Twins Paradox explained in special relativity

with an animation sans space-time diagram.

Happily (one might say), 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 Twins 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 less than himself.

Unhappily, seemingly every examiner of relativity since Einstein has commented much too carelessly about this "missing time."

An exhaustive search through relativity books, articles and now the Internet, turns up nothing but 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 dissappear 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 (space-time) 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 within a given inertial frame.

Einstein, and everyone since him, has focused on the symmetrically mutual 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. Those two realities are inseparable. They are one and the same reality.

Regardless of the fact that the structure of space is ever evolving, the twins paradox (twin 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 the "God's eye view" or the view from a higher dimension, not to an unchanging structure. In this context, no twins 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.

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

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 relation to the universe. 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: The most revered relativist of our time, John A. Wheeler of Princeton, states in no uncertain terms that during no interval of the preceding scenarios does anyones clock run any slower than anyone elses. Instead he attributes the disparity in the clock readings to a "misperception" on the part of the inbound astronaut.

This might also surprise you: Virtually all commentators on relativity sign on to that explanation. The "misperception" explanation (often called a "miscalculation") is interminably bound with the "sudden tilt of a line of simultaneity", "Einstein's clock synchronization" and a "jump in time". They are all one and the same thing.

When an actual change of clock speed 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, the messenger of moments, 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 which changes frames, whereby they use a very awkward 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.

The actual distances and speeds relative to the universe 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.

Time-keeping, distance and speed are interminably bound in one equation. Therefore, actual differences in clock rates implies actual length contraction dependent on actual speed relative to the universe. 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 the universal (absolute) frame of reference, clock functioning is seen to be dependent on the speed of light. Similarly, the postulated need for stability at the base of our structures (which parallels the Principle of Relativity) in combination with the constant speed of light and the notion that no information can exceed the speed of light, dictates length contraction for objects in motion relative to the universal frame of reference (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.

  Basis:  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 speed.


Postulate 2:

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

  Basis:  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.



(One quick comment about General Relativity (GR) is in order: Just as in Special Relativity (SR), GR, as formulated, addresses strictly measures (identically observations). The key feature the two theories share is that the speed of light is treated as a constant only as measured. Just as there is an advantage in treating the speed of light as simply a measured constant in SR, so too is there such an advantage in GR.

In SR, Einstein was able to make an absolute frame of reference superfluous by postulating only the constant measured speed of light. In GR, he made Mach's Principle superfluous by again holding to only a postulated measured speed of light.

For an actual understanding of what generates the measured effects of SR, we begin with the absolute nature of light, meaning we acknowledge that it has a constant speed in reality. In the process, we obtain all Einstein's results of measured effects.)

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Here begins a less formal and more detailed look at the situation:



There is no clock paradox (twin paradox or twins paradox).

The reason there is no paradox is that clocks in different inertial frames actually do (typically) run at different rates, leading to an obvious difference in their registered time upon reuniting. And yes, the effective (experimental) equivalence of inertial frames is preserved, in complete agreement with Einstein's special relativity.

Regarding A and B of different inertial frames, taking measure of each other as they pass by each other, here is the typical exchange between a professor (or author) and the student (or reader):

  Professor:

  Person A will regard person B's clock to be slower and person B's
  spaceship to be shorter, and person B will regard A's clock to
  be slower and A's spaceship to be shorter.

  Student:

  What is the truth of the matter?

  Professor:

  There is no truth of the matter.  One person's reality is as
  valid as the other's.

  Student:

  Then why does one person age more than the other over the course
  of a round trip between them?

  Professor:

  It is the party that changes inertial frames that will age the 
  least over the course of the round trip.  We can illustrate
  this with a spacetime diagram (space-time diagram).  See right
  here -- the party who changes frames suddenly has overlooked a
  stretch of time passage for the party who did not change frames.