Re: The Real TWINS Paradox - the Simplest Version

Gerald L. O'Barr wrote:

Alen <al...@xxxxxxxxxxxxxxx> wrote:

THE REAL TWINS PARADOX - The Simplest Version

Let it be supposed, in the following scenario,
that 'acceleration' is able to be accomplished
in a manner, perhaps on some
electromagnetic basis, that applies an identical
accelerating force to every particle in an
observer's reality, including himself,
his vehicle, and all his instruments, thus eliminating > any detectable gravitational effect of acceleration
by the accelerated observer.

Let A and B be two observers who start a long distance > apart, in the same inertial frame, and let them have
synchronised clocks. Let A and B be accelerated
towards one another, in accordance
with the above specification, until they reach a
mutual relative velocity of v, at which time the
acceleration ceases. Let the
acceleration be applied, independently of the
observers own actions, by a random choice among
one of three possible methods:



<DELETES BY O'Barr>

O'Barr's answers to this paradox of the twins,
starting with fixed distance between the twins!

Twin A and B are in a common rest frame, with
clocks properly synced.

Twin A is at point zero, time zero, and twin B at
point 1 ly (Light year) and time zero.

At time zero, let A move towards B with a velocity
of 0.866c, B remains at rest.

In the rest frame, which will be the same in terms
of twin B's data, it will take twin A 1/(0.866) years
to reach twin B. 1/(0.866) = 1.155 years.

At this time, twin B clock will show this time of
1.155 years, and twin A will show a time one-half of
this time, or 0.577 years.

There is no question at all about what twin B
sees happening and in what twin B measures.
Everything for twin B is clear and obvious. But what
will twin A see? (Twin A can use his own local
observers to verify all that happens, etc.)

Twin A sees some very interesting things. First
of all, twin A does not have to know that he
accelerated. He can look at the stars around him and
he will know that he has accelerated. He does not
have to feel anything. And this aberration that he
sees includes a new position for twin B. Twin B will
appear to be relocated, to be 2 ly away, but still
with a clock that shows zero, and with a velocity of
0.866c. And thus, twin A will see the following:
The rate of twin B's clock will be going slow, at a
rate of one-half of normal. And according to twin
A's data of the location of twin B and his velocity,
it will 2.31 years for these two twins to meet.
Thus, at this point,
twin B's clock will show half of this value, or 1.155
years. And this is exactly what it will be. And of
course twin A's clock at this point will show a time
of 0.577 years.
Now in all this, it is not important if twin A or
twin B was the one to move, this problem would still
have each twin to calculate the correct final
results for the same reasons as given above.

And if they both moved at one-half of 0.866c in
the rest frame, to make their relative velocity to be
0.866c, then they will each see the other to have
moved farther away, but at a lesser amount, and
they will each see the other
moving differently than with a relative velocity of
0.866c. They will each end up with the same time on
their clocks. In the rest frame, it will still take
1.155 years to meet, but the time on their clocks
will each be 1.155 * 0.901 = 1.04 years.

How come no one can see these things? Why do we
always seem to get things wrong when we do such
simple problems? In each of these problems, what
is seen by each is clear and exact, and what the
final results are clear and exact.
Now I did not take time to double check any
of this, but this should at least get you to
consider what has to be considered in order to
understand the basics. I hope you all know
about the aberration of light, and that this
aberration is not just a change in the
angle of veiw, but also a change in position.
Of course, if you have a change in the
angle of view, there had to be an effective
change in position, didn't it?

Thanks for reading.
Gerald L. O'Barr <globarr...@xxxxxxxxx>

This is absolutely correct, and I will add that I said the same thing, although with far less clarity and detailed information, earlier in this thread. And I have to ask the same question, namely why doesn't everyone know this? When I said:

"If A is accelerated, his clocks will be behind B's clocks when they meet, vice-versa if B is accelerated, and they will have the same time if both are accelerated."

even Sue, who knows far more math and physics than I do (and probably ever will), said:

"Ahh... no. That doesn't agree with my references.

http://www.bartleby.com/173/12.html
http://farside.ph.utexas.edu/teaching/em/lectures/node114.html";

Now I confess that I haven't bothered to read her references, but I shouldn't HAVE to read them, because she should never have posted them! EVERYONE should know exactly what happens in this situation, so what's going on? My only guess, so far, is that people believe that the universe is far more relativistic than what the actual equations of relativity tell us it is. Yes, we can use any inertial reference frame AS IF it was the absolute reference frame, and get the right answers, BUT, the chosen IRF must be used THROUGHOUT the experiment. In other words, we CANNOT shift among several IRF's during an experiment and get the right answers! In this example, if A starts out in one IRF, then accelerates to a different IRF, we CANNOT expect to be able to predict what will happen by viewing everything relative to A at all times. In a completely relativistic universe, yes, we could do this, but although the universe is indeed relativistic, it isn't THAT relativistic. We could even use the IRF that A eventually ends up in to predict the results AS LONG AS we use that particular IRF throughout the analysis!

The only exception is when some observer has a constant acceleration, either linear or centripetal, in which case we can replace his acceleration with an equivalent gravitational field and get the right answer. But if that acceleration changes, as in the clock paradox, then that's it. As Wolfgang Rindler pointed out many years ago in Essential Relativity, we can then get the right answer ONLY if we use the velocities of the objects relative to a SINGLE IRF throughout the experiment. Yes, the REASON we must do this is unpleasant, if you want to believe that everything is completely relativistic, but that's too bad, and more to the point, physicists should tell people the truth about what we can do and must do in order to predict the results of experiments, regardless of any ideological implications.

As a side note, the fact that we can use any SINGLE IRF to predict the outcome of events means that special relativity is actually far more powerful than most people realize; as long as no strong gravitational fields are involved, and quantum mechanical effects don't play a significant role, then SR can solve the problem, even if EVERY object and observer undergoes occasional or continuous acceleration, and changes in acceleration. The only "catch" is that all velocities must be measured relative to a SINGLE IRF throughout the experiment. Technically, an IRF is an "absolute" object, since it is defined as having an acceleration of zero relative to ... whatever is responsible for inertia (we KNOW this is the medium of space, we just don't always want to say so ;-). Einstein wanted to reduce the presence of "absolutes" to a minimum, and so declared that all velocities in a problem are relative to a single inertial OBSERVER, instead of relative to a single IRF. One can admire his desire to reduce the presence of absolutes to a minimum (although an inertial observer is, by definition, in an IRF, which technically defeats the purpose), but it resulted in a crippled understanding of SR, which most people believe, to this day, cannot be used to solve problems in which everyone is accelerating, even though it can EASILY solve such problems.

Phil

P.S. Okay, I'll read Sue's references, but I'm telling you now, either they're taken out of context, or they're as confused as everyone else.
.

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