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# The Twins Paradox and the speed of light

Author Topic:   The Twins Paradox and the speed of light
Taq
Member
Posts: 9651
Joined: 03-06-2009
Member Rating: 3.2

 Message 226 of 230 (680638) 11-20-2012 11:54 AM Reply to: Message 225 by NoNukes11-20-2012 11:15 AM

Re: 1 G is 1 G
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.
I knew I was wrong, I was just curious WHY I was wrong, so thanks for the correction.

 This message is a reply to: Message 225 by NoNukes, posted 11-20-2012 11:15 AM NoNukes has not replied

cavediver
Member (Idle past 3180 days)
Posts: 4129
From: UK
Joined: 06-16-2005

 (3)
 Message 227 of 230 (680661) 11-20-2012 1:03 PM Reply to: Message 224 by NoNukes11-20-2012 11:11 AM

Re: Twin paradox space time diagram
Is that incorrect, or am I missing your point completely?
Sort of, but it's damn difficult explaining this stuff back and forth in text like this. I should set up an EvC Skype account
What we are doing is trying to construct a 4d path through space-time for each of our two twins, and then measuring the length of these paths. Artificially arranging a constant velocity trip to some star system, using infinite accelerations to generate that velocity, to reverse the direction at the star system, and then bring the twin to rest back at earth is one way to make life easy in working out the length of the total 4d path. But to say that the length of the path "depends" on the velocity at an particular point, is like... well, like the following:
start at a point. Move distance $\color{white} x$. Turn through an angle $\color{white} \alpha$ and reverse for a distance $\color{white} y$. How far are you from the origin? Answer $\color{white} \sqrt{x^2+y^2-2xy\cos\alpha}$
So does your distance from the origin depend on $\color{white} x$? Well, sort of, but only if that is how you arrange your path. You could have spiralled out from your starting point for a distance $\color{white} x$, with say a widening of $\color{white} x/4$ per revolution. Now the relation between $\color{white} x$ and your distance back to the origin is totally different.
What I'm trying to say, is that you are getting hung up on the precise way you are arranging your particular path through space-time that you are attributing to it importance that just isn't there.
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.
Am I making any sense?

 This message is a reply to: Message 224 by NoNukes, posted 11-20-2012 11:11 AM NoNukes has replied

 Replies to this message: Message 228 by NoNukes, posted 11-20-2012 3:26 PM cavediver has replied

NoNukes
Inactive Member

 (1)
 Message 228 of 230 (680678) 11-20-2012 3:26 PM Reply to: Message 227 by cavediver11-20-2012 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

cavediver
Member (Idle past 3180 days)
Posts: 4129
From: UK
Joined: 06-16-2005

 Message 229 of 230 (680770) 11-21-2012 6:20 AM Reply to: Message 228 by NoNukes11-20-2012 3:26 PM

Re: Twin paradox space time diagram
The SR result is completely understandable using GR and the equivalence principle.
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.

 This message is a reply to: Message 228 by NoNukes, posted 11-20-2012 3:26 PM NoNukes has replied

 Replies to this message: Message 230 by NoNukes, posted 11-21-2012 1:18 PM cavediver has not replied

NoNukes
Inactive Member

 Message 230 of 230 (680845) 11-21-2012 1:18 PM Reply to: Message 229 by cavediver11-21-2012 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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