twin paradox

neopolitan

I had to laugh.

The clock in question has one specific function, which I stated. In the modern world we are overrun by ordinary clocks, I have about five in front of me (computer, alarm, wall clock, time on mobile, time on printer, oh, and one on the wireless phone unit, so it is six). I didn't even consider that designing a special clock to give time elapsed for "A" might cause "B" undue hardship :)

cheers,

neopolitan

atyy

Is your point that everyone ages according to his own proper time, and that B can calculate the proper time of A?

matheinste

Hello neopolitan.

Quote:-

---So if you were designing this clock, what would it do?---

Why would i need such a clock. Why not just calculate A's time. Should you wish for a display of the results of this time calculation then that is easy enough.

Matheinste.

Fredrik

(Units such that c=1). So if a signal is emitted at (0,0) and received at (x,x), the event that occurred a time x before the event (x,x) (at spatial coordinates x I assume) has coordinates (0,x) and is simultaneous with the emission (0,0). At least we agree about something. We have found that a simultaneity line is a line of constant time coordinate.

So far this definition of simultaneity agrees with the one I posted in #18, but have you really thought about what it means? Do you agree or disagree with my claim that the blue lines are simultaneity lines of the rocket when it's moving away from Earth? What about the simultaneity lines when the rocket has turned around?

But your claim was of the form "if [something that's 100% true] then we get weird deliveries", so your point must have been that the true statement was actually false. (Reductio ad absurdum). But your claim was false. You were wrong to think that the assumption implies something obviously incorrect ("weird deliveries").

This isn't a valid argument.

I haven't been able to decrypt what you're saying here. What two events? I assume that one is (20,16) in A's frame, but what's the other one? Also, a world line is a curve that represents the motion of an object. You want to imagine something moving from (20,16) to some other event? Why?

You're much too focused on those signals. I don't see how they are relevant at all. You seem to think that they somehow forbid us from using the inertial frame associated with B's return trip, but you haven't given us a reason for that.

The way you talk about these things is pretty strange to me. How is it not a characteristic of the real universe that two different global coordinate systems disagree about stuff? And what "discontinuity" are you talking about? What function is supposed to be discontinous? All we have here are (at least) two inertial frames that describe things differently.

Al68

It would run slower than a "standard" clock (by the appropriate factor dependent on relative velocity) for all inertial motion. When it senses the acceleration (turnaround), it would run faster than "normal" by a factor proportional to the rate of acceleration and proportional to its distance from "A"s clock.

While such a clock would not be "needed", it is interesting to note how it would have to work. It would have to be rigged so that acceleration would cause it to speed up. Great question, neopolitan. Why am I the only person to even attempt to answer it?

Al

matheinste

Hello Al68.

This is purely a reply to your remark in #40.

To disagree with a point of view is absolutely acceptable as is my right to put forward my view, which on this subject is very much mainstream. I know you do not mean to criticise religion as such ( but it would not bother me if you do ) but the implication is that answers i have given to the best of my admittedly limited ability are given as a matter of unthinking, blind faith, in the manner of a crusade. My answers and those of many others on this question may in your eyes be incorrect but do not deserve to be called religious with all the underlying disparaging connotations of the word. The word itself is of course not offensive but its implications in your remark are.

Matheinste

Al68

Matheinste, my reference to religion was not to imply unthinking or blind faith, just to point out that in science, unlike religion, "well known and accepted" does not equal "correct and not subject to revision". Of course, I realized my remark was out of line when I reread it after posting. That's why I deleted it right away. My apologies.

Al

P.S. I don't believe your answer on this question is incorrect, just incomplete.

phyti

You are missing the fact that the traveling twin, his clock, and everything in his space can/ship is functioning at a slower rate, therefore he ages more slowly. Referring to the drawing, he records 8 earth years during his 7, while moving at .6c.

Jumping time is a misconception due to the instantaneous reversal of direction. In reality, it would be a gradual process and the earth signal frequency would increase accordingly.

Attached Thumbnails

 

neopolitan

The two events are "A" and "B" at the time when "B" turns around. Since there is no separation speed there should be no simultaneity disagreement, both should (with the application of SR calculations) agree that these events are (t=20,x=0), "A"'s position according to "A" and (12,0), "B"'s position according to "B". (Couplets are: (20,0), (20,16) and either (12,-9.6), (12,0) or (12,0),(12,9.6) depending on "B"'s choice of origin since both choices have some merit even if the former is standard.)

The something moving from one event to another event is the information which I have discussed previously, a signal. A signal moving from "A" to "B". My contention is that even if "B" undergoes a change of frame, the calculations which "B" uses should not be used in such a way to indicate that this signal sent by "A" at (20,0) was simultaneous with any event at "B" earlier than (12,0).

That is a consequence of the implication in your diagram (Twins.PNG) that according to "B", "A" suddenly ages 25.6 years.

With the information that "B" has to hand, there is no need to make such a ridiculous claim - even if it may be standard simultaneity fare.

The signals are an attempt to get you to understand that it is unreasonable and unnecessary to state that "A" suddenly ages 25.6 years. The signals are also representative of the information flow from "A" to "B". There is real information about "A" which is accessible to "B", but it is speed limited so "B" will never get it instantaneously. The best "B" can do is use the information received to make projections which are valid for the prevailing frame.

This sudden ageing of 25.6 years is the discontinuity that I am referring to.

The 25.6 years is based on realigning the frames with the end result, so that "A" is a nice 40 years old when "B" gets there.

However, it is not real. The clock I discussed with Matheinste won't suddenly scroll forward from 7.2 to 32.8 years. And here is why not ... the 32.8 year figure is based on "A" not moving at all during the 20 years. That means that the clock would have to somehow predict the future.

This is totally separate from the issue that the calculation behind the 32.8 years is based on a combination of situations, the bastard son of two frames, and that the calculation totally ignores how information flows in the universe.

"B" should, at the turnaround, make a projection that "A" has aged a total of 20 years. Not 32.8 years.

cheers,

neopolitan

PS Perhaps you might like to create a chart which maps the "A" events which are, according to "B", simultaneous with "B" events. Make all the events ageing events, ie '"B" has aged x days, this is simultaneous, according to "B" with "A" having aged y days' and plot y against x.

In my version, there will be a straight line (with a little bump in the middle if I am going to be pedantic), since "B" effectively maintains the same speed the whole time (0.8c) and I will not be ignoring the information that "B" receives.

In your version, there will be three straight lines - (0,0) to (12,7.2), (12,7.2) to (12,32.8) and (12,32.8) to (24,40).

Which sounds more representative of a realworld situation?

PPS phyti has approximately the right sort of diagram. His figures are for a shorter trip and show the situation in a different way, but at each end of phyti's diagonal lines are the simultaneous events which I suggest you chart, Fredrik.

Al68

I think everyone agrees with that, assuming that you mean when the ship comes to momentary rest with earth. That's when earth's clock will read 20 yrs. The 32.8 yrs is what the earth clock will read according to "B" after the acceleration and the ship is headed back. The earth clock readings of 7.2, 20, and 32.8 yrs are only a "jump" in time seen by the ship if we consider the turnaround instantaneous. We could just as easily say earth's clock jumps from 7.2 to 20 during an instantaneous deceleration, then from 20 to 32.8 during an instantaneous acceleration. And we could break it down into segments as small as we like, and for each segment during the acceleration, earth's clock will advance more than the ship's clock according to "B" (or co-moving inertial observers).

Al

Fredrik

That's what I thought you meant, but you said weird things like that there's a world line that connects them.

You seem to be missing the point of the twin paradox. The false conclusion that there is a paradox was found by considering both twins' points of view, and doing it incorrectly. You can't solve that problem by saying that B's point of view is unnecessary. A resolution must explain why B is younger when they meet again, even though B can say (correctly) that his brother is aging at a slower rate at any point during the trip except the turnaround

I know. I didn't ask because I needed to hear that part of the answer. I asked what function is supposed to be discontinuous to get you to think about how you can't even specify that function without explicitly mentioning the switch from one inertial frame to another.

No, it just has to keep track of the rocket's position and velocity at all times. The rest is a straightforward calculation. And yes, if you slow down on the way back, it will go backwards. If you programmed it right, that is.

It should ignore that. Think about what a coordinate system is. It's just a function that assigns numbers (coordinates) to events.

Half way through the turnaround, yes. (When A and B have the same velocity). But not when the turnaround is complete.

Check out for example the second text box from the bottom in my spacetime diagram. It states both what B is experiencing at the event where the blue line intersects B's world line, and what A is experiencing at the event where the blue line intersects A's world line. (Reminder: the blue line is a simultaneity line of B).

Simultaneous? They aren't simultaneous unless the signals are transmitted by tachyons moving at 1.25c.

This discussion doesn't seem to be going anywhere, so I might withdraw from it after this.

Al68

No, but if it works the way I described earlier, the time (according to the "normal" clock "B") it would take for this special clock to advance from 7.2 to 32.8 yrs would be inversely proportional to the rate of acceleration. Since the rate of acceleration can't realistically equal infinity, the special clock won't "jump" time, some time will elapse on the "B" clock while the special clock advances from 7.2 to 32.8 yrs smoothly (assuming the rate of acceleration is constant). And this special clock would not need to predict the future, if the ship stops accelerating at any time, the clock would sense the lack of acceleration and resume running slow by the gamma factor compared to clock "B".

Al

yogi

I have a different take in the twins thing - first of all, solve the problem by reducing it to two one way trips - and double the result to get the total age difference - so on the outward bound one way trip use two clocks, one on earth, one at the destination - they are synchronized in the earth frame and always read the same - the distance to the traget is vt where t is the lapsed time in the earth-target frame, and ct is the temporal distance the earth frame has moved during the one way trip - so the space time path followed by the traveler is a composite of the the space and temporal increments - during this interval, the travelers clock logs a time t' and the temporal distance for the traveler is ct'

so (ct)^2 = (ct')^2 + (vt)^2 from which you get Gamma and the amount of time that difference between the two frames, that is t' = Gamma(t)

You don't have to send signals, you don't need to get involved with turn around accelerations, and it doesn't make any difference whether the earth-target frame is moving or the traveler - all you need is Minkowski orthogonality of space and time and realize that each frame has taken a different space time path so since one frame has moved only in time and the other frame has experienced both a space and time increment - the intervals will be equal, but the components of the interval in each case will be different

neopolitan

Fredrik and Al,

Perhaps we can break the deadlock if you explicity state the assumptions of your conclusion(s).

Here are the assumptions of my conclusion, as far as I can tell:

• "B" keeps track of signals from "A".
  
• "B" is aware of accelerations undergone.
  
• "B" assumes under the conditions of the experiment that "A" does not undergo any significant accelerations.
  
• "B" is aware of relativity and uses that knowledge appropriately in calculations.
  
• "B" calculates "A"'s age on an ongoing basis.
  
• Most significantly: "B" does not at any time assume that the prevailing inertial frame is eternally valid (due to awareness of accelerations).

I do think that the last is important, and is possibly the sticking point.

Please present your assumptions, then have a go at mine, if you so wish.

cheers,

neopolitan

PS as yogi points out, signals are not really strictly necessary, assumption 4 would eliminate the need for assumption 1. But I keep the signals to force some real universe thinking in the example.

Al68

I think he might be referring to a function describing clock "A" in B's frame, which would have a discontinuity if we assume the rate of acceleration to be infinity, and the elapsed time on clock "B" to be zero during the turnaround. The earth's clock would read 7.2 then 32.8 yrs, but not values in between. But this is just an artifact of treating the turnaround as instantaneous. If we say the turnaround is just "near" instantaneous, then the earth's clock will advance from 7.2 to 32.8 very quickly according to clock "B", but it will read all times in between with no discontinuity.

Al

Al68

Hi neopolitan,

I actually see what you're saying, I think. I answered your question about how a clock would work that is supposed to show earth time on the ship. And I agree with you that there is a discontinuity associated with instantaneous turnaround, but it's not real because instantaneous turnaround is not possible. Such a clock would simply run fast relative to clock "B" during any acceleration (toward earth). And it would always show the time on earth simultaneous with any moment on the ship (or a co-moving inertial frame).

I would use your assumptions, although #1 wouldn't be necessary.

Al

neopolitan

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.

Acceleration qua acceleration has no effect on timing, only as a consequence of the altered relative speeds. (And simultaneity is only altered as a consequence of altered relative velocities.)

cheers,

neopolitan