Acceleration is not important in the twin paradox

[md65536]

Decraig, this example is quite good, but I don't "feel" the release from the paradox using it. Others might.

It resonates with me because it adds additional details that can help to figure out what's going on. It is interesting to consider that an experiment can be made symmetrical just by adding stuff to mirror anything asymmetrical. However it doesn't change the "paradox", because while A and B are symmetrical, and A' and B' are symmetrical, the original asymmetry between A and B+B' remains.

 

 

The most fundamental difficulty seems to me to be reconciling symmetry with the outcome of the inertial triplet and the a=1 accelerating triplet in post 391 above. Each is in motion relative to the other, and they meet up again after their first crossing. So a naive application of special relativity would say that each's clock runs slow to the other, and thus at their second meeting each must observe the other's clock to be behind his own -- which is plainly false. It cannot be that each clock runs slower to the other.

But that's the accepted interpretation if or while the clocks are moving inertially.

 

What is the case when there's constant acceleration (but no gravity) like in post #391? Is it right to say that the other observer's clock is always running at a slower or equal rate, but the continuous change in velocity corresponds to a continuous change in simultaneity that can have the remote clock advance beyond a local clock? Or is it right to say that since time dilation refers to the actual difference of elapsed time, and the effects of the continuous change to simultaneity can't be separated out, there's no sense in saying the remote clock ever ticks slower when it is always effectively ticking at an advanced rate?

[JVNY]

Here is one approach (which I think follows the alternative you mention that one might not be able to separate out the slow ticking from the effect of changing simultaneity), along with a couple of citations objecting to it.

 

In order for there to be relative motion, someone has to accelerate. When he accelerates and gains speed, the other frame length contracts toward him, and a row of clocks laid out along the length of the other frame desynchronizes because of the relativity of simultaneity. The more distant the clock is from the accelerated observer, the farther ahead in time it will present in his frame after the contraction. Think of the clocks in the other frame as odometers, spinning up as they length contract the original distance toward the accelerated observer. The farther away a clock originally was, the more distance it has to cover in the contraction to keep the contraction proportionate -- so the more distant the clock the more it contracts toward the observer and the more it advances in the observer's frame, like an odometer advancing as a vehicle moves a great distance. Each clock thereafter ticks slower in the observer's frame, but each successive clock that he passes is ahead of the prior one. The net result -- the clock advancement effect exceeds the slower ticking rate, so as the observer passes along the row of clocks in the other frame and reads their times in series, they run (as a series) faster than his clock. Every clock in the other frame remains synchronized in that other frame (because that frame did not accelerate), so time is passing faster throughout that frame (including for a stay at home twin) than it is for the accelerated observer. This clock advancement effect is from our other discussion at: http://www.scienceforums.net/topic/80036-relative-aging-without-acceleration/, which has links to more detailed explanations, including the use of this to explain the twin paradox.

 

That said, others object to this concept of clock advancement. See for example this response to the claim that the clock advances as described above and explains the paradox:

 

"No, I am as against quick advancing of the clock (I called it scrolling) from 7.2 years to 32.8 years as I am against the clock being 7.2 years one moment and 32.8 years the next." from http://www.physicsforums.com/showthread.php?s=c51bf4a98b8d0910836daef7b994a123&t=257843&page=3

 

Here's another that seems to object to the concept, based on the view that the math does not work out:

 

"The point of using an abrupt acceleration (and long outward and return journeys) is that the amount of clock-advancement that the earth observer /might/ see during the turnaround acceleration stage can't possibly compensate for the timelag that builds up in the coasting stage, unless the earth observer sees clocks going backwards or signal overlaps or some other sort of apparent breakdown of visual causality that's not supposed to happen in current theory." from http://sci.physics.relativity.narkive.com/YPFnUziq/what-killed-special-relativity.2

 

I find that the math always works out if the accelerated observer completes the trip along the row of clocks, but there are some issues if he does not. Say the observer accelerates quickly to a very high speed, then just as quickly decelerates back to rest. The clocks in the other frame would advance as described above with the acceleration, then regress with the deceleration (actually spin backwards in the decelerating observer's frame). This seems unusual. The final difference in proper clock times between the accelerating observer and the stay at home twin depends on the amount of time that the accelerating observer spends at speed, so a quick acceleration followed by a quick deceleration will not generate very much final difference in proper time between him and the stay at home twin -- yet it seems to lead to a lot of clock advancement followed by clock regression, which does seem odd.

[md65536]

I find that the math always works out if the accelerated observer completes the trip along the row of clocks, but there are some issues if he does not. Say the observer accelerates quickly to a very high speed, then just as quickly decelerates back to rest. The clocks in the other frame would advance as described above with the acceleration, then regress with the deceleration (actually spin backwards in the decelerating observer's frame). This seems unusual. The final difference in proper clock times between the accelerating observer and the stay at home twin depends on the amount of time that the accelerating observer spends at speed, so a quick acceleration followed by a quick deceleration will not generate very much final difference in proper time between him and the stay at home twin -- yet it seems to lead to a lot of clock advancement followed by clock regression, which does seem odd.

Yes, the math always works out. There's no issue there with SR's predictions, only with how they're interpreted. I don't even see an issue with interpretation, because the back-and-forth change in simultaneity has no real lasting and measurable effect. The "current time on Earth according to the traveler" is just a relation, without any causal connection between "now" for the traveler and the changeable "now" on Earth. The actions of the distant twin doesn't "cause" clock advancement and regression on Earth, it just determines the twin's current relationship with Earth time.

 

Your example is like the Andromeda "paradox":

http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument

(Though after reading it, the Andromeda "paradox" seems more philosophical and less interesting.)

Edited December 4, 2013 by md65536