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Author Topic:   The Twins Paradox and the speed of light
NoNukes
Inactive Member


Message 221 of 230 (680600)
11-20-2012 10:18 AM
Reply to: Message 220 by cavediver
11-20-2012 10:02 AM


Re: Twin paradox space time diagram
Yes, of course. If only minimal periods of acceleration are used, then the accelerations must be very large (if we are talking about relativistic speeds) and thus the equivalent gravitational field is large, and the time dilation significant.
Perhaps I am doing a poor job of posing what I perceive to be the issue.
I don't question that the time dilation can be significant during those periods.
But the amount of time dilation during those periods is independent of the length of the moving twin's trip (Provided of course that the moving twin does not accelerate during the other portions of the trip). Yet we expect that the aging differential between the twins will be function of the length of the trip.
I don't see how focusing on the accelerated portions explains this relationship between trip length and aging differential.

Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison.
If there is no struggle, there is no progress. Those who profess to favor freedom, and deprecate agitation, are men who want crops without plowing up the ground, they want rain without thunder and lightning. Frederick Douglass

This message is a reply to:
 Message 220 by cavediver, posted 11-20-2012 10:02 AM cavediver has replied

Replies to this message:
 Message 222 by cavediver, posted 11-20-2012 10:53 AM NoNukes has replied

  
NoNukes
Inactive Member


(1)
Message 224 of 230 (680621)
11-20-2012 11:11 AM
Reply to: Message 222 by cavediver
11-20-2012 10:53 AM


Re: Twin paradox space time diagram
Nope, we don't. And what's more, it can't be. The length of the trip (if you mean the time duration, or the distance of the trip) is an observer-dependent quantity.
Yes. The length of the trip is an observer-dependent quantity. But the length and duration of the trip as measured from the stay at home twin's perspective is a fixed value.
And I am suggesting that if we use the length as measured from the frame of the at rest twin, that the difference in ages (measured in years) between the twin that leaves and the twin that stays home varies with the length of the trip (in time or distance) and the speed of the rocket ship measured in the stat at home twin's frame. The ratio of the measured time difference for the stay at home twin is a measure of the velocity only (in the SR only version of the problem).
I've never seen a calculation of the twin problem that suggested otherwise. For example I refer here to the Specific Example in the wikipedia article
Twin paradox - Wikipedia.
In the example, the time difference accumulates at a rate dependent on the velocity of the space craft (in the stay at home twin's frame) however the accumulate number of years is proportional to the time experienced by the stay at home twin during the traveling twins trip. Is that incorrect, or am I missing your point completely?
Edited by NoNukes, : No reason given.
Edited by NoNukes, : No reason given.

Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison.
If there is no struggle, there is no progress. Those who profess to favor freedom, and deprecate agitation, are men who want crops without plowing up the ground, they want rain without thunder and lightning. Frederick Douglass

This message is a reply to:
 Message 222 by cavediver, posted 11-20-2012 10:53 AM cavediver has replied

Replies to this message:
 Message 227 by cavediver, posted 11-20-2012 1:03 PM NoNukes has replied

  
NoNukes
Inactive Member


Message 225 of 230 (680622)
11-20-2012 11:15 AM
Reply to: Message 223 by Taq
11-20-2012 11:02 AM


Re: 1 G is 1 G
So if the spacecraft accelerated at 1 G both there and back while the other twin was on Earth also experiencing 1 G then they should be the same age? Their clocks should tick at the same speed relative to each other?
No. Gravitational time dilation is related to differences in potential of the gravitational field and not to the magnitude of the acceleration. For example, in a uniform gravitational field there would be no time dilation experienced based on changing position in the gravitational field.

Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison.
If there is no struggle, there is no progress. Those who profess to favor freedom, and deprecate agitation, are men who want crops without plowing up the ground, they want rain without thunder and lightning. Frederick Douglass

This message is a reply to:
 Message 223 by Taq, posted 11-20-2012 11:02 AM Taq has replied

Replies to this message:
 Message 226 by Taq, posted 11-20-2012 11:54 AM NoNukes has not replied

  
NoNukes
Inactive Member


(1)
Message 228 of 230 (680678)
11-20-2012 3:26 PM
Reply to: Message 227 by cavediver
11-20-2012 1:03 PM


Re: Twin paradox space time diagram
If you assume the infinite accelerations, then you are in the nice position of being able to work out the time difference from the velocities. But that is because you have given yourself these infinite accelerations to make the situation easy. The time dilation itself is not arising from the velocities even though we are using the values of the velocities to work out the total time difference.
After pondering this for quite a bit, and doing some reading, I came up with an alternate explanation that I'd like to try out on you.
Using the equivalence principle method on the finite acceleration as applied, we find that the gravitational potential difference at turn around is actually related to the separation between the twins at the turn around point. In fact the relation ship is phi = (a * d), assuming a is a constant acceleration. This is enough to account for what I thought was an issue. There will indeed be longer aging differentials for longer 'straight line' trips using Einstein's GR solution.
This means of course that the critic's objection to Einstein was completely off base. The SR result is completely understandable using GR and the equivalence principle. I'm sorry that I cannot give you back your five minutes.

Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison.
If there is no struggle, there is no progress. Those who profess to favor freedom, and deprecate agitation, are men who want crops without plowing up the ground, they want rain without thunder and lightning. Frederick Douglass

This message is a reply to:
 Message 227 by cavediver, posted 11-20-2012 1:03 PM cavediver has replied

Replies to this message:
 Message 229 by cavediver, posted 11-21-2012 6:20 AM NoNukes has replied

  
NoNukes
Inactive Member


Message 230 of 230 (680845)
11-21-2012 1:18 PM
Reply to: Message 229 by cavediver
11-21-2012 6:20 AM


Re: Twin paradox space time diagram
The point to take away is the fundemental difference between the observer dependent "explanations" and the actual 4d geometry of the situation, which is the true "physics" so to speak.
Well, I was able to do the 4d stuff for SR. I think my problem involved not applying the equivalence principle properly. But I get to fall back on actually being an engineer and not a scientist.

Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
The apathy of the people is enough to make every statue leap from its pedestal and hasten the resurrection of the dead. William Lloyd Garrison.
If there is no struggle, there is no progress. Those who profess to favor freedom, and deprecate agitation, are men who want crops without plowing up the ground, they want rain without thunder and lightning. Frederick Douglass

This message is a reply to:
 Message 229 by cavediver, posted 11-21-2012 6:20 AM cavediver has not replied

  
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