adjusted twin paradox

8/3/2019 Adjusted Twin Paradox

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The Adjusted Twin Paradox

Imagine that at some time in the future we have the technology to actually perform the

Twin Paradox experiment with a set of twins and a spaceship that can travel atrelativistic speeds. Since the twins are, in a way, the same person in two places at thesame time, we will assume they experience the exact same rate of the passage of time.

As soon as B, the traveling brother, begins to accelerate towards relativistic speeds, hisexperience of the rate of change begins to slow, and his brother A's original experienceof the rate of change begins to become faster relative to B. Since B is moving in anaccelerated frame of reference, his experience of the rate of change is slower than theexperience of A. Formally, the Lorentz transformation has been used to calculate thevariance in relative time between A and B; hence the Twin Paradox.

Assume twin B is going to travel 0.8 times the speed of light. Let v/c = 0.8

Therefore, = 3/5, and =5/3. At the midpoint of Bs journey, we cancalculate that:

Assuming that when A experiences 10 units of time and B experiences 6 units of time,both A and B are at the temporal midpoint of the time it takes for B to return. According

to the Twin Paradox, the twin that stayed ( A ) will be 20 units of time older when Breturns, and the twin that traveled ( B ) will be 12 units of time older when B returns.However, unknown to the experimenters in our example, there is an unaccounted foraspect to this paradox given that A and B exist in relative frames of reference. Since Aand B exist in relative frames of reference with different rates of time, we will apply theExistics equations as calibration to the Lorentz transformation.

Since A and B no longer experience the same rate of change, and since the rate of


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change relative to A is faster than the rate of change relative to B, then A is in the futurerelative to B, and B is in the past relative to A. A and B are interacting through relativeframes of reference, and the time variance transformation from Existics must be applied.

(see Existics101.pdf)

There exists an A and a B in the past, present and future, all simultaneously, and theyare all about to switch positions in relation to each other. Since A is at a faster rate ofchange relative to B, A will end up interacting with a B from a faster rate of changeframe of reference. Also, since B is at a slower rate of change relative to A, B will endup interacting with an A from a slower rate of change frame of reference.


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At the midpoint, where B is neither going away from nor towards A, B is in anaccelerated frame of reference relative to A.

A relative to A, or (A)A, is in the future relative to B, and B relative to B, or (B)B, is in thepast relative to A.

A relative to B, or(A)B, is at a slower rate of change than (A)A, and B relative to A, or(B)A is at a faster rate of change than (B)B.


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Since B is agingslower than A, time relative to A is faster than time relative to B. WhenA (relative to himself) is at the midpoint, B (relative to himself) is slightly behind in timeand is approaching the midpoint. When B (relative to himself) reaches the midpoint, A(relative to himself) is slightly ahead of B in time.

We can now calculate the relative time variance between A and B.

When A is at the midpoint, B is slightly behind:

B is at 5.545 units of time relative to himself.

When B has progressed onto being at the midpoint, A is slightly ahead:A is at 10.909 units of time relative to himself.

The problem is this: if A is ahead of B in time, then who does A interact with when Barrives relative to A and relative to B? The answer is this: (B)A arrives to meet with A; Barrives to meet with (A)B. Remember, we are dealing with an extra dimension of time,and relative frames of reference.

Since (A)B is slower than A, and since B previously had the same rate of change as A,not only does time relative to B need to speed up towards the rate of change of (A)B asB decelerates, but an additional speeding-up of time is needed so that when Bdecelerates to a complete stop, that the objective rate of change relative toBis thesame as the objective rate of change relative to (A)B.


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In other words, B previously coexisted with A experiencing the same rate of the passageof time. However, B has descended down the y-coordinate of time (passage or rate ofchange). Therefore, B now travels in the x-coordinate direction (period or linear time)slower than it previously did. Since both A and B are now operating at different rates ofchange, they interact with different As and B's through relativistic corresponding newrates of change; relative to each other. (A)B interacts with B, and (B)A interacts with A.

A is at a faster rate of change than (A)B, and B is at a slower rate of change than (B)A.(B)A comes from a faster rate of change compared to the initial B, and (A)B is at aslower rate of change compared to the initial A.

The result is that B arrives having had a faster rate of change than predicted, and Barrives at an earlier time than expected. B is older than expected, arriving early. This is


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an additional time displacement for A and B, relative to their common center of time;unaccounted for in Relativity. Both A and B, through relative frames of reference, affectthe others existence, and both have a time displacement centered around the lineartime of the common event (interaction) relative to A and B; regardless of who travels.

Since (B)A is farther in the future relative to B, (B)A will arrive at the event relative to A(event A) prior to B, collapsing the possibility for B to arrive at event A. Since (B)A isahead in time, that means that (B)A has a faster rate of change than B.


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Since (A)B is farther in the past relative to A, (A)B has a slower rate of change than A.Therefore, B will arrive at the event relative to B (event B) corresponding with (A)B.

Since A and B have shifted away from sharing the same experience of the passage oftime relative to one another, both A and B undergo an additional shift in time, so thatwhen B decelerates and approaches A, they can interact at corresponding rates ofchange.

Therefore, when B finally arrives at A, he knows he took longer than he should haveand says, "Sorry I am late!" However, A looks at his brother with astonishment andsays, "Oh, you have arrived early!" To both of their surprise, the clock that B took withhim reports that B took longer to arrive than predicted. Also, the clock that A had withhim reports that B has arrived ahead of schedule.

This essay, which was originally written in the winter of 2002-2003, accounts for thesuperluminal and subluminal velocities of the neutrino measured by experiment throughthe application of the Existics equations to the Lorentz Transformation.

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