Twin Paradox Explained

in Special Relativity

with a link to an animation

Cite the book, Relativity Trail
Luebeck, R. Relativity Trail. Mpls: L B Writ Publishing, (2008)

Cite this web page

See also: Relativity in Absolute Terms
It is a concise and more comprehensive document.

Einstein never commented on where the missing time went regarding his conclusion that two clocks, once synchronized, would show a time differential upon being reunited at the end of a uniform linear motion journey.

This scenario became known as the Twin Paradox, with the clocks being replaced by twin brothers, one of whom journeys away and then returns to find his stay-at-home brother has aged more than himself.

An exhaustive search through relativity books, articles and now the Internet, typically turns up the standard "jump in time" explanation, whereby a returning astronaut suddenly inherits, at her turn-around point, "a new meaning of simultaneity" in keeping with Einstein's clock synchronization, causing hundreds of years to disappear in a twinkling.

While a spacetime diagram (space-time diagram) will predict a time differential between two reunited clocks, it cannot explain where the missing time has gone, spacetime itself being based on Einstein's clock synchronization. Nothing in Einstein's treatment addresses actual clock rates (or actual length or actual light speed). Einstein's treatment is limited to measures obtained by an observer of a given inertial frame. Identically, spacetime has no physical reality. It is strictly a convenient mathematical construct, limited in scope by Einstein's particular clock synchronization method.

Small wonder that John A. Wheeler, in his book Spacetime Physics, made three attempts to resolve the twin paradox and failed three times, considering that he limited himself to Einstein's narrow interpretation.

Einstein himself never attempted to explain what he called a "peculiar consequence" - the time differential between reunited clocks, now known as the twin paradox.

Even Wheeler, who promotes the purely relative approach used by Einstein, acknowledges in his book that there is no physical experiment which can distinguish the purely relative approach from an absolute approach, which Wheeler refers to as "ether theory B".

[Wheeler, J., Taylor, E. (1992). Spacetime Physics, second edition. W. H. Freeman: New York, p. 88.]

Einstein focused on the symmetrical measures obtained across inertial frames, for which Einstein's clock synchronization scheme works fine (although it is not needed). His clock synchronization sheds no light on where the missing time has gone regarding two reunited clocks (actually regarding any two clocks where one has undergone a change of frame, reunited or not).

That two reunited clocks show a disparity in their recorded time is proof that the two clocks experienced actual differing clock rates while in differing states of uniform linear motion. If the disparity one can see at the same place moment is a reality, then so too is the notion of actual differing clock rates a reality. They are one and the same reality.

Regardless of the fact that the structure of the universe is ever evolving, the twin paradox (twins paradox or clock paradox) can be understood only in the context of an absolute frame of reference, in which the speed of light is constant in an absolute sense, while clock rates and lengths of rigid bodies vary in an absolute sense. "Absolute sense" here refers to a system at rest with the sum total of the cosmos. In this context, no twin paradox arises because clock rates do actually vary.

Such treatment of special relativity is completely consistent with, and in fact subsumes, Einstein's special relativity, with its effective (observational) equivalence of inertial frames, including the consistent measured speed of light in all inertial frames. Einstein's treatment of special relativity can easily be diagrammed against a stationary frame of reference. And note that such frame of reference, a frame at rest with the sum total of the cosmos, cannot be experimentally discerned.

   A discussion of the twin paradox of special
   relativity must incorporate the transfer of clock
   information from an "outgoing" astronaut to an
   "incoming" astronaut; otherwise acceleration would
   need to be involved, and acceleration is not involved
   in any kinematical effects of special relativity. The
   time differential between two reunited clocks is
   deduced through purely uniform linear motion
   considerations, as seen in Einstein's original paper
   on the subject, as well as in all subsequent
   derivations of the Lorentz transformations.

Consider the following simple situation upon which all physicists will agree:

An outbound astronaut can start his clock as he passes by Earth. That outbound astronaut's clock might record 100 hours during his outbound journey. An inbound astronaut can start his clock at the moment he passes by the outbound astronaut. The inbound astronaut's clock might record 100 hours during his inbound journey. The Earth clock might show a reading of 250 hours at the moment the inbound astronaut passes by Earth. Thus, the Earth clock will register 250 hours while the combined recorded time for the outbound and inbound astronauts' clocks is only 200 hours. One can thus hold two renunited clocks in ones hand and see a disparity of 50 hours.

(If, instead, a second astronaut had started his clock as he passed Earth, and were traveling fast enough to overtake the first astronaut, then the combined recorded time of the Earth clock and the second astronaut's clock would be less than the recorded time of the first astronaut's clock. The time contraction formula is not linear. The time registered on a clock is dependent on the combination of speed and distance covered in absolute terms. Thus, the party that changes inertial frames will be the party whose clock registers the least time.)

Refer to the diagram below. There is a link to an animation of this diagram, with included photon clocks, at the bottom of this page.

You might find the following surprising:

Most commentators on relativity state in no uncertain terms that during no interval of the preceding scenarios does anyone's clock run any slower than anyone elses. Commentators will often appeal to the experience of force associated with a change of inertial frames, as if some force could affect the starting of a clock. Just as acceleration is not involved in the "paradox", neither is any force.

More frequently, commentators attribute the disparity in the clock readings to a "sudden tilt of a line of simultaneity". These commentators don't realize it, but that "sudden tilt" (or "jump in time") is dictated by Einstein's clock synchronization, a clock synchronization which is not required to deduce any of the measured effects of relativity.

As we noted, John A. Wheeler, in his book Spacetime Physics, made three attempts to resolve the twin paradox and failed three times. He never stood a chance, as he limited himself to Einstein's narrow interpretation - that of simply assuming symmetrical measures across inertial frames.

Without Einstein's clock synchronization, there is no space-time and there are no lines of simultaneity or world lines. Einstein's clock synchronization is a convention. It is optional, and limited in scope. All the measuring results of relativity can be deduced independent of Einstein's clock synchronization. Therefore, spacetime is optional. Spacetime is simply a geometrical representation of Einstein's clock synchronization, and has no physical reality. A person cannot travel along a world line, because there is no world line. A world line is simply a geometrical construct. A person can travel through space while his clock is ticking. That is all a person can do.

A spacetime diagram is not an explanation for what has created the time differential between two reunited clocks. Rather, it can only repeat Einstein's prediction, devoid of explanation, just as Einstein never had an explanation.

With or without Einstein's clock synchronization, there will be a time differential, and the party who changes frames to facilitate the reunion will be the one who ages the least.

When an actual change of clock rate is denied, a "jump in time" is automatically incorporated. But that "jump in time" simply stems from Einstein's clock synchronization, a clock synchronization which is not required to deduce the mutual and symmetrical effects of relativity. Einstein's clock synchronization is defined such that light serves as the messenger of moments. By that I mean that Einstein tells us to call simultaneous whatever appears simultaneous, with observers in different inertial frames thus free to form opposing conclusions about what is simultaneous.

They form these opposing conclusions due to the fact that light has a finite speed, causing a delay in ones perception of any distant event, regardless of the distance involved. That leads directly to the conclusion of a "jump in time" for a party that changes frames, whereby they use a lattice of clocks synchronized according to Einstein's formula (tB - tA = t'A - tB), with the "jump in time" built in for any situation involving a change of inertial frame.

Using a rational measuring paradigm, whereby the two parties check each other's clock status with the regular sending of radio signals, a noted asymmetry in time keeping differences between A and B builds incrementally, with the asymmetry being first noted at the moment of B's turn-around.

What has created the time differential?

The time registered on a person's clock is dependent on the combination of their speed relative to light speed and distance covered in relation to the universe. The party that changes inertial frames will be the party whose clock registers the least time over the course of a "round trip".

The actual distances relative to the universe and actual speeds relative to light speed will vary depending on which party changes frames, but the parties involved cannot possibly detect that. That is in keeping with the postulates and deductions of special relativity.

The time contraction formula [t' = t * sqr rt of (1 - v^2)] is not linear. That is why the party who changes frames to bring the two parties back together will register the least amount of time on his clock with the symmetry of the situation preserved. This is seen with clarity when everything is charted out in absolute terms.

Time-keeping, distance and speed are bound in one equation. Therefore, actual differences in clock rates implies actual length contraction dependent on actual speed relative to light speed. Actual length contraction works in combination with actual time-keeping contraction to preserve the symmetry of measures across inertial frames.

This can all be charted out against an absolute frame of reference, which is simply the sum total of the cosmos, or equivalently, the view from a higher dimension, where light rays and all other phenomena are charted out in absolute terms.

From that vantage point, clock speeds and lengths of rigid bodies are seen in absolute terms and the time differential is easily explained by virtue of actual differences in clock rates.

In this treatment of special relativity, incorporating an absolute frame of reference, clock functioning is seen to be dependent on the speed of light. Similarly, the postulated need for stability (synchronization) at the atomic scale (which parallels the Principle of Relativity) in combination with the constant speed of light and the notion that no transmission of information can exceed the speed of light, dictates length contraction for objects in motion relative to the universal (absolute) frame of reference.

(In fact, all processes -- chemical, biological, measuring apparatus functioning, human perception involving the eye and brain, the communication of force -- everything, is constrained by the speed of light. There is clock functioning at every level, dependent on light speed and the inherent delay at even the atomic level.)

Postulate 1:

  The speed of light is constant and is the 
  maximum speed for any phenomena, including 
  the transmission of positioning information.


  Experiments towards the end of the nineteenth
  century pointed towards a transformational 
  relationship between matter and energy 
  (radioactivity experiments).
  Einstein's interpretation of Max Planck's
  solutions for discreet energy levels 
  introduced the notion of light existing as 
  a massless photon.  Being massless, the photon
  would necessarily possess constant and maximum

Postulate 2:

  Stability (synchronization) is required 
  at the base of our structures (specifically
  atomic functioning).          


  This simply parallels the Galilean Principle 
  of Relativity.

All of Einstein's results stem from these two postulates. These two postulates may look similar to Einstein's postulates, but are not his postulates.

Other documents which are recommended reading before reading the book:

Relativity in Absolute Terms. My most comprehensive online document. A concise overview of why special relativity must be diagrammed in absolute terms.

Twin Paradox Animation on youtube. Contains textual description not found in the document below.

Twin Paradox Animation. Alternative text, and animation of the twin paradox. (Embedded youtube animation.)

Free pdf file of the book:

Relativity Trail, free pdf format, with 192 pages, 65 diagrams and 75 illustrations, will provide you with complete detailed algebraic derivations of all the kinematical effects of special relativity. Everything is charted out in absolute terms against the rest state of the universe for perfect clarity as well as soundness of theoretical basis. It is the totality of the universe that imparts the inertial properties of clock rates and lengths which generate the effects of relativity. This is explained in detail in Relativity Trail.

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