Nature of Time Dilation and Length Contraction

Why assume a change that cannot be detected?

 

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Raphael:

I am not assuming that, I'm stating it. If every clock connected to your frame of reference reduced its rate by the same degree, how could you detect it? If your question is in regard to the utility of the approach, well I think it is the logical 'mechanism' that would cause us to observe the whole rest of the universe differently after we accelerate ourselves. We would see the change, we just wouldn't see it in ourselves.

 

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Relativity concernes itself with the ratio of the rates of clocks in a moving frame with respect to the rates of clocks at rest. It doesn't make much sense to ask what the absolute rate of time is in your frame. As far as you're concerned, all the processes in your frame are running at the normal rate. It is the processes in other, moving frames that slow down compared with the processes in your frame.

 

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This is indeed the way it works, and that's why it's "relativity". What you observe is *relative* to your own frame of reference. You will *never* observe your own yardsticks shrinking or your own clocks running slow. Relativity doesn't say your particular viewpoint is anything special, but it *does* say that your viewpoint is just as valid as anyone else's, no matter what speed you're travelling at.

If you take off in a rocket and, from the viewpoint of a stationary observer, approach the speed of light, it will appear to you that the entire universe has become squashed in the direction of your travel. To you, it is the rest of the universe whose rulers have become squashed and whose clocks are running at the wrong speed, not your own.

 

There is something to be said about whether a statement could be an assumption, but it would be offtopic.

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There is nothing wrong with the idea that it is possible that our mechanism was changed. But if the change cannot be detected by us, how do we "prove" it? If proof is found lacking, what then becomes of the idea?

 

Hi Dale,

Just to continue our previous conversation, I think maybe a distinction can be drawn here. You are certainly correct that spacetime in general relativity is always locally Lorentzian; this is a basic assumption. Maybe it will one day be possible to understand why this is so, but right now it is definitely a fixed part of the theory. So this local geometry is fixed, but the global geometry is a dynamical element of the theory. I think this is not really what you were talking about.

What special relativity tells us is that the behavior of rods and clocks is not independent of their motion. For example, one could reasonably ask why a rod moving with respect to you gets shorter. There is a schematic answer to this question, though a complete solution is obviously out of the question. One can solve the Newton-Maxwell equations for an electron orbiting a proton when the center of mass of the whole system is moving relative to you. What you find is that the orbit of the electron is squished in the direction of motion by the Lorentz factor. In so far as rods are held together by electromagnetic forces (in an appropriate quantum description), length contraction appears immediately. Now suppose you have a rod sitting in space and you accelerate yourself relative to the rod. If you now measure the length of the rod, you find that it is shorter. You clearly have not done anything to the rod, but what you have done is change what you mean by length and time. In this sense, length and time are physical properties that you define. However, I don't think we are actually in much disagreement about these things.

 

Hi dav,

I have discussed this with you before, but to just to reiterate, I would contend that the notion of an aether is not the next step. If you want to dream up this thing called the aether and give it all the properties of the thing I call spacetime, then I can't stop you. However, your aether won't be much like the aethers that came before; it will be just another name for spacetime. Why does it need density, say? These are all extraneous concepts that don't appear to get you anything. If you could show that your aether model predicts new experimental results or that it is otherwise a more economical and elegant description of Nature, then I think your argument would be more valid. I have yet to see either of these things demonstrated.

 

I don't think so either. IMO the most important thing about any theory is its predictive ability. As long as we agree on the predictions and as long as the predictions agree with reality then there is no substantive disagreement.

Btw, were you ever going to finish your Lorentz-Voigt description?

-Dale

 

My apologies, Dale, I forgot all about it! And the conclusion is so beautiful too! I will resurrect that other thread and continue my mad ramblings there.

 

Okay, let’s try this example in trying to visualize time dilation.

Start with two cars, A and B. They start at the same point and drive at the same speed in slightly different directions.
How would thing appear from the perspective car A?
Something like this:

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Here A and B are represented by the labeled spheres. The horizontal lines represent the progress of the two cars with respect to A’s own progress. Note that B progresses in the direction that A is moving more slowly than A does.

Now here’s how things look from B’s perspective:

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Here, it is A that is perceived to lag behind B in the direction that B is moving.

The point being that each car measures the other as moving more slowly as measured against its own progress.

Now let’s replace the cars with clocks and instead of plotting two spatial dimensions we plot spatial separation against time; the vertical direction as time and the horizontal as space.

If we go back and look at the first diagram, we see that clock A moves straight up. Meaning that it progresses through time but not through space. In this diagram, clock A is considered at rest. Clock B moves to right as it moves upward; its distance from A increases with time and, thus it is moving at a constant velocity. Note that its progress through time lags behind that of A. IOW, from A’s perspective, clock B ticks slower.

Looking at the second diagram, clock B is considered at rest, and it is A that is moving. Here, we see that from B’s perspective, it is A that progresses more slowly, and thus A that ticks slower.

 

Now let’s consider how this applies to the Twin Paradox. In this case, travels out a certain distance at a constant speed and then returns at the same speed.

From A’s perspective it looks like this

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B goes out, turns around and then comes back. When it returns to A’s location it is still behind A in time, and thus less time has passed for it (we assume that B matches A’s velocity at the end. Thus if the animation were to continue, B would lag behind A by a constant amount as they move upward in the diagram.

Now consider the situation if we assume that B, on its outward leg, is at rest.

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During the first phase, A lags behind B.
Then B starts to move to the left(accelerates towards A). In order to intersect A, it must move to the left faster than A. Thus, from the perspective from our frame of rest, it now progresses through time slower than A. So much so, that once it intersects A, it is now behind it, and more time has passed for A, just like at the end of the first diagram. So it doesn’t matter which frame you consider “at rest” you get the same result.

How about if if we travel with B?

Then we get something like this:

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It starts out like the last diagram, but once we reach the turnaround point of B, we switch to the new rest frame for B. As a result, A “jumps forward in time” from B’s perspective. After which, A again progresses through time slower than B. But, because of the forward jump in time, B never completely “catches up” with A. So once again, at the end, less time has passed for B than has for A.

 

In the last diagram, A seems to “jump” to its new position, but this is just because the change of velocity for B happens between frames.

The following slows down the process:

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During the acceleration of B, A runs fast from the perspective of B.
Going back to our car analogy, it is like when you turn a corner and objects that were behind your left shoulder are now in front of your left shoulder.

This analogy also helps in visualizing the Relativity of Simultaneity.

Imagine we have a third clock C, at rest with respect to A, but removed by some distance from A.
This is the situation from the rest frame of A and C:

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Note that A and C read and keep the same time.

Now from the rest frame of B:

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Note that from B’s perspective, While A and C tick at the same rate, C lags behind A. thus if A and C read the same time in the rest frame of A, C reads less time than A in the rest frame of B.

 

Length contraction can also be shown.

Consider the distance between A and C from the perspective of B. Since distance in this example is measured left to right, It is only the left to right separation of A and C that B measures, and thus B measures the distance between A and C as less than A and C measures it.

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Now, this is not meant to be a perfect analogy, but just an attempt to show how simple changes in perspectives can lead to what we consider “real” changes to time and space because, in Relativity, time and space themselves depend on perspective.

 

Nice diagrams, Janus!

 

While the answer is not actually obvious (nor correctly provided) the question is simple:


"How can you justify claiming spatial length contraction as a physical property when the emperically demonstrated affect of motion produces time dilation in the moving clock that FULLY accounts for the accumulated trip time by the clock with no physics (mathematical) room for any spatial length changes.????"


Understanding this you are left with a more correct view being that the moving observer merely calculates a higher velocity due to the slower running of his clock.

v' = d / t' is the correct physics. d' = vt' imposes a calculated value in one frame onto another frame and further ignores the fact that t' tick rate does not equal the t tick rate.

 

MacM, I already showed you months ago that c is frame-variant under your transform. So much for "fully accouts for ... "

-Dale

 

This one is very good Janus, and it shows the crux of the main source of confusion. Would it be possible to have some "features" on the lines? Some tick marks or some other visual indication that A is remaining "in place" as the line rotates and not sliding along the line during the rotation.

-Dale

 

Sorry but that does not answer the question, it merely points out we do not yet understand the universe.

 

False.

True.

-Dale

 

stop joking, time is a concept, it can't dilate except in hell.