The Twin Paradox
in a Euclidean Manifold

T   
o make a feasible absolute reference frame, it must be compatible with experiments based on relativity theory (which in turn rests on a bad foundation, i.e. Michelson-Morley). The view from a different perspective may serve to further elucidate the matter.

The twin 'paradox' is somewhat clouded by what I call a "poof factor".
A & B are identical twins. B leaves the planet for some time at high velocity, returns and when he opens his spaceship door ----- poof! ---- he has no beard while his brother's is down to the floor. We wish to examine what each brother sees (as well as a few other observers) if they continually watch everbody else.

As already shown, this is actually impossible but we may, at least, imagine it to be possible.

Let A and B be the above brothers, C will be the distant cousin (1 light year away) and D an observer in an identical spaceship stationary at 1/2 light year down the path to C.

What does each observer actually see if he is always looking at everybody else?

  • A :
    This observer sees C in normal time but one year retarded
    D in normal time 1/2 year retarded
    B accelerates to an apparent velocity of less than 1/2c (since B is receeding from A) and his time is greatly slowed such that when A sees B arrive at C after an apparent lapse of 2 years, B hasn't aged appreciably but C appears to be 2 years older .
  • B :
    B (looking back at A) sees him aging normally but only a few seconds worth. Remember, B is travelling away from A at a speed very close to that of light leaving A.
    C appears to age very fast. About 2 years worth in just a few seconds.
    D appears to age very fast for half the trip then very slowly thereafter. When arriving at C, D appears to be one year older.
  • C :
    He sees A and D age normally 1 year and 1/2 year later respectively
    B leaves A and appears to age normally for about two seconds and then arrives at C, seeming to travel at many times light velocity (B is just behind the light arriving a C which notifies C that B has just blasted off from A)
  • D :
    D sees A and C age normally 1/2 year after the fact.
    B appears to arrive at D's position in seconds while aging normally then pass by and slow to less than 1/2 light velocity so that the remaining trip to C requires a further year as measured by D. During the last half of the trip B appears to age very slowly such that he arrives at C not having aged to any appreciable extent.
On the return trip, everything is the same as the above for the inverse people since the return is simply symmetric with the outbound trip.

When B stops back on A, everyone appears to be aging at a normal rate but B is two years younger than everyone else.

The "Rub"

Here's the problem:
When B is passing D the situation appears to be logically symmetric but isn't physically symmetric. D must see B differently than B sees D for in the end D observes B to be younger while B observes D to be older. When does this occur from the viewpoint of either party (B,D) who are always observing the other?

Most science writers employ the poof factor and run over the problem like it doesn't exist. Well, if you sweep dirt under the rug it's clean ... isn't it?

If B leaves A and D leaves from C and they pass in the middle, then you might have B seeing D and vice versa in the same way. But what about the direction of travel of A and C through the cosmos. Every bit of matter has an "acceleration history" so that to have a truly symmetric situation, the two ships must have equal but opposite accelerative histories when they pass, i.e. we have to subtract out their proper motions relative to the backdrop of galaxies (that is, all motion not generated by the Hubble expansion).

The absolute reference frame is just where everyone thinks it is after all.

The problem is one of logic/semantics. Obviously, we can always logically assert that "I'm not moving, you are!" or, "I'm not moving, the rest of the universe is!" and be right in the strictest logical sense. But since this argument is true for everyone always, it has no utility as a logical concept (except to generate the big "... so what?"). Some confuse the logical/physical aspect of theory which is all the same in the long run but which may be divergent in the short run.

Addendum 04-04-00:
If the universe were infinite in duration (both forward and backward in time) ... then ... no object would have any acceleration history different from any other. If it is finite in the backward direction (consistent with big bang theories) ... then ... each particle has such a history and special relativity necessarily makes a false prediction concerning what two passing observers would see out their portholes when viewing one another at the time of passing.
While it is quite true that one cannot detect the absolute reference frame by doing an experiment confined to the one inertial frame you are doing it in, we can detect it (in principle, down to uncertainty limitations) by observing the backdrop of stars. I'm here refering to the absolute frame which has physical utility.

This whole problem of logical/physical is 'gummed' up by the necessity of there being embodied in existence a backdrop, stage or reference frame in which to do business. I had the idea once that perhaps if one could "grab onto" the whole universe and throw it rearward, one might then be propelled forward thereby conserving linear momentum. But this is not possible because quantitive information cannot be transmitted at greater than light speed.

Imagine the universe as a ladder of infinite length. You are on the ladder. Now climb the ladder. You move up but does the universe move down? Of course not. A "compression" of the ladder moves down the ladder and an "expansion" moves up ahead of you just sufficient to balance the linear momentum books.
Physical means logical with a condition attached (in this case the finite velocity of quantitive data transmission).



Next Page


Ebtx Home Page