Friday, November 20, 2015

Upvote - Downvote - Comment: Why Nobody Grocks the Twin Paradox

Jonathan DoolinGenerator of Hypotheses (and College Physics and Astronomy Professor)
What always really bugs me about these explanations of the twin paradox is that they usually seem to say "there's something different about the accelerating twin." But they are always very vague about what that difference is.

But the differences need not be vague.  Everything can easily be derived from the Lorentz Transformation equations, and there is no mystery to it. 

If you have an object receding from you at near the speed of light, it will appear to be moving, at a maximum, of 50% of the speed of light. 

Why?  (Answer this question for yourself, and if you agree, Upvote, if you don't agree, downvote, and post a comment.)

On the other hand, if you have an object approaching you near the speed of light, there is NO LIMIT to it's maximum apparent speed. 

Why?  (Answer this question for yourself.  If you agree, upvote.  If you don't agree, downvote, and post a comment.)

Now, when you look at a fast approaching, or fast receding object are you looking at where the object is now?  No.  You're looking at where the object WAS when it emitted or reflected the light.  That emission or reflection of light is an "event" which happened at a place and time in your perceptions.  It has physical coordinates of (t,x,y,z)  Space and time.

What happens when you accelerate toward a past event in Special Relativity?   It moves away from the observer, and back in time.  Again, do the math yourself.  If you agree, Upvote.  If you don't agree, Downvote and post a comment.)

But yes, if you accelerate toward an event in the past, Lorentz Transformation equations say it moves away and back in time.  That's good, because it makes everything consistent with what I said earlier: 

As the moving twin is moving away from the sun, he's going to see the sun moving away at less that half the speed of light.   When he turns around, he's going to see the image of the sun jump away from him--lurching away from him spatially.  And it will also (from his perspective) lurch backward in time... So the emission/reflection event happened much further away and longer ago.  So at the "instant of acceleration" is when the earth has suddenly aged in his point-of-view.

(Video explanation added, November 7)
The video explains what is meant by "if you have an object receding from you at near the speed of light, it will appear to be moving at a maximum of 50% of the speed of light." 

It also explains why the distance traveled by the earth in the second leg of the inbound  frame is much greater than the distance traveled by the earth in the first leg of the outbound frame
Jonathan Doolin
I thought I would provide this reference... This is a free video game which I think does a pretty good job of showing what relativistic motion really "looks like"

A Slower Speed of Light

You can see as you play it that accelerating forward makes objects in front of you appear to move away, and when you accelerate backwards, the objects in front of you appear to come closer. 

Some people think of this phenomenon as an "optical illusion" but it isn't.  The images are coming from the actual coordinates of actual light-reflection events.  Are these coordinates observer dependent?  Yes.  Are these coordinates frame dependent?  Yes.   Are these differences illusory?  NO.
Erik Anson
You seem to be suggesting that SR is a matter of light travel delay effects. I'm assuming that you know that that isn't the case, but your answer focusing on them so much that readers may be confused.
Jonathan Doolin
You find my willingness to explore the traveling-twin's point-of-view confusing.  I should ask, are you actually finding it confusing, surprising, unbelievable, or incorrect? 

Confusion is when you are unaware of all the facts; or you may have some of them wrong; so they don't all fit together.  Surprise is when you see something that you didn't expect. 

For people able to accept surprises, putting an emphasis on that surprise can often clear up the confusion. 

Most of the literature on the twin paradox does not discuss any observations made by the traveling twin, except for an obsession with the traveling-twin's clock. There is a widespread unwillingness to analyze the twin paradox from the traveling-twin's point-of-view.  I think that the traveling-twin's observations are relevant to the twin paradox question, and describing them will greatly increase the "surprise" but greatly decrease the "confusion".

So I'm trying to present the most surprising asymmetry of the problem (other than the well-known fact that their clocks don't match up at the end):  Namely, the way the earth JUMPS AWAY from the accelerating twin when he/she accelerates towards it.  This fact deserves EMPHASIS because it is SURPRISING.  (Not DEEMPHASIS because it is CONFUSING.)

The fact that the earth JUMPS AWAY from the traveling twin on turnaround, is a fact that I expect many readers to find surprising...  I strongly suspect that even some people who consider themselves experts on the subject are unaware of this fact, since it doesn't seem to appear anywhere in the literature I've seen; although it does show up quite prominently in the video game from MIT.  A Slower Speed of Light
(They do this without words, and it actually looks pretty natural.)

But just to make it clear, this JUMPING AWAY is NOT a result of light-travel-delay-effects.  It is an effect of switching inertial reference frames.  By the Lorentz Transformations this happens whenever you take any distant observed event  and accelerate toward it.  That event jumps away from you backward in space, and backward in time.

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