Why is the time dimension different from the 3 space dimensions

[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