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Consider the twins paradox with a slight variation:

Twins A and B are in separate space ships both capable of going at the speed of light instantly (i.e. without any acceleration). Both ships are stationary relative to each other in intergalactic space facing in opposite directions. They synchronize their clocks.

Then Twin A sees ship B zooms off to the "right" at the speed of light, and ship B travels a round trip of 8 years. Twin A sees ship B recede away from him at the speed of light (in fact, ship A just disappears).

When ship B returns, Twin B's clock will show he has been gone 8 years. But from Twin B's perspective, it's ship A that zooms off to the "left" at the speed of light, does an 8 light year round trip, and according to Twin A's clock, he has also been gone 8 years.

So they both would agree that one has been away from the other 8 years, and both have aged the same amount of time.

It would seem clocks do not actually run slower as they move closer to the speed of light. So is time dilatation just an illusion?

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marked as duplicate by Brandon Enright, Alfred Centauri, Valter Moretti, John Rennie, Waffle's Crazy Peanut Mar 6 at 9:33

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possible duplicate of Is time dilation an illusion? –  Nick Stauner Mar 6 at 0:42
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Don't start a question by assuming the impossible. Just don't. In any case saying "they don't accelerate" and then claiming that they do change speeds shows a basic misunderstanding. And as always, if you draw the world-lines diagram you can sort this out. –  dmckee Mar 6 at 0:56
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This is not--in fact--a variation at all. It is the same old problem with the same old answer, only Peter has tried to avoid the usual answer by misrepresenting what acceleration is (i.e he has introduced an infinite acceleration and claim that it is not acceleration). –  dmckee Mar 6 at 1:00
    
whether there is acceleration or not does not influence the Twins Paradox. There are two frames of reference Spaceship A and Spaceship B. They are moving Relative to each other. whether A is moving or B is moving is equivalent. –  Peter Mar 6 at 10:14
    
Peter, there are three inertial frames in your setup. Frame A, Frame B (on the outbound leg) and frame B' (on the return leg). The fact that the ship B does not remain at rest in a single frame for the whole experiment is the origin of the difference. –  dmckee Mar 6 at 15:12

1 Answer 1

There is no frame of reference that has speed c relative to any other frame of reference. This is well known in Special Relativity.

Thus, if it were the case that either spaceship were at speed c in some frame of reference, there is no "synchronizing clocks", there is no "spaceship A sees..." or "spaceship B sees..." because there is no frame of reference in which spaceship A or B is at rest.

This 'question' follows a common pattern: (1) stipulate something that is impossible according to some theory is the case and then (2) purport to conclude something about the theory such as "time dilation is an illusion".

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Spaceship A is a Frame of Reference as is Spaceship B a different frame of Reference. –  Peter Mar 6 at 17:44
    
Spaceship A is a Frame of Reference as is Spaceship B a different frame of Reference. The speed of light ONLY applies to EMR. By assuming no acceleration A sees B moving away and B sees A moving away - their "views" are equivalent. Clocks or vibrating atoms do not change relative to their velocity - they may appear to by a"stationary" observer but they don't actually go slower. To purport that they do is not only counter intuitive but a misunderstanding of SR –  Peter Mar 6 at 17:53
    
@Peter, this is a well known, well understood and elementary result from SR: if something moves with speed c in one frame of reference, it moves with speed c in all frames of reference. This is why c is called an invariant speed. Thus, if spaceship A moves with speed c in the lab frame, it moves with speed c in all frames of reference, i.e., there is is no reference frame in which spaceship A is at rest thus, spaceship A is not a reference frame. –  Alfred Centauri Mar 6 at 18:10
    
The speed C is only invariant and only applicable for EMW –  Peter Mar 7 at 2:05
    
The speed C is only invariant and only applicable for EMW. It is both the measured speed of "light" EMW and is also derived from Maxwells equations.Inside Spaceship A all the classical laws of physics apply, whether moving at a constant velocity or at rest relative to another Frame of Reference. The other Frame of Reference is spaceship B. A Third Frame of Reference is unnecessary –  Peter Mar 7 at 2:11

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