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Time Dilation and Twin Paradox Revisited
16 years 11 months ago #19842
by PhilJ
Replied by PhilJ on topic Reply from Philip Janes
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by TV</i>
The formal way to apply <i>SR</i> to cases with acceleration is through Lorentz boosts -- essentially tiny velocity steps condensed into a short time span.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I’ve instinctively been approaching <i>GR</i> problems that way all along. This amounts to a numerical alternative to <i>GR</i>. If you set it up as a computer program, it serves as a test of whether <i>GR</i> was correctly derived by Minkowski. Unfortunately, I don’t have the software to do that. I downloaded a free version of VisualBasic2, but had no success installing it.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by TV</i>
The experimental way is to recognize cyclotron results showing that acceleration has no effect on clocks or aging, even at levels as high as 10^19 g (where g is the acceleration of gravity at Earth's surface, 10 m/s/s).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">As I (mis)understand <i>GR</i>, the immediate “effect” of acceleration on clocks is based on the assumption that the acceleration will continue indefinitely in one direction. (Galaxies billions of light years away become many times closer the instant you step on the gas in your automobile.) Where acceleration is cyclically reversing direction, those immediate “effects” are meaningless; only the end result of a trip matters. I confess that I don’t know how to apply either <i>GR</i> or Lorentz boosts to such a problem, nor do I know what end result to expect.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by TV</i>
The logical way to deal with acceleration is to eliminate it. Another twin approaching from the opposite direction can replace the traveling twin as they pass and compare ages, then complete the journey back to Earth instead of the traveler. That way, nobody ever accelerates.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">This is not the scenario originally posed by Einstein, so it is no excuse for not laughing at his joke. If I were a comedian, I’d hate to face a houseful of killjoys like you. Nevertheless, I shall try to analyze your scenario, as follows: [I’m ashamed to admit how many wrong answers I got before settling on the following. Hope I got it right, this time.]
In the reference frame of the home bases (x, t):
Base A & base B are stationary at x = 0 and x = +1 cy (light year), respectively. The base clocks remain synchronized with each other throughout the trip. Twin A and twin B leave behind their respective twins at their respective home bases and board ship A and ship B, respectively. The ships back up, accelerate forward, and then coast past their respective home bases at 3/4 c relative to the bases. {Gamma = 1/sqrt(1-3/4) = 2} All of the clocks are synchronized (t = 0, t' = 0, t'' = 0) as the ships pass their respective home bases; they continue coasting equally in opposite directions toward one another. The ships’ clocks are ticking off ½ second for each second on the bases’ clocks (delta t' = delta t/2). At t = 2/3 year, the travelers pass the half-way point and compare clocks, which for that instant are in agreement at t' = t'' = 1/3 year. They continue and coast past their respective destination bases at t = 4/3 year and t' = t'' = 2/3 year. The traveling twins are then 1/3 year younger than the stay-at-home twins.
In the reference frame of ship A (x', t'):
At the beginning of the journey, ship A’s own clock is synchronized with that of base A (t = t' = 0); base B is ½ cy away (at x' = +½ ly) with its clock indicating t = +1 year, and ticking off ½ second for each second on the ship’s clock (delta t = delta t'/2). Ship B is already well under weigh, somewhere between the two bases. The journey of ½ cy at 3/4 c lasts 2/3 year (delta t' = 2/3 year), during which base B’s clock ticks off 1/3 year (delta t = 1/3 year), making it read t = +4/3 year.
In the reference frame of ship B (x'', t''):
At the beginning of the journey, ship B’s own clock is synchronized with that of base B (t = t'' = 0); base A is ½ cy away (at x'' = +½ ly) with its clock indicating t = +1 year, and ticking off ½ second for each second on the ship’s clock (delta t = delta t''/2). Ship A is already well under weigh, somewhere between the two bases. The journey of ½ cy at 3/4 c lasts 2/3 year (delta t'' = 2/3 year), during which base A’s clock ticks off 1/3 year (delta t = 1/3 year), making it read t = +4/3 year.
As for position and time of one ship in the other ship’s reference frame, I think I must be misapplying the formula for addition of relativistic velocities. Using the formula, W = (w+v)/(1+(vw/c^2)), I add v = 3/4 c & w = 3/4 c and I get 24/25 c with gamma = 28/100. That doesn’t sound reasonable to me; before I proceed, I’d like to get a second opinion.
Anyway, I don’t see any paradox here.
The formal way to apply <i>SR</i> to cases with acceleration is through Lorentz boosts -- essentially tiny velocity steps condensed into a short time span.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I’ve instinctively been approaching <i>GR</i> problems that way all along. This amounts to a numerical alternative to <i>GR</i>. If you set it up as a computer program, it serves as a test of whether <i>GR</i> was correctly derived by Minkowski. Unfortunately, I don’t have the software to do that. I downloaded a free version of VisualBasic2, but had no success installing it.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by TV</i>
The experimental way is to recognize cyclotron results showing that acceleration has no effect on clocks or aging, even at levels as high as 10^19 g (where g is the acceleration of gravity at Earth's surface, 10 m/s/s).<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">As I (mis)understand <i>GR</i>, the immediate “effect” of acceleration on clocks is based on the assumption that the acceleration will continue indefinitely in one direction. (Galaxies billions of light years away become many times closer the instant you step on the gas in your automobile.) Where acceleration is cyclically reversing direction, those immediate “effects” are meaningless; only the end result of a trip matters. I confess that I don’t know how to apply either <i>GR</i> or Lorentz boosts to such a problem, nor do I know what end result to expect.
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by TV</i>
The logical way to deal with acceleration is to eliminate it. Another twin approaching from the opposite direction can replace the traveling twin as they pass and compare ages, then complete the journey back to Earth instead of the traveler. That way, nobody ever accelerates.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">This is not the scenario originally posed by Einstein, so it is no excuse for not laughing at his joke. If I were a comedian, I’d hate to face a houseful of killjoys like you. Nevertheless, I shall try to analyze your scenario, as follows: [I’m ashamed to admit how many wrong answers I got before settling on the following. Hope I got it right, this time.]
In the reference frame of the home bases (x, t):
Base A & base B are stationary at x = 0 and x = +1 cy (light year), respectively. The base clocks remain synchronized with each other throughout the trip. Twin A and twin B leave behind their respective twins at their respective home bases and board ship A and ship B, respectively. The ships back up, accelerate forward, and then coast past their respective home bases at 3/4 c relative to the bases. {Gamma = 1/sqrt(1-3/4) = 2} All of the clocks are synchronized (t = 0, t' = 0, t'' = 0) as the ships pass their respective home bases; they continue coasting equally in opposite directions toward one another. The ships’ clocks are ticking off ½ second for each second on the bases’ clocks (delta t' = delta t/2). At t = 2/3 year, the travelers pass the half-way point and compare clocks, which for that instant are in agreement at t' = t'' = 1/3 year. They continue and coast past their respective destination bases at t = 4/3 year and t' = t'' = 2/3 year. The traveling twins are then 1/3 year younger than the stay-at-home twins.
In the reference frame of ship A (x', t'):
At the beginning of the journey, ship A’s own clock is synchronized with that of base A (t = t' = 0); base B is ½ cy away (at x' = +½ ly) with its clock indicating t = +1 year, and ticking off ½ second for each second on the ship’s clock (delta t = delta t'/2). Ship B is already well under weigh, somewhere between the two bases. The journey of ½ cy at 3/4 c lasts 2/3 year (delta t' = 2/3 year), during which base B’s clock ticks off 1/3 year (delta t = 1/3 year), making it read t = +4/3 year.
In the reference frame of ship B (x'', t''):
At the beginning of the journey, ship B’s own clock is synchronized with that of base B (t = t'' = 0); base A is ½ cy away (at x'' = +½ ly) with its clock indicating t = +1 year, and ticking off ½ second for each second on the ship’s clock (delta t = delta t''/2). Ship A is already well under weigh, somewhere between the two bases. The journey of ½ cy at 3/4 c lasts 2/3 year (delta t'' = 2/3 year), during which base A’s clock ticks off 1/3 year (delta t = 1/3 year), making it read t = +4/3 year.
As for position and time of one ship in the other ship’s reference frame, I think I must be misapplying the formula for addition of relativistic velocities. Using the formula, W = (w+v)/(1+(vw/c^2)), I add v = 3/4 c & w = 3/4 c and I get 24/25 c with gamma = 28/100. That doesn’t sound reasonable to me; before I proceed, I’d like to get a second opinion.
Anyway, I don’t see any paradox here.
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16 years 11 months ago #3151
by Thomas
Replied by Thomas on topic Reply from Thomas Smid
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by greg87</i>
<br />It seems to me that elapsed time would seem to slow down for an observer of a craft approaching light speed just as the sound seems to trail further behind an airplane approaching the speed of sound. The speed of sound is dependant on the medium through which it travels, but it does not limit the speed of the projectile. A propeller driven craft cannot break the sound barrier for it uses the medium of sound (air) for propulsion just as thrust/momentum engines cannot push through the barrier of light speed. Chemical burning occurs faster than sound but not faster than light. If gravity moves (its effects felt) faster than light, then a gravity engine could break the light speed barrier.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Although I wouldn't agree with your suggestion, the comparison to the situation of a propeller aircraft not being able to reach the speed of sound is actually not so bad: as I have suggested on my page A Newtonian Relativistic Electrodynamics , the inability to reach the speed of light in particle accelerators could be explained by a velocity dependent electromagnetic force, i.e. the particle simply doesn't 'see' the accelerating field anymore as it approaches c with regard to the objects creating the field. If one could manage to co-move these objects with the particle (or if one would use other forces than electromagnetic ones), then the speed of light should be exceeded.
Thomas
<br />It seems to me that elapsed time would seem to slow down for an observer of a craft approaching light speed just as the sound seems to trail further behind an airplane approaching the speed of sound. The speed of sound is dependant on the medium through which it travels, but it does not limit the speed of the projectile. A propeller driven craft cannot break the sound barrier for it uses the medium of sound (air) for propulsion just as thrust/momentum engines cannot push through the barrier of light speed. Chemical burning occurs faster than sound but not faster than light. If gravity moves (its effects felt) faster than light, then a gravity engine could break the light speed barrier.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
Although I wouldn't agree with your suggestion, the comparison to the situation of a propeller aircraft not being able to reach the speed of sound is actually not so bad: as I have suggested on my page A Newtonian Relativistic Electrodynamics , the inability to reach the speed of light in particle accelerators could be explained by a velocity dependent electromagnetic force, i.e. the particle simply doesn't 'see' the accelerating field anymore as it approaches c with regard to the objects creating the field. If one could manage to co-move these objects with the particle (or if one would use other forces than electromagnetic ones), then the speed of light should be exceeded.
Thomas
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16 years 11 months ago #20640
by Thomas
Replied by Thomas on topic Reply from Thomas Smid
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
The logical way to deal with acceleration is to eliminate it.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
That's essentially what I have done in the thought experiment suggested on my page Time Dilation and Twin Paradox Debunked . Not only does it not involve any acceleration, but it it is absolutely symmetric, and it is therefore impossible to single out a preferred frame of reference. This logically proves the impossibility of timedilation and thus the logical and mathematical inconsistency of the Lorentz transformation (I have shown the errors in Einsteins derivation both for his original 1905 derivation as well as his later algebraic derivation ) .
Thomas
The logical way to deal with acceleration is to eliminate it.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
That's essentially what I have done in the thought experiment suggested on my page Time Dilation and Twin Paradox Debunked . Not only does it not involve any acceleration, but it it is absolutely symmetric, and it is therefore impossible to single out a preferred frame of reference. This logically proves the impossibility of timedilation and thus the logical and mathematical inconsistency of the Lorentz transformation (I have shown the errors in Einsteins derivation both for his original 1905 derivation as well as his later algebraic derivation ) .
Thomas
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16 years 11 months ago #19113
by tvanflandern
Replied by tvanflandern on topic Reply from Tom Van Flandern
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
<br />This logically proves the impossibility of timedilation and thus the logical and mathematical inconsistency of the Lorentz transformation<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Perfect symmetry does no such thing, as anyone who takes the time to understand SR can readily see. (Remember, I think SR and time dilation are wrong, but on experimental grounds, not logical grounds.)
Why not observe proper protocol for posting on this Message Board and, instead of links to your own web site (which are discouraged here), provide a detailed comparison of your reasoning with that in the Meta Science treatment of the twins paradox available on this web site at metaresearch.org/cosmology/gravity/gps-twins.asp ? The peer-reviewed and published Meta Science treatment introduces a very instructive tool: It uses a GPS-style Earth clock as a second clock on board the traveling twin's spaceship so the traveler can always directly compare his own time to Earth time.
Such a comparison of your approach to ours could be helpful for pointing out errors or potential improvements in at least one of the two approaches. Simply making claims and posting foreign links is unlikely to go anywhere useful, especially because so many people fail to understand relativity properly, with the result that most major journals will no longer accept papers "logically disproving SR". -|Tom|-
<br />This logically proves the impossibility of timedilation and thus the logical and mathematical inconsistency of the Lorentz transformation<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Perfect symmetry does no such thing, as anyone who takes the time to understand SR can readily see. (Remember, I think SR and time dilation are wrong, but on experimental grounds, not logical grounds.)
Why not observe proper protocol for posting on this Message Board and, instead of links to your own web site (which are discouraged here), provide a detailed comparison of your reasoning with that in the Meta Science treatment of the twins paradox available on this web site at metaresearch.org/cosmology/gravity/gps-twins.asp ? The peer-reviewed and published Meta Science treatment introduces a very instructive tool: It uses a GPS-style Earth clock as a second clock on board the traveling twin's spaceship so the traveler can always directly compare his own time to Earth time.
Such a comparison of your approach to ours could be helpful for pointing out errors or potential improvements in at least one of the two approaches. Simply making claims and posting foreign links is unlikely to go anywhere useful, especially because so many people fail to understand relativity properly, with the result that most major journals will no longer accept papers "logically disproving SR". -|Tom|-
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16 years 11 months ago #20712
by Thomas
Replied by Thomas on topic Reply from Thomas Smid
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
<br />This logically proves the impossibility of timedilation and thus the logical and mathematical inconsistency of the Lorentz transformation<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Perfect symmetry does no such thing, as anyone who takes the time to understand SR can readily see. (Remember, I think SR and time dilation are wrong, but on experimental grounds, not logical grounds.)
Why not observe proper protocol for posting on this Message Board and, instead of links to your own web site (which are discouraged here), provide a detailed comparison of your reasoning with that in the Meta Science treatment of the twins paradox available on this web site at metaresearch.org/cosmology/gravity/gps-twins.asp ? The peer-reviewed and published Meta Science treatment introduces a very instructive tool: It uses a GPS-style Earth clock as a second clock on board the traveling twin's spaceship so the traveler can always directly compare his own time to Earth time.
Such a comparison of your approach to ours could be helpful for pointing out errors or potential improvements in at least one of the two approaches. Simply making claims and posting foreign links is unlikely to go anywhere useful, especially because so many people fail to understand relativity properly, with the result that most major journals will no longer accept papers "logically disproving SR". -|Tom|-
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
I beg to disagree. It is not necessary to understand SR in order to prove the mere fact <i>that</i> time dilation is logically inconsistent. If you have an absolutely symmetric situation where A can in all respects make the same claims as B, then it is logically impossible that clocks should show a different time when compared. The links I gave then merely explain (for the interested reader) <i>why</i> this logically inconsistent prediction of SR arises.
Thomas
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
<br />This logically proves the impossibility of timedilation and thus the logical and mathematical inconsistency of the Lorentz transformation<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Perfect symmetry does no such thing, as anyone who takes the time to understand SR can readily see. (Remember, I think SR and time dilation are wrong, but on experimental grounds, not logical grounds.)
Why not observe proper protocol for posting on this Message Board and, instead of links to your own web site (which are discouraged here), provide a detailed comparison of your reasoning with that in the Meta Science treatment of the twins paradox available on this web site at metaresearch.org/cosmology/gravity/gps-twins.asp ? The peer-reviewed and published Meta Science treatment introduces a very instructive tool: It uses a GPS-style Earth clock as a second clock on board the traveling twin's spaceship so the traveler can always directly compare his own time to Earth time.
Such a comparison of your approach to ours could be helpful for pointing out errors or potential improvements in at least one of the two approaches. Simply making claims and posting foreign links is unlikely to go anywhere useful, especially because so many people fail to understand relativity properly, with the result that most major journals will no longer accept papers "logically disproving SR". -|Tom|-
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">
I beg to disagree. It is not necessary to understand SR in order to prove the mere fact <i>that</i> time dilation is logically inconsistent. If you have an absolutely symmetric situation where A can in all respects make the same claims as B, then it is logically impossible that clocks should show a different time when compared. The links I gave then merely explain (for the interested reader) <i>why</i> this logically inconsistent prediction of SR arises.
Thomas
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16 years 11 months ago #19376
by tvanflandern
Replied by tvanflandern on topic Reply from Tom Van Flandern
<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Thomas</i>
<br />It is not necessary to understand SR in order to prove the mere fact <i>that</i> time dilation is logically inconsistent. If you have an absolutely symmetric situation where A can in all respects make the same claims as B, then it is logically impossible that clocks should show a different time when compared.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If you have no interest in learning SR, you are welcome to conduct your life any way you choose. But if you did have some interest in communicating with others on this subject, then you must learn the theory.
In SR, time is not a thing that exists for all observers. It is a frame-dependent concept, and is location-dependent within frames. Read the paper at the link I provided, and you will see your error of logic. There is <i>no such thing as "remote simultaneity"</i> in SR. If you and I are co-located at some instant, but have a high relative speed, we will not agree about what time it is right "now" in Tokyo, and neither of us will be wrong.
Take an Earth clock along on the trip and you can see what happens. In SR, clocks in other frames tick slower than our own, but frame time passes by faster than our own. And that situation is perfectly symmetric. The traveling twin exchanges elapsed clock time for elapsed frame time when direction reversal occurs, even when that is done by switching twins without any acceleration.
Learn it or ignore it, but don't claim some sort of intellectual superiority based on "logic" that denies the two premises on which SR is built. -|Tom|-
<br />It is not necessary to understand SR in order to prove the mere fact <i>that</i> time dilation is logically inconsistent. If you have an absolutely symmetric situation where A can in all respects make the same claims as B, then it is logically impossible that clocks should show a different time when compared.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If you have no interest in learning SR, you are welcome to conduct your life any way you choose. But if you did have some interest in communicating with others on this subject, then you must learn the theory.
In SR, time is not a thing that exists for all observers. It is a frame-dependent concept, and is location-dependent within frames. Read the paper at the link I provided, and you will see your error of logic. There is <i>no such thing as "remote simultaneity"</i> in SR. If you and I are co-located at some instant, but have a high relative speed, we will not agree about what time it is right "now" in Tokyo, and neither of us will be wrong.
Take an Earth clock along on the trip and you can see what happens. In SR, clocks in other frames tick slower than our own, but frame time passes by faster than our own. And that situation is perfectly symmetric. The traveling twin exchanges elapsed clock time for elapsed frame time when direction reversal occurs, even when that is done by switching twins without any acceleration.
Learn it or ignore it, but don't claim some sort of intellectual superiority based on "logic" that denies the two premises on which SR is built. -|Tom|-
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