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Time Dilation And Observer Size

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I quote a section from the Wikipedia website, (please, no groaning):

“In the theory of relativity, time dilation is an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses.

An accurate clock at rest with respect to one observer may be measured to tick at a different rate when compared to a second observer's own equally accurate clocks. This effect arises neither from technical aspects of the clocks nor from the fact that signals need time to propagate, but from the nature of spacetime itself.”

The last phrase from the first sentence, “or differently situated from gravitational masses.”, causes me to ask the following question.

Let us suppose that I am on a spaceship speeding along, say near the speed of light, and there is another spaceship many times smaller with an intelligent life-form the size of an ant, speeding along in the opposite direction.

Will the size difference of the observers have any affect upon the time dilation?

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The clue is in the beginning of the sentence, it says "In the theory of relativity" hence they refer both to special and general relativity.

In special relativity you have this typical time dilatation thing everyone heard about, like the twins where one of them travels for 2 years at some speed away and back to earth and then the one who comes back is much younger than the one who stayed.

In general relativity you have all the time stuff due to gravity curving space-time, my favorite example of this is an astronaut falling into a black hole: for himself it is a matter of microseconds till he crossed the event horizon for an observer far away the unlucky astronaut never reaches the event horizon, he is just red-sghifting more and more.

Wrt your last question, I do not remember the exact calculations to do so I can not give values, but the answer is "yes, but...". GR says that gravity also affects time dilatation, but I think in this case it is a very very small effect and even less important when considering the size of the effect due to special relativity when travelling almost at the speed the of light.

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I asked this question because there are some physical things taking place that we humans can't seem to adequately explain. Our great scientists have laid down some laws related to physics, but even these appear to fall short when different sizes are introduced, (quantum physics for example). The speed of light cannot be exceeded, but entanglement indicates it can. I wonder, at times, if there is something so large, we can't see it.  Various tests on indiviuals' brains indicate we don't see a great percentage of the things that go on around us. In other words our brain concentrates on what it considers to be important, and basically ignores the rest. Are we "it"? Or are we just a tiny part of a really big "it"?

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I would have answered "no", but meaning a case where the mass of the observers is not defined or taken to be the same. What Sanctus is referring to is that more massive observer would be seen as its own time dilation source.

But that fact aside, it is important to understand that "observer" is idealized as a point object, because as soon as you have an observer with volume, all the different parts of the observer are also observers themselves. Your left eye is a different observer from the right eye. And with relativistic simultaneity, no one will agree which "photons" will hit the eyes simultaneously.

So basically complex observers become semantically undefinable if you want to be really accurate. That is why there's all the talk about differences in time dilation in the front end and in the back end of an accelerating ship.

I would also comment that that Wikipedia quote "This effect arises neither from technical aspects of the clocks nor from the fact that signals need time to propagate, but from the nature of spacetime itself” is philosophically a bit naive. Space-time is an ontological interpretation of relativity; in fact special relativity pre-dates space-time. It would actually be more accurate to say that the effect arises from the fact that signals need time to propagate, but that might be seen as little bit confusing statement without further explanations.

I just wrote a post explaining this thing little bit from a historical perspective, you should find it interesting to think about;

Various tests on indiviuals' brains indicate we don't see a great percentage of the things that go on around us. In other words our brain concentrates on what it considers to be important, and basically ignores the rest. Are we "it"? Or are we just a tiny part of a really big "it"?

Have you also thought about the slightly different angle; that a large part of what we see is a result of how we happen to represent the world in our mind. If colors are wavelengths, then things don't have colors apart from how we see them. If solid objects are solid and made visible because of electromagnetic forces, then objects have no microscopic shapes or walls, other than how we choose to define those walls according to some specific interaction. And there's nothing we can do to verify that some particle is still "made of the same stuff" between two different observations, other than defining valid rules that make it so, and believing those rules.

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An interesting effect, not often thought about, is connected to the twin experiment, where one twin after traveling near the speed of light, has their time slow down and they appear to be younger than their earth twin.  Although time has permanently changed for one of the twins, his distance contraction is reversible, with his size returning to the original size of his brother, or does it? I have never heard anyone say he will be permanently smaller due to lingering distance contraction.

If the size returns back (both reunited twins are 6 feet, exactly), but one is younger, then space-time is not impacted uniformly, but rather time behaves differently, maybe because time only travels in one direction and can't rebound like distance.

In the case of the younger twin, he will retain extra time potential or potential in time, but he will retain zero distance potential causing his local space-time to have lingering or excess time relativity.

If we have more time capacitance than balanced space-time (lingering relativistic age plus earth space-time reference). The implication would be him aging via space-time2. I am not sure what that brings to the table, but maybe an increase in the number of coincidences around him.

Edited by HydrogenBond
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"The speed of light cannot be exceeded, but entanglement indicates it can."

Not really, etanglement can't be used for transmitting information faster than light (at least as far as we know nowadays). If you want I can elaobarate on that

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HB, it is not so strange, remember it is all relative :-). I mean as long as one of the twins is travelling his length is contracted and his time passes slower compared to the twin. When back to earth length is no more contracted and time passes at the same rate for both so everything is back to normal. So both time and space are back to normal, there is no reason that there should be any lingering effect of the travelling guy beeing shorter when back, just like there is no reason that there is a lingering effect of the twin who travelled still aging slower when back to earth.

It is not about reversibility just about moving wrt each other or not.

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HB, it is not so strange, remember it is all relative :-). I mean as long as one of the twins is travelling his length is contracted and his time passes slower compared to the twin. When back to earth length is no more contracted and time passes at the same rate for both so everything is back to normal. So both time and space are back to normal, there is no reason that there should be any lingering effect of the travelling guy beeing shorter when back, just like there is no reason that there is a lingering effect of the twin who travelled still aging slower when back to earth.

It is not about reversibility just about moving wrt each other or not.

The difference is, one twin remains always younger, but not forever shorter. When the younger twin returns to earth, the progression of time and space are now the same for both twins, but he does not lose his extra youth. That extra youth is retained, but he now he ages in the future at the same rate due to being in the same reference as the earth twin. He will always remain younger on the earth, and will outlive his twin, because the slowing of time due to his travel, will retain a capacitance in time.

This is why I said we need to measure the space clocks. If the clock lost time,  does it correct itself once it reaches the earth, back to NASA time. Or is there a permanent time lag increment of a fraction of a second, with both moving the same pace at NASA?

Does the size stay forever smaller with a distance or size lag? If not, space-time is better represented by space-time2, to account for this extra or less time from (-x to x).  This would impact red shift since the energy measured comes from matter that may have excess or deficit time potential.

We need to measure the clocks for permanent time lag and size lag.

Edited by HydrogenBond
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To make my point clearer, consider this scenario. Instead of twins, we have twin clocks.  One clock is send on a space ship moving at relativistic speed away and the other stays on earth. The moving clock appears to be losing time. The earth clock says 1PM and the moving clock says 12 noon, so there is a one hour lag. The earth clock is 1 meter in diameter and the moving clock now appear to be 0.9 meters due to distance contraction.

The moving clock comes back to earth when it's clock says 1PM. The earth clock is now at 2;10 PM, but now with the second hands of both clocks are moving at the same speed due to one reference. Does the time leg in the travel clock correct itself or is the moving clock forever one hour 10 minutes behind?

How about the size, does the 0.9 distance contracted clock snap back to one meter in our reference, or is the clock also forever distance lagged to 0.9 meters? I would guess only the time lag is retained a because the flow of time can only go forward and not backwards to self correct. While distance is reversible and will resume earth size.

Edited by HydrogenBond
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As long as they stay immobile wrt each other, the travelling clock will stay forever 1h10 behind.

I see exactly what you mean, don't worry. The problem in your thinking is that you compare apple with lemons: you have to compare the RELATIVE clock-ticking speed between the 2 clocks or the relative lengths/diameters of them. If you do so then when back on earth both things are the same. Instead, you are comparing elapsed time and then argue that since the length comes back to original the elapsed time should as well. What should and does come back to normal is the clock ticking-speed.

If there where a time-thing surviving like you say there should/might be a length-thing surviving, the clock which travelled should keep ticking slower when back on earth. This has not been measured

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