Understanding Time Dilation in Einstein's Special Theory of Relativity

[phyti]

al68, post 247

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".

When the two synchronized clocks separate and are brought together after traveling different paths, compared in the same ref. frame, how do we explain the time difference if the rates never changed?

jesse, post 250

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

He knows enough about frame dependency, I think he's frustrated with all the interrogation style tactics, and the unrelated side issues. Why should a response to a simple question go on for so long. Some people want to understand why in physical terms, not in abstract theoretical terms.

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?

Not if it's about perception, and that's the key and the obstacle for most discussions regarding SR. It's 100 years plus and the debate is still going strong!

Do you think space contracts?

cos, post 1

A. Einstein:
"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."

That's what he said, so what's the problem?

 

[JesseM]

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?

Not if it's about perception, and that's the key and the obstacle for most discussions regarding SR. It's 100 years plus and the debate is still going strong!

There's no debates about SR among physicists, only among people who think there should be some "real truth" about frame-dependent quantities. And "not if it's about perception" doesn't make any sense unless you're referring to visual perception, but cos already said he wasn't talking about that (he wanted to correct for the Doppler effect when comparing times). If you think there's a sense in which different observers can have different "perceptions" about the ratio between the rates two clocks are ticking, but we're not talking about either visual perceptions or comparing the ratio in two different frames, then please explain.

Do you think space contracts?

I don't know what this question means. Certainly the distance between two objects can be smaller in one frame than it is in another frame.

cos, post 1

A. Einstein:
"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."

That's what he said, so what's the problem?

The problem is that, #1 Einstein may have been talking about accumulated time over a whole rotation rather than an instantaneous comparison which is what cos wants to talk about, and #2, even if Einstein was talking about an instantaneous comparison then he was obviously talking about a comparison in the rest frame of the polar clock, there's no way Einstein would deny that comparison of instantaneous clock rates is always frame-dependent as cos seemed to do.

 

[cos]

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.

Clock B is ticking over at the same rate as was clock A before A started moving and because A is ticking over at a slower rate than B then A is ticking over at a slower rate than it was before it started moving as determined by clock B's unchanging tick rate.

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.

It makes no difference that in section 4 he didn't calculate the relative clock rates however he did effectively, analogously, imply that A is ticking over at a slower rate than B and if that's not him referring to relative tick rates I don't know what else you could call it!

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.

In order for clock A to move to B's location A must undergo acceleration as do his clocks in the extended version of his 1905 section 4 STR i.e. his 1918 Naturwissenschaften article.

(It is interesting to note that when Galileo prepared his manuscript for Two New Sciences he had already been castigated by 'authorities' for his support of a non-geocentric universe so he wrote that work in the form of a purely hypothetical discussion between a teacher and two of his students.

When Einstein wrote his Dialog About Objections to the Theory of Relativity he had already been castigated by his colleagues for, in part, his comment in general theory that the special theory law of the constancy of the speed of light required modification so he similarly presented that work as a purely hypothetical discussion this time between a relativist and a critic.)

Although neither acceleration or gravity were used as reference frames in section 4 acceleration was involved!

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".

You wrote, above "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." yet now point out that "Earth's clock only runs super fast in the ship's accelerated frame during the turnaround."

Whilst he did not use that phrase ("...any clock ticks slower or faster "than it was before") in section 4 he implied that A ticks slower than it did before it started moving on the basis of his analogous comment that clock A 'goes more slowly' (i.e. ticks over at a slower rate) than B which is ticking over at the same rate as was clock A before A started moving!

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".

So Einstein's implication in general theory regarding a clock that is located in a strong gravitational field is ticking over at a slower rate than it would if it were to be located at high altitude (as happened to the clocks in The 19176 Wallops Island experiment) is wrong?

If a clock is taken from the top of a very tall tower to the base of that tower it will not then be ticking over at a slower rate than it was when it was atop the tower?

Nothing happens to either clock. See above.

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.

The ship observer comes under the category of ALL observers! He therefore agrees that his clock 'goes more slowly' than the Earth clock not only in the Earth's frame but also in his own frame and that's why his clock physically lags behind the Earth clock when he returns to the planet!

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.

Your depiction #1 has no relationship whatsoever to my OP nor to any of my arguments.

#2. "In the ship's frame..." The ship's frame is an inanimate object! It neither observes nor determines nor calculates nor predicts nor opines nor breaks wind!

It is the astronaut who (ditto)!

From a naive and solipsist astronaut's point of view his clock does not run slower than it did when he was stationary prior to firing his rockets and accelerating back to the planet (i.e. that it is not 'going more slowly' than the Earth clock and that his clock is 'going more slowly' than it was before he accelerated) but he insists that "...the Earth clock runs...very much faster..." than his own clock and on the basis of his insistence that his clock has not changed then it can only, in his opinion and not the non-existent opinion of the inanimate ship's frame, be the Earth clock that 'goes faster' than it did before he started accelerating.

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.

What is true is that those clocks will do what they do regardless of what any observer "thinks". The traveled clock will (according to Einstein) 'go more slowly' than the stationary clock.

I am of the opinion that in the Hafele-Keating experiment their clocks did 'go more slowly' than the laboratory clocks during all sections of that first leg when they accelerated away from, moved in a closed curve around, and eventually decelerated upon landing back at Washington.

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.

It is also consistent with the point of view of an astronaut who knows that his clock is 'going more slowly' than it did before he started moving!

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.

Einstein's general theory gravitational time variation is not "...due to a change in relative velocity between the clock and the reference frame..." but is a result of it's varying locations in a gravitational field and (on the basis of his principle of equivalence) an analogous change in the rate of operation of clock A is initiated by it's acceleration!

I am of the opinion that (irrespective of what any observer or an inanimate frame thinks) a clock on the rim of a spinning disc is, according to Einstein, 'going more slowly' (i.e. is ticking over at a slower rate) than an identical clock at the center of that disc and that a clock that is made to move from the center of the disc to it's rim will progressively tick over at slower and slower rates as it accelerates and, when it arrives at the rim, will be ticking over at a slower rate than it was at the center of the rim thus that it has incurred a change in it's rate of operation - it's 'tick rate'.

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.

Several contributors to this thread have consistently, and in my opinion erroneously (and annoyingly), referred to what different (inanimate) frames 'determine' is taking place however as I have also repeatedly pointed out my argument is not in respect to those (nonexistent, purely hypothetical) frames but to what the traveler determines!

Prior to moving to B's location A learns that, according to Einstein, his clock will be 'going more slowly' than it is before he starts out and although he can determine no variation in it's rate of operation whilst he is moving he accepts the fact that it is 'going more slowly' than it was before he started moving in the same way that a person moving down a mountain (or away from the center of a spinning disc) knows, all appearances to the contrary, that their clock is progressively slowing down as they enter progressively stronger gravitational tidal areas (or as their speed increases).

 

[cos]

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.

His comment regarding "...absolute time passage relative to the stationary clock..." was in relation to the difference between A and B when A arrives at B' location.

Clock A lags behind B because A went more slowly (i.e. ticked over at a slower rate) than clock B.

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.

It matters not if anyone notices this; the relevant factor is that this is what clock A does.

 

[JesseM]

I am of the opinion that (irrespective of what any observer or an inanimate frame thinks) a clock on the rim of a spinning disc is, according to Einstein, 'going more slowly' (i.e. is ticking over at a slower rate) than an identical clock at the center of that disc and that a clock that is made to move from the center of the disc to it's rim will progressively tick over at slower and slower rates as it accelerates and, when it arrives at the rim, will be ticking over at a slower rate than it was at the center of the rim thus that it has incurred a change in it's rate of operation - it's 'tick rate'.

For the benefit of phyti and anyone else who doubts that cos doesn't understand frame-dependence, here he explicitly contrasts the sense in which he is talking about one clock "going more slowly" with what "any observer or an inanimate frame thinks".

Several contributors to this thread have consistently, and in my opinion erroneously (and annoyingly), referred to what different (inanimate) frames 'determine' is taking place however as I have also repeatedly pointed out my argument is not in respect to those (nonexistent, purely hypothetical) frames but to what the traveler determines!

In relativity anytime physicists talking about a traveler "determining" anything about clock rates, they always understand this to mean "what the traveler calculates about the clock rates in whatever frame he's using (normally his inertial rest frame at that moment)". If you think you know of a way to "determine" quantitative truths about clock rates (and all statements in physics about rates should be quantitative, not just a qualitative 'goes more slowly') that doesn't involve making use of a particular frame, please present it (and keep in mind what I said about there being no way to 'correct for the Doppler effect' that doesn't involve picking a particular choice of frame).

But it seems to me that you have no idea how your statements would correspond to any sort of actual numerical comparison of clock rates, that you're basically just taking Einstein's statement as a sort of "holy writ" that's supposed to settle the argument, the way a religious fundamentalist would do (and like a fundamentalist you ignore the context of particular statements, in this case a context which makes it a sure bet that Einstein was either talking about elapsed time over a full rotation, or comparing the rate in the frame of the pole even if he wasn't totally explicit about the frame-dependence of his statement). This is exactly what you seem to do in the paragraph following the previous one I quoted:

Prior to moving to B's location A learns that, according to Einstein, his clock will be 'going more slowly' than it is before he starts out and although he can determine no variation in it's rate of operation whilst he is moving he accepts the fact that it is 'going more slowly' than it was before he started moving

If you weren't allowed to refer to Einstein's words, would you have any independent physical argument for saying A's clock is "going more slowly" after he accelerates, in a non frame-dependent sense? (again, there's no debate over the fact that A's clock is going more slowly after he accelerates in the inertial frame of the clock at the pole)

 

[cos]

cos, post 1

"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."

That's what he said, so what's the problem?

I may be breaching etiquette but was that question addressed to me?

If so, there is no problem.

My reason for providing that quote was that, in my opinion, he meant that a clock at the equator will tick over at a slower rate than a clock at one of the poles thus that, by extension, if a clock is moved from one of the poles to the equator it will progressively be ticking over at slower and slower rates (than it was when it was at the pole) as it's speed relative to the polar clock increases irrespective of the fact that as far as the person accompanying this clock is concerned it's rate of operation appears to have remained constant in the same way that a person descending a mountain will be of the opinion that his clock's rate of operation remains unchanged irrespective of the fact that he (presumably) knows that a clock's rate of operation decreases as it enters progressively stronger gravitational tidal areas.

 

[Dale]

When the two synchronized clocks separate and are brought together after traveling different paths, compared in the same ref. frame, how do we explain the time difference if the rates never changed?

One took a shorter path through spacetime.

A close analogy is the following. Consider two corners of a triangle. One leg forms a straight path between the two corners and the other two legs form a bent path. If you use rulers to measure the two paths you find different measurements. Would you explain the difference by saying that one ruler "shrunk"?

 

[Dale]

This is a very minor point, but since cos is avoiding directly addressing the real issue...

#2. "In the ship's frame..." The ship's frame is an inanimate object!

It is perfectly valid to speak of the rest frame of inanimate objects. "The ship's frame" is shorthand for "any orthonormal coordinate system where the ship's velocity is 0."

 

[Al68]

It makes no difference that in section 4 he didn't calculate the relative clock rates however he did effectively, analogously, imply that A is ticking over at a slower rate than B and if that's not him referring to relative tick rates I don't know what else you could call it!

He calculated the relative tick rates in B's inertial frame.

In order for clock A to move to B's location A must undergo acceleration as do his clocks in the extended version of his 1905 section 4 STR i.e. his 1918 Naturwissenschaften article.

SR can handle acceleration relative to inertial frames just fine.

You wrote, above "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." yet now point out that "Earth's clock only runs super fast in the ship's accelerated frame during the turnaround."

Einstein uses GR, not SR, to analyze the accelerated frame of the ship in his 1918 paper. That was the whole point of the paper.

The ship observer comes under the category of ALL observers! He therefore agrees that his clock 'goes more slowly' than the Earth clock not only in the Earth's frame but also in his own frame and that's why his clock physically lags behind the Earth clock when he returns to the planet!

That's simple not true according to SR. Unless by "his own frame" you mean Earth's rest frame, since he is at rest with Earth when he returns.

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.

Your depiction #1 has no relationship whatsoever to my OP nor to any of my arguments.

#2. "In the ship's frame..." The ship's frame is an inanimate object! It neither observes nor determines nor calculates nor predicts nor opines nor breaks wind!

Exactly. The predictions of SR apply to frames, not necessarily to the opinion of humans.

It is also consistent with the point of view of an astronaut who knows that his clock is 'going more slowly' than it did before he started moving!

That would be correct in Earth's frame. Which was my statement 1. above which the astronaut knows.

Several contributors to this thread have consistently, and in my opinion erroneously (and annoyingly), referred to what different (inanimate) frames 'determine' is taking place however as I have also repeatedly pointed out my argument is not in respect to those (nonexistent, purely hypothetical) frames but to what the traveler determines!

Frames can't make "determinations". Determinations are made about frames. The tick rate of a clock depends on reference frame. A traveler should determine what is true in each frame. But the truth in each frame will still be the truth whether or not it is observed or calculated by a traveler.

I have referred to reference frames because they are what a clock's relative tick rate depends on, not because your argument was or wasn't regarding them.

In Einstein's 1905 and 1918 papers, every calculation is for a particular reference frame. In section 4, the reference frame is the rest frame of clock B. The reference frame used for every calculation is apparent from the context, and made clear earlier in the paper, even if it isn't repeated throughout.

The results of each calculation are valid in that frame for any observer. If the observer is at rest in that frame, then his observations will match the results calculated for that frame. If not, he can still agree that the results are true for the frame they are calculated for, but not in his rest frame.

 

[Al68]

When the two synchronized clocks separate and are brought together after traveling different paths, compared in the same ref. frame, how do we explain the time difference if the rates never changed?

Because the elapse of proper time on a clock also depends on distance traveled between the clock readings. The distance traveled by clock A in B's frame is not equal to the distance traveled by clock B in A's frame.

 

[cos]

In a previous message you wrote -

"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"."

To which I responded -

"So Einstein's implication in general theory regarding a clock that is located in a strong gravitational field is ticking over at a slower rate than it would if it were to be located at high altitude (as happened to the clocks in The 19176 Wallops Island experiment) is wrong?

If a clock is taken from the top of a very tall tower to the base of that tower it will not then be ticking over at a slower rate than it was when it was atop the tower?"

I also wrote -

“I am of the opinion that in the Hafele-Keating experiment their clocks did 'go more slowly' than the laboratory clocks during all sections of that first leg when they accelerated away from, moved in a closed curve around, and eventually decelerated upon landing back at Washington.

Whilst I have determined to respond to all of your arguments you pointedly and deliberately refused to respond to those matters and other salient points as a result of which you have lost all credibility as far as I am concerned.

Correspondence terminated.

 

[matheinste]

Hello cos.

Quote:-
----Correspondence terminated.-----

If this is the end of the thread then it has proved my theory incorrect and unfair to you. Only another 20 replies are required to achieve the record number of replies for the Relativity forum. I thought perhaps this was what you were aiming for.

It is much lower down the list in order of the number of views. Perhaps many people lost interest. It has become a bit repetitive. Section 4 has become one of the most used terms in the English language.

Matheinste

 

[JesseM]

"So Einstein's implication in general theory regarding a clock that is located in a strong gravitational field is ticking over at a slower rate than it would if it were to be located at high altitude (as happened to the clocks in The 19176 Wallops Island experiment) is wrong?

What quote of Einstein are you referring to? I'm sure Einstein never claimed or implied that at any given moment a clock at a lower altitude is ticking slower than a clock at higher altitude in some non-coordinate-dependent sense, although this would probably be true in any practical coordinate system for dealing with a planet's gravity like Schwarzschild coordinates...also, it's of course true in any coordinate system that if two clocks are synchronized when next to each other, then one clock is put at a higher altitude and left there for a while while the other clock remains at a lower altitude, if they are brought together again the clock at the lower altitude will have elapsed less time. If you have any Einstein quotes where he talks about clocks at lower altitudes in a gravitational field ticking slower, I imagine an examination of the context would show it's clear or at least plausible that he was referring to one of these two ideas. But the fact that clocks at lower altitudes tick slower in a practical coordinate system like Schwarzschild coordinates in no way implies that you couldn't come up with some ungainly coordinate system where at a particular instant the clock at the lower altitude was the one ticking faster. Also, it in no way implies there is any non-coordinate-dependent sense in which we can compare the rate two clocks are ticking. Of course you never once on this thread provided any actual quantitative method of comparing the rate of two clocks in a non-coordinate-dependent sense, so as I said in post #255, you are just behaving like a religious fundamentalist who thinks that quoting some passages from the Holy Book of Einstein settles the argument (passages which are taken out of context, and can easily be interpreted in ways that don't contradict what everyone on the thread has been telling you about the frame dependence of clock rate comparisons).

 

[cos]

Hello cos.

Quote:-
----Correspondence terminated.-----

If this is the end of the thread then it has proved my theory incorrect and unfair to you. Only another 20 replies are required to achieve the record number of replies for the Relativity forum. I thought perhaps this was what you were aiming for.

It is much lower down the list in order of the number of views. Perhaps many people lost interest. It has become a bit repetitive. Section 4 has become one of the most used terms in the English language.

Matheinste

My comment was addressed to, and directed at, one person and one person alone.

Ya' got nothin' better to do?

 

[atyy]

I am of the opinion that in the Hafele-Keating experiment their clocks did 'go more slowly' than the laboratory clocks during all sections of that first leg when they accelerated away from, moved in a closed curve around, and eventually decelerated upon landing back at Washington.

Do you use the plural "laboratory clocks" to indicate a notional lattice of clocks with respect to which the traveling clocks go more slowly?

 

[cos]

Do you use the plural "laboratory clocks" to indicate a notional lattice of clocks with respect to which the traveling clocks go more slowly?

I used the plural 'clocks' as it is my understanding that one atomic clock was considered not to be accurate enough for reasons of comparisons ergo they used three clocks in the laboratory and three in the aircraft and took an average of the elapsed time registered by each group as their comparison figures.

Apparently Essen was of the opinion that no atomic clock (or groups thereof) was accurate enough to be capable of determining the tiny variation (59ns. - predicted to be 40 ns.) that took place.

 

[atyy]

I used the plural 'clocks' as it is my understanding that one atomic clock was considered not to be accurate enough for reasons of comparisons ergo they used three clocks in the laboratory and three in the aircraft and took an average of the elapsed time registered by each group as their comparison figures.

Doesn't Will say that the clocks are compared with a notional lattice of "stationary" clocks? Hence, the rates of the clocks in the air and on the surface are not compared with each other, but with the lattice clocks. So the rate of a clock in the air relative to the rate of the lattice clocks is different from the rate of a clock on the surface relative to the lattice clocks, but there is no comparison of the rates of the clocks in the air relative to the rates of the clocks on the surface.

 

[Al68]

"So Einstein's implication in general theory regarding a clock that is located in a strong gravitational field is ticking over at a slower rate than it would if it were to be located at high altitude (as happened to the clocks in The 19176 Wallops Island experiment) is wrong?

Not wrong. Frame dependent.

If a clock is taken from the top of a very tall tower to the base of that tower it will not then be ticking over at a slower rate than it was when it was atop the tower?"

Yes, in the rest frame of the tower. Not in every frame.

Whilst I have determined to respond to all of your arguments you pointedly and deliberately refused to respond to those matters and other salient points as a result of which you have lost all credibility as far as I am concerned.

Sorry if I haven't addressed every single statement in your posts. I only addressed the ones I considered most relevant due to time considerations.

Correspondence terminated.

OK.

 

[Al68]

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’ ...

Well, if the ship observer believes that his clock ran slower than the Earth clock "really" the whole time, including before the turnaround, how did the clocks know in advance which clock would lag behind the other?

How would the clocks know in advance which clock would accelerate to join the other, and therefore which clock would lag behind the other?

 

[Dale]

Sorry if I haven't addressed every single statement in your posts. I only addressed the ones I considered most relevant due to time considerations.

I think that is how I got on his ignore list too. When someone makes a long rambling post with a dozen questions usually there are one or two key points that, once addressed, resolve the whole issue. So I tend to reply to only one or two points at a time also.

If someone really wants a response to a point then they should limit themselves to that single point in a post by itself.

 

[Al68]

I think that is how I got on his ignore list too. When someone makes a long rambling post with a dozen questions usually there are one or two key points that, once addressed, resolve the whole issue. So I tend to reply to only one or two points at a time also.

If someone really wants a response to a point then they should limit themselves to that single point in a post by itself.

That's becoming a long list, too. I thought I was being pretty nice considering he repeatedly ignored the point a lot of us were trying to get across. Unless he really doesn't understand the concept of reference frames.

 

[phyti]

One took a shorter path through spacetime.

A close analogy is the following. Consider two corners of a triangle. One leg forms a straight path between the two corners and the other two legs form a bent path. If you use rulers to measure the two paths you find different measurements. Would you explain the difference by saying that one ruler "shrunk"?

I won't if you don't!

 

[phyti]

Because the elapse of proper time on a clock also depends on distance traveled between the clock readings. The distance traveled by clock A in B's frame is not equal to the distance traveled by clock B in A's frame.

If two synchronized clocks become out of synch when compared in the same frame, there is a physical explanation why, worn parts, weak battery, etc.
In the example with one clock moving away and returning, if the clocks literally ticked at the same rate for the duration of the trip, there would be no difference, The number of ticks would be invariant, yet we know the rate depends on the speed of the clock. The fact that one clock shows less ticks than the other (in the second case) when compared in a common frame is equivalent to the first case, and requires a physical explanation, not an abstract model representation.
Your statement from post 247 initiated this response.

No clock changes its tick rate.

If you are as rigorous as you require others to be, then a qualified statement might add "in it's own reference frame".

 

[Dale]

I won't if you don't!

Sorry, I can't tell from this comment if you understood the analogy and how a clock could be said to not change its rate despite the difference in acumulated time.

 

[cos]

Doesn't Will say that the clocks are compared with a notional lattice of "stationary" clocks? Hence, the rates of the clocks in the air and on the surface are not compared with each other, but with the lattice clocks. So the rate of a clock in the air relative to the rate of the lattice clocks is different from the rate of a clock on the surface relative to the lattice clocks, but there is no comparison of the rates of the clocks in the air relative to the rates of the clocks on the surface.

Will writes "...the rate of a moving clock must always be compared to a set of clocks that are in an inertial frame...a set of clocks that are at rest with respect to the center of the Earth." i.e. your 'notional lattice of stationary clocks'.

He continues "The ground clock is moving at a speed determined by the rotation rate of the Earth and thus ticks more slowly than the fictitious inertial clocks; the flying clock is moving even more quickly relative to the inertial clocks, so it is ticking even more slowly. Thus time dilation makes the flying clock run slowly relative to the ground clock."

In other words Will points out that there is 'a comparison of the rates of the clocks in the air relative to the rates of the clocks on the surface' and that the clocks aboard the aircraft tick over at a slower rate than the laboratory clocks.

 

[atyy]

Will writes "...the rate of a moving clock must always be compared to a set of clocks that are in an inertial frame...a set of clocks that are at rest with respect to the center of the Earth." i.e. your 'notional lattice of stationary clocks'.

He continues "The ground clock is moving at a speed determined by the rotation rate of the Earth and thus ticks more slowly than the fictitious inertial clocks; the flying clock is moving even more quickly relative to the inertial clocks, so it is ticking even more slowly. Thus time dilation makes the flying clock run slowly relative to the ground clock."

In other words Will points out that there is 'a comparison of the rates of the clocks in the air relative to the rates of the clocks on the surface' and that the clocks aboard the aircraft tick over at a slower rate than the laboratory clocks.

Well, I should have said no "direct comparison" for clarity. There point is that it's the lattice clocks against which the direct comparison is being made, with the indirect comparisons between the flying and surface clocks working out so that the eastward flying clocks go slow, while the westward flying clocks go fast. So the lattice clocks or "reference frame" is very important.

 

[Al68]

If two synchronized clocks become out of synch when compared in the same frame, there is a physical explanation why, worn parts, weak battery, etc.
In the example with one clock moving away and returning, if the clocks literally ticked at the same rate for the duration of the trip, there would be no difference, The number of ticks would be invariant, yet we know the rate depends on the speed of the clock. The fact that one clock shows less ticks than the other (in the second case) when compared in a common frame is equivalent to the first case, and requires a physical explanation, not an abstract model representation.

The physical explanation is that time itself passes at different rates for different observers/clocks. a clock that is not broken will reflect this. The number of "ticks" shown on each clock will be proportional to the time elapsed for each clock. The details of how a particular clock keeps good time is a side issue, since we are assuming that all clocks used in SR have the same tick rate relative to the proper time elapsed.

No clock changes its tick rate.

If you are as rigorous as you require others to be, then a qualified statement might add "in it's own reference frame".

Why would I add that when the clock's rate was always frame dependent. If the tick rate is different for different observers, it's because the observers are at different relative velocities, not because the clock itself changes in any way.

In other words, a clock runs at the constant rate of T*sqr(1-v^2/c^2) where v is the relative velocity between the clock and an inertial reference frame, and T is time in that reference frame. Only the relative rate between a clock and observer changes, because the relative velocity of the observer changes, not because the clock changes.

Saying the clock's rate changed is like saying the moon "changed" its position from my left to my right because I turned around. Sure the relative position of the moon did change, but I don't need to explain what "happened" to the moon.

 

[cos]

Al68 wrote:- "Sorry if I haven't addressed every single statement in your posts. I only addressed the ones I considered most relevant due to time considerations."

This is not a continuation of that discussion but is a general note to the several people that have made similar comments.

I note that it is always the more salient points and questions in my postings that are ignored due to the fact that a response to same would mean a commitment by the respondent which is why I specifically raised those matters.

My responses tend to be lengthy due to the fact that the messages to which they apply are themselves of extreme length or else I am forced to break things down into extended simple explanations and/or provide analogies.

When people respond with (as far as I am concerned) totally irrelevant comments such as 'not according to other reference frames' I am forced to respond to such arguments pointing out that the determinations arrived at by numerous other reference frames have no bearing whatsoever - no affect - on those arrived at by the observer in the reference frame in which the event takes place.

When I explain this to those people and they respond with 'not according to other reference frames' and refuse to respond to my relevant points of view I tend to become a bit upset with their intolerance however I am of the opinion that they are deliberately maintaining this attitude for no other reason than to upset me which I see as being arrogant harassment.

 

[DrGreg]

When people respond with (as far as I am concerned) totally irrelevant comments such as 'not according to other reference frames' I am forced to respond to such arguments pointing out that the determinations arrived at by numerous other reference frames have no bearing whatsoever - no affect - on those arrived at by the observer in the reference frame in which the event takes place.

When I explain this to those people and they respond with 'not according to other reference frames' and refuse to respond to my relevant points of view I tend to become a bit upset with their intolerance however I am of the opinion that they are deliberately maintaining this attitude for no other reason than to upset me which I see as being arrogant harassment.

The reason everyone keeps going on about other reference frames is because that's the only way you will ever understand how relativity works. If you really only want to ever consider a single reference frame then there is no explanation for relativity. You will just have to accept that's the way it is without understanding why.

 

[JesseM]

When people respond with (as far as I am concerned) totally irrelevant comments such as 'not according to other reference frames' I am forced to respond to such arguments pointing out that the determinations arrived at by numerous other reference frames have no bearing whatsoever - no affect - on those arrived at by the observer in the reference frame in which the event takes place.

Events don't take place "in" one reference frame or another, reference frames are just ways of assigning position and time coordinates to events in spacetime. Similarly, if I want to do some land surveying, there are different ways I could place a coordinate grid on the patch of land I'm interested in, and in different choices of coordinate grids, the same rock might be labeled with different x and y coordinates. But the rock obviously isn't "in" one coordinate grid or another, it's just there, on the ground.

 

[cos]

Will writes "...the rate of a moving clock must always be compared to a set of clocks that are in an inertial frame...a set of clocks that are at rest with respect to the center of the Earth." i.e. your 'notional lattice of stationary clocks'.

He continues "The ground clock is moving at a speed determined by the rotation rate of the Earth and thus ticks more slowly than the fictitious inertial clocks; the flying clock is moving even more quickly relative to the inertial clocks, so it is ticking even more slowly. Thus time dilation makes the flying clock run slowly relative to the ground clock."

In other words Will points out that there is 'a comparison of the rates of the clocks in the air relative to the rates of the clocks on the surface' and that the clocks aboard the aircraft tick over at a slower rate than the laboratory clocks.

Well, I should have said no "direct comparison" for clarity.

Will's comparison of the rate of the flying clock relative to the inertial clocks compared to the rate of the ground clock relative to the inertial clocks is a direct comparison!

One clock (the ground clock) is ticking over at a slower rate than the inertial clocks and another clock (the flying clock) is ticking over at a slower rate than the ground clock. If that data is not determined as a result of a direct comparison between the rate of operation of the flying clock compared with the rate of operation of the ground clocks I don't see how else this determination is arrived at other than by direct comparison between their respective rates of operation.

According to the Hafele-Keating experiment - if I am looking at a clock attached to an aircraft that is moving past me from West to East it will by direct comparison be ticking over at a slower rate than my own clock (allowing, of course - as did Will - for any Doppler and gravitational time variation effect).

If I am located in 'empty' space standing alongside a stationary clock (Einstein's section 4 clock B) and another clock (Einstein's clock A) is moving in a closed curve around me I will see it continuously ticking over at a slower rate than my own clock by direct comparison.

The point is that it's the lattice clocks against which the direct comparison is being made, with the indirect comparisons between the flying and surface clocks working out so that the eastward flying clocks go slow, while the westward flying clocks go fast. So the lattice clocks or "reference frame" is very important.

I read Will's book in about 1992 (and specifically it's reference to the HKX many times since then) and am fully aware of the relevance of his reference to "...a set of clocks that are in an inertial frame."

My argument is in relation to the irrelevance of the point of view of a person traveling past the planet whose 'opinion' or 'determination' or 'calculation' or 'prediction' has no bearing or affect whatsoever on what the clocks are actually doing.

From the point of view of all observers in the ground clocks' (quasi-inertial) reference frame the Eastward flying clock is ticking over at a slower rate than their own clock.

Unlike some people - if I am looking at an aircraft that is flying overhead I am of the opinion that that I am stationary and that it is moving i.e. that it is not the atmosphere that has been made to move relative to it's wings - an opinion that, as far as I am concerned, is asinine.

 

[cos]

]When people respond with (as far as I am concerned) totally irrelevant comments such as 'not according to other reference frames' I am forced to respond to such arguments pointing out that the determinations arrived at by numerous other reference frames have no bearing whatsoever - no affect - on those arrived at by the observer in the reference frame in which the event takes place.

When I explain this to those people and they respond with 'not according to other reference frames' and refuse to respond to my relevant points of view I tend to become a bit upset with their intolerance however I am of the opinion that they are deliberately maintaining this attitude for no other reason than to upset me which I see as being arrogant harassment.

The reason everyone keeps going on about other reference frames is because that's the only way you will ever understand how relativity works.

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

I am only interested in what Einstein wrote in section 4!

If you really only want to ever consider a single reference frame then there is no explanation for relativity. You will just have to accept that's the way it is without understanding why.

In all of my postings I fully accept that there are at least two reference frames - that of the observer and that of a moving clock.

 

[Mentz114]

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

I am only interested in what Einstein wrote in section 4!

Why ? You're obsessed. Is this really an intellectual exercise ? Picking over the bones of an old paper and looking for literalisms is a waste of time. What do you hope to achieve ?

 

[JesseM]

Unlike some people - if I am looking at an aircraft that is flying overhead I am of the opinion that that I am stationary and that it is moving i.e. that it is not the atmosphere that has been made to move relative to it's wings - an opinion that, as far as I am concerned, is asinine.

The problem is that you apparently refuse to accept that it's meaningless to talk about whether something is "moving" (or the 'rate' a clock is ticking) except in the context of a particular reference frame (coordinate system), in physics there is no non frame-dependent way to talk about "rate of movement", it's an intrinsically frame-dependent concept. And as I said before, physical events don't occur "in" one frame or another, so there is no one frame that defines the "real truth" about a particular set of events.

By the way, suppose someone fires a bullet inside the plane, with the right speed and direction so that the bullet is at rest relative to you on the surface of the Earth--would you say it was more "asinine" to describe the air inside the plane moving relative to the bullet, or the bullet inside the plane moving relative to the air inside the plane?

 

[Al68]

Al68 wrote:- "Sorry if I haven't addressed every single statement in your posts. I only addressed the ones I considered most relevant due to time considerations."

This is not a continuation of that discussion but is a general note to the several people that have made similar comments.

I note that it is always the more salient points and questions in my postings that are ignored due to the fact that a response to same would mean a commitment by the respondent which is why I specifically raised those matters.

I can appreciate that. I didn't realize that the points I didn't respond to were particularly important.

My responses tend to be lengthy due to the fact that the messages to which they apply are themselves of extreme length or else I am forced to break things down into extended simple explanations and/or provide analogies.

When people respond with (as far as I am concerned) totally irrelevant comments such as 'not according to other reference frames' I am forced to respond to such arguments pointing out that the determinations arrived at by numerous other reference frames have no bearing whatsoever - no affect - on those arrived at by the observer in the reference frame in which the event takes place.

When I explain this to those people and they respond with 'not according to other reference frames' and refuse to respond to my relevant points of view I tend to become a bit upset with their intolerance however I am of the opinion that they are deliberately maintaining this attitude for no other reason than to upset me which I see as being arrogant harassment.

My habit of being specific about reference frames is an effort to be accurate, not intolerant. Especially when speaking of something (such as a clock's rate "slowing down") that is particularly dependent on reference frame, since a statement that is true in a particular reference frame is simply not true in general.

 

[atyy]

I read Will's book in about 1992 (and specifically it's reference to the HKX many times since then) and am fully aware of the relevance of his reference to "...a set of clocks that are in an inertial frame."

My argument is in relation to the irrelevance of the point of view of a person traveling past the planet whose 'opinion' or 'determination' or 'calculation' or 'prediction' has no bearing or affect whatsoever on what the clocks are actually doing.

From the point of view of all observers in the ground clocks' (quasi-inertial) reference frame the Eastward flying clock is ticking over at a slower rate than their own clock.

Unlike some people - if I am looking at an aircraft that is flying overhead I am of the opinion that that I am stationary and that it is moving i.e. that it is not the atmosphere that has been made to move relative to it's wings - an opinion that, as far as I am concerned, is asinine.

OK, I won't press the point on direct versus indirect comparisons, since the only point of that distinction was that the notional lattice of clocks or reference frame is necessary for the sorts of rate comparisons being discussed - a point on which we seem to agree. In a particular situation in which a specific physical clock and a specific lattice clock have identical worldlines, it is conventional and convenient jargon to say that the reference frame belongs to that specific physical clock (and observer). However, the lattice fills all of "space", and is present wherever any physical clocks are, so in another non-jargony sense, the lattice does not belong to only one physical clock, but belongs to any physical clock (and observer), whether or not its/her wordline coincides with any lattice clock. In the Hafele-Keating experiment as presented by Will, there is no lattice clock whose worldline coincides with the wordline of a physical clock (or observer), so by conventional jargon, the reference frame used does not belong to any physical clock (or observer). However, in the non-jargony sense, the lattice used belongs to all observers, and any observer can use any lattice. Since any observer can use any lattice, and there are an infinite number of lattices she can use, she should always state which lattice she is using (perhaps by using the conventional jargon for naming lattices), if she wishes others to understand what she is saying.

Edit: Will, for example, specifies the lattice he uses as "at rest with respect to the center of the earth".

 

[phyti]

The physical explanation is that time itself passes at different rates for different observers/clocks. a clock that is not broken will reflect this. The number of "ticks" shown on each clock will be proportional to the time elapsed for each clock. The details of how a particular clock keeps good time is a side issue, since we are assuming that all clocks used in SR have the same tick rate relative to the proper time elapsed.Why would I add that when the clock's rate was always frame dependent. If the tick rate is different for different observers, it's because the observers are at different relative velocities, not because the clock itself changes in any way.

In other words, a clock runs at the constant rate of T*sqr(1-v^2/c^2) where v is the relative velocity between the clock and an inertial reference frame, and T is time in that reference frame. Only the relative rate between a clock and observer changes, because the relative velocity of the observer changes, not because the clock changes.

I'll try again. The two clocks are synchonous initially.
After the trip, the two clocks are together in the same frame, with one clock showing fewer ticks than the other. There is no relative motion. Where did the missing ticks go, or what caused the difference in readings?

 

[Al68]

If two synchronized clocks become out of synch when compared in the same frame, there is a physical explanation why, worn parts, weak battery, etc.
In the example with one clock moving away and returning, if the clocks literally ticked at the same rate for the duration of the trip, there would be no difference, The number of ticks would be invariant, yet we know the rate depends on the speed of the clock. The fact that one clock shows less ticks than the other (in the second case) when compared in a common frame is equivalent to the first case, and requires a physical explanation, not an abstract model representation.

If you're asking what physical mechanism "causes" the differential clock readings, I would say it's the same physical mechanism that causes a clock to keep proper time in its own frame.

In the case of a simple light clock (which measures how long it takes light to travel between two points in the clock's frame), it's easy to see that the physical mechanism that causes time dilation is the exact same mechanism that causes the velocity of light to be constant relative to every observer (instead of relative to its source).

And I mean "No clock changes its tick rate" in the same way I would say that a train whistle doesn't "change its pitch" when it passes me. The statement that "the whistle doesn't change its pitch" is entirely consistent with the statement "the relative pitch of the whistle changes" when the train passes, if we realize why the pitch changes.

Similarly, the statement "the clock didn't change its tick rate" is consistent with the statement "the clock's relative tick rate changed", the change just isn't caused by the clock.

 

[JesseM]

I'll try again. The two clocks are synchonous initially.
After the trip, the two clocks are together in the same frame, with one clock showing fewer ticks than the other. There is no relative motion. Where did the missing ticks go, or what caused the difference in readings?

Say two cars start at the same position A on flat 2D surface, and their odometers show the same reading. Then they drive along different paths along the surface to a different position B, where they meet and compare odometer readings. One car took a straight-line path between A and B, the other took a non-straight path, so since we know a straight line is the shortest distance between any two points, naturally the odometer reading of the car that took the straight path won't have increased as much as the odometer reading of the car that took a non-straight path. Where did the missing odometer increments go, or what caused the difference in readings?

 

[DrGreg]

I'll try again. The two clocks are synchonous initially.
After the trip, the two clocks are together in the same frame, with one clock showing fewer ticks than the other. There is no relative motion. Where did the missing ticks go, or what caused the difference in readings?

The ends of two tape measures are together. For the first 6 inches, the tapes are side-by-side and measure the same distance. Then one continues in a taut straight line, from its 6-inch mark to its 18-inch mark. The other is slack and takes a different route. Further along, both tape measures come together and run side-by-side one more. But where the taut tape measures 18 to 24 inches along this section, the slack tape measures 20 to 26 inches. Where did the missing two inches go, or what caused the difference in readings?

(If this sounds like JesseM's post, that's because we both posted at almost the same time as each other.)

 

[neopolitan]

I note that it is always the more salient points and questions in my postings that are ignored due to the fact that a response to same would mean a commitment by the respondent which is why I specifically raised those matters.

My responses tend to be lengthy due to the fact that the messages to which they apply are themselves of extreme length or else I am forced to break things down into extended simple explanations and/or provide analogies.

Salience is a relative thing. What is salient to one observer may not be salient to another observer. The question we should be asking is: are your salient points really salient, or are the points that everyone else seems to take as salient the true salient points?

As for trying to extract salient points from lengthy dissertations, you will run into problems with the relativity of salience. By that I mean that one comment (c) you make might have 0.6s (60% salience factor) relative to an argument (Э) relative to observer A and 0.8s (80% salience factor) relative to another argument (Б) relative to observer B but the salience of c to argument Э relative to observer B may be 0.2s or even 0s (the argument is at rest relative to observer B).

Then you have to take into account the paragraphical separation (p) of comments and arguments and the relativistic effect on salience. And don't get me started on the relative length of words (L_w) and sentences (L_s) and their use in phrasing both comments (^cП_ws) and arguments (^aП_ws).

But I stress, we should be investigating which points are really, truly, physically salient. We can't do that ourselves from first principles, of course, we should consult the Holy Book, "On the Salience of the Non-Moving Arguments", Section 4.

cheers,

neopolitan

 

[Mentz114]

neopolitan:

But I stress, we should be investigating which points are really, truly, physically salient. We can't do that ourselves from first principles, of course, we should consult the Holy Book, "On the Salience of the Non-Moving Arguments", Section 4.

Ha-ha. Well put. As I enquired earlier - what's this thread about ? Is Cos trying to show that Einstein was initially as confused as everyone else about the implications of SR ? So what if he was ?

 

[cos]

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

I am only interested in what Einstein wrote in section 4!

Why ? You're obsessed. Is this really an intellectual exercise ? Picking over the bones of an old paper and looking for literalisms is a waste of time. What do you hope to achieve ?

My intention is in relation to Einstein's comment in Relativity - that special theory is invalidated by gravity - showing that the results of particle acceleration experiments that are said to ratify special theory's concept of a 'light barrier' are similarly invalidated.

I attribute your deprecatory attitude to ignorance.

 

[Mentz114]

My intention is in relation to Einstein's comment in Relativity - that special theory is invalidated by gravity - showing that the results of particle acceleration experiments that are said to ratify special theory's concept of a 'light barrier' are similarly invalidated.

I don't remember you saying this before. Why not start a thread with this topic instead of banging on about section 4.

I attribute your deprecatory attitude to ignorance.

Yes. Ignorance of what you're trying to say caused by your failure to communicate clearly.

 

[Dale]

Salience is a relative thing. ... we should consult the Holy Book, "On the Salience of the Non-Moving Arguments", Section 4

best post of the thread!

 

[JesseM]

My intention is in relation to Einstein's comment in Relativity - that special theory is invalidated by gravity

Of course Einstein also said that when it comes to the equations of the general theory, these equations hold good in all coordinate systems, not just the inertial systems used in special relativity--this would include the non-inertial coordinate systems that you have said before you don't like, such as a coordinate system where the Earth's clock suddenly starts ticking much faster relative to coordinate time or where objects can undergo huge coordinate accelerations without feeling any G-forces. Read chapter 28 of Relativity where Einstein writes the following (note that the translator here uses the word 'reference body' for what people on this thread have been calling a reference frame or coordinate system):

We can state this general principle of relativity in still another form, which renders it yet more clearly intelligible than it is when in the form of the natural extension of the special principle of relativity. According to the special theory of relativity, the equations which express the general laws of nature pass over into equations of the same form when, by making use of the Lorentz transformation, we replace the space-time variables x, y, z, t, of a (Galileian) reference-body K by the space-time variables x', y', z', t', of a new reference-body K'. According to the general theory of relativity, on the other hand, by application of arbitrary substitutions of the Gauss variables x1, x2, x3, x4, the equations must pass over into equations of the same form; for every transformation (not only the Lorentz transformation) corresponds to the transition of one Gauss co-ordinate system into another.

If we desire to adhere to our “old-time” three-dimensional view of things, then we can characterise the development which is being undergone by the fundamental idea of the general theory of relativity as follows: The special theory of relativity has reference to Galileian domains, i.e. to those in which no gravitational field exists. In this connection a Galileian reference-body serves as body of reference, i.e. a rigid body the state of motion of which is so chosen that the Galileian law of the uniform rectilinear motion of “isolated” material points holds relatively to it.

Certain considerations suggest that we should refer the same Galileian domains to non-Galileian reference-bodies also. A gravitational field of a special kind is then present with respect to these bodies (cf. Sections XX and XXIII).

In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity. The motion of clocks is also influenced by gravitational fields, and in such a way that a physical definition of time which is made directly with the aid of clocks has by no means the same degree of plausibility as in the special theory of relativity.

For this reason non-rigid reference-bodies are used which are as a whole not only moving in any way whatsoever, but which also suffer alterations in form ad lib. during their motion. Clocks, for which the law of motion is any kind, however irregular, serve for the definition of time. We have to imagine each of these clocks fixed at a point on the non-rigid reference-body. These clocks satisfy only the one condition, that the “readings” which are observed simultaneously on adjacent clocks (in space) differ from each other by an indefinitely small amount. This non-rigid reference-body, which might appropriately be termed a “reference-mollusk,” is in the main equivalent to a Gaussian four-dimensional co-ordinate system chosen arbitrarily. That which gives the “mollusk” a certain comprehensibleness as compared with the Gauss co-ordinate system is the (really unqualified) formal retention of the separate existence of the space co-ordinate. Every point on the mollusk is treated as a space-point, and every material point which is at rest relatively to it as at rest, so long as the mollusk is considered as reference-body. The general principle of relativity requires that all these mollusks can be used as reference-bodies with equal right and equal success in the formulation of the general laws of nature; the laws themselves must be quite independent of the choice of mollusk.

So, in the end you can see he refers to any arbitrary (Gaussian) non-inertial coordinate system as a "reference-mollusk", and goes on to say "all these mollusks can be used as reference-bodies with equal right and equal success in the formulation of the general laws of nature", meaning that every arbitrary non-inertial coordinate system is considered equally valid in general relativity, in much the same way that every inertial coordinate system is considered equally valid with respect to the laws of special relativity.

 

[Dale]

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

This certainly explains a lot. Then your posts do not belong on this forum.

 

[jtbell]

What gives you the impression that I want to "...understand how relativity works."? I do NOT!

OK, that's it. It's clear that you are wasting our time, and we are wasting yours. This thread is done.