Understanding Time Dilation in Einstein's Special Theory of Relativity

[DrGreg]

Thanks for the illustration DrGreg! Did you use any special graphing program to put those together or just make it in a drawing program? I'd like to find some simple program to put together spacetime diagrams quickly, they'd come in handy on a lot of these threads...

No, I just used Microsoft Powerpoint as a drawing tool (the 2007 version conveniently is able to export as PNG which I can then crop to size before uploading, otherwise I could have done a screen dump).

In the past I've used the specialist software MATLAB to draw accurate graphs, but that was using someone else's computer. I think you could use Microsoft Excel, or other graph-plotting software, in a similar way. But in this case I just drew some lines and circles and arranged them by eye.

 

[cos]

So the observer is located at the center of the wheel; he determines that the rim clock (A) is moving around him at v and, applying Einstein's section 4 STR equation (i.e. "...the equation is used in the inertial frame in which the center clock is at rest."), he calculates the slower rate at which the rim clock is ticking compared to his own clock's rate of operation (i.e. clock B).

Still located at the center of the wheel is he not entitled to be of the opinion that if he moved to A's location that his clock would, then, also be ticking over at the same slower rate than a central clock?

Yes, but it's not just his opinion, it's objective fact in his frame.

Thank you.

Is he not entitled to be of the opinion that the same 'law' of physics that causes clock A to tick over at a slower rate than B would equally affect his clock?

Yes, he is.

Ditto.

If he sends another clock, that is synchronous with his clock, out to A's location would he not, then, see that clock ticking over at a slower rate than it was before it moved?

Yes, he would. But not everyone would. Some hypothetical observers would see that same clock tick at a faster rate than it did before it moved. Because in some reference frames, it "runs slower" and in some frames it "runs faster" than it did when it was at the center.

So he sends another clock to A's location and determines the objective fact that that clock is ticking over at a slower rate than it was before it moved (ergo slower than his own clock) however he then takes into account that from the point of view of some hypothetical observers that clock "runs slower" or "runs faster" than it did when it was at the center of the wheel.

Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?

Are any of the numerous hypothetical observers entitled to realize that whilst that relocated clock is, from their point of view (in accordance with their mathematical calculations, determinations, predictions,*******) ticking over at a slower rate (or faster rate) than it was when it was at the center of the wheel that in the original observer's frame the relocated clock is ticking over at a slower rate than it was before it moved?

Does anything that those hypothetical observers determine have any affect whatsoever on that clock?

I suggest that they do not!

For all intents and purposes, as far as the real observer, is concerned those hypothetical observers are just that!

For all intents and purposes, as far as the real observer is concerned, those hypothetical observers do not exist!

Having determined the objective fact that a clock at the rim is ticking over at a slower rate than his own clock and having sent a clock to A's location and determined the objective fact that it is then ticking over at a slower rate than his own clock he moves to A's location.

Before he moves from the center of the wheel - you agree with me that he can determine that when he moves to the rim his clock will then be subjected to the same 'law' of physics that caused the rim clock to be ticking over at a slower rate than his centrally located clock - that his clock will be ticking over at a slower rate than it is whilst he is still at the center of the wheel.

He moves to A's location; is he then not entitled to be of the opinion that the same 'law' of physics that caused the rim clock to be ticking over at a slower rate than the central clock no longer applies to him and his clock?

Prior to moving from the center of the wheel he notices that a clock at that location is stationary alongside him. It is (relative to him) not spinning on an axis and he is not being subjected to any g force (he is actually spinning very slowly - it is a wheel of enormous diameter - but cannot feel that he is on the basis that it is an otherwise empty universe).

He moves to the wheel rim which he knows is spinning around it's hub on the basis that, having arrived at that location, he is now looking at a central clock that is spinning on it's axis but, more importantly, he is then being subjected to an enormous g force attempting to move him further away from the center of the wheel ergo he knows that his is not an inertial frame.

He knows (having previously determined the speed at which a clock on the rim is spinning around the center of the wheel) that his clock is moving at that same speed ergo applies Einstein's equation and determines the, then, slower rate of operation of his clock.

It is ticking over at it's 'proper' time but he knows that it is (as is Einstein's section 4 clock traveling in a closed curve around an at rest clock) moving and that in accordance with section 4 (as well as his determination of an objective fact whilst he was at the center of the wheel) it is 'going more slowly' than it was before he moved to the rim.

I'm not suggesting that he must or that he should arrive at this conclusion but that he could!

 

[atyy]

Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?

Yes.

Does anything that those hypothetical observers determine have any affect whatsoever on that clock?

No.

I'm not suggesting that he must or that he should arrive at this conclusion but that he could!

I can arrive at any conclusion I want any time.

Proposed answers only. If they don't make sense, read what JesseM has to say!

 

[Al68]

So he sends another clock to A's location and determines the objective fact that that clock is ticking over at a slower rate than it was before it moved (ergo slower than his own clock) however he then takes into account that from the point of view of some hypothetical observers that clock "runs slower" or "runs faster" than it did when it was at the center of the wheel.

Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?

Well, like I pointed out, that's only an objective fact in his frame. Those other hypothetical observers agree with the objective fact that clock "C" slowed down in the frame of your observer.

The same laws of physics that caused the clock to "slow down" in your observer's frame also caused the same clock to "speed up" in other frames, whether actual observers are present or not. After all, your observer is hypothetical as well.

Whether or not the clock slowed down or sped up is frame dependent, not observer dependent or a matter of opinion.

 

[JesseM]

So he sends another clock to A's location and determines the objective fact that that clock is ticking over at a slower rate than it was before it moved (ergo slower than his own clock) however he then takes into account that from the point of view of some hypothetical observers that clock "runs slower" or "runs faster" than it did when it was at the center of the wheel.

Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?

Again, it is meaningless to talk about clock rates without specifying a choice of frame. He believes that the clock at the edge of the wheel is ticking slower in the frame where he is at rest, and so does the hypothetical observer at rest in a different frame. Likewise, the hypothetical observer B at rest in the other frame believes that the clock at the center is ticking slower than the clock at the edge (at some specific moment) in the frame where that observer B is at rest, and the observer at the center of the wheel agrees. Either observer can make determinations/predictions/calculations in any frame they choose, and as long as they specify which frame a particular statement about clock rates is meant to apply in, their statements will be objective facts that all observers should agree on. On the other hand, if you talk about clock rates without specifying a choice of frame, your statements are too ill-defined to be judged true or false.

He knows (having previously determined the speed at which a clock on the rim is spinning around the center of the wheel) that his clock is moving at that same speed ergo applies Einstein's equation and determines the, then, slower rate of operation of his clock.

It is ticking over at it's 'proper' time but he knows that it is (as is Einstein's section 4 clock traveling in a closed curve around an at rest clock) moving and that in accordance with section 4 (as well as his determination of an objective fact whilst he was at the center of the wheel) it is 'going more slowly' than it was before he moved to the rim.

I'm not suggesting that he must or that he should arrive at this conclusion but that he could!

He can certainly conclude that his clock is now going more slowly in the inertial rest frame where the center of the wheel is at rest, and every possible observer would agree with that statement. But if you don't add that qualifier about which frame you mean your statements to apply to, but just say something like "my opinion is that his clock is moving more slowly once he's at the rim of the wheel", then you aren't making well-defined statements about physics.

 

[atyy]

He moves to the wheel rim which he knows is spinning around it's hub on the basis that, having arrived at that location, he is now looking at a central clock that is spinning on it's axis but, more importantly, he is then being subjected to an enormous g force attempting to move him further away from the center of the wheel ergo he knows that his is not an inertial frame.

Now that he's moved to the rim, hasn't the inertial observer at the centre become hypothetical? If hypothetical observers and the frames that one may associate with them are disallowed, how is he supposed to determine that his clock is ticking more slowly in the inertial frame associated with the hypothetical observer at the centre of the wheel? If that particular hypothetical observer and associated inertial frame is allowed, how then would other hypothetical observers and their frames be disallowed?

Again, I defer to JesseM on all serious matters.

 

[cos]

So he sends another clock to A's location and determines the objective fact that that clock is ticking over at a slower rate than it was before it moved (ergo slower than his own clock) however he then takes into account that from the point of view of some hypothetical observers that clock "runs slower" or "runs faster" than it did when it was at the center of the wheel.

Does that determination arrived at by some hypothetical observer affect his opinion, determination, prediction, calculation, ******* (insert your choice of word) of the clock's slower rate? Does it alter the objective fact that that clock is ticking over at a slower rate than the central clock?

Well, like I pointed out, that's only an objective fact in his frame. Those other hypothetical observers agree with the objective fact that clock "C" slowed down in the frame of your observer.

Those other hypothetical observers can realize that in my observer's frame his clock does slow down!

The determinations arrived at, or opinions expressed, by hypothetical observers have absolutely no application whatsoever to, nor any affect on, what my observer determines!

According to Einstein's section 4 the rate of operation of clock C depends on whether it accelerates or clock B accelerates and it would very much be appreciated (but I believe I am wasting my time pointing out) that my postings relate solely to section 4 STR!

The same laws of physics that caused the clock to "slow down" in your observer's frame also caused the same clock to "speed up" in other frames, whether actual observers are present or not.

My postings are specifically in relation to what my observer determines not what other observers determine. I repeat - The determinations arrived at, or opinions expressed, by hypothetical observers have absolutely no application whatsoever to, nor any affect on, what my observer determines!

After all, your observer is hypothetical as well.

A childish and valueless comment!

Whether or not the clock slowed down or sped up is frame dependent, not observer dependent or a matter of opinion.

And it is exclusively my observer's frame to which my postings specifically apply!

 

[cos]

If hypothetical observers and the frames that one may associate with them are disallowed, how is he supposed to determine that his clock is ticking more slowly in the inertial frame associated with the hypothetical observer at the centre of the wheel? If that particular hypothetical observer and associated inertial frame is allowed, how then would other hypothetical observers and their frames be disallowed?

If you seek to contribute something worthwhile to this thread you could at least try to get your facts straight.

 

[atyy]

What inertial observer at the center? In my posting I make no reference to an inertial observer that has remained at the center of the wheel when my observer moves to the rim.

My observer moves to the rim as a result of which there is no observer at the center of the wheel. There is only a clock with which he compares rates of operation.



If you seek to contribute something worthwhile to this thread you could at least try to get your facts straight.

You are funny! :rofl:

 

[atyy]

BTW, are the clocks at the centre and the rim (Einstein?) synchronizable?

 

[Al68]

Those other hypothetical observers can realize that in my observer's frame his clock does slow down!

Yes they would.

The determinations arrived at, or opinions expressed, by hypothetical observers have absolutely no application whatsoever to, nor any affect on, what my observer determines!

That's right. The equations give the exact same answer regardless of what any observer thinks (including yours).

According to Einstein's section 4 the rate of operation of clock C depends on whether it accelerates or clock B accelerates and it would very much be appreciated (but I believe I am wasting my time pointing out) that my postings relate solely to section 4 STR!

Well, since section 4 doesn't contradict any other section, I don't see the problem.

My postings are specifically in relation to what my observer determines not what other observers determine. I repeat - The determinations arrived at, or opinions expressed, by hypothetical observers have absolutely no application whatsoever to, nor any affect on, what my observer determines!

That's right. Whatever the answer is is objectively true in that frame and doesn't even need any observer present to be true.

And it is exclusively my observer's frame to which my postings specifically apply!

That's what I thought, which is why a lot of my answers were yes with the caveat "in his frame".

The only reason I pointed out that whether or not clock C "slows down" or "speeds up" is frame dependent is just to make it clear that nothing is actually "physically happening" to the clock in any universal sense.

I know it seems pedantic to always state the frame that the velocity (and therefore the relative tick rate) of the clock is relative to, but the factor [sqrt(1-v^2/c^2) is different for different values of v, and v is different for different reference frames.

And the reason it's called relativity is because each result obtained is relative to a particular frame, and not true in any other (absolute) sense.

 

[atyy]

Rindler, http://books.google.com/books?id=fUj_LW51GfQC&printsec=frontcover#PPA185,M1

Hmmm, if I'm reading Rindler's discussion beginning from the bottonm of p185 correctly, then the clock at the centre and the rim can be made Einstein synchronous, in which case it could be said to be ticking more slowly in a frame independent manner. If I remember correctly, clocks stationary in two different Lorentz inertial frames cannot be Einstein synchronized, hence "ticking more slowly" in that case only has a frame dependent meaning. Just thinking intuitively here, is this actually correct?

 

[john 8]

It seems like you're suggesting that something physically happens to the clocks. This is simply not the case. The rate that a clock ticks is simply a frame dependent quantity. It's different for different reference frames. Saying that a clock actually changes its "ticking rate" is like saying that a car "slowed down" because its relative speed is different for different observers in relative motion. And the fact that the cars relative speed depends on reference frame doesn't mean that the observers disagree, they will agree that the relative speed of the car frame dependent. .

Hi Al68.

I swear that I am not singling you out. I was browsing other threads and this caught my attention.

You say that the rate that a clock ticks is simply a frame dependent quantity. Really? Correct me if I am wrong, but are not all clocks man made machines that are designed to tick or move at a predetermined rate that is determined by man? A clock is not some thing that motivated to tick or count off numbers by some outside influence, a clock is not motivated by some exterior force that move it’s inner workings. A clock is just a machine designed to move or count off numerical increments according to how it was made. A clock will tick at the same rate in any frame of reference, how that is perceived by man is another story. A clock's motion is not dependent on a frame of reference, it will always move or count off numbers at a predetermined rate that can only be changed by changing the amount of energy applied to the actual structure or inner workings of the clock. Right?

 

[john 8]

Alright, I have read though most of this thread and have seen a few outpoints that need to be resolved regarding time dilation.

First thing that needs to be established is the exact way in which a clock is motivated to move or count off numbers. Is energy being applied to it in some manner to motivate this machine called a clock?

If No, than please explain or give a reference on how a clock move or changes without any energy being involved.

If yes, than what types of energy can be used to motivate the machine called a clock?

Can electricity be used? Yes

Can spring tension be used? Yes

Can the motion of mass (as in a water clock, an atomic clock) be used? Yes

I am sure some of you could think of other ways in which energy can be used to motive a clock, but in all of these different types of energy that can be thought of that in actuality cause a change in a clock, is time an energy that can be detected by a clock or has the ability to change the workings of this machine known as a clock.

You see the question of time dilation can only be answered when it has been established what causes a change in any clock and is time an actual physical thing that has the ability to cause change in a clock.

If you say that time is indeed is a physical thing and can actually influence the workings of a clock, then you would have to explain how this occurs. It has not been described in any writings on this planet.

In order for there to be a physical occurrence of time dilation, time would have to be a form of energy and you would need to have a physical measuring device that is capable of detecting this form of energy called time.

So. To those of you who think that time dilation is an actual physical occurrence, can you explain how this phenomenon works, or at least show a reference that explains it.

If you say that experiments on time dilation have been done to prove the occurrence. Let me remind you that two machines that go out of synch after being moved around only goes to show that machines can go out of synch, saying that this out of synch occurrence is due to some influence of a thing that physics has never defined as a thing that is a form of energy is absurd.

Physics does not define time as a form of energy, yet it takes energy to change a clock. So in order to have the occurrence known as time dilation to be an actual physical phenomenon time has to be a form of energy. You cannot have it both ways.

You can argue and protest all that you like. Science does not recognize time as a form of energy. Time dilation involves the notion that this thing called time is being dilated, and the only way to measure this dilation is with a machine known as a clock. Clocks are only motivated by energy. So in order for this time thing to influence a clock this time thing has to be a form of energy.

Let the discussion begin.

 

[matheinste]

Alright, I have read though most of this thread and have seen a few outpoints that need to be resolved regarding time dilation.

First thing that needs to be established is the exact way in which a clock is motivated to move or count off numbers. Is energy being applied to it in some manner to motivate this machine called a clock?

If No, than please explain or give a reference on how a clock move or changes without any energy being involved.

If yes, than what types of energy can be used to motivate the machine called a clock?

Can electricity be used? Yes

Can spring tension be used? Yes

Can the motion of mass (as in a water clock, an atomic clock) be used? Yes

I am sure some of you could think of other ways in which energy can be used to motive a clock, but in all of these different types of energy that can be thought of that in actuality cause a change in a clock, is time an energy that can be detected by a clock or has the ability to change the workings of this machine known as a clock.

You see the question of time dilation can only be answered when it has been established what causes a change in any clock and is time an actual physical thing that has the ability to cause change in a clock.

If you say that time is indeed is a physical thing and can actually influence the workings of a clock, then you would have to explain how this occurs. It has not been described in any writings on this planet.

In order for there to be a physical occurrence of time dilation, time would have to be a form of energy and you would need to have a physical measuring device that is capable of detecting this form of energy called time.

So. To those of you who think that time dilation is an actual physical occurrence, can you explain how this phenomenon works, or at least show a reference that explains it.

If you say that experiments on time dilation have been done to prove the occurrence. Let me remind you that two machines that go out of synch after being moved around only goes to show that machines can go out of synch, saying that this out of synch occurrence is due to some influence of a thing that physics has never defined as a thing that is a form of energy is absurd.

Physics does not define time as a form of energy, yet it takes energy to change a clock. So in order to have the occurrence known as time dilation to be an actual physical phenomenon time has to be a form of energy. You cannot have it both ways.

You can argue and protest all that you like. Science does not recognize time as a form of energy. Time dilation involves the notion that this thing called time is being dilated, and the only way to measure this dilation is with a machine known as a clock. Clocks are only motivated by energy. So in order for this time thing to influence a clock this time thing has to be a form of energy.

Let the discussion begin.

Any elementary textbook on Special Relativity or even Wikipedia will explain these things.

Matheinste.

 

[cos]

BTW, are the clocks at the centre and the rim (Einstein?) synchronizable?

They are synchronized before the wheel starts spinning.

 

[DrGreg]

cos

Let me present an analogy to show why your obsession with which clock is "really" ticking slower, regardless of frame, is misguided.

Two astronauts Alice and Bob are traveling together in deep space (far from any gravity) and on their travels they encounter a number of pairs of objects. As they find each pair, they both take a photo, simultaneously. The results are below: the top row are Alice's photos; the bottom row are Bob's.

(Note: this is assumed to take place in a Newtonian universe. Ignore relativistic distortions to the photos.)

Now, looking at the first pair of photos on the left, which line has the steepest slope (or steepest gradient, if you prefer)? In Alice's photo, it looks like the blue line. But it Bob's photo, it looks like the red line. cos, which of the two lines really, physically, actually has the steepest slope?

Similarly, for the middle pair of photos, which line, the red or the blue, really, physically, actually has the steepest slope?

Similarly, for the rightmost pair (which is supposed to be a 3D blue helix wrapped around a red axis) which line, the red or the blue, really, physically, actually has the steepest slope?

If you say these are all nonsense questions, that is exactly my point.

Here, slope is a ratio of two distances, vertical height divided by horizontal width. The analogy is with your example of a ratio of two times.

 

[Al68]

A clock's motion is not dependent on a frame of reference, it will always move or count off numbers at a predetermined rate that can only be changed by changing the amount of energy applied to the actual structure or inner workings of the clock. Right?

Are you aware that energy is frame dependent, even in classical physics? So the "amount of energy applied to the actual structure or inner workings of the clock" would itself depend on the reference frame.

And when I say that the rate a clock ticks is frame dependent, that's within SR assuming that the clock keeps perfect time. Mathematically, the value of [sqrt(1-v^2/c^2)] will be different for different values of v, and v for any specific clock is different for different reference frames.

I won't bother claiming that SR is correct, so just assume that anything I've said in this thread has the caveat "according to SR", since that's the theory being discussed.

 

[Al68]

Rindler, http://books.google.com/books?id=fUj_LW51GfQC&printsec=frontcover#PPA185,M1

Hmmm, if I'm reading Rindler's discussion beginning from the bottonm of p185 correctly, then the clock at the centre and the rim can be made Einstein synchronous, in which case it could be said to be ticking more slowly in a frame independent manner.

Well if you just alter the clock at the rim to run at the same rate as the center clock in the rim clock's frame, they would stay in synch just because then the rim clock would not be keeping proper time. ie it would run slow relative to its own proper time and relative to a "good" local clock stationary with it.

 

[phyti]

There isn't really room for differing "opinions" in SR, there are just statements of fact about what is true in a given frame, no one ever disagrees about what's true in a specific frame. It's certainly true that in the inertial frame where the center of the wheel is at rest, an observer's clock will tick slower if he moves from the center to the edge of the wheel. But without the context of a particular frame, it's meaningless to offer "opinions" about which clock is ticking slower at a given moment.

Einstein had opinions, and derived the theory you are discussing!
The 'opinion' in the quoted post by cos is 'drawing a conclusion based on fact'.
He is merely repeating the experiment as stated, and according to postulate 1 (your favorite), expects consistent physics. Per your reply, you agree.

It's certainly true that in the inertial frame where the center of the wheel is at rest, an observer's clock will tick slower if he moves from the center to the edge of the wheel.

The context is there (if you take time to read it), and your last statement isn't needed.

 

[phyti]

... Time dilation involves the notion that this thing called time is being dilated, and the only way to measure this dilation is with a machine known as a clock. Clocks are only motivated by energy. So in order for this time thing to influence a clock this time thing has to be a form of energy.

Let the discussion begin.

Energy is transferred at light speed via photons. Unlike material particles, light moves independently of its source and at a constant speed. If an object moves, the internal process of energy transfer takes longer on average. Time is not a thing, it's a relationship between events. The observer matches an event to a clock event (tick), the same as matching the end of an object to a mark on a ruler, i.e. measurement. The rate of ticks therefore depends on the speed of the clock. Anything that has a uniform periodic rate, your pulse, the Earth rotation, yearly cycle, atomic vibrations, etc. can be used, depending on the precision required.

 

[JesseM]

Einstein had opinions, and derived the theory you are discussing!

I said "no rooms for differing opinions within SR", meaning among those who already accept the theory and are discussing conclusions made using the theory.

It's certainly true that in the inertial frame where the center of the wheel is at rest, an observer's clock will tick slower if he moves from the center to the edge of the wheel.

The context is there (if you take time to read it), and your last statement isn't needed.

cos did eventually say he was talking about the frame of the observer at the center of the wheel, but it took a lot of prodding from other people before he did so. And it's still not completely clear to me that he would agree with the following:
1. That conclusions in all inertial frames are equally valid, even ones in which no observer happens to be at rest
2. That different observers never have differing opinions on any statements as long as the context of what frames they're talking about is clear
3. That an observer is not "naturally" required to use the frame where he is at rest when making statements about clock rates

 

[atyy]

Well if you just alter the clock at the rim to run at the same rate as the center clock in the rim clock's frame, they would stay in synch just because then the rim clock would not be keeping proper time. ie it would run slow relative to its own proper time and relative to a "good" local clock stationary with it.

And is it true that such a thing couldn't be done with two clocks moving at different constant velocities relative to a Lorentz inertial frame?

 

[atyy]

In addition to whether two particular clocks can be (rate?, Einstein?) synchronized, there is the question of whether that synchronization agrees with slow clock transport. Jammer refers to Rumpf's study on this: http://books.google.com/books?id=vuTXBPvswOwC&printsec=frontcover#PPA288,M1.

 

[phyti]

We can design the clocks to emit flashes of light at hourly intervals. Position an observer M above the center clock on the axis of the orbit, and assume a 24 hr orbit. A real world scenario will include a distant star as a reference for one orbit. M will count 24 flashes per orbit from the center clock. M will count less than 24 flashes per orbit from the moving clock, per time dilation.
The distance is constant between flashes and M for each clock, thus no doppler effect. The frequency of events/flashes matches the frequency of perception/detection. If M moves relative to the two clock system, the perceived frequency of flashes will change, but the clock event frequencies will not.
The motion of M alters his perception but not the physics of clock function.

I specifically make a distinction between event (light emission) and perception (light detection), in case it's causing any confusion for cos specifically, and anyone else in general.
Even Einstein ignored this, using them interchangably. An astronomer would not show you one of those beautiful Hubble photos of star fields and galaxies, and try to convince you they are all the same distance from here.

 

[cos]

And the reason it's called relativity is because each result obtained is relative to a particular frame, and not true in any other (absolute) sense.

In section 4 STR Einstein pointed out that a clock (A) which, having accelerated, moves to the location of another clock (B) clock A will, whilst A is moving, 'go more slowly' (i.e. tick over at a slower rate) than the stationary clock.

Observers A and B will eventually both agree that A lags behind B and I see no reason why they cannot both agree that A ticked over at a slower rate than B thereby creating this lag.

I'm not talking about what either of them 'sees' or 'calculates' or 'predicts' or ‘determines’ during that trip but about what they agree to after the trip.

If A accepts that Einstein was right - that his clock did tick over at a slower rate than B as Einstein suggests it will then he could also, upon repeating that experiment, be of the opinion that whilst he is moving his clock is ticking over at a slower rate than clock B irrespective of the fact that it's rate of operation has seemingly remained unchanged.

Prior to accelerating A is looking at a pulsar that is 'ticking over' at the same rate as his clock. On the basis that (according to Einstein) having moved - his clock is 'going more slowly' than it was before he started moving he will see that pulsar ticking over at a faster rate than his own clock however for him to be of the opinion that his clock's rate of operation has remained unchanged whilst the far-distant pulsar (some millions of light years away and lateral to his direction of travel) is now (virtually instantaneously) spinning on its axis at a faster rate than it was before he started moving is, in my opinion, (to put it mildly) a 'very silly' attitude.

Sections 1 through 3 of STR refer to fully reciprocal phenomena; clock A ‘is’ ticking over at a slower rate than B from B’s inertial frame perspective and clock B ‘is’ ticking over at a slower rate than A from A’s inertial frame perspective however in section 4 he points out that the phenomena is not fully reciprocal; that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.

Contributors point out that I should specify to which frame’s point of view I am referring. In your opinion - to which frame was Einstein referring when he effectively, analogously wrote that clock A ‘goes more slowly’ than clock B?

Some people insist that whilst A is accelerating B was, according to his calculations, ticking over at a faster rate than his own clock but that when A takes his foot off the gas pedal B is instantaneously ticking over at a slower rate than his own clock.

He accelerates to an experimentally maximum attained instantaneous velocity thereby generating a gamma factor of 400 000. At that instant clock B ‘is’, according to his calculations, ticking over at the rate of 400 000 seconds for each of his own seconds.

He flicks a switch extinguishing his rockets and at that very instant clock B reverts from being 400 000 times faster than his own clock and instantaneously[i/] reverts to being 400 000 times slower than his clock!

Is he not likely to be of the opinion that an 800 000 x instantaneous reversal might have some affect on that clock’s mechanism to say nothing of what it might do to an observer accompanying clock B?

On the basis that, whilst still accelerating, A sees clock B (on Earth) ticking over 400 000 times faster than his own clock he must also ‘see’ (i.e. determine) that not only Earth seconds are passing at that enormous rate but also it’s minutes, hours and days. For Earth days to be ticking over at the rate of 400 000 for each of his own days it would have to be spinning on it’s axis at some 640 000 000K-h.

To make matters worse - he stops accelerating whereupon the planet instantaneously stops spinning at 640 million kilometres an hour and virtually stops spinning on it’s axis (it is ‘then’ spinning at some 400 centimeters an hour in lieu of 1 600 kilometers an hour).

People point out that A knows that in B’s reference frame (i.e. the planet’s reference frame) the Earth is not spinning on it’s axis at 640 000 000K-h but at 1 600K-h. If the Earth is not spinning 400 000 times faster than it was then neither is the second hand of clock B yet this is precisely what it is claimed he will ‘see’ (determine, predict).

Proponents of that ‘logic’ (?) point out that the faster rate of B’s ‘tick’ during periods of acceleration exceed the slower rate of B’s tick whilst A is moving with uniform velocity thus this is, they insist, the reason why A and B find that A ultimately lags behind B.

If I am located at an axial point (i.e. the North Pole) of a large spinning, massless and transparent sphere in outer space looking at a clock on that sphere’s rim (i.e. it's equator) I will, according to Einstein’s section 4 STR see that clock ‘going more slowly’ (i.e. ticking over at a slower rate) than my clock.

It matters not that a person alongside that clock sees my clock ticking over at a faster rate than his clock. My presentation is from my point of view, not his!

I send another clock along a line of longitude on that sphere toward the sphere’s equator. As I watch it it progressively ticks over at slower and slower rates than my own clock as it’s speed relative to me increases (it is accelerating).

That clock arrives at the sphere’s equator whereupon it is then ticking over at the same rate as the original equatorial clock ergo at a slower rate than my own clock.

I have every right to assume that if I were to carry another clock along that same line of longitude that it, too, would progressively be ticking over at a slower and slower rate than a polar clock in precisely the same way as the clock I previously dispatched ticked over at a progressively slower rate i.e. the law of physics that physically altered the dispatched clock’s rate of operation as it accelerated will equally apply to my reference frame and to my clock.

I suspect that somebody will respond that from the point of view of observer XYPG on planet Poplex which is in a deadly spiral toward a black hole my clock will not progressively slow down however the views expressed, or opinions held, or determinations made, by that observer have absolutely no affect whatsoever on my observations or determinations and it is MY determinations and predictions to which my postings apply not those of potentially countless hypothetical observers.

People insist that my (actually Einstein’s) comment that clock A will tick over at a slower rate than B is pointless unless I specify to which reference frame I am referring however my comment has always been in reference to ’my’ frame (i.e. observer A’s frame).

 

[cos]

Let me present an analogy to show why your obsession with which clock is "really" ticking slower, regardless of frame, is misguided.

<snip>

If you say these are all nonsense questions, that is exactly my point.

I am of the opinion that they are irrelevant questions.

In section 4 Einstein stated that a clock that moves toward (or is made to move in a closed curve around) another clock will 'go more slowly' (i.e. will tick over at slower rate) than the stationary clock.

If I am located at an axial point (i.e. the North Pole) of a large spinning, massless and transparent sphere in outer space looking at a clock on that sphere’s rim (i.e. it's equator) I will, according to Einstein’s section 4 STR see that clock ‘going more slowly’ (i.e. ticking over at a slower rate) than my clock.

It matters not that a person alongside that clock sees my clock ticking over at a faster rate than his clock. My presentation is from my point of view, not his!

I send another clock along a line of longitude on that sphere toward the sphere’s equator. As I watch it it progressively ticks over at slower and slower rates than my own clock as it’s speed relative to me increases (it is accelerating).

That clock arrives at the sphere’s equator whereupon it is then ticking over at the same rate as the original equatorial clock ergo at a slower rate than my own clock.

I have every right to assume that if I were to carry another clock along that same line of longitude that it, too, would progressively be ticking over at a slower and slower rate than a polar clock in precisely the same way as the clock I previously dispatched ticked over at a progressively slower rate i.e. the law of physics that physically altered the dispatched clock’s rate of operation as it accelerated will equally apply to my reference frame and to my clock.

 

[DrGreg]

I am of the opinion that they are irrelevant questions.

The point of my post was to illustrate that that there are some questions (such as "which way is 'up' when there's no gravity?") to which there is no "real" answer, only an answer relative to a frame, and different frames may disagree on what their answer is.

If you are interested only in a single frame, and you choose to describe measurements in that frame as "real", then there's nothing to discuss.

 

[JesseM]

Observers A and B will eventually both agree that A lags behind B and I see no reason why they cannot both agree that A ticked over at a slower rate than B thereby creating this lag.

Only if they both agree to use the frame in which they are currently at rest to make statements about clock rates. There is nothing that prevents them from using some other frame, it's a matter of arbitrary choice. You're talking as though an observer's inertial rest frame can somehow be taken as intrinsically representing that observer's "perspective", but there's no real basis for that; why are you so resistant to actually spelling out what frame you want the observers to use when you make statements like this?

I'm not talking about what either of them 'sees' or 'calculates' or 'predicts' or ‘determines’ during that trip but about what they agree to after the trip.

It's misleading to use the word "sees" as if it were synonymous with the other ones which refer to frame-dependent calculations. What you see visually is determined by when the light from different events strikes you, unlike frame-dependent calculations this is not a matter of arbitrary choice, all frames will agree in their predictions about what time shows on your clock when you first see the light from a distant event. The rate you see a clock ticking is in general different from the rate you calculate it to be ticking in the frame where you're at rest--for example, as A is approaching B, B will see A's clock ticking faster than his own, even though in B's rest frame A's clock is really ticking slower than his own. In order to determine when things happen in a given frame, you have to take the times you saw events and do some abstract calculations in order to determine when the events "really" happened in that frame, and it's just as easy to do the calculations using a frame where you are not at rest as it is to do the calculations for the frame where you are at rest.

Prior to accelerating A is looking at a pulsar that is 'ticking over' at the same rate as his clock. On the basis that (according to Einstein) having moved - his clock is 'going more slowly' than it was before he started moving he will see that pulsar ticking over at a faster rate than his own clock however for him to be of the opinion that his clock's rate of operation has remained unchanged whilst the far-distant pulsar (some millions of light years away and lateral to his direction of travel) is now (virtually instantaneously) spinning on its axis at a faster rate than it was before he started moving is, in my opinion, (to put it mildly) a 'very silly' attitude.

This is exactly what is true in one particular non-inertial frame where A was at rest throughout this process, there's nothing silly about it, it's just a matter of how you define your coordinate system. Probably this is why physicists typically use words like "real" "physical" to refer only to coordinate-independent facts, because it would sound kind of silly to say that there was a real, physical change in the pulsar's rate of spinning at the moment A accelerated; but if you wish to defy convention and use these words to refer to coordinate-dependent facts, then you have to say that there was a real, physical change in the pulsar's rate of spinning in A's non-inertial rest frame (unless you want to specify that 'real' and 'physical' can refer only to coordinate-dependent statements made in inertial frames, but in that case you won't be able to make any statements about which of two clocks is 'really' ticking faster if the clocks are at different locations in curved spacetime, like clocks at the top and bottom of a mountain, since all coordinate systems in non-infinitesimal regions of curved spacetime are non-inertial).

Sections 1 through 3 of STR refer to fully reciprocal phenomena; clock A ‘is’ ticking over at a slower rate than B from B’s inertial frame perspective and clock B ‘is’ ticking over at a slower rate than A from A’s inertial frame perspective however in section 4 he points out that the phenomena is not fully reciprocal; that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.

He doesn't say a single thing about non-inertial frames in section 4. If you disagree, please quote some part of section 4 that you think is referring to non-inertial frames.

Contributors point out that I should specify to which frame’s point of view I am referring. In your opinion - to which frame was Einstein referring when he effectively, analogously wrote that clock A ‘goes more slowly’ than clock B?

He didn't use the words "goes more slowly" but rather said A "lags behind" B, which might be taken merely to mean that A's reading is less than B's reading when they meet. But even if you interpret "lags behind" to mean "goes more slowly", he did refer to a specific frame in that section, the "stationary" frame K in which the clocks A and B were initially at rest and synchronized:

From this there ensues the following peculiar consequence. 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 which has remained at B by (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

Note that in this translation Einstein routinely uses the word "system" to refer to what we have been calling a "frame", and he also made clear that K referred to a coordinate system in section 3.

He accelerates to an experimentally maximum attained instantaneous velocity thereby generating a gamma factor of 400 000. At that instant clock B ‘is’, according to his calculations, ticking over at the rate of 400 000 seconds for each of his own seconds.

He flicks a switch extinguishing his rockets and at that very instant clock B reverts from being 400 000 times faster than his own clock and instantaneously[i/] reverts to being 400 000 times slower than his clock!

Is he not likely to be of the opinion that an 800 000 x instantaneous reversal might have some affect on that clock’s mechanism to say nothing of what it might do to an observer accompanying clock B?

You don't appear to appreciate that non-inertial coordinate systems make exactly the same predictions about frame-independent facts as inertial ones in SR, so any purely local predictions you could make about the "clock's mechanism" or an "observer" (like whether any part of the clock breaks, or whether the observer is injured) will be exactly the same in a non-inertial frame as an inertial one. Keep in mind that in a non-inertial coordinate system, coordinate accelerations (even very large ones) need not be accompanied by G-forces as would be true in an inertial frames, because there can be "pseudo-gravitational forces" to cancel them out--again, please read this section of the twin paradox page.

On the basis that, whilst still accelerating, A sees clock B (on Earth) ticking over 400 000 times faster than his own clock he must also ‘see’ (i.e. determine) that not only Earth seconds are passing at that enormous rate but also it’s minutes, hours and days. For Earth days to be ticking over at the rate of 400 000 for each of his own days it would have to be spinning on it’s axis at some 640 000 000K-h.

To make matters worse - he stops accelerating whereupon the planet instantaneously stops spinning at 640 million kilometres an hour and virtually stops spinning on it’s axis (it is ‘then’ spinning at some 400 centimeters an hour in lieu of 1 600 kilometers an hour).

People point out that A knows that in B’s reference frame (i.e. the planet’s reference frame) the Earth is not spinning on it’s axis at 640 000 000K-h but at 1 600K-h. If the Earth is not spinning 400 000 times faster than it was then neither is the second hand of clock B yet this is precisely what it is claimed he will ‘see’ (determine, predict).

Yes, these things will be true in one particular non-inertial coordinate system--what's your objection, aside from some sort of aesthetic distaste? As long as one properly applies the laws of physics in this non-inertial coordinate system, all predictions made about coordinate-independent facts (the facts most physicists would refer to as 'physical' ones, even if you don't) will be exactly the same as those made using an inertial coordinate system.

If I am located at an axial point (i.e. the North Pole) of a large spinning, massless and transparent sphere in outer space looking at a clock on that sphere’s rim (i.e. it's equator) I will, according to Einstein’s section 4 STR see that clock ‘going more slowly’ (i.e. ticking over at a slower rate) than my clock.

It matters not that a person alongside that clock sees my clock ticking over at a faster rate than his clock. My presentation is from my point of view, not his!

Only if you choose to define "your point of view" as "your inertial rest frame". Again, unlike what an observer sees visually which is intrinsic to his worldline, what happens in an observer's rest frame is a matter of abstract calculations, they could just as easily do the calculations from the perspective of a frame where they are moving at 0.99c and choose to refer to that as adopt the arbitrary convention that this frame shall be referred to as "their point of view".

I send another clock along a line of longitude on that sphere toward the sphere’s equator. As I watch it it progressively ticks over at slower and slower rates than my own clock as it’s speed relative to me increases (it is accelerating).

And again, the rate you see it ticking will be different than the rate it's ticking in your inertial rest frame (although they will both be slower than your clock).

I have every right to assume that if I were to carry another clock along that same line of longitude that it, too, would progressively be ticking over at a slower and slower rate than a polar clock

You have a "right" to assume that if you want to continue to calculate things from the perspective of the inertial frame where you were at rest at the pole even once you have started moving from the pole. On the other hand, if you want to calculate things from the perspective of a frame moving relative to the pole--perhaps your instantaneous inertial rest frame as you are in motion--then you have an equal "right" to assume your clock is ticking faster than a clock at the pole. Both statements are correct given that you make clear which frame you want to use, but if you don't make it clear, these statements are simply too ill-defined to be right or wrong.

I suspect that somebody will respond that from the point of view of observer XYPG on planet Poplex which is in a deadly spiral toward a black hole my clock will not progressively slow down however the views expressed, or opinions held, or determinations made, by that observer have absolutely no affect whatsoever on my observations or determinations and it is MY determinations and predictions to which my postings apply not those of potentially countless hypothetical observers.

No, YOU can make determinations from whatever frame you choose, you don't have to use the inertial frame where you are at rest. And even if you want to (arbitrarily) define "your determinations" as determinations made using inertial frame where you are at rest while at the pole, why don't you then also want to define "your observations" once you have started moving relative to the pole as determinations made in the inertial frame where you are instantaneously at rest at that moment, or even using the non-inertial frame where you have remained at rest throughout the whole journey?

People insist that my (actually Einstein’s) comment that clock A will tick over at a slower rate than B is pointless unless I specify to which reference frame I am referring however my comment has always been in reference to ’my’ frame (i.e. observer A’s frame).

That's fine as long as you understand this is an arbitrary matter of choice, there is no intrinsic reason a given observer has to calculate things from the perspective of the inertial frame where they happen to be at rest (and as I said it's puzzling why you continue to refer to the pole's rest frame as 'my' frame even once you have started moving relative to the pole). Aside from this, you have made some statements about non-inertial frames which definitely suggest confusion between coordinate-dependent facts and coordinate-independent ones (like suggesting that a large coordinate acceleration in a non-inertial frame would somehow imply a clock or observer would be damaged).

 

[atyy]

that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.

A statement like this would be true in B's inertial frame. I don't understand what you mean by A's non-inertial reference frame. It is clear that you have specified A to be a non-inertial observer, but how are you specifying A's non-inertial reference frame?

Do you intend Eq. 3, 4 of http://relativity.livingreviews.org/Articles/lrr-2003-1/ ?

Or do you intend Eq 2 of http://journals.iut.ac.ir/ijpr/efullv5n3y2005p63-67.pdf?

If any case how are you defining simultaneity in order to compare rates of spatially separated clocks at the "same time"? Are you using constant coordinate time, or hypersurfaces orthogonal to a 4-vector in the spacetime direction of the A's worldline?

 

[cos]

The point of my post was to illustrate that that there are some questions (such as "which way is 'up' when there's no gravity?") to which there is no "real" answer, only an answer relative to a frame, and different frames may disagree on what their answer is.

The point of my OP was to show that having arrived at B's location and having found that his clock lags behind clock B observer A is entitled to agree with Einstein that his clock 'went more slowly' (i.e. ticked over at a a slower rate) than clock B so if he repeats that experiment he is further entitled to be of the opinion that whilst his clock is ticking over at it's normal rate (e.g. at the same rate as his heart-beat) it is in reality ticking over at a slower rate than it was before he started moving as evidenced by that previous experiment and will lag behind clock B no matter when he looks at his clock.

Midway through his journey his clock will lag behind B by some 50% of the amount by which it lag behind B when he arrives at B's location on the basis that the t in Einstein's equation .5tv^2/c^2 is 50% of the total time for the journey.

In his book Was Einstein Right? Clifford M Will depicted a variation of Einstein's Principle of Simultaneity describing a train passenger moving past three people on the embankment A, B and C. (251, Oxford,1990)

A and C are equidistant from B. At the moment that the passenger (having moved past A) is directly in line with B that person illuminates a light the beams from which reach A and C simultaneously at which instant they synchronize their clocks but, according to Will, from the passenger's point of view that light will reach C before it reaches A thus, from the passenger's point of view, the clocks are not synchronized.

The passenger gets off at the next station and catches a cab back to the scene and finds, to his immense surprise, that in reality the clocks are synchronized!

He can argue until he's blue in the face that the clock's are not synchronized thus that somebody has played a trick on him by resetting one of those clocks however the simple fact is he is denying reality!

The opinions expressed, or determinations arrived at, by countless other reference frames have absolutely no bearing whatsoever on A's determinations nor on the rate of operation of his clock in the same way that the observations made by Will's train passenger does not prevent the clocks from being synchronized.

You wrote that in a gravity free location there is no "real" answer to the question as to which way is 'up'. There is a gathering of transparent space ships all at different angles to each other and all stationary. A command goes out to all ships to place a specific item in their upper bunks.

I, for one, would be very surprised if I saw Fred, in a ship that is 'upside down' to me, place his item in a bunk at his floor level not at the other one near his eye-level as is mine in my ship.

If you are interested only in a single frame, and you choose to describe measurements in that frame as "real", then there's nothing to discuss.

I have, all along, endeavored to point out that I am only interested in a single frame! A's frame!

 

[cos]

that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.

A statement like this would be true in B's inertial frame. I don't understand what you mean by A's non-inertial reference frame. It is clear that you have specified A to be a non-inertial observer, but how are you specifying A's non-inertial reference frame?

He powers up his main drive system and hits the gas pedal; he feels a force pushing him into his seat thus realizes that his is now an non-inertial reference frame. That's how I'm specifying that A's is a non-inertial reference frame and I believe that it is simple enough to stand on it's own without the application of any mathematical equation.

If any case how are you defining simultaneity in order to compare rates of spatially separated clocks at the "same time"? Are you using constant coordinate time, or hypersurfaces orthogonal to a 4-vector in the spacetime direction of the A's worldline?

An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time".

 

[atyy]

He powers up his main drive system and hits the gas pedal; he feels a force pushing him into his seat thus realizes that his is now an non-inertial reference frame. That's how I'm specifying that A's is a non-inertial reference frame and I believe that it is simple enough to stand on it's own without the application of any mathematical equation.

No, all that that specifies is that A is a non-inertial observer. It does not specify a frame. A frame is a method of assigning four numbers to every point in spacetime.

An observer looks at a distant clock and can also see his own clock simultaneously due to the fact that it is in his line of sight and that's how he compares rates of spatially separated clocks at the "same time".

Curiously the way you define things here, no frame is needed - all frames inertial and non-inertial will give the same answer.

I haven't calculated, so I'm going to guess and defer to Al68, JesseM, DaleSpam, DrGreg or anyone else that might have actually done the calculation. Consider two standard clocks (ie. clocks that will tick at the same rate when they are in the same place), one is stationary in an inertial frame K, and the other moves with constant speed relative to the inertial frame K in a circle centered on the stationary clock. The stationary clock sends out light pulses separated by delta of its proper time. The moving clock will receive those pulses at less than delta of its proper time. If one wishes to specify using t and v (as Einstein did) the amount by which the moving clock has gone slow, then one will need to use the inertial frame K (colloquially called the inertial frame of the stationary clock).

 

[Al68]

If A accepts that Einstein was right - that his clock did tick over at a slower rate than B as Einstein suggests it will then he could also, upon repeating that experiment, be of the opinion that whilst he is moving his clock is ticking over at a slower rate than clock B irrespective of the fact that it's rate of operation has seemingly remained unchanged.

He could be of any opinion he likes. Einstein never made any prediction about anyone's opinion. It's objective fact that clock B ticks slower than clock A in both B's inertial frame and the rotating frame.

Prior to accelerating A is looking at a pulsar that is 'ticking over' at the same rate as his clock. On the basis that (according to Einstein) having moved - his clock is 'going more slowly' than it was before he started moving...

Einstein didn't say this. He said clock A would tick slower than clock B, and his calculation was in the rest frame of clock B.

he will see that pulsar ticking over at a faster rate than his own clock however for him to be of the opinion that his clock's rate of operation has remained unchanged whilst the far-distant pulsar (some millions of light years away and lateral to his direction of travel) is now (virtually instantaneously) spinning on its axis at a faster rate than it was before he started moving is, in my opinion, (to put it mildly) a 'very silly' attitude.

Sections 1 through 3 of STR refer to fully reciprocal phenomena; clock A ‘is’ ticking over at a slower rate than B from B’s inertial frame perspective and clock B ‘is’ ticking over at a slower rate than A from A’s inertial frame perspective however in section 4 he points out that the phenomena is not fully reciprocal; that from A’s non-inertial reference frame B does not tick over at slower rate than his own clock but that his clock exclusively ticks over at the slower rate.

relative to clock B, that's right. Because in A's non-inertial frame, clock B is slower than clock A. (even though this is not shown in section 4, section 4 only shows the calculation from B's inertial frame.)

Contributors point out that I should specify to which frame’s point of view I am referring. In your opinion - to which frame was Einstein referring when he effectively, analogously wrote that clock A ‘goes more slowly’ than clock B?

He was referring to B's inertial frame. That's clear from his calculation.

Is he not likely to be of the opinion that an 800 000 x instantaneous reversal might have some affect on that clock’s mechanism to say nothing of what it might do to an observer accompanying clock B?

He can have any opinion he wants, but SR predicts what a clock would read if it works at the same rate regardless of such forces.

On the basis that, whilst still accelerating, A sees clock B (on Earth) ticking over 400 000 times faster than his own clock he must also ‘see’ (i.e. determine) that not only Earth seconds are passing at that enormous rate but also it’s minutes, hours and days. For Earth days to be ticking over at the rate of 400 000 for each of his own days it would have to be spinning on it’s axis at some 640 000 000K-h.

To make matters worse - he stops accelerating whereupon the planet instantaneously stops spinning at 640 million kilometres an hour and virtually stops spinning on it’s axis (it is ‘then’ spinning at some 400 centimeters an hour in lieu of 1 600 kilometers an hour).

People point out that A knows that in B’s reference frame (i.e. the planet’s reference frame) the Earth is not spinning on it’s axis at 640 000 000K-h but at 1 600K-h. If the Earth is not spinning 400 000 times faster than it was then neither is the second hand of clock B yet this is precisely what it is claimed he will ‘see’ (determine, predict).

Who's claiming that the second hand of Earth's clock is spinning fast in Earth's frame?

Proponents of that ‘logic’ (?) point out that the faster rate of B’s ‘tick’ during periods of acceleration exceed the slower rate of B’s tick whilst A is moving with uniform velocity thus this is, they insist, the reason why A and B find that A ultimately lags behind B.

Do you mean proponents like Einstein in his 1918 paper where he says "However, this is more than compensated by a faster pace of U1 (earth clock) during partial process 3 (acceleration)...The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4 (inertial motion). This consideration completely clears up the paradox that you brought up" ?

People insist that my (actually Einstein’s) comment that clock A will tick over at a slower rate than B is pointless unless I specify to which reference frame I am referring however my comment has always been in reference to ’my’ frame (i.e. observer A’s frame).

Well, if you're just saying the same thing the rest of us are saying, I don't quite see your point in this thread.

 

[Dale]

I have, all along, endeavored to point out that I am only interested in a single frame! A's frame!

How can you possibly be interested in A's frame? It is non-inertial and you reject non-inertial frames. You cannot have it both ways, if you want to do an analysis in a non-inertial frame then you must be willing to use fictitious forces in the analysis. They are an inescapable feature of non-inertial frames. This is not Einstein's requirement, but predates him by centuries.