Understanding Time Dilation in Einstein's Special Theory of Relativity

[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.

 

[john 8]

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. .

I am not aware of this. Are you suggesting frames of reference emanate energy? If so, how far out does this energy emanate from a given reference frame?

What type of energy is being applied? Electromagnetic?

For example, I am driving in my car in the city, I am driving in a straight line at a constant velocity, are you suggesting that the frame of reference that I occupy is physically applying energy to the people on the street, the people in their buildings, the objects all around me, all the objects in the buildings, and depending on how far this energy can influence other things, could I include planes in the sky, boats on the ocean and other more distant things and people as those things that are influenced or having energy applied to them by my frame of reference?

Really, I am not aware of this notion that energy is frame dependent. If my example is incorrect then could you please give an example, or refer me to something that gives an example. I am familiar with Einstein’s book on relativity, if there is an example in there could you please give me the chapter.

One last thing just to be clear. Do you think that this notion of frame dependent energy is a real physical phenomenon that actually occurs in this universe on a daily basis?

If so, man I would really like you to tell me what type of energy this is or where I can research it more.


Thank you.

 

[john 8]

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.

Thank you for your input. I do not want to be picky here, but not all energy is transferred at the speed of light. If I drop a ball the potential energy is converted to kinetic energy and that kinetic energy is transferred to the ground at whatever the velocity of the ball was when it contacted the ground. But that is a minor point.

I am much more interested in what you said about time. You said time is not a thing, I agree. So in this whole theory of time dilation, what do you think is actually being dilated? If time is not a thing, then what is being dilated do you think? Or are you of the mindset, like me, that time dilation is not a real physical occurrence?

 

[JesseM]

I am not aware of this. Are you suggesting frames of reference emanate energy? If so, how far out does this energy emanate from a given reference frame?

The point is that there is no single objective truth about "how much energy there is" at a single instant, each frame has its own definition of the amount of energy in the world (or in any finite part of it) at any given time, but it works out that the amount of energy calculated in each inertial frame will remain constant from one moment to the next. Similarly, there is no objective truth about "how fast an object is moving"--for example, if you and I have a relative velocity of 20 meters/second, then in my rest frame I am at rest while you have a velocity of 20 m/s, while in your rest frame you are at rest while I have a velocity of 20 m/s, velocity is inherently frame-dependent. Since the kinetic energy of an object is a function of its velocity (equal to (1/2)mv^2 in Newtonian mechanics, equal to (\frac{1}{\sqrt{1 - v^2/c^2}} - 1)*mc^2 in relativity, the two being approximately equal when v is small compared to c), so the fact that velocity is frame-dependent may help you see why energy would be frame-dependent too.

Also, do you understand that a "frame" is just a coordinate system for assigning spatial coordinates x,y,z and time coordinate t to arbitrary events? It isn't a physical thing, it's just a way of labelling points in space and time, which then allows you to express the laws of physics as equations telling you how the positions of different objects are expected to change as a function of time in that system of coordinates. This is true in Newtonian physics as well as relativity (as is the fact that both velocity and energy are frame-dependent).

 

[cos]

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).

You may aware that your depiction is effectively identical to Einstein's section 4 STR picture of a clock (A) that is made to travel in an eccentric closed curve relative to the clock which has remained at rest (B) but that your version is more related to Einstein's polar-equatorial clock depiction (which is determined on the basis of "under otherwise identical conditions." i.e. the polar clock could be mounted an a tower placing it at the same distance from the Earth's center of gravity as is the equatorial clock).

An observer located alongside clock B that "...is stationary in an inertial frame K..." notices that clock A is ticking over at a slower rate than his own clock and determines "...using t and v (as Einstein did)" the amount by which the moving clock goes slow.

Observer B sends another clock (B1) to A's location whereupon he finds that clock B1 is then ticking over at the same rate as clock A ergo at a slower rate than it was before it moved to the rim and at an identically slower rate than his own clock. As that clock moves away from him (ergo it is orbiting him at increasing speeds) he notices that it's rate of operation decreases accordingly.

Having read, and accepted, Einstein's section 4 depictions of a clock that has been made to travel in a closed curve relative to a stationary clock and an equatorial clock relative to a polar clock observer B knows that it is the factor v in Einstein's equation that has determined the actual variation in the rate of operation of clock B1 ergo it is the speed at which B1 is now moving that has determined it's slower rate of operation.

Observer B moves to the rim.

He knows that his speed is increasing (he is accelerating) thus that at any given instant his velocity is greater than it was the previous instant so when he applies his v to Einstein's equation he determines the amount by which his clock is then ticking over at a specific slower rate than it was when he was stationary at the center of the wheel.

He looks at his own clock which is ticking over at it's normal rate so when he looks at the central clock and determines that it is ticking over at a faster rate than his own clock he can either assume that some indeterminable force has made that clock tick over at a faster rate than it was when he was alongside same OR that his clock is (indeterminably) ticking over at a slower rate than it was before he started moving as did the previously dispatched clock B1.

Prior to the above situation the wheel is not spinning; there are clocks (and observers) that are Einstein's section 4 "...stationary clocks at the points A and B of K which, viewed in the stationary system, are synchronous."

The wheel is made to spin.

Observer A on the rim experiences a force of acceleration thus knows that his is the moving clock which Einstein stipulated "...must go more slowly..." (i.e. tick over at a slower rate) than the stationary clock.

If that observer (now moving at a constant speed around B thus experiencing a force as the result of his centripetal acceleration) is of the opinion that he has not started moving but that it is clock B that has started spinning on it's axis (as a result of which it is, in his opinion, now ticking over at faster rate than it was before it started spinning) he is, in my opinion, not only contradicting Einstein's section 4 but is indicating gross stupidity.

There is, I submit, nothing in Einstein's section 4 presentation (or for that matter in any of the previous STR sections) which suggest that a clock that is made to spin on it's axis will tick over at a faster rate than it did before it started spinning!

If anything it should tick over at a slower rate than it was before it started spinning however that is not what observer A 'determines'.

 

[atyy]

To be honest, I don't know really what Einstein was thinking (too many reasonable possibilities). But on the basis of your definition of "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"." in post #207, for this particular pair of clocks (A circling, B "stationary"), A sees B run fast (time dilation), and B sees A run slow (transverse Doppler), so A and B can consistently say that B runs slow compared to A by your definition for comparing rates. And yes, the circling clock is the one that slowed, not the "stationary" one, if we stipulate quite reasonably that inertial clocks in special relativity do not change their rate of ticking. And as far as I can tell, your definition is an operational definition in terms of frame independent quantities.

So now what is the problem about "If anything it should tick over at a slower rate than it was before it started spinning however that is not what observer A 'determines'."? Also, do you mean spinning or orbiting?

 

[atyy]

Ok, I see that you do mean "spinning". I am very tempted to say an ideal clock is a point, so it doesn't spin.

Anyway, instead of using ""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"" which you defined in post #207, another inequivalent way of defining what A determines is to set up a non-inertial frame in which the time coordinate along A's wordline is A's proper time. There are several ways of doing this, and several ways of defining "same time" and comparing "rates". Non-inertial frames usually give me a headache, and asking frame dependent questions is just a matter of definitions which don't yield different predictions regarding experimental results. I can also use any inertial frame to make predictions of experimental results, and since global inertial frames exist in special relativity, I and A can use them if they are more convenient. A frame is just a way of addressing spacetime points/events. For example, we can say the White House's address is 1600 Pennsylvania Ave, or 38.898648N, 77.037692W. It shouldn't bother us that 1600 >> 38.9. We can use any address we want - it doesn't change the physical location of the White House.

 

[cos]

Einstein never made any prediction about anyone's opinion.

Totally irrelevant albeit suitably disparaging comment! I made no suggestion that he did!

It's objective fact that clock B ticks slower than clock A in both B's inertial frame and the rotating frame.

Huh? Typo or total contradiction of Einstein's section 4? I'll assume that you meant to write that clock A ticks slower than clock B in both B's inertial frame and the rotating frame.

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" ?

Yeah - that's right - people like Einstein who also said, 3 years later "As far as..." but you already know the rest.

His phrase "...the propositions of mathematics..." in that comment applies, in my opinion, to his reference above to "The calculation..."

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.

From what I can see you are making completely opposing comments about A's and B's respective rates of operations hance i can see no agreement on my behalf to those conflicting comments.

 

[cos]

atyy,

Allow me to quote relevant sections of my OP:

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

"In section 4 STR Einstein wrote -

"If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be a .5tv^2/c^2 second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."

What do people think he meant by the phrase "...must go more slowly..."?

Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?

On the (probably erroneous) basis that some people may agree that he did I follow that up with the question - On the basis of his depiction of a clock that is made to move in a closed curve around another clock is it correct for me to assume that Einstein meant that the clock that is moving in a closed curve will “go more slowly”(i.e. tick over at a slower rate) than the clock “which has remained at rest.”?

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

 

[atyy]

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".

Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?

My opinion is that Einstein meant the second of your proposed interpretations ("incur time dilation"), which is a frame dependent interpretation. However, I think you have cunningly shown that your first interpretation ("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"."), a frame independent one, is also plausible. Deciding between the interpretations is a matter of literary analysis, and asking whether he meant "on average" or "exclusively" etc.

 

[cos]

However, I think you have cunningly shown that your first interpretation ("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"."), a frame independent one, is also plausible. Deciding between the interpretations is a matter of literary analysis, and asking whether he meant "on average" or "exclusively" etc.

I am of the opinion that you have, using the word 'cunningly', deliberately disparaged my comments.

 

[JesseM]

cos, atyy is distinguishing between what an observer sees visually and what they calculate is true in a given frame, the same issue I was talking about in post 204 when I wrote:

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.

If when you said 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" you did not mean to talk about how fast the distant clock appeared to be ticking visually but rather about how fast it was calculated to be ticking in the observer's frame, then perhaps you should clarify. As I said, in the thought-experiment where A and B are initially at rest with respect to each other and then A moves to meet with B, B will see A's clock ticking faster than his own due to the Doppler effect, in spite of the fact that in B's rest frame A's clock was "really" ticking more slowly than his own as it moved.

 

[JesseM]

As far as I am concerned it makes no difference whatsoever if I 'look' at this event from a frame dependent point of view or a frame independent point of view I take Einstein's word for it that my clock is ticking over at a slower rate than clock B.

In fact I do not 'look' at this event from a frame dependent point of view or a frame independent point of view but sit back serenely, confidently, of the opinion that Einstein was right; that my clock is ticking over at a slower rate than it was before I started moving.

This shows that you still don't understand or accept the basic point everyone on the thread has been making: namely, that any statement about which clock is "ticking at a slower rate" at a given time is by definition frame-dependent (unless you're talking about visual appearances, but in that case you should accept that B sees A's clock ticking faster than his own, not slower). Unless there was a miscommunication and you actually don't disagree with this (in which case please say so), my opinion is that this thread should probably be shut down, since many people have told you that this is the standard view that would be accepted by any physicist (including Einstein, who specifically referred to the fact that he was talking about the 'stationary system' K, and never suggested anything about one clock ticking slower than another in a frame-independent sense), and it's against the rules to intentionally use this forum as a platform to argue for contrarian ideas about physics.

 

[atyy]

As far as i am concerned there is no distinction between my interpretations.

I am of the opinion that you have, using the word 'cunningly', deliberately disparaged my comments.

No, "cunningly" is a compliment. However, it seems that you have been more cunning than you realize! Whether or not I have actually done my calculations correctly as to what special relativity predicts for each of your interpretations, there is certainly a great, and fundamental, difference between your interpretations. Read JesseM's post #221, or study the distinction between "sees" and "computes" drawn here: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html.

 

[Dale]

Einstein clearly understood that a clock's rate was frame dependent. Hence his derivations in the first few sections and his repeated specification of the reference frame, including in section 4.

 

[Al68]

Huh? Typo or total contradiction of Einstein's section 4? I'll assume that you meant to write that clock A ticks slower than clock B in both B's inertial frame and the rotating frame.

OOps, that was a typo on my part.

In A's non-inertial frame clock B is faster than his own clock (A) not slower!

Another typo on my part. Sorry about that, I know the last thing this thread needs are those kind of mistakes.

Einstein 'said' that clock A would tick slower than clock B (which I take it corrects your typo above) because A is made to move relative to clock B!

Yes, that does correct my typo. Clock A ticks slower than clock B in B's inertial frame (the frame in which A is in motion). Clock A also ticks slower than clock B in the rotating frame, although the equation in section 4 is not valid for that frame, since both clocks are at rest in the rotating frame, using that equation would give a contradictory result in that frame (ie that the clocks run at the same rate).

According to your comment, he was not only referring to B's inertial frame but also to A's non-inertial frame.

No, he was referring to B's inertial frame, I was referring to both. He never made the calculation from A's non-inertial frame in section 4.

When he refers to the difference in the elapsed proper time of different clocks between events (ie departure and arrival of a clock moved in a closed curve), he is not referring to any particular frame, since proper time is not frame dependent.

So SR 'predicts' (or can be shown to) that a clock can instantaneously revert from being 400 000 times slow to being 400 000 times fast and we are expected to believe that because SR says this that it can take place in reality?

"As far as the propositions of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."

Wow, I was going to use that same exact quote to answer you. The above (not those exact numbers) happens in the accelerated frame of the ship in Einstein's 1918 paper, whether or not you consider that reality is up to you. Lots of funny things happen in accelerated frames, even in classical physics. Light does not travel at c, it doesn't even take a straight path relative to accelerated frames. Force does not equal mass times acceleration. The trajectory of an object moving in a straight line relative to an inertial frames takes a curved path relative to an accelerated frame.

I read that as indicating that Einstein may have been of the opinion that whilst the fully internally balanced, self-sufficient, mathematical propositions of SR can be shown to indicate that this will take place without totally destroying that clock in reality the clock will be destroyed!

No, he was showing what would happen if the clock is not destroyed. He made no claim as to whether a clock would or wouldn't be destroyed.

If he determines that, in it's own reference frame, the Earth clock is not ticking over at a rate of 400 000 seconds for each of his own seconds (or at the rate of one second for each of his own 400 0000 seconds depending on his direction of travel and location of his foot relative to the gas pedal) why would he be of the opinion that it is ticking over at a faster (or slower) rate than his own clock?

In Einstein's 1918 paper, the Earth clock is ticking many times faster than the ship clock in the ship's accelerating reference frame, not in Earth's frame.

 

[Al68]

For example, I am driving in my car in the city, I am driving in a straight line at a constant velocity, are you suggesting that the frame of reference that I occupy is physically applying energy to the people on the street, the people in their buildings, the objects all around me, all the objects in the buildings, and depending on how far this energy can influence other things, could I include planes in the sky, boats on the ocean and other more distant things and people as those things that are influenced or having energy applied to them by my frame of reference?

I am saying that, in your example, kinetic energy equals 0.5 times mass times relative velocity squared in classical physics, so the kinetic energy of any of those people/objects depends on reference frame, since relative velocity depends on reference frame. In your example, a person standing in the street would have kinetic energy in the rest frame of the car equal to 0.5 times their mass times the relative velocity squared. Obviously the kinetic energy of any object is frame dependent, since relative velocity is frame dependent.

Really, I am not aware of this notion that energy is frame dependent. If my example is incorrect then could you please give an example, or refer me to something that gives an example. I am familiar with Einstein’s book on relativity, if there is an example in there could you please give me the chapter.

One last thing just to be clear. Do you think that this notion of frame dependent energy is a real physical phenomenon that actually occurs in this universe on a daily basis?

If so, man I would really like you to tell me what type of energy this is or where I can research it more.

Well, if you're referring to kinetic energy, any classical physics textbook will do.

 

[cos]

No, "cunningly" is a compliment.

I am of the opinion that whether the word 'cunning' is meant as a disparagement or a compliment depends on who is using the word and to whom they are referring.

Websters - 'cunning': characterized by wiliness and trickery.

You wrote "I think you have cunningly shown..." whereas you could have written "I think you have shown..."

However, it seems that you have been more cunning than you realize! Whether or not I have actually done my calculations correctly as to what special relativity predicts for each of your interpretations, there is certainly a great, and fundamental, difference between your interpretations.

When my observer looks at a distant clock as in my comment viz -

"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"."

he is aware of and deletes any Doppler effect as I have pointed out in previous messages.

Would be so kind as to point out to me the "great and fundamental difference" between my comments -

"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"."

and

"Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?"

 

[phyti]

Thank you for your input. I do not want to be picky here, but not all energy is transferred at the speed of light. If I drop a ball the potential energy is converted to kinetic energy and that kinetic energy is transferred to the ground at whatever the velocity of the ball was when it contacted the ground. But that is a minor point.

I am much more interested in what you said about time. You said time is not a thing, I agree. So in this whole theory of time dilation, what do you think is actually being dilated? If time is not a thing, then what is being dilated do you think? Or are you of the mindset, like me, that time dilation is not a real physical occurrence?

Transfer of energy via photons was referring to the atomic level, but I wasn't specific about that.

Time is a measurement process, and not exclusive to science. People used the monthly cycles for agricultural purposes and the daily cycles for most other human affairs. The clock is a sequence of standard events, and events in the world are matched to the current clock event. It's the same as measuring a dimension with a ruler. In both cases, the results are recorded for future purposes, such as ordering, comparisons, and predictions. It is a human conceptual tool. The light clock is the simplest way to demonstrate how motion affects the physical clock function. Then the subjective nature of time is apparent, because the effect applies to all material objects, which includes the observer, i.e. altered perception.
As an example, if a drawing contains a scale of 1 unit = 1', and the object is drawn 2 units, the object dimension is 2'. If the drawing is reduced to half size, the object still measures 2'. It's a matter of scale.
As for a simple example of energy transfer, consider a flat bed truck with two boxes separated by 10'. A bee transfers pollen (energy) from the rear box to the front box, and returns. The bee has one speed relative to the air, 10' per second, air resistance is ignored, and the bee cannot be seen because of stealth technology. If truck speed v = 0 fps, transfer time t = 1 sec. If v = 1 fps, t = 10/9 sec. etc., ... and finally, if v= 10 fps, the trip is never completed. The point being, the faster the truck moves, the longer the trip time.

 

[JesseM]

When my observer looks at a distant clock as in my comment viz -

"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"."

he is aware of and deletes any Doppler effect as I have pointed out in previous messages.

But of course, there is no frame-independent way to "delete any Doppler effect", the ratio between the frequency you see the ticks and the "actual" frequency of the ticks depends on the choice of frame you wish to do your calculations in. So do you still stand by your statement (the one I quoted in post #222) that there is some frame-independent sense in which one clock is ticking slower than another, or do you agree that this is an inherently frame-dependent question?

I would suggest that other posters try to get a clear answer on whether he thinks one clock is ticking slower than another in a frame-independent way, since he isn't responding to my posts.

 

[Al68]

The wheel is made to spin.

Observer A on the rim experiences a force of acceleration thus knows that his is the moving clock which Einstein stipulated "...must go more slowly..." (i.e. tick over at a slower rate) than the stationary clock.

If that observer (now moving at a constant speed around B thus experiencing a force as the result of his centripetal acceleration) is of the opinion that he has not started moving but that it is clock B that has started spinning on it's axis (as a result of which it is, in his opinion, now ticking over at faster rate than it was before it started spinning) he is, in my opinion, not only contradicting Einstein's section 4 but is indicating gross stupidity.

Clock B would not be spinning on its axis relative to that observer. In the rotating frame, in which A is stationary, clock B would remain stationary and not spinning.

Clock B would be spinning relative to an inertial frame in which the wheel was stationary, then started spinning, and in such frame, the rate of clock B would be the same as it was before the wheel started spinning.

 

[cos]

Einstein 'said' that clock A would tick slower than clock B (which I take it corrects your typo above) because A is made to move relative to clock B!

Another typo on my part. Sorry about that, I know the last thing this thread needs are those kind of mistakes.

I allowed for and corrected your typo' however I still insist that "Einstein 'said' that clock A would tick slower than clock B because A is made to move relative to clock B!

...whether or not you consider that reality is up to you.

The traveler (on the basis that 'observation'; measurement'; 'prediction'; 'calculation' determine reality) is of the opinion that it is reality!

I am of the opinion that any intelligent person should be aware of the fact that if a clock instantaneously changes from being 400 000 times faster than the astronaut's clock to being 400 000 times slower this would have a devastating effect - not only on the clock itself but also on the planet on which that clock is located.

I believe that in the first half of last century if somebody had suggested to Einstein that in the future somebody were to construct a particle accelerator capable of generating gamma factors in excess of 400 000 and asked Einstein "What would happen to a clock that instantaneously reverts from being 400 000 times faster than the astronaut's clock to being 400 000 times slower?" Einstein most likely would have responded that no clock is capable of doing so and may also have pointed out that "As far as the propositions of mathematics are certain [as are those of special theory] they do not refer to reality."

In Einstein's 1918 paper, the Earth clock is ticking many times faster than the ship clock in the ship's accelerating reference frame, not in Earth's frame.

Not only 'in the ship's accelerating reference frame' but also in the traveler's mind!

On the basis that the traveler 'determines' or 'predicts' or 'measures' that the Earth clock is ticking many times faster than it actually is then he (assuming an inability to apply logic and knowledge) is of the opinion that it is ticking many times faster than it was before he started accelerating and this 'fact' is part of his explanation as to why his clock physically lags behind the Earth clock when he returns to the planet.

 

[JesseM]

I am of the opinion that any intelligent person should be aware of the fact that if a clock instantaneously changes from being 400 000 times faster than the astronaut's clock to being 400 000 times slower this would have a devastating effect - not only on the clock itself but also on the planet on which that clock is located.

As I said in post #204:

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.

A coordinate system is just a way of labeling events, you can assign physical events any coordinates you like. For example, if I take the events of my clock reading 20 seconds and 21 seconds and arbitrarily assign them the same position coordinate, then take the event of my clock reading 22 seconds and arbitrarily assign it a position coordinate 1000 light-years away, then in this coordinate system the clock has gone from being at rest between the first and second reading to moving 1000 light-years between the second and third reading, which (assuming I also assign each reading a time-coordinate 1 second apart) obviously means a huge coordinate acceleration! But merely by choosing to affix these labels to the events I haven't caused any coordinate-independent physical change in the clock, any more than changing the word I use for my residence from "house" (the English label) to "casa" (the Spanish) causes a physical change in my house.

Of course, in inertial coordinate systems there is a direct correlation between coordinate acceleration and the coordinate-independent effects of acceleration (like the G-force measured by an accelerometer), but if you switch to a non-inertial coordinate system you have to rewrite the equations representing the "laws of physics" to fit the new coordinate system, and you always do so in a way that leads the equations in the new coordinate system to make the same predictions about coordinate-independent physical facts that you made using the inertial equations in the inertial coordinate system. With the new equations tailored to the non-inertial coordinate system, there will not necessarily be any regular correlation between coordinate acceleration and the coordinate-independent effects of acceleration such as measurable G-forces.

 

[cos]

Clock B would not be spinning on its axis relative to that observer. In the rotating frame, in which A is stationary, clock B would remain stationary and not spinning.

My apologies, I unintentionally confused a person on the rim of a wheel with someone who starts moving in a closed curve around clock B in which case clock B would be spinning on it's axis from A's point of view. Alternately clock B could be mounted on a base that is not affected by the wheel's spin.

OTOH, if a clock (not an idealized 'point') is made to spin on it's own axis the 'points that 'are' it's axis would remain stationary whilst all of it's constituent atoms would progressively incur increasing rates of time dilation as their distance from the axis increases.

Clock B would be spinning relative to an inertial frame in which the wheel was stationary, then started spinning, and in such frame, the rate of clock B would be the same as it was before the wheel started spinning.

In other words - an observer located at the center of the wheel.

I made no suggestion that he would be of the opinion that his own clock varied in it's rate of operation.

 

[atyy]

Would be so kind as to point out to me the "great and fundamental difference" between my comments -

"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"."

and

"Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?"

"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"."
Here the comparison is between (i) the time intervals between the receipt of successive signals as read from the clock that receives the signals, versus (ii) the the time intervals between the sending of successive signals as read off from the clock sending the signals.

"Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?"
Here "space" is filled (notionally) with a lattice of standard ideal clocks. As a clock Y moves through space, it will intersect successively with different lattice clocks. When a tick on Y occurs (say tick Y1), we look at the lattice clock with which Y happens to be intersecting, and read off the time (say L1) on that particular lattice clock. We repeat the procedure as Y moves through space obtaining a series of ticks from Y (Y1,Y2,Y3,...) and corresponding lattice clock readings (L1,L2,L3,...). We compare the Y2-Y1 versus L2-L1. If Y2-Y1 is less than L2-L1, then we say that Y has undergone time dilation compared to the lattice clocks.

 

[cos]

"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"."

Here the comparison is between (i) the time intervals between the receipt of successive signals as read from the clock that receives the signals, versus (ii) the the time intervals between the sending of successive signals as read off from the clock sending the signals.

There is no comparison between those signals. There is only the determination arrived at by the traveler.

So, allowing for and removing the Doppler effect, the traveler determines on the basis of Einstein's section 4 comment that his (having been accelerated hence now moving) clock is ticking over at a slower rate than the stationary clock (and by applying Einstein's equation) that his clock is ticking over at a slower rate than the other clock.

"Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?"

Here "space" is filled (notionally) with a lattice of standard ideal clocks. As a clock Y moves through space, it will intersect successively with different lattice clocks. When a tick on Y occurs (say tick Y1), we look at the lattice clock with which Y happens to be intersecting, and read off the time (say L1) on that particular lattice clock. We repeat the procedure as Y moves through space obtaining a series of ticks from Y (Y1,Y2,Y3,...) and corresponding lattice clock readings (L1,L2,L3,...). We compare the Y2-Y1 versus L2-L1. If Y2-Y1 is less than L2-L1, then we say that Y has undergone time dilation compared to the lattice clocks.

In other words - yes - clock Y (clock A in Einstein's section 4 depiction) has undergone time dilation compared to the lattice clocks (clock B in Einstein's section 4 depiction).

Ergo, in my opinion, saying the same thing, albeit in a much more fanciful manner as my comment viz -

"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"."

 

[Dale]

So do you still stand by your statement (the one I quoted in post #222) that there is some frame-independent sense in which one clock is ticking slower than another, or do you agree that this is an inherently frame-dependent question?

I would suggest that other posters try to get a clear answer on whether he thinks one clock is ticking slower than another in a frame-independent way, since he isn't responding to my posts.

Apparently I am on his ignore list too for being so rude as to ask the same question and make the same point.

Einstein was clearly aware that the rate of a clock is a frame-dependent quantity. That completely resolves this thread.

 

[JesseM]

Apparently I am on his ignore list too for being so rude as to ask the same question and make the same point.

Einstein was clearly aware that the rate of a clock is a frame-dependent quantity. That completely resolves this thread.

To atyy and Al68: if you guys are going to continue debating cos, could you please try to press him on this question of whether he stands by the claim that there is a frame-independent sense in which one clock ticks faster than another? There's really no excuse for him not to answer the question--if he's just not answering because he doesn't want to run afoul of the rules about not disputing mainstream theories, keep in mind that you are free to ask questions like "I don't understand why physicists say X when it seems like it would make more sense to say Y", as long as you are willing to lay out your argument for thinking Y would make sense and actually listen to and address the arguments about why mainstream physicists say X rather than Y.

 

[Al68]

I allowed for and corrected your typo' however I still insist that "Einstein 'said' that clock A would tick slower than clock B because A is made to move relative to clock B!

That's exactly what he said. And that's what I've said, except the typos.

If Einstein had been observer B in his depiction he could have said to the traveler that clock A lags behind clock B due to the fact that the traveler's clock, having accelerated, was 'going more slowly' (ticking over at a slower rate) than his (Einstein's) stationary clock B in the same way that he said that an equatorial clock (under otherwise identical conditions) will 'go more slowly' than a polar clock as will a clock that is made to move in a closed curve relative to another clock and in the same way (albeit an anachronism) as did the Hafele-Keating clocks in the first leg of their experiment.

Whether or not he would have made such a comment is beside the point; he could have.

That's essentially what he was saying, I agree.

"Not those exact numbers?" Isn't that covered by my comment "..can be shown to..."?

I only meant that Einstein didn't actually provide details in his 1918 paper.

I am of the opinion that any intelligent person should be aware of the fact that if a clock instantaneously changes from being 400 000 times faster than the astronaut's clock to being 400 000 times slower this would have a devastating effect - not only on the clock itself but also on the planet on which that clock is located.

Why would Earth's clock be destroyed? Nothing is "happening" to Earth's clock. Einstein was saying that the Earth clock ticks at different rates in different reference frames, not that the Earth clock changes in any way. Why would anything "happen" to Earth's clock because the ship accelerates. Nobody is saying any such thing.

Not only 'in the ship's accelerating reference frame' but also in the traveler's mind!

And in the Earth twin's mind. They both agree on every fact. "In the ship's frame" does not mean "in the ship observer's opinion". Every observer agrees on everything, if they agree that Einstein's analysis is correct.

On the basis that the traveler 'determines' or 'predicts' or 'measures' that the Earth clock is ticking many times faster than it actually is then he (assuming an inability to apply logic and knowledge) is of the opinion that it is ticking many times faster than it was before he started accelerating and this 'fact' is part of his explanation as to why his clock physically lags behind the Earth clock when he returns to the planet.

Who said any clock was "ticking faster than it actually is"? Einstein is saying that the Earth clock ticks at different rates in different reference frames, not that the Earth clock changes its tick rate.

There seems to be a fundamental misunderstanding here. I don't understand why you refer to the "opinion" of an observer. Every observer that believes SR is correct will necessarily have the same opinion. Are you referring to observers that disagree about whether SR is correct or not?

And you speak of clocks as if a single clock might change its own tick rate, instead of Einstein's revelation that the rate of any clock is frame dependent. A single clock ticks at different rates in different reference frames without anything "happening" to the clock.

Maybe if you just stated exactly what it is that I, or someone else in this thread has said that you disagree with and why, it would help clear things up.

 

[phyti]

I am saying that, in your example, kinetic energy equals 0.5 times mass times relative velocity squared in classical physics, so the kinetic energy of any of those people/objects depends on reference frame, since relative velocity depends on reference frame. In your example, a person standing in the street would have kinetic energy in the rest frame of the car equal to 0.5 times their mass times the relative velocity squared. Obviously the kinetic energy of any object is frame dependent, since relative velocity is frame dependent. Well, if you're referring to kinetic energy, any classical physics textbook will do.

If this is correct, then all other static mass M, other cars, buildings, etc., moving at -v (relative to the car), would produce .5Mv^2. This is not equal to .5mv^2, with m= to car mass. Where is the conservation of energy rule?

 

[Dale]

Conservation is a completely different concept from invariance. If a quantity is conserved that means that its value before and after some interaction is the same in a single reference frame. If a quantity is invariant that means that different reference frames will agree on the value.

Energy is conserved, but frame variant. So each reference frame will disagree about the amount of energy a given object has, but they will all agree that energy is conserved. In a reference frame where the energy starts out high it will stay high, etc. This is a result of Newtonian mechanics and has nothing to do specifically with relativity.

 

[Al68]

If this is correct, then all other static mass M, other cars, buildings, etc., moving at -v (relative to the car), would produce .5Mv^2. This is not equal to .5mv^2, with m= to car mass. Where is the conservation of energy rule?

The conservation of energy rule does not say that .5Mv^2=.5mv^2. The conservation rule simple says that energy is conserved in any interaction, not that it's equal to the energy of a different object in another frame.

 

[phyti]

The conservation of energy rule does not say that .5Mv^2=.5mv^2. The conservation rule simple says that energy is conserved in any interaction, not that it's equal to the energy of a different object in another frame.

From a previous quote to cos:

In your example, a person standing in the street would have kinetic energy in the rest frame of the car equal to 0.5 times their mass times the relative velocity squared.

All other objects in a similar state relative to the car would have kinetic energy per this formula. The occupant of the car asks "What is the source of all that enegy?".
That is my question. Shouldn't the city-car system have a constant energy?

 

[JesseM]

All other objects in a similar state relative to the car would have kinetic energy per this formula. The occupant of the car asks "What is the source of all that enegy?".
That is my question. Shouldn't the city-car system have a constant energy?

It does have constant energy in any inertial frame--why wouldn't it? In the inertial frame in which the car is at rest at that moment (and will remain at rest as long as the car moves inertially), the entire city has a kinetic energy equal to half its mass times the relative velocity between car and city squared, while the car has zero kinetic energy because it's at rest. Sure that's a lot of kinetic energy, but it's still an energy that stays constant with time, there was never a time when the energy increased in this frame.

 

[cos]

...I still insist that Einstein 'said' that clock A would tick slower than clock B because A is made to move relative to clock B!

That's exactly what he said. And that's what I've said...

I believe that we could dispense with the rest of this message on the basis of your agreement.

Einstein is (hypothetically) standing alongside an observer (A) who is about to move to the location of another clock (B) which is going to remain 'at rest'.

Einstein tells A that due to the fact that he (A) will be moving to B's location his clock (A's clock) will tick slower than clock B ergo at a slower rate than Einstein's clock (B1) which will remain at his (Einstein's) location i.e. that A's clock will tick over at a slower rate than it is before he makes that move (i.e. "Einstein 'said' that clock A would tick slower than clock B because A is made to move relative to clock B") irrespective of the fact that whilst he is moving his (A's) clock's rate of operation will appear to remain unchanged i.e. it will appear to be ticking over at the same rate as it was before he started moving.

A starts moving toward B and notices that his clock's rate of operation appears not to have changed. It is still ticking over at the same rate as his heartbeat and there is no experiment that he can carry out that would indicate that it is not ticking over at the same rate as it was before he started moving however he accepts Einstein's comment thus realizes that his clock is ticking over at a slower rate than it was before he started moving (i.e. "Einstein 'said' that clock A would tick slower than clock B because A is made to move relative to clock B.").

A person is located in a windowless room. He looks at his clock (and the results of numerous internal dynamic experiments) and there is nothing to tell him if the room is moving with uniform velocity or is stationary.

He moves to the deck of his ship and, through a window, sees a clock (B) that he determines is also stationary and some distance away.

He is now clock A in Einstein's section 4 depiction "...at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous..."

He hits the 'go' button for his drive system as a result of which the ship accelerates; he hits the 'stop' button. He is, having read Einstein's special theory, of the opinion that, relative to his original location, he is, having accelerated, now moving toward clock B and because "Einstein 'said' that clock A would tick slower than clock B because A is made to move relative to clock B." he knows, all appearances to the contrary, that his clock is ticking over at a slower rate than it was prior to him hitting the go button.

People insinuate, and even insist, that I am, with my comments, seeking to invalidate or challenge special theory. I’m not!

If my arguments do invalidate or challenge special theory (which I believe they do not ) then other than the fact that I created an awareness of same that’s not my problem!

In his book Relativity, the Special and General Theory Einstein wrote (76, Crown, 1916) that the results of special theory are effectively invalidated by the presence of gravity and on the basis of the principle of equivalence I am of the opinion that he could also have stated that the same (STR) results are similarly invalidated by acceleration.

I'm of the opinion that the people who insist that I am contradicting or challenging special theory may not, themselves, have previously been aware of the implications arising from section 4 or, if they are aware, are attempting to conceal those implications.

I am of the opinion that any intelligent person should be aware of the fact that if a clock instantaneously changes from being 400 000 times faster than the astronaut's clock to being 400 000 times slower this would have a devastating effect - not only on the clock itself but also on the planet on which that clock is located.

Why would Earth's clock be destroyed? Nothing is "happening" to Earth's clock. Einstein was saying that the Earth clock ticks at different rates in different reference frames, not that the Earth clock changes in any way. Why would anything "happen" to Earth's clock because the ship accelerates. Nobody is saying any such thing.

The astronaut arrives back at the planet and finds that his clock lags behind the Earth clock. His explanation for this conclusive evidence is that according to his calculations the Earth clock was ticking over at a faster rate than it was before he commenced the return journey.

If he knows that nothing happened to Earth's clock - that it was not ticking over at a faster rate than it was before he commenced his return trip - his explanation has no validity! It is nonsensical! Ergo although his calculations showed him what 'is' taking place it was not!

"As far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Knowing that nothing has happened to the Earth clock - that it did not undergo a change in it's rate of operation - the astronaut has no right whatsoever to insist that his clock lags behind the Earth clock in accordance with his claim that the Earth clock is ticking over at a faster rate than it was before he started moving because that's what his calculations showed!

And in the Earth twin's mind.

The Earth twin’s determinations have absolutely nothing whatsoever to do with what the traveler determines!

They both agree on every fact. "In the ship's frame" does not mean "in the ship observer's opinion".

When the ship observer arrives back at the planet and finds that his clock lags behind the Earth clock he refuses to accept the possibility that it was his clock that was ‘going more slowly’ so he explains that lag by insisting that during sections of his return trip the Earth clock was ‘going faster’ than his own clock and, on the basis of his opinion that his clock rate remains unchanged, faster than it was before he started moving.

The ship’s frame is an inanimate object it has no opinion!

Every observer agrees on everything, if they agree that Einstein's analysis is correct.

If all observers agree that the traveler’s clock is ‘going more slowly’ (i.e. ticking over at a slower rate) than the Earth clock why should the ship observer not agree?

Who said any clock was "ticking faster than it actually is"?

I made no suggestion that anybody said that any clock was “ticking faster than it actually is” and I am of the opinion that you deliberately made that statement in an attempt to belittle my comments.

Einstein is saying that the Earth clock ticks at different rates in different reference frames, not that the Earth clock changes its tick rate.

It is not Einstein’s comments to which this section of my argument refers but to those of the traveler who insists that, according to his calculations, it is the Earth clock that, at some point, was ticking faster than it was before he started his return journey.

There seems to be a fundamental misunderstanding here. I don't understand why you refer to the "opinion" of an observer. Every observer that believes SR is correct will necessarily have the same opinion. Are you referring to observers that disagree about whether SR is correct or not?

I refer to the “opinion” of the traveler who insists that his clock was not ‘going more slowly’ but that the Earth clock was ‘going faster’ than it was before he commenced the return trip.

Had I been referring to “observers that disagree about whether SR is correct or not” I would have stated that fact and would not have deliberately concealed same as you seem to be implying!

And you speak of clocks as if a single clock might change its own tick rate, instead of Einstein's revelation that the rate of any clock is frame dependent. A single clock ticks at different rates in different reference frames without anything "happening" to the clock.

According to Einstein - a clock that is made to move relative to a stationary clock will ‘go more slowly’ (i.e. will tick over at a slower rate) than the stationary clock i.e. at a slower rate than it was before it started moving on the basis that the stationary clock’s rate of operation remains unchanged.

At the start of this post you quoted my comment viz. -

“...Einstein 'said' that clock A would tick slower than clock B because A is made to move relative to clock B!”

and you responded -

“That's exactly what he said. And that's what I've said...”

On the basis that clock B’s rate of operation remains unchanged and that clock A is going more slowly than B then A is going more slowly than it was before it started moving as represented by B’s (unchanging) rate of operation.

On the basis that Einstein 'said' that clock A would tick slower than clock B (i.e. tick over at a slower rate than it did before it started moving) because A is made to move (a fact with which you obviously agree) then, according to Einstein, clock A incurs “... a change in it’s own tick rate...” in exactly the same rate as it would if a gravitational field suddenly appeared and affected only clock A but not clock B (Einstein’s 1918 Naturwissenschaften depiction).

Maybe if you just stated exactly what it is that I, or someone else in this thread has said that you disagree with and why, it would help clear things up.

I am of the opinion that I have already responded to things that have been said in this thread with which I disagree and have pointed out in my replies why it is that I disagree with those responses ergo I have no intention of repeating those arguments.

 

[JesseM]

People insinuate, and even insist, that I am, with my comments, seeking to invalidate or challenge special theory. I’m not!

If you claim that there is a frame-independent sense in which one clock ticks slower, you do. Why do you refuse to answer the simple question of whether you're arguing this?

In his book Relativity, the Special and General Theory Einstein wrote (76, Crown, 1916) that the results of special theory are effectively invalidated by the presence of gravity and on the basis of the principle of equivalence I am of the opinion that he could also have stated that the same (STR) results are similarly invalidated by acceleration.

The equations of physics that hold in inertial frames (such as the equation relating time dilation to coordinate velocity) don't work in non-inertial ones, if that's all you mean (and in spacetime which is curved by gravity, all coordinate systems covering large regions of spacetime are non-inertial, although you can still have 'locally inertial frames' in an infinitesimally small region of curved spacetime). But if you mean that even in flat spacetime with no gravity, acceleration invalidates the idea that all inertial frames are equally valid (will you give a yes-or-no answer if this is what you mean?), then that would contradict both SR and GR, it's an opinion that all modern physicists would disagree with and so would Einstein.

 

[phyti]

cos; re: post 244

People insinuate, and even insist, that I am, with my comments, seeking to invalidate or challenge special theory. I’m not!

Of course you are not. Einstein never said it is mandatory that you assume a relative rest frame. He showed that if you did, it doesn't alter physics, only conclusions. You can accept your motion, make the appropiate adjustments, and go on your way.

 

[Al68]

A starts moving toward B and notices that his clock's rate of operation appears not to have changed. It is still ticking over at the same rate as his heartbeat and there is no experiment that he can carry out that would indicate that it is not ticking over at the same rate as it was before he started moving however he accepts Einstein's comment thus realizes that his clock is ticking over at a slower rate than it was before he started moving (i.e. "Einstein 'said' that clock A would tick slower than clock B because A is made to move relative to clock B.").

If Einstein meant "ticking at a slower rate than it was before", he would have said that. Since he only meant "slower than clock B because it's made to move relative to B", that's what he said. There is a HUGE difference.

In his book Relativity, the Special and General Theory Einstein wrote (76, Crown, 1916) that the results of special theory are effectively invalidated by the presence of gravity and on the basis of the principle of equivalence I am of the opinion that he could also have stated that the same (STR) results are similarly invalidated by acceleration.

The equations of SR are not valid in accelerated reference frames. Einstein's 1905 paper makes that perfectly clear. That's why he never calculated the relative clock rates in A's accelerated frame in section 4.

The Equivalence principle equates the proper acceleration due to the presence of a gravitational field with an accelerated (non-inertial) reference frame. Neither was used as a reference frame in section 4. Only later on did he establish a way to use accelerated reference frames.

The astronaut arrives back at the planet and finds that his clock lags behind the Earth clock. His explanation for this conclusive evidence is that according to his calculations the Earth clock was ticking over at a faster rate than it was before he commenced the return journey.

If he knows that nothing happened to Earth's clock - that it was not ticking over at a faster rate than it was before he commenced his return trip - his explanation has no validity! It is nonsensical! Ergo although his calculations showed him what 'is' taking place it was not!

Earth's clock only runs super fast in the ship's accelerated frame during the turnaround. Einstein never claims any clock ticks slower or faster "than it was before". No clock changes its tick rate. Every clock's tick rate depends on reference frame. The difference in a clock's tick rate in a different frame is not due to the clock ticking slower or faster "than it was before".

Knowing that nothing has happened to the Earth clock - that it did not undergo a change in it's rate of operation - the astronaut has no right whatsoever to insist that his clock lags behind the Earth clock in accordance with his claim that the Earth clock is ticking over at a faster rate than it was before he started moving because that's what his calculations showed!

Nothing happens to either clock. See above.

If all observers agree that the traveler’s clock is ‘going more slowly’ (i.e. ticking over at a slower rate) than the Earth clock why should the ship observer not agree?

The ship observer does agree that the ship's clock ticked slower than the Earth clock in Earth's frame.

1. In Earth's frame, the ship clock runs slower than Earth's clock at all times.
2. In the ship's frame, the Earth's clock runs slower than the ship's clock during inertial motion, and very much faster than the ship's clock during the turnaround.

1. and 2. do not contradict each other in any way. Both twins agree that both statements are true. Both statements are objective fact (if you believe Einstein is right), so they are both true regardless of what any observer "thinks", anyway.

The end result of the ship's clock reading less than the Earth clock at the reunion is consistent with both 1. and 2. above.

The reason that the rate of a clock is different in different reference frames is not because any clock "changes its tick rate". Nothing happens to any clock in Einstein's 1905 or 1918 paper that changes its tick rate. Einstein never claims that anything "happens" to any clock.

Anytime Einstein refers to a clock as "going more slowly" it is due to a change in relative velocity between the clock and the reference frame, not due to any change in the clock itself.

This is clear in Einstein's papers, since logically, a single clock could not simultaneously tick at different tick rates in different frames any other way.

On the basis that the traveler 'determines' or 'predicts' or 'measures' that the Earth clock is ticking many times faster than it actually is then he (assuming an inability to apply logic and knowledge) is of the opinion that it is ticking many times faster than it was before he started accelerating and this 'fact' is part of his explanation as to why his clock physically lags behind the Earth clock when he returns to the planet.

Who said any clock was "ticking faster than it actually is"?

I made no suggestion that anybody said that any clock was “ticking faster than it actually is” and I am of the opinion that you deliberately made that statement in an attempt to belittle my comments.

I have no intention to belittle anyone. I'm sorry if you took it that way. It's obviously very difficult to explain the concept of time dilation in a way that makes it clear that it's not due to any "change" of any clock's operation.

 

[Al68]

From a previous quote to cos:

All other objects in a similar state relative to the car would have kinetic energy per this formula. The occupant of the car asks "What is the source of all that enegy?".
That is my question. Shouldn't the city-car system have a constant energy?

If you mean that the kinetic energy of the car relative to the city should be equal to the kinetic energy of the city relative to the car, then no, they should not be equal.

Each one should be constant as long as the relative velocity is constant, and energy is conserved in each frame.

 

[callena]

What do people think he meant by the phrase "...must go more slowly..."?

They tick at the same rate locally. They just experience time differently. His comment was on absolute time passage relative to the stationary clock.

Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock?

The only one who could notice this would be the stationary observer if he could see the moving clock as it ticked.

 

[JesseM]

cos; re: post 244

People insinuate, and even insist, that I am, with my comments, seeking to invalidate or challenge special theory. I’m not!

Of course you are not. Einstein never said it is mandatory that you assume a relative rest frame. He showed that if you did, it doesn't alter physics, only conclusions. You can accept your motion, make the appropiate adjustments, and go on your way.

So phyti, you don't think this statement of cos' contradicts relativity?

As far as I am concerned it makes no difference whatsoever if I 'look' at this event from a frame dependent point of view or a frame independent point of view I take Einstein's word for it that my clock is ticking over at a slower rate than clock B.

In fact I do not 'look' at this event from a frame dependent point of view or a frame independent point of view but sit back serenely, confidently, of the opinion that Einstein was right; that my clock is ticking over at a slower rate than it was before I started moving.

Do you think that a statement about which of two clocks is ticking faster than the other at a given moment can be anything other than frame-dependent in SR?