... now a scalar is a vector!
Not saying it's useless, it just makes no real life physical sense.

[TheAlkemist]

another thing. LENGTH and DISTANCE are NOT synonymous. At least not in science.

LENGTH = used to qualify SHAPE of (one) object
DISTANCE = used to qualify the relationship between (two) objects

There's a QUALITATIVE difference.

People often use these terms interchangeably. They talk about the length of time and concepts like 'time dilation'. What does this mean? You can only distort the SHAPE of an OBJECT. So is time an object?

Again, if these are only metaphors then how can this "science" objective? These circular definitions just introduce avenues for all kinds of circular arguments. What good science shouldn't allow.

[Time Machine]

People often use these terms interchangeably. They talk about the length of time and concepts like 'time dilation'. What does this mean? You can only distort the SHAPE of an OBJECT. So is time an object?

Again, if these are only metaphors then how can this "science" objective? These circular definitions just introduce avenues for all kinds of circular arguments. What good science shouldn't allow.

I could be very much mistaken, but you can distort the shape of a force.
Does this mean time is a force?
Please excuse me if I am way off here. I do get your circular arguments comment, but isn't that how new concepts are born?

[ghwellsjr]

Why? If you don't muddle qualifiers and quantifiers there shouldn't be a problem. You should be able to objectively qualitatively define the distance between 2 objects in space by the relationship between their coordinates AND further define that distance relationship using a quantifying concept. My issue is in the packaging. When you start assigning attributes like directionality to abstract concepts like time.
I agree with you, there shouldn't be a problem, but unfortunately, Mother Nature doesn't agree with us and, so, we lose. It does make a difference which co-ordinate system we use and there is no way for us to determine which one is the correct one, so that is why we use the four-vector interval.

Time is placed orthogonal to the three components of space in the "imaginary" direction and it works and that is why we do it. If you don't like it you need to come up with another scheme that works but you can't stick to the one you have because it doesn't work.

[phyti]

The coordinate system specifies the locations of the objects.
The dimension system specifies the shapes of the objects.
The vector system specifies the motion of the objects.
Coordinates and dimensions and vectors are all concepts used to qualify the situation. At this point, yes, it should make no difference how you analyze the situation if you stay consistent with these systems.

However...in order to quantify the situation we invented another abstract concept called numbers. Specifically number lines. And herein lies the mysterious merger of quantifying and qualifying concepts--numbers (quantifier) and lines (geometric qualifier) respectively. At which point numbers (with magnitude) have now inherited directionality. Vectors inherit magnitude, time inherits directionality.
-Your descriptions are confusing and overly complicated.
Numbers were/are used for expressing magnitudes, and have been for all of human history. Distances were/are expressed informally as magnitudes with a direction, and formally as vectors. There is no difference between coordinates and dimensions, they are both spatial intervals. The length of an object is the difference between the coordinates of the ends of the object.

Why? If you don't muddle qualifiers and quantifiers there shouldn't be a problem. You should be able to objectively qualitatively define the distance between 2 objects in space by the relationship between their coordinates AND further define that distance relationship using a quantifying concept. My issue is in the packaging. When you start assigning attributes like directionality to abstract concepts like time. It's like talking about the direction of love, anger, or the color blue. these are all concepts which only have meaning in the context of the relationship between at least two objects. Eg., anger vs sadness, love vs hate, red vs blue, etc
-Time is a scalar (number/magnitude) and thus has no direction. The time variable was mathematically manipulated for the purpose of treating it as another dimension.

This is not a trivial issue of semantics. When we use words in science, we must use them consistently as an objective criterion.

No. Sound like convenient mathematical magic to me. :frown: "Abra-kadabra!"... now a scalar is a vector!
Not saying it's useless, it just makes no real life physical sense.
-A vector/tensor/matrix can contain any number of mixed type of values/attributes, as long as the values are manipulated in a consistent manner. Eg. A personal 'vector' (name, height, weight, eye color, etc...), useful in an employee database.

post#9:
People often use these terms interchangeably. They talk about the length of time and concepts like 'time dilation'. What does this mean? You can only distort the SHAPE of an OBJECT. So is time an object?
-Processes, mechanical, chemical, etc. are mediated by light. Light speed is constant in space and independent of its origin. When objects such as clocks move, the associated processes slow down. The clock slices time into longer intervals, therefore the clock readings are relative for the observer moving with the clock.

Again, if these are only metaphors then how can this "science" objective? These circular definitions just introduce avenues for all kinds of circular arguments. What good science shouldn't allow.
-Science can only measure real world processes, create conceptual models that mimic reality, and keep the ones that are successful. The concepts science uses are all ideal metaphors, just as images are not the objects in the image. We experience the world indirectly.
[/QUOTE]

[TheAlkemist]

I could be very much mistaken, but you can distort the shape of a force.
Does this mean time is a force?
Please excuse me if I am way off here. I do get your circular arguments comment, but isn't that how new concepts are born?How can you distort a force? A force has no shape and isn't physical object. You can only distort physical objects that have shape. If you're talking about distorting the vector (or tensor) that describes a force then that's a figurative statement. Just like the statement; "spreading love".
I'm not saying the concept of force is useless of meaningless because it's not!

New concepts should be born from scientific methodology so that the language used to describe them is as objective as possible. For example the concept, viscosity. Viscosity describes how forces change the dimensions of a fluid using corresponding vectors. You never hear people talking about "distorting" the viscosity of a fluid. You distort the shape of the fluid by changing the dimensions that describe its state.
This makes more sense to me.


I agree with you, there shouldn't be a problem, but unfortunately, Mother Nature doesn't agree with us and, so, we lose. It does make a difference which co-ordinate system we use and there is no way for us to determine which one is the correct one, so that is why we use the four-vector interval.
Please explain. I'm confused.

Time is placed orthogonal to the three components of space in the "imaginary" direction and it works and that is why we do it. If you don't like it you need to come up with another scheme that works but you can't stick to the one you have because it doesn't work.If it works so good why is gravity a problem? Why aren't the SM and GR compatible? Does this have anything to do with the mathematical formulations of these models? Just asking. Thanks.

[TheAlkemist]

-Your descriptions are confusing and overly complicated.
Numbers were/are used for expressing magnitudes, and have been for all of human history. Distances were/are expressed informally as magnitudes with a direction, and formally as vectors. Actually they are very simple and objective. I never said that numbers were not used to express magnitudes. They are and very useful at that. But, how can you use an informal definition on the one hand and then incorporate it into a formal definition on the other and hope to maintain consistency when trying to describe things objectively? When you rely on circular definitions and assume synonyms doesn't this confuse things? I thought math was about formal objective descriptions? I know science is supposed to be. Just because this is how people have been doing it since history doesn't make it correct.

Distance and length are NOT synonymous. There is a non-trivial,
qualitative difference between length and distance. Length is used to describe the shape of a continuous object. Distance is used to describe the space between 2 indivisible objects. Look up the definition of distance in any standard English dictionary and that's the definition you'll get; the space between two things.

The length of an object is the difference between the coordinates of the ends of the object.Do you agree that an object is made up of discrete atoms/particles separated by (a very very considerable amount of) space? I think most of the physics community does. If so, then which coordinates of what particle are you measuring from to determine the length of the object?:confused:

There is no difference between coordinates and dimensions, they are both spatial intervals. I disagree. Coordinates describe location/position. Dimensions describe shape/structure. Above you said that length is the difference between coordinates of the ends. If you're now saying coordinates = dimensions then you're saying length is the difference between the dimensions of the ends. :confused: This makes absolutely NO sense. How is a dimension a "spatial interval"?
See what I mean.

-Time is a scalar (number/magnitude) and thus has no direction. The time variable was mathematically manipulated for the purpose of treating it as another dimension. Could I well it magic then? Because this mathematical manipulation has created a physical thing from concept. A number changes to an object. Only objects have direction. I'm not being facetious.


-A vector/tensor/matrix can contain any number of mixed type of values/attributes, as long as the values are manipulated in a consistent manner. Eg. A personal 'vector' (name, height, weight, eye color, etc...), useful in an employee database.Fair enough. How consistently and objectively do you think your so-called personality vector can be applied? I have strong doubts that it can. But I have a few computer science buddies working on AI that would be earger to know.:cool:


-Processes, mechanical, chemical, etc. are mediated by light. Light speed is constant in space and independent of its origin. When objects such as clocks move, the associated processes slow down. The clock slices time into longer intervals, therefore the clock readings are relative for the observer moving with the clock. :confused: The clock slices time? Since you can only slice through a continuous object, then are you suggesting that time is a continuous? But yoou say time is a dimension and you said above that dimensions are spatial intervals. :confused: So are you slicing through the intervals? I'm confused.


-Science can only measure real world processes, create conceptual models that mimic reality, and keep the ones that are successful. The concepts science uses are all ideal metaphors, just as images are not the objects in the image.Fair enough. I have no issue with metaphors. We can't avoid them as they're pervasive in everyday life. It's the consistency and potential for ambiguity and circular arguments that I have issue with. And by what criteria do you measure success?

I'll leave it here because I don't think this is the appropriate forum for the direction this might be heading.

[DaveC426913]

There are space-like dimensions and time-like dimensions. They are not the same, but they are all part of our 4-dimensional spacetime.

[Passionflower]

What does "time" really mean?
i really don't know that.
In special and general relativity time for an observer is simply the length between two events that cross his worldline, this length is physically measured by a clock. O more generally it is the calculated length between two events with a timelike distance between them over an arbitrary path

[inflector]

I asked a similar question earlier:

http://www.physicsforums.com/showthread.php?t=424757

I found the reply by marcus to be most helpful. He made me aware of the FXQi contest on the nature of time:

http://www.fqxi.org/community/forum/category/10

In particular, the essay by Julian Barbour, which won the contest, was very interesting and insightful. I'm not sure I agree with his conclusions yet, but I find it very interesting.

[phyti]

Actually they are very simple and objective. I never said that numbers were not used to express magnitudes. They are and very useful at that. But, how can you use an informal definition on the one hand and then incorporate it into a formal definition on the other and hope to maintain consistency when trying to describe things objectively? When you rely on circular definitions and assume synonyms doesn't this confuse things? I thought math was about formal objective descriptions? I know science is supposed to be. Just because this is how people have been doing it since history doesn't make it correct.

-The reference to informal use is to emphasize that a rigid definition is not needed for practical applications. Travel directions can be very general, eg., 10 miles down route 7 just past Wal-Mart. Scientific study obviously requires more rigid definitions with minimum ambiguity. My reply to the op's question about the meaning of time... it depends on the context. So it goes with definitions, it depends on the purpose.
Here's part of a paper on knowledge which mentions your concern about circular reasoning.

To form knowledge the mind;
--perceives reality,
--forms concepts to model reality,
--predicts reality from these concepts,
--keeps the concepts as knowledge when prediction matches reality.
--modifies the concepts after more perception

knowledge is a set of concepts used as a reference for understanding
By definition knowledge is always incomplete because all reality is never perceived.
For simplicity, a concept is defined within a context that excludes other concepts.
--Other concepts may not be relevant to the purpose.
--There may be relevant concepts that have not been created.
--An approximate definition may be sufficient for the purpose.
Definition is a relative referencing process.
--A definition is expressed in terms of other definitions.
--This process can be circular or incomplete.
Forming knowledge is a continuous process of refinement.
Knowledge is only as good as its definition.

[phyti]

Distance and length are NOT synonymous. There is a non-trivial,
qualitative difference between length and distance. Length is used to describe the shape of a continuous object. Distance is used to describe the space between 2 indivisible objects. Look up the definition of distance in any standard English dictionary and that's the definition you'll get; the space between two things.

Do you agree that an object is made up of discrete atoms/particles separated by (a very very considerable amount of) space? I think most of the physics community does. If so, then which coordinates of what particle are you measuring from to determine the length of the object?:confused:

I disagree. Coordinates describe location/position. Dimensions describe shape/structure. Above you said that length is the difference between coordinates of the ends. If you're now saying coordinates = dimensions then you're saying length is the difference between the dimensions of the ends. :confused: This makes absolutely NO sense. How is a dimension a "spatial interval"?
See what I mean.

Chemistry and quantum theory demonstrate that matter is discrete, 2 yeses.

Coordinates are measured from a common origin (by definition).
Three dimensions are sufficient for simple rectangular solids.
1. Place a ruler with the 'o' mark at one end and read the value 10 where the other end contacts the ruler. The length is 10-0=10.
2. Place the ruler with the '4' mark at one end and read the value 14 where the other end contacts the ruler. The length is 14-4=10.
The only difference is where you designate the origin. You are still measuring space.
If 3 4" widgets are end to end, we have 12" of widgets. If the middle one is removed, there is still 4" of space between the other 2, whether it's occupied or not!

[TheAlkemist]

-The reference to informal use is to emphasize that a rigid definition is not needed for practical applications. Travel directions can be very general, eg., 10 miles down route 7 just past Wal-Mart. Scientific study obviously requires more rigid definitions with minimum ambiguity. My reply to the op's question about the meaning of time... it depends on the context. So it goes with definitions, it depends on the purpose.
Here's part of a paper on knowledge which mentions your concern about circular reasoning.

To form knowledge the mind;
--perceives reality,
--forms concepts to model reality,
--predicts reality from these concepts,
--keeps the concepts as knowledge when prediction matches reality.
--modifies the concepts after more perception

knowledge is a set of concepts used as a reference for understanding
By definition knowledge is always incomplete because all reality is never perceived.
For simplicity, a concept is defined within a context that excludes other concepts.
--Other concepts may not be relevant to the purpose.
--There may be relevant concepts that have not been created.
--An approximate definition may be sufficient for the purpose.
Definition is a relative referencing process.
--A definition is expressed in terms of other definitions.
--This process can be circular or incomplete.
Forming knowledge is a continuous process of refinement.
Knowledge is only as good as its definition.
I agree with the general gist of what you've said, except the red highlighted. In science, I think it's even more important to be as objective as possible in practical situations.

For example, how does one consistently communicate the concept of a 'time-line' when people have different definitions of what a line is. Is a line, by one definition, a series of points? Or is it, by another definition, the empty space between 2 points? Or a continuous extended rectangle? Do you see how either one of these definitions has a very significant and non-trivial consequence on the meaning of a 'time-line'?

[TheAlkemist]

Chemistry and quantum theory demonstrate that matter is discrete, 2 yeses.

Coordinates are measured from a common origin (by definition).
Three dimensions are sufficient for simple rectangular solids.
1. Place a ruler with the 'o' mark at one end and read the value 10 where the other end contacts the ruler. The length is 10-0=10.
2. Place the ruler with the '4' mark at one end and read the value 14 where the other end contacts the ruler. The length is 14-4=10.

coordinates specify the location or position of one thing. What you described is simply using a ruler to measure the length of a shape. It has nothing to do with coordinates.


The only difference is where you designate the origin. You are still measuring space.
If 3 4" widgets are end to end, we have 12" of widgets. If the middle one is removed, there is still 4" of space between the other 2, whether it's occupied or not! You can't measure space. You measure objects in space. You can only talk about the distance between 2 objects in space. But not the length of space. Length is an attribute reserved for shapes.

And you said: "The length of an object is the difference between the coordinates of the ends of the object." and then... "The only difference is where you designate the origin."

Which is what i'm asking you. What exact point (coordinate position/location) in the solid object you're measuring, are you designating as the origin?

[phyti]

coordinates specify the location or position of one thing. What you described is simply using a ruler to measure the length of a shape. It has nothing to do with coordinates.


You can't measure space. You measure objects in space. You can only talk about the distance between 2 objects in space. But not the length of space. Length is an attribute reserved for shapes.

And you said: "The length of an object is the difference between the coordinates of the ends of the object." and then... "The only difference is where you designate the origin."

Which is what i'm asking you. What exact point (coordinate position/location) in the solid object you're measuring, are you designating as the origin?

When you measure the length of an object, you're measuring the space between the molecule at one end and the molecule at the other end. Whether there is matter in between them is irrelevant.
Objects 1,2, and 3 are small diameter spheres positioned inline. d= center to center distance.
Measure d1 between objects 1 and 2.
Measure d2 between objects 2 and 3.
S is the sum d1+d2. Isn't S the total distance/space between objects 1 and 3?

[yuiop]

Space is what prevents everything being in the same place and time is what prevents everything happening at the same time. :tongue:

Informally most laypersons think of coordinates as specifying a physical location, but in physics, coordinates specify an event, which specifies a location and a time. For example, you might arrange a meeting for next Monday, 10AM in the conference room, then the event is clearly defined and there is a greater chance of actually meeting than if the place or the time are left out. As has already been said, space and time are both specify intervals between events. When you think really hard about it, spatial distance can be just as mysterious as time. For example, when walking down a road you might gauge the distance by counting fence posts, but what about gauging distance crossing a great void in space where there are no fence posts? One way to do that would be to measure your velocity and then time how long it takes to cross the void, or similarly you might send a radar signal across the void and work out the distance from how long it takes the signal to return. Thought of like this, it is easy to see that time and space are intimately related. Consider a hermit that never leaves his cave. You might think it is easy to specify his physical location without specifying a time, but it turns out that this is not true. His physical location in July is different to his physical location in December because the Earth has moved to the other side of the Sun in that time. His physical location in December 2009 is different to his physical location in December 2010 because the Sun has moved a short way around the Galaxy in that time. It becomes clear that the physical location of our apparently stationary hermit is time dependent. This intimate relationship between time and spatial distance even extends to the simple measurement of a length of an object. Let us say we have an object that in one metre long. If the object is moving relative to us and we measure the physical location of the front of the object at 1PM and the physical location of the back of the object at 2PM and subtract the two measurements, then we might conclude that the object is a mile long. Clearly, to make a sensible measurement of the moving object's length, we have to specify that the spatial coordinates of the ends of the objects are measured at the same time, or allow for the velocity and the time difference of the coordinates to calculate the proper length and so even the simple measurement of the length of a humble object requires we take time into our considerations.

Time has always been a part of Galliean coordinates and making time a coordinate component is not a new invention of Einstein or relativity. Relativity just complicates things by demanding that you also specify who's time measurement is being used to specify an event, because time in relativity is not universal as in Newtonian physics.

[TheAlkemist]

When you measure the length of an object, you're measuring the space between the molecule at one end and the molecule at the other end. Whether there is matter in between them is irrelevant.
Objects 1,2, and 3 are small diameter spheres positioned inline. d= center to center distance.
Measure d1 between objects 1 and 2.
Measure d2 between objects 2 and 3.
S is the sum d1+d2. Isn't S the total distance/space between objects 1 and 3?
OK. I see where the issue is now. It's a question of matter, space, discreteness and coherence. Which might be outside the scope of this forum? I don't know.

But to answer your question, since 1, 2 and 3 are separate objects and not a single coherent object, then no. The distance between 1 and 3 would have to be measured from the surface of 1 to the surface of 3.

[TheAlkemist]

Space is what prevents everything being in the same place and time is what prevents everything happening at the same time. :tongue: good one:rofl:

Informally most laypersons think of coordinates as specifying a physical location, but in physics, coordinates specify an event, which specifies a location and a time. For example, you might arrange a meeting for next Monday, 10AM in the conference room, then the event is clearly defined and there is a greater chance of actually meeting than if the place or the time are left out.Most laypersons?:confused: I thought an event was a dynamic thing...something that happens over some period of time. An occurrence. So are you saying time is a coordinate? :confused: Someone else said it was a "dimension". Now i'm really confused.
And your analogy is bad. If you leave out the day and time you can still locate the conference room. When the conference (event) takes place is a separate issue which can be determined in relation to another/other object(s), whose location(s) can be described by a different set of coordinates--however you chose to calibrate it.


As has already been said, space and time are both specify intervals between events. When you think really hard about it, spatial distance can be just as mysterious as time. For example, when walking down a road you might gauge the distance by counting fence posts, but what about gauging distance crossing a great void in space where there are no fence posts? One way to do that would be to measure your velocity and then time how long it takes to cross the void, or similarly you might send a radar signal across the void and work out the distance from how long it takes the signal to return.If there are no fence posts and you're the only one in this void of space how would you measure velocity? Also, if velocity is measured as change in position with time you have to measure the time elapsed as you move somehow don't you? Or are you suggesting that you can measure velocity without measuring /recording time?
And as for the radar thing, don't you need another object for the radar's radio waves to hit off of and return?


Thought of like this, it is easy to see that time and space are intimately related. Consider a hermit that never leaves his cave. You might think it is easy to specify his physical location without specifying a time, but it turns out that this is not true. His physical location in July is different to his physical location in December because the Earth has moved to the other side of the Sun in that time. His physical location in December 2009 is different to his physical location in December 2010 because the Sun has moved a short way around the Galaxy in that time. It becomes clear that the physical location of our apparently stationary hermit is time dependent.This is an interesting point you bring up. But I would have to disagree. What's more fundamental here is motion. Space and motion being the most fundamental concepts. Time is a results from the motion of space (or more popularly, things in space).

So in a sense yes, time is connected to space but only through motion. We perceive time because matter (or more fundamentally, space) moves.

Think about your object that's fully characterized by it's spacetime coordinates. You know it's location and "time". Now lets say the object never ever moves. What meaning does time have then? In fact, the velocity of light and the vibration of crystals (both moving things) are the foundations of time in physics.

It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive by means of the changes (motion) of things.-- Ernst Mach


This intimate relationship between time and spatial distance even extends to the simple measurement of a length of an object. Let us say we have an object that in one metre long. If the object is moving relative to us and we measure the physical location of the front of the object at 1PM and the physical location of the back of the object at 2PM and subtract the two measurements, then we might conclude that the object is a mile long. No! The premise of your argument is false. You don't measure the length of an object by subtracting coordinates. Especially an object in motion! What you've described is simply a measurement of the DISTANCE between two positions; one occupied by the front of a moving object @ 1PM and the other occupied by the back of the moving object at 2PM. Concluding the LENGTH of the object from this DISTANCE is wrong!

Clearly, to make a sensible measurement of the moving object's length, we have to specify that the spatial coordinates of the ends of the objects are measured at the same time, or allow for the velocity and the time difference of the coordinates to calculate the proper length and so even the simple measurement of the length of a humble object requires we take time into our considerations.Sure. If you chose to measure the length of the object as the difference between two coordinates that specify positions at the ends of the object in some calibrated coordinate space then fine. But this would only make sense in the case of a static object. When you move the object the coordinates of the ends change. If you wana determine the length of the object using the coordinates you'd have to stop the object.
From what I learned in physics, a particle in a 3D coordinate space can be described by a position vector (drawn from the origin/reference to the particle). This give the relative position and direction of the particle. What determines whether the particle is at rest or in motion is the change of the vector with respect to the reference frame. If the reference frame doesn't change over time, then the object is pretty much at rest and you can measure the true length.



Time has always been a part of Galilean coordinates and making time a coordinate component is not a new invention of Einstein or relativity. Relativity just complicates things by demanding that you also specify who's time measurement is being used to specify an event, because time in relativity is not universal as in Newtonian physics.What exactly do you mean by coordinate component? An Galileo even said motion was more fundamental than time. Heck, motion was his shtick.

[Godswitch]

Time has 3 basic elements

Past - Present - Future

Both the present and future elements can be altered, the past is always constant

Of course you could argue the Past is not always a constant element because time itself is always moving forward so the past then becomes the present and so on

[DaveC426913]

... the past then becomes the present ...
It must be an interesting world you live in then. Or should I say...

.neht ni evil uoy dlrow gnitseretni na eb tsum tI

:wink:

[TheAlkemist]

Time has 3 basic elements

Past - Present - Future

Both the present and future elements can be altered, the past is always constant

Of course you could argue the Past is not always a constant element because time itself is always moving forward so the past then becomes the present and so on
Exactly. That's why theses notions of divided time always fall to the paradox of Zeno.



It must be an interesting world you live in then. Or should I say...

.neht ni evil uoy dlrow gnitseretni na eb tsum tI

:wink: lol

[Time Machine]

How can you distort a force? A force has no shape and isn't physical object. You can only distort physical objects that have shape. If you're talking about distorting the vector (or tensor) that describes a force then that's a figurative statement. Just like the statement; "spreading love".
I'm not saying the concept of force is useless of meaningless because it's not!

New concepts should be born from scientific methodology so that the language used to describe them is as objective as possible. For example the concept, viscosity. Viscosity describes how forces change the dimensions of a fluid using corresponding vectors. You never hear people talking about "distorting" the viscosity of a fluid. You distort the shape of the fluid by changing the dimensions that describe its state.
This makes more sense to me.



Please explain. I'm confused.

If it works so good why is gravity a problem? Why aren't the SM and GR compatible? Does this have anything to do with the mathematical formulations of these models? Just asking. Thanks.

With regards to my likening time to a force and statement concerning a force being shaped. Just a thought process: If electricity can be shaped into light bulbs, the strong force into nuclear whatevers and radiation into xray machines then IF time could be considered to be "force like" then it would explain dilation in the form of a shape as you mentioned.

Time as a dimension works mathematically and was derived as such.
If time dilations could be monitored according to the amount of time lapsed in each moment, could a new system of maths be derived?
In the event that time and gravity are linked, would this new system of maths incorporate gravity?

[khemist]

What exactly do you mean by coordinate component? An Galileo even said motion was more fundamental than time. Heck, motion was his shtick.

That doesnt make any sense. Without time, there is no motion. However, the converse is not true. Even if there is no motion, time can still be effecting the object. We can do this by setting a particular object at the center of a particular coordinate system.

Dimension is a convenient way to specify how many numbers (or anything else) are needed to tell an objects location in a particular coordinate system. For example, in an N-Dimensional coordinate system (N being any real number) there are N coordinates needed to have a location. We CAN have some of those coordinates be zero, in which case the "space" that the vector is in is isomorphic to another space. If I have one vector, the "space" it is in, called a vector space, is isomorphic to R^1, because a vector is a straight line.

If I have 2 vectors, v = <1,1,0> and u = <0,1,0>, and I span those vectors on, in this case, because I have 3 coordinates, I have a 3 dimensional coordinate system (R^3), while the SPAN is in fact isomorphic to R^2, although the vector space created by the span is still in R^3.

I hope this helps...

edit: I guess this doesnt even come close to answering the OP's question.
From what I understand, time is simply a passage of events, or a coordinate in our 3+1 dimensional world (3 spacial + 1 time). I think what you might be attempting to ask is what makes time go, or why does the arrow of time always point the same direction (although it might not be the same magnitude). It could have to do with entropy, though my knowledge in this is not as strong. Maybe in a year or so I can help more :P

[TheAlkemist]

That doesnt make any sense. Without time, there is no motion. However, the converse is not true. Even if there is no motion, time can still be effecting the object. We can do this by setting a particular object at the center of a particular coordinate system.No. The converse is true. Time doesn't exist outside of the dynamics (motion) of matter. Motion is how we humans experience, perceive and interpret periodicity. When you understand this it will be very clear and obvious to u.

You can confirm this connection between time and motion by simply thinking about any clock. All clocks function on the repeating motion of matter, from pendulum clocks, early watches which used rotating cog wheels, to modern clocks which operate by repeating vibrations of crystals. The official measure of time is an atomic clock which uses the natural resonance frequency (motion) of the cesium atom to measure time. For longer time cycles we use the repeating motion of the earth's orbit about the sun. Based on this, Western civilization has agreed on conventions (maybe enforced it...whatever) called we called days, months and years. All human means of calibrating time, even before clocks, were all based on motion of matter.[/quote]

Dimension is a convenient way to specify how many numbers (or anything else) are needed to tell an objects location in a particular coordinate system. For example, in an N-Dimensional coordinate system (N being any real number) there are N coordinates needed to have a location. We CAN have some of those coordinates be zero, in which case the "space" that the vector is in is isomorphic to another space. If I have one vector, the "space" it is in, called a vector space, is isomorphic to R^1, because a vector is a straight line.

If I have 2 vectors, v = <1,1,0> and u = <0,1,0>, and I span those vectors on, in this case, because I have 3 coordinates, I have a 3 dimensional coordinate system (R^3), while the SPAN is in fact isomorphic to R^2, although the vector space created by the span is still in R^3.

I hope this helps...Dimensions might be "a convenient way" to specify location but I think is flawed. In science, dimensions specify the shape and structure of matter. Coordinates specify the location of matter. In our 3D world, we have a coordinate system of determining the position of an object with respect to longitude, latitude and altitude. You are conflating two separate systems; dimensions and coordinates.


edit: I guess this doesnt even come close to answering the OP's question.
From what I understand, time is simply a passage of events, or a coordinate in our 3+1 dimensional world (3 spacial + 1 time). I think what you might be attempting to ask is what makes time go, or why does the arrow of time always point the same direction (although it might not be the same magnitude). It could have to do with entropy, though my knowledge in this is not as strong. Maybe in a year or so I can help more :PI agree with ONLY the red highlighted if u add "the effect of" between "simply" and "a".
And no, i'm not asking what makes time go. Time doesn't "go" anywhere. Things "go". We express/record our experience of that movement/periodicity as time. Math uses the conceptual construct called "number lines". Then call it a 4th dimension called time.

What i think ur talking about, the time reversal symmetry and "the arrow of time" paradox and it's relationship to entropy is a problem i'm not really concerned with because I don;t think about time like that in the first place.:biggrin:

[cshum00]

I love these forums because it always moves away from answering the original post. I try to give it a shot into answering the original question.

The original post question is: Why is time a dimension?

Let's first try to define what dimension is. Let's start with 2 dimensions. 2-dimensions in mathematics can be represented as 2 axis perpendicular to each other. If we add another dimension, we can visually think of it as adding a third axis orthogonal (orthogonal is the same as perpendicular except that perpendicular is a word only used for 2-dimensions) to the existing 2-dimensions.

What confuses people is when scientists say that adding an extra dimensions is the same as adding extra "space" or degree of freedom into the picture. When scientists say space, they don't mean the physical space where you can put an real and physical object. They mean the mathematical meaning of space where you have an extra axis which you can represent graphically in a sheet of paper. When scientists say 2-dimensions in space, they only mean 2-axis perpendicular to each other which you can graphically plot and nothing physical in real-life.

So, when scientists say that time is a spatial dimensions; they mean that it is useful for the mathematics to have an extra axis to analyze on a graph how time relates to other axes which could be distance, force, velocity, etc. Treating time as a dimensions is not controversial as you can see.

What is rather counter-intuitive, is that physics treats time not only as a independent variable but also as a dependent variable. Meaning, that time is no longer universal but the value of it can be changed and influenced by other factors. In the case of special relativity in physics, time can be changed by the 3 other dimensions of distance.

[ghwellsjr]

Wasn't this covered in my post #11 and #6 as well as many others?

[TheAlkemist]

I love these forums because it always moves away from answering the original post. I try to give it a shot into answering the original question.

The original post question is: Why is time a dimension?

Let's first try to define what dimension is. Let's start with 2 dimensions. 2-dimensions in mathematics can be represented as 2 axis perpendicular to each other. If we add another dimension, we can visually think of it as adding a third axis orthogonal (orthogonal is the same as perpendicular except that perpendicular is a word only used for 2-dimensions) to the existing 2-dimensions.this is one of the several MATHEMATICAL definitions of 2-dimensions. This is NOT a scientific definition.

What confuses people is when scientists say that adding an extra dimensions is the same as adding extra "space" or degree of freedom into the picture. When scientists say space, they don't mean the physical space where you can put an real and physical object. They mean the mathematical meaning of space where you have an extra axis which you can represent graphically in a sheet of paper. When scientists say 2-dimensions in space, they only mean 2-axis perpendicular to each other which you can graphically plot and nothing physical in real-life.This is incorrect and misleading. I'm a scientist. When we say space we simply mean...space. Space is that which has no shape or dimension. An object's shape can be specified or characterized by 3 dimensions; length, width and height, in space. These are parsimonious scientific definitions. Now if mathematicians by whatever convenient convention choose to call this "3-D space", whatever. IMO, the term "spatial dimension" is a misnomer.




So, when scientists say that time is a spatial dimensions; they mean that it is useful for the mathematics to have an extra axis to analyze on a graph how time relates to other axes which could be distance, force, velocity, etc. Treating time as a dimensions is not controversial as you can see.Scientists don't say this. Well...good scientists at least. Treating time as a dimension may not be controversial in the establishment but it's certainly self-contradicting and leads to irrational conclusions.

What is rather counter-intuitive, is that physics treats time not only as a independent variable but also as a dependent variable. Meaning, that time is no longer universal but the value of it can be changed and influenced by other factors. In the case of special relativity in physics, time can be changed by the 3 other dimensions of distance.Which is why using it as a dimension is irrational. And mathematics does this not physics.

[TheAlkemist]

Wasn't this covered in my post #11 and #6 as well as many others?

you last post (#11) was:
I agree with you, there shouldn't be a problem, but unfortunately, Mother Nature doesn't agree with us and, so, we lose. It does make a difference which co-ordinate system we use and there is no way for us to determine which one is the correct one, so that is why we use the four-vector interval.

Time is placed orthogonal to the three components of space in the "imaginary" direction and it works and that is why we do it. If you don't like it you need to come up with another scheme that works but you can't stick to the one you have because it doesn't work.

and i replied:



Please explain. I'm confused.

If it works so good why is gravity a problem? Why aren't the SM and GR compatible? Does this have anything to do with the mathematical formulations of these models? Just asking. Thanks.

and i waited ...

[cshum00]

this is one of the several MATHEMATICAL definitions of 2-dimensions. This is NOT a scientific definition.
Yes, you are right; that is not a scientific definition. I just wanted to paint a picture of how dimensions can be represented in mathematics. Unless, you are saying that the scientific definition of dimension is not based on the mathematical definition of dimensions. If so, then correct me and define it for me in proper, easy and lame words so that someone with no knowledge can understand it.


This is incorrect and misleading. I'm a scientist. When we say space we simply mean...space. Space is that which has no shape or dimension. An object's shape can be specified or characterized by 3 dimensions; length, width and height, in space. These are parsimonious scientific definitions. Now if mathematicians by whatever convenient convention choose to call this "3-D space", whatever. IMO, the term "spatial dimension" is a misnomer.

Yes, you are right. "Spatial dimension" and "3-Dimensional space" have two different meanings. But a person with no knowledge of science will think of both of them as one and same thing. Depending on the context of the speech, scientists still might refer 3-D space as just "space". And thinking of spatial dimension as the mathematical model is not wrong neither since its representation in mathematics was based on it.


Scientists don't say this. Well...good scientists at least. Treating time as a dimension may not be controversial in the establishment but it's certainly self-contradicting and leads to irrational conclusions.
Sorry, that was my fault. I shouldn't have said "spacial" dimension but just dimension. I just wanted to say that treating time as a dimension is nothing new but rather the way it is used in Special Relativity is non-intuitive.


Which is why using it as a dimension is irrational. And mathematics does this not physics.
No, i didn't say that using dimension is irrational. I am saying that time is mostly visualized as one universal time and mostly as the independent variable. What i meant by "irrational" was non-intuitive. I guess i should have carefully picked the words. What i meant to say in t he last paragraph was that it is non-intuitive to think of time can depend on a spacial dimension; like the way it is used in Special Relativity for time dilation.

[ghwellsjr]

Wasn't this covered in my post #11 and #6 as well as many others?
you last post (#11) was:
I agree with you, there shouldn't be a problem, but unfortunately, Mother Nature doesn't agree with us and, so, we lose. It does make a difference which co-ordinate system we use and there is no way for us to determine which one is the correct one, so that is why we use the four-vector interval.

Time is placed orthogonal to the three components of space in the "imaginary" direction and it works and that is why we do it. If you don't like it you need to come up with another scheme that works but you can't stick to the one you have because it doesn't work.

and i replied:


Please explain. I'm confused.

If it works so good why is gravity a problem? Why aren't the SM and GR compatible? Does this have anything to do with the mathematical formulations of these models? Just asking. Thanks.


and i waited ...

My contribution to this thread was to answer Parbat's question, "How can we say 'time' is a dimension?" from post #3 after I asked him to elaborate on his nebulous original question from post #1.

I was pointing out to him and to you that the reason we treat time as an added "dimension" to normal vectors with three components is so that we can arrive at an invariant "distance" between two events which are separated both in space and time. I pointed out that just as the three components of normal vectors are orthogonal to each other, the "time" component in a four-vector is also orthogonal to the three "space" compontents because it is placed in the "imaginary" direction. Since you had previously used the term "orthogonal", I assumed you would know what that meant. Maybe I should have suggested that anyone who might still be confused on this issue should look up "spacetime interval" for a more complete explanation.

I understood your posts to mean that you didn't see any problem with determining distances between events and you said you didn't understand why we combine time and space to get the spacetime interval. I was trying to help you understand that aspect of Special Relativity.

But your follow-on posts revealed that you were not taking in what I was saying and others were also trying to help you see what a four-vector was all about (which is the topic of this thread) and so when you asked me, "Why aren't the SM and GR compatible?", I didn't want you or anyone to know how stupid I was because I have no idea what SM is and I didn't know that it was incompatible with GR, so I just hoped I could let it slide but now you have brought it up again and so I must confess, I'm stupid, I have no idea what you are asking about. Someone else is going to have to answer.

[TheAlkemist]

Yes, you are right; that is not a scientific definition. I just wanted to paint a picture of how dimensions can be represented in mathematics. Unless, you are saying that the scientific definition of dimension is not based on the mathematical definition of dimensions. If so, then correct me and define it for me in proper, easy and lame words so that someone with no knowledge can understand it.I already did but i'll do it again.

A dimension is a concept that attributes shape/structure to a physical object. In scientific convention, the shape/structure of physical objects in space are described by 3 dimensions; length, width and height.

Yes, you are right. "Spatial dimension" and "3-Dimensional space" have two different meanings. But a person with no knowledge of science will think of both of them as one and same thing. Depending on the context of the speech, scientists still might refer 3-D space as just "space". And thinking of spatial dimension as the mathematical model is not wrong neither since its representation in mathematics was based on it.if "spatial" in "spatial dimension" and "space" in "3-dimensional space" just implies that the object that's being described by the dimensions is in space, I have no issue with that. But i doubt this is what is meant. I think what's meant is that space itself has dimensions, i.e., shape and structure. I just don't agree with this abstraction. Unless, like u said, you're talking about "mathematical objects"... which are just conceptual models. And again, I'm not saying they are wrong or aren't useful, they certainly are.


Sorry, that was my fault. I shouldn't have said "spacial" dimension but just dimension. I just wanted to say that treating time as a dimension is nothing new but rather the way it is used in Special Relativity is non-intuitive.no need to apologize. and i agree with u, it's non-intuitive. but not only that, it's also ambiguous and very fuzzy.


No, i didn't say that using dimension is irrational. I am saying that time is mostly visualized as one universal time and mostly as the independent variable. What i meant by "irrational" was non-intuitive. I guess i should have carefully picked the words. What i meant to say in t he last paragraph was that it is non-intuitive to think of time can depend on a spacial dimension; like the way it is used in Special Relativity for time dilation.i didn't say that u did (i don't think u ever did though). I'm the one that's saying it's irrational and also INCONSISTENT. As you have pointed out.

[TheAlkemist]

My contribution to this thread was to answer Parbat's question, "How can we say 'time' is a dimension?" from post #3 after I asked him to elaborate on his nebulous original question from post #1.

I was pointing out to him and to you that the reason we treat time as an added "dimension" to normal vectors with three components is so that we can arrive at an invariant "distance" between two events which are separated both in space and time.I understand whytime is added as an extra-dimension. It's simply to make the mathematics and the theory workable. Adding the property of invariance to the dimensions using time presupposes that time has directionality--forward and backward. Maths uses the "number line" (that can go in both directions, +ve and -ve) and calls it time. And now that time has been endowed with number and line attributes you can do things like dilate, warp and bend, etc. it...much like a physical object.
But i realize that this may make it easy to visualize and the theory makes useful predictions. No problem with that. Only thing is that when u start having concepts (mathematical objects) interacting with physical objects things can get messy and confusing imo. Like here:
What is rather counter-intuitive, is that physics treats time not only as a independent variable but also as a dependent variable. Meaning, that time is no longer universal but the value of it can be changed and influenced by other factors. In the case of special relativity in physics, time can be changed by the 3 other dimensions of distance.


I pointed out that just as the three components of normal vectors are orthogonal to each other, the "time" component in a four-vector is also orthogonal to the three "space" compontents because it is placed in the "imaginary" direction. Since you had previously used the term "orthogonal", I assumed you would know what that meant. Maybe I should have suggested that anyone who might still be confused on this issue should look up "spacetime interval" for a more complete explanation.I know what orthogonal means. And placing time in an "imaginary" direction is no problem now that it's been morphed into a number line. The concept of spacetime interval embodies basically everything i said above.


I understood your posts to mean that you didn't see any problem with determining distances between events and you said you didn't understand why we combine time and space to get the spacetime interval. I was trying to help you understand that aspect of Special Relativity.

But your follow-on posts revealed that you were not taking in what I was saying and others were also trying to help you see what a four-vector was all about (which is the topic of this thread) and so when you asked me, "Why aren't the SM and GR compatible?", I didn't want you or anyone to know how stupid I was because I have no idea what SM is and I didn't know that it was incompatible with GR, so I just hoped I could let it slide but now you have brought it up again and so I must confess, I'm stupid, I have no idea what you are asking about. Someone else is going to have to answer.sorry, i shouldn't have abbreviated. SM = Standard Model and GR = General Relativity. Maybe i mean Quantum Mechanics (as described by the SM) and GR.

I guess what i'm getting from the answers to Prabat's question is just explanations of how making time a number line makes the mathematics workable.

[ghwellsjr]

I was aware that QM is not compatible with SR because it is not invariant under Lorentz transformation (unless this has been resolved since I learned that) which, I suppose, means that it is also not compatible with GR.

I am very confused on your position and what you are trying to say throughout this thread. I have been trying to help you understand what a four-vector is and how it allows us to define a frame-independent spacetime interval between two distant (in both space and time) events.

Have I been wasting my time because you already understand all this? If yes, could you have explained it all to Parbat?

Do you disagree with the concept of the spacetime interval? If yes, is that because you believe it is unnecessary and the same issue can be addressed some other way?

[cshum00]

A dimension is a concept that attributes shape/structure to a physical object. In scientific convention, the shape/structure of physical objects in space are described by 3 dimensions; length, width and height.


I don't think you are defining dimension in general but rather you are defining spacial dimension here. If i am not wrong, the abstraction of dimension in science does not limits the attributes of just "shape/structure" but in additional to those also to more abstract properties like time, mass and so on; in which these attributes and properties does not only describe/define a physical object but the entire physical reality. Where in the case of spatial dimension, it is a set 3 dimensions of lengths each orthogonal to each other; where each dimension has the name of length, width and height.

[pervect]

There are a large number of related but different concepts in mathematics relating to dimension, but one of the most primitive concepts (in my opinion, probably the most primitive concept) needed to define dimension is a set of points, and a concept of "neighborhood" or "open balls".

When you can define what points are "near" other points in your set because they are in the same neighborhood or "open ball", you have what mathemeticians call a topological space.

This minimum of structure is the bare minimum of what you need before the concept of dimensoinality makes sense. If you just have a random set of points, and no notion of which points are neighbors, you can't really come up with any meaningful concept of dimension.

The concept of dimension that's mathematically applicable when you do have a topological space is probalby not particularly well known, it's called the "hausdorff covering dimension". It relates to the amount of unavoidable overlap you need to completely cover your entire universal set. For instance, to cover a line with open balls requires a minimum overlap of two, some points will be in two different balls when you make a complete cover. To cover a plane some points would have to be in three different covering sets, and in general your minimum cover will require some points to be in n+1 open balls, where n is the usual notion of the dimensionality of the space.

While you can apply the above definitions to finite sets of points, they really aren't that interesting unless you deal with infinite sets.

[Phrak]

I can have 3 dimensions of space, and add one dimension of temperature and add pressure and throw in attitude for a 6 dimensional mathematical space. It's not a very interesting space. Pressure doesn't have a lot to do with distances nor attitude, nor attitude with pressure or temperature.

What makes 3 dimensional space more than three arbitrary things stuck together, is that we can make a distance measure using the Pythagorean theorem no matter how we rotate our chosen X,Y,Z coordinates around.

The same sort of thing is true for spacetime (and yes, there are Lorentz invariant quantum theories). In this case, the distance (called the interval so we don't confuse it with spacial distance) is unchanged when space and time coordinates are rotated about.

Does this solve any issues in the foregoing discussion?

[DaleSpam]

this is one of the several MATHEMATICAL definitions of 2-dimensions. This is NOT a scientific definition.

.... Now if mathematicians by whatever convenient convention choose to call this "3-D space", whatever. IMO, the term "spatial dimension" is a misnomer.

... Treating time as a dimension may not be controversial in the establishment but it's certainly self-contradicting and leads to irrational conclusions.

Which is why using it as a dimension is irrational. And mathematics does this not physics.I have seen this sort of anti-math diatribe on occasion, usually by serious crackpots and cranks. It is fundamentally wrong.

As long as a theory uses some mathematical framework to make predictions about experimental results then the fact that some particular element of the theory is also a purely mathematical object does not make it non-scientific. The use of mathematics in science, particularly physics, is important for making sure that the predictions are logically self-consistent. The treatment of time as a dimension is both mathematical (it is one dimension of a pseudo-Euclidean space) and scientific (the mathematical "norm" in this space is equal to the physical duration measured by a clock).

Because the math is used by a theory to make measurable predictions the denigration above is not warranted. When scientists say that time is the fourth dimension they mean that there are physical predictions (which can be experimentally tested) that can be made by constructing a four-dimensional mathematical space and equipping it with a certain "norm". So far, those mathematical predictions have been thoroughly tested and found to be physically correct.

[TheAlkemist]

I was aware that QM is not compatible with SR because it is not invariant under Lorentz transformation (unless this has been resolved since I learned that) which, I suppose, means that it is also not compatible with GR.

I am very confused on your position and what you are trying to say throughout this thread. I have been trying to help you understand what a four-vector is and how it allows us to define a frame-independent spacetime interval between two distant (in both space and time) events.

Have I been wasting my time because you already understand all this? If yes, could you have explained it all to Parbat?I apologize if if I didn't make position clear from the beginning (though I think I did). I simply do not agree with the inconsistent usage of the term "dimension".

Do you disagree with the concept of the spacetime interval? If yes, is that because you believe it is unnecessary and the same issue can be addressed some other way?Yes and yes.

I don't think you are defining dimension in general but rather you are defining spacial dimension here. If i am not wrong, the abstraction of dimension in science does not limits the attributes of just "shape/structure" but in additional to those also to more abstract properties like time, mass and so on; in which these attributes and properties does not only describe/define a physical object but the entire physical reality. Where in the case of spatial dimension, it is a set 3 dimensions of lengths each orthogonal to each other; where each dimension has the name of length, width and height.OK, then why u can't have just tag on, say, temperature, and static charge yo x,y,z,t and call it 5D?

[TheAlkemist]

While you can apply the above definitions to finite sets of points, they really aren't that interesting unless you deal with infinite sets.why?

[ghwellsjr]

Do you disagree with the concept of the spacetime interval? If yes, is that because you believe it is unnecessary and the same issue can be addressed some other way?
Yes and yes.
I'd like to hear how you determine the "distance" between to widely separated events in space and time that is invariant when observed from different frames of reference. In other words, how do you address the issue that "spacetime interval" addresses?

[TheAlkemist]

I can have 3 dimensions of space, and add one dimension of temperature and add pressure and throw in attitude for a 6 dimensional mathematical space. It's not a very interesting space. Pressure doesn't have a lot to do with distances nor attitude, nor attitude with pressure or temperature.

What makes 3 dimensional space more than three arbitrary things stuck together, is that we can make a distance measure using the Pythagorean theorem no matter how we rotate our chosen X,Y,Z coordinates around.

The same sort of thing is true for spacetime (and yes, there are Lorentz invariant quantum theories). In this case, the distance (called the interval so we don't confuse it with spacial distance) is unchanged when space and time coordinates are rotated about.

Does this solve any issues in the foregoing discussion?Ur right, temperature, pressure and attitude have nothing to do with shape. As for spacetime, this interval u speak of is simply a number-line that's been added as an extra "time dimension". A metric for duration so to speak. The purpose of adding this is to endow the model with Lorentz symmetry right? Is this in anyway related to the concept of T-symmetry? If so, isn't the the physical universe we observe time asymmetric (because of 2nd Law of thermodynamics?).
Hope i'm not way off here...

[TheAlkemist]

The use of mathematics in science, particularly physics, is important for making sure that the predictions are logically self-consistent.But there are several cases where it introduces self-contraction.

What qualifies one as a crack-pot?


The treatment of time as a dimension is both mathematical (it is one dimension of a pseudo-Euclidean space) and scientific (the mathematical "norm" in this space is equal to the physical duration measured by a clock). physical duration? as opposed to non=physical duration?:confused:
How was it measured before clocks were invented?

Because the math is used by a theory to make measurable predictions the denigration above is not warranted. When scientists say that time is the fourth dimension they mean that there are physical predictions (which can be experimentally tested) that can be made by constructing a four-dimensional mathematical space and equipping it with a certain "norm". So far, those mathematical predictions have been thoroughly tested and found to be physically correct.Denigration? :confused:OK. I'll stop because it seems like i'm upsetting some people. Not my intention. Making predictions isn't the only crireria for what makes a theory correct by the way.

[DaleSpam]

But there are several cases where it introduces self-contraction. No. There are several cases where it introduces confusion in beginning students, but not self-contradiction. That is the whole point of establishing a unified mathematical framework for a theory.

Making predictions isn't the only crireria for what makes a theory correct by the way.Making accurate predictions about the results of experiments is the only scientific criteria. Other criteria amount philosophical or personal preference.

[TheAlkemist]

I'd like to hear how you determine the "distance" between to widely separated events in space and time that is invariant when observed from different frames of reference. In other words, how do you address the issue that "spacetime interval" addresses?u realize that implicit in ur question is the notion of measuring time as a distance? besides, spacetime interval addresses an issue created by the conception of space and time as a single entity. it's like a custom designed solution.
My short answer to ur question is that it's irrational and conceptually impossible to measure space (emptiness) between objects. U measure the physical object in space. But i'll leave it here. i'm not changing any minds in here anyway. and i'm not trying to offend anyone. just commenting.

[TheAlkemist]

No. There are several cases where it introduces confusion in beginning students, but not self-contradiction. That is the whole point of establishing a unified mathematical framework for a theory. Ok.

"The term 4-D means that it takes 3 spacial coordinates and 1 temporal coordinate to specify the position of a point or event.

"An object is said to have as many dimensions as there are axes required to locate its position in space"

Are both definitions above correct?



Making accurate predictions about the results of experiments is the only scientific criteria. Other criteria amount philosophical or personal preference.Ok. ur right.

[ghwellsjr]

u realize that implicit in ur question is the notion of measuring time as a distance?
That's why I put "distance" in quotes, so that you would not take exception to my terminology because I can't tell what terminology you prefer.
besides, spacetime interval addresses an issue created by the conception of space and time as a single entity. it's like a custom designed solution.
Spacetime does not create the issue, nature does, and spacetime interval is a solution.

My short answer to ur question is that it's irrational and conceptually impossible to measure space (emptiness) between objects. U measure the physical object in space. But i'll leave it here. i'm not changing any minds in here anyway. and i'm not trying to offend anyone. just commenting.
But you said you could solve the same problem that "spacetime interval" solves except by another method. Now are you telling me that you don't believe there is any solution?

Let's take, for example, the first half of the twin paradox. The twins (or two identical clocks) start out at the same age (or set to the same time) at the same location. One of them accelerates away and travels at a high speed for awhile and then decelerates and comes to rest with respect to the first twin (or clock) some distance away. This defines two events: the first is when the traveler starts out and the second is when the traveler stops. When this situation is analyzed from different frames of reference, different answers will be determined for the actual physical distance the traveler traversed and for the actual physical time that it took the traveler to make the trip. Do you agree? If yes, then how do you reconcile the different measurements of distance and time? If no, then please explain why.

[cshum00]

OK, then why u can't have just tag on, say, temperature, and static charge yo x,y,z,t and call it 5D?

You can as long as it is mathematically useful. Physical "spacial dimension" only has 3 dimensions x,y,z. Time is a dimension but not a spacial dimension. Because Special Relativity uses both spacial dimension and time dimension then we combine them so that it is mathematically useful and we call it "space-time dimension".

I am just saying that you were not defining dimension abstractly enough but you are rather defining spacial dimension in specific instead.

[Phrak]

Ur right, temperature, pressure and attitude have nothing to do with shape. As for spacetime, this interval u speak of is simply a number-line that's been added as an extra "time dimension". A metric for duration so to speak. The purpose of adding this is to endow the model with Lorentz symmetry right? Is this in anyway related to the concept of T-symmetry? If so, isn't the the physical universe we observe time asymmetric (because of 2nd Law of thermodynamics?).
Hope i'm not way off here...

As in space alone, there is no preferred direction in spacetime that you can call the time direction. In this regard they are inseparable, unlike space+temperature, say. A Lorentz symmetry is more of a rotational symmetry, similar to rotating spacial vector.

[DaveC426913]

As in space alone, there is no preferred direction in spacetime that you can call the time direction. In this regard they are inseparable, unlike space+temperature, say. A Lorentz symmetry is more of a rotational symmetry, similar to rotating spacial vector.

I could be misunderstanding you but the time dimension is different from the other spatial dimensions; it is "timelike", whereas the others are "spacelike". At least one defining distinction between the two is that timelike dimension(s) only permit movement in one direction.

[DaleSpam]

"The term 4-D means that it takes 3 spacial coordinates and 1 temporal coordinate to specify the position of a point or event.

"An object is said to have as many dimensions as there are axes required to locate its position in space"

Are both definitions above correct?The first is basically correct, although I would have been more specific (e.g. "The term 4-D spacetime"). The second is not correct, it seems to be describing the dimensionality of a space and not the dimensionality of an object as it says.

[Phrak]

I could be misunderstanding you but the time dimension is different from the other spatial dimensions; it is "timelike", whereas the others are "spacelike".

It was in my opinion that to throw in that sort of detail would cloud the issue at the level of understanding of the question. However I didn't make my case very well, did I?

To try again: <We cannot pick-out any one direction in spacetime and say "this is the time direction". Observers in relative motion will not agree. In this regard space and time are inseparable.> How's that?

At least one defining distinction between the two is that timelike dimension(s) only permit movement in one direction.

I don't know what the meaning of movement in time is. However, world lines of classical and incoherent particles are confined to the interior of the light cone.

To be really abstract, the difference is that rotations in space have a real valued parameter of rotation, whereas rotations between space and time have an equivalent imaginary parameter. But this doesn't really tell us what class of objects must have their world lines confined to the interior of the light cone... hmm...

[ghwellsjr]

My short answer to ur question is that it's irrational and conceptually impossible to measure space (emptiness) between objects. U measure the physical object in space.
I hope you realize that the issue we are talking about isn't confined to distances between objects in empty space, the same issue exists between the shape of a single physical solid object on the surface of good old earth. The Michelson-Morley experiment is what started this whole thing. It was a single very large, very solid, very massive object that seemed to be changing its dimensions simply by being rotated. How do you understand Lorentz contraction when applied to MMX?

[Phrak]

The Michelson-Morley experiment is what started this whole thing. It was a single very large, very solid, very massive object that seemed to be changing its dimensions simply by being rotated. How do you understand Lorentz contraction when applied to MMX?

I'm not sure what you are attempting to infer, but the Michelson Morley experiment yielded null results. They measured no difference in dimensions, or anything else.

[ghwellsjr]

MMX was the inspiration for Lorentz to explain the null result by saying that the physical dimension of the apparatus was contracted along the direction of the aether wind. Michelson, on the other hand, believed that he could not measure the aether wind because he thought the earth was dragging the aether along with it.

[John232]

I don't think even the best physicst can explain exactly why time is a dimension. The best explanation I have read in any book written by one is that if they where to point out on a map the exact coordinates where you will meet them you would never be able to meet them there without knowing when they will be there. Then the time coordinate allows your meeting.

[DaleSpam]

I don't think even the best physicst can explain exactly why time is a dimension. The best explanation I have read in any book written by one is that if they where to point out on a map the exact coordinates where you will meet them you would never be able to meet them there without knowing when they will be there. Then the time coordinate allows your meeting.Seems like even amateur physicists can explain exactly why time is a dimension.

[TheAlkemist]

That's why I put "distance" in quotes, so that you would not take exception to my terminology because I can't tell what terminology you prefer.

Spacetime does not create the issue, nature does, and spacetime interval is a solution.

But you said you could solve the same problem that "spacetime interval" solves except by another method. Now are you telling me that you don't believe there is any solution?

Let's take, for example, the first half of the twin paradox. The twins (or two identical clocks) start out at the same age (or set to the same time) at the same location. One of them accelerates away and travels at a high speed for awhile and then decelerates and comes to rest with respect to the first twin (or clock) some distance away. This defines two events: the first is when the traveler starts out and the second is when the traveler stops. When this situation is analyzed from different frames of reference,different answers will be determined for the actual physical distance the traveler traversed and for the actual physical time that it took the traveler to make the trip. Do you agree? If yes, then how do you reconcile the different measurements of distance and time? If no, then please explain why.No. I believe theres a fundamental error in the relativist's notion of distance. What's actually being measured as "distance" is actually "distance traveled". hence why "distance" is defined in terms of c. Relativity alludes to the qualitative static distance (between two objects or "events") but explains the theory with respect to dynamic distance traveled. Case in point is the phenomenon of "length contraction".
If i'm standing 20 yards away from a tree (where there's a measuring device) and a muon zips past me at near the speed of light, relativity theory says that the distance between the muon an the tree contracts. Now did the static distance between me and the tree shrink or was it the distance between the muon and the tree? And if the answer is the later, then say there's a rock between me and the tree, did the distance between the rock and tree also shrink?


You can as long as it is mathematically useful. Physical "spacial dimension" only has 3 dimensions x,y,z. Time is a dimension but not a spacial dimension. Because Special Relativity uses both spacial dimension and time dimension then we combine them so that it is mathematically useful and we call it "space-time dimension".

I am just saying that you were not defining dimension abstractly enough but you are rather defining spacial dimension in specific instead.As far as i'm concerned, time is not a dimension. it's simply a number line. it's then endowed with orthogonality and combined with the 3 "spatial" dimensions. as such mathematicians have simply just created, lie u said, a useful framework for modeling the physics of objects in space.

As in space alone, there is no preferred direction in spacetime that you can call the time direction. In this regard they are inseparable, unlike space+temperature, say. A Lorentz symmetry is more of a rotational symmetry, similar to rotating spacial vector.So what's the preferred direction of temperature?


I hope you realize that the issue we are talking about isn't confined to distances between objects in empty space, the same issue exists between the shape of a single physical solid object on the surface of good old earth. The Michelson-Morley experiment is what started this whole thing. It was a single very large, very solid, very massive object that seemed to be changing its dimensions simply by being rotated. How do you understand Lorentz contraction when applied to MMX?
I understand it as an indirect inference from a null-experiment.

[Mentz114]

No. I believe theres a fundamental error in the relativist's notion of distance. What's actually being measured as "distance" is actually "distance traveled". hence why "distance" is defined in terms of c. Relativity alludes to the qualitative static distance (between two objects or "events") but explains the theory with respect to dynamic distance traveled.


In flat spacetime distance can be defined as coordinate separation in a consistent way. What is a ruler but a stick with coordinates marked off ? In SR each inertial observer has a set of coordinates and a definition of distance. The Lorentz transformation allows us to transform the coordinates between frames.

Case in point is the phenomenon of "length contraction".

Which is what happens when a distance in one frame is expressed in the coordinates of another frame.

It is completely consistent and your assertion
there's a fundamental error in the relativist's notion of distance
is incorrect.

[ghwellsjr]

Case in point is the phenomenon of "length contraction".
If i'm standing 20 yards away from a tree (where there's a measuring device) and a muon zips past me at near the speed of light, relativity theory says that the distance between the muon an the tree contracts.
SR says that in your rest frame, the muon itself is contracted but the distance the muon has to travel is not contracted. In the rest frame of the muon, the distance between you and the tree is contracted but not the muon itself. That's why it can survive long enough to make the trip.
Now did the static distance between me and the tree shrink or was it the distance between the muon and the tree? And if the answer is the later, then say there's a rock between me and the tree, did the distance between the rock and tree also shrink?
There are two answers depending on whether you are using your rest frame or the rest frame of the muon. In your rest frame the distance between the rock and the tree does not shrink. In the rest frame of the muon, the distance between the rock and the tree is shrunk.

You can use either rest frame (or any other frame) to analyze the situation and they will all get the same answer, which is even though the half-life of the muon is too small for it to survive traveling "long" distances", from your rest frame, it survives because it's clocks are running slow and from its rest frame, it survives because it doesn't have very far to travel.

[ghwellsjr]

I hope you realize that the issue we are talking about isn't confined to distances between objects in empty space, the same issue exists between the shape of a single physical solid object on the surface of good old earth. The Michelson-Morley experiment is what started this whole thing. It was a single very large, very solid, very massive object that seemed to be changing its dimensions simply by being rotated. How do you understand Lorentz contraction when applied to MMX?
I understand it as an indirect inference from a null-experiment.
Yes, that is very true. I'm glad you agree with me and everyone else on this point.

[alkadh455]

Wow, what a question. Well, we all know that time is the duration it takes actions to happen. Time is the fourth dimension, as Einstein viewed it. People before Einstein, like Newton, viewed time as a definite quantity. They viewed it as a definite measurement that is the same for everybody. Then came Einstein, and said that time is in fact relative, it is not an equivalent quantity for everyone. First, he said that the ultimate speed of the universe is the speed of light (you can't go faster than the speed of light). He also said that time is a relative measurement, it depends on your speed; the closer you travel to the speed of light, the slower time beats. Also, time beats faster if you are away from gravitational pull (that's why our GPS works the way it does. It has to take General Theory of Relativity into consideration).That is our basic understanding of time.Time travel to the future is very possible, you just have to go on fast speeds and you age less than your twin, you are in some sense a traveler to the future, However, we don't really know for time travel to the past, because you can't change your past. There are also some new theories on time such as wormholes, and string theory's tiny curled up extra dimensions... The subject of time is really a huge subject, and physicists are still investigating on time.

[cshum00]

As far as i'm concerned, time is not a dimension. it's simply a number line. it's then endowed with orthogonality and combined with the 3 "spatial" dimensions. as such mathematicians have simply just created, lie u said, a useful framework for modeling the physics of objects in space.


You are getting it all wrong. Time IS a dimension. The problem is that you are mixing between "spacial dimension" and dimension in general!!

In math, dimension can be ANYTHING! as long as you can represent it on a number line and have it to be useful for mathematical representations and calculations.

In science, dimension takes a further step and says that it is anything that is a FUNDAMENTAL QUANTITY that that is why we assign a symbol for it's dimension.
http://en.wikipedia.org/wiki/Physical_quantity#Base_quantities.2C_derived_quant ities_and_dimensions

TIME is a FUNDAMENTAL QUANTITY! You don't have to trust the wiki link that i sent you but search and look around books and you will find that TIME IS INDEED A DIMENSION!!

Stop being stubborn and saying that when a scientist say dimension they must mean spacial dimension; which IS NOT!! Spacial dimension is a subset of dimension!!!

As for the word space part, mathematicians do use the word space when they could actually mean just dimension. Meaning when mathematicians say space, they don't mean spacial dimension but dimension in general and it occurs!! And for scientists who have deep math background do so as well!! That is why some people misunderstand that when some scientist say space referring to spacial dimension of space which might not be the case depending on the content of the speech!!

[Passionflower]

TIME IS INDEED A DIMENSION!!

In Galilean spacetime time is surely a dimension, but is that the case in relativity?

I think in relativity time is the length of a path between two events in four dimensions. You think I am wrong?

[cshum00]

In Galilean spacetime time is surely a dimension, but is that the case in relativity?

I think in relativity time is the length of a path between two events in four dimensions. You think I am wrong?

I think you are right. In the contents of your speech, you are clearly referring that the "length of a path" of the "four dimensions" that you are working on. Your thinking actually resembles to a filmstrip where each strip of the film is a point of the time path and inside each strip instead of a 2-D space dimension picture, you have a 3-D dimension picture.

Edit:I think that "path" is good enough. "Length of a path" would be more like the total amount of time specific time-frame.

[Passionflower]

I think you are right. In the contents of your speech, you are clearly referring that the "length of a path" of the "four dimensions" that you are working on. Your thinking actually resembles to a filmstrip where each strip of the film is a point of the time path and inside each strip instead of a 2-D space dimension picture, you have a 3-D dimension picture.

Edit:I think that "path" is good enough. "Length of a path" would be more like the total amount of time specific time-frame.
So it appears that you agree.
If that is so then time cannot be something else as well right? Thus do you agree that time is not a dimension?

[cshum00]

So it appears that you agree.
If that is so then time cannot be something else as well right? Thus do you agree that time is not a dimension?

I am confused. How does agreeing that time is one of the 4 dimensions you mentioned leads to that time is not a dimension?

[Passionflower]

I am confused. How does agreeing that time is one of the 4 dimensions you mentioned leads to that time is not a dimension?
Where did I write that "time is one of the 4 dimensions"?

[cshum00]

Where did I write that "time is one of the 4 dimensions"?

Ok, then what are those 4 dimensions then? If time is not one of those 4-dimensions then i would disagree. I guess that i did not get the right picture for your statement.

[Passionflower]

Ok, then what are those 4 dimensions then? If time is not one of those 4-dimensions then i would disagree. I guess that i did not get the right picture for your statement.
Ok, so let's assume that one of the 4 dimensions is time then what is the length of a path between two events in those 4 dimensions?

[cshum00]

Ok, so let's assume that one of the 4 dimensions is time then what is the length of a path between two events in those 4 dimensions?

Ok, it would be like i mentioned before on my edit:
Edit:I think that "path" is good enough. "Length of a path" would be more like the total amount of time specific time-frame.

In other words, it would be the total amount of time that it takes from one event to the second event.

[Passionflower]

Ok, it would be like i mentioned before on my edit:


In other words, it would be the total amount of time that it takes from one event to the second event.
Yes and that is not time?

[DrGreg]

Passionflower, are you aware of the difference between coordinate time (http://en.wikipedia.org/wiki/Coordinate_time), which is one of the 4 dimensions of spacetime (for a given choice of coordinates), and proper time (http://en.wikipedia.org/wiki/Proper_time) which is the "length" of a 4-dimensional curve or line (and is independent of any choice of coordinates)?

[cshum00]

@Passionflower
Ok, i think i got the root of our problem and the solution.

Let's start with your original statement:
"I think in relativity time is the length of a path between two events in four dimensions."

-First, i will modify your statement to: "Time is a path between two events in four dimensions."
-I remove the word relativity because i am not sure in which relativity you are referring to; the general or special. Also, specifying special relativity will make one of the four dimensions to time which in our case we don't want to.
-It is not length because they are two different things. For example, length would be like: it took five minutes for me to write my essay. While for time i would be saying, according to Easter Time clock, i finished my essay at 10:42AM.
...
-This will require us to look at dimension not as the scientific meaning of dimension but the mathematical one. When i say this, i mean anything CAN be a dimension.
-Saying that, we will look at event as a dimension. For example, e1 (event1), e2 (event2) and so on.
-So, according to the modified statement we are looking at time as t(e, x, y, z) where e=event, x=spacial-dimension1, y=spacial-dimension1, z=spacial-dimension3.
-In other words, time is a function of event, and 3 spatial dimensions. And length of the path of 2 points of time would be how much time lapsed between two events.
-This support the filmstrip idea where each event would be each snapshot on the film, and the difference in length between two film strips is the total time it took for those two events to happen.

Now, the next problem is when i said that time is one of the four dimensions.
-In the case of viewing time as part of the dimension, i would actually be defining event as a function of time and the 3 spatial dimensions or e(t, x, y, z).
-So, if we see time as a function of event, we would intuitively make event as a dimension.
-And if we make time as a dimension, we intuitively create an event function instead.
-Next, is what is the length of the path between two events? It is NOT the total amount of time between two events. I was wrong. Yes, sorry and i apologize. I don't know what it means unless we give a meaningful value to each point of event.

[Passionflower]

Passionflower, are you aware of the difference between coordinate time (http://en.wikipedia.org/wiki/Coordinate_time), which is one of the 4 dimensions of spacetime (for a given choice of coordinates), and proper time (http://en.wikipedia.org/wiki/Proper_time) which is the "length" of a 4-dimensional curve or line (and is independent of any choice of coordinates)?
Coordinate time is a dimension on a chart of spacetime. But mapping an observer's proper time onto the coordinate time axis of a chart is not the same as claiming that one single spacetime dimension represents time. It does not, time is represented by a path between two events inside this spacetime. For a Galilean spacetime you would be correct but not for a Minkowski spacetime.

While proper time always describes what a physical clock measures, coordinate time may or may not do that. Clearly coordinate time cannot be a dimension of time because if we have a simple spacetime with two observers taking a different path with a different length between two events then clearly coordinate time cannot represent time for both observers, time for each observer is the path length between the events not the coordinate time. Yes we can use different coordinates for each observer but then we are not talking about dimensions of spacetime but observer dependent charts where the proper time is modeled by using the time dimension of the coordinate chart for that particular observer.

Don't mix up a coordinate chart of spacetime with spacetime itself.

[cshum00]

I am but what is the point?

While proper time always describes what a physical clock measures, coordinate time may or may not do that. Clearly coordinate time cannot be a dimension of time because if we have a simple spacetime with two observers taking a different path with a different length between two events then clearly coordinate time cannot represent time for both observers, time for each observer is the path length between the events not the coordinate time. Yes we can use different coordinates for each observer but then we are not talking about dimensions of spacetime but simply observer dependent maps where the proper time is modeled by using the time axis of the coordinate chart for that particular observer. But then we mix up the chart with spacetime itself.
I am confused. Unless you mean something else by coordinate, isn't time as a coordinate the same as time being a dimension?

About the problem of two observers not being represented in a single graph is because each observer's coordinate system is shifted with respect to each other. For example, if my origin is not your origin but shifted on a certain way, then when i say this point of space, it wont be the same point of space in your coordinate system. That is why we need to do transformations.

Edit: BTW, did my previous post clear our misunderstandings.

Just because we are defining time as a function of other coordinates, it doesn't mean that time is not a dimension. For example, i would define a function to be z(x,y); but it doesn't mean that z is not a dimension. And most importantly, time is a fundamental quantity which adds the requirement of being a dimension for science.

[Passionflower]

I am confused. Unless you mean something else by coordinate, isn't time as a coordinate the same as time being a dimension?

Think about the different between a coordinate system of spacetime and spacetime itself. Two different things.


About the problem of two observers not being represented in a single graph is because each observer's coordinate system is shifted with respect to each other. For example, if my origin is not your origin but shifted on a certain way, then when i say this point of space, it wont be the same point of space in your coordinate system. That is why we need to do transformations.
So clearly you must realize you are dealing with charts of spacetime not spacetime itself.

Time is a path in spacetime not a dimension of spacetime. If time would be a dimension of spacetime all observers would agree on such time as is the case in Galilean spacetime.

[cshum00]

Think about the different between a coordinate system of spacetime and spacetime itself. Two different things.
Then to clear things up, i have been using them as the same thing. I don't get what you mean by coordinate. Can you explain further?


So clearly you must realize you are dealing with charts of spacetime not spacetime itself.

Time is a path in spacetime not a dimension of spacetime. If time would be a dimension of spacetime all observers would agree on such time as is the case in Galilean spacetime.
I am confused here. How can you see time dilation if you are on the Galilean spacetime? The reason why Galilean relativity could not do gave discrepancy errors was is because it did not have transformation of coordinates (which is what Special Relativity did). I think your problem lies that you don't understand that each observer is in their own coordinate system which needs to be transformed to that they could agree on what they are observing.

[Passionflower]

I think your problem lies that you don't understand that each observer is in their own coordinate system
I don't understand that each observer is in their own coordinate system?

So let me try to follow you, each observer is in their own coordinate system and all these unique coordinate systems relate how to spacetime and in particular the specific dimension you claim is time?

[cshum00]

So let me try to follow you, each observer is in their own coordinate system and all these unique coordinate systems relate how to spacetime and in particular the specific dimension you claim is time?

Not only time, but also for the 3-spacial dimensions too. There is also length contraction. I don't want to be rude but i am guessing that you didn't actually go through the mathematics of it but only read the conclusions instead. .Although the conclusions might be counter-intuitive, if you actually follow through the mathematics and the reason for such transformations; you should be able to have a better understanding of it

[Passionflower]

I don't want to be rude but i am guessing that you didn't actually go through the mathematics of it but only read the conclusions instead. .Although the conclusions might be counter-intuitive, if you actually follow through the mathematics and the reason for such transformations; you should be able to have a better understanding of it
As I said before I think that time is a path in spacetime not a dimension of spacetime. Feel free to introduce mathematics to show how wrong I am.

[cshum00]

As I said before I think that time is a path in spacetime not a dimension of spacetime. Feel free to introduce mathematics to show how wrong I am.

The word space-time refes to 3-spacial dimensions and one time dimension!

Let's modify your statement so that you see what are you saying mathematically.

x is a path in x-y dimension not a dimension of x-y.
Or mathematically, x = x(x, y)!!

I think you missed my last post on page 5. You got mixed with my other earlier comments. Read my last post on page 5 which clarifies our earlier arguments then come back and explain to me what you mean by coordinates and how come time is not a dimension since I am unable to picture your problem.

[Passionflower]

The word space-time refes to 3-spacial dimensions and one time dimension!

Do you seriously think that such an argument would convince me?

Let's modify your statement so that you see what are you saying mathematically.

x is a path in x-y dimension not a dimension of x-y.
Or mathematically, x = x(x, y)!!t

Surely you must be joking!

[cshum00]

Do you seriously think that such an argument would convince me?
No, i am not trying to convince you. It is the truth. Research the word spacetime. It is just like i said. It means 3-spacial dimensions and one time dimension.
http://en.wikipedia.org/wiki/Spacetime

Surely you must be joking!
No, i am not joking. Ask a mathematician to translate that statement to math for you and see what you get. I might be wrong but your statement is just as outrageous as it is.

[DaveC426913]

Passionflower, conventional spacetime is defined as the 3 physical spatial dimensions and one timelike dimension.

It is not really open to interpretation or opinion.


There are theories that posit other numbers, and you are welcome to refer to them, or alternately, develop a paper for your own ideas and submit it to the appropriate forum.

But again, not really an opinion thing.


Perhaps when you are describing a path, you are referring to the fact that timelike dimensions are distinct from space-like dimensions in that timelike dimensions allow movement in only one direction - forward - and at a constant speed. We must travel through the time dimension.

[Passionflower]

It is not really open to interpretation or opinion.
Well so if we have one single time dimension then what is a path in spacetime according to you?

[DaveC426913]

Well so if we have one single time dimension then what is a path in spacetime according to you?

A path could go from [xyzt] to [x'y'z't'].

Because we have freedom in spatial dimensions, we could instead have chosen to go from [x'y'z't] to [xyxt'], but we cannot go from [x'y'z't'] to [xyzt].

[Passionflower]

A path could go from [xyzt] to [x'y'z't'].

Because we have freedom in spatial dimensions, we could instead have chosen to go from [x'y'z't] to [xyxt'], but we cannot go from [x'y'z't'] to [xyzt].
???

Are you going to explain what you think a path in spacetime repesents?

[DaveC426913]

No, I'm simply trying to stop you from violating PF guidelines in your attempt to freely interpret what you think spacetime and spacelike and timelike dimensions are.

You asked me what a path through 4D spacetime might be. I obliged. It will be defined by the connection between two points each defined by 4 coordinates.

[Passionflower]

violating PF guidelines
What guidelines am I violating?

So I take it you are not going to explain to me what you think a path in spacetime represents?

[DaveC426913]

What guidelines am I violating?
Not 'are', but are heading that way, or so it seems. You seem to be creating you own definitions for dimenion and spacetime.

The PF rules put a leash on overly-speculative posts. PF is about mainstream physics.

I'm not trying to be a heavy, I'm just cutting to the chase of the argument you've been having for about 20 posts. Spacetime is a well-known concept.


So I take it you are not going to explain to me what you think a path in spacetime represents?

You ask the oddest questions. Path is your word. Represent is your word. Why am I obliged to answer a question for which you frame the vocabulary?

[Passionflower]

You ask the oddest questions. Path is your word. Represent is your word. Why am I obliged to answer a question for which you frame the vocabulary?
Really that is odd?
You accuse me of creating my own definitions or being overly speculative and you are not familiar with paths in spacetime?

Despite you recognition as a 'Science Advisor' on this forum I am seriously questioning your expertise in this matter.

You accuse me of being overly speculative, what do I speculate about?

[DaveC426913]

You accuse me of creating my own definitions or being overly speculative and you are not familiar with paths in spacetime?

Who said I am not familiar?

You've gone from shouting down cshum00 to shouting at me. You are very confrontational in your discussion style.


I don't really have any contribution to the discussion, except my original point of order, which is that spacetime is a conventional concept.

[Passionflower]

You've gone from shouting down cshum00 to shouting at me. You are very confrontational in your discussion style.

I am not confrontational, the only person who is confrontational is you as you accuse me of something without any base.

[DaveC426913]

I am not confrontational, the only person who is confrontational is you as you accuse me of something without any base.

That must be difficult.

The point has been made. Keep closer to established science. Avoid over-speculation.

[Passionflower]

Avoid over-speculation.
What do you think I wrote is speculation?
If you accuse someone shouldn't you at least mention what you think I wrote is speculation?

[DaveC426913]

"...time is not a dimension..."
"Time is a path in spacetime not a dimension of spacetime."
"I think that time is a path in spacetime not a dimension of spacetime."

[Passionflower]

"...time is not a dimension..."
"Time is a path in spacetime not a dimension of spacetime."
"I think that time is a path in spacetime not a dimension of spacetime."
And you think that is speculative?

You do not think that you measure time by integrating the traversed path in spacetime?

Let's say we have 5 observers traveling between two events, their pathlenghts are different. Which dimension shows time for all those observers? The answer is no dimension, as the time for each observer is the length of their path in spacetime.

If you think that is speculative then I seriously question your understanding of relativity. That is not a problem by itself but then do not accuse someone of posting speculative postings.

[cshum00]

I have been keeping it quiet for a while. How about you answer my questions first.

-I asked you several times what you mean by coordinates and yet you haven't answered that question to me.

You do not think that you measure time by integrating the traversed path in spacetime?
-You are saying that:
t(x, y, z, t) = \int_a^b \sqrt{ (\frac{\partial x}{\partial s})^2 + (\frac{\partial y}{\partial s})^2 + (\frac{\partial z}{\partial s})^2 + (\frac{\partial t}{\partial s})^2} \partial s
Then show us how you got there because i have no idea where that came from. (note that the fourth dimension in this integration is still time)
-I also told that spacetime means 3-spatial dimension and one time dimension.
-Yet, you keep using it as if spacetime has four dimensions and there are 3-spacial dimension and no time dimension. And yet, you never answered me what the fourth dimension would be if it is not time.

Let's say we have 5 observers traveling between two events, their pathlenghts are different. Which dimension shows time for all those observers? The answer is no dimension, as the time for each observer is the length of their path in spacetime.
-The answer is that you keep using Gallilean/General/Newtonian coordinates instead of transformed coordinates.

If you think that is speculative then I seriously question your understanding of relativity. That is not a problem by itself but then do not accuse someone of posting speculative postings.
-Ok, if ignoring the definition of spacetime is not speculative then what is?

[Passionflower]

-I asked you several times what you mean by coordinates and yet you haven't answered that question to me.

Coordinates, as opposed to spacetime, is like a map of spacetime, a projection while spacetime is the reality we live in. Each observer in this spacetime can have a unique measure of time, this is unlike a Galilean spacetime where all time is identical for all observers.


-Yet, you keep using it as if spacetime has four dimensions and there are 3-spacial dimension and no time dimension. And yet, you never answered me what the fourth dimension would be if it is not time.

Observers observe slices of spacetime as space while time is orthogonal to this spactial slice. But different observers observe different slices. There is no single dimension in spacetime that is time.

For instance consider an accelerating observer in spacetime, this observer's worldline is curved, at each point we can make a foliation of spacetime that is space and time, sometimes called 3D+1, for this observer but it pseudo rotates in spacetime at each moment of the acceleration.

[cshum00]

Ok, thanks for trying to explaining things. I am still confused so i need more details in order to get the picture you have in your mind.

-First, how are you defining spacetime? You keep using spacetime while i keep telling you that the word spacetime uses time as a dimension. Use another word because spacetime can't be the word you are referring to (if you think that time is not a dimension).

Coordinates, as opposed to spacetime, is like a map of spacetime, a projection while spacetime is the reality we live in. Each observer in this spacetime can have a unique measure of time, this is unlike a Galilean spacetime where all time is identical for all observers.
-Ok, let's forget about spacetime at the moment. Let me try it with just physical space not spacetime. A map of physical space would be 3 coordinates; which is exactly the mathematical concept of 3 dimension. Then how come you say that coordinate doesn't mean dimension?
-Then this brings me to the next question of how are you defining dimension?

Observers observe slices of spacetime as space while time is orthogonal to this spactial slice. But different observers observe different slices. The is no single common dimension in spacetime that represents time.
-Again, having something orthogonal to something else is the idea of dimensions so that you can have an extra coordinate to navigate on while you are denying that time is not a dimension.

-And here is the last question, if a coordinate system is not the same as a dimensional system. Then what is the difference?

[Passionflower]

-Again, having something orthogonal to something else is the idea of dimensions so that you can have an extra coordinate to navigate on while you are denying that time is not a dimension.
Yes but this is a chart for a particular observer of spacetime, e.g. a particular foliation of space and time. Try to distinguish between a chart or a map of something and the real thing.

[cshum00]

Please answer the other questions as well.

Yes but this is a chart for a particular observer of spacetime, e.g. a particular foliation of space and time. Try to distinguish between a chart or a map of something and the real thing.
The problem is that you just tell me to compare it when i don't see the difference. Rather than just tell me to compare it, tell me what is the difference. That way get to the point faster.

[Passionflower]

Please answer the other questions as well.


The problem is that you just tell me to compare it when i don't see the difference. Rather than just tell me to compare it, tell me what is the difference. That way get to the point faster.
Let's take an example, suppose we have an inertial observer who uses a chart of spacetime that maps his spatial dimensions the way he measures it and orthogonal to that he maps his time. He, for the sake of argument, defines that time in spacetime is orthogonal to his space. Now he accelerates, what will happen? Well the original chart no longer maps onto his space and time foliation. He could Fermi walker transport this chart so that at all times his foliation of space and time is as he measures it but then the chart pseudo rotates (pseudo because spacetime is a Minkowski spacetime and not an Euclidean spacetime) wrt spacetime. The one real dimension in spacetime he defined as time before acceleration is no longer time for him.

Spacetime as it exists in nature has four dimensions, it is however a mistake to claim that one of these dimensions is time, as I said before each observer can have a different view of what represents space and time and what for one observer is time may be a combination of space and time for another observer.

In general relativity the difference between a chart and spacetime itself becomes even more painful, especially in spacetimes that are non-stationary. Think in this context about the background independence of GR, something which distinguishes GR from QM.

[ghwellsjr]

Ever since your first post on this thread, you have not used the term "spacetime interval":
In Galilean spacetime time is surely a dimension, but is that the case in relativity?

I think in relativity time is the length of a path between two events in four dimensions. You think I am wrong?
Is that because you are talking about something entirely different?

[matheinste]

As I said before I think that time is a path in spacetime not a dimension of spacetime. Feel free to introduce mathematics to show how wrong I am.

Excuse the lack of rigor but Mathematically the definition of the dimension of a vector space is the least number of coordinate terms required to uniquely define the "position" of any (maybe abstract point) object within that vector space. However, when dealing with vector spaces modelling physical situations there are practical restrictions involved. We choose three spatial and one time axis, orthogonal to the spatial subspace, to suit our needs.
These axes are usually taken to be our physically defined dimensions althouggh they are really coordinate axes. So a dimension is really just a number describing a certain property of a vector space. We need to choose four coordinate to obtain four coordinates for the event we wish to define and we usually call these axes dimensions to suit our idea of what a dimension is physically.

A timelike interval, or path in spacetime can be regarded as a coordinate axis if the time axis is taken as part of the usual coordinate system asigned by an observer at rest with respect to that coordinate system. Of course in this somewhat special circumstance the other three coordinate numbers required as the spacetime coordinate of events along the time axis are all zero. But for non inertial observers this is not a practical proposition.


In the case of physical dimensions, for an observer at rest and so having the time dimension as one of his coordinate axes, each dimension for that observer is usually taken as being mutually orthogonal to the others, but this is really to suit physics and is not necessary mathematically where the only requirement is for the coordinate axes to be not linearly dependent.

Matheinste.

[Passionflower]

A timelike interval, or path in spacetime can be regarded as a coordinate axis if the time axis is taken as part of the usual coordinate system asigned by an observer at rest with respect to that coordinate system. Of course in this somewhat special circumstance the other three coordinate numbers required as the spacetime coordinate of events along the time axis are all zero. But for non inertial observers this is not a practical proposition.

A coordinate axis is not the same as a dimension of spacetime. Same story here, a chart used to map spacetime is mistaken for spacetime itself.

Again if we assume for the sake of argument that a particular dimension of spacetime is time then all observers would have to agree this dimension represents time but that is not the case as different observers are oriented differently in spacetime. What is time for one observer is a mixture of space and time for another observer.

[DaleSpam]

There seems to be a lot of confusion on this thread with people "talking past" each other. In relativity treminology can often be confusing and the same word can be used to identify different concepts. So I hope the following helps:

1) Spacetime is a 4-dimensional pseudo-Riemannian manifold with a (-+++) signature. The dimensionality and the signature of the manifold are coordinate-independent properties of the manifold. One of these dimensions is singled out from the others (in a coordinate independent sense) by the signature and is called the "timelike" dimension. In this sense "time is a dimension of spacetime".

2) On the other hand the reason that spacetime is 4D is because at each point in the manifold you can construct an orthonormal basis (for the tangent space) with 4 basis vectors. One of these basis vectors will be timelike and the others will be spacelike. You can call the timelike basis vector "time", but it is not unique. There are an infinite number of possible sets of basis vectors at each point. So none of these individual time basis vectors can be said to be "the" time basis vector in a coordinate independent sense.

3) At each point along a worldline in spacetime it is possible to construct a tangent vector. This tangent vector can be classified as timelike, spacelike, or lightlike (null). If the tangent vector is timelike at every point along a worldline then the whole worldline is said to be timelike and it can represent the motion of a massive particle. The length of a timelike worldline is the called the proper time, and it is a coordinate independent scalar quantity.

Most of the confusion on this thread seems to be that everyone is using the same word for all three distinct concepts.

[Passionflower]

One of these dimensions is singled out from the others (in a coordinate independent sense) by the signature and is called the "timelike" dimension.
Ok, so which one is the one singled out?

I am asking because I do not agree there is such a singled out dimension, I think 'rotating' our manifold gives us the same physical description, any direction can represent the timelike dimension.

You say in a coordinate independent sense, so let's say we have 5 observers going from event A to B with different path lengths. How, in a coordinate independent way, do they determine this singled out "timelike" dimension?

Do you agree or disagree that time for each of those observers is the length of the path on this manifold and that this is not represented by one single dimension of the manifold?

[DaleSpam]

Ok, so which one is the one singled out?The one with the negative signature.

I am asking because I do not agree there is such a singled out dimension, I think 'rotating' our manifold gives us the same physical description, any direction can represent the timelike dimension.You can't rotate a manifold, that doesn't make sense.

You say in a coordinate independent sense, so let's say we have 5 observers going from event A to B with different path lengths. How, in a coordinate independent way, do they determine this singled out "timelike" dimension?By looking at the signature. The observers have nothing to do with it. Remember, this refers to the dimensionality of the space, not some specific direction or vector within the space.


Do you agree or disagree that time for each of those observers is the length of the path on this manifold and that this is not represented by one single dimension of the manifold?Yes, I agree that proper time (see 3 above) is the length of a timelike worldline. But there are other usages of the word "time", as I pointed out above.

[Passionflower]

Yes, I agree that proper time (see 3 above) is the length of a timelike worldline.

Ok, I am glad you agree.


But there are other usages of the word "time", as I pointed out above.
I must be slow. So in what way do you think the "timelike" dimension of the manifold is time?

[cshum00]

Let's take an example, suppose we have an inertial observer who uses a chart of spacetime that maps his spatial dimensions the way he measures it and orthogonal to that he maps his time. He, for the sake of argument, defines that time in spacetime is orthogonal to his space. Now he accelerates, what will happen? Well the original chart no longer maps onto his space and time foliation. He could Fermi walker transport this chart so that at all times his foliation of space and time is as he measures it but then the chart pseudo rotates (pseudo because spacetime is a Minkowski spacetime and not an Euclidean spacetime) wrt spacetime. The one real dimension in spacetime he defined as time before acceleration is no longer time for him.
The problem is that this not only happen to the time dimension. It also happens to the spacial dimensions. There is also length contraction when traveling at speed close to light, the observers won't agree on the distance seen to be traveled. In that case, not only time won't be a dimension but also space would be dimensionless according to your analogy.

Spacetime as it exists in nature has four dimensions, it is however a mistake to claim that one of these dimensions is time, as I said before each observer can have a different view of what represents space and time and what for one observer is time may be a combination of space and time for another observer.
If time is not the fourth dimension in the spacetime, then what is? Don't just tell me that "if time is the fourth dimension, what is its' length?" Tell me, in your analogy; what is the fourth dimension in spacetime if time isn't the one?

[Passionflower]

The problem is that this not only happen to the time dimension. It also happens to the spacial dimensions. There is also length contraction when traveling at speed close to light, the observers won't agree on the distance seen to be traveled. In that case, not only time won't be a dimension but also space would be dimensionless according to your analogy.

What is a spatial dimension for one observer can be a mixture of time and space for another observer.


If time is not the fourth dimension in the spacetime, then what is?
Not one single dimension of spacetime is space or time since this would imply an absolute space and time as in the case of Galilean spacetime.

As I wrote, by now like four times or more, what for one observer is time is a mixture of space and time for another observer or what for one observer is a spatial dimension is a mixture of space and time for another observer. While for an accelerating observer this constantly changes. Why does that seem so hard to understand?

[cshum00]

As I wrote, by now like four times or more, what for one observer is time is a mixture of space and time for another observer or what for one observer is a spatial dimension is a mixture of space and time for another observer. While for an accelerating observer this constantly changes. Why does that seem so hard to understand?
It is almost impossible to understand you for me because you keep using words that have solid definitions in a totally different meaning.

What is a spatial dimension for one observer can be a mixture of time and space for another observer.

Not one single dimension of spacetime is space or time since this would imply an absolute space and time as in the case of Galilean spacetime.
Ok, so you are saying that neither space or time are dimensions? I agree with you that in Galilean spacetime thinks of absolute time and space but even if you are in Minkowski spacetime you still uses both space and time as dimensions.

[Passionflower]

It is almost impossible to understand you for me because you keep using words that have solid definitions in a totally different meaning.

All right let's turn things around.

Suppose we have an observer that determined the 'timelike' dimension of spacetime as DaleSpam described (I think this does not make any sense, but for the sake of argument I assume we found it) is the time dimension. Now this observer starts to accelerate for 5 seconds? What do you think will happen? Where is the time dimension after 2 seconds and where is it after 4 seconds. Please answer that question.

[cshum00]

All right let's turn things around.

Suppose we have an observer that determined the 'timelike' dimension of spacetime as DaleSpam described (I think this does not make any sense, but for the sake of argument I assume we found it) is the time dimension. Now this observer starts to accelerate for 5 seconds? What do you think will happen? Where is the time dimension after 2 seconds and where is it after 4 seconds. Please answer that question.

The spacetime view of the observer changes meaning each dimensions gets transformed around. Just as simple as that.

Edit: Let me as you this. What is so exceptional about "dimension" that time and space can't be a dimension?

[Passionflower]

The spacetime view of the observer changes meaning each dimensions gets transformed around. Just as simple as that.

But there is only one spacetime right and one dimension is time (at least that is what you claim) right? Or are you saying that there are many spacetimes?

[cshum00]

But there is only one spacetime right and one dimension is time (at least that is what you claim) right? Or are you saying that there are many spacetimes?

Are you playing philosophy? Yes, there is "one" time dimension. Just because it gets transformed it doesn't mean that it is not itself. Just because you grew older doesn't mean that you are not yourself. Yes, in philosophy you can play with the words and way that the you one second ago is not the you at the moment. But in your logic you are creating an infinite amount of yourself everytime the present becomes the past; and each one of them is a different you.

I knew you were getting there. You have been using random words or trying to find a specific word so that you can mock around with it. I love philosophy myself but there are reasons things have a solid definitions in science so that they don't get tossed around with multiple meanings.

There is nothing wrong with transforming the dimension since the current reference frame has been changed due to acceleration; it is the same spacetime dimension on a different shape.

[cshum00]

But there is only one spacetime right and one dimension is time (at least that is what you claim) right? Or are you saying that there are many spacetimes?

Are you playing philosophy? Yes, there is "one" time dimension. Just because it gets transformed it doesn't mean that it is not itself. Just because you grew older doesn't mean that you are not yourself. Yes, in philosophy you can play with the words and say that the you one second ago is not the you at the moment. But in your logic you are creating an infinite amount of yourself everytime the present becomes the past; and each one of them is a different you. And each of those different you(s) are independent at freewill form each other.

I knew you were getting there. You have been using random words or trying to find a specific word so that you can mock around with it. I love philosophy myself but there are reasons things have a solid definitions in science so that they don't get tossed around with multiple meanings.

There is nothing wrong with transforming the dimension since the current reference frame has been changed due to acceleration; it is the same spacetime dimension on a different shape.

[Passionflower]

There is nothing wrong with transforming the dimension since the current reference frame has been changed due to acceleration; it is the same spacetime dimension on a different shape.
So the spacetime dimension gets transformed, only for the accelerating observer or all observers? Hopefully you will now see that you cannot maintain that one single dimension of spacetime is time. Or do you still think that the spacetime we live in gets transformed by an accelerating observer? If so, how does this transform impact other observers?

[cshum00]

So the spacetime dimension gets transformed, only for the accelerating observer or all observers? Hopefully you will now see that you cannot maintain that one single dimension of spacetime is time. Or do you still think that the spacetime we live in gets transformed by an accelerating observer? If so, how does this transform impact other observers?

Yep, no doubt about it. You are just turning this into something philosophical which can just drag on forever as long as we twist things up into our own advantage like all philosophical arguments do.

Let's make it this way, you say that the second observer have a different spacetime because the current view his/her spacetime is different from the first observer who is accelerating. It could just twist this around and say that it is the same spacetime that is just transformed to his current view. As a proof, the second observer only has to accelerate to the same syncrohization so that the spacetime view of his is just like the first observer. It is the same spacetime in a different transformed view due to the fact that he is not accelerating.

Let's end this pointless argument because you are just trying to use words to make a invalid argument when in the first place you had to change the original meaning of spacetime just to create an argument when it actually clearly states that it is 3-spacial dimensions and one time dimension.

[Passionflower]

Let's make it this way, you say that the second observer have a different spacetime because the current view his/her spacetime is different from the first observer who is accelerating.

No, I am not saying that at all, there is only one spacetime we are living in. I am saying that spacetime is 4 dimensional but, unlike in Galilean spacetime, no single dimension is time or space. Different classes of observers will measure space and time differently because their measure of space and time are pseudo rotated wrt each other in spacetime.

However we can clearly determine what is time in spacetime, time is an observer's path in spacetime. Clearly a path in spacetime and a dimension of spacetime are two different things.

By the way an observer observes only 3 dimensions, clocks record time.

it actually clearly states that it is 3-spacial dimensions and one time dimension.
What clearly states?

[cshum00]

No, I am not saying that at all, there is only one spacetime we are living in. I am saying that spacetime is 4 dimensional but, unlike in Galilean spacetime, no single dimension is time or space. Different classes of observers will measure space and time differently because their measure of space and time are pseudo rotated wrt each other in spacetime.
Here is the thing, if time was not a dimension we can't transform time meaning we can only transform the 3 spacial dimensions which is the problem what the Galilean transforms used to cause.

However we can clearly determine what is time in spacetime, time is an observer's path in spacetime. Clearly a path in spacetime and a dimension of spacetime are two different things.
Ok? Neither you or I ever said anything against that statement: a path in spacetime and a dimension of spacetime are two different things. So, how does this relate to anything we are talking about? You said that accelerating observer spacetime dimension looks different from a non-accelerating observer, then their spacetime dimensions must be different. I never said anything about path, i only said that they are the same spacetime dimensions and to proof it you only have to accelerate the non-accelerating observer to so that his spacetime view looks the same as the accelerating one. It is the same spacetime just that each of them are seeing different things due to their conditions. It is like having 2 observers one in front of a light distorting glass while another one standing front of a car. Both will see the same car but differently due to the different conditions. And yet, it is the same car that is standing in front of them.

What clearly states?
Spacetime clearly states that it is composed of 3-spacial dimensions and one time dimension.

[Passionflower]

Here is the thing, if time was not a dimension we can't transform time meaning we can only transform the 3 spacial dimensions which is the problem what the Galilean transforms used to cause.

How do you suppose to transform time, you can't transform time, time is what a clock measures.

Ok? Neither you or I ever said anything against that statement: a path in spacetime and a dimension of spacetime are two different things. So, how does this relate to anything we are talking about?

Well if we agree that the length of an observer's path, for instance between to events, is time you cannot also say that it is a dimension of spacetime.

You said that accelerating observer spacetime dimension looks different from a non-accelerating observer, then their spacetime dimensions must be different.

I never said that, please try to read clearly. An accelerating observer, for as long as he is accelerating, keeps (pseudo) rotating his spatial foliation wrt spacetime dimensions.

It is the same spacetime just that each of them are seeing different things due to their conditions. It is like having 2 observers one in front of a light distorting glass while another one standing front of a car. Both will see the same car but differently due to the different conditions. And yet, it is the same car that is standing in front of them.

That is simply incorrect.

Here is an analogy: think of spacetime as a fixed box, different classes of observers will be rotated wrt each other inside this box, the effect will be that lengths and durations are not perceived equally. The analogy is not perfect of course, fist of all we need a 4 dimensional box and second spacetime is not a Euclidean but a Minkowskian (or when curved a Lorentzian) manifold, and observers are pseudo rotated.

Spacetime clearly states that it is composed of 3-spacial dimensions and one time dimension.
Can we agree that spacetime is a real thing? Einstein's EFE represent a particular spacetime, obviously we cannot express our universe analytically in this equation because it is far to complicated but our universe is a spacetime nevertheless. Then what do you mean by 'spacetime states', you describe it as some kind of definition only.

[cshum00]

How do you suppose to transform time, you can't transform time, time is what a clock measures.
Lorentz transformation and or Minkowskian geometry takes time as a dimension and then transform time dimension in order to calculate time dilation.

Well if we agree that the length of an observer's path, for instance between to events, is time you cannot also say that it is a dimension of spacetime.
I never said anything about agreeing on the length of the path. I only said about the shape of the dimensions would transform.

I never said that, please try to read clearly. An accelerating observer, for as long as he is accelerating, keeps (pseudo) rotating his spatial foliation wrt spacetime dimensions.

Here is an analogy: think of spacetime as a fixed box, different classes of observers will be rotated wrt each other inside this box, the effect will be that lengths and durations are not perceived equally. The analogy is not perfect of course, fist of all we need a 4 dimensional box and second spacetime is not a Euclidean but a Minkowskian (or when curved a Lorentzian) manifold, and observers are pseudo rotated.
That is exactly i have been saying and that it requires to take time as a dimension. My analogy for the car and glass was a oversimplified analogy but the same.

Can we agree that spacetime is a real thing? Einstein's EFE represent a particular spacetime, obviously we cannot express our universe analytically in this equation because it is far to complicated but our universe is a spacetime nevertheless. Then what do you mean by 'spacetime states', you describe it as some kind of definition only.
I have no problem agreeing that spacetime is a real thing. The problem is that you say that spacetime are not made of dimensions.

Let me ask you this then. How in the world are you going to work on Minkowskian spacetime if time is not a dimension? Show me the mathematics.

[Passionflower]

The problem is that you say that spacetime are not made of dimensions.

I never said that. You really need to read more accurately.


How in the world are you going to work on Minkowskian spacetime if time is not a dimension? Show me the mathematics.
I do that all the time. To calculate an observer's time between two events one needs to take the length of the path, one generally does this by integration.

[cshum00]

I never said that. You really need to read more accurately.
Ok, let's try to match each other thoughts for a second and lay out our commonalities and differences.

First, let's start with what we have in common.
-We both agree that there is actually such thing as spacetime.
-We both agree that Galilean spacetime is somewhat faulty but Minkowski is correct.

What we don't agree on is:
-You say that one of spacetime dimensions is not time. I say time is one of spacetime dimensions.
-You say that Time is a path in spacetime not a dimension of spacetime. while i say that the path in spacetime is just a path in spacetime but not time.

So, we can conclude that our main conflict is with time and spacetime. I am saying that time is a dimension and it is also a dimension in spacetime.

So let's start with your analogy. You say that there are four dimensions in spacetime. Three of the four dimensions are spacial dimensions and there last one is something but not time. Time cannot be a dimension of spacetime because when an observer accelerates his old time dimension gets transformed and it is no longer the old time dimension. Therefore it can't be a dimension and neither the one for spacetime.

Now, using the same analogy of time and because of time dilation the time dimension; it transforms time dimension so it cant be a dimension. There is also the other three spacial dimensions in spacetime. The three other spacial dimensions can have length contraction according to specail relativity; which is a transformation of three spacial dimensions. But according to your analogy, spacial dimensions can't be dimensions neither because it transforms just like time! Then if that is true, then what are the dimensions in spacetime?!

I do that all the time. To calculate an observer's time between two events one needs to take the length of the path, one generally does this by integration.
Ok, show them to me. Both the formulas and the derivations. I bet you that right from the beginning of the derivations they use time as a dimension. Show them to me otherwise i can't see the whole picture.

[Passionflower]

Ok, let's try to match each other thoughts for a second and lay out our commonalities and differences.

First, let's start with what we have in common.
-We both agree that there is actually such thing as spacetime.
-We both agree that Galilean spacetime is somewhat faulty but Minkowski is correct.

Yes a Galilean spacetime has a notion of absolute time, in fact this is nothing but the fourth dimension of Galilean spacetime. Adjusted for special relativity we have a Minkowski spacetime, adjusted for mass and energy we have a Lorentzian spacetime.


You say that one of spacetime dimensions is not time. I say time is one of spacetime dimensions.

Correct, none of the four dimensions of spacetime can be called time or space because that would imply absolute space and time. Each class of observers has their own notion of what orientation in spacetime consists of space (and orthogonal to that time). In other words what is space and time is observer dependent in relativity not a property of the spacetime dimensions.


-You say that Time is a path in spacetime not a dimension of spacetime. while i say that the path in spacetime is just a path in spacetime but not time.

Correct.


So let's start with your analogy. You say that there are four dimensions in spacetime. Three of the four dimensions are spacial dimensions and there last one is something but not time.

No that is not what I am saying, what I am saying is that each class of observers will observe an identical dimension of spacetime differently, some will say it is space while others will say it is some mixture of space and time. One observer is not more right in relativity than another observer so one must conclude that no single dimension of spacetime can rightfully be identified as time or space.


Time cannot be a dimension of spacetime because when an observer accelerates his old time dimension gets transformed and it is no longer the old time dimension. Therefore it can't be a dimension and neither the one for spacetime.

I agree that time is not a dimension of spacetime but I do not agree with the argumentation you describe above. However when an observer accelerates he constantly adjusts his notion of space wrt spacetime because he pseudo rotates in spacetime. Interestingly in this respect is Fermi Walker transport which illustrates this.

[cshum00]

Looks like we made some progress. Now that we have some stuff on the same page, let's try to do it similarly with the stuff we disagree on.

So our problem are still on
-Time
-Spacetime
-Spacail dimensions (new)

One observer is not more right in relativity than another observer so one must conclude that no single dimension of spacetime can rightfully be identified as time or space.
1) How does that one observer not being right in relativity than another observer conclude to no single dimension of spacetime can rightfully identified as time or space? You did a huge jump there. It almost seemed to me that you are trying to relate two completely unrelated subjects.

2) So, now you conclude that neither time or space are dimensions of spacetime? Then what are the dimensions of spacetime? You were saying that there were 4-dimensions from the beginning right? What are they?

3) You still haven't shown me the formulas and its derivation we talked about. Show them to me.

So, there are 3 questions above. Don't just pick and choose to answer the ones that favor you. Answer them completely.

[DaleSpam]

So in what way do you think the "timelike" dimension of the manifold is time?In the sense that it must be measured with clocks.

[Passionflower]

In the sense that it must be measured with clocks.
So are you saying that a clock does not measure the path length between two events in spacetime but instead measures an interval of a single dimension of spacetime?

So for two different observers traveling between these two events with different path lengths, would you claim that they each measure an interval of the same dimension of spacetime?

[ghwellsjr]

Passionflower, back in post #111, I asked you:
Ever since your first post on this thread, you have not used the term "spacetime interval":
In Galilean spacetime time is surely a dimension, but is that the case in relativity?

I think in relativity time is the length of a path between two events in four dimensions. You think I am wrong?
Is that because you are talking about something entirely different?
And now for the first time you are using the word "interval" in the same sentence with "spacetime" but not the term "spacetime interval":
So are you saying that a clock does not measure the path length between two events in spacetime but instead measures an interval of a single dimension of spacetime?

So for two different observers traveling between these two events with different path lengths, would you claim that they each measure an interval of the same dimension of spacetime?
So I still can't tell if you are talking about the "spacetime interval" or something else.

But, just in case you are talking about "spacetime interval", let me explain what it is and then you can tell me if it helps.

First you have to understand what an event is. It is nothing more than a specified location (in three dimensions) at a specified time as defined by a specified coordinate system. It does not necessarily have anything to do with observers or paths or any actual event, although it may. You can then transform the event (location plus time) to any other coordinate system and the numbers you get to describe the four components of the event could be totally different.

In Galilean spacetime, if you have two events, the spacial distance between any two events can be calculated by taking the square root of the sum of the squares of the differences in the three dimensions and the time difference is merely the difference in the two times. Then if you transform the two events into a different coordinate system, even though all the numbers are different to describe the locations and times of the two events, if you perform the same computation, you will get the same answers for the spacial distance and time difference between the same two events defined by the second coordinate system, even if this second coordinate system is in motion with respect to the first one.

By Galilean spacetime, we mean that the relative speed between the two coordinate sytems, otherwise known as frames of reference, is much less than the speed of light.

But if the two coordinate systems (frames of reference) have a high speed between them, then the calculations that we did under the Galilean spacetime do not give the same spacial distance and time difference in the two frames of reference. However, we can define a new "distance" or "difference" between the two events which is called the "spacetime interval" that will be the same no matter what frame of reference we do the computation in, but instead of getting two numbers, a spacial distance and time difference, we get just one, the spacetime interval, based on a calculation of the two previous values.

The computation is very similar to the spacial distance, in fact we start with that prior to taking the square root but instead we subtract the square of the time difference multiplied by the square of the speed of light.

It should be no surprise that this computaton yields a frame invariant quantity, since we use the Lorentz Transform to produce the numbers for the second frame of reference, and the transform guarantees that the spacetime interval is frame invariant.

Does that help or are you talking about something completely different?

[DaleSpam]

So are you saying that a clock does not measure the path length between two events in spacetime but instead measures an interval of a single dimension of spacetime?

So for two different observers traveling between these two events with different path lengths, would you claim that they each measure an interval of the same dimension of spacetime?What is an "interval of a dimension"?

Btw, it is hard to be sure, but I think you are confusing usages 1) and 2) above. I.e. You seem to always think in terms of a direction or a basis vector (2) instead of a dimension (1). The dimensionality of a space is a geometric property which exists independent of any coordinate system. Can you formulate your question without respect to any coordinate system? (e.g. Without any observers' perspective)

[Passionflower]

So in what way do you think the "timelike" dimension of the manifold is time?In the sense that it must be measured with clocks.
So then explain yourself.

I claim that the time as measured by a clock between two events is the length of the path of this clock in spacetime. You claim that that the clocks measure the "timelike" dimension of spacetime to read time.

So consider a few clocks going from event A to event B, all have a different path length in spacetime. You agree that the manifold has four dimensions, are you perhaps claiming that their paths are all perpendicular to what you call the "timelike" dimension of the manifold so that they can measure the "timelike" dimension of spacetime?

I included a spacetime diagram showing the spacetime paths of those clocks going from event A to event B:
http://img713.imageshack.us/img713/9677/event.gif
I claim that time for each clock is the path length calculated by using a Minkowski metric.

Now why do you think the vertical dimension, which is what you call the "timelike dimension of spacetime is time?

[DaveC426913]

Passionflower, can what you are saying about time-as-a-path as opposed to time-as-a-dimension not just as easily be said about any of the spatial dimensions?

If I take a meandering route from Chicago to New York, I follow a path that moves through three spatial dimensions. Someone else might take a different, longer path. It seems analagous that you'd claim that x and y are not dimensions, since my personal x and y are different from someone else's.

[Passionflower]

If I take a meandering route from Chicago to New York, I follow a path that moves through three spatial dimensions. Someone else might take a different, longer path. It seems analagous that you'd claim that x and y are not dimensions, since my personal x and y are different from someone else's.
One difference is that in spacetime we have paths between events not paths between spatial locations.

If you and I leave Chicago at the same time and we arrive in New York at the same time and we take different paths our clocks may not agree on how long the trip took despite that we traversed through the same amount of, what DaleSpam calls, "timelike" dimension (See the above spacetime diagram)

For a good understanding I like everyone to contrast a Galilean spacetime and a Minkowski spacetime. Time is clearly a dimension in Galilean spacetime, I do not think anyone will disagree with that.

In Galilean spacetime our watches would always show the same time because in Galilean spacetime we actually could consider the time dimension as the time that a clock measures. We would simply look at how much we traversed in the time dimension to get the elapsed time of the trip. In Galilean spacetime the time and space dimensions are uniquely time and space for all observers.

But now contrast this with a Minkowski spacetime, here it is no longer that straightforward. In a Minkowski spacetime there is no longer a unique time and space dimension. Both you and I traversed the same amount of "timelike" dimension going from Chicago to New York, however our clocks still may not read the same time. We cannot simply take, as in the case of Galilean spacetime, the amount of time dimension traversed as the elapsed time, no instead we need to take the length of the path to get the elapsed time.

Minkowski recognized this very early when he made the famous statement:
The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself and time by itself are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

[cshum00]

Minkowski recognized this very early when he made the famous statement:
The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself and time by itself are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.


You still haven't answered my three questions above. Please answer them.

Also, Minkowski's statement doesn't say anything about space and time not being dimensions. Rather, it is saying that space alone and time alone won't do the cut so we have to put them together.

And in my point of view, what the statement is saying is that since space was already 3-dimensions and time a dimension by itself; we combine them together so that we get a precise mathematical result of 4-dimensions which is called spacetime (which is exactly what i have been saying from the very beginning).

[Passionflower]

You still haven't answered my three questions above. Please answer them.

Also, Minkowski's statement doesn't say anything about space and time not being dimensions. Rather, it is saying that space alone and time alone won't do the cut so we have to put them together.

And in my point of view, what the statement is saying is that since space was already 3-dimensions and time a dimension by itself; we combine them together so that we get a precise mathematical result of 4-dimensions which is called spacetime (which is exactly what i have been saying from the very beginning).
Well please comment on the spacetime diagram below, the vertical axis is what DaleSpam calls the "timelike" dimension. We see five travelers between event A and B all taking different paths in spacetime.

So how do you think we calculate the time for the various travelers between these two events?

If time is a dimension, like in the case of Galilean spacetime, the elapsed time for all observers is the same, namely the height. But in case of a Minkowski spacetime it is the length of the paths (and in Minkowsi spacetime the paths that looks longest in the diagram are actually the shortest) and not the height. As you can see most of the paths are curved, which indicates those travelers underwent proper acceleration. To obtain the lengths we have to integrate. The obtained lengths are the elapsed times.
Do you agree with that?
http://img713.imageshack.us/img713/9677/event.gif

[DaleSpam]

So then explain yourself.To locate any event requires three rods and one clock (minimally), thus there are three dimensions of space and one of time.

I claim that the time as measured by a clock between two events is the length of the path of this clock in spacetime. ... I claim that time for each clock is the path length calculated by using a Minkowski metric.
Sure, I clearly mentioned proper time as the third common usage of the word already.

You seem to think that I am saying you are wrong. I am not. I am simply pointing out that (as is common in relativity) the terminology is sloppy and there is more than one meaning in common usage.

Now why do you think the vertical dimension, which is what you call the "timelike dimension of spacetime is time?Again, you are confusing the first and second usages. "Vertical" is a direction, not a dimension. In your spacetime diagram the vertical direction would be coordinate time for a reference frame where the starting and ending events are colocated.

[Passionflower]

You seem to think that I am saying you are wrong. I am not.

Well you can't have your cake and eat it too. If you agree with me I cannot understand how you can maintain that time is a dimension in a Minkowski (and Lorentzian) spacetime.

Please point out in the above referenced spacetime diagram where you think the time dimension is. If the diagram was a diagram of a Galilean spacetime I would agree that the vertical axis represents time but not in the case of a Minkowskian spacetime.


I am simply pointing out that (as is common in relativity) the terminology is sloppy and there is more than one meaning in common usage.

Well it looks you are fully supporting this sloppy usage. We now have people in this forum who think time is not calculated by taking the length of a path in spacetime because they are taught time is instead a dimension.


You are of the opinion that a Minkowski spacetime has a time dimension am I right?

So then explain that for the 5 observers drawn (except the one having a straight line) in the spacetime diagram we cannot simply take the total amount progressed in this particular dimension to obtain the total time as we could have if the spacetime were Galilean?

To me that answer is simple: because we are not talking about a Galilean spacetime, instead we are talking about a Minkowski spacetime where the time is calculated by taking the length of the path not just the amount progressed against the, what you call, "timelike", dimension.

[DaleSpam]

Well you can't have your cake and eat it too.This is a rather absurd comment. I merely point out that a word has more than one definition (used by the community as a whole) and therefore I am trying to "have my cake and eat it too" according to you.

Well it looks you are fully supporting this sloppy usage. On the contrary, I have been the only participant attempting to clarify usage. This thread is a prime example of how confusion can be fostered by participants not being specific and clear.

In particular I would recommend that you use the term "coordinate time" to indicate the 2nd meaning above and the term "proper time" to indicate the 3rd. Currently you are not clearly distinguishing between the two meanings in your posts.

[Passionflower]

In particular I would recommend that you use the term "coordinate time"
All observers in our universe observe proper time all the other times are really 'make believe times'. The term coordinate time hardly ever has a physical meaning in relativity especially in curved spacetime. Hardly an argument for calling such a thing time, let alone a dimension.

Comparing Galilean spacetime and Minkowski spacetime is a very good exercise. Trying to understand why in the case of Galilean spacetime, time can rightfully be called a dimension and why that is not correct for Minkowski spacetime.

I think there are two main problems in relativity education, first the "time is a dimension" argument and second the "acceleration does not matter" argument. With it, pages of confusion are created with people proclaiming paradoxes that are really not paradoxes at all. But the origin is bad education.

Perhaps you missed my question to you as you did not answer it:

Could you please point out in the above referenced spacetime diagram where you think the time dimension is?

[ghwellsjr]

Passionflower, back in post #111, I asked you:

And now for the first time you are using the word "interval" in the same sentence with "spacetime" but not the term "spacetime interval":

So I still can't tell if you are talking about the "spacetime interval" or something else.

But, just in case you are talking about "spacetime interval", let me explain what it is and then you can tell me if it helps.

First you have to understand what an event is. It is nothing more than a specified location (in three dimensions) at a specified time as defined by a specified coordinate system. It does not necessarily have anything to do with observers or paths or any actual event, although it may. You can then transform the event (location plus time) to any other coordinate system and the numbers you get to describe the four components of the event could be totally different.

In Galilean spacetime, if you have two events, the spacial distance between any two events can be calculated by taking the square root of the sum of the squares of the differences in the three dimensions and the time difference is merely the difference in the two times. Then if you transform the two events into a different coordinate system, even though all the numbers are different to describe the locations and times of the two events, if you perform the same computation, you will get the same answers for the spacial distance and time difference between the same two events defined by the second coordinate system, even if this second coordinate system is in motion with respect to the first one.

By Galilean spacetime, we mean that the relative speed between the two coordinate sytems, otherwise known as frames of reference, is much less than the speed of light.

But if the two coordinate systems (frames of reference) have a high speed between them, then the calculations that we did under the Galilean spacetime do not give the same spacial distance and time difference in the two frames of reference. However, we can define a new "distance" or "difference" between the two events which is called the "spacetime interval" that will be the same no matter what frame of reference we do the computation in, but instead of getting two numbers, a spacial distance and time difference, we get just one, the spacetime interval, based on a calculation of the two previous values.

The computation is very similar to the spacial distance, in fact we start with that prior to taking the square root but instead we subtract the square of the time difference multiplied by the square of the speed of light.

It should be no surprise that this computaton yields a frame invariant quantity, since we use the Lorentz Transform to produce the numbers for the second frame of reference, and the transform guarantees that the spacetime interval is frame invariant.

Does that help or are you talking about something completely different?
Passionflower, are you ever going to answer my question, are you talking about the "spacetime interval"?

[Passionflower]

Passionflower, are you ever going to answer my question, are you talking about the "spacetime interval"?
A spacetime interval is the distance between two events in spacetime this is not necessarily the same as the length of an observer's path between two events. In some cases however they could be identical namely in the case the observer takes the largest possible travel time between these events.

[matheinste]

A spacetime interval is the distance between two events in spacetime this is not necessarily the same as the length of an observer's path between two events. In some cases however they could be identical namely in the case the observer takes the largest possible travel time between these events.

This is not a post telling people how to use various terms but just a post to explain the difficulties I find. Perhaps it will help others.

I find that the mathematical definition of the spacetime interval describes umambiguously, as of course a mathematical definition should do, what the interval means. As has been said, and something of which I am also guilty, using imprecise words or words which can have varied meanings does not help. The problem I find with using words to describe the interval is finding ones that convey the idea of a straight line in spacetime. The value of the interval is usually not the same as that of the path, although if the object is travelling inertially it is, and so the interval is often loosely defined as a the legth of a straight line path between events.

I seem to remember in an early section of Eddington's classic Mathematics of General Relativity that he describes the interval and proper time as measures rather than lengths or times.

Matheinste.

[DaleSpam]

All observers in our universe observe proper time all the other times are really 'make believe times'.Nonetheless, it is one of the common meanings for the word "time" and when you want to refer to this meaning you should clarify by using the term "coordinate time". The fact that you dislike "coordinate time" does not make the concept go away, and people who seek to communicate their ideas should be aware of it and be clear about it.

Your whole approach on this thread is to be sloppy and unclear about your terminology. You have presented a bunch of correct arguments about why coordinate time is coordinate dependent and therefore not a dimension in a coordinate-independent sense. If you had simply used the phrase "coordinate time" you could have saved yourself a lot of writing and a lot of disagreement.

Could you please point out in the above referenced spacetime diagram where you think the time dimension is?Sure. As soon as you point out on the surface of a piece of paper where the x and y dimensions are.

[ghwellsjr]

Passionflower, are you ever going to answer my question, are you talking about the "spacetime interval"?A spacetime interval is the distance between two events in spacetime this is not necessarily the same as the length of an observer's path between two events. In some cases however they could be identical namely in the case the observer takes the largest possible travel time between these events.
In any and all those cases where they are identical, do you have any problem, issue, complaint, concern or question with the spacetime interval?

[Passionflower]

Dalespam I am trying to understand your position, you accuse me of being sloppy so I take it you have no objection to give your exact position about time being a dimension of spacetime. Since you seem to agree that time as measured by a clock is the length of a path in spacetime it appears that you find that our universe has two measures of time.

Earlier in this thread you wrote:
Seems like even amateur physicists can explain exactly why time is a dimension.
Are you still supporting this statement? And do you think this statement is exact (e.g. not sloppy)?

So please explain exactly why time is a dimension.

You have presented a bunch of correct arguments about why coordinate time is coordinate dependent and therefore not a dimension in a coordinate-independent sense.

So what are you implying that time is a dimension of spacetime but only in a coordinate dependent way?

With regards to being sloppy, I find it sloppy to state that "time is a dimension of spacetime". Time is what a clock measures, the time between two events for a clock is the path the clock travels between these two events in spacetime. A path is clearly not a dimension.

[TheAlkemist]

You are getting it all wrong. Time IS a dimension. The problem is that you are mixing between "spacial dimension" and dimension in general!!

In math, dimension can be ANYTHING! as long as you can represent it on a number line and have it to be useful for mathematical representations and calculations.

In science, dimension takes a further step and says that it is anything that is a FUNDAMENTAL QUANTITY that that is why we assign a symbol for it's dimension.
http://en.wikipedia.org/wiki/Physical_quantity#Base_quantities.2C_derived_quant ities_and_dimensions

TIME is a FUNDAMENTAL QUANTITY! You don't have to trust the wiki link that i sent you but search and look around books and you will find that TIME IS INDEED A DIMENSION!!

Stop being stubborn and saying that when a scientist say dimension they must mean spacial dimension; which IS NOT!! Spacial dimension is a subset of dimension!!!

As for the word space part, mathematicians do use the word space when they could actually mean just dimension. Meaning when mathematicians say space, they don't mean spacial dimension but dimension in general and it occurs!! And for scientists who have deep math background do so as well!! That is why some people misunderstand that when some scientist say space referring to spacial dimension of space which might not be the case depending on the content of the speech!!No. I'm not the one mixing dimensions here. Define a term within a given context and stick to it. I have no issue with that. What i have issue with is when terms are used inconsistently within the same dissertation. x,y,z as dimensions are used to ascribe structure and shape to physical objects. u now add an extra dimension (time) to this framework that has nothing to do with shape or structure. but it's treated geometrically, the same as x,y,z...dilated, warped, distorted, etc. So if time is a fundamental QUANTITY of matter, what is the time of a brick? I can tell u the length, width and height by simply measuring it.

[DaleSpam]

So if time is a fundamental QUANTITY of matter, what is the time of a brick? I can tell u the length, width and height by simply measuring it.I can tell you the duration of a brick simply by measuring it also.

[TheAlkemist]

I can tell you the duration of a brick simply by measuring it also.:confused: the duration of a brick? please explain.

[ghwellsjr]

So if time is a fundamental QUANTITY of matter, what is the time of a brick? I can tell u the length, width and height by simply measuring it.
Can you measure the distance from one corner of a brick to the opposite corner? For example, can you measure how far it is from the front, lower left corner to the rear, upper right corner?

[TheAlkemist]

I love philosophy myself but there are reasons things have a solid definitions in science so that they don't get tossed around with multiple meanings.
funny u say this because i stated this in one of my first posts but when a dimension can be literally anything that kind of sets the stage for lots of confusion doesn't it?

[TheAlkemist]

Can you measure the distance from one corner of a brick to the opposite corner? For example, can you measure how far it is from the front, lower left corner to the rear, upper right corner?yes. with a brick it's gonna be tricky, but with a wooden block, a saw and some measuring tape. Why?

[DaleSpam]

:confused: the duration of a brick? please explain.Sure. The length, width, and height are the distances from where it begins to where it ends in three orthogonal directions. Similarly there is a duration from when it begins to when it ends. It is exactly analogous to length, width, and height.

If your qualification for something being a dimension is that it be related to the extent of a brick then time is clearly a dimension.

[DaleSpam]

Dalespam I am trying to understand your position, you accuse me of being sloppy so I take it you have no objection to give your exact position about time being a dimension of spacetime.My personal position is that the three different usages of the word "time" I mentioned earlier are all legitimate (http://www.physicsforums.com/showpost.php?p=3003323&postcount=114) and you are confusing the issue by using different definitions interchangeably.

So please explain exactly why time is a dimension.Spacetime is a 4D pseudo-Riemannian manifold with three dimensions of space and one dimension of time. Do you understand what this means both mathematically and physically? Do you understand that the dimensionality and the signature of a manifold are coordinate-independent invariants? This is the first meaning that I described.

So what are you implying that time is a dimension of spacetime but only in a coordinate dependent way?Time is also the label given to the timelike vector of an orthonormal basis at any point in the manifold. Since there are an infinite number of basis sets this vector is not unique. Also, since usually an orthonormal basis is constructed from the coordinates this basis usually depends on the coordinates. This is the second meaning that I described and is usually identified by the clarifying phrase "coordinate time".

Proper Time is what a clock measures, the time between two events for a clock is the "length" of the path the clock travels between these two events in spacetime. A length of a path is clearly not a dimension.I have clarified your statement, which was essentially correct. This is the third meaning that I described and is usually identified by the phrase "proper time".

The problem with this thread is that you have your prefered definition for the word time (proper time) and refuse to admit that it is common for words to have multiple meanings. You are not the supreme leader of science, and it is not up to you to unilaterally change definitions. There are multiple meanings to many words and if you would like to contribute usefully then you should be familiar with them all. You are correct that proper time is not a dimension, you are incorrect to conclude that there is therefore no sense in which time is a dimension.


"There's a sign on the wall
But she wants to be sure
'Cause you know sometimes words have
Two meanings"

-Led Zeppelin, Stairway to Heaven

[ghwellsjr]

Can you measure the distance from one corner of a brick to the opposite corner? For example, can you measure how far it is from the front, lower left corner to the rear, upper right corner?yes. with a brick it's gonna be tricky, but with a wooden block, a saw and some measuring tape. Why?
Do you agree that whatever tricky means you are considering is not measuring the diagonal distance of the brick but an indirect method that you assume will give you the same answer?

And do you agree that you could also have measured the height, length, and width of the brick and calculated the diagonal distance by taking the square root of the sum of the squares of the three measurements and you would get exactly the same answer?

[cshum00]

Ok, to clear the problems with whether time is a dimension or not i guess we would have to re-state the definition of various terms and how each term relate to each other.

Vetors
a) Vector is a quantity that has both a magnitude and direction.
b) When representating a vector on a coordinate system, the tail of the vector can be positioned on top of any point of the coordinate system; which makes the vector independent from a specific location or independent of any point of reference.
c) There are vector operations that allow us to re-shape, shift, rotate and transform vectors.

Dimensions
-Mathematical definition of dimensions:
a) Dimensions are special vectors where these vectors will become part of number lines for a new coordinate system.
b) The relation of each vectorial space may and may not be of an orthogonal basis.
-Scientific definition of dimensions:
a) For the purpose of calculations, it has the same as the mathematical meaning except;
b) a dimension (in science) must be a fundamental quantity and because of its importance it is given a fundamental unit for the purpose of dimensional analysis.

Fundamental Unit and Quantity
Is an important quantity which can be measured and which other units will be based on. For example, force is made of the fundamental quantities of mass, time and length.

Dimensional Analysis
Is a way to make sure that a calculation is done correctly and that the computation done does not mix different units improperly.

Time
a) Time is a measuring system used to sequence events, to compare the durations of events and the intervals between them.
b) Time is a fundamental quantity and bears the fundamental units of [s] seconds.

Proper Time thanks to DaleSpam for clarifying
Is the time elapsed by a moving or accelerating observer.

The way proper time is measured is the follows:
-From the relation between proper time and time of the outside observer in spacetime:
\Delta t = \frac{\Delta t_p}{\sqrt {1 - \frac {(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 }{c}}}
-Solve for proper time and in a continuous curve, \Delta is replaced with d.
dt_p = \sqrt {{1 - \frac {(dx)^2 + (dy)^2 + (dz)^2}{c}} dt
-Integrate both sides:
t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c}} dt
Which is the line integral of a path or curve D.

@Passionflower
-First, proper time only defines the time of a moving or accelerating observer.
-To define the time for a an observer that it not accelerating, you would still have to transform the proper time so that you get the time for the non-accelerating observer.
-Proper time is the total amount of time elapsed by someone who is accelerating. Meaning it is scalar and not the measuring system as i defined time.
-What are the units of the proper time? It is still seconds. And applying dimensional analysis i still get that the proper time is just a point or group of points or value of the dimensional system of time.
-Proper time does not say anything about time not being a dimension; it is just saying that an accelerating observer is experiencing a different rate of time flow.

@TheAlkemist
So if time is a fundamental QUANTITY of matter, what is the time of a brick?
Fundamental quantity does not refer to matter but to the real world in general. The real world is not only composed of matter but also space which in our case we use length. It is also composed of matter which is why we use mass. It is also composed of sequence of events which is why we use time.

Let's say this, if fundamental quantity only refers to matter then length can't be a fundamental quantity. Just because you are specifying what is the volume you don't necessarily specify its mass because it could have variable density.

Please TheAlkemist, read about fundamental quantities and dimensional analysis.

[Passionflower]

-First, proper time only defines the time of a moving or accelerating observer.

Proper time is what a clock measures, all observer's measure proper time on their clock regardless of their state of motion.

By the way an observer has only two states, inertial and accelerating. Whether an observer is moving is obviously a relative concept since there is no such thing as absolute motion and absolute time in relativity. (thing to think about in this context: if there is no absolute time and space are time and space really dimensions in Minkowski spacetime?)


-To define the time for a an observer that it not accelerating, you would still have to transform the proper time so that you get the time for the non-accelerating observer.

The time for a non-accelerating observers is the time on his clock and this is his proper time.


-Proper time is the total amount of time elapsed by someone who is accelerating. Meaning it is scalar and not the measuring system as i defined time.

Accelerating or not, an observer's clock measures proper time, always.


-What are the units of the proper time? It is still seconds.

You could take any unit you want.


And applying dimensional analysis i still get that the proper time is just a point or group of points or value of the dimensional system of time.

?


-Proper time does not say anything about time not being a dimension; it is just saying that an accelerating observer is experiencing a different rate of time flow.

Time flows at one second per second for all observers.

[TheAlkemist]

Sure. The length, width, and height are the distances from where it begins to where it ends in three orthogonal directions. Similarly there is a duration from when it begins to when it ends. It is exactly analogous to length, width, and height.

If your qualification for something being a dimension is that it be related to the extent of a brick then time is clearly a dimension.that's not my definition. I suggest we stick to my actually definition of dimension: a concept used to specify the structure/orientation or shape/geometry of a physical object. These are qualitative attributes. Duration is a quantitative attribute.

my first post in this thread: http://www.physicsforums.com/showpost.php?p=2961415&postcount=4

Time is a quantifier of the duration or intervals between events.

I point to an object and ask u what shape is it. If it has a defined shape u name it (square, octogon, tetrahedron, etc). If it doesn't u qualify it with it's dimensions. I might ask you how long, wide or high is it. You go measure it with a calibrated device. I point to the same object again and i ask u, what time is it. Please tell me how u go about answering this. Thanks.

[TheAlkemist]

The problem with this thread is that you have your prefered definition for the word time (proper time) and refuse to admit that it is common for words to have multiple meanings. You are not the supreme leader of science, and it is not up to you to unilaterally change definitions. There are multiple meanings to many words and if you would like to contribute usefully then you should be familiar with them all. You are correct that proper time is not a dimension, you are incorrect to conclude that there is therefore no sense in which time is a dimension.I agree with this. A word can have a meaning within a specific context that different from it's meaning in another. This is how language is. My problem, what confuses me, is when a word's meaning in one context is applied in another different context. Don't u see how this can be an issue?

[TheAlkemist]

Do you agree that whatever tricky means you are considering is not measuring the diagonal distance of the brick but an indirect method that you assume will give you the same answer?

And do you agree that you could also have measured the height, length, and width of the brick and calculated the diagonal distance by taking the square root of the sum of the squares of the three measurements and you would get exactly the same answer?
Yes, in the first case you're right! I just realized that. And you're also right in the second case. The only way i can measure the internal dimension of a continuous solid object is by inference--if this is what u mean by "indirect method". Now i'm assuming you're about to tell me how this is related to or analogous with the measurement of the time of this object?

[cshum00]

Did you read my entire post or only my direct dialog for you? If you read the entire post you should have seen how things piece together.

Proper time is what a clock measures, all observer's measure proper time on their clock regardless of their state of motion.
Yes, that is correct.

Whether an observer is moving is obviously a relative concept since there is no such thing as absolute motion and absolute time in relativity.
Yes, i agree that there is no such thing as absolute motion or absolute time.

(thing to think about in this context: if there is no absolute time and space are time and space really dimensions in Minkowski spacetime?)
Yes, even if there is no absolute time and space they are still dimensions in Minkowski spacetime. I know you have an idea of Minkowski spacetime, but read about it again. I bet you will see that Minkowski treat space and time as dimensions.

The time for a non-accelerating observers is the time on his clock and this is his proper time.

Accelerating or not, an observer's clock measures proper time, always.
Yes, that is right but it still doesn't say anything about it not being a dimension.

You could take any unit you want.
You mean i should say it can be kilograms when it is seconds? Just kidding. I know you mean take any measurable unit that is used for time.

Time flows at one second per second for all observers.
Yes and no. Proper time of an observer or of observers that are on the same rate of motion have the same rate of second per second time flow. However, for observers whose rate of motion is not the same, a second being elapsed in my proper time can be a day on the elapsed proper time of another observer.

Here is the problem of treating time in general as proper time. Because everyone has their own proper time, i know how much time has passed between two events in my time but i don't know how much it has lapsed in your proper time.

In order to calculate how much time has lapsed in your proper time, we have to treat time in general as a dimension and then do vector transformations so that my proper time dimension looks the same as yours. Then i can say what time your proper time measured.

[ghwellsjr]

By the way an observer has only two states, inertial and accelerating. Whether an observer is moving is obviously a relative concept since there is no such thing as absolute motion and absolute time in relativity. (thing to think about in this context: if there is no absolute time and space are time and space really dimensions in Minkowski spacetime?)
This is absolutely not true. SR is all about picking one single frame of reference at a time. In that frame, all times and positions, and therefore, all states of motion are absolute. A frame is a coordinate system of three dimensions of space and one of time. The locations and motions of all objects, observers, clocks, rulers, and anything else you want to consider are defined and discussed in terms of that one reference frame. Then, if you want, you can transform everything into a new reference frame that is relative to the first one and calculate the new times and positions of all the same objects, observers, clock, rulers, etc.

It is a mistake, a misunderstanding and an abuse of SR to think that every object, observer, clock, ruler, etc. is in its own frame relative to all the other objects, observers, clocks, rulers, etc. in their own frames all at the same time.

[ghwellsjr]

Do you agree that whatever tricky means you are considering is not measuring the diagonal distance of the brick but an indirect method that you assume will give you the same answer?

And do you agree that you could also have measured the height, length, and width of the brick and calculated the diagonal distance by taking the square root of the sum of the squares of the three measurements and you would get exactly the same answer?Yes, in the first case you're right! I just realized that. And you're also right in the second case. The only way i can measure the internal dimension of a continuous solid object is by inference--if this is what u mean by "indirect method". Now i'm assuming you're about to tell me how this is related to or analogous with the measurement of the time of this object?
No, I wasn't going to introduce time into the discussion, at least, not yet.

What I wanted to point out is that if you have two different ways to determine a distance between two points (diagonally opposite corners of a brick), one where you actually made a measurement, which is what I thought you were suggesting, something along the lines of placing the brick between two objects and then measuring the distance between the objects and the other where you measure some other components, the three dimensions of the brick and then calculate the distance, they both should yield the same result. In other words, any meaningful determination of a parameter that we want to discuss, like the "distance" between two points, should always get the same answer, don't you agree?

[ghwellsjr]

Passionflower--
A spacetime interval is the distance between two events in spacetime this is not necessarily the same as the length of an observer's path between two events. In some cases however they could be identical namely in the case the observer takes the largest possible travel time between these events.In any and all those cases where they are identical, do you have any problem, issue, complaint, concern or question with the spacetime interval?
Are you ever going to answer my question?

[neophysicist2]

"Time is what happens when nothing else is happening"

Surely if NOTHING else is happening, time stands still. If nothing is happening, everything is frozen, nothing moves and that includes clocks. If clocks do not move there is no time. ie. NOTHING moving equals no time passing.

[ghwellsjr]

"Time is what happens when nothing else is happening"

Surely if NOTHING else is happening, time stands still. If nothing is happening, everything is frozen, nothing moves and that includes clocks. If clocks do not move there is no time. ie. NOTHING moving equals no time passing.
I guess you didn't notice the tongue in Richard Feynman's cheek.

[nismaratwork]

"Time is what happens when nothing else is happening"

Surely if NOTHING else is happening, time stands still. If nothing is happening, everything is frozen, nothing moves and that includes clocks. If clocks do not move there is no time. ie. NOTHING moving equals no time passing.

There is a difference between a measurement problem and a fundamental one. For space as we experience it to exist, time is involved as a fourth dimension... and if that were to "go away", the universe would be VERY different. It's not a lack of activity that stops time, that just makes it meaningless from a large perspective (like eventual universal heat death).

[neophysicist2]

"I guess you didn't notice the tongue in Richard Feynman's cheek"

No, only replying to second post in this thread, so what did Richard Feynman mean?

"For space as we experience it to exist, time is involved as a fourth dimension and if that were go away..."

Obviously the universe is never going to stand still, this is hypothetical, but I do not see how time can pass/exist IF there is no movement. If nothing moves, nothing changes and time is all about change.

[DaveC426913]

No, only replying to second post in this thread, so what did Richard Feynman mean?

This thread is on its 11th page, well past the initial clarifying of the question and into the nuts and bolts. Asking about what a throw-away quote from post 2 at this point is tantamount to a derailment of the thread.

[FlexGunship]

Is there anything fundamentally wrong with defining a dimension as: any metric required to specify the location of an event?

I believe Brian Greene used this definition to great success. Certainly, it leaves out the details of coordinate stretching, but as far as specifying what could qualify as a dimension, surely this is a reasonable start?

In physical theories including additional spacetime dimensions, the only reason that these dimensions are necessary is because they are used to explain the location of an event which does not adequately "fit" in traditional 4D spacetime.

I happen to like the "office building" analogy. In order to specify the location of a meeting, you need the floor number, the 2D location on that floor, and the correct time. Four dimensions o specify the location of an event.

[neophysicist2]

"...tantamount to a derailment of the thread"

Point was, with regard to recent discussion over time being another dimension, if its' existence is dependent on relative movement/change then surely it is not a dimension in its' own right.

[cshum00]

"...tantamount to a derailment of the thread"

Point was, with regard to recent discussion over time being another dimension, if its' existence is dependent on relative movement/change then surely it is not a dimension in its' own right.

That is certainly an interesting point. If the entire word were to be at halt in motion then each proper time will lead to zero since the line integral of a zero path is zero.

What about your point of view? Do you think that time is dependent or independent? Special Relativity says it is dependent but with your example i think it should be dependent. So i am in a state of confusion at the moment.

[ghwellsjr]

"Time is what happens when nothing else is happening"

Surely if NOTHING else is happening, time stands still. If nothing is happening, everything is frozen, nothing moves and that includes clocks. If clocks do not move there is no time. ie. NOTHING moving equals no time passing.

"...tantamount to a derailment of the thread"

Point was, with regard to recent discussion over time being another dimension, if its' existence is dependent on relative movement/change then surely it is not a dimension in its' own right.
The point is, everyone knows what time is and like the original poster, you also are wondering about how it can be a dimension. I really don't know what most of the posters on this thread are concerned about because they won't be specific about their concerns. I explained what I believe the issue with time being involved as a "dimension" here:

But, just in case you are talking about "spacetime interval", let me explain what it is and then you can tell me if it helps.

First you have to understand what an event is. It is nothing more than a specified location (in three dimensions) at a specified time as defined by a specified coordinate system. It does not necessarily have anything to do with observers or paths or any actual event, although it may. You can then transform the event (location plus time) to any other coordinate system and the numbers you get to describe the four components of the event could be totally different.

In Galilean spacetime, if you have two events, the spacial distance between any two events can be calculated by taking the square root of the sum of the squares of the differences in the three dimensions and the time difference is merely the difference in the two times. Then if you transform the two events into a different coordinate system, even though all the numbers are different to describe the locations and times of the two events, if you perform the same computation, you will get the same answers for the spacial distance and time difference between the same two events defined by the second coordinate system, even if this second coordinate system is in motion with respect to the first one.

By Galilean spacetime, we mean that the relative speed between the two coordinate sytems, otherwise known as frames of reference, is much less than the speed of light.

But if the two coordinate systems (frames of reference) have a high speed between them, then the calculations that we did under the Galilean spacetime do not give the same spacial distance and time difference in the two frames of reference. However, we can define a new "distance" or "difference" between the two events which is called the "spacetime interval" that will be the same no matter what frame of reference we do the computation in, but instead of getting two numbers, a spacial distance and time difference, we get just one, the spacetime interval, based on a calculation of the two previous values.

The computation is very similar to the spacial distance, in fact we start with that prior to taking the square root but instead we subtract the square of the time difference multiplied by the square of the speed of light.

It should be no surprise that this computaton yields a frame invariant quantity, since we use the Lorentz Transform to produce the numbers for the second frame of reference, and the transform guarantees that the spacetime interval is frame invariant.
And you will note that it isn't time that is the fourth dimension, it is time multiplied by the speed of light, which is the distance that light travels for the time in question. So I don't know what the big concern is.

[cshum00]

The point is, everyone knows what time is and like the original poster, you also are wondering about how it can be a dimension. I really don't know what most of the posters on this thread are concerned about because they won't be specific about their concerns. I explained what I believe the issue with time being involved as a "dimension" here:


I think neophysicist2's question is more like this:
-Let's assume that it is possible for the entire world to be in a motionless state.
-Proper time is dependent to the spacial dimensions x, y, z or also defined as:

t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt

-Meaning that proper time in the world of motionless state will yield to the line integral path of 0 (zero).
-Then does it mean that time has come to a complete stop for the world that is at the motionless state?

[matheinste]

I think neophysicist2's question is more like this:
-Let's assume that it is possible for the entire world to be in a motionless state.
-Proper time is dependent to the spacial dimensions x, y, z or also defined as:

t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt

-Meaning that proper time in the world of motionless state will yield to the line integral path of 0 (zero).
-Then does it mean that time has come to a complete stop for the world that is at the motionless state?

With regard to the universe being in a motionless state I assume this means that all entities within it are at spatially at rest with respect to each other. Now is it implicit in the statement that time has somehow ceased to move onwards. If it does not then entities still have a path through spacetime. Anyway given that the question does not assume the answer we sort of come to a deeply philosphical question, does time exist if there are no means of measuring it. Clocks require some sort of repetitive cycle, impossible if you remove all happenings right down to a subatomics level and lower. It is a question I have not given much thought to but my intitial reaction is that time becomes irrelevant and meaningless.

Another interesting thought. I believe, that classically, that is ignoring quantum effects, once all things have ceased to move, if that is ever possible, they can never start to do so again.

Matheinste.

[DaleSpam]

t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt

-Meaning that proper time in the world of motionless state will yield to the line integral path of 0 (zero).Look carefully at the equation. If dx=dy=dz=0 then the proper time is not zero, it is in fact maximized.

[FlexGunship]

Look carefully at the equation. If dx=dy=dz=0 then the proper time is not zero, it is in fact maximized.

i.e. no movement through z, y, x implies maximum movement through t.

[DaleSpam]

My problem, what confuses me, is when a word's meaning in one context is applied in another different context. Don't u see how this can be an issue?Obviously, that is why I have posted my many comments in this thread clarifying the most relevant meanings of the word time.

[DaleSpam]

that's not my definition. I suggest we stick to my actually definition of dimension: a concept used to specify the structure/orientation or shape/geometry of a physical object.Can you cite any mainstream reference for this definition?


These are qualitative attributes. Duration is a quantitative attribute. Your first statement is simply false. Distance and duration are both quantitative. A brick is e.g. 7 cm in height by 10 cm in width by 20 cm in length by 100 years in duration. All quantitative.

I point to an object and ask u what shape is it. If it has a defined shape u name it (square, octogon, tetrahedron, etc). If it doesn't u qualify it with it's dimensions.Exactly the same with time, except that we have fewer words for 4D shapes so we make up new ones like "light cone" and "helical worldline", etc.

I might ask you how long, wide or high is it. You go measure it with a calibrated device. I point to the same object again and i ask u, what time is it. Please tell me how u go about answering this.With a clock. Btw, your phrasing is wrong here. You are confusing e.g. length with position.

[DaveC426913]

I point to an object and ask u what shape is it. If it has a defined shape u name it (square, octogon, tetrahedron, etc). If it doesn't u qualify it with it's dimensions. I might ask you how long, wide or high is it. You go measure it with a calibrated device. I point to the same object again and i ask u, what time is it. Please tell me how u go about answering this. Thanks.

Shape is a qualititative measurement, yes. No one is talking about shape except you.

Asking 'what is the time of a brick' is like asking 'what is the x of a brick?' Poorly worded, but we can deduce what you meant.

Length, width and height are quantitative. I can specify the brick's x, y and z extent as arbitrarily precisely as I want. I can also specify its extent in time. It came into existence on Aug 23, 2003, and ceased to exist *WHAM* now.



Point of order: correct spelling is actually a PF rule.

http://www.physicsforums.com/showthread.php?t=414380
"...posts are required to show reasonable attention to written English communication standards. This includes the use of proper grammatical structure, punctuation, capitalization, and spelling. SMS messaging shorthand, such as using "u" for "you", is not acceptable."

[Passionflower]

I can also specify its extent in time. It came into existence on Aug 23, 2003, and ceased to exist *WHAM* now.

Different clocks do not necessarily agree on the age of an object.

[cshum00]

Look carefully at the equation. If dx=dy=dz=0 then the proper time is not zero, it is in fact maximized.

i.e. no movement through z, y, x implies maximum movement through t.

Then that is the answer. I just don't see the mathematics of it, can you guys help me?

Let's say that x, y, z are functions of [s] a dummy parametric variable. Then parametric equations of the curve is:
x(s)=k_1; y(s)=k_2; z(s)=k_3
dx(s)=0; dy(s)=0; dz(s)=0
dt = 0ds
\int_D = \int_0^0

Then:

t_p = \int_0^0 0 \sqrt {1 - \frac{(0)^2 + (0)^2 + (0)^2}{c^2}} ds

I must be doing something wrong since i get zeros everywhere. I get that the parametric curve is zero. The limits of integration is zero.

Edit: Ok, i see where i started wrong. The general line integral is:
\int_D f(x,y,z) ds
And the parametric form of the line integral is:
\int_a^b f(x(t),y(t),z(t)) \sqrt {(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2 + (\frac{dz}{dt})^2}dt

This means that the proper time equation:
t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt
is already in its parametric form where t (time) is the parametric variable. It doesn't change the fact that:
x(s)=k_1; y(s)=k_2; z(s)=k_3
dx(s)=0; dy(s)=0; dz(s)=0

But i still don't get the following:
-\int_D implies the integral around the curve D but the limits of the parametric form of the line integral are plain limits a and b.
-Even assuming that they are just limits a and b, what are a and b since my parametric variable is time but time is what i want to calculate too?

[DaveC426913]

Different clocks do not necessarily agree on the age of an object.Likewise different rulers do not necessarily agree on its length.

Point made in favour of time being a dimension like space.

[Ich]

-Even assuming that they are just limits a and b, what are a and b since my parametric variable is time but time is what i want to calculate too?
Don't use the same word for different things. Suppressing two dimensions, you have
ds²=-dt²+dx², IOW
dtau² = dt²-dx²,
where tau is proper time, and t is coordinate time. Two different things.
Now obviously you integrate t, so your bounds a,b are different coordinate times.
Likewise, x is not a function of tau, but a function of t.
Integrating the formula from t1 to t2 gives Delta tau, the elapsed proper time.

[Passionflower]

Point made in favour of time being a dimension like space.
So because different clocks record different ages of an object in sapcetime is a point in favor of time being a dimension of spacetime?

[cshum00]

Don't use the same word for different things. Suppressing two dimensions, you have
ds²=-dt²+dx², IOW
dtau² = dt²-dx²,
where tau is proper time, and t is coordinate time. Two different things.
Now obviously you integrate t, so your bounds a,b are different coordinate times.
Likewise, x is not a function of tau, but a function of t.
Integrating the formula from t1 to t2 gives Delta tau, the elapsed proper time.

Sorry for mixing up proper time and coordinate time.

I know i might be wrong but i am just trying to piece the information you gave me with what i have.
x(t)=k_1; y(t)=k_2; z(t)=k_3
dx(t)=0; dy(t)=0; dz(t)=0
\int_D = \int_{t_1}^{t_2}
t_p = \tau = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt
\tau = \int_{t_1}^{t_2} \sqrt {1 - \frac{(0)^2 + (0)^2 + (0)^2}{c^2}} dt
\tau = \int_{t_1}^{t_2} \sqrt {1} dt = \int_{t_1}^{t_2} 1 dt
\tau = t |_{t_1}^{t_2} = t_2 - t_1 = \Delta t

-How do i know what are the coordinate time values t_1 and t_2?
-If i did something wrong please point it out again. Also, please show me the entire calculation please so that i can see the entire picture faster.

[DaveC426913]

So because different clocks record different ages of an object in sapcetime is a point in favor of time being a dimension of spacetime?

In that, using your example, you have shown another way they are similar, yes.

Note what it requires for the clocks to show different ages; it requires a difference in frames of reference. Same with spatial dimensions. Objects observed at relativistic velocities will be measured as shorter in a spatial dimension just as they are measured longer in the time dimension.

[nismaratwork]

In that, using your example, you have shown another way they are similar, yes.

Note what it requires for the clocks to show different ages; it requires a difference in frames of reference. Same with spatial dimensions. Objects observed at relativistic velocities will be measured as shorter in a spatial dimension just as they are measured longer in the time dimension.

To me, this seems intuitive once you accept Relativity.

To neophysicist... sorry about the late reply, but my internet died a terrible death for a bit there. You could imagine a universe without any discernable motion and time could still be a dimension there. Perhaps you have a classical universe at absolute rest, but it is still capable of being perturbed. Even in thought experiments or pondering your view of time as a measure of change is just that: a measurement problem. Time can be a dimension even when it's not measurable, and that in my view is another point in favor of time as just another dimension like any other.

If it isn't, 4-Momentum/Velocity, etc... makes no sense... yet it works.

[Passionflower]

Note what it requires for the clocks to show different ages; it requires a difference in frames of reference. Same with spatial dimensions.
Hold on so the dimensions of spacetime are frame dependent? Frame dependent dimensions? What are frame dependent dimensions?

Let me ask you this: do you think spacetime has a notion of absolute space and time? Are the, what you call time ans space dimensions, of spacetime absolute?

[DaveC426913]

Hold on so the dimensions of spacetime are frame dependent?I did not say this. How do you get that from what I said?

[Passionflower]

I did not say this. How do you get that from what I said?
Ok, so then do you say they are fame independent?

[DaveC426913]

Ok, so then do you say they are fame independent?

Dimensions are, our measurements of things in them is not.

[DaleSpam]

Are the, what you call time ans space dimensions, of spacetime absolute?The dimensionality of a manifold and the signature of the metric are both invariants.

[Passionflower]

Dimensions are, our measurements of things in them is not.
I see, let me get this straight so you are calling the dimensions of spacetime space and time but we cannot measure them?

[Passionflower]

The dimensionality of a manifold and the signature of the metric are both invariants.
I agree with that, that is exactly the reason why the dimensions of spacetime cannot be called pure space and time because space and time separately are not invariants for observers only in combination they are.

This, what you call, timelike dimension of spacetime do you think that is a measure of some kind of absolute time and for space dimension absolute space? A sort of LET kind of interpretation?

[DaveC426913]

I see, let me get this straight so you are calling the dimensions of spacetime space and time but we cannot measure them?
What do you mean measure "them"? Measure a dimension? One does not measure a dimenson; it is a continuum. You measure something in a dimension.

If I measure the width of a brick, that is utterly independent of its length or height. It must have a width and height, but measuring its width tells me nothing about its length or width (because they are orthagonal).

Likewise, if I measure the duration of the brick, it is also independent of its length and width and height. All 4 are orthagonal.

[DaveC426913]

Hold on so the dimensions of spacetime are frame dependent? Frame dependent dimensions? What are frame dependent dimensions?
Are the, what you call time ans space dimensions, of spacetime absolute?

I see, let me get this straight so you are calling...


...A sort of LET kind of interpretation?

Passionflower, there's got to be a better way of discussing this than trying to put words in other peoples' mouths.

[DaleSpam]

I agree with that, that is exactly the reason why the dimensions of spacetime cannot be called pure space and time because space and time separately are not invariants for observers only in combination they are.I don't think anyone has called them "pure space and time", whatever that means.

I don't know where you pulled the LET from. This is basic GR. Spacetime is a 4D pseudo-Riemannian manifold with three dimensions of space and one dimension of time. Do you understand what that means?

[Passionflower]

What do you mean measure "them"? Measure a dimension? One does not measure a dimenson; it is a continuum. You measure something in a dimension.

Ok fair enough, if I the measure time between two events in spacetime, do you think all observers agree on how much time is between them? You call time a dimension of spacetime right?

Likewise, if I measure the duration of the brick, it is also independent of its length and width and height. All 4 are orthagonal.
Let me ask you this do you understand the difference between a Galilean spacetime and a Minkowski spacetime? Do you understand that time and space are not independent in spacetime?

[DaleSpam]

Do you understand that time and space are not independent in spacetime?Do you understand that x, y, and z are not "independent" in space? If you do then it should be clear that being "independent" is not a requirement for a dimension. In fact, if it were "independent" in this sense then it wouldn't be a dimension in the same mathematical space.

[Passionflower]

I don't think anyone has called them "pure space and time", whatever that means.

Ok, fair enough then what kind of time is it? Coordinate time perhaps? You call a coordinate dependent entity a dimension of spacetime the spacetime we live in?

This is basic GR. Spacetime is a 4D pseudo-Riemannian manifold with three dimensions of space and one dimension of time. Do you understand what that means?
Spacetime is certainly a 4D pseudo-Riemannnian manifold I completely agree with that. No single dimension of this manifold can be attributed to time and space for all observers, in fact in non-stationary spacetimes no single observer will measure the, what you call, timelike dimension as time and no single observer will measure the spacelike dimensions as space as GR is basically a background independent theory.

Unlike in the case of Galilean spacetime time for any observer is the path length between two events not the amount traveled in the timelike dimension.

[DaleSpam]

Spacetime is certainly a 4D pseudo-Riemannnian manifold I completely agree with that.OK. So, in your understanding, what distinguishes a 4D pseudo-Riemannian manifold from a 4D Riemannian manifold?

[Passionflower]

OK. So what distinguishes a 4D pseudo-Riemannian manifold from a 4D Riemannian manifold?
The metric has a different signature.

While a Riemannian manifold has a positive definite metric a pseudo-Riemannian (or Lorentzian) manifold does not. Due to this, distance exists in three classes, timelike, spacelike and nulllike.

But the key interest wrt dimensions is the comparison between the classical Galilean spacetime, where both the space and time dimensions physically relate to the observer's measure of space and time, and the Minkowski spacetime (and also a Lorentzian spacetime) where this direct mapping is lost. What consists of physical time and physical space depends on the observer's orientation in spacetime, e.g. how the observer is oriented wrt the dimensions of spacetime. In other words what an observer measures as space and time is not universally true, each observer could in principle have a unique view of what consists of space and time. Now one could build a coordinate system around each individual observer with three spatial and one time dimension but obviously this coordinate system is not the same as the spacetime itself.

[DaleSpam]

The metric has a different signature.Exactly. Specifically four dimensions of space (++++) vs one dimension of time and three of space (-+++).


While a Riemannian manifold has a positive definite metric a pseudo-Riemannian (or Lorentzian) manifold does not. Due to this, distance exists in three classes, timelike, spacelike and nulllike.Right, and this cannot happen unless the manifold has at least one dimension of time.

It is fine if you choose to avoid this terminology in your writing (just as it is ok to avoid "relativistic mass"), but because of what you describe here it is standard terminology to say that time is a dimension. What you have described is the essence of that statement.

[Passionflower]

Exactly. Specifically four dimensions of space (++++) vs one dimension of time and three of space (-+++).

At the manifold level we have no need to distinguish between physical space and time, all we need to do is have four dimensions organized as +--- or -+++ (they are equivalent). Then we add a metric that satisfies the EFE. Then if we want the time between two events on an observer's clock we have to take the length of a path that varies potentially over all four dimensions of spacetime.


Right, and this cannot happen unless the manifold has at least one dimension of time.

All that is required for something to be a pseudo-Riemannian manifold is the signature (well actually there are a few other conditions, which I am sure you are familiar with, but they are not a distinguishing factor wrt a vanilla Riemannian manifold), what physically constitutes space or time is not answered at this level it is answered after we introduce a valid instance of the EFE and then, physically, time is a length of a path not a dimension.

It is fine if you choose to avoid this terminology in your writing (just as it is ok to avoid "relativistic mass"), but because of what you describe here it is standard terminology to say that time is a dimension. What you have described is the essence of that statement.
I have no trouble finding time a dimension in the coordinate system of an observer. Of course an observer observes three spatial dimensions and a time dimension orthogonal to this but this is not the same as calling time a dimension of spacetime, time is a dimension of an observer yes but not of spacetime. Also note that this observer effectively has a Galilean coordinate system, even an accelerating observer can have such a coordinate system, for instance one that is Fermi-Walker transported. But wrt spacetime such a coordinate system constantly (pseudo) rotates. Thus the time dimension of the coordinate chart constantly (pseudo) rotates wrt to the "timelike" dimension of the manifold.

[DaleSpam]

all we need to do is have four dimensions organized as +--- Excellent.

I am going to disengage at this point. Not because I believe that I have convinced you, but because I realize that we agree on the important physics/math and the remaining disagreement is only a matter of semantics. I try to avoid semantic arguments once I have identified them as such since they are frustrating and unimportant.

[TheAlkemist]

No, I wasn't going to introduce time into the discussion, at least, not yet.

What I wanted to point out is that if you have two different ways to determine a distance between two points (diagonally opposite corners of a brick), one where you actually made a measurement, which is what I thought you were suggesting, something along the lines of placing the brick between two objects and then measuring the distance between the objects and the other where you measure some other components, the three dimensions of the brick and then calculate the distance, they both should yield the same result. In other words, any meaningful determination of a parameter that we want to discuss, like the "distance" between two points, should always get the same answer, don't you agree?
Yes, if the metric (measuring device, ruler, what ever) used to calculate the distance is same.



Can you cite any mainstream reference for this definition? Any dictionary. Here's one: http://www.merriam-webster.com/dictionary/dimension
(definition "b")

Your first statement is simply false. Distance and duration are both quantitative. A brick is e.g. 7 cm in height by 10 cm in width by 20 cm in length by 100 years in duration. All quantitative.I meant length by the way, which is not synonymous with distance or else their definitions would be circular). Anyway, an object has the quality of length before you make a measurement with a ruler or whatever. For the purposes of math, length (and distance) are actually itineraries. But I think I'm done with this issue. I will respectfully bow out. :smile:

Exactly the same with time, except that we have fewer words for 4D shapes so we make up new ones like "light cone" and "helical worldline", etc.But you can't point to a light cone or a helical worldline.

With a clock. Btw, your phrasing is wrong here. You are confusing e.g. length with position.So I have a static brick on a table, exactly what would I be measuring using a clock? And how am I confusing length and position?





Length, width and height are quantitative. I can specify the brick's x, y and z extent as arbitrarily precisely as I want. I can also specify its extent in time. It came into existence on Aug 23, 2003, and ceased to exist *WHAM* now.
So by "extent in time" you mean from when you first observe it, t1, to when it ceases to exist, t2?

[DaleSpam]

Any dictionary. Here's one: http://www.merriam-webster.com/dictionary/dimension
(definition "b")Excellent reference. See definition 1a. Time is specifically listed as a dimension.


Anyway, an object has the quality of length before you make a measurement with a ruler or whatever.Same with the quality of duration.


But you can't point to a light cone or a helical worldline.Sure you can, although I am not sure what relevance "pointability" has in this conversation.

[ghwellsjr]

No, I wasn't going to introduce time into the discussion, at least, not yet.

What I wanted to point out is that if you have two different ways to determine a distance between two points (diagonally opposite corners of a brick), one where you actually made a measurement, which is what I thought you were suggesting, something along the lines of placing the brick between two objects and then measuring the distance between the objects and the other where you measure some other components, the three dimensions of the brick and then calculate the distance, they both should yield the same result. In other words, any meaningful determination of a parameter that we want to discuss, like the "distance" between two points, should always get the same answer, don't you agree?
Yes, if the metric (measuring device, ruler, what ever) used to calculate the distance is same.
Nowadays, you can buy measuring devices that use laser beams. Do you consider them to give the same results as rulers do?

[DaveC426913]

So I have a static brick on a table, exactly what would I be measuring using a clock?
We cannot freely move through the t dimension; that's what makes it timelike. We are doomed to pass through it eternally at a constant rate.

If we could move thorugh it freely, we would move to the beginning of the object's existence in time and place a t1 (just like I could move to the beginning of the object's existence in the x dimension and place an x1).



So by "extent in time" you mean from when you first observe it, t1, to when it ceases to exist, t2?
t1 is when the brick first becomes definably a brick. Its existence has nothing to do with my observation of it.

In the x dimension, it is not a brick at x0 (an inch to its left), it is a brick at x1 through x2 and is no longer a brick at x3 (an inch to its right).

In the t dimension, it is not a brick at t0 (a minute before it is formed), it is a brick from t1 through t2, and is no longer a brick at t3 (one minute after it is destroyed).

[nismaratwork]

We cannot freely move through the t dimension;that's what makes it timelike. We are doomed to pass through it eternally at a constant rate.

I add a vote (and I voted for you getting humor again!!) for you as the most able to depress me with a single sentence. It's true, and it's well said, but ouch.

If we could move thorugh it freely, we would move to the beginning of the object's existence in time and place a t1 (just like I could move to the beginning of the object's existence in the x dimension and place an x1).



t1 is when the brick first becomes definably a brick. Its existence has nothing to do with my observation of it.

In the x dimension, it is not a brick at x0 (an inch to its left), it is a brick at x1 through x2 and is no longer a brick at x3 (an inch to its right).

In the t dimension, it is not a brick at t0 (a minute before it is formed), it is a brick from t1 through t2, and is no longer a brick at t3 (one minute after it is destroyed).

I wonder if the some of the confusion here comes from the ability to use distance and time interchangeably in some circumstances, because as you say it, this seems like the clearest of points to make about time.

[TheAlkemist]

Excellent reference. See definition 1a. Time is specifically listed as a dimension. ok.

Same with the quality of duration.What if the object isn't moving?

Sure you can, although I am not sure what relevance "pointability" has in this conversation.It's relevant because there's a difference between objects and concepts and the two shouldn't be conflated. Don't you agree?

[Ich]

It's relevant because there's a difference between objects and concepts and the two shouldn't be conflated.
A brick is most certainly a 4-dimensional object.
As opposed to the concept of 3-dimensional bodies, which itself stems from the concept of simultaneity at a distance, which is derived from an errorneous generalization of slow-speed observations.

[DaveC426913]

What if the object isn't moving?

No such thing.

What you can say is that it is not moving wrt some frame of reference (like your own).

[DaleSpam]

What if the object isn't moving?Then it is at rest. :rolleyes:

[TheAlkemist]

Nowadays, you can buy measuring devices that use laser beams. Do you consider them to give the same results as rulers do?But isn't a laser beam 'ruler' is an indirect measuring device that infers distance from the speed of light? I think I see where you are going with this but i'm really curious to see so i'll say yes.



We cannot freely move through the t dimension; that's what makes it timelike. We are doomed to pass through it eternally at a constant rate.

If we could move thorugh it freely, we would move to the beginning of the object's existence in time and place a t1 (just like I could move to the beginning of the object's existence in the x dimension and place an x1).From what I understand here, you are saying you can't measure the brick's time with a clock because you can't go back in time to the beginning of the brick's existence and make the t1 measurement? Please correct me if i'm wrong.

t1 is when the brick first becomes definably a brick. Its existence has nothing to do with my observation of it.I wasn't suggesting that your observation brings the brink into existence. I'm not Deepak Chopra. Fine. I'll rephrase the question: So by "extent in time" you mean from when you first measure it, t1, to when it ceases to exist, t2?

In the x dimension, it is not a brick at x0 (an inch to its left), it is a brick at x1 through x2 and is no longer a brick at x3 (an inch to its right).

In the t dimension, it is not a brick at t0 (a minute before it is formed), it is a brick from t1 through t2, and is no longer a brick at t3 (one minute after it is destroyed).Ok. So does everyone get to chose their own t1 and t2 as they deem fit?


I wonder if the some of the confusion here comes from the ability to use distance and time interchangeably in some circumstances...I think so.

[TheAlkemist]

A brick is most certainly a 4-dimensional object.
As opposed to the concept of 3-dimensional bodies, which itself stems from the concept of simultaneity at a distance, which is derived from an errorneous generalization of slow-speed observations.Wait what?:confused:


No such thing.

What you can say is that it is not moving wrt some frame of reference (like your own).Ok. I'm not going to argue with you about this any more. But I have one last question. So is it safe to say that physics does not deal with static concepts at all?


Then it is at rest. :rolleyes:Why are you rolling your eyes?:confused: Did I ask a stupid question? If an object is at rest and time requires motion then... you know what, never mind.

I'm gonna withdraw from this discussion and just casually observe from the sidelines from now.

[cshum00]

Ok. I'm not going to argue with you about this any more. But I have one last question. So is it safe to say that physics does not deal with static concepts at all?


-The reason why dimensions doesn't have an absolute frame of reference does not have to do with physics but the mathematical concept of it.
-In mathematics, dimensions are special vectors that become a coordinate system.
-Just like when mapping a vector onto a coordinate system, there is no fixed position we have to place it on. Similarly, when mapping the dimensions onto the real world; there is no fixed origin but we happen to choose the frame of reference.

[DaleSpam]

So is it safe to say that physics does not deal with static concepts at all? There is a whole branch of classical mechanics called statics. And equilibria and conserved quantities are very important precisely because they are static.

[slider123]

Can anyone help me with this one!,i dont think its a very original question but keeps recurring in my head..
If time existed before the big bang,then it seems to me that time in the past may be infinite ie :That if there is no beginning of time the past therefore must be infinite,..If this is correct and the past is infinite ,then how could we reach the present time ,,ie have we waited an eternity to be born ,,which then leads me to conclude a contridictve answer that maybe by logic that time does not exist at all ..Or am i just talking a load of

[bobc2]

Ok, fair enough then what kind of time is it? Coordinate time perhaps? You call a coordinate dependent entity a dimension of spacetime the spacetime we live in?

Spacetime is certainly a 4D pseudo-Riemannnian manifold I completely agree with that. No single dimension of this manifold can be attributed to time and space for all observers, in fact in non-stationary spacetimes no single observer will measure the, what you call, timelike dimension as time and no single observer will measure the spacelike dimensions as space as GR is basically a background independent theory.

Unlike in the case of Galilean spacetime time for any observer is the path length between two events not the amount traveled in the timelike dimension.

Passionflower, I've been browsing through your posts on this thread. You seem to have an interesting concept of time vs. spacetime. But, I'm having a little difficulty having a clear understanding of your conept. Are you regarding the universe as a 4-dimensional space populated by 4-dimensional spatial objects (in the context of a fundamental physical description)? Time would then just be an available parameter useful in computing changes in position along a spatial 4th dimension (DX4 = c(Dt)? The more fundamental understanding of time would then be outside of a discussion of physics, i.e., a metaphysical discussion involving memory, consciousness, etc.(more appropriate for the philosopy forum)?

[King Wildog]

We talk about the scale of time, which should help one to realize it only exists in concept. Even an inch is a concept- an object is actually exactly that long, but we concieved an inch to more easily percieve it in respect with other objects. So time then is absolutely constant as is an inch. An object can be acted on however it may- completely changing its lifespan, but never did time change. Perception of time is so easily confused with actual time which is more of a duration or measure of how much energy must be applied to an object to speed up happenings.

If I were to kick a clock across the lot, should I then be confused to read the time and find it off calibration?-- King Wildog

I use this absolutely unplagiarized self-quote to kick start conversations on Time and my notion of an object's endurance to its environment that changed the read on your brilliant timepiece. If I stick a clock in the oven I am also unsurprized by the results- but if I run really, really fast- well I must have changed time and not anyway have I affected my clock. I'm not OK with that. Our clocks have always been awesome attempts at guaging time for us. In fact, we make them better and better in an attempt to make them more rugged or resistent to our environment. In fact, I have a water resistant watch, for example.

A clock is just a mechanical repeating device invented to produce our best at constance, because our brain loves to compare things. So if you abuse or misuse your clock you will void its warrantee, and you will affect its ability to do its job.

[DaveC426913]

We talk about the scale of time, which should help one to realize it only exists in concept. Even an inch is a concept- an object is actually exactly that long, but we concieved an inch to more easily percieve it in respect with other objects. So time then is absolutely constant as is an inch. An object can be acted on however it may- completely changing its lifespan, but never did time change. Perception of time is so easily confused with actual time which is more of a duration or measure of how much energy must be applied to an object to speed up happenings.

If I were to kick a clock across the lot, should I then be confused to read the time and find it off calibration?-- King Wildog

I use this absolutely unplagiarized self-quote to kick start conversations on Time and my notion of an object's endurance to its environment that changed the read on your brilliant timepiece. If I stick a clock in the oven I am also unsurprized by the results- but if I run really, really fast- well I must have changed time and not anyway have I affected my clock. I'm not OK with that. Our clocks have always been awesome attempts at guaging time for us. In fact, we make them better and better in an attempt to make them more rugged or resistent to our environment. In fact, I have a water resistant watch, for example.

A clock is just a mechanical repeating device invented to produce our best at constance, because our brain loves to compare things. So if you abuse or misuse your clock you will void its warrantee, and you will affect its ability to do its job.

I am not really sure what your point is. Are you asking a question? Or are you purporting a new theory of your own?

Regardless, you should probably start a new thread.

[King Wildog]

Thanks for replying. I felt I was on topic. Sorry, are we not talking about time? I am brand new to this Forum, so I'm not quite ready to start a new thread. I was hoping to actually find a thread to reply to which would give me some experience talking about this subject. In my everyday life I have noone to discuss this with. I don't think I make up theories. I think I iterate points which may be less than mainstream, but it does seem some share my views. I haven't been here long enough to be disagreeing with anyone here. My credentials are modest at best- High school physics and a lot of Discovery and Science channel. I am an Ammonia refrigeration maintenance supervisor- so I am a novice dabbler in many subjects such as refrigeration, chemistry, thermodynamics, meteorology, electricity, mechanics, educational instruction, management- I am certainly a layman, so I am not touting myself as a professor. I disagree with relativity theory, though, and any notions of time travel. I say time travel is impossible- and I don't mean physically impossible- I mean absolutely impossible. The present tense is the only real tense. The past is only a memory or telling of what occured in a past presence. The future is only a prediction of a future presence. I watched Hawking hoping his latest appearance was to shed new light on time travel and time itself to those of learned background- but no- I was left still shaking my fist at the TV. You see most are left to accept time for what someone tells them because most don't understand time enough to even have an opinion on it. I know I understand time as well as- in fact, obviously better than even Hawking himself. I truly did laugh out loud when I imagined a full grown man acting as a child would running around really fast trying to timetravel.

Hopefully my two cents weren't ill spent.

[DaleSpam]

I don't think I make up theories. I think I iterate points which may be less than mainstream, but it does seem some share my views.This forum is for discussing mainstream physics only. Please read the rules about overly speculative posts. There are many other forums on the internet for speculation, this one is for education.

I disagree with relativity theory, though.But nature disagrees with you, and only her vote counts:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

I would encourage you to go elsewhere if you just want to expound an anti-relativity viewpoint and pat yourself on the back for being so visionary. On the other hand, if you want to learn some actual physics then you are welcome to stay, but you must abide by the rules which you agreed to when you signed up.

[bobc2]

...In relativity, we have four coordinates that are used in order to specify an event. It doesn't make sense in relativity to treat a time coordinate differently from a spatial coordinate, because when one observer is in motion relative to another observer, each observer's measurements of time and distance are related to the other observer's measurements by equations that don't break apart cleanly into time and space equations.

That is one of the most efficient and insightful comments about spacetime I've seen on this forum--and worth a repost at this point. Thanks, bcrowell.

[khemist]

Thanks for replying. I felt I was on topic. Sorry, are we not talking about time? I am brand new to this Forum, so I'm not quite ready to start a new thread. I was hoping to actually find a thread to reply to which would give me some experience talking about this subject. In my everyday life I have noone to discuss this with. I don't think I make up theories. I think I iterate points which may be less than mainstream, but it does seem some share my views. I haven't been here long enough to be disagreeing with anyone here. My credentials are modest at best- High school physics and a lot of Discovery and Science channel. I am an Ammonia refrigeration maintenance supervisor- so I am a novice dabbler in many subjects such as refrigeration, chemistry, thermodynamics, meteorology, electricity, mechanics, educational instruction, management- I am certainly a layman, so I am not touting myself as a professor. I disagree with relativity theory, though, and any notions of time travel. I say time travel is impossible- and I don't mean physically impossible- I mean absolutely impossible. The present tense is the only real tense. The past is only a memory or telling of what occured in a past presence. The future is only a prediction of a future presence. I watched Hawking hoping his latest appearance was to shed new light on time travel and time itself to those of learned background- but no- I was left still shaking my fist at the TV. You see most are left to accept time for what someone tells them because most don't understand time enough to even have an opinion on it. I know I understand time as well as- in fact, obviously better than even Hawking himself. I truly did laugh out loud when I imagined a full grown man acting as a child would running around really fast trying to timetravel.

Hopefully my two cents weren't ill spent.
It would do you some good to read up on material relating to relativity and how time is dilated. You will also find that relativity does nothing to predict time travel, just a change in the rate of clocks ticking at in two different reference frames, and it has nothing to do with the fact that clocks are past their warranty date...

Your approach to time is not a physical question but a philosophical question.

[jtbell]

I am brand new to this Forum

In that case I suggest you click on the "Rules" link at the top of every page here, and note particularly the section on Overly Speculative Posts.

[Zephyr777]

I thought Pyotr Ouspenskii was quite concise in his explanation of time as it pertains to our understanding of the proposed dimensional structure of the universe. Events that occurred have equal relevance with respect to measurements as events that are still occurring, and those that have yet to occur. That is why we keep records and make predictions about the outcome of the experiments we are performing.

Perhaps the reason why there seems to be so much difficulty understanding time dilation is because the four-vector model is incomplete and fails to account for all three dimensions of time?

In that case I suggest you click on the "Rules" link at the top of every page here, and note particularly the section on Overly Speculative Posts.

I believe you are also being a little too stringent in your interpretation of the rules. The section you refer to clearly states that only, "Poorly formulated personal theories, unfounded challenges of mainstream science..." will not be tolerated. According to the rules, as long as his statements are well formulated and/or founded challenges to mainstream science, then he is well within his rights to question this stuff. After all, up until 1914, 'mainstream science' was rather convinced that electrons resided in the nucleus of the atom, and until the 1940's that it was not possible to travel faster than the speed of sound.

[jtbell]

Perhaps the reason why there seems to be so much difficulty understanding time dilation is because the four-vector model is incomplete and fails to account for all three dimensions of time?

Can you provide a reference to a peer-reviewed article in a professional physics journal that discusses three-dimensional time? I didn't find anything with a quick Google search.

According to the rules, as long as his statements are well formulated and/or founded challenges to mainstream science, then he is well within his rights to question this stuff.

If someone in the professional physics community has taken up an idea and published it in a peer-reviewed journal, then it is fair game here. Sometimes we accept articles that have been "published" only on arxiv.org, but this is on a case-by-case basis because that site is not peer-reviewed.

If it is the poster's own personal unpublished theory, then it can be discussed (here on PF) only in the Independent Research forum (http://www.physicsforums.com/forumdisplay.php?f=146).

The physics forums are for physics topics, i.e. related to things that we can actually do experiments about, at least in principle. We have a philosophy forum (http://www.physicsforums.com/forumdisplay.php?f=112) for philosophical and metaphysical discussions.

[DaleSpam]

I believe you are also being a little too stringent in your interpretation of the rules. Hi Zephyr777, welcome to PF?

jtbell is correct. This forum is not for philosophy and it is not for speculation and it is not even for the advancement of physics as a whole. All of those have their value and their place, but the purpose of this form is for education. There are many forums without moderation where you can go if you want to speculate and philosophize, and there are many scientific conferences that you can attend if you want to advance physics. This is not the place for those, and to permit that on this forum would be to lose the thing that makes it unique and valuable.

[bobc2]

Perhaps the reason why there seems to be so much difficulty understanding time dilation is because the four-vector model is incomplete and fails to account for all three dimensions of time?

If you would look at some of the many posts on this forum dealing with time dilation you would see that there are many experienced physicists and students on here who demonstrate a good understanding of time dilation. I don't think they are having any difficulty at all.

I am a relatively new-comer and have been very impressed with the presentations on this forum (unlike those of some of the less disciplined forums). I'm sure the standards maintained here account in some measure for the quality of the contributers attracted to this site.

[Zephyr777]

Don't misunderstand me. I do not promote people filling this forum with asinine questions or ridiculous philosophical rhetoric. However, there can be no real education without at least some speculation. I agree with jtbell about not letting people rant openly about things they don't understand, or disagree with, but we shouldn't be so Nazi-istic in our approach. The rules allow for well formulated personal theories in this forum, as well as legitimate challenges to mainstream science. I am not suggesting the original poster of this thread is either. I was merely attempting to lower the tone of the discussion a little, which I seem to have done.
Complain if you like, but send your complaints to the moderators. Let the moderators decide what is appropriate, and what is not.

As far as the three-dimensions of time, you would not find a reference by doing a quick search on Google. Google is a helpful tool, but it's not complete. You may be correct, however, in assuming there have been no recently published (peer-reviewed) articles on the subject. It is a rather old idea that some physicists kick around from time to time, but few people have the ability to rightly apply it to any area of physics, and thus it is not a generally accepted concept.

Bobc2, I agree with you, as well. The comment was mostly meant for the originator of this post, who seems to be having much trouble understanding the current concept of time. Although most of the people in this forum don't SEEM to have trouble understanding it -- they know what it is, and are able to apply it proficiently in a rudimentary fashion -- there are still a great many people who cannot apply the concept in a more advanced fashion.

For instance, it is generally understood that distant galaxies are expanding faster at greater intervals. This is based largely on calculations of the galactic red-shift, which most of us are all-too familiar with. However, many people forget that the light we are looking at from those galaxies much farther away, also takes much longer to reach us. So, for example, when we look at the Messier 87 galaxy, we see the redshift of that particular galaxy as it was approximately 5,000 years ago. If we look at ESO 137-001, we will see the red-shift of that particular galaxy as it was approximately 260,000 years ago. If we see that the redshift for ESO 137-001 is greater than M87, we may then reasonably conclude that the expansion has actually been slowing with time, rather than increasing with distance.

[DaleSpam]

The rules allow for well formulated personal theories in this forum, as well as legitimate challenges to mainstream science.Where do they allow that?

[raynicolle]

Everything you have said is excellent, but you stopped too soon. You should also have said that your choice of co-ordinate system should not make any difference in how you analyze a situation, don't you agree?

Well, that's the problem. When we try to define the distance between to events, widely separated in distance and time, we will get different answers for every co-ordinate system we use and that's no fun.

So to solve this problem we use a new kind of vector that includes both the normal three-component vector for space and the normal scalar for time, and we call it a four-vector. Then we invent (or discover) a way to calculate a new "distance" called "interval" that is always the same, no matter which co-ordinate system we use to describe, characterize, or analyze any situation.

Does that make sense to you?

What if there is NO distance between events because all events occur in the "universal NOW"? Time is not like a river because events are always in the 'now'. Then there is no need for a dimension called 'time'. There is only need for a useful-but-imaginary measuring concept. Hey, maybe that is what the 4th dimension is?