Twin Paradox: Einstein's Explanation and Alternative Interpretations

[Dale]

whilst I appreciate that you are, perhaps, providing a more general conceptual tool in relation to the twin paradox it is not the 'twin paradox' per se in which I am particularly interested

As I already mentioned previously the utility of Minkowski geometry is not in any way limited to the twin paradox. It is generally applicable to all scenarios, including the section 4 that has captivated your attention, the astronaut scenario, the mountain scenario, and any other scenario you will invent or encounter. It is a complete mathematical framework for attacking any problem in special relativity with immediate application to general relativity also.

In many fields of study one examines special case solutions because the more general approach is overly cumbersome or otherwise intractable. You take appropriate limits and examine the results in the hope of gaining some insight, but you recognize that your insights are inherently approximations of the intractable general approach and can fail. Such is not the case for Minkowski geometry, it is both completely general and more straightforward than other approaches to special relativity. It is one of the rare instances where you do not need to sacrifice generality for convenience.

Although Einstein's chapter 4 is 'one particular section of one particular work' I fail to see any reason why it should be ignored or not taken into consideration.
...
Ignoring, or in our discussions not taking into account, 'one particular section of one particular work' will not make it go away.

I never suggested you ignore it nor did I suggest it was wrong. I simply provided a better conceptual framework for understanding it.

Do you think it is reasonable to ignore such a useful tool simply because it was not explicitly presented in the seminal manuscript?

 

[cos]

Once a reference frame is stated to be "real", the traveling clock is the one that "really" slows - in the sense that it lags.

I don't understand what you mean by 'Once a reference frame is stated to be "real'" but does your comment that 'the traveling clock is the one that "really" slows - in the sense that it lags.' mean not just that the traveling clock (Einstein's clock A) is found to lag behind the 'stationary' clock (Einstein's clock B) when A arrives at B's location or does it mean that the traveling clock physically 'goes more slowly than' the stationary clock whilst it is moving? In other words - that the traveling clock ticks over at a slower rate than it did before it started moving - that the traveling clock incurs time dilation whilst it is moving?

If so, then an observer accompanying clock A is fully entitled to realize that although his clock appears to be ticking over at the same rate as it was before they started moving that it is, in reality, ticking over at a slower rate than it was before they started moving.

If this is correct then the claim in relation to which I made the original posting - that the astronaut insists that his clock is not ticking over at a slower rate than it did before he started moving back to the planet but that it is the Earth clock (Einstein's clock B) that is physically ticking over at a faster rate than it was before he started moving and only during his period of acceleration is, as I suspected, in contradiction of special theory - specifically chapter 4.

The astronaut's concept of 'reality' is not limited to what he sees nor even to what he, applying the Lorentz transformations, predicts as some people insist but should also take into account what he knows in the same way that whilst a person sees a steel rod appear to bend at the surface of a body of water this is not taking place in reality- the rod does not bend.

 

[cos]

I never suggested you ignore it nor did I suggest it was wrong. I simply provided a better conceptual framework for understanding it.

By 'understanding it' are you referring to the twin paradox per se or to Einstein's reference to clocks A and B of K and the subsequent relocation of A?

Although it may be a better conceptual framework I (as one of those annoying self-taught people including Faraday who was similarly ignorant of mathematical processes) find the Minkowski concepts far more complicated than Einstein's depiction.

Do you think it is reasonable to ignore such a useful tool simply because it was not explicitly presented in the seminal manuscript?

On the basis that I, due to my ignorance, prefer to keep things as simple as possible - yes.

 

[atyy]

I don't understand what you mean by 'Once a reference frame is stated to be "real'" but does your comment that 'the traveling clock is the one that "really" slows - in the sense that it lags.' mean not just that the traveling clock (Einstein's clock A) is found to lag behind the 'stationary' clock (Einstein's clock B) when A arrives at B's location or does it mean that the traveling clock physically 'goes more slowly than' the stationary clock whilst it is moving? In other words - that the traveling clock ticks over at a slower rate than it did before it started moving - that the traveling clock incurs time dilation whilst it is moving?

If so, then an observer accompanying clock A is fully entitled to realize that although his clock appears to be ticking over at the same rate as it was before they started moving that it is, in reality, ticking over at a slower rate than it was before they started moving.

If this is correct then the claim in relation to which I made the original posting - that the astronaut insists that his clock is not ticking over at a slower rate than it did before he started moving back to the planet but that it is the Earth clock (Einstein's clock B) that is physically ticking over at a faster rate than it was before he started moving and only during his period of acceleration is, as I suspected, in contradiction of special theory - specifically chapter 4.

The astronaut's concept of 'reality' is not limited to what he sees nor even to what he, applying the Lorentz transformations, predicts as some people insist but should also take into account what he knows in the same way that whilst a person sees a steel rod appear to bend at the surface of a body of water this is not taking place in reality- the rod does not bend.

The statement of a reference frame is crucial for any of the statements in your first two paragraphs to make sense, let alone be true or false. They are true in a particular reference frame. That is why I said, "Once a reference frame is stated to be 'real'".

An ideal clock does not incur time dilation only at the instant of acceleration.

Your example of a rod that appears bent illustrates that it is crucial to state the reference frame. Just because a person sees a rod bend at the surface of the water does not mean that the rod does not bend. He needs to know the angle at which he is looking relative to the surface of the water and the angle at which the rod enters the water. Similarly, one should always state the reference frame when talking about time dilation as real, for without it, the astronaut will never be able to know reality.

 

[cos]

The statement of a reference frame is crucial for any of the statements in your first two paragraphs to make sense, let alone be true or false. They are true in a particular reference frame. That is why I said, "Once a reference frame is stated to be 'real'".

You didn’t answer my question:-

“I don't understand what you mean by 'Once a reference frame is stated to be "real'" but does your comment that 'the traveling clock is the one that "really" slows - in the sense that it lags' mean not just that the traveling clock (Einstein's clock A) is found to lag behind the 'stationary' clock (Einstein's clock B) when A arrives at B's location or does it mean that the traveling clock physically 'goes more slowly than' the stationary clock whilst it is moving? In other words - that the traveling clock ticks over at a slower rate than it did before it started moving - that the traveling clock incurs time dilation whilst it is moving?”

I try to the very best of my ability to respond directly to questions asked by (most) people and I think it is only courteous for them to reciprocate.

What do you mean by “The statement of a reference frame...”?

In that paragraph I intimated that if the traveling clock physically ticks over at a slower rate in its own reference frame than it did before it started moving then it physically ticks over at a slower rate than it did before it started moving regardless of the possibility that somebody viewing it from another reference frame may, or may not, determine otherwise!

The point of view of, or determinations made from, another reference frame has absolutely nothing whatsoever to do with what the clock does only with what they think the clock is doing!

I have absolutely no interest whatsoever in what an observer in another reference frame determines or does not determine on the basis that his determinations (observations; measurements; predictions) have absolutely NO physical affect on that clock!

My second paragraph to which you referred was:-

“If so, then an observer accompanying clock A is fully entitled to realize that although his clock appears to be ticking over at the same rate as it was before they started moving that it is, in reality, ticking over at a slower rate than it was before they started moving.”

Are you unable to see that when I referred to what an observer accompanying clock A realizes that I am talking about what takes place in THAT observer’s reference frame?

An ideal clock does not incur time dilation only at the instant of acceleration.

I did NOT say that it DOES!

A clock starts to incur time dilation at the instant of acceleration!

Your example of a rod that appears bent illustrates that it is crucial to state the reference frame. Just because a person sees a rod bend at the surface of the water does not mean that the rod does not bend. He needs to know the angle at which he is looking relative to the surface of the water and the angle at which the rod enters the water.

I hate to disillusion you but a steel rod does NOT bend when it is placed into a tank of water!

The observer KNOWS the angle at which he is looking relative to the surface of the water AND the angle at which the rod enters the water because he is LOOKING AT the event!

Similarly, one should always state the reference frame when talking about time dilation as real, for without it, the astronaut will never be able to know reality.

In my first paragraph where I talked about the moving clock ‘going more slowly than’ the stationary clock the same phenomenon applies to observers in both reference frames. Clock A ‘goes more slowly than’ clock B as far as both observers are concerned!

In my second paragraph I specifically referred to what an observer accompanying clock A determines and if that’s not ‘stating the reference frame’ (i.e. identifying same) I fail to see what else you would call it!

 

[JesseM]

In that paragraph I intimated that if the traveling clock physically ticks over at a slower rate in its own reference frame than it did before it started moving then it physically ticks over at a slower rate than it did before it started moving regardless of the possibility that somebody viewing it from another reference frame may, or may not, determine otherwise!

Of course, "its own reference frame" needs clarification. In SR one typically looks only at inertial reference frames (because these are the only frames where SR laws such as 'moving clocks run slow' are guaranteed to apply), and there is no inertial frame where the clock is at rest both before and after the acceleration. You can look at the frame of an inertial observer who was at rest relative to the clock before it accelerated, and in this frame the clock ticks slower after it accelerates; or, you can look at the frame of an inertial observer who is at rest relative to the clock after it accelerated, and in this frame the clock was ticking slower before the acceleration. You may choose to ignore my posts, but hopefully others can see that your statement above is unclear without clarification about which of these two frames is being called the clock's "own reference frame" (unless you are talking about a non-inertial frame, in which case as I said the standard laws about moving clocks running slow can no longer be expected to apply in this frame).

 

[Fredrik]

The clock's "own reference frame" can be interpreted in more than one way. Two options occur to me:

1. The co-moving inertial frame.

2. The local non-inertial frame constructed by taking the world line to be the time axis, with proper time as the time coordinate, and letting the spatial coordinates be defined by the "radar" definition of simultaneity in the largest neighborhood of the world line where this is possible.

The funny thing about these two options is that both of them say the same thing about the ticking rate of any clock in its own reference frame: It's always the same. No clock can have a higher ticking rate in its own frame than any other. (How would you define "ticking rate" if not as "proper time"/"coordinate time"? In both 1 and 2 above, coordinate time is proper time, so the ticking rate is always 1).

 

[Dale]

By 'understanding it' are you referring to the twin paradox per se or to Einstein's reference to clocks A and B of K and the subsequent relocation of A?

I thought I was very clear that I am referring to understanding all of SR including Einstein's reference to clocks A and B, the twin paradox, and everything else. This is what I meant by "generally applicable" above. I have repeated this statement at least 3 times already. The geometric approach applies to your question as well as to everything else in SR.

Although it may be a better conceptual framework I (as one of those annoying self-taught people including Faraday who was similarly ignorant of mathematical processes) find the Minkowski concepts far more complicated than Einstein's depiction.

On the basis that I, due to my ignorance, prefer to keep things as simple as possible - yes

That is, frankly, nothing more than an absurd excuse. Einstein's depiction in section 4 used much more math than I have here, so I don't think your excuse is even valid. I have provided you a very non-mathematical and intuitive introduction to Minkowski geometry as it applies to relativity with the analogy to drivers and odometers. This is a simple and powerful analogy that will allow you to intuitively grasp any SR scenario involving a single spatial dimension. If you cannot even make the minimal mental effort required to understand that simple analogy then you really are not that interested in learning SR.

Again, I am willing to answer questions you might have about the analogy and how to apply it. I am sure there are many open points for confusion and I am willing to work with you to clarify them, but so far it seems that you have dismissed it entirely without making any effort.

 

[paw]

As the astronaut starts to accelerate for the return trip he will see his clock continuously appearing to be ticking over at a constant rate however, due to the fact that his velocity (v) is increasing his clock will, in accordance with Einstein's chapter 4 equation (.5tv²/c²), be 'going more slowly' than it was at a lesser instantaneous velocity.

Whether you realize it or not, this statement makes it appear you believe there is some sort of absolute motion. I think that misunderstanding is at the heart of your inability to accept the many correct interpertations you have been given by JesseM, DS et al.

To demonstrate how this statement of yours is meaningless in any physical way, imagine an astronaut in a completely enclosed, inertial spaceship. The astronaut is in free fall within his ship. He cannot in any physical way determine whether he is moving or at rest. Do you agree so far?

Now suppose he ignites the engine and applies 1g accelleration for 1sec. Does he now (do you) think he is going faster than before the acceleration? How would he know?

He had no way of knowing how fast he was moving, or even IF he was moving, to begin with. He also had no way of knowing his orientation wrt any possible motion. All he knows is that he underwent an acceleration. To an outside observer he may have slowed down, speeded up or even stayed at the same speed but changed direction.

So please tell me how could he possibly say his clock 'will be going more slowly' than it was?

I hope you can see from this there is no way to make any statement about clocks ticking more slowly in anything but a relative sense. You MUST specify a reference frame to make any sense at all. And if you accept SR you must also accept that all inertial frames are equally valid so for any frame where clock A is seen to tick more slowly than clock B you can find a frame where B ticks more slowly than A.

This is what JesseM and others have been saying all along and it's why their various analyses from various different frames are valid and correct.

 

[cos]

The clock's "own reference frame" can be interpreted in more than one way. Two options occur to me:

1. The co-moving inertial frame.

This is what I mean by 'in its own reference frame'. In other words, as far as an observer accompanying that clock is concerned.

The funny thing about these two options is that both of them say the same thing about the ticking rate of any clock in its own reference frame: It's always the same. No clock can have a higher ticking rate in its own frame than any other. (How would you define "ticking rate" if not as "proper time"/"coordinate time"? In both 1 and 2 above, coordinate time is proper time, so the ticking rate is always 1).

I refer you to my analogy of an observer at the top of a mountain who moves to sea-level.

In both locations he could be of the opinion that the ticking rate of clocks at those locations is the same as his own clock at those locations thus that the sea-level clock and the mountain top clock are ticking over at the same rate as each other or he could apply his knowledge of gravitational time dilation and realize that what appears to be taking place is not reality. That the sea-level clock, as well as his own clock at that location, are physically ticking over at a slower rate than the mountain top clocks.

I know, full well, that this is applicable to general theory whereas my argument is in relation to special theory however the analogy is in respect to what the observer applying his knowledge determines is taking place.

Similarly, an observer accompanying Einstein's paragraph 1, chapter 4, clock A although of the opinion that the clock appears to be ticking over at the same rate as it was before they started moving it is physically 'going more slowly' than it was before they started moving.

In the same way, when Hafele and Keating conducted the first leg of their experiment they would have been fully justified in realizing that although their clocks appeared to be ticking over at their normal rate their clocks were, in fact, ticking over at a slower rate than they were before the flight commenced - that the eventual difference between their clocks and the laboratory clocks is due to the fact that their clocks physically ticked over at a slower rate than the laboratory clocks NOT that the laboratory clocks ticked over at a faster rate than they did prior to the commencement of the flight.

Having determined that their clocks lag behind the laboratory clocks what other conclusion could they have arrived at other than that their clocks ticked over at a slower rate during the flight than they did before the flight commenced?

Having arrived at B's location and finding that his clock lags behind clock B what conclusion can the observer accompanying clock A in Einstein's paragraph 1, chapter 4, depiction (knowing that prior to his relocation A and B were synchronized) arrive at other than that his clock must have ticked over at a slower rate than clock B?

On the assumption that he realizes that, all appearances to the contrary, his clock did tick over at a slower rate than it did before they started moving if he repeats the experiment he could, during that transit period, realize that whilst the rate of operation of his clock (A) appears to be normal it is, as indicated by his previous trip, physically ticking over at a slower rate than it was before they started moving.

 

[JesseM]

This is what I mean by 'in its own reference frame'. In other words, as far as an observer accompanying that clock is concerned.

Fredrik's option 1 was not really specific enough--it's still not clear whether you're talking about a non-inertial observer who was accompanying clock A both before and after it accelerated, or about an inertial observer who is accompanying it after the acceleration, but saw A in motion relative to himself prior to that. Again, even if you refuse to answer requests for clarification from me, perhaps someone else can press you on this question.

I refer you to my analogy of an observer at the top of a mountain who moves to sea-level.

In both locations he could be of the opinion that the ticking rate of clocks at those locations is the same as his own clock at those locations thus that the sea-level clock and the mountain top clock are ticking over at the same rate as each other or he could apply his knowledge of gravitational time dilation and realize that what appears to be taking place is not reality. That the sea-level clock, as well as his own clock at that location, are physically ticking over at a slower rate than the mountain top clocks.

I know, full well, that this is applicable to general theory whereas my argument is in relation to special theory however the analogy is in respect to what the observer applying his knowledge determines is taking place.

In the general theory there is the principle of "diffeomorphism invariance" (see this article) which allows you to construct your coordinate systems in absolutely any way you like and still find that the Einstein field equations give correct predictions. Although it probably would not be very practical, you certainly could construct a coordinate system where at some particular instant the mountain-top clock is ticking slower than the sea-level clock, although this coordinate system will agree with all other coordinate systems in predictions about local events like how fast observers positioned at each clock will see the other clock ticking (they both agree the sea-level clock appears to be ticking slower) or what the two clocks will read when brought together (if the clocks were initially synchronized at sea level before the second clock was placed on the mountain, the sea-level clock will have elapsed less time when they're brought together again). In the general theory just as in the special theory, there is no single absolute truth about which of two clocks is ticking faster at a particular instant.

Similarly, an observer accompanying Einstein's paragraph 1, chapter 4, clock A although of the opinion that the clock appears to be ticking over at the same rate as it was before they started moving it is physically 'going more slowly' than it was before they started moving.

If you're talking about an inertial observer, this is of course wrong. This observer will find that clock B was ahead of clock A before A accelerated (they were not initially synchronized in his frame), and that B was ticking slower than A after A accelerated, but because of B's "head start" it is still ahead when A catches up to it.

Having arrived at B's location and finding that his clock lags behind clock B what conclusion can the observer accompanying clock A in Einstein's paragraph 1, chapter 4, depiction (knowing that prior to his relocation A and B were synchronized) arrive at other than that his clock must have ticked over at a slower rate than clock B?

Your comment "knowing that prior to his relocation A and B were synchronized" shows that you still do not understand the relativity of simultaneity (there's a good introduction here)--assuming A and B were synchronized in B's rest frame as Einstein suggested, then in the frame of an inertial observer who sees A at rest after the acceleration, A and B were not synchronized in his own frame prior to the acceleration--from his perspective the procedure used to "synchronize" A and B was simply incorrect, because it assumed that light moves at the same speed in all directions in B's rest frame, whereas this observer assumes that light moves at the same speed in all directions in his own frame (and 'synchronization' of clocks at different locations involves sending light-signals from one to the other in SR). You can see from Einstein's own words in Chapter VIII and Chapter IX of one of his books that simultaneity is relative to one's choice of frame, there is no single absolute truth about whether two clocks are synchronized.

Since a failure to appreciate the relativity of simultaneity seems to be the key to your misunderstanding of Einstein's section 4 thought-experiment, I recommend that anyone else discussing the issue with you emphasizes this point, if you are unwilling to engage in discussion with me.

 

[cos]

I thought I was very clear that I am referring to understanding all of SR including Einstein's reference to clocks A and B, the twin paradox, and everything else. This is what I meant by "generally applicable" above. I have repeated this statement at least 3 times already. The geometric approach applies to your question as well as to everything else in SR.

I was confused by your reference in one sentence to 'generally applicable' and, in another sentence 'understanding it', excuse me for attempting to unravel my confusion.

That is, frankly, nothing more than an absurd excuse. Einstein's depiction in section 4 used much more math than I have here, so I don't think your excuse is even valid.

Einstein's depictions in paragraphs 1 through 3 of section 4 to which my postings specifically apply contain one single mathematical equation which I find to be superfluous to his comment that A lags behind B and that the same result is arrived at when A is made to move in any polygonal line and if A is made to move in a a closed curve NON of which requires any mathematics to be understood. I am of the opinion that the single mathematical equation that he provides is not in relation to whether or not clock A 'goes more slowly' than B but is in relation to how much A lags behind B!

I have provided you a very non-mathematical and intuitive introduction to Minkowski geometry as it applies to relativity with the analogy to drivers and odometers. This is a simple and powerful analogy that will allow you to intuitively grasp any SR scenario involving a single spatial dimension. If you cannot even make the minimal mental effort required to understand that simple analogy then you really are not that interested in learning SR.

I am not interested in learning SR! I believe that I have never made any comment in that respect!

I have pointed out on numerous occasions (much more than 3 times already) that my specific interest is in relation to paragraphs 1 through 3 of chapter 4!

Again, I am willing to answer questions you might have about the analogy and how to apply it. I am sure there are many open points for confusion and I am willing to work with you to clarify them, but so far it seems that you have dismissed it entirely without making any effort.

I realize that I hereby leave myself open to criticism again however to what do you refer by the word 'analogy'?

To what do you refer by the word 'it' in your assumption that I have dismissed 'it' entirely?

Contrary to your assumption I assure you that I have made every effort to understand, and respond to, messages from people of reasonable attitude.

Let's get back to basics.

In paragraph 1, chapter 4, OEMB Albert Einstein wrote:-

"If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other one..."

There is, as far as I can tell, only two explanations as to why A is found to lag behind B:

1. During that trip A ticks over at a slower rate than it did before it started moving OR -

2. The rate of operation of clock B increases whilst A is moving.

My original posting was in relation to the claim by some relativists that A (the astronaut's clock) does not tick over at a slower rate than it did before he started his return journey but that clock B (the Earth-bound twin's clock) ticks over at a faster rate than it did before the astronaut started his return trip.

My response to that claim back in the mid-90s was that in my opinion it contradicted Einstein's chapter 4 depictions and in an attempt to attain the opinion of members of an obviously more prestigious group than the one in which that claim was made I posted the concepts in this group.

I am of the (presumably correct) opinion that the Hafele-Keating experiment was based on Einstein's paragraph 3, chapter 4, depiction of a clock being made to move in a curved path around an 'at rest' identical clock. In his book 'Was Einstein Right' Clifford Will pointed out that both legs of the HKX should be looked at from the point of view of all of those clocks (the traveled clocks and the laboratory clocks) moving around a hypothetical master clock at the center of the planet.

When Hafale and Keating arrived back at the laboratory and found that their clocks lagged behind those clocks they could either have assumed that, all appearances to the contrary, their clocks are physically 'going more slowly' than they did before the flight commenced OR that the laboratory clocks as well as every other clock on the planet are physically 'going faster' than they did before the flight commenced.

I am of the opinion that Hafele and Keating (et al) would have preferred the former explanation thus had they repeated that first leg of the experiment they could have realized that although their clocks appeared to have remained unchanged they were, in reality, physically ticking over at a slower rate than they were before the flight commenced thus at a slower rate than the laboratory clocks as determined by the results of their first trip.

Please answer this question - in your opinion, would Hafele or Keating have been able to realize, during that repeat performance, that their clocks, all appearances to the contrary, were physically ticking over at a slower rate than they were before the flight commenced?

I am of the opinion that an observer accompanying clock A in Einstein's paragraph 1, chapter 4, OEMB depiction could, if he repeats that experiment, be of the opinion that although his clock appears to be ticking over at the same rate as it was before he started moving that it is, in reality, 'going more slowly' than it was before he started moving AND that an astronaut returning to Earth could also arrive at that conclusion.

 

[cos]

Whether you realize it or not, this statement makes it appear you believe there is some sort of absolute motion. I think that misunderstanding is at the heart of your inability to accept the many correct interpertations you have been given by JesseM, DS et al.

Please explain the difference between my statement that the astronaut starts to accelerate (i.e. he starts to move) and Einstein's paragraph 1, chapter 4 comment that clock A is made to move?

Admittedly Einstein's depiction does not take into account that clock A accelerates however other than a mathematical proposition which Einstein described as not referring to reality the idea that clock A instantaneously attains a velocity without undergoing acceleration is not, as far as I am concerned, the physical realities to which the subject of physics should be applied.

To demonstrate how this statement of yours is meaningless in any physical way, imagine an astronaut in a completely enclosed, inertial spaceship. The astronaut is in free fall within his ship. He cannot in any physical way determine whether he is moving or at rest. Do you agree so far?

According to the principle of relativity - yes.

Now suppose he ignites the engine and applies 1g accelleration for 1sec. Does he now (do you) think he is going faster than before the acceleration? How would he know?

During that period of acceleration he knows that he is moving relatively to his situation before he started accelerating due to the fact that he feels a force of acceleration and he has put his foot on the gas pedal however on the basis that he was not moving before he accelerated he is not 'going faster than before the acceleration' (on the bais that he was not 'going fast' before he accelerated) but knows that he is moving relatively to his previous 'at rest' situation.

Having taken his foot off the gas pedal he knows that he is still moving away from his original location and because he knows that he accelerated at 1g for 1 second he knows his rate of travel away from that original location.

He had no way of knowing how fast he was moving, or even IF he was moving, to begin with. He also had no way of knowing his orientation wrt any possible motion. All he knows is that he underwent an acceleration. To an outside observer he may have slowed down, speeded up or even stayed at the same speed but changed direction.

The point of view of an outside observer has absolutely nothing whatsoever to do with what the person you described determines!

So please tell me how could he possibly say his clock 'will be going more slowly' than it was?

'He', in my depiction, is an observer accompanying Einstein's paragraph 1, chapter 4, OEMB presentation of clocks A and B or an astronaut who has returned to the planet following an out-and-return voyage both of whom, unlike your astronaut, are able to compare the time on their clock with those of Einsteins clock B or the astronaut's stay-at-home twin's clock.

Your depiction makes no allowance whatsoever for him to compare his clock with Einsteins clock B or the Earth-bound twin's clock but let's assume that, having previously looked out a window, he determines that he is analogous to Einstein's chapter 4 clock A located at one of the points A and B of K with his twin located in an identical ship at point B and his clock is, as Einstein depicted therein, synchronous with clock B's clock.

He moves away from the window and carries out several experiments in order to determine if he (and his twin) are stationary or are moving at the same uniform velocity with no success.

He starts moving toward his twin and, in accordance with Einstein's paragraph 1, chapter 4, depiction he will find, upon his arrival at B's location, that his clock lags behind his twin's clock.

He can either assume that the lag was caused by his clock ticking over at a slower rate than it was before he started moving or that his twin's clock was ticking over at a faster rate than it was before he (A) started moving.

I hope you can see from this there is no way to make any statement about clocks ticking more slowly in anything but a relative sense. You MUST specify a reference frame to make any sense at all. And if you accept SR you must also accept that all inertial frames are equally valid so for any frame where clock A is seen to tick more slowly than clock B you can find a frame where B ticks more slowly than A.

So on the basis that we can find a frame where B ticks more slowly than A where, upon those clock moving together, it will be found that B lags behind A the fact that this contradicts Einstein's suggestion that the complete opposite takes place - that A lags behind B - is, apparently, of no relevance.

This is what JesseM and others have been saying all along and it's why their various analyses from various different frames are valid and correct.

I repeat my comment above - "The point of view of an outside observer has absolutely nothing whatsoever to do with what the person you described determines!

Although 'various analyses from various different frames' may very well be 'valid and correct' they are only 'valid and correct' from their point of view and have absolutely nothing whatsoever to do with what an observer accompanying Einstein's clock A or an astronaut making an out-and-return journey determine!

The fact that an observer in a different frame may determine that Einstein's chapter 4 clock B ticks more slowly than A this has no affect whatsoever on what takes place in Einstein's depiction or during the astronaut's trip!

 

[matheinste]

Hello cos.

Quote:-

----There is, as far as I can tell, only two explanations as to why A is found to lag behind B:

1. During that trip A ticks over at a slower rate than it did before it started moving OR -

2. The rate of operation of clock B increases whilst A is moving.
---------------------------------------------------------------------------

Quote:-

I am not interested in learning SR! I believe that I have never made any comment in that respect!
------------------------------------------------------------

There is another interpretation open to an observer colocated with clock A. This would be:- I, unlike some people, who by their own admission have no wish to study SR, have done so and conclude that because I have traveled with clock A along a non inertial spacetime path, whereas the other clock, B, has remained on an inertial path, I will have have accumulated less proper time than clock B, as predicted by SR, and so the time on the clock colocated with me will show an earlier time than that on clock B. I.e. it will lag clock B.

Matheinste.

 

[Dale]

I am not interested in learning SR!

If that were true then you would not be reading Einstein's writings on the subject nor asking questions about it.

There is, as far as I can tell, only two explanations as to why A is found to lag behind B:

1. During that trip A ticks over at a slower rate than it did before it started moving OR -

2. The rate of operation of clock B increases whilst A is moving.

The whole reason I am bringing up the geometric approach is because these are not the only two explanations. Here is a driving analogy. Two drivers reset their odometers, they each drive due north on parallel roads and note that their odometers read the same. Then, driver A's road bends towards driver B's road. When they meet they notice that driver A's odometer now reads more than driver B's.

Attached is a geometric figure showing the situation. You can print it out and perform the following little experiment. Take two identical rulers and with ruler A measure the length of path A between a0 and a1, with ruler B measure the length of path B betwen b0 and b1. Note that they are the same. Now, with ruler A measure the length of path A between a1 and a2, with ruler B measure the length of path B betwen b1 and b2. Note that this time they are not the same, the measurement for A is longer.

You could certainly explain this by either of the following two explanations:
1) ruler (or odometer) A shrinks during the second measurement
2) ruler (or odometer) B expands during the second measurement

But do you really think those are the only two explanations possible? Do you not think that a third explanation is at least concievable?
3) the distance between a1 and a2 is greater than the distance between b1 and b2

Now, finally, if we replace the y-axis with t (in units where c=1) and if we replace the distance measured with rulers or odometers (Euclidean metric) with the interval measured with clocks (Minkowski metric) then we have a geometric spacetime diagram of exactly the situation described in section 4. Can you not see the geometric third explanation?
3) the interval between a1 and a2 is smaller than the interval between b1 and b2

I hope this more detailed explanation clarifies the "odometer analogy". I hope it also clarifies the fact that this geometric approach is applicable to the section 4 scenario. It is very easy to derive the equation Einstein presents in section 4 from the Minkowski metric, but I will spare you the math.

I encourage you to ask further questions about Minkowski spacetime.

 

[RandallB]

There is, as far as I can tell, only two explanations as to why A is found to lag behind B:

1. During that trip A ticks over at a slower rate than it did before it started moving OR -

2. The rate of operation of clock B increases whilst A is moving.

You potential explanations here are incomplete and IMO get at the root of your confusion.
First option 2 should be rejected as unrealistic as no change can occur to B since it remains stationary in a single frame. SR certainly will not support the #2 option.

But #1 is much to incomplete an explanation;
it has three different possibilities you have not detailed (or considered) since in the travel of A it must use two different Frames; one outbound and one inbound;
this gives four possibilities for the rate of clock A wrt B:

a) both A outbound and A inbound run FAST wrt B
b) both A outbound and A inbound run SLOW wrt B
c) A outbound runs SLOW and A inbound run FAST wrt B
d) A outbound runs FAST and A inbound run SLOW wrt B

SR only rejects option “a”
but based on the given information of the problem “b” “c” or “d” could be true.
Options “c” & “d” work as long as the amount of time A spends at the slow rate is long enough when summed with the time built up by A at the fast rate nets to a total time less than experienced by B for the duration of the round trip.

One of the three conditions will be observed by any random observer C moving at any fixed speed wrt B and will always give the same net change from start to finish for both A & B (B always less than A by the same amount) no matter what speed you use for observer C.

 

[paw]

According to the principle of relativity - yes.

Good. We're making some progress. You agree the astronaut in a closed ship cannot know anything about his state of motion before the acceleration. Not his speed nor his direction. Keep this in mind.

Having taken his foot off the gas pedal he knows that he is still moving away from his original location and because he knows that he accelerated at 1g for 1 second he knows his rate of travel away from that original location.

He does not! He only knows his state of motion is different than it was before. It could be faster, slower or even the same depending on whether the acceleration was in the direction of his (unknown) motion, against it or at an angle. Only an outside observer could make the distinction.

The point of view of an outside observer has absolutely nothing whatsoever to do with what the person you described determines!

It most certainly does. Only an outside observer can make a meaningful statement about the astronauts state of motion before or after the acceleration.

'He', in my depiction, is an observer accompanying Einstein's paragraph 1, chapter 4, OEMB presentation of clocks A and B or an astronaut who has returned to the planet following an out-and-return voyage both of whom, unlike your astronaut, are able to compare the time on their clock with those of Einsteins clock B or the astronaut's stay-at-home twin's clock.

Your 'observer accompanying Einstein's paragraph 1, chapter 4, OEMB presentation' IS an outside observer. It is this outside observer, who you won't allow me or anyone else to reference, that is fooling you into believing the astronaut can make a meaningful statement of his inertial motion. If you remove this outside observe, as I have done above, you'll realize that the astronaut cannot make a prediction about how his clock is ticking in any absolute sense.

 

[phyti]

for those who inquired;

The calibration curve is referred to in the book by Max Born, and I've seen it mentioned on other forums, but don't know if it's a popular term. In essence it is the hyperbola t = sqrt(x^2+1), shown in the drawing. The point where the observers (green) path intersects it, represents his unit of time on the vertical time scale. His path angle is determined by his speed, thus the relation between clock rate and speed is still there, i.e., incorporated into the geometry of the space-time diagram. The 45° (red) line is the asymptote to the hyperbola, and never meets it. It is also the light path, so even if a clock could move at c, it would never tick.

 

[phyti]

from JesseM post 31;

So, if A suddenly decelerates and comes to rest in this frame when it reads 0 seconds, B will already read 16 seconds at the "same moment" in this frame. From then on B will be moving towards A at 0.8c, and hence slowed down by a factor of 0.6 in this frame while A now ticks at the normal rate in this frame since it's at rest.

You state A is at rest, therefore he measures 20 ls, only B who still moves at .8c would measure 12 ls.

 

[matheinste]

Hello phyti.

The clibration curve, hyperbolae, invariant hyperbolae, appears in many books on relativity. The one i have open at the moment is Schutz - a First Course in General Relativity, page 17. It is as you describe it. Rindler, Essential Relativity, page 39 has a more complicated drawing than that of Schutz. I have seen it in other books not at present to hand. These drawings make it clear that the scale of the original and the trnsformed axes is not the same.

Matheinste

 

[JesseM]

You state A is at rest, therefore he measures 20 ls, only B who still moves at .8c would measure 12 ls.

This argument suggests confusion about length contraction--the observer "at rest" does not always measure the longest length (of course, there is no absolute truth about who's at rest in relativity anyway, it's all relative to your choice of frame), rather the observer at rest relative to the thing being measured measures the longest length, if the thing being measured is moving in A's frame, then A will measure a shorter length. I stated that the initial distance between A and B was 20 ls in B's rest frame, meaning that if you had a rod 20 ls long in this frame with B attached to one end, then A would originally be positioned next to the other end. So naturally in the frame where B is moving at 0.8c--the frame where A is "at rest" after A accelerates (though in this frame A was also moving at 0.8c before it accelerated)--the rod is moving at 0.8c too, so the rod must be 12 light-seconds long in this frame. So naturally if B was at one end and A was at the other end before A accelerated, that means A and B were 12 light-seconds apart in this frame before A accelerated and came to rest.

 

[cos]

Hello cos.

There is another interpretation open to an observer colocated with clock A. This would be:- I, unlike some people, who by their own admission have no wish to study SR, have done so and conclude that because I have traveled with clock A along a non inertial spacetime path, whereas the other clock, B, has remained on an inertial path, I will have have accumulated less proper time than clock B, as predicted by SR, and so the time on the clock colocated with me will show an earlier time than that on clock B. I.e. it will lag clock B.

I have, over the past 25 years, studied SR however I make no claim that I have learned SR.

Your false accusation that I have no wish to study SR is totally unwarranted but like most critics honesty seems to be something that you conveniently ignore.

Would you please explain the difference between your determining that your clock has 'accumulated less proper time than clock B' and determining that your clock has ticked over at a slower rate than clock B?

Wouldn't your clock accumulate less proper time because it has ticked over at a slower rate than clock B?

Won't your clock 'lag behind clock B' due to the fact that whilst it was moving it was ticking over at a slower rate than it was before it started moving?

Other than having ticked over at a slower rate than it was before it started moving what other explanation is there for the fact that A lags behind B - that A accumulates less proper time than B - other than that, during that trip, A ticked over at a slower rate than B and at a slower rate than it was before it started moving?

 

[phyti]

If A perceives the separation of himself and B as 12 ls while moving at .8c, he won't perceive the separation the same when he decelerates to 0. He would be in the frame prior to their mutual acceleration. Do you understand your own posts, or did you post in haste without proof reading?

 

[JesseM]

If A perceives the separation of himself and B as 12 ls while moving at .8c, he won't perceive the separation the same when he decelerates to 0. He would be in the frame prior to their mutual acceleration. Do you understand your own posts, or did you post in haste without proof reading?

You are apparently jumping to incorrect conclusions about my posts, try asking for clarification before assuming I'm the one making a mistake. I'm just talking about what is happening in a particular inertial frame, not what the non-inertial clock A "perceives". In this inertial reference frame, both A and B are initially moving at 0.8c with a separation of 12 light-seconds, then A decelerates and comes to rest in this frame while B continues to move towards A at 0.8c. If you like, you can think of this frame as representing the viewpoint of a third object C that always moves inertially, with A coming to rest relative to C after (but not before) A accelerates.

What do you mean by the word "perceives", anyway? Do you understand that even for an inertial observer, what they see visually is differently from what is true in their own inertial rest frame? For example, if a clock is approaching an inertial observer at 0.6c, then in his own rest frame the clock will be slowed down by a factor of sqrt(1 - 0.6^2) = 0.8, but what he will see visually is that it appears to be sped up by a factor of 2 due to the relativistic Doppler effect. Likewise, although an object moving at 0.6c in his frame will be shrunk in length along the axis of motion by a factor of 0.8 due to Lorentz contraction, visually he will see the length as unchanged due to Penrose-Terrell effect. The length and time between ticks in his frame must be based on correcting for the fact that the light from successive ticks (or the light from different parts of the object) had different distances to travel to reach his eyes. For example, if in 2036 I see the image of a ship 26 light years away according to my ruler with its clock reading 50 years, and then 4 years later in 2040 I see an image of the same ship 20 light years away according to my ruler with its clock reading 58 years (meaning I visually saw the clock advance 8 years in 4 years of my time, so it looks like it's sped up by a factor of 2), then I can correct for the time the light from each event took to reach me and conclude that the first event happened at a time-coordinate of 2036 - 26 = 2010 in my frame, and the second happened at a time-coordinate of 2040 - 20 = 2020 in my frame, meaning that in my frame the clock actually took 10 years to advance 8 years from 50 to 58, so it was slowed down by a factor of 0.8 in my frame.

At first I thought maybe you understood this, and when you were talking about what A "perceives", you might have meant what would be true in a non-inertial reference frame where A is at rest both before and after the acceleration. But you said A was initially "moving at .8c" so this wouldn't make sense--obviously in a coordinate system where A is at rest, A's coordinate velocity is always zero. In any case, the problem with non-inertial coordinate systems is that unlike with inertial frames there's no single "correct" way to define the coordinate system of a non-inertial observer, you can design a coordinate system in which that observer is at rest in any of an infinite number of different ways, which will give different answers about things like the distance between objects and the rates clocks are ticking and which events are simultaneous.

 

[cos]

I am not interested in learning SR!

If that were true then you would not be reading Einstein's writings on the subject nor asking questions about it.

Studying SR is a far cry from learning it!

There is, as far as I can tell, only two explanations as to why A is found to lag behind B:

1. During that trip A ticks over at a slower rate than it did before it started moving OR -

2. The rate of operation of clock B increases whilst A is moving.

The whole reason I am bringing up the geometric approach is because these are not the only two explanations. Here is a driving analogy. Two drivers reset their odometers, they each drive due north on parallel roads and note that their odometers read the same. Then, driver A's road bends towards driver B's road. When they meet they notice that driver A's odometer now reads more than driver B's.

Attached is a geometric figure showing the situation. You can print it out and perform the following little experiment. Take two identical rulers and with ruler A measure the length of path A between a0 and a1, with ruler B measure the length of path B betwen b0 and b1. Note that they are the same. Now, with ruler A measure the length of path A between a1 and a2, with ruler B measure the length of path B betwen b1 and b2. Note that this time they are not the same, the measurement for A is longer.

You could certainly explain this by either of the following two explanations:
1) ruler (or odometer) A shrinks during the second measurement
2) ruler (or odometer) B expands during the second measurement

But do you really think those are the only two explanations possible? Do you not think that a third explanation is at least concievable?
3) the distance between a1 and a2 is greater than the distance between b1 and b2

Now, finally, if we replace the y-axis with t (in units where c=1) and if we replace the distance measured with rulers or odometers (Euclidean metric) with the interval measured with clocks (Minkowski metric) then we have a geometric spacetime diagram of exactly the situation described in section 4. Can you not see the geometric third explanation?
3) the interval between a1 and a2 is smaller than the interval between b1 and b2

I hope this more detailed explanation clarifies the "odometer analogy". I hope it also clarifies the fact that this geometric approach is applicable to the section 4 scenario. It is very easy to derive the equation Einstein presents in section 4 from the Minkowski metric, but I will spare you the math.

I encourage you to ask further questions about Minkowski spacetime.

I find your reference to lengths to be confusing. Are you suggesting that in Einstein's chapter 4 depiction an observer alongside clock B determines that the distance traveled by A is less than the distance determined by A on the basis that the distance A to B contracts from A's point of view?

On the basis of the fully reciprocal nature of SR - as far as B is concerned the distance A to B also contracts due to the fact that A is moving however I fail to see that your analogy has anything to do with Einstein's suggestion that the moving clock 'goes more slowly' than the stationary clock.

My extremely limited understanding of Minkowski spacetime is that it is based on mathematical propositions which, according to Einstein, do not refer to reality.

If a concept can only be explained by the application of mathematics and cannot be presented in simple everyday language it is not, in my opinion, reality.

I am not suggesting that mathematics is not of extreme importance but that it does not, by itself, provide proof of a concept or of a theory as some people insist.

 

[cos]

You potential explanations here are incomplete and IMO get at the root of your confusion.
First option 2 should be rejected as unrealistic as no change can occur to B since it remains stationary in a single frame. SR certainly will not support the #2 option.

You apparently did not see my original posting in which I argued that option 2 is unrealistic!

But #1 is much to incomplete an explanation;
it has three different possibilities you have not detailed (or considered) since in the travel of A it must use two different Frames; one outbound and one inbound;
this gives four possibilities for the rate of clock A wrt B:

a) both A outbound and A inbound run FAST wrt B
b) both A outbound and A inbound run SLOW wrt B
c) A outbound runs SLOW and A inbound run FAST wrt B
d) A outbound runs FAST and A inbound run SLOW wrt B

SR only rejects option “a”
but based on the given information of the problem “b” “c” or “d” could be true.
Options “c” & “d” work as long as the amount of time A spends at the slow rate is long enough when summed with the time built up by A at the fast rate nets to a total time less than experienced by B for the duration of the round trip.

Perhaps you might care to read my comment to which you refer but to save you having to locate same I herewith reproduce it:-

*********************

"In paragraph 1, chapter 4, OEMB Albert Einstein wrote:-

"If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other one..."

There is, as far as I can tell, only two explanations as to why A is found to lag behind B:

1. During that trip A ticks over at a slower rate than it did before it started moving OR -

2. The rate of operation of clock B increases whilst A is moving.

*********************

Where, in that comment is there any application that 'in the travel of A it must use two different Frames; one outbound and one inbound.'?

You wrote:-

c) A outbound runs SLOW and A inbound run FAST wrt B
d) A outbound runs FAST and A inbound run SLOW wrt B

Neither of these ideas comply with Einstein's chapter 4 depiction which indicates that A inbound (as per your reference c)) runs slow wrt to B and if A had initially been at rest alongside and synchronous with B and had moved the same distance as Einstein's A to B and at the same velocity it, too, would lag behind B by the same amount as does A's clock in Einstein's depiction.

It would not, as you suggest in d), run FAST!

One of the three conditions will be observed by any random observer C moving at any fixed speed wrt B and will always give the same net change from start to finish for both A & B (B always less than A by the same amount) no matter what speed you use for observer C.

There is no random observer C either in Einstein's chapter 4 depictions or in the astronaut's out-and-return journey but even if there was then his observations have absolutely nothing whatsoever to do with the observations made by A or B.

His observations will have no physical affect whatsoever on A's or B's clocks!

His observations are of no interest whatsoever to A or B.

 

[Dale]

Are you suggesting that in Einstein's chapter 4 depiction an observer alongside clock B determines that the distance traveled by A is less than the distance determined by A on the basis that the distance A to B contracts from A's point of view?

No, this is not what I said. Please note very carefully my choice of words above. When I use the word "distance" I am referring to the Euclidean metric s²=x²+y²+z² in space. When I use the word "interval" I am referring to the Minkowski metric s²=-t²+x²+y²+z² in spacetime. The spacetime interval does not contract, it is absolute or frame invariant, not relative, and all observers agree on it.

The frame-invariant spacetime interval from a1 to a2 is less than the frame-invariant spacetime interval from b1 to b2. All observers will agree on this regardless of any relative motion.

This is important, please respond: Do you see how the diagram I drew represents the scenario described by Einstein in section 4? (even if you don't understand or accept the Minkowski spacetime interval)

My extremely limited understanding of Minkowski spacetime is that it is based on mathematical propositions which, according to Einstein, do not refer to reality.

Minkowski geometry is simply a mathematical framework for SR so it "refers to reality" as much as any other formulation of SR (which is very well).

I am not suggesting that mathematics is not of extreme importance but that it does not, by itself, provide proof of a concept or of a theory as some people insist.

Agreed. Validation of a scientific theory is only by experiment.

 

[cos]

Good. We're making some progress. You agree the astronaut in a closed ship cannot know anything about his state of motion before the acceleration. Not his speed nor his direction. Keep this in mind.

His speed and his direction - relatively to what?

As far as he is concerned his internal dynamic experiments indicate that he is at rest!

He could also assume that his ship is moving with uniform velocity but relatively to what is it moving? To the universe? There could be numerous observers all in different reference frames who would totally disagree with each other about how fast his ship is moving and in which direction it is traveling. Which of those numerous observations is the 'correct' one?

Relatively to one of those observers he could be accelerating but relatively to another observer he could be decelerating! Which opinion is the 'correct' one?

According to various observers his ship could be moving up or down; left or right; backwards or forwards. Which 'observation' of the direction in which the ship is moving is 'real'?

[QUOTE cos]Having taken his foot off the gas pedal he knows that he is still moving away from his original location and because he knows that he accelerated at 1g for 1 second he knows his rate of travel away from that original location.

He does not! He only knows his state of motion is different than it was before. It could be faster, slower or even the same depending on whether the acceleration was in the direction of his (unknown) motion, against it or at an angle. Only an outside observer could make the distinction.

Knowing that his state of motion 'is different than it was before' he knows that he is now moving at a different speed than he was before. On that basis he cannot then be traveling at the same speed as he was before he accelerated!

As pointed out above, a number outside observers could be of the opinion that the ship was initially moving in the opposite direction to its exhausts (i.e. that it is moving forward) whilst just as many could argue that from their point of view it was moving in the opposite direction. Whose opinion is the 'correct' one?

[QUOTE cos]The point of view of an outside observer has absolutely nothing whatsoever to do with what the person you described determines!

It most certainly does. Only an outside observer can make a meaningful statement about the astronauts state of motion before or after the acceleration.

Which of the potential dozens of outside observers all located in different reference frames 'can make a meaningful statement about the astronaut's state of motion before or after the acceleration.'? All of them? Are all of those totally opposing points of view meaningful statements? Or are they only 'meaningful statements' as far as the person that made them is concerned?

Your 'observer accompanying Einstein's paragraph 1, chapter 4, OEMB presentation' IS an outside observer. It is this outside observer, who you won't allow me or anyone else to reference, that is fooling you into believing the astronaut can make a meaningful statement of his inertial motion. If you remove this outside observe, as I have done above, you'll realize that the astronaut cannot make a prediction about how his clock is ticking in any absolute sense.

My mistake - I meant to write "an observer accompanying [clock A in] Einstein's paragraph 1, chapter 4, OEMB presentation" however my then reference to "an astronaut who has returned to the planet following an out-and-return voyage.." should have provided a clue that I was talking about an observer accompanying Einstein's clock A.

Neither the observer accompanying Einstein's clock A nor the returning astronaut are outside observers.

Good. We're making some progress. You agree the astronaut in a closed ship cannot know anything about his state of motion before the acceleration. Not his speed nor his direction. Keep this in mind.

His speed and his direction - relatively to what?

As far as he is concerned his internal dynamic experiments indicate that he is at rest!

He could also assume that his ship is moving with uniform velocity but relatively to what is it moving? To the universe? There could be numerous observers all in different reference frames who would totally disagree with each other about how fast his ship is moving and in which direction it is traveling. Which of those numerous observations is the 'correct' one?

Relatively to one of those observers he could be accelerating but relatively to another observer he could be decelerating! Which opinion is the 'correct' one?

According to various observers his ship could be moving up or down; left or right; backwards or forwards. Which 'observation' of the direction in which the ship is moving is 'real'?

[QUOTE cos]Having taken his foot off the gas pedal he knows that he is still moving away from his original location and because he knows that he accelerated at 1g for 1 second he knows his rate of travel away from that original location.

He does not! He only knows his state of motion is different than it was before. It could be faster, slower or even the same depending on whether the acceleration was in the direction of his (unknown) motion, against it or at an angle. Only an outside observer could make the distinction.

Knowing that his state of motion 'is different than it was before' he knows that he is now moving at a different speed than he was before. On that basis he cannot then be traveling at the same speed as he was before he accelerated!

As pointed out above, a number outside observers could be of the opinion that the ship was initially moving in the opposite direction to its exhausts (i.e. that it is moving forward) whilst just as many could argue that from their point of view it was moving in the opposite direction. Whose opinion is the 'correct' one?

[QUOTE cos]The point of view of an outside observer has absolutely nothing whatsoever to do with what the person you described determines!

It most certainly does. Only an outside observer can make a meaningful statement about the astronauts state of motion before or after the acceleration.

Which of the potential dozens of outside observers all located in different reference frames 'can make a meaningful statement about the astronaut's state of motion before or after the acceleration.'? All of them? Are all of those totally opposing points of view meaningful statements? Or are they only 'meaningful statements' as far as the person that made them is concerned?

Your 'observer accompanying Einstein's paragraph 1, chapter 4, OEMB presentation' IS an outside observer. It is this outside observer, who you won't allow me or anyone else to reference, that is fooling you into believing the astronaut can make a meaningful statement of his inertial motion. If you remove this outside observe, as I have done above, you'll realize that the astronaut cannot make a prediction about how his clock is ticking in any absolute sense.

My mistake - I meant to write "an observer accompanying clock A in Einstein's paragraph 1, chapter 4, OEMB presentation" however my then reference to "an astronaut who has returned to the planet following an out-and-return voyage.." should have provided a clue that I was talking about an observer accompanying Einstein's clock A.

Neither the observer accompanying Einstein's clock A nor the returning astronaut are outside observers and unlike your astronaut in a closed ship my astronaut can look through a window similarly the observer accompanying Einstein's clock A can see clock B and, having experienced a force of acceleration, knows that he is moving toward B in the same way that the astronaut returning to the planet knows that he is doing so.

Whilst you are referring to a purely hypothetical situation where an astronaut cannot see outside his ship (thus is 'without reference to any outside point') my depiction is in relation to more of a reality. Unlike your astronaut in a closed ship my astronaut can look through a window.

It is ludicrous to suggest that I won't allow you or anyone else to reference an outside observer however on the basis that what an outside observer determines has no affect whatsoever on what is taking place in the astronaut's reference frame I see no reason whatsoever for anybody to repeatedly insist that it does.

Those same people, and others, continue to refuse to respond to my question regarding Hafele's or Keating's ability to realize, whilst hypothetically repeating the first leg of their experiment, that their clocks are ticking over at a slower rate than they were before the flight commenced regardless of the fact that they appear to be ticking over at their usual rate.

 

[JesseM]

My mistake - I meant to write "an observer accompanying [clock A in] Einstein's paragraph 1, chapter 4, OEMB presentation" however my then reference to "an astronaut who has returned to the planet following an out-and-return voyage.." should have provided a clue that I was talking about an observer accompanying Einstein's clock A.

Neither the observer accompanying Einstein's clock A nor the returning astronaut are outside observers.

Ah, so this comment finally makes clear that you are talking about a non-inertial observer who is at rest relative to A at all times, rather than an inertial observer who is at rest relative to A only after A finishes accelerating. The problem here is that unlike with inertial observers, there is no "standard" way to construct a coordinate system for a non-inertial observer--you can pick anyone of an infinite number of different coordinate systems in which that observer is at rest at all times, coordinate systems which may have completely different definitions of simultaneity. With inertial observers, there is a clear physical motivation for constructing their coordinate system in the standard way--it makes sense that an inertial observer would want to use rigid rulers at rest relative to themselves to measure distance, and clocks at rest relative to themselves to measure time, and if different clocks in their system are synchronized using the Einstein synchronization convention (in which clocks are synchronized based on the assumption that light moves at the same speed in all directions in this coordinate system--Einstein discusses this synchronization procedure in section 1 of the 1905 paper), then all the different inertial coordinate systems constructed in this way will find that the laws of physics obey the same equations in their respective coordinate systems.

But with non-inertial observers, there is no such "natural" procedure for constructing their coordinate system since the laws of physics will obey different equations from inertial frames regardless of how you do it. So, just because A and B were synchronized in the frame of an inertial observer at rest relative to B, there is no basis for claiming that in the frame of a non-inertial observer who starts out at rest relative to B but then accelerates along with A, we still have to say that A and B were initially synchronized--you could construct a non-inertial coordinate system with a definition of simultaneity such that they'd have been initially synchronized, but you could equally well construct a different non-inertial coordinate system with a definition of simultaneity such that they weren't synchronized from the start, it's purely a matter of aesthetic taste. And the crux of your argument seems to be your claim that A and B were initially synchronized from the perspective of the observer moving along with A, so that if B is ahead when they meet up that must mean A was running slow--well, if the observer's "perspective" is meant to be shorthand for the coordinate system the observer is using (presumably one in which the observer is at rest at all times), it's purely a matter of taste whether this observer uses a coordinate system where A and B were initially synchronized or whether he uses one where they were out-of-sync, neither coordinate system is any more valid physically than the other. On the other hand, if the observer's "perspective" is supposed to mean something other than his coordinate system, then the burden is on you to explain what it does mean, and why you think A and B were initially synchronized from the observer's "perspective" just because they were originally synchronized in the inertial coordinate system where A and B were initially at rest.

 

[matheinste]

Hello cos.

This is purely so that I can see if my interpretation of what you are saying is correct so that we can avoid any misunderstandings. I realize that while there is any possibility of you thinking that I do not understand what you are saying you will, understandably, not take any answers seriously. Ignoring any later complicayions does the summary below describe your thoughts.


We have two clocks A and B at rest relative to each other. These clocks have been synchronized while at rest relative to each other using the Einstein synchronization procedure. Clock B remains in its original state of inertial motion throughout. Clock A moves to clock B. It is found that when A and B meet clock A lags clock B. They are now back at rest relative to each other. The clocks were originally in sync when at rest relative to each other but now are not because B’s clock lags behind A’s. Nothing has happened to B, and he knows this, so his clock’s rate of ticking must have remained the same the whole time. However A has moved, and both he and B know it, and so both conclude that the change in the situation must be due to A’s movement. So they conclude that A’s movement has caused A’s clock rate to slow during its relative motion and not B’s clock rate to speed up.

We assume that there are no direct effects to clock rates due to acceleration itself.

Matheinste

 

[paw]

His speed and his direction - relatively to what?

That's the whole point. Without reference to anything outside the ship he cannot say anything about his state of motion. If he can't say anything about his state of motion he can't say anything about the behaviour of his clocks.

As far as he is concerned his internal dynamic experiments indicate that he is at rest!

Yes. Again that's my point. He has no way to say anything about his state of motion without reference to something outside his ship.

He could also assume that his ship is moving with uniform velocity but relatively to what is it moving? To the universe? There could be numerous observers all in different reference frames who would totally disagree with each other about how fast his ship is moving and in which direction it is traveling. Which of those numerous observations is the 'correct' one?

Exactly the point JesseM was making earlier to which you objected.. All inertial frames are equally valid. No one of them can claim any special 'correctness'.

Relatively to one of those observers he could be accelerating but relatively to another observer he could be decelerating! Which opinion is the 'correct' one?

According to various observers his ship could be moving up or down; left or right; backwards or forwards. Which 'observation' of the direction in which the ship is moving is 'real'?

Neither and neither. No observer in any inertial frame can claim to be correct. Which is again exactly the point I (and others) have been making all along.

Knowing that his state of motion 'is different than it was before' he knows that he is now moving at a different speed than he was before. On that basis he cannot then be traveling at the same speed as he was before he accelerated!

He knows he is moving at a different velocity than he was before. His speed could be faster, slower or even the same as it was before (in the frame where he was at rest before accelerating). You do understand the difference between speed and velocity don't you? If the acceleration was applied correctly he could be going the same speed but in a different direction (wrt the initial rest frame).

As pointed out above, a number outside observers could be of the opinion that the ship was initially moving in the opposite direction to its exhausts (i.e. that it is moving forward) whilst just as many could argue that from their point of view it was moving in the opposite direction. Whose opinion is the 'correct' one?

Exactly. Only an outside observer could make this distinction as I aready stated. The astronaut cannot make this distinction without reference to something outside the ship. He cannot know his state of motion before the acceleration so he cannot know it after the acceleration. Therefore he cannot claim his clocks are running slow in any meaningful sense.

Which of the potential dozens of outside observers all located in different reference frames 'can make a meaningful statement about the astronaut's state of motion before or after the acceleration.'? All of them? Are all of those totally opposing points of view meaningful statements? Or are they only 'meaningful statements' as far as the person that made them is concerned?

All inertial frames can make meaningful statements about the astronauts state of motion both before and after the acceleration. All the apparently opposing pov are meaninful to the observer who makes them. Further, they could all make calculations that will agree with each other after a suitable transform.

It is ludicrous to suggest that I won't allow you or anyone else to reference an outside observer however on the basis that what an outside observer determines has no affect whatsoever on what is taking place in the astronaut's reference frame I see no reason whatsoever for anybody to repeatedly insist that it does.

This is getting to the heart of why you can't seem to properly interpert Einsteins scenario. You are analyzing it from the pov of a non inertial observer, the observer accompanying clock A (the astronaut). I have been attempting to remove that outside observer to show you how the astronaut cannot make any valid claim about the rate his clock is ticking at (beyond the fact it appears to him to be ticking normally). If you still can't see it, after basically agreeing with my statements, then I guess you'll have to stick with your incorrect analysis and continue to believe SR is somehow flawed.

 

[RandallB]

I heard it in a movie – “How can you be so obtuse? – Is it intentional?

Where, in that comment is there any application that 'in the travel of A it must use two different Frames; one outbound and one inbound.'?

There is no “Twins Paradox” without one twin returning to the other. The only way A can get back to B is no make two trips one outbound the inbound. Period.
If that is not clear to you – then you have no chance of understanding this.

If you think you can turn the twin problem into a one way trip – that does not belong in a thread titled “twin paradox”!
You cannot do twins with a oneway trip, without taking Einstein quotes completely out of context - most importantly ignoring his point that simultaneity can only exist for two things that are collocated next to each other; as in when Clock A and B are next to each other on the outbound trip and when they pass next to each other again during the inbound trip by B.

You wrote:-

c) A outbound runs SLOW and A inbound run FAST wrt B
d) A outbound runs FAST and A inbound run SLOW wrt B

Neither of these ideas comply with Einstein's chapter 4 depiction which indicates that A inbound (as per your reference c)) runs slow wrt to B and if A had initially been at rest alongside and synchronous with B and had moved the same distance as Einstein's A to B and at the same velocity it, too, would lag behind B by the same amount as does A's clock in Einstein's depiction.

It would not, as you suggest in d), run FAST!

There is no random observer C either in Einstein's chapter 4 depictions or in the astronaut's out-and-return journey but even if there was then his observations have absolutely nothing whatsoever to do with the observations made by A or B.

His observations will have no physical affect whatsoever on A's or B's clocks!

His observations are of no interest whatsoever to A or B.

If you have not already done the math to see this is true you are not even trying.
Just pick 5 different “C” observers to calculate and record all the times and locations for Clocks A & B wrt to the stationary observer C.
C1 anywhere on the B ref frame
C2 on a frame moving 0.5c wrt B in the outbound direction.
C3 on the 0.8c outbound frame used by A for part of the time.
C4 on a frame moving 0.5c wrt B in the inbound direction
C5 on the 0.8c inbound frame used by A for part of the time.

Just remember the turnaround point is defined in just one frame so C must calculate where that is in the stationary frame it is using. None of the 5 “C” observers will agree with each other on almost anything concerning where when and how fast except for two measurements! They will all agree and predict the same times on clocks A & B when they pass each other at the start and the time on each clock when A returns to meet B again. All showing the traveler A to have aged less even though one of the observers clearly saw the A clock running FAST wrt B for one leg of the trip.
You don’t need to take my word for it – just do the math for yourself.

 

[phyti]

JesseM;
This is the most ridiculous posting I've encountered yet with regard to confusing the issue, and lack of comprehension of posts. It reminds me of the psychiatrist who after passing someone who says "good morning", thinks, "I wonder what he meant by that?".
To make the point as simple as possible, if A is at rest relative to this distance of 20 ls, which is marked off with some type of markers, then when he is moving at .8c, you say the distance is shrunk to 12 ls. If he decelerates to 0, then he is no longer moving relative to the markers, and the distance is now 20 ls. It can't be 12 ls when moving
at .8c and 12 ls when moving at 0, but that is what you said in post 31!

 

[phyti]

Hello cos.

This is purely so that I can see if my interpretation of what you are saying is correct so that we can avoid any misunderstandings. I realize that while there is any possibility of you thinking that I do not understand what you are saying you will, understandably, not take any answers seriously. Ignoring any later complicayions does the summary below describe your thoughts.


We have two clocks A and B at rest relative to each other. These clocks have been synchronized while at rest relative to each other using the Einstein synchronization procedure. Clock B remains in its original state of inertial motion throughout. Clock A moves to clock B. It is found that when A and B meet clock A lags clock B. They are now back at rest relative to each other. The clocks were originally in sync when at rest relative to each other but now are not because B’s clock lags behind A’s. Nothing has happened to B, and he knows this, so his clock’s rate of ticking must have remained the same the whole time. However A has moved, and both he and B know it, and so both conclude that the change in the situation must be due to A’s movement. So they conclude that A’s movement has caused A’s clock rate to slow during its relative motion and not B’s clock rate to speed up.

We assume that there are no direct effects to clock rates due to acceleration itself.

Matheinste

You have my vote, that is the context of the case described in the book. The point A.E. is making is, when the clocks are compared, there is a difference, and that decides the behavior of the clocks. He is not discussing equivalent frames, or how many ways to skin a cat. The relativity police however are looking for someone they think is trying to overthrow the status quo. As I said before, history is full of it.

 

[cos]

This is important, please respond: Do you see how the diagram I drew represents the scenario described by Einstein in section 4? (even if you don't understand or accept the Minkowski spacetime interval)
Minkowski geometry is simply a mathematical framework for SR so it "refers to reality" as much as any other formulation of SR (which is very well).

Does the diagram you drew show that clock A does not lag behind clock B? Does it show that clock A does not 'go more slowly' (i.e. tick over at a slower rate) than clock B?

 

[cos]

We have two clocks A and B at rest relative to each other. These clocks have been synchronized while at rest relative to each other using the Einstein synchronization procedure. Clock B remains in its original state of inertial motion throughout. Clock A moves to clock B. It is found that when A and B meet clock A lags clock B. They are now back at rest relative to each other. The clocks were originally in sync when at rest relative to each other but now are not because B’s clock lags behind A’s. Nothing has happened to B, and he knows this, so his clock’s rate of ticking must have remained the same the whole time. However A has moved, and both he and B know it, and so both conclude that the change in the situation must be due to A’s movement. So they conclude that A’s movement has caused A’s clock rate to slow during its relative motion and not B’s clock rate to speed up.

The underlined section of your comment is incorrect in that, according to Einstein, A's clock lags behind B's clock.

Other than that - I am of the opinion that, apart from your comment "..both conclude that the change in the situation must be due to A’s movement. So they conclude that A’s movement has caused A’s clock rate to slow during its relative motion and not B’s clock rate to speed up" this is precisely what Einstein stated in paragraph 1, chapter 4 of OEMB.

Your comment applies to my interpretation of why A lags behind B.

 

[JesseM]

JesseM;
This is the most ridiculous posting I've encountered yet with regard to confusing the issue, and lack of comprehension of posts.

We are discussing the example I gave in post #31, and the statements I made about this example--are you really so presumptuous that you would accuse me of failing to comprehend my own posts? Are you willing to consider even for a second that maybe there was a misinterpretation on your end?

To make the point as simple as possible, if A is at rest relative to this distance of 20 ls, which is marked off with some type of markers, then when he is moving at .8c, you say the distance is shrunk to 12 ls. If he decelerates to 0, then he is no longer moving relative to the markers, and the distance is now 20 ls. It can't be 12 ls when moving
at .8c and 12 ls when moving at 0, but that is what you said in post 31!

I can only repeat that in post #31 I was not talking about what things looked like from A's perspective, I was talking about what things look like in a frame where B is moving at 0.8c at all times (I think I already made this pretty obvious in my previous post to you when I said 'I'm just talking about what is happening in a particular inertial frame, not what the non-inertial clock A "perceives"'). A is not an inertial observer, there is no single "correct" way to construct the coordinate system for non-inertial objects, and thus no single "correct" answer to how things look from their perspective, you could construct a coordinate system where the non-inertial observer A is always at rest and the distance from A to B is 50 trillion light years if you want, this distance would be no more or less correct as a statement of how things look from A's "perspective" than any other distance because all non-inertial coordinate systems are equally valid, it's only for inertial objects that there is a standard "correct" way to construct their rest frame and thus a single "correct" answer to what distances look like in their rest frame (I'm trying to avoid any presumptions about what you do or don't understand about SR, but if you have any objection to this sentence, you are indeed failing to understand something important about the difference between inertial and non-inertial frames in SR). Once again, I am only talking about how things look from the perspective of the inertial frame where B is always moving at 0.8c, and I made that perfectly clear in post #31:

So, in the frame where A and B are initially moving at 0.8c, they will be out-of-sync by (0.8c)*(20 light-seconds)/c^2 = 16 seconds. Since we are picking a frame where B is moving in the direction of A, B is the trailing clock here, so its time is the one that's ahead by 16 seconds. So, if A suddenly decelerates and comes to rest in this frame when it reads 0 seconds, B will already read 16 seconds at the "same moment" in this frame. From then on B will be moving towards A at 0.8c, and hence slowed down by a factor of 0.6 in this frame while A now ticks at the normal rate in this frame since it's at rest. 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. During this time A will advance forward by 15 seconds but B will only advance forward by 15*0.6 = 9 seconds. Since A started out reading 0 seconds at the moment it came to rest, and B started out reading 16 seconds "at the same moment" in this frame, then when B catches up with A, A will read 0 + 15 = 15 seconds, while B will read 16 + 9 = 25 seconds. So, in this frame we get the exact same prediction that A is behind B by 10 seconds when they meet, in spite of the fact that in this frame A was ticking faster than B after A accelerated, not slower.

Can you not see that my repeated uses of the phrase "in this frame" were referring to the inertial frame where B was moving at 0.8c at all times, not any kind of non-inertial frame belonging to A where the equations of SR wouldn't apply? Do you not understand that if B has a rod attached to it which is 20 ls long in B's inertial rest frame, so that A was next to the other end of the rod before it accelerated, then in this inertial frame where B (and the rod) is moving at 0.8c at all times, the rod will be 12 ls long at all times, regardless of how A changes speed? There is never a moment--before, during, or after A's acceleration--where the rod is 20 ls long in this frame, it's always 12 ls long in this frame!

 

[cos]

That's the whole point. Without reference to anything outside the ship he cannot say anything about his state of motion. If he can't say anything about his state of motion he can't say anything about the behaviour of his clocks.

On the basis that “he cannot say anything about his state of motion” his speed and motion can only be determined by an outside observer and due to the fact that numerous outside observers can determine numerous different speeds and directions of travel for his ship none of them has the right to state that their interpretation is the correct one.

Ergo anyone of those observers who insists that the ship was originally moving relatively to him at a certain speed and in a certain direction thus that when he fires his engine he is decelerating is insisting that the ship was moving at that speed without taking into account the fact that it could, from the point of view of another outside observer be stationary. That first observer insists that the ship does not accelerate but that it decelerates and that this is in his opinion, for the astronaut in your ship, reality.

Yes. Again that's my point. He has no way to say anything about his state of motion without reference to something outside his ship.

And that’s my point! Your depiction has absolutely nothing whatsoever to do with my depiction of an astronaut (or Einstein's observer A) who have reference to an outside point.

Exactly the point JesseM was making earlier to which you objected. All inertial frames are equally valid. No one of them can claim any special 'correctness'.

My point precisely - an outside observer cannot claim any special correctness if he ‘determines’ that from his point of view the ship was moving in reverse (i.e. in the direction of its main engine’s exhaust pipe) thus that it decelerates when that astronaut steps on the gas pedal and comes to a stop relatively to the outside observer.

Your outside observer could be of the opinion that ‘all inertial frames are equally valid’ thus that before the astronaut gunned his engines he could in his inertial frame have been ‘at rest’ thus that in his (the astronaut’s) reference frame he is accelerating.

I believe that at this point it is well worth repeating your comment that “All inertial frames are equally valid. No one of them can claim any special 'correctness.'”

Therefore for anyone to suggest that your astronaut could be moving backwards and decelerates coming to a stop this is only the opinion of one single outside observer whose determinations have absolutely no affect whatsoever on what is taking place in your astronaut’s reference frame.

Neither and neither. No observer in any inertial frame can claim to be correct. Which is again exactly the point I (and others) have been making all along.

So the observer in a reference frame who determines that the ship was already moving and that it decelerated to a stop is not entitled to claim that his observation is the correct one and that determinations arrived at by the astronaut in that ship (that he has accelerated) are wrong!

So your suggestion that, having gunned his engines, the astronaut’s impression that he is moving is negated by an outside observer’s opinion to the contrary does not comply with your suggestion that “No observer in any inertial frame can claim to be correct.”

He knows he is moving at a different velocity than he was before. His speed could be faster, slower or even the same as it was before (in the frame where he was at rest before accelerating).

QUOTE: “in the frame where he was at rest[.B] before accelerating.”

You do understand the difference between speed and velocity don't you? If the acceleration was applied correctly he could be going the same speed but in a different direction (wrt the initial rest frame).

QUOTE: “wrt the initial rest frame.”

Exactly. Only an outside observer could make this distinction as I already stated. The astronaut cannot make this distinction without reference to something outside the ship. He cannot know his state of motion before the acceleration so he cannot know it after the acceleration. Therefore he cannot claim his clocks are running slow in any meaningful sense.

All inertial frames can make meaningful statements about the astronauts state of motion both before and after the acceleration. All the apparently opposing pov are meaninful to the observer who makes them. Further, they could all make calculations that will agree with each other after a suitable transform.

QUOTE: “All the apparently opposing pov are meaningful to the observer who makes them.”

They are meaningful to the observer who makes them but they have no effect whatsoever on what actually takes place in the astronauts reference frame.

Although to perhaps one of those potentially numerous outside observer’s he could appear to have been moving thus decelerated when he guns his engines this is just one pov and does NOT mean that it is reality merely that, in his opinion, it appears to be reality.

For you to suggest that he could have been moving and decelerated to a stop you are allocating the responsibility of the determination of reality to one out of possibly dozens of outside observers all with varying points of view.

Reality as far as I am concerned is what takes place in the astronaut’s reference frame and on the basis that he determines that he is initially at rest then the pov of one outside observer out of dozens has no effect whatsoever on what the astronaut determines.

This is getting to the heart of why you can't seem to properly interpret Einstein's scenario. You are analyzing it from the pov of a non inertial observer, the observer accompanying clock A (the astronaut). I have been attempting to remove that outside observer to show you how the astronaut cannot make any valid claim about the rate his clock is ticking at (beyond the fact it appears to him to be ticking normally). If you still can't see it, after basically agreeing with my statements, then I guess you'll have to stick with your incorrect analysis and continue to believe SR is somehow flawed.

The observer accompanying clock A is NOT an outside observer who you have apparently been attempting to remove.

The observer accompanying clock A is the only observer who can claim to be correct but only when he arrives at B’s location and - ‘looking out of his window’ - finds that his clock lags behind clock B.

Whilst you have steered the discussion away from this fact - he can either conclude that B ticked over at a faster rate than his clock as per the nonsensical claim to which my op referred OR that his clock ticked over at a slower rate than B.

Returning to his original location and repeating the experiment he would then be fully justified in believing that although the rate of operation of his clock appears to be unchanged it is, most likely, as it did during his first trip, ticking over at a slower rate than it was before he commenced that second journey in the same way that Hafele and Keating making a hypothetical repeat of the first leg of their experiment would have been fully justified in assuming that their clocks are ticking over at a slower rate than they were before the flight commenced in precisely the same way that they did during the first trip.

 

[cos]

There is no “Twins Paradox” without one twin returning to the other. The only way A can get back to B is no make two trips one outbound the inbound. Period.
If that is not clear to you – then you have no chance of understanding this.

My reference to ‘that comment’ was in relation to Einstein’s comment regarding clock A moving to B’s location which does not allow for two trips.

If you think you can turn the twin problem into a one way trip – that does not belong in a thread titled “twin paradox”!

Having taken my comment out of context you are side-stepping my argument that there would be no difference to Einstein’s conclusion that A lags behind B if A moved to B’s location (i.e. the twin’s return journey) or if A was initially alongside and synchronous with B and traveled away from B for the same distance, and at the same velocity (i.e. the twin’s outward-bound journey), as A’s trip to B’s location

You cannot do twins with a oneway trip, without taking Einstein quotes completely out of context

I didn’t; you took my comments out of context.

According to Einstein’s paragraph 1, chapter 4, OEMB depiction when the astronaut makes his outward bound trip his clock will lag behind his twin’s clock by precisely the same amount as it additionally lags behind the twin’s clock on his return journey by .5tv²/c².

most importantly ignoring his point that simultaneity can only exist for two things that are collocated next to each other;

Where, in any of my messages did I ignore that point?

as in when Clock A and B are next to each other on the outbound trip and when they pass next to each other again during the inbound trip by B.

What are you talking about? A and B are not, in Einstein’s chapter 4 depiction, “next to each other on the outbound trip.” nor are they “next to each other on the outbound trip.” in the twin paradox!

A and B do not “pass next to each other again during the inbound trip by B.” In the twin paradox. A (the astronaut’s clock) arrives at B’s location (his twin’s clock) it does not pass B.

If you have not already done the math to see this is true you are not even trying.

I have not already done the math due to the fact that I cannot do the math however I agree with Einstein that “As far as the propositions of mathematics are certain; they do not refer to reality.” I am of the opinion that physics should be a subject that deals with reality.

Just pick 5 different “C” observers to calculate and record all the times and locations for Clocks A & B wrt to the stationary observer C.

There are no ‘C’ observers either in Einstein’s depiction or the twin paradox. Determinations arrived at, or predictions made, by purely hypothetical observers C have absolutely no affect whatsoever on what physically takes place in A’s or B’s reference frames. I am of the opinion that physics should be a subject that deals with reality.

 

[Dale]

Does the diagram you drew show that clock A does not lag behind clock B? Does it show that clock A does not 'go more slowly' (i.e. tick over at a slower rate) than clock B?

Forget for a moment about what the clocks show. Do you see how the diagram represents the kinematics, the motion, of the clocks? In other words, do you see that a vertical line represents a clock at rest and a diagonal line represents a moving clock? Can you piece those rules together to see that the diagram correctly represents the motion of the clocks in Einstein's chapter 4?

 

[matheinste]

Hello cos.

In reply to your post #186. Thanks for pointing out my error. It is of course not what i meant. You say that you agree with my interpretation of waht you are saying. Thats helpful. I am currently busy with less interesting things but will get back as soon as.

Just to recap without comment from me. -- You are saying that Einstein says in the place quoted that the difference in clock readings is due to A's movement. ---That A's clock slowed down during the journey is your interpretation of why there is a difference.

Matheinste.

 

[RandallB]

There are no ‘C’ observers either in Einstein’s depiction or the twin paradox. Determinations arrived at, or predictions made, by purely hypothetical observers C have absolutely no affect whatsoever on what physically takes place in A’s or B’s reference frames. I am of the opinion that physics should be a subject that deals with reality.

Nobody said that the selection of C will change the reality of anything, only what the observer thinks might be real.
But you are not using reality when you insist on arguing the twins as a one way trip, because you can not justify which POV give the correct and “real” view of reality; the view from Clock B or the view from moving clock A.

I know enough about the many folks that have tried to help you in this thread to know they all know much more than you about the Twins than you. And yet in over 180 posts you don’t seem to have learned a single think since your OP. That’s because you are arguing instead of listening and learning.

I’m all for reality so you tell use which view is the correct view of reality A or B when the only thing they agree on is the start time when A passes B and both set there clocks to O (zero). All the other C frames I mentioned (that you refuse to do the math on) also agree that A & B both simultaneously read “0” at that defined starting point. But never again will any two reference frames agree on what both A & B read simultaneously in your one way problem – never!
So if you big on reality; which frame is giving you the correct version of reality and just how do you justify your choice of frame as correct?

However if you do the twins correctly and have A turnaround at a well defined time or place and eventually pass the ‘stationary’ B again all frames will continue to disagree about almost every thing except one and only one thing. Each and every frame will show the same times for both A & B (with A less than B) at the moment A & B pass each other again.
After you do the math how can you every create a reality where the returning A twin was anything but younger than B. Not only do all frames agree A will be younger they all agree on the same ages and differences.
That all frames agree to the same reality at the point the two come back together – is the only point that can be taken as being “real” in the Twins Paradox.
But as to the other predictions made by the various ref. frames; nothing (at least within SR rules) can rule out any of as incorrect or not “real”.
And if you cannot rule out any frame as incorrect you cannot assume anyone frame is in reality logging time simultaneously including your own.
Meaning no matter how well you use light or radio signals to synchronize clocks from coast to coast on zulu time – you cannot depend on them all in reality hitting 12:00:00 simultaneously only that in your POV in this frame of reference they appear to.

You will not understand SR or Twins until you understand that,
and you best first step to actually learning something about it is DO THE DARN MATH.
It really is not that hard.

 

[cos]

Forget for a moment about what the clocks show. Do you see how the diagram represents the kinematics, the motion, of the clocks? In other words, do you see that a vertical line represents a clock at rest and a diagonal line represents a moving clock? Can you piece those rules together to see that the diagram correctly represents the motion of the clocks in Einstein's chapter 4?

On the basis that 'what the clocks show' is the central issue of my argument I see no reason whatsoever for me to forget that phenomenon even for just a moment.

I am of the opinion that the diagram is an interpretation of what the math shows and as far as I am concerned the reality of 'what the clocks show' takes precedence.

I can only repeat my question "Does the diagram you drew show that clock A does not lag behind clock B? Does it show that clock A does not 'go more slowly' (i.e. tick over at a slower rate) than clock B?"

Unless you can answer this important and overriding question we should forget the whole thing.

If the diagram shows that A does not lag behind B thus that A does not 'go more slowly' than B then as far as I am concerned the diagram contradicts Einstein's chapter 4 regardless of the fact that, as you point out, it "correctly represents the motion of the clocks in Einstein's chapter 4?." It is not their motion with which I am concerned; my interest lies specifically in what happens to clock A.

 

[cos]

You are saying that Einstein says in the place quoted that the difference in clock readings is due to A's movement. ---That A's clock slowed down during the journey is your interpretation of why there is a difference.

That's what I'm saying.

In his 1918 article Einstein said the same thing - that it was the clock that changed reference frames that physically 'goes more slowly than' (my interpretation being 'ticks over at a a slower rate than' or 'incurs time dilation relatively to') the clock (B) that does not change reference frames (i.e. does not accelerate).

 

[Dale]

as you point out, it "correctly represents the motion of the clocks in Einstein's chapter 4?."

I am going to take this as a "yes" that you do understand how vertical lines represent objects at rest in the given reference frame and how slanted lines represent objects moving in that frame and therefore you agree that the diagram correctly represents the motion of the clocks in section 4.

I can only repeat my question "Does the diagram you drew show that clock A does not lag behind clock B? Does it show that clock A does not 'go more slowly' (i.e. tick over at a slower rate) than clock B?"

Unless you can answer this important and overriding question we should forget the whole thing.

The diagram shows that the interval between a1 and a2 is shorter than the interval between b1 and b2. Therefore A, having measured a shorter interval than B, will read less when they meet. Again, this is seen to be a property of the path rather than a property of the clocks. Both clock A and B correctly measured the interval of their respective paths through spacetime, but clock A took a "shortcut" so it reads less than clock B.

 

[cos]

Nobody said that the selection of C will change the reality of anything, only what the observer thinks might be real.

The argument was that A and B may not initially have been at rest as Einstein depicted but that from (a purely imaginary) C's point of view A and B may have initially been moving at v relatively to him thus that A did not accelerate then move toward B at v but that A decelerated (and came to a stop in C's reference frame) and that B moved toward A at v (i.e. at v relatively to C) thus that it was B that was moving thus that it was B that 'went more slowly' than A.

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!

But you are not using reality when you insist on arguing the twins as a one way trip, because you can not justify which POV give the correct and “real” view of reality; the view from Clock B or the view from moving clock A.

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?

On the basis that an observer located alongside clock B and an observer accompanying clock A have both read and agree with Einstein's chapter 4 depiction as well as his 1918 article they can both be of the opinion that A is 'going more slowly' (i.e. ticking over at a slower rate) than B.

In paragraph 1, chapter 4, Einstein refers to a one way trip however in paragraph 2 he points out that the same results will be arrived at "if the clock moves from A to B in any polygonal line." An astronaut's out-and-return trip IS a polygonal line!

The astronaut travels at the same velocity (v) for the same period of time (t) and covers the same distance ergo both trips comply with Einstein's one way depiction and his polygonal line depiction.

I know enough about the many folks that have tried to help you in this thread to know they all know much more than you about the Twins than you. And yet in over 180 posts you don’t seem to have learned a single think since your OP. That’s because you are arguing instead of listening and learning.

I have no doubt whatsoever that back in 1905 Einstein was told that the many folks that had tried to explain to him that Newton's theory invalidated his theory also knew more about the subject of physics than he did.

You are obviously laboring under the misapprehension that my OP was an attempt to learn something by listening to the opinions of others - it was NOT!

It was a statement in relation to which numerous responses have tried to convince me that the pov of an external observer has validity - it does NOT!

I’m all for reality so you tell use which view is the correct view of reality A or B when the only thing they agree on is the start time when A passes B and both set there clocks to O (zero).

That situation NEVER ARISES neither in Einstein's chapter 4 NOR his 1918 article!

It is similarly inapplicable comments such as yours that create confusion!

All the other C frames I mentioned (that you refuse to do the math on) also agree that A & B both simultaneously read “0” at that defined starting point.

Even if I were capable of 'doing the math on' all the other C frames you mentioned I would refuse to apply that math to the situation referred to in Einstein's chapter 4 or his 1918 article on the basis that the opinion expressed by (i.e. the mathematical determinations arrived at by) numerous C frames has absolutely no affect whatsoever on what A and B determine!

On the basis of the 'Relativity of Simultaneity' NONE of the C frames "agree that A & B both simultaneously read “0” at that defined starting point." i.e. the starting point depicted by Einstein in paragraph 1, chapter 4 where A is at a fixed distance from B. Try to get your facts straight!

But never again will any two reference frames agree on what both A & B read simultaneously in your one way problem – never!

I never, in any of my postings, made any comment in relation to an agreement or otherwise as to the simultaneity of those clocks ergo your comment is totally unwarranted and inapplicable!

So if you big on reality; which frame is giving you the correct version of reality and just how do you justify your choice of frame as correct?

On the basis of my assumption that observers located in both frames (A and B) have read and fully agree with Einstein's chapter 4 as well as his 1918 article then both frames will realize that reality is that clock A (the astronaut's clock) 'goes more slowly' (i.e. ticks over at a slower rate than) B (the Earth clock).

However if you do the twins correctly and have A turnaround at a well defined time or place and eventually pass the ‘stationary’ B again all frames will continue to disagree about almost every thing except one and only one thing. Each and every frame will show the same times for both A & B (with A less than B) at the moment A & B pass each other again.

After you do the math how can you every create a reality where the returning A twin was anything but younger than B. Not only do all frames agree A will be younger they all agree on the same ages and differences.

Has anything I have written given you the impression that I was saying that A will not lag behind B?

That all frames agree to the same reality at the point the two come back together – is the only point that can be taken as being “real” in the Twins Paradox.

I believe that when Einstein wrote in his chapter 4 that a clock at the equator "must go more slowly...than a precisely similar clock at one of the poles under otherwise identical conditions." he was of the opinion that this is real!

His paragraph 1 depiction of clock A moving to B's location effectively incorporates the same factor - clock A will 'go more slowly' than B thus arrives at B's location lagging behind B.

But as to the other predictions made by the various ref. frames; nothing (at least within SR rules) can rule out any of as incorrect or not “real”.

I don't know if it would come under the heading of an SR 'rule' however on the basis that it is part of SR Einstein's paragraph 3, chapter 4 indicates to me that he was suggesting that although an observer located at the equator (on a hypothetical massless transparent sphere the size of the Earth) might 'see' the 'stationary' polar clock ticking over at a faster rate than his own clock thus insist that this is reality Einstein suggested that it is not reality; he suggested that the equatorial clock physically ticks over at a slower rate than the polar clock.

An observer accompanying Einstein's paragraph 1, chapter 4 clock A in accordance with SR's chapters 1 through 3 'rules' would determine or predict that clock B, moving toward him at v, is ticking over at a slower rate than his own clock thus that when he arrives at B's location it should, according to his predictions in accordance with SR rules, lag behind his own clock however he finds, much to his surprise, that his clock lags behind B as Einstein suggested it would.

And if you cannot rule out any frame as incorrect you cannot assume anyone frame is in reality logging time simultaneously including your own.

What do you mean by 'logging time simultaneously'?

An astronaut, having read and fully accepted Einstein's chapter 4 depiction as well as his 1918 article, can come to the conclusion that although his clock appears to be ticking over at its normal rate it is, in reality, ticking over at a slower rate than it was before he started moving.

Having carried out the first leg of their experiment and discovering that their clocks lagged behind the laboratory clocks Hafele and Keating would have been fully justified in concluding that, during their flight, their clocks were physically ticking over at a slower rate than they were before the flight commenced analogous to the fact that a clock at the equator will, according to Einstein, tick over at a slower rate (i.e. 'go more slowly') than a clock at one the poles.

In his book 'Was Einstein Right? Clifford M Will points out that Einstein's polar clock is analogous to a hypothetical master clock at the center of the planet.

In paragraph 3, chapter 4, Einstein points out that if a clock is made to move in a closed curve around an 'at rest' clock the moving clock (as will his equatorial clock) 'go more slowly' than the at rest clock (i.e. the master clock, above) in accordance with the equation .5tv²/c².

Therefore the laboratory clocks in Washington tick over at a slower rate than a master clock and because of their faster rate of travel (v in Einstein's equation) the clocks in the first leg of the HKX went more slowly than the laboratory clocks.

If they had repeated that same trip Hafele and Keating would have been fully justified in realizing, all appearances to the contrary, that their clocks were, in reality, ticking over at a slower rate than they were before the flight commenced.

Meaning no matter how well you use light or radio signals to synchronize clocks from coast to coast on zulu time – you cannot depend on them all in reality hitting 12:00:00 simultaneously only that in your POV in this frame of reference they appear to.[/QUOTE

Irrelevant! Nothing whatsoever to do with what the astronaut determines is taking place in his own reference frame.

You will not understand SR or Twins until you understand that,

Irrelevant! 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.

and you best first step to actually learning something about it is DO THE DARN MATH.
It really is not that hard.

On the basis of my agreement with Einstein that as far as the propositions of mathematics are certain they do not refer to reality I see absolutely no reason whatsoever to 'DO the darn math' on the basis that my interest is IN reality!

 

[cos]

The diagram shows that the interval between a1 and a2 is shorter than the interval between b1 and b2. Therefore A, having measured a shorter interval than B, will read less when they meet. Again, this is seen to be a property of the path rather than a property of the clocks. Both clock A and B correctly measured the interval of their respective paths through spacetime, but clock A took a "shortcut" so it reads less than clock B.

I'm going to take this (that clock A reads less than clock B) as a "no" in response to my question ""Does the diagram you drew show that clock A does not lag behind clock B?"

Would you please respond to my second, and much important question "Does [the diagram you drew] show that clock A does not 'go more slowly' (i.e. tick over at a slower rate) than clock B?"

 

[Dale]

I'm going to take this (that clock A reads less than clock B) as a "no" in response to my question ""Does the diagram you drew show that clock A does not lag behind clock B?"

Correct, that is what I said. The diagram shows that clock A does lag behind clock B on their reunion since the interval it travels is shorter.

Would you please respond to my second, and much important question "Does [the diagram you drew] show that clock A does not 'go more slowly' (i.e. tick over at a slower rate) than clock B?"

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).

 

[cos]

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'?

 

[Dale]

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 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