Twin Paradox: Einstein's Explanation and Alternative Interpretations

[cos]

Unfortunately, Einstein was wrong about that, a clock at the equator does not "go more slowly" than one at the poles*. Here is http://arxiv.org/PS_cache/gr-qc/pdf/0501/0501034v2.pdf" you might like on the subject, it is very light on math. Basically, the SR and GR effects cancel each other out.

*I.e. no net transverse/gravitational Doppler effect

OK I read that paper. I had assumed that Einstein's comment "under otherwise identical conditions." would have (albeit, perhaps, inadvertently) allowed for the effects of gravity (i.e. altitude and the Earth's greater diameter at the equator) but what about Einstein's similar comment in relation to a clock that moves in a closed curve around an 'at rest' clock?

Does the traveled clock end up, as Einstein suggested, lagging behind the 'stationary' clock?

Does that traveled clock 'go more slowly' than the stationary clock in order to end up lagging behind same?

Did the Hafele-Keating clocks 'go more slowly' than the laboratory clocks? i.e. did they tick over at a slower rate than the laboratory clocks after gravitational time variation effects were taken into account and removed from the equations as Will's did in 'Was Einstein Right?'?

I'm specifically talking about what physically happened to those clocks not what a Minkowski spacetime diagram 'shows'.

You wrote - "...the SR and GR effects cancel each other out." however was Einstein's comment regarding clocks at the equator and at one of the poles applicable to SR?

Was the paper to which you refer published in a peer-reviewed science journal? Has it been accepted by the physics community?

 

[atyy]

Audoin and Guinot, p9, 10:

"The postulate leaves no room for differential ageing of the various natural phenomena. ... Although it has never yet been found to fail, it may one day be brought into question by experimental progress."

"...Einstein's general relativity has appeared on the scene. According to this theory, only local time can be directly measured with a clock. In other words, it is the proper time of this clock or an observer in the immediate vicinity that is measured. The time ...over an extended region of space including, for example, the Solar System, is just a coordinate time freely chosen ... and to which no physical reality is attributed."

http://books.google.com/books?hl=en...=X&oi=book_result&resnum=1&ct=result#PPA10,M1

 

[Idjot]

Shouldn't clocks on opposite sides of the planet serve to test this theory? They are facing away from one another and both under 1G. According to Relativity, what's the difference?
Gravity is acceleration. The real challenge is how to actually observe one from the perspective of the other. The "paradox" is really only an observatory phenomena. Only if one of them accelerates more than the other will there be any real dilation and that will take place on the clock under more acceleration (resulting in a higher velocity relative to 'Big Ben'). When the faster clock returns to 1G all observers will notice the dilation effect on the faster clock, even relative to the paradox. Wrap your head around that :)

 

[cos]

Audoin and Guinot, p9, 10:

"The postulate leaves no room for differential ageing of the various natural phenomena. ... Although it has never yet been found to fail, it may one day be brought into question by experimental progress."

"...Einstein's general relativity has appeared on the scene. According to this theory, only local time can be directly measured with a clock. In other words, it is the proper time of this clock or an observer in the immediate vicinity that is measured. The time ...over an extended region of space including, for example, the Solar System, is just a coordinate time freely chosen ... and to which no physical reality is attributed."

On the basis that your first paragraph relates to Poincare's postulate and the second paragraph relates to general theory I assume that this message is not in relation to my argument which is specifically in relation to special theory.

 

[Dale]

what about Einstein's similar comment in relation to a clock that moves in a closed curve around an 'at rest' clock?

Does the traveled clock end up, as Einstein suggested, lagging behind the 'stationary' clock?

Does that traveled clock 'go more slowly' than the stationary clock in order to end up lagging behind same?

Such a scenario would be much better as it deals only with SR effects and does not add GR effects into the mix. For convenience let us speak of clock A on the rim of a rotating "wheel type" space station, and clock B in the hub. If we were to draw the spacetime diagram we would get http://upload.wikimedia.org/wikipedia/commons/thumb/8/87/060322_helix.svg/250px-060322_helix.svg.png" like the one posted by JesseM in post 133 as the worldline of clock A. The worldline of clock B would simply be the axis of the helix.

Note, that clocks A and B never meet so you have to define the endpoints of each worldline completely separately. One typical choice would be to choose the intersection of each worldline with a "beginning" and an "ending" hypersurface of simultaneity, usually defined using Einstein synchronization in the rest frame of the hub.

Now, if you do that you find that the interval along worldline A is shorter than the interval along worldline B. So if clock A and B are set to zero at the beginning then clock A will read less than clock B at the ending. Each clock still measures the same 1 second/light-second along their respective paths, but clock A just travels a shorter path.

In case you missed them in the paragraph above that is a yes for your "lagging" question and a no for your "go more slowly" question. In (Euclidean) geometrical terms this scenario is analogous to the fact that the distance from the Atlantic coast to the Pacific coast is shorter when measured from Veracruz to Acapulco than when measured from New York to Los Angeles.

 

[matheinste]

Hello cos.

I feel that eventually this frame will slowly come to an end because people will realize that you cannot be convinced by logical reasoning. You will feel able to claim you are right by default because people have given up, not because they think you are right but through sheer frustration. I hereby claim the dubious honour of being the first to give up, unless someone in some other frame has already done so.

Matheinste

 

[RandallB]

On the basis of C's point of view that B 'goes more slowly' (i.e. ticks over at a slower rate) than A then, when the clocks are bought together, B should lag behind A but that's not what Einstein said! He specifically stated the complete opposite - that A lags behind B!

Would you please explain the difference between A moving the distance A to B at v (the astronaut's return trip)and A moving the distance B to A at v (the astronaut's outward bound trip)? Einstein's equation applies equally to both trips!

Could you please explain why you are of the opinion that Einstein's equation .5tv²/c² applies to a journey in one direction but not to a journey over an identical distance in the opposite direction?

I have no interest in 'understanding SR' per se but only in what Einstein wrote in chapter 4 and its application to an astronaut's out-and return journey.

All of that is made clear when you just do the simple math from all 5 “C” observer views. That will help you understand SR!
But you make it clear you do not want to understand SR
--- I can only assume you intentionally just want to be argumentative and I do see why you came to these forums at all.
Waste others time but not mine - I’ll unsubscribe from this thread.
IMO a mentor should lock it simply as a lost cause; you are not listening to anyone.

 

[cos]

Such a scenario would be much better as it deals only with SR effects and does not add GR effects into the mix. For convenience let us speak of clock A on the rim of a rotating "wheel type" space station, and clock B in the hub. If we were to draw the spacetime diagram we would get http://upload.wikimedia.org/wikipedia/commons/thumb/8/87/060322_helix.svg/250px-060322_helix.svg.png" like the one posted by JesseM in post 133 as the worldline of clock A. The worldline of clock B would simply be the axis of the helix.

Note, that clocks A and B never meet so you have to define the endpoints of each worldline completely separately. One typical choice would be to choose the intersection of each worldline with a "beginning" and an "ending" hypersurface of simultaneity, usually defined using Einstein synchronization in the rest frame of the hub.

Now, if you do that you find that the interval along worldline A is shorter than the interval along worldline B. So if clock A and B are set to zero at the beginning then clock A will read less than clock B at the ending. Each clock still measures the same 1 second/light-second along their respective paths, but clock A just travels a shorter path.

In case you missed them in the paragraph above that is a yes for your "lagging" question and a no for your "go more slowly" question. In (Euclidean) geometrical terms this scenario is analogous to the fact that the distance from the Atlantic coast to the Pacific coast is shorter when measured from Veracruz to Acapulco than when measured from New York to Los Angeles.

Whilst you point out that clocks A and B never meet this does not comply with Einstein's chapter 4 depiction which starts off with two synchronous clocks alongside each other. One of them moves in a closed curve until it returns to its original location and is once again alongside the other clock where it is found that the traveled clock will lag behind the clock that has remained at rest.

On the basis that they do meet we, presumably, do not "have to define the endpoints of each worldline completely separately."

The rest of your post applies to the mathematically determined Minkowski spacetime concept which, as I have pointed out on several occasions, is not - according to Einstein - reality.

I note that you declined to respond to my question regarding the HKX and other salient points so I will repeat same:-

***********
Did the Hafele-Keating clocks 'go more slowly' than the laboratory clocks? i.e. did they tick over at a slower rate than the laboratory clocks after gravitational time variation effects were taken into account and removed from the equations as Will's did in 'Was Einstein Right?'?

I'm specifically talking about what physically happened to those clocks not what a Minkowski spacetime diagram 'shows'.

Was the paper to which you refer published in a peer-reviewed science journal? Has it been accepted by the physics community?

***********

Here is another question which although applicable to GR also applies to Einstein's chapter 4 SR depiction specifically a polygonal line clock A relocation but which has similarly been ignored by others in this thread - an observer is located on top of a mountain; he notes that a clock at that location ticks over at the same rate as his own clock which is obviously ticking over at it's 'normal' rate. He moves to sea-level and again notes that a clock at that location ticks over at the same rate as his own clock - which is still ticking over at it's 'normal' rate.

Does he insist that the clock at the top of the mountain and the clock at sea-level are ticking over at the same rate as each other as determined by his observations or does he apply his knowledge of the Wallops Island experiment and general theory and realize that although the sea-level clock appears to be ticking over at the same rate as the mountain top clock it is physically ticking over at a slower rate?

An astronaut comes to a stop at the end of his outward-bound journey and notes the rate of operation of his clock. He then accelerates and again looks at his clock which, although appearing to be ticking over at a normal rate, is physically ticking over at a slower rate than it was before he started accelerating in the same way that the above mentioned mountain-descending observer's clock ticks over at a slower rate than it did before he started moving.

My specific interest is in relation to what is physically happening to the clocks!

Although I am of the opinion that this analogy is highly relevant it will most likely be emitted from your response as were the above-referred to salient points.

 

[Idjot]

Although I am of the opinion that this analogy is highly relevant it will most likely be emitted from your response as were the above-referred to salient points.

That's "omitted" not "emitted". You must have a non-qwerty board.

Sorry, I couldn't help myself.

 

[phyti]

JesseM post 187;

Since the initial distance between them is 12 light-seconds in this frame, it will take 12/0.8c = 15 seconds for B to catch up with A.

The shrinking distance is the alternate explanation by B instead of his time dilation. [.6*(20/.8)=15]

During this time A will advance forward by 15 seconds but B will only advance forward by 15*0.6 = 9 seconds.

Here you are applying time dilation twice! You have done this before on previous posts.

A is not moving at .8c, therefore his clock will not experience B's dilation, and B cannot apply his dilation to A's clock.

 

[JesseM]

The shrinking distance is the alternate explanation by B instead of his time dilation. [.6*(20/.8)=15]

Where did you get the idea that it is the "alternate explanation by B", or that it is supposed to be an alternative to time dilation? It is simply an expression of how length contraction works in the frame where B is moving at 0.8c.

During this time A will advance forward by 15 seconds but B will only advance forward by 15*0.6 = 9 seconds.

Here you are applying time dilation twice! You have done this before on previous posts.

A is not moving at .8c, therefore his clock will not experience B's dilation, and B cannot apply his dilation to A's clock.

Your language is completely confusing, I'm not saying anything about how B would "apply his time dilation" to anything (I have no idea what you mean by that phrase), I'm talking about what's going on with both clocks in the frame where B is moving at 0.8c. Can you please stop talking about what is "experienced" by one object or another or another, since I've already told you very emphatically I'm not talking about that at all (and your own ideas on this subject seem confused to me), and stick to what I was talking about in post #31, namely how things work in this particular inertial frame where B is always moving at 0.8c?

Do you agree that in the frame where B is moving at 0.8c, the ticks of B's clock are slowed down by a factor of 0.6, so when 15 seconds of coordinate time pass in this frame, B ticks forward by 15*0.6 = 9 seconds? Do you agree that after A comes to rest in this frame, A's clock thereafter ticks at the normal rate in this frame, so when 15 seconds of coordinate time pass in this frame, A ticks forward by 15 seconds? Do you agree that if B is attached to a rod which is 20 ls long in B's rest frame (which is also the rod's rest frame, call it frame #1), then in this second frame where B and the rod are moving at 0.8c (call this frame #2), the rod will be 12 ls long? Please tell me specifically whether you disagree with any of these 3 statements (if you do, then there is some error in your understanding of inertial frames in SR).

 

[cos]

That's "omitted" not "emitted". You must have a non-qwerty board.

Sorry, I couldn't help myself.

Don't apologise!

Thanks for the correction. The error was due to my typical rash hastiness in responding.

 

[cos]

Hello cos.

I feel that eventually this frame will slowly come to an end because people will realize that you cannot be convinced by logical reasoning. You will feel able to claim you are right by default because people have given up, not because they think you are right but through sheer frustration. I hereby claim the dubious honour of being the first to give up, unless someone in some other frame has already done so.

Matheinste

I am of the opinion that if this forum had been in existence in 1905 and Einstein had posted his theory in same there would have been numerous (and harsh) responses from Newtonians trying to convince him of the errors of his ideas using logical reasoning and quoting the extant laws however the support provided by Max Planck would similarly have forced those critics to give up in sheer frustration.

One down - 3(?) to go.

 

[JesseM]

I am of the opinion that if this forum had been in existence in 1905 and Einstein had posted his theory in same there would have been numerous (and harsh) responses from Newtonians trying to convince him of the errors of his ideas using logical reasoning and quoting the extant laws however the support provided by Max Planck would similarly have forced those critics to give up in sheer frustration.

Einstein in 1905 probably would have been willing to address any reasoned arguments made against him, instead of ordering people not to repeat arguments he didn't like to hear (but hadn't actually addressed) and then giving them the silent treatment if they didn't obey his commands.

 

[atyy]

Below are quotes from Einstein's 1905 "On the Electrodynamics of Moving Bdies". Bolding added by me.

http://www.fourmilab.ch/etexts/einstein/specrel/www/
http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf

Section 1: And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or--what comes to the same thing--to evaluate the times of events occurring at places remote from the watch. ... We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" ... It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it "the time of the stationary system."

Section 2: So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.

Section 4: What is the rate of this clock, when viewed from the stationary system?

Edit: I do not wish to give the impression that truth is determined by quoting authority. But I believe the quotes are helpful for putting the discussion in context.

 

[cos]

Below are quotes from Einstein's 1905 "On the Electrodynamics of Moving Bdies". Bolding added by me.

http://www.fourmilab.ch/etexts/einstein/specrel/www/
http://www.pro-physik.de/Phy/pdfs/ger_890_921.pdf

Section 1: And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or--what comes to the same thing--to evaluate the times of events occurring at places remote from the watch. ... We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" ... It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it "the time of the stationary system."

Section 2: So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.

Section 4: What is the rate of this clock, when viewed from the stationary system?

Edit: I do not wish to give the impression that truth is determined by quoting authority. But I believe the quotes are helpful for putting the discussion in context.

It is refreshing change to find a response that is attempting to clarify the situation rather than resorting to personal attacks or obfuscate the discussion with totally irrelevant materiel however your quoted Section 1 refers to "to connect in time series of events occurring at different places." and Section 2 "the concept of simultaneity." and due to the fact that my posting has no relationship to these concepts they have no application to my argument.

Re: Section 4: What is the rate of which clock? My reference is only to the astronaut's clock when viewed in his reference frame.

I trust that I did not give the impression that, in my opinion, truth is determined by quoting authority. The only 'truth' to which I refer is the fact that it is true that Einstein presented the quoted depictions.

 

[JesseM]

Re: Section 4: What is the rate of which clock? My reference is only to the astronaut's clock when viewed in his reference frame.

If A is the astronaut, A is a non-inertial observer, and there is no single non-inertial coordinate system that qualifies as his "frame". Just because A and B were initially synchronized in B's inertial rest frame, that does not mean that there is any physical justification for saying they must have been initially synchronized in the non-inertial "frame" of A (you could construct a non-inertial coordinate system where A is at rest at all times and A and B were initially synchronized, but you could construct myriad other non-inertial coordinate systems where A was at rest at all times and A and B were not initially synchronized, none of them would uniquely qualify as A's 'frame').

 

[Idjot]

It is a ‘contradiction’ of the laws of physics that the astronaut, having accelerated to an instantaneous velocity of close to the speed of light (thereupon generating a gamma factor of 40,000), would be of the opinion that the planet is spinning on its axis at around 64 million k-h.

I've been following this thread for awhile and I don't have any elaborate quotes or formulas or insults to add but I am curious about this statement from quite a few pages ago when this thread was young and innocent:

As to the above quote: Common sense says that if the astronaut's time has slowed in passing everything else should appear to be moving faster. He and his his brain receptors would have to slow down relative to Earth time and because light would remain constant Earth would have to appear to him be spinning faster. But the Paradox says that he will observe Earth spinning more slowly, right? Which one makes more sense? As contradictory as it seems to you by law for him to see it, if the astronaut were to count those revolutions, when he returned to Earth the number would have been right. Many days would have passed to his few. But you say the laws say he wouldn't see things correctly until he returned, right? Are you saying he would view Earth spinning more slowly until his return?
Don't get me wrong though because I think I agree with you.

 

[Dale]

Whilst you point out that clocks A and B never meet this does not comply with Einstein's chapter 4 depiction which starts off with two synchronous clocks alongside each other. One of them moves in a closed curve until it returns to its original location and is once again alongside the other clock where it is found that the traveled clock will lag behind the clock that has remained at rest.

On the basis that they do meet we, presumably, do not "have to define the endpoints of each worldline completely separately."

The rest of your post applies to the mathematically determined Minkowski spacetime concept which, as I have pointed out on several occasions, is not - according to Einstein - reality.

That is simply a twins scenario, which I already covered as did others. In any case, at the risk of being repetitive, the geometric approach is the same as it has been all the other times. The two twins take different paths between the separation and reunion events. One of those paths has a shorter interval than the other, but each clock runs at 1 second/light-second along their respective paths. Again, it is nothing more than one clock taking a shortcut through spacetime.

I note that you declined to respond to my question regarding the HKX and other salient points so I will repeat same:-

***********
Did the Hafele-Keating clocks 'go more slowly' than the laboratory clocks? i.e. did they tick over at a slower rate than the laboratory clocks after gravitational time variation effects were taken into account and removed from the equations as Will's did in 'Was Einstein Right?'?

I'm specifically talking about what physically happened to those clocks not what a Minkowski spacetime diagram 'shows'.

Again, this is simply another twins scenario, same explanation as above.

Was the paper to which you refer published in a peer-reviewed science journal? Has it been accepted by the physics community?

Obviously yes. Don't you recognize arXiv?

Here is another question which although applicable to GR also applies to Einstein's chapter 4 SR depiction specifically a polygonal line clock A relocation but which has similarly been ignored by others in this thread - an observer is located on top of a mountain; he notes that a clock at that location ticks over at the same rate as his own clock which is obviously ticking over at it's 'normal' rate. He moves to sea-level and again notes that a clock at that location ticks over at the same rate as his own clock - which is still ticking over at it's 'normal' rate.

Does he insist that the clock at the top of the mountain and the clock at sea-level are ticking over at the same rate as each other as determined by his observations or does he apply his knowledge of the Wallops Island experiment and general theory and realize that although the sea-level clock appears to be ticking over at the same rate as the mountain top clock it is physically ticking over at a slower rate?

An astronaut comes to a stop at the end of his outward-bound journey and notes the rate of operation of his clock. He then accelerates and again looks at his clock which, although appearing to be ticking over at a normal rate, is physically ticking over at a slower rate than it was before he started accelerating in the same way that the above mentioned mountain-descending observer's clock ticks over at a slower rate than it did before he started moving.

The geometric approach to relativity always applies. It is always the same answer. Pick any worldline in any scenario through any spacetime and calculate the interval along the worldline in order to get the proper time elapsed on a clock. All clocks tick at their normal rate along any worldline, and it is only the interval along which they travel that differs. I thought you would understand this by now. This simplicity and generality is the beauty and power of the spacetime geometric approach.

Although I am of the opinion that this analogy is highly relevant it will most likely be emitted from your response as were the above-referred to salient points.

I am trying to help you here, but you have to understand that your posts are long and rambling with lots of repetitive questions. You cannot reasonably expect me to re-answer the same question that has already been answered a bunch of times. Your claim that anyone here is avoiding your questions is patently absurd. It makes me think that you are not even making a good-faith effort to understand our various points. You have not been ignored; you have been answered and re-answered with multiple people trying many different approaches to get through to you as you ask and re-ask the same questions over and over.

My specific interest is in relation to what is physically happening to the clocks!

I have noticed that you use this phrase fairly often, usually with the word "physically" in italics. When most physicists use the word "physically" they mean something that can be experimentally measured and is coordinate independent. The value of the geometric approach is exactly that. The spacetime interval is both coordinate independent and directly measurable so it is "physical". That is precisely why I have been presenting it to you, because it is physical. I get the impression that you think geometry is non-physical. I don't know why you would think that, but in fact geometry lies at the heart of all physics from Newton's laws to GR.

This is another important question, please respond. What do you mean by "physical" if not the usual meaning of something experimentally measurable and coordinate independent?

 

[jtbell]

It looks like neither side is going to budge and the participants are simply getting testier and testier, so there is no useful purpose in continuing this discussion.