What is the true nature of time?

[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 traveling 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.

 

[Dale]

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_quantities_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 spatial 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 spatial 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.

 

[Dale]

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.

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 going to be tricky, but with a wooden block, a saw and some measuring tape. Why?

 

[Dale]

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.

 

[Dale]

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 (https://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 preferred 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 going to 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 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: https://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 preferred 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 spatial 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 spatial 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 spatial 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 spatial 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 spatial 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 spatial dimensions x, y, z or also defined as:
<br /> t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt<br />
-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 spatial dimensions x, y, z or also defined as:
<br /> t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt<br />
-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.

 

[Dale]

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

 

[Dale]

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.

 

[Dale]

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.

https://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 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:
<br /> t_p = \int_0^0 0 \sqrt {1 - \frac{(0)^2 + (0)^2 + (0)^2}{c^2}} ds<br />
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: <br /> t_p = \int_D \sqrt {1 - \frac{(dx)^2 + (dy)^2 + (dz)^2}{c^2}} dt<br /> 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.