QualifyingQualia » Sun Sep 28, 2014 5:50 pm wrote:I have a question for physics: why does it treat time as a fourth dimension and not simply a modification of the “ordinary” three dimensions? It seems the idea of space-time treats time as something separate from normal three dimensional space and not just the periodicity (or change) of that space. In other words, why do you treat time as if it's an object and not a process? I could never figure this out. Cheers.
Maybe it is not as bad as you think. You have to distinguish between the words people use and what they actually do. If you've read GR stuff extensively you've seen it said over and over again "coordinate time is not anybody's real time" or words to that effect:
it does not, as a rule, correspond to any real physical clock.You'll never be able to explain this to your friends:
the 4th dimension is just a convention. They won't believe you until they've taken a college course in GR.
So the GR people are already doing what you want, in a sense. You have a whole lot of 3-geometries and you pile them up, to show the CHANGE. To represent the PROCESS like you say. And naturally if you stack all those 3-geometries up you get a 4-D thing.
but the 4th D is not a representation of real time it is just a conventional "coordinate" parameterAnd there is more. You can forget the original slicing and make a new slicing. A slicing is called a "foliation" after the latin word for LEAVES. Like you leaf thru a book, you leaf thru the changes in geometry.
And GR allows you to go over to a new slicing or a new foliation. Its equation and its solutions are "foliation invariant". So you KNOW that the 4th coordinate is meaningless because you can change it more or less at will, in a prescribed manner which also adjusts the solutions so they remain solutions.
Actual TIME time comes into GR when you have an observer and his life follows a "world line" threading thru the 4D thing, going here and there fast and slow into strong gravity curvature and back out into weak curvature, and he carries a physical CLOCK, some device with a reasonably reliable process going at some frequency that we compare ...
Damn,I have to walk the dog...Well that was quick, she did her job in our garden right by the front door.
So it is not maybe how you were thinking. There is, in GR, a puzzle called "the problem of time" which not finally solved to everyone's satisfaction. It seems to many GR experts that GR (which is our basic theory of matter interacting with geometry and from which we get our most accurate time-predicitons) is itself a TIMELESS THEORY. This shows itself in many ways. The "Hamiltonian" of the theory if you know of that, a basic tool in standard dynamics, is identically zero on solutions. There is the foliation invariance, you can reparametrize the 4trh at will, it is physically meaningless, etc etc, and the quantum GR equation (the so called Wheeler DeWitt equation) has no time parameter in it at all! Despite this people get along fine because they just take a particular solution, and run an observer through it, and then use that observers clock (for whatever limited purposes they need it for). Processes go along their merry way (along many separate paths of time)
This is the so called "many fingered time"picture people often refer to.
By radical simplification you can FORCE the existence of a global time in one particular solution, as is done in cosmology. But as a rule there IS NO GLOBAL TIME in General Relativity.
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Also people confuse the 1905 SPECIAL theory, SR, with the 1915 GR theory which superseded it. SR has time as a coordinate, so time is a "4th dimension". But SR does not have gravity. Space cannot expand, no curvature it is a really primitive dumb theory, but it is very useful as a LOCAL APPROXIMATION. It is approximately right in weak gravity over limited periods of time. the 1915 GR theory was developed BECAUSE of the severe limitations of the 1905 SR, and to include gravity. And it is at that point that this puzzling timelessness came in, and this foliation invariance, and this "many-fingered time" picture came in.
then the 4th dim became a conventional arbitrary parameter of change not corresponding to a reading on a clock. It became "coordinate time", the height of the pile when you stack up 3D geometries, like the height of a stack of plastic cups or plates. Not real physical time anymore.
The moment you try to explain this people will not believe you and they will start talking about 1905 SR, whose "time is the 4th dimension" cliché has crept into everybody's mind and into our common language, so it is a knee-jerk mental prejudice. I don;t have time to make this an orderly post. Too much other stuff to do. Hope you get something out of it anyway.