Twin Paradox Animation

diagramming special relativity in an

absolute frame of reference





Citation information and annotation for 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.






This diagram will be animated further down the page.

Before moving on to the twin paradox animation,
you should take a minute to familiarize yourself
with some basic information by reading these
few paragraphs:



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.)

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 the reading of the clock time of the other party") is dictated by Einstein's clock synchronization, a clock synchronization which is not required to deduce any of the measured effects of relativity.

The renowned physicist John A. Wheeler, in his book Spacetime Physics, made three attempts to resolve the twin paradox and failed, by his own admission. He never stood a chance, as he limited himself to Einstein's narrow interpretation - that of simply assuming symmetrical measures across inertial frames, which incorporates a hopelessly circular definition of inertial frame.

Regarding that circular definition of inertial frame:

In Spacetime & Electromagnetism, Lucas and Hodgson, using the space-time paradigm, wrestle with the twin paradox for fifteen pages, and claim no resolution.

In a footnote on page 73, they write: "Is it fair to give the Earth-bound twin the vertical world line? Does not that beg the question in his favour? Why not draw another diagram with his world line set at an angle to the vertical, and his lines of simultaneity correspondingly inclined (but at a contrary angle) to the horizontal?" [J.R. Lucas & P.E. Hodgson, Spacetime & Electromagnetism, p 70-84.]

That alternative diagramming of the situation is identical to the consideration that one might just as well consider that it is the Earth, along with the entire cosmos, that changes inertial frames. That, in fact, is something we hear often from commentators on the twin paradox. Of course, that simply makes the twin paradox unresolvable, as either party can then lay equal claim to being the party that ages the least. This is demonstration that one must consider the entirety of the cosmos, the imparter of inertial properties, to be the judge of the matter regarding actual motion.

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

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, space-time is optional. Space-time 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.

Even John Wheeler, who promotes the purely relative approach used by Einstein, acknowledges in his book Spacetime Physics 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.]

In contrast with the space-time argument: When the two parties check the status of each other's clock with the regular sending of radio pulses, they note an incrementally increasing time differential, first noted at the turn-around point. That real-world experiment reveals the real incremental increase of time differential. [William Geraint Vaughan Rosser (1991). Introductory Special Relativity, Taylor & Francis Inc. USA, pp. 67-68.]

In short:

Space-time is a construct, dependent on an optional clock synchronization method, and generates a false jump in time reading.

Space itself is not a construct, nor is time-keeping. And a real-world experiment reveals a real-world incremental increase in the time differential.

Why should we expect anything different? The 'stay-at-home' twin does not age several years in a twinkling just because some distant inbound astronaut starts his watch as he passes an outbound astronaut.

It is precisely ones motion with respect to the universe that dictates the actual clock rate, resulting in the actual time differential upon reuniting with the other party.

You should re-read the four previous paragraphs, carefully.

Einstein's clock synchronization method creates a pseudo reality for two inertial frames, whereby the parties of different inertial frames are free to reach opposing conclusions about what distant events are simultaneous. In reality, no one should conclude anything about what is simultaneous, as we know that our perceptions of distant events are constrained by the speed of light.

Einstein's clock synchronization (tB - tA = t'A - tB) has the "jump in time" built in for any situation involving a change of inertial frame.

Thus, a space-time diagram is not an explanation for what has created the time differential between 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.

What has created the time differential?

Photons, being massless, move at constant speed relative to the universe, and dictate time-keeping of every nature. (At the subatomic level, we also speak of virtual photon events, wherein communication occurs at light speed without any energy exchange.)

(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.)

The time registered on a person's clock is dependent on the combination of their speed relative to light speed and distance covered in absolute terms. The time contraction formula is not linear. Thus, the party that changes inertial frames will be the party whose clock registers the least time over the course of a "round trip". This is seen with clarity when everything is charted out in absolute terms.

The twin paradox (and all of special relativity) can be analyzed in the context of the absolute frame of reference, wherein the sum total of the universe constitutes an experimentally indiscernible rest state. Though experimentally indiscernible, such frame of reference shows, in an actual sense, what is generating the observational effects of special relativity.

A few details from Relativity Trail:

   Symmetry of Measuring.  Diagrams and equations 
   demonstrating the symmetry of clock rate and length 
   measures across inertial frames.  

   Twin Paradox Analysis.  Diagrams and equations 
   demonstrating the symmetry of measures and time 
   differential regarding case 1 and case 2.  

Note that time-keeping, distance and speed are bound in one equation. Thus, to acknowledge various states of actual motion relative to the universe (as opposed to merely observed differences) is to acknowledge various states of actual clock rates (as opposed to merely observed differences) and various states of actual lengths of rigid bodies (as opposed to merely observed differences).

Although the universe is expanding, special relativity easily holds true at any conceivable scale of distance at which we might test the theory.

==========================================

The animations below illustrate two basic possibilities for completing a round trip between two parties. They produce identical time differentials, demonstrating the impossibility of anyone determining their true motion status relative to the universe.

i.e. - none of the parties involved can assume anything about their actual state of motion; thus they cannot know whether they are participating in scenario 1 or scenario 2. The blue circle in the diagram represents nothing but a point in space where a clock start/stop event occurs.



For maximum clarity, the trips themselves involve just a light second or two in distance, and all parties make use of photon clocks which are a whopping 1/2 light second in width. The photon clocks tell the story of time contraction.

The horizontal white lines represent the travelers. They each carry a photon clock. There are three clock start/stop events - A, B, and C. The fact that time differential is identical in both scenarios (twin paradox animation 1 and twin paradox animation 2) confirms that one cannot experimentally detect ones true motion status with respect to the universe.

Scenario 1:

In the twin paradox animation below, an astronaut and a space station occupant start their clocks as the astronaut passes by. A second, incoming, astronaut starts his clock as he passes by the first astronaut. The incoming astronaut and the space station occupant stop their clocks as the incoming astronaut passes by the space station.



If the video has ended, and you want to replay it, click on the replay button at the lower left corner of the video box.

Scenario 2:

In the twins paradox animation below, an astronaut and a space station occupant start their clocks as the astronaut passes by. A second, also outbound, astronaut starts his clock as he passes by the space station. This second astronaut chases down the first astronaut. As the first astronaut is caught, both astronauts stop their clocks.



The time contraction formula is easily obtained from the above diagrams. For instance, in the first diagram (animation), the clock at rest with the universe ticks off one cycle while the traveling clock ticks off .8 of a cycle. A simple application of the Pythagorean Theorem yields the following formula:

       t' = t * sqr rt of ( 1 - V^2 )

where t' is the time recorded by the traveler, t is universal time (full clock rate, since at rest with the universe), and v is the speed of the traveler.

Keep in mind that the traveler, moving at .6 light second per second of universal time, went a distance, in absolute terms, of .6 light second.

A photon went the same distance in the station's clock as it did in the traveler's clock, namely, 1 light second.

Thus,

       0.8 = 1 * sqr rt of ( 1 - 0.6^2)

       = 1 * sqr rt of ( 1 - 0.36)

       = 1 * sqr rt of ( 0.64 )

       = 0.8

(There is no need to use c (light speed) in the equation, since we are using units of light seconds. Light travels one light second in one second.)

See the book Relativity Trail for more details, including an analysis of how all parties involved assess each other's clock speed and lengths in symmetrical fashion, as well as detailed derivations of length contraction, the Lorentz transformations and e = mc^2.



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.


Symmetry of Measuring. Diagrams and equations demonstrating the symmetry of clock rate and length measures across inertial frames.


Twin Paradox Analysis. Diagrams and equations demonstrating the symmetry of measures and time differential regarding case 1 and case 2.


Twin Paradox Explained. An expanded discussion of the failure of spacetime diagrams.


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


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 a system at rest with respect to the totality 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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