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Re: [Phys-l] twin paradox question





In a message dated 12/18/2010 8:37:25 PM Eastern Standard Time,
zubarsky@gmail.com writes:

I have always wondered something about the twin paradox. If one twin is
moving away from the Earth at high speed time moves slower for him
compared
to his brother. If the brother on Earth were able to see his brother on
the
fast moving ship everything would appear in slow motion. Here is my
question. If the on the fast moving space ship were to look at the Earth
is
it moving away from him at a very high speed too. So doesn't everything
on
Earth appear to be moving in slow motion compared to time on the space
ship?
So, why upon return is the traveling twin young and the twin that stayed
on
Earth old? I don't get it.
Thanks,
Mike Barr

First a few comments about understanding:
PER and science education research has shown that understanding requires
using multiple representations. Unfortunately physics classes often just
use the algebraic representation which give answers easily, but which
obscures the concepts. So kinematics needs graphical, pictorial,
descriptive, and lastly algebraic representations. So to understand the
twin paradox, you need to look at it from many different points of view.
The space time diagrams are very powerful and give answers easily. But that
power often obscures things, and can be very unsatisfying. To the person
who has the concepts space-time diagrams are helpful, but to those who
don't, they aren't.

I will treat just half the voyage using some very old fashioned concepts:

At one time people looked at relativity by considering what you "observed".
This would be not what you see. So if the twins are exchanging radio
message the messages are what they see. Then using this information they
observe that certain things are going on. So knowing about the Doppler
shift and both know their relative speeds they conclude or observe that the
other twin has slowed down by the time dilation factor.

So the twin on earth observes the other twin as going to Alpha Centauri in
about 4 years at 99% of the speed of light. From listening to the other
twins messages he finds the moving twin has only aged a few weeks while
traveling to the nearby star. At this point I will presume that the
traveler twin stays at the star for a while because he finds a green goddess
girl friend.

But what does the traveling twin observe? He observes that the distance to
the nearest star has been shortened by the Lorentz contraction factor, so it
only takes a few weeks to get there. He also observes that his twin is
slowed down by the time dilation factor while he is traveling.

But something interesting happens when he slows down to dock with a planet
at Alpha Centauri. After he has decelerated he is now in the same frame as
his brother and the distance between Earth & AC is now 4 light years.
Goodness! His stay at home brother's messages indicate that he is not much
older than when the journey began so the wandering brother concludes his
Earthly twin must be 4 years older while he has not aged much at all.

The wandering brother will conclude something "funny" happened during the
slowing down.

There is an asymmetry in what happens to the brothers. One stays in an
almost Galilean frame, while the other experiences dramatic accelerations
and changes frames.

Now let us bring in an interesting factor. Let us say that intelligent
creatures have put permanent outposts at regular positions on the way to AC.
And let us suppose they have synchronized the clocks with Earth by knowing
how far they are and the speed of light they can sycronize all of the clocks
on the way to AC. I suppose these could be restaurants and stopovers for
weary travelers.

But the wandering twin "observes" something funny. He observes the clocks
as being mis-syncronized. So the clock at AC is 4 years ahead of the one at
Earth, and each clock along the way is similarly off. So while he is
traveling he will say someone has cheated. But when he finishes slowing
down he will observer that the clocks have "miraculously" been put right.

The "paradox" is that this type of thing defies common sense, but is
perfectly consistent with relativity. Both twins end up agreeing when they
are in the same frame, but disagree while they are in different frames. A
paradox is something that common sense gaily mocks. See the dictionary
definition "a statement or proposition that seems self-contradictory or
absurd but in reality expresses a possible truth." So in this sense there
really is a paradox. The dictionary also has "a self-contradictory and false
proposition" and "an opinion or statement contrary to commonly accepted
opinion". So paradoxes can be true, but may be perceived as false or
confusing. So I submit that this is truly a paradox from the point of view
of accepted common sense, even though it is scientifically sound. My
favorite paradox is Frederick's age vs number of birthdays.

Notice that there are many ways to analyze the twin paradox. I think this
first way has some appeal to the novice. The space-time diagram is very
appealing to the expert. But ST diagram is a representation that may be
confusing to the novice. But for full understanding put together the
various explanations and try to understand how they fit together.

Unfortunately experts usually assume that their way of explaining things is
best and only way for novices. But the PER research shows that this is very
false. Novices have to construct their understanding and can't just jump to
a fully abstract way of thinking. There are a few exceptional students who
do seem to jump. I suspect that they often go through the same stages of
thinking, but often very quickly. They also usually have advanced thinking
ability. For how the thinking ability is related to learning concepts look
at Anton Lawson's papers in JRST.

John M. Clement
Houston, TX