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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?

John Rennie
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Peter
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  • possible duplicate of Is time dilation an illusion? – Nick Stauner Mar 06 '14 at 00:42
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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 --- ex-moderator kitten Mar 06 '14 at 00:56
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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 --- ex-moderator kitten Mar 06 '14 at 01:00
  • 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 06 '14 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 --- ex-moderator kitten Mar 06 '14 at 15:12
  • The Frame of reference for B is not dependent on the direction he is moving. A self enclosed space ie a space ship is its frame of reference. The point is without acceleration A and cannot tell who is moving - its equivalent. And yes this question has been explored before and not answered satisfactory. Members with high "scores' close the thread to prevent us "less informed" members from wasting their time which they consider a closed subject. – Peter Mar 06 '14 at 17:26
  • "The Frame of reference for B is not dependent on the direction he is moving." While it is true that we haven't said what direction frame B is moving relative frame A and that time dilation does not depend on that direction, you are simply wrong to suggest that the return leg is the same inertial frame as the outbound leg. – dmckee --- ex-moderator kitten Mar 08 '14 at 03:25
  • The traditional presentation of Time Dilation is direction dependent. Normally the the x axis is used Time dilation and length contraction is along the x axis. Where the one inertial Frame moves relative to another that is considered "stationary" relative to it. There is no Time dilation along the y or z directions.

    Furthermore The inertial frame does not change relative to which direction its moving along the x direction.

    Also this example is only considering the observers 'in' A or B.

    Not from an observer in a third frame of reference in which A and/or B are moving.

     – Peter Mar 09 '14 at 11:38

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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".

Alfred Centauri
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  • Spaceship A is a Frame of Reference as is Spaceship B a different frame of Reference. – Peter Mar 06 '14 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 06 '14 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 06 '14 at 18:10
  • The speed C is only invariant and only applicable for EMW – Peter Mar 07 '14 at 02:05
  • 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 07 '14 at 02:11
  • @Peter, I see no possible profit in discussing this with you further. – Alfred Centauri Mar 07 '14 at 02:19