Time as Dimension: Unveiling the Mystery

[Yanah]

I just do not understand why it is so essential for time to be a dimension. I'm by no means a specialist in this field, and I don't really know the core workings of relativity, but why is it that time must be, or at least is almost always referred to as a dimension? The only way I seem to be able to look at time logically is that it is the speed at which energy affects, or passes through, or whatever it does to mass.

If it really is crucial for time to be a dimension, could someone please refer me to the equations or whatever that require it to be?

 

[pervect]

You are probably putting too much baggage on what is necessary to consider something a dimension.

Look at the defintion from dictionary.com

http://dictionary.reference.com/search?q=dimension

# Mathematics.

1. The least number of independent coordinates required to specify uniquely the points in a space.
2. The range of such a coordinate.

Treating time as a dimension is just a recognition of the fact that it takes a coordinate to tell you "when" an event occurs.

While this is the only requirement for time to be treated as a dimension, there is a little more to this story. According to relativity, time and space are not able to be considered as separate entities.

Let us say that you have two points that are located a distance "L" apart that occur at "the same time" according to a stationary observer.

A moving observer will see the two events a shorter distance apart (the distance will be Lorentz contracted). Furthermore, the events will now appear NOT to be at the same time (simultaneity is relative).

One way of describing this state of affairs is to say that time and space are not seperable, that they form a space-time continuum.

By the defintion of "dimension", the space-time continuum has 4 dimensions - 3 coordinates are needed to locate a particle in space, and one coordinate is needed to locate the particle in time.

 

[Yanah]

You know, as much as I've wondered, I've never actually looked up the dictionary definition of a dimension? Go figure.

Thanks. Boy, do I feel stupid. :)

 

[pmb_phy]

You know, as much as I've wondered, I've never actually looked up the dictionary definition of a dimension? Go figure.

Thanks. Boy, do I feel stupid. :)

It should be noted that time is a part of a set of all events. An event is something which is represented by two things - a location and a time (where and when). This set is reffered to as spacetime. In relativity it is of great use to utilize spacetime in describing the world.

Pete

 

[RandallB]

Yanah

Don’t accept just calling time a dimension as justification for creating a fourth dimension. It is not that simple, defining "when" an event occurs has already been done in classical Newtonian physics. That’s simple 3-D as we know and experience with time used as a marker to define how long ago things happened, how long the will take to happen, and when in the future a predicable event will happen.

Classical physics gets along just fine with 3-D. And Einstein did not just say – gee if I call time a dimension then ……..
For one thing with just time as a dimension he still would have nothing to warp!
What Einstein did was much more significant than that, and he needed about ten years of help with the math to get it to work.

What he did was define something NEW. Think of these four dimensions as 4 things you have never heard of before and cannot directly measure anyone of them! Call them A, B, C, D (not x, y, z) none of the four are the same as what you call x, y, or z. Nor are any of the four the same as what you call “time”. But consider all four the same to each other and by mathematically allowing the four new dimensions to interact with each other. Warping the points in this new design of 4-D space within carefully defined rules to get things to fit Einstein reached what he was looking for – transforms that would mathematically define what we see as 3-D space and “local time”. Building a space and time we experience as Newtonian classical, but provide the warping of the four dimensional space to account for gravity, while explaining time and spatial anomalies associated with large masses the classical cannot. Accounting for gravity without using particle exchanges between masses (gravitons) as quantum theories expect. Mass just reacts to how the 4-D space is curved by mass.
Don't expect anyone of those 4 dimensions to tie back to anyone dimension you experience in "3-D" and especially don’t expect anyone of them to tie to what you experience as “time”.

The distinction is huge; I’m not trying to tell you what the right answers are. Just don’t be satisfied with “when in time” as the defining element of an extra dimension. It doesn’t begin to explain the idea or how it is really used it is not that simple.

 

[coalquay404]

Yanah

Don’t accept just calling time a dimension as justification for creating a fourth dimension. It is not that simple, defining "when" an event occurs has already been done in classical Newtonian physics. That’s simple 3-D as we know and experience with time used as a marker to define how long ago things happened, how long the will take to happen, and when in the future a predicable event will happen.

Classical physics gets along just fine with 3-D. And Einstein did not just say – gee if I call time a dimension then ……..
For one thing with just time as a dimension he still would have nothing to warp!
What Einstein did was much more significant than that, and he needed about ten years of help with the math to get it to work.

Quite the contrary. Although it may not be made explicit in introductory courses, classical physics *does not* get by with only three dimensions. If one considers the time evolution of a three-dimensional classical system, the presence of a fourth dimension corresponding to time is always (at least implicitly) assumed. The difference between classical and relativistic physics does not lie in the existence of a fourth dimension but in the interpretation of this fourth dimension with respect to the three spatial dimensions.

 

[Intuitive]

Can anybody actually prove Mathmatically that any Dimension is without time?

 

[coalquay404]

Can anybody actually prove Mathmatically that any Dimension is without time?

It's an axiom.

 

[HallsofIvy]

Can anybody actually prove Mathmatically that any Dimension is without time?

Far from saying "it's an axiom" as coalquay404 did, I have to ask what in the world do you mean by that? What does it mean to say that a dimension is "without time"? Whatever you mean by it, I suspect the answer is "No, you can't prove that mathematically", because "time" is not a mathematical concept.

 

[RandallB]

Although it may not be made explicit in introductory courses, classical physics *does not* get by with only three dimensions. If one considers the time evolution of a three-dimensional classical system, the presence of a fourth dimension corresponding to time is always (at least implicitly) assumed.

I disagree, Newton did not, and any real classical view does not, treat time as a dimension or even require that it implicitly be assumed as some kind of mathematical equivalent of a dimension.

It might be nice to make Classical and our modern non-classical views seem to be just disputes over the correct interpretation of an already existing Classical fourth dimension of time. (Those poor old fogies, they just did think to call time a dimension.)
But NO, The fundamental difference between them is much larger than such a trivialization.

 

[pmerrill]

Wasn't there a discussion back in the 20s or 30s regarding whether time actually existed? While the three dimensions exists through our senses, I think it was argued that time only existed because we had a memory. The human mind can remember the "past" and recognise it was different than the present and that became "time". If humans did not have a memory, then we would not experience time at all.

Maybe the 3d are all we need? Perhaps the reason matter can't outpace a photon has something to do with the structure of space since energy and matter are manifestations of the same thing, but different. Since time is innate to us we have wrapped it around most of our world, before, after, causation, velocity, speed. It would be interesting to hear the old arguments, anyone have a reference to the papers?

 

[robphy]

pmerrill,
you may be interested in
http://www.spacetimesociety.org/
http://www.spacetimesociety.org/conferences.html
If I get my act together, I may try to make the next one (in 2008?.. when "Minkowski spacetime turns 100").

 

[abvgd]

Treating time as a dimension is just a recognition of the fact that it takes a coordinate to tell you "when" an event occurs.

The problem as I (being a complete layman to the subject) see it with this definition is that a dimension is a geometrical construct, with a continuous set of coordinates. However, you can't move from point n in time to point n-1, you can only move in one direction, to point n+1, making time, what, half-dimensional? Another thing, in a non-relativistic sense of time (for instance, let's ponder that all green aliens in the universe wherever they are located agree that the universe is currently 13.7 billion years old), if everybody and everything at every point in time is located at the same time-coordinate wouldn't this make time something more reminiscent of a singularity than of any kind of dimension? Because only in a singularity must everything be located at the exact same point...