- #71
PeterDonis
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ash64449 said:the first statement is false
Why? How does TT account for that portion of HT's worldline in his calculation?
ash64449 said:the first statement is false
PeterDonis said:How does TT account for that portion of HT's worldline in his calculation
ash64449 said:why should we account for it?
PeterDonis said:But your analysis "from TT's viewpoint" does not show how TT makes that prediction.
ash64449 said:at the turn around, the elapsed proper time jumped from 3.6 years to 16.4 years for the clock at the earth(from TT's point of view)
Especially given that what you visually see has no such anomaly, nor is there any such anomaly if you are continually exchanging messages with HT.PeterDonis said:Ok, so what if TT were moving towards HT, but then turned around to move away again? (For example, suppose we are analyzing a modified scenario in which TT goes out, comes part way back, turns around and goes out again, and then comes all the way back.) That would make HT's "elapsed proper time now" go backwards. Do you consider that a viable "point of view" for TT to take?
PeterDonis said:For example, suppose we are analyzing a modified scenario in which TT goes out, comes part way back, turns around and goes out again, and then comes all the way back
ash64449 said:Do you mean the scenario in which TT leaves HT, in the middle of the journey,TT rotates,reach planet and TT reach HT again?
PeterDonis said:The scenario I am talking about, which I don't think had been discussed in this thread before I brought it up, would be described using the HT's rest frame as follows: TT leaves and travels outbound to a distant location (planet, space station, whatever); then TT turns around and heads back towards HT; halfway back, TT turns around again and heads back to the planet/space station/whatever; then TT turns around and heads back all the way to HT and they meet up again.
In this scenario, when TT turns around the second time (when he's gone halfway back to HT, and turns around to head outward again), by your definition of the TT's "point of view", the HT's elapsed proper time will go backwards.
By admitting that the momentarily comoving inertial frame is not a reasonable model for a zig zag traveler's measurements because their past is different and any operational approach to setting up coordinates will be completely different.ash64449 said:No.it won't
EDIT: As i exactly calculated, it seems to me that it will.. How can this anomaly be addressed?
PeterDonis said:Do you consider that a viable "point of view" for TT to take
PAllen said:A way to describe a criterion for reasonable observation based coordinates is that anything you see is considered simultaneous to some event in your past later than anything else you've already seen (and assigned). Basically, you are modeling light delay. Any model meeting this criterion will provide consistent coordinates for anything you can see.
What they see when they meet is invariant - the same for any valid coordinates.ash64449 said:Can you show me what your telling by answering to the question as to what HT and TT will see their clocks reading when both meet again according to PeterDonis's scenario?
I think that is the best way to understand what you are telling.
PAllen said:What they see when they meet is invariant - the same for any valid coordinates.
I already answered this a couple of times. TT sees HT clock going forward at all times in a zig zag trajectory. That is why TT should find it hard to accept a model that has HT clock going backwards, contrary to what they see.ash64449 said:This raises me a question. Does TT actually 'see' proper time of HT go backwards as i addressed?
Yes. For this example Doppler factor is 1/3 for the case when TT moves away from HT and 3 when TT moves towards HT. By using this I can explain Twin Paradox.PAllen said:If you apply this over the different legs, you will find that it correctly shows the final resulting clock comparison.
PAllen said:Especially given that what you visually see has no such anomaly, nor is there any such anomaly if you are continually exchanging messages with HT.
What is actually seen includes time dilation; I suppose that you used "relativistic Doppler" which includes time dilation, and it's necessary for symmetry of observations between inertial reference systems that are in relative motion. Classical Doppler doesn't include it.ash64449 said:[..] What is actually seen is correctly explained by Doppler factor-which means time slowing down(Time Dilation) cannot be seen by any observer. [..] .
harrylin said:What is actually seen includes time dilation
ash64449 said:What will be the reading of the clocks when TT and HT meet up again according to your scenario according to my analysis?
ash64449 said:I think If i use HT's rest frame, TT's travel along the space-time is a zig-zag path and by using the relationship between HT's proper time and TT's proper time, i can see what their clocks will read at the end of the scenario.
ash64449 said:By calculation, I see HT should read 30 years while TT should read 18 years.
I'm afraid that I can't follow your reasoning, which looks unnecessarily complex to me. A feature of the so-called "twin paradox" is that in the end the clocks are compared side by side, and we can see that the times they display differ considerably. Can you think of a more striking way to "see" time dilation?ash64449 said:Yes. It includes Time Dilation .But we don't see Time Dilation.
I can explain Doppler factor PAllen was talking about .I involve only calculation for a single outgoing scenario.
Consider HT send a signal when it's 1 year for him.
Then the signal will reach TT after 4 years which is 5 years of travel for TT in HT's rest frame.
Now using Time Dilation formula, we find only 3 years elapsed for TT.
So TT think 1 year has passed for HT when 3 years is passed for TT. This is what TT 'see'.
If i consider to work in TT's rest frame,only 1.8 years has been passed for HT and not 1 year when 3 years is passed.
Doppler factor includes Time Dilation but we don't see the Effect of Time Dilation. If so, Then TT should have thought 1.8 years passed for HT when 3 years has been passed for TT, But TT see 1 year pass for HT. So we don't see Time Dilation.
harrylin said:"see" time dilation
"Seeing" always includes a certain amount of interpretation of what it is that you think you are seeing.ash64449 said:I think Time Dilation means this: When a observer moves relative to us, Time slows down for him relative to us.(not depend on which direction observer moves)
The question that needs to be addressed here is whether we see Time Dilation with our eyes.
The Answer is No. Because We see Relativistic Doppler Effect which include Time Dilation. We 'see' time beats at slower rate for an observer which is moving away from you and we 'see' time run at a faster rate when the observer move towards you. This effect is the one we 'see' which is not Time Dilation. What we see is Relativistic Doppler Effect which includes Time Dilation.
This is the one what i said at the previous post.
What is that interpretation?harrylin said:"Seeing" always includes a certain amount of interpretation of what it is that you think you are seeing.
Ehm no. Just try to come up with an example of such a thing that you are looking for, and in which you do not interpret! (and compare for example post #7 of this thread).ash64449 said:What is that interpretation?
You may wish to read about "transverse Doppler".ash64449 said:What we see is Relativistic Doppler Effect which includes Time Dilation.
ash64449 said:Let the distance between the Earth and planet be 8 light years.(rest length between them)
Let speed of the traveling twin(TT) be 0.8c in both part's of the scenario.
...
In the frame HT uses, TT is moving and hence time runs slower for TT. So HT predicts TT would measure 20*0.6=12 years to reach earth. And hence concludes that in between the events 'TT leaves the earth' and 'TT reaches the earth', proper time elapsed for TT is 12 years and proper time elapsed for HT is 20 years and hence TT is 8 years younger than HT.
TT can use radar coordinates just like before to construct this diagram but here I show some of the significant radar signals that TT employs:PeterDonis said:The scenario I am talking about, which I don't think had been discussed in this thread before I brought it up, would be described using the HT's rest frame as follows: TT leaves and travels outbound to a distant location (planet, space station, whatever); then TT turns around and heads back towards HT; halfway back, TT turns around again and heads back to the planet/space station/whatever; then TT turns around and heads back all the way to HT and they meet up again.