Why is the time dimension different from the 3 space dimensions

[scottbekerham]

General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?

 

[nitsuj]

General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?

I'm having a simular issue understanding the time "dimension".

In 3D you need 3 coordinates for a location, what is the fourth coordinate for? Is it equivelant to "meet me at xyz @ 10:30am"? Is that 4D coordinates?

 

[TrickyDicky]

I'm having a simular issue understanding the time "dimension".

In 3D you need 3 coordinates for a location, what is the fourth coordinate for? Is it equivelant to "meet me at xyz @ 10:30am"? Is that 4D coordinates?

Exactly.

 

[Passionflower]

In 3D you need 3 coordinates for a location, what is the fourth coordinate for? Is it equivelant to "meet me at xyz @ 10:30am"? Is that 4D coordinates?

It is in a Galilean spacetime but not in a Minskowski or Lorentzian spacetime.

 

[nitsuj]

It is in a Galilean spacetime but not in a Minskowski or Lorentzian spacetime.

What is the time coordinate a reference to?

 

[Passionflower]

What is the time coordinate a reference to?

Time between two events is the length of the path in spacetime not a dimension of spacetime.

In simple spacetimes we can chose a map or chart where one dimension uniquely represents time, however in more complex spacetimes that is not possible.

 

[bcrowell]

Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?

There is no known reason why spacetime has to be be 3+1 (3 spatial dimensions plus one time dimension) and not 4+1, 2+1, etc. Various speculative theories such a string theory or loop quantum gravity may be able to explain this, but those theories are actually not really full-fledged theories yet, and they have never been tested against experiment, so there's currently no way to know if they're right.

 

[nitsuj]

Time between two events is the length of the path in spacetime not a dimension of spacetime.

Yea, back to my trouble with understanding why time is referred to as a dimension.

In at least some remote sense, is the time dimension similar to an index for the other 3Ds when measuring a distance?

 

[Passionflower]

Yea, back to my trouble with understanding why time is referred to as a dimension.

Many seem to do so, something I do not understand.

Clearly time is a dimension in Galilean spacetime and I do not believe anyone would disagree with that. In a Galilean spacetime time is the same for all observers, and "10:30" is "10:30" for everybody however that is not the case in a Minkowski or Lorentzian spacetime.

Why some people persists in calling time a separate dimension in Minkowski or Lorentzian spacetime is beyond my comprehension, because I consider it inaccurate. Because they just do so as a matter of speaking.

 

[nitsuj]

...they just do so as a matter of speaking.

Oh

I actually thought about it, trying to understand in what sense it was a dimension.

Why not 3D + a constant [STRIKE]for forces[/STRIKE]

 

[WannabeNewton]

Oh

I actually thought about it, trying to understand in what sense it was a dimension.

Why not 3D + a constant [STRIKE]for forces[/STRIKE]

In the case of a 4 -manifold, if you decided to keep anyone x^{\alpha } = const. then you're just defining a hyper-surface of that x^{\alpha }, kind of like keeping t = const., thereby defining a 3 - surface at some instant of time. If you want a 4 - manifold though (as is needed with space - time) you need four functions x^{\alpha } as ,roughly speaking, keeping one or some constant defines a sub manifold of that 4 - manifold.

 

[nitsuj]

In the case of a 4 -manifold, if you decided to keep anyone x^{\alpha } = const. then you're just defining a hyper-surface of that x^{\alpha }, kind of like keeping t = const., thereby defining a 3 - surface at some instant of time. If you want a 4 - manifold though (as is needed with space - time) you need four functions x^{\alpha } as ,roughly speaking, keeping one or some constant defines a sub manifold of that 4 - manifold.

My cats breath smells like cat food...

I have no idea what your saying. What you are calling manifolds, were called dimensions in the previous post.

 

[WannabeNewton]

My cats breath smells like cat food...

I have no idea what your saying. What you are calling manifolds, were called dimensions in the previous post.

What I'm trying to say is that if you keep one of the coordinates constant then you can't have a 4 - dimensional space - time. If, say, you kept time constant then you're looking at a 3 - dimensional surface at that instant of time. Now you have me wondering what cat food smells like though.

 

[atyy]

I'm having a simular issue understanding the time "dimension".

In 3D you need 3 coordinates for a location, what is the fourth coordinate for? Is it equivelant to "meet me at xyz @ 10:30am"? Is that 4D coordinates?

Yes, that's right. When people talk about time as a dimension, they are referring to coordinate time of a Lorentz inertial frame. It is a dimension in the sense that switching to another Lorentz inertial frame, what was previously coordinate time is now mixed up as coordinate space and coordinate time. In a sense, you can rotate the axes in spacetime, just as you can rotate them in space.

 

[atyy]

General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?

It is better to say that time directions are different from space directions. A time direction is a direction in spacetime in which a stationary observer moves. Let's say some guy A is stationary, moving only in time. Another guy B moving at speed v relative to A will have a different time. But we can make B stationary too, by considering A to be moving at speed -v relative to B. Since B can be considered stationary, he too defines a time direction. Since we can have people moving at all sorts of velocities relative to A, and we can similarly define many other time directions. However, there are no observers moving faster than the speed of light relative to A. All the faster than light directions are therefore considered space directions.

 

[TrickyDicky]

I'm having a simular issue understanding the time "dimension".

In 3D you need 3 coordinates for a location, what is the fourth coordinate for? Is it equivelant to "meet me at xyz @ 10:30am"? Is that 4D coordinates?

Yes, that's right. When people talk about time as a dimension, they are referring to coordinate time of a Lorentz inertial frame.

It is in a Galilean spacetime but not in a Minskowski or Lorentzian spacetime.

Time between two events is the length of the path in spacetime not a dimension of spacetime.

No wonder nitsuj (or any relativity newbie) are confused about this if they keep getting this kind of apparently contradictory answersassionflower: no, time is not a dimension -atty: yes, it is.
At least atty clarifies that he is talking about coordinate time (dt^2 in a Lorentzian manifold line element, with positive or negative sign depending on the signature convention used:(3,1) or (1,3)), which is clearly a dimension in Lorentzian spacetimes, if it wasn't we wouldn't talk about 4-spacetimes instead of 3-spaces.
I guess Passionflower must be referring to proper time (d\tau^2 or ds^2 in Minkoski line element) when he says that in Minkowski spacetime time is not a dimension, if so he should have made that clear IMO considering not everyone will know the difference.

 

[ZealScience]

I think there is no necessity that time and space are the same. Because time is closely related to space measurement, change in space components affects time component. I think this is the only reason that time is another dimension. Also, looking at the tensors, sometimes just those special properties of time lead to the special features of geometry of space-time.

 

[nitsuj]

What I'm trying to say is that if you keep one of the coordinates constant then you can't have a 4 - dimensional space - time. If, say, you kept time constant then you're looking at a 3 - dimensional surface at that instant of time. Now you have me wondering what cat food smells like though.

c is constant

 

[WannabeNewton]

c is constant

C isn't a coordinate though.

 

[nitsuj]

C isn't a coordinate though.

Oh good point! c is not a coordinate.

3D + a constant for forces

is hardly me suggesting time is a coordinate.

 

[TrickyDicky]

3D + a constant for forces

is hardly me suggesting time is a coordinate.

Did you see post #16?

 

[WannabeNewton]

Oh good point! c is not a coordinate.

3D + a constant for forces

is hardly me suggesting time is a coordinate.

In your original post, "forces" was crossed out. It simply read 3D + a constant by which I assumed you meant keeping one of the four coordinate functions constant.

 

[nitsuj]

Did you see post #16?

I did see,

Does that mean a ticking clock is propertime and not considered a dimension?

And Coordinate time (as in meet me at xyz at 10:30) is a coordinate and in that sense is a dimension.

 

[TrickyDicky]

I did see,

Does that mean a ticking clock is propertime and not considered a dimension?

And Coordinate time (as in meet me at xyz at 10:30) is a coordinate and in that sense is a dimension.

Roughly speaking, yes.

 

[ghwellsjr]

I did see,

Does that mean a ticking clock is propertime and not considered a dimension?

And Coordinate time (as in meet me at xyz at 10:30) is a coordinate and in that sense is a dimension.

Coordinate time and coordinate location only has meaning if you know the coordinate system in which they are specified. So your example would be better put to say, "meet me at xyz at 10:30 Eastern Standard Time" which defines an event in one coordinate system and would be the same event as "meet me at xyz at 7:30 Pacific Standard Time" which defines an event in a different coordinate system.

 

[nitsuj]

Coordinate time and coordinate location only has meaning if you know the coordinate system in which they are specified. So your example would be better put to say, "meet me at xyz at 10:30 Eastern Standard Time" which defines an event in one coordinate system and would be the same event as "meet me at xyz at 7:30 Pacific Standard Time" which defines an event in a different coordinate system.

Oh sorry, I was talking about the imaginary planet ticktocka. They don't have time zones there, or traditional clocks. they all just count up. The clock in the example just happened to be at 10:30. Which is equally meaningless to you as timezones to inhabitants of ticktocka.

 

[bobc2]

General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?

It is not difficult to regard at least one universe model as one consisting of four spatial dimensions. The 4-D universe is populated by 4-dimensional objects. A typical characteristic of these 4-D objects is that they are very short along their X1, X2, and X3 dimensions (we can describe their sizes in the first 3 dimensions using the inch unit). But the size of the 4-D objects along their X4 dimension may be of the order of 10^13 miles or much more. So, one thing making the 4th dimension so different is the shape of the objects occupying the 4-D space (long along X4 and short along X1, X2, and X3).

But the most remarkable aspect of this model is that some aspect of observers exhibits a 3-D characteristic that moves along the observer's X4 axis at the speed of light. And as the observer moves along X4 he experiences a continuous sequence of 3-D worlds. And special relativity theory tells us that observers moving at different velocities relative to each other experience different instantaneous 3-D cross-section views of the 4-D universe.

So, time is associated with the 4th dimension only because nature, for some inexplicable mysterious reason moves the consciousness along the 4th dimension at light speed. That does not make X4 a time dimension--no more than a path along a highway is regarded as a time dimension just because you can mark off clock times along the highway corresponding to the time when points along the highway points are passed.

Here is a sketch showing a black coordinate system and a blue coordinate system. The blue system represents the inertial frame for a blue guy moving at relativistic speed relative to the black frame. We identify an instant of time for each observer which represents "NOW" for each observer. But notice that the instantaneous 3-D space experienced as "NOW" for each observer is different. At that instant of time, the observers are occupying two different 3-D worlds.

So, the blue guy's 3-D world intersects an earlier time along the black X4 axis as compared to the "NOW" time for his own blue X4 axis. Thus, the blue guy sees the black X4 clock running slower than his own. But, the black guy sees the blue guy's clock running slower. But, these effects are strictly a result of the different 3-D cross-section views of the two observers. So, time dilation simply results from differences in continuous sequences of 3-D cross-section views of 4-D objects in a 4-D universe.

 

[ghwellsjr]

Does that mean a ticking clock is propertime and not considered a dimension?

And Coordinate time (as in meet me at xyz at 10:30) is a coordinate and in that sense is a dimension.

Coordinate time and coordinate location only has meaning if you know the coordinate system in which they are specified. So your example would be better put to say, "meet me at xyz at 10:30 Eastern Standard Time" which defines an event in one coordinate system and would be the same event as "meet me at xyz at 7:30 Pacific Standard Time" which defines an event in a different coordinate system.

Oh sorry, I was talking about the imaginary planet ticktocka. They don't have time zones there, or traditional clocks. they all just count up. The clock in the example just happened to be at 10:30. Which is equally meaningless to you as timezones to inhabitants of ticktocka.

If the inhabitants of ticktocka use only one standard coordinate system of xyzt, then they can consider time to be absolute and all stationary clocks in that one coordinate system will have proper times equal to the coordinate times. But if some of them use a different coordinate system that is offset in space and/or time and/or moving with respect to the "standard" coordinate system, then the clocks that are stationary in that second coordinate system will have proper times equal to the coordinate times in that second coordinate system.

The values assigned to the four parameters x,y,z and t for a given "event" can all be different between the two coordinate systems. It doesn't matter whether we call them "values" or "parameters" or "coordinates" or "dimensions", these terms all mean the same thing. They are just the four numbers that we use in a coordinate system (which is also called a Frame of Reference) to specify a particular location at a particular time.

 

[TrickyDicky]

It is not difficult to regard at least one universe model as one consisting of four spatial dimensions...

Just with the caveat that the OP refers to GR and the model you present is an SR (flat universe) model.

 

[IRobot]

well locally in GR you have Poincaré invariance, that's where the 'difference' between time and space appears

 

[nitsuj]

If the inhabitants of ticktocka use only one standard coordinate system of xyzt, then they can consider time to be absolute and all stationary clocks in that one coordinate system will have proper times equal to the coordinate times. But if some of them use a different coordinate system that is offset in space and/or time and/or moving with respect to the "standard" coordinate system, then the clocks that are stationary in that second coordinate system will have proper times equal to the coordinate times in that second coordinate system.

The values assigned to the four parameters x,y,z and t for a given "event" can all be different between the two coordinate systems. It doesn't matter whether we call them "values" or "parameters" or "coordinates" or "dimensions", these terms all mean the same thing. They are just the four numbers that we use in a coordinate system (which is also called a Frame of Reference) to specify a particular location at a particular time.

The imaginary planet Ticktocka doesn't exist anymore. However I imagine they did use xyzt for location of an event.

ghwellsjr: "But if some of them use a different coordinate system that is offset in space and/or time and/or moving with respect to the "standard" coordinate system, then the clocks that are stationary in that second coordinate system will have proper times equal to the coordinate times in that second coordinate system. "

Why are you forcing this point, we're clearly talking about a planet here. Okay, yes your point regarding timezones is a good one, thanks for the contribution.

 

[ghwellsjr]

Does that mean a ticking clock is propertime and not considered a dimension?

And Coordinate time (as in meet me at xyz at 10:30) is a coordinate and in that sense is a dimension.

Why are you forcing this point, we're clearly talking about a planet here. Okay, yes your point regarding timezones is a good one, thanks for the contribution.

I'm trying to answer your questions with regard to the terms "proper time", "coordinate time" and "dimensions". Have they been answered to your satisfaction?

 

[nitsuj]

I'm trying to answer your questions with regard to the terms "proper time", "coordinate time" and "dimensions". Have they been answered to your satisfaction?

Oh sorry, Yea my question regarding this have been answered to my satisfaction. And thanks for the help. I thought you were purposefully throwing in a red heering with the timezone thing, since I see it as a moot point when differentiating between propertime and coordinate time.

What a trip to consider this stuff so deeply. The rhythmic ticking of a clock seems a different measurement than the display on the clock. One measures the flow and will always be right from my perspective, the other is directly referenced from the frame where the clock was syncronized. The clock as a whole brings these two together (space-time) and gives a usefull measurement for coordinating events. Given our small variances in relative velocities, this goes unoticed as being seperate. Just my understanding though, not sure of the accuracy of details.

 

[Wes Tausend]

General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?

My understanding is that time is a dimension, the 4th dimension, and it is at 90° to the other 3 dimensions, xyz, which are also all 90° from one another. I read this in an old library book, so the info may be somehow obsolete.

Please be easy on me, this is my first post here.

Wes
...

 

[WannabeNewton]

My understanding is that time is a dimension, the 4th dimension, and it is at 90° to the other 3 dimensions, xyz, which are also all 90° from one another. I read this in an old library book, so the info may be somehow obsolete.
...

I assume when you say the axes are at 90 degrees to each other that the bases are orthogonal (because in SR orthogonality of vectors doesn't necessarily imply that they are perpendicular). This isn't generally true for all metrics that act as solutions to Einstein's equation. You can usually tell which basis isn't orthogonal to which by looking for respective cross - terms of them in the metric.

 

[nitsuj]

My understanding is that time is a dimension, the 4th dimension, and it is at 90° to the other 3 dimensions, xyz, which are also all 90° from one another. I read this in an old library book, so the info may be somehow obsolete.

Please be easy on me, this is my first post here.

Wes
...

Yea that's my understanding of how it is represented graphically

 

[bobc2]

I assume when you say the axes are at 90 degrees to each other that the bases are orthogonal (because in SR orthogonality of vectors doesn't necessarily imply that they are perpendicular). This isn't generally true for all metrics that act as solutions to Einstein's equation. You can usually tell which basis isn't orthogonal to which by looking for respective cross - terms of them in the metric.

WannabeNewton, I think the idea of time as a physical dimension has no understandable meaning. Rather, consider the 4th dimension as a spatial dimension, X4--just like X1, X2, and X3. Physics really does not deal with the concept of time as a fundamental aspect of reality, anymore than it deals with things like consciousness, emotion, free will, etc. Time in physics is a numbering for the sequence of events in a 4-dimensional universe.

Clocks mark off a sequence of time numbers as time passes. But, just because you can mark off time measurements along the 4th dimension does not make time replace the actual spatial dimension--that is, it does not make the 4th dimension a time dimension.

Observers all move along their 4th spatial dimension at the speed of light. So, you can compute the distance traveled along the 4th dimension just by multiplying the elapsed time by c (speed of light, and distance = ct, i.e., c times t). A mechanical clock is a physical object that posts a sequence of time readings along the 4th dimension. But the clock itself is a 4-dimensional object extending along the 4th dimension.

Let's say that automobiles always drive 60 mph along a certain highway that goes from point A to B. You could put up sign posts along the highway going from point A to point B which display the elapsed times from starting at point A. The signs could be spaced 1 mile apart, incrementing the time displays by one minute. Just because you can observe the time as you travel along the highway does not mean that the highway is a time dimension. Mathematically, we just identify time as a parameter. Thus, it's no different for your 4th dimension highway that you travel along at the speed of light--your "world line" as it is known in special relativity.

 

[WannabeNewton]

While I agree with everything you said, respectfully I don't see what it has to do with the time basis not being necessarily orthogonal to the other bases.

 

[bobc2]

While I agree with everything you said, respectfully I don't see what it has to do with the time basis not being necessarily orthogonal to the other bases.

Sure, WannabeNewton. O.K. I just wanted to make sure we were on the same page regarding the understanding of the 4th dimension as a spatial dimension with clocks just marking off time numbers as the observer moves along his spatial 4th dimension at the speed of light.

But, yes, the other part of it is that your 4th dimension coordinate (in your own rest frame), X4, is perpendicular to X1, X2, and X3.

However, in your rest system, the X4 coordinates for all other observers moving with respect to your rest coordinates are not at all perpendicular to their respective X1, X2, and X3 coordinates. The sketches below attempt to illustrate this. I show your own rest system, with X4 perpendicular to X1, X2, and X3, as the black coordinates (X2 and X3 are suppressed for ease of interpretation). There are a sequence of pictures that include the blue coordinate systems for different observers moving with respect to your rest system--each different case corresponds to an observer (blue coordinates) moving with a different velocity.

The upper right sketches show that other observers have their own rest system as well and know how to represent your coordinates in their systems--and your X4 is not at all rotated 90 degrees from X1.

But one thing is in common with all coordinate systems: A photon world line always bisects the angle between X1 and X4. This of course results in all observers measuring the same ratio of distance between X4 and X1. Thus, dX4/dX1 = 1.0 or, dX4/c = dt, or dX4/dt = c.

 

[Phrak]

Time can be thought to be a dimension on par, or nearly on par, with spatial dimensions because it is convenient and insightful to do so.

Ref. rotational groups

 

[bobc2]

Time can be thought to be a dimension on par, or nearly on par, with spatial dimensions because it is convenient and insightful to do so.

Ref. rotational groups

Hi Phrak. Please elaborate a little on what you mean by time on par with spatial dimensions. Is it because as an observer moves along the 4th spatial dimension he can rescale the distance to provide time marks along the 4th dimension by using t = X4/c ? Thanks.

 

[Phrak]

I was alluding to the extension of the orthogonal group SO(3) to the Lorentz group.

 

[rationalist76]

I'm having a simular issue understanding the time "dimension".

In 3D you need 3 coordinates for a location, what is the fourth coordinate for? Is it equivelant to "meet me at xyz @ 10:30am"? Is that 4D coordinates?

Precisely :D

You would have a 3D coordinate graph, along with a time aspect to it. It all works in the Mathematical background, yet i am not exactly the most knowledgeable on the topic tbh

 

[nitsuj]

Precisely :D

You would have a 3D coordinate graph, along with a time aspect to it. It all works in the Mathematical background, yet i am not exactly the most knowledgeable on the topic tbh

ghwellsjr Clairified the statement for me. The time has to reference some frame to have any meaning as a time coordinate, which is different from time itself.

 

[GrayGhost]

General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ?

This question always fascinates me. We do perceive time differently from space, in everyday experience. Time allows for the measure of change or progression. Here's the thing though ...

While you hold yourself stationary and progressing only thru time, others moving relatively hold you in motion progressing thru both space and time. Therefore, what is one's measure of time, is another's measure of space and time. Then one must ask ... is time really any different from space? Well, even though relativity shows a relation between space and time that Newton did not, there is still this "progression" we all experience. We attribute said progression to the existence of time, while in the presence of space. Bottom line, it requires "both space and time" to define change (or progression). Simply can't do it without one or the other. Both concepts are required, and the concepts are not the same. Even in a Minkowski 4-space diagram, there is a progression for otherwise nothing could move. Time is required to model it, or something that serves the same purpose. Far as I know, GR did not do away with the concept time. Am I mistaken in that respect?

GrayGhost

 

[harrylin]

I'm having a simular issue understanding the time "dimension".
[..]

I had the same problem, and I think that it is caused by an ambiguity in language - "dimension" has different meanings. See:
- http://dictionary.reference.com/browse/dimension
- http://en.wikipedia.org/wiki/Dimension
- http://en.wikipedia.org/wiki/Dimensional_analysis

Thus, although in common language there are three spatial dimensions, in mathematical descriptions of physical quantities and processes "dimension" can simply stand for a physical quantity.
If we describe processes with three spatial and one temporal dimensions, we have a description with a total of four dimensions.

Harald