Understanding Time Dilation in Einstein's Special Theory of Relativity

[Al68]

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

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

 

[phyti]

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

From a previous quote to cos:

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

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

 

[JesseM]

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

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

 

[cos]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

And in the Earth twin's mind.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

and you responded -

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

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

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

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

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

 

[JesseM]

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

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

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

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

 

[phyti]

cos; re: post 244

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

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

 

[Al68]

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

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

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

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

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

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

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

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

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

Nothing happens to either clock. See above.

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

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

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

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

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

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

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

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

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

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

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

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

 

[Al68]

From a previous quote to cos:

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

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

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

 

[callena]

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

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

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

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

 

[JesseM]

cos; re: post 244

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

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

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

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

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

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

 

[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.