What is the true nature of time?

[Parbat]

What does "time" really mean?

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? 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? Or is this merely an attribute that mathematicians (or Einstein) added to create a model/manifold for doing the math? (Minkowski Space-time?)

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.

 

[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? 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? Or is this merely an attribute that mathematicians (or Einstein) added to create a model/manifold for doing the math? (Minkowski Space-time?)

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.

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? Or is this merely an attribute that mathematicians (or Einstein) added to create a model/manifold for doing the math? (Minkowski Space-time?)

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. "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. "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?

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. 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.

-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.

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. 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:

https://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?

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. 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.

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.

good one

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? 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? 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 let's 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

 

[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

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 doesn't 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 doesn't 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 spatial + 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 doesn't 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 doesn't 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 spatial + 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

I 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.

 

[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 spatial 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 spatial 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 spatial distance) is unchanged when space and time coordinates are rotated about.

Does this solve any issues in the foregoing discussion?

 

[Dale]

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 spatial 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?
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? 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.

 

[Dale]

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.