Understanding Time Dilation in Einstein's Special Theory of Relativity

[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?

 

[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.