by cos
P: 212
 Quote by DaleSpam Correct. It shows that clock A does not physically "go more slowly" than clock B, it just takes a shorter path through spacetime. But along this path clock A still ticks over at the same rate as clock B does along its path (i.e. both tick at 1 second/light-second).
So would a similar diagram show that the equatorial clock to which Einstein referred in chapter 4 does not, as he suggested 'go more slowly than a clock at one of the poles'?
Mentor
P: 17,329
 Quote by cos So would a similar diagram show that the equatorial clock to which Einstein referred in chapter 4 does not, as he suggested 'go more slowly than a clock at one of the poles'?
Unfortunately, Einstein was wrong about that, a clock at the equator does not "go more slowly" than one at the poles*. Here is a little paper 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
P: 212
 Quote by DaleSpam Unfortunately, Einstein was wrong about that, a clock at the equator does not "go more slowly" than one at the poles*. Here is a little paper 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?
 Sci Advisor P: 8,657 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&...esult#PPA10,M1
 P: 77 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 :)
P: 212
 Quote by 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."
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.
Mentor
P: 17,329
 Quote by cos 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 a helix 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.
 P: 1,060 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
P: 1,544
 Quote by cos 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.
P: 212
 Quote by DaleSpam 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 a helix 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.
P: 77
 Quote by cos 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.
P: 421
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.
P: 8,470
 Quote by phyti 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.
Quote by phyti
 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).
P: 212
 Quote by Idjot 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.
P: 212
 Quote by 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
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.
P: 8,470
 Quote by cos 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.
 Sci Advisor P: 8,657 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.
P: 212
 Quote by 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.
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.

 Related Discussions Special & General Relativity 9 Special & General Relativity 16 Special & General Relativity 10 Special & General Relativity 105