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(Permalink) Posted: April 23 2011,09:55   

Quote (Robin @ April 22 2011,10:29)
# Techne Says:
April 13th, 2011 at 11:12 am

Hello olegt,

What do you think is the relationship between time and change (change as in stuff changing position or from one thing to another etc.)?

A) Time exist as a result of change. Time is an intellectual abstraction and a mathematical expression to quantify change. Without change there is no time sort of like without mass there is no gravity.
B) Time exists as some distinct entity or dimension that is different or distinct from the process of change. Time exist as a dimension irrespective of whether there are things that are changing or not.

Comment by Techne — April 13, 2011 @ 11:12 am

I freely admit that I have difficulty visualizing the concept of relativity. I get the gist, but have difficulty when it gets down to the nitty-gritty as it were.

As such, while I know that time becomes a "real" dimension in relativity, I don't fully understand why and still wonder, as Techne does in question a, why time can't be an illusionary product of change. Can one of you folks elaborate on that?

Hi Robin,

You're getting into an area that overlaps more with philosophy and psychology than physics. Human perception of time makes things too complicated, so physicists prefer to stay away from that and instead concentrate on the behavior of simpler objects such as clocks under various experimental circumstances. In essence, we use an operational definition of time: it is whatever a precise clock measures. We take it from there leaving it to philosophers to debate what exactly time is.

For centuries, it was taken for granted that time is absolute. In practical terms, it was thought that all clocks should agree. This worked fine until physicists discovered that light is electromagnetic waves. Waves need a medium to travel in, so this medium was called the luminiferous aether. Our experience with other waves taught us that waves travel with a fixed speed relative to the medium, so by measuring the time of propagation one could determine how fast and in which direction we are moving relative to the aether.

Unfortunately, all experimental attempts at detecting our motion relative to the aether (such as the Michelson-Morley experiment) failed: the measured speed of light did not seem to depend on the speed of the observer. Lorentz and others came up with a theory that explained the null result of Michelson and Morley by suggesting that the physical forces work so that all objects moving relative to the aether contract and all characteristic times dilate by the such amounts that the measured ratios of spatial displacements to time periods give the same speed of light c.

This was a working explanation but it was a bit unsatisfactory. It painted the constancy of the speed of light in different inertial frames as an elaborate illusion: the speed wasn't really the same, but the meter sticks and clocks in moving frame were out of whack. On top of this, the theory relied on the existence of a very special reference frame, in which things were hunky-dory: the meter sticks really were 1 meter long and the clocks ticked exactly once every second. In other frames, things appeared to work in the same way.

Worst of all, this state of affairs made a travesty out of the principle of relativity (all inertial frames are equivalent). The reliance on the aether suggested, on the one hand, that the principle of relativity was wrong in theory: the aether frame is "more equivalent" than the other inertial frames. On the other hand, you couldn't detect the lack of equivalence, so the principle of relativity was right in practice! These things drove physicists nuts.

So Einstein's proposed a radical solution:
(1) the principle of relativity works, all inertial frames are equivalent,
(2) light travels at the same speed in all inertial frames,
(3) but time flows differently in two frames moving relative to each other.
Point 1 is near and dear to a physicist's heart. It is a cornerstone of physics. Point 2 has been confirmed experimentally over and over again. Point 3 sounds extremely radical to a non-physicist, particularly to a philosopher. But to a physicist who uses an operational definition of time (whatever is measured by clocks) this is more or less a restatement of Lorentz's idea. So 1+2 was enough of a sugar coat to let #3 go down.

Incidentally, in Einstein's original theory of special relativity time was not combined with the spatial coordinates to make a four-dimensional continuum. Spacetime was invented by Einstein's math teacher Minkowski. That was quite useful in practical terms because a point moving through space could be visualized as a line in spacetime. Kinematics (dependence of coordinates on time) was reduced to geometry of worldlines and Lorentz transformations became mere rotations in spacetime. In ordinary space, rotations conserve the length of a line. In spacetime, the analog of length is called the interval. Its conservation is related to the constancy of the speed of light.

Spacetime might look like a fancy mathematical concept, but it turned out to be extremely useful in physics. It linked special relativity (physics in inertial reference frames) to the geometry of a flat four-dimensional space.* Einstein realized that he could reduce the kinematics in a non-inertial reference frame to the geometry of a curved spacetime. This realization constitutes one half of the general theory of relativity.**

OK, this comment is about 800 words long, or 100 millitorley according to the latest calibration. I'd better stop before everyone's eyes glaze over.

*To be sure, the space is a bit weird: the square of the distance in it is not the sum of squares of all coordinates. You add the squares of the spatial coordinates and subtract the square of the time coordinate.

**The other half is the principle of equivalence: gravity can be simulated by accelerated motion. Remember feeling heavier in an elevator starting up? It's not an illusion, that's how gravity works.

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