Understanding Time Dilation in Einstein's Special Theory of Relativity

[jtbell]

So, does this thread basically boil down to a disagreement over the meanings of words like "physical" and "reality"? If so, then this properly belongs in the philosophy forum, IMO.

 

[neopolitan]

So, does this thread basically boil down to a disagreement over the meanings of words like "physical" and "reality"? If so, then this properly belongs in the philosophy forum, IMO.

I think cos is moving towards something like this:

"if the slowing down of clocks is supposed to real or physical, then something is amiss, and if results (like the twin paradox) suggest that only one clock ran slow, then the mathematics should be suspected, rather than the reality or physical results"

cos,

I am not saying categorically that that is your contention, it is merely what I think you are saying.

However, I should point out that you have to take into account everything in a situation like the twin's paradox. Specifically, you need to consider simultaneity (I say this even though this is not my favoured approach). Both twins will calculate that the other twin's clock ran slow during the inertial phases. What the twins will not agree on is how long those inertial phases lasted.

So the results will be (time on a slow clock running for a longer time) and (time on a slow clock running for a shorter time). The change in direction was an event that was colocal with the acelerated twin, but not colocal with the twin who was inertial throughout, which means that - taking into account simultaneity - the stationary twin will calculate that the traveling twin turned around later than traveling twin calculated. This is totally in agreement with the fact that the traveling twin's clock ran slow compared to the stationary twin.

So if you like, both clocks really ran slow, the traveling twin really turned around later than was said on his clock and at the end of the journey one clock will really show more time elapsed than shown on the other - and both clocks are showing the real time elapsed for that clock.

cheers,

neopolitan

 

[cos]

cos,

It appears that you have had some misfortune, but it is not relevant to the discussion.

It is relevant to the discussion inthat, in the discussion you made what I considered to be snide and belittling comments which were themselves not relevant to the discussion.

"I am of the opinion that Einstein obviously did not reject maths but that he insisted that it does not refer to reality."

This is central.

You are taking one quote and misrepresenting it terribly.

You should try to take Einstein's comments in context. In 1917 he found that his equations showed that the universe is expanding. He then spent quite a few years trying to fit a cosmological constant in order to make the universe static. In other words, the mathematics were telling him that the universe is expanding and "reality" was telling him it isn't.

Edwin Hubble came to the rescue with observations which showed that the universe is in fact expanding and Einstein's maths were correct, not his perception of what must be real.

It is my understanding that Hubble argued that the greater redshift of the more distant galaxies was not an indication that the universe is expanding thus he would not have accepted the veracity of Einstein's calculations that it is!

So, I put it to you again, try the maths. The maths worked for Einstein...

Einstein's maths indicated the amount by which, in his opinion, clock A lags behind B and, as Einstein pointed out, because A lags behind B it must have 'gone more slowly' (i.e. ticked over at a slower rate) than B whilst A was moving.

According to Einstein's section 4 maths, clock A is ticking over at a slower rate than clock B but according to the maths employed by the observer accompanying clock A it is B that is ticking over at a slower rate than his clock.

Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!

HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math?

You are, I believe, confusing Einstein's depiction of a non-inertial observer with his previously depicted inertial observer.

You would probably be better off if you search for one of his papers or essays written after 1929.

I assume that you have read his papers and essays written after 1929 and to save time not only for myself but also for others that may be following this thread perhaps you would be so kind as to nominate just one of those papers showing that he recanted or amended his section 4 STR comments.

Albert Einstein's 1905 article 'On the Electrodynamics of Moving Bodies' is said to be the foundation of modern-day physics and in that article he indicates that inertial observers that are moving relative to each other will both determine that the other person's clock will be running slower than their own however in section 4 of that same article he shows that an observer who has accelerated will not find that the other clock is ticking over at a slower rate than their own clock but at a faster rate!

 

[Dale]

According to Einstein's section 4 maths, clock A is ticking over at a slower rate than clock B but according to the maths employed by the observer accompanying clock A it is B that is ticking over at a slower rate than his clock.

Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!

HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math?

His math is fine and does not give an erroneous answer, you just made a mistake. Clock A is non-inertial, so the acompanying observer correctly determines that the other clock "physically" runs faster overall. In fact, all reference frames (including both inertial and non-inertial frames) will agree that clock B runs faster on average.

 

[matheinste]

Hello cos.

Probably of no consequence but in an early traslation of about 1920 part of your quoted text reads:-

-----From this, we conclude that a clock placed at the equator must be slower by a very small amount than a similarly constructed clock which is placed at the pole, all other conditions being identical.-----

The words "be slower" are used rather than "gone more slowly". The words "balance clock" do not appear. This may of course be due to the transators M.N. Saha and S.N. Bose.

I am not drawing any conclusions from this, it is just a point of interest.

Mateinste

 

[cos]

His math is fine and does not give an erroneous answer, you just made a mistake. Clock A is non-inertial, so the acompanying observer correctly determines that the other clock "physically" runs faster overall. In fact, all reference frames (including both inertial and non-inertial frames) will agree that clock B runs faster on average.

On the assumption that "..the accompanying observer correctly determines that the other clock "physically" runs faster overall." and on the assumption that he is an enquiring scientist is it not possible that he might ask himself what force has made clock B PHYSICALLY run faster than it did before he started moving?

He is an astronaut returning to the planet following turn-around; he 'sees' Earth clocks ticking over at a faster rate than they did before he started accelerating hence he 'sees' shorter Earth seconds than he did before he started moving thus he must also 'see' Earth minutes, hours and days to also 'be' ticking over at a faster rate than they were before he started moving ergo he 'sees' the Earth spinning on its axis and orbiting the sun at a considerably faster rate than it did before he started moving.

Is he not likely to ask himself what physical force has made the planet spin faster on its axis and orbit the sun at a much faster rate than it did before he started his return journey?

Although he 'determines' that the Earth clock 'is' running faster than it did before he started moving and that the planet 'is' spinning faster on its axis than they did before he started accelerating is he not likely to realize that this is nothing more than a (mathematically generated) illusion created by his non-inertial motion?

In section 4 STR Einstein pointed out, in effect, that clock A, having moved to clock B's location will lag behind clock B due to the fact that clock A 'goes more slowly' (i.e. ticks over at a slower rate) than clock B not that clock B would leap ahead of clock A thus that clock B would incur time contraction which I believe was for Einstein an anathema.

You wrote "... all reference frames (including both inertial and non-inertial frames) will agree that clock B runs faster on average." and i agree with that comment; clock B does 'run faster' than A due to the fact that, as Einstein pointed out, clock A runs slower than B however for them to be of the opinion that clock B runs faster than it did before A started moving is erroneous - according to Einstein's section 4 STR.

According to Einstein - clock A ticks over at a slower rate than it did before it started moving NOT that B starts ticking over at a faster rate. Clock A accelerates and it is, according to Einstein, this factor that physically causes it to tick over at the slower rate. There is no force, no action on it's behalf which causes clock B to physically tick over at a faster rate than it did before A started moving.

 

[cos]

So, does this thread basically boil down to a disagreement over the meanings of words like "physical" and "reality"? If so, then this properly belongs in the philosophy forum, IMO.

It is not simply a disagreement over the words "physical" and "reality" but a disagreement over those words as they apply to Einsteins section 4 STR depictions.

 

[cos]

Hello cos.

Probably of no consequence but in an early traslation of about 1920 part of your quoted text reads:-

-----From this, we conclude that a clock placed at the equator must be slower by a very small amount than a similarly constructed clock which is placed at the pole, all other conditions being identical.-----

The words "be slower" are used rather than "gone more slowly". The words "balance clock" do not appear. This may of course be due to the transators M.N. Saha and S.N. Bose.

I am not drawing any conclusions from this, it is just a point of interest.

Mateinste

My reference was specifically in relation to Einstein's 1905 paper not any other translation.

In section 4 he wrote -

"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."

 

[neopolitan]

cos,

I assume that you are referring to the section titled "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks" since that section ends with:

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.

Shortly before, in that same section:

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by 1/2 tv²/c² (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

Now it should be remembered that this is Einstein. If I wrote something similar on this forum, I would probably be appropriatedly chastised for an inaccuracy - perhaps not for being incorrect, but for not clearly stating something.

The time t is the time occupied in the journey from A to B, in the frame of the clock which remains stationary. According to the stationary clock, the clock which was moved traveled a distance of x = v.t.

I'd say that the time t' on the moving clock at the end of that journey would be:

$$\gamma ( t - x.v / c^{2} ) = \gamma ( t - t.v^{2} / c^{2} ) = \gamma t (1 - v^{2} / c^{2} ) = t / \gamma$$

The difference is therefore $$\Delta = t - t' = t ( 1 - 1 / \gamma) \approx 1/2t . v^{2} / c^{2}$$.

When that moving clock stops, there are a number of ticks from the "stationary" clock still traveling to catch up, x/(c-v) = vt/(c-v) worth. Those ticks in transit will, when added to the ticks already received, show that the more time has elapsed has elapsed on the stationary clock, even though that time elapsed at a slower rate.

So Einstein's answer, while possibly not immediately intuitive, is not erroneous.

cheers,

neopolitan

 

[neopolitan]

My reference was specifically in relation to Einstein's 1905 paper not any other translation.

In section 4 he wrote -

"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."

I have to admit that I laughed out aloud at this.

Einstein's paper was written in German. The original text can be seen http://de.wikibooks.org/wiki/A._Einstein:_Kommentare_und_Erl%C3%A4uterungen:_Zur_Elektrodynamik_bewegter_K%C3%B6rper:_Kinematischer_Teil:_%C2%A74" .

The 1920 translation is of the same paper. A translation today (using more modern language) would be a translation of the same paper.

cheers,

neopolitan

 

[Dale]

On the assumption that "..the accompanying observer correctly determines that the other clock "physically" runs faster overall." and on the assumption that he is an enquiring scientist is it not possible that he might ask himself what force has made clock B PHYSICALLY run faster than it did before he started moving?

He is an astronaut returning to the planet following turn-around; he 'sees' Earth clocks ticking over at a faster rate than they did before he started accelerating hence he 'sees' shorter Earth seconds than he did before he started moving thus he must also 'see' Earth minutes, hours and days to also 'be' ticking over at a faster rate than they were before he started moving ergo he 'sees' the Earth spinning on its axis and orbiting the sun at a considerably faster rate than it did before he started moving.

Is he not likely to ask himself what physical force has made the planet spin faster on its axis and orbit the sun at a much faster rate than it did before he started his return journey?

Certainly. And the answer would be the fictitious forces present in his non-inertial frame.

I don't mind how you use the word "physical", but you need to be self-consistent. You cannot claim that frame-variant quantities, like the rate of a clock, are "physical" and then exclude the frame-variant fictitious forces from being "physical" also. In a non-inertial reference frame fictitious forces can do work, can have potential energy, can cause mechanical stress and strain, and have many other measurable effects.

Although he 'determines' that the Earth clock 'is' running faster than it did before he started moving and that the planet 'is' spinning faster on its axis than they did before he started accelerating is he not likely to realize that this is nothing more than a (mathematically generated) illusion created by his non-inertial motion?

Yes, that is why they are called fictitious forces. That is also why he is not likely to try to do the analysis in his non-inertial rest frame, but is more likely to do the analysis in some inertial frame.

You wrote "... all reference frames (including both inertial and non-inertial frames) will agree that clock B runs faster on average." and i agree with that comment; clock B does 'run faster' than A due to the fact that, as Einstein pointed out, clock A runs slower than B however for them to be of the opinion that clock B runs faster than it did before A started moving is erroneous - according to Einstein's section 4 STR.

According to Einstein - clock A ticks over at a slower rate than it did before it started moving NOT that B starts ticking over at a faster rate. Clock A accelerates and it is, according to Einstein, this factor that physically causes it to tick over at the slower rate. There is no force, no action on it's behalf which causes clock B to physically tick over at a faster rate than it did before A started moving.

Your explanation is correct only in the inertial reference frame where B is at rest. In other reference frames there will be other explanations. But all reference frames will agree on the conclusion.

 

[cos]

cos,

I assume that you are referring to the section titled "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks" since that section ends with:

"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."

On the basis that this precisely the comment to which I refer I fail to see how you could possibly be of the opinion that I may not have been '...referring to the section titled "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks."'

It would be very much appreciated if we could adhere to relevant matters.

Shortly before, in that same section:

"From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by 1/2 tv2/c2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."

Now it should be remembered that this is Einstein. If I wrote something similar on this forum, I would probably be appropriatedly chastised for an inaccuracy - perhaps not for being incorrect, but for not clearly stating something.

You may not have noticed but Einstein's comments have been criticized in this forum! Einstein has, somewhat belatedly, been chastised!

The time t is the time occupied in the journey from A to B, in the frame of the clock which remains stationary. According to the stationary clock, the clock which was moved traveled a distance of x = v.t.

And according to the traveler the distance he travels is less than the distance from A to B as measured by the stationary observer.

When that moving clock stops, there are a number of ticks from the "stationary" clock still traveling to catch up, x/(c-v) = vt/(c-v) worth. Those ticks in transit will, when added to the ticks already received, show that the more time has elapsed has elapsed on the stationary clock, even though that time elapsed at a slower rate.

What on Earth does "...there are a number of ticks from the 'stationary' clock still traveling to catch up." mean?

When the moving clock stops, A and B could press switches whereupon both clocks stop ticking so any 'ticks in transit' would be out of luck. Their time will have expired and they can no affect on the times registered by clocks A and B.

So Einstein's answer, while possibly not immediately intuitive, is not erroneous.

I made no suggestion whatsoever that Einstein's answer is erroneous!

 

[cos]

Certainly. And the answer would be the fictitious forces present in his non-inertial frame.

My references are to reality and I am of the opinion that fictitious forces do not come under that category.

I don't mind how you use the word "physical", but you need to be self-consistent. You cannot claim that frame-variant quantities, like the rate of a clock, are "physical" and then exclude the frame-variant fictitious forces from being "physical" also. In a non-inertial reference frame fictitious forces can do work, can have potential energy, can cause mechanical stress and strain, and have many other measurable effects.

Yes, that is why they are called fictitious forces. That is also why he is not likely to try to do the analysis in his non-inertial rest frame, but is more likely to do the analysis in some inertial frame.

So if something cannot be logically identified or physically determined it comes under the heading of a 'fictitious force'? It was a fictitious force that many years ago exchanged my tooth for a dime.

The concept of a 'fictitious force' is in my opinion a desperate grasping at straws analogous to the 'parallel universes' escape-clause, suitably impossible-to-disprove, concept.

People who believe in God are criticized by others for their faith in a 'fictitious force' yet apparently some people are apparently of the opinion that a non-material 'force' can result in an equal and opposite reaction provided the results supply the solution they seek.

Your explanation is correct only in the inertial reference frame where B is at rest. In other reference frames there will be other explanations. But all reference frames will agree on the conclusion.

Einstein indicated that clock A will lag behind B due to the fact that, whilst it is moving, clock A 'goes more slowly' (ticks over at a slower rate) than clock B.

It has been pointed out in relation to my previous thread in this forum that there could be third observer, C, relative to whom A and B were initially moving at v. When A accelerates he, from C's point of view, decelerates and comes to a stop in C's reference frame (thus ticks over at the same rate as C's clock) whereas B keeps moving relative to C at v thus from C's point of view clock B is ticking over at a slower rate than his own clock ergo also at a slower rate than clock A so when A 'accelerates' back to B's location (in B's reference frame, decelerates and comes to a stop alongside B) it is, in C's opinion, clock B that will lag behind A.

C moves to B's location and comes to a stop alongside A and B and finds, much to his consternation, that B does not lag behind A as indicated by his 'calculations' or 'determinations' or 'predictions' but that A lags behind B!

 

[neopolitan]

I made no suggestion whatsoever that Einstein's answer is erroneous!

Einstein's maths indicated the amount by which, in his opinion, clock A lags behind B and, as Einstein pointed out, because A lags behind B it must have 'gone more slowly' (i.e. ticked over at a slower rate) than B whilst A was moving.

According to Einstein's section 4 maths, clock A is ticking over at a slower rate than clock B but according to the maths employed by the observer accompanying clock A it is B that is ticking over at a slower rate than his clock.

Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!

HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math?

?

What on Earth does "...there are a number of ticks from the 'stationary' clock still traveling to catch up." mean?

When the clocks are not colocated it takes time for the information from one clock to reach the other. The information travels at the speed of light. If the moving clock "looked" back at the stationary clock (as per Einstein's scenario), just before stopping, it would see only the time on the stationary clock that happened, in the moving clock's frame, x'/c ago (where x' is the separation that the moving clock thinks that it has from the stationary clock based on the traveling time). There will be more information still in transit.

Given that we can't agree as to whether you are saying Einstein's maths was erroneous or not, or that what he said matches with his maths, I don't feel this is going anywhere.

If you have a go at the maths, you will see that it matches the "reality" of what Einstein said (at least wrt to the 1905 paper). Until you do that, I really think I have to agree with Jtbell, at least in part, this is not a physics discussion. I just don't think it qualifies as philosophy either.

cheers,

neopolitan

 

[Ich]

C moves to B's location and comes to a stop alongside A and B and finds, much to his consternation, that B does not lag behind A as indicated by his 'calculations' or 'determinations' or 'predictions'

Then why don't you help C with his predictions? Let the movement be sinusoidal, and let the "clock rate" be adjusted by -1/2 v². Sometimes a decent calculation saves many lines of philosophical debate.

 

[Al68]

"...on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other ."

In other words, according to Einstein, something physically happens to the moving clock. It is no longer synchronized with the inertial clock.

No, that's not why they're no longer in synch.

Having, during his trip, 'determined' that B is, as you say, running slow compared to his clock that is at rest in his frame he arrives at B's location to find that B does not lag behind (having 'run slower' than) his clock but that his clock lags behind B.

No. The ship's twin knows 2 things during the outbound inertial part of the trip:
1. Earth's clock runs slower than the ship's clock in the ship's frame.
2. The ship's clock runs slower than Earth's clock in Earth's frame.

When he stops at the turnaround, the ship's twin doesn't "find" that his clock ran slower than Earth's clock, he knew all along that the ship's clock ran slower than Earth's clock in Earth's frame.

The idea (during the astronaut's period of acceleration following turn around) that the stationary clock incurs time contraction (i.e. 'is' ticking over at a faster rate than it was before he accelerated) was, for Einstein, an anathema and it it is his depictions to which I refer not interpretations arrived at by anybody else.

The relative ticking rate of clocks is frame-dependent, not absolute. Nothing changed with Earth's clock during the turnaround, the relative speed of the ship changed. Earth's clock didn't change its ticking rate, we changed which frame we're referring to, and the ticking rate of a clock is frame dependent.

It seems that you're ignoring Einstein's most important contribution to modern physics, that the rate that any clock runs is dependent on the relative speed of the observer. That means that if someone changes his speed relative to a given clock, the rate of that clock will be different. Not because the clock changed, but because the reference frame of the observer changed.

 

[Dale]

My references are to reality and I am of the opinion that fictitious forces do not come under that category.

That is fine by me, but then neither should coordinate time (and therefore the rate of a clock wrt coordinate time). Again, I don't care how you use the words "physical" or "real" but you need to be consistent.

The concept of a 'fictitious force' is in my opinion a desperate grasping at straws analogous to the 'parallel universes' escape-clause, suitably impossible-to-disprove, concept.

This is also fine, but if you do not like fictitious forces then you cannot do any analysis in any non-inertial frame. You must stick exclusively to inertial frames. As I mentioned previously, all inertial frames agree on the results also.

It has been pointed out in relation to my previous thread in this forum that there could be third observer, C, relative to whom A and B were initially moving at v. When A accelerates he, from C's point of view, decelerates and comes to a stop in C's reference frame (thus ticks over at the same rate as C's clock) whereas B keeps moving relative to C at v thus from C's point of view clock B is ticking over at a slower rate than his own clock ergo also at a slower rate than clock A so when A 'accelerates' back to B's location (in B's reference frame, decelerates and comes to a stop alongside B) it is, in C's opinion, clock B that will lag behind A.

No, you have forgotten that A is moving at 2v/(1+v²/c²) on the second leg of the trip. Since A travels at a faster speed than B, A experiences more time dilation than B. Also, that second leg lasts for a longer coordinate time in C's frame. Because of that, C is of the (correct) opinion that A will lag behind B when they meet and that A was "physically" slower than B on average. Again, all frames agree on this result.

 

[Al68]

Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!

This is not true. Observer A makes no such prediction. Each twin will make the same prediction. That is that when they reunite, A's clock will read less elapsed time than B's clock.

What might be a source of confusion is that the fact that time dilation is symmetrical, but proper elapsed time is not. The reason that the ship's clock readings coincide with the end result of elapsed time is because the ship's clock is local to every relevant event and therefore represents the proper elapsed time for the ship for every event in every frame. That is not true of Earth's clock. Earth's clock is local to the departure and return only, so only those readings represent proper time for the Earth twin in a different frame. For events not local to earth, the Earth clock represents proper time in Earth's frame only. Clocks in relative motion only read proper time locally, not at a distance. So an Earth clock reading in the ship's frame does not represent the proper time in Earth's frame for any event not local to earth, like the ship's turnaround.

If that's what you mean by not being "reality", then just say so and I think everyone would agree.

HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math

He got no erroneous answer. All of his math gave correct answers. And it's not contradictory because he didn't confuse reciprocal time dilation between the twins' clocks with the non-symmetrical elapsed time of the clocks.

 

[Al68]

You would probably be better off if you search for one of his papers or essays written after 1929.

Hi, neopolitan,

I think Einstein's best work was prior to 1929, despite not being perfect.

His 1918 paper on the twins paradox is nothing like the way cos is interpreting it. The only difference between it and standard resolutions is that instead of using an instantaneous turnaround with Earth's clock "jumping" ahead suddenly, he uses a realistic acceleration turnaround with Earth's clock "running fast" in the ship's frame during the turnaround. It's essentially the same as the standard resolutions, at least as far as this topic is concerned.

 

[cos]

I think cos is moving towards something like this:

"if the slowing down of clocks is supposed to real or physical, then something is amiss, and if results (like the twin paradox) suggest that only one clock ran slow, then the mathematics should be suspected, rather than the reality or physical results"

cos,

I am not saying categorically that that is your contention, it is merely what I think you are saying.

However, I should point out that you have to take into account everything in a situation like the twin's paradox. Specifically, you need to consider simultaneity (I say this even though this is not my favoured approach). Both twins will calculate that the other twin's clock ran slow during the inertial phases. What the twins will not agree on is how long those inertial phases lasted.

(I missed this posting; perhaps because it was a response to jtbell.)

I assume that you are here referring to an astronaut's out-and-return journey. You wrote "...during the inertial phases." There is only one inertial phase i.e. when the astronaut comes to a stop at the end of his outward-bound trip.

So the results will be (time on a slow clock running for a longer time) and (time on a slow clock running for a shorter time). The change in direction was an event that was colocal with the acelerated twin, but not colocal with the twin who was inertial throughout, which means that - taking into account simultaneity - the stationary twin will calculate that the traveling twin turned around later than traveling twin calculated. This is totally in agreement with the fact that the traveling twin's clock ran slow compared to the stationary twin.

"This is totally in agreement with the fact that the traveling twin's clock ran slow compared to the stationary twin." that's what I'm saying!

So if you like, both clocks really ran slow, the traveling twin really turned around later than was said on his clock and at the end of the journey one clock will really show more time elapsed than shown on the other - and both clocks are showing the real time elapsed for that clock.

"...both clocks really ran slow..." In his 1918 article Einstein attempted to overcome the paradox that 'both clocks run slow' suggesting that it is only the clock that experiences a force of acceleration that incurs time dilation not the stationary clock ergo, according to that article which, in my opinion, directly complies with his 1905 depiction of A moving in a polygonal path to B's location, both clocks do NOT 'run slow'.

I reiterate that it is Einstein's work to which I specifically refer not to interpretations of same by anyone else!

 

[cos]

You are quite welcome, but you should be aware that I am open-minded on the subject of the meaning of the word "physical". I am willing to take either position for the sake of communication. Also, I suspect (again just guessing) that Einstein's opinion changed after Minkowski.

I would really appreciate it if we could limit the discussion to facts rather than suppositions.

However, since your opinion appears to be firm that frame-dependent quantities can be considered "physical", then it should come as no surprise that clock A can "physically" tick over at a slower rate than clock B in one frame whilst clock B can "physically" tick over at a slower rate than clock A in another frame describing the exact same situation. The same thing happens with all other frame-variant "physical" quantities like energy, momentum, speed, etc. (e.g. clock A can "physically" have more speed than clock B in one frame and vice versa in another frame).

The idea "that clock A can "physically" tick over at a slower rate than clock B in one frame whilst clock B can "physically" tick over at a slower rate than clock A in another frame describing the exact same situation.." Is I believe the 'paradox' that Einstein attempted to solve in his 1918 article wherein he presented that it is only the clock that experiences forces of acceleration that ticks over at the slower rate not the clock that has remained inertial thus that, according to that article (which I believe was merely an extension of his section 4 comments), Einstein effectively pointed out that clock B does not tick over at a slower rate than A.

Perhaps you could show me where, in your opinion, Einstein's shows in section 4 STR or his 1918 article that the inertial clock, B, ticks over at a slower rate than A. Prior to section 4 STR he does show that clock A ticks over at a slower rate than clock B in one frame whilst clock B ticks over at a slower rate than clock A in another frame however it is specifically his section 4 depiction to which I refer.

On the basis that, according to your comment, A 'determines' or 'calculates' or 'predicts' that B is ticking over at a slower rate than his own clock he would arrive at B's location anticipating that 'because' it ticked over at a slower rate than his own clock B will lag behind his clock however he finds, in reality, that his clock lags behind B!

 

[Mentz114]

On the basis that, according to your comment, A 'determines' or 'calculates' or 'predicts' that B is ticking over at a slower rate than his own clock he would arrive at B's location anticipating that 'because' it ticked over at a slower rate than his own clock B will lag behind his clock however he finds, in reality, that his clock lags behind B!

You've repeated this a number of times.

So what ? I'm not in the least perturbed. When I look in a mirror left and right are reversed, if I look through a telescope things look nearer. Nothing to lose sleep over.

 

[cos]

Then why don't you help C with his predictions? Let the movement be sinusoidal, and let the "clock rate" be adjusted by -1/2 v². Sometimes a decent calculation saves many lines of philosophical debate.

Why should I 'help C with his predictions'?

Why should I let his movement be in the nature of a curve having the form of a sine wave? Why can't he, as most sensible astronaut's would, travel in a direct route to C's location?

Sometimes a 'decent calculation' can create obfuscation.

 

[matheinste]

Cos

To observers in relative inertial motion each will see the others clock running slow due to the effects time dilation. This is fundamental to Einstein and SR. In the example you give, Enstein's clock moving in a closed path is non inertial and so factors other than time dilation must be taken into account. The non-inertial clock will show less accumulated time on its return. That is fact. Beacuse it shows a reading which lags behind that of the inertial clock you could perhaps say either that it has ticked slower for the same amount of time or that it has ticked at the same rate for a shorter length of time. I am unsure of your interpretation but I suspect the former would be what you describe as a physical change. Perhaps that is what your question boils down to i.e ticking slower for the same time as the inertial clock or ticking at the same rate as the inertial clock for less time than the inertial clock.

There is no scenario in which two clocks can separate and reunite with both having remained in inertial motion throughout. So the scenario Einstein descibes is not a denial of reciprocal time dilation.

Matheinste.

 

[JesseM]

On the basis that, according to your comment, A 'determines' or 'calculates' or 'predicts' that B is ticking over at a slower rate than his own clock he would arrive at B's location anticipating that 'because' it ticked over at a slower rate than his own clock B will lag behind his clock however he finds, in reality, that his clock lags behind B!

As long as you stick to inertial frames, all frames will always agree about what two clocks read when they meet each other (and therefore whose time is behind), in spite of the fact that they may disagree about which clock was ticking slower at a given moment. Are you suggesting otherwise?

 

[neopolitan]

There is only one inertial phase i.e. when the astronaut comes to a stop at the end of his outward-bound trip.

I was perhaps unclear about what I meant about "inertial phase", there are four or five inertial phases and I was only referring to two, the inertial phases in which the twins are not at rest with respect to each other. There are two or three more inertial phases: at rest together before, at rest with respect to each other in the middle and at rest together after. The other phases are when one twin accelerates (first in one direction and then in the other direction ,possibly in two stages, and finally in the first direction again to decelerate). The other twin remains inertial throughout.

"This is totally in agreement with the fact that the traveling twin's clock ran slow compared to the stationary twin." that's what I'm saying!

But my comment was directly after a passage in which I said that during inertial phases (as defined above) both twins' clocks run slow with respect to the other. That is not what you seem to be agreeing to.

I reiterate that it is Einstein's work to which I specifically refer not to interpretations of same by anyone else!

I am going to make a huge assumption here. You are monolingual.

If you were fluently bilingual, or multilingual, you could not possibly believe that a paper could be translated from German into English without being interpreted. A word for word transliteration would be nigh on impossible to read and impossible to understand. What would be easy to comprehend when transliterated from German to English would be the mathematics, which I find rather amusing.

Perhaps I am wrong and you are fluent in German, in which case, you may be better off working directly from the German rather than the 1922 translation by W. Perrett and G.B. Jeffery, which I took to be your source (and this is why I posted words from it earlier, because there are apparently other translations). But so long as you quote English words and claim Einstein wrote them, you are just making yourself look silly.

cheers,

neopolitan

 

[jtbell]

I reiterate that it is Einstein's work to which I specifically refer not to interpretations of same by anyone else!

Physics is not like literature or history, in which "original sources" have primary importance.

With all due respect to Einstein, one should not attach any more weight to his writings about relativity than to those of the many physicists who have refined, tested, and extended his ideas during the past century. His papers are not the last word about SR, and not the "bible" of SR. I consider them to be mainly of historical interest today.

Similarly, we don't consider Newton's "Principia Mathematica" as having precedence over all other works on classical mechanics, nor do we consider Maxwell's works as uniquely defining for classical electrodynamics.

 

[cos]

When the clocks are not colocated it takes time for the information from one clock to reach the other.

Nothing that I have written (nor, in my opinion, to which Einstein referred in his section 4 depiction) says anything about the time that it takes for the information from one clock to reach the other!

If the moving clock "looked" back at the stationary clock (as per Einstein's scenario), just before stopping...

To which of Einstein's scenario are you now referring? I can only assume that you are referring to an astronaut who has traveled out into space who, 'just before stopping' (i.e. just before coming to a stop at the end of his outward bound journey) 'looks back' at his twin's clock yet I see nothing in Einstein's section 4 depictio where he refers to that scenario.

In Einstein's initial polygonal line trip the traveler looks ahead to the stationary clock however I am of the opinion that his 'determination' (that B is, as has been claimed, ticking over at a slower rate than his own clock) is based on his calculations not on his perception of what clock B appears to be doing.

it would see only the time on the stationary clock that happened, in the moving clock's frame, x'/c ago (where x' is the separation that the moving clock thinks that it has from the stationary clock based on the traveling time). There will be more information still in transit.

You are, here, apparently referring to light travel time which I thought we had agreed the astronaut allows for!

Given that we can't agree as to whether you are saying Einstein's maths was erroneous or not, or that what he said matches with his maths, I don't feel this is going anywhere.

If I had written that I was of the opinion that Einstein's maths was erroneous (which I believe I have not!) you would be able to quote my comment.

My suggestion is that the astronaut's maths is erroneous on the basis that it shows him that clock B is ticking over at a slower rate than his own clock yet he arrives at B's location to find that, in reality, it is his clock that lags behind, having 'gone more slowly' than) B!

If you have a go at the maths, you will see that it matches the "reality" of what Einstein said (at least wrt to the 1905 paper). Until you do that, I really think I have to agree with Jtbell, at least in part, this is not a physics discussion. I just don't think it qualifies as philosophy either.[/QUOTE]

On that basis perhaps you should stop contributing to a discussion that, at least in part, is not, in your opinion, a physics discussion.

 

[JesseM]

My suggestion is that the astronaut's maths is erroneous on the basis that it shows him that clock B is ticking over at a slower rate than his own clock yet he arrives at B's location to find that, in reality, it is his clock that lags behind, having 'gone more slowly' than) B!

No, the fact that one clock lags behind is not proof that it was ticking more slowly--you're forgetting to take into account the relativity of simultaneity. In some frames clock B may be ticking slower than clock A and yet clock A will still be behind when they meet, because A and B did not start out in sync in the first place in these frames. Consider Einstein's example in section 4 of the 1905 paper:

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by $$(1/2)tv^2/c^2$$ (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

Suppose for example A and B are a distance of 60 light-seconds apart in the "stationary" frame K, and both are synchronized in this frame. Then if A is moved at 0.6c towards B at the moment when both clocks read a time of t=0, it will take 100 seconds in this frame for A to reach B, during which time A will only tick 80 seconds due to time dilation (the Lorentz factor being 1.25), so when A meets B, B will read t=100 seconds while A reads t=80 seconds.

Now consider things from the perspective of the inertial frame where A and B were initially moving at 0.6c and then A was accelerated to come to rest in this frame while B continued to move towards it at 0.6c. In this frame the clocks were not synchronized initially, so when A read t=0, B already read t=36 seconds according to this frame's definition of simultaneity. Then it takes 80 seconds in this frame for B to reach A (because the initial distance between them was 48 light-seconds in this frame due to length contraction, and 48 light-seconds/0.6c = 80 seconds), during which time B only ticks forward by 80/1.25 = 64 seconds due to time dilation, meaning B reads t=36 + 64 = 100 seconds when they meet, while A reads t=80 seconds when they meet. So you see that both frames make the same prediction about their respective times, even though in the first frame A was ticking slower while in the second frame B was ticking slower.

 

[neopolitan]

If you have a go at the maths, you will see that it matches the "reality" of what Einstein said (at least wrt to the 1905 paper). Until you do that, I really think I have to agree with Jtbell, at least in part, this is not a physics discussion. I just don't think it qualifies as philosophy either.

On that basis perhaps you should stop contributing to a discussion that, at least in part, is not, in your opinion, a physics discussion.

Don't you love language?

I agree with Jtbell, at least in part. This is not a physics discussion.

I disagree with Jtbell, at least in part. This is not a philosophy discussion.

Recently Mentz114 told someone not to write in capitals because it is indicative of an unhinged mind - an example, totally not about physics but toally unhinged is http://www.geocities.com/Baja/5692/". Your increasing use of bold, and underline, concerns me.

No matter what emphasis you place on an inherently incorrect statement, it will remain an inherently incorrect statement.

If I had written that I was of the opinion that Einstein's maths was erroneous (which I believe I have not!) you would be able to quote my comment.

So, I put it to you again, try the maths. The maths worked for Einstein...

Einstein's maths indicated the amount by which, in his opinion, clock A lags behind B and, as Einstein pointed out, because A lags behind B it must have 'gone more slowly' (i.e. ticked over at a slower rate) than B whilst A was moving.

According to Einstein's section 4 maths, clock A is ticking over at a slower rate than clock B but according to the maths employed by the observer accompanying clock A it is B that is ticking over at a slower rate than his clock.

Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!

HE has 'done the math' yet finds that it gave an erroneous answer. Of what value his math?

 

[cos]

[cos] "...on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other ."

In other words, according to Einstein, something physically happens to the moving clock. It is no longer synchronized with the inertial clock.

[A168]No, that's not why they're no longer in synch.

I did NOT refer to WHY they're no longer in synch but pointed out that according to Einstein they ARE no longer in synch.

In his 1918 article (which, in my opinion, was effectively an extension of his 1905 section 4 depiction) Einstein points out that the clocks are 'no longer in synch' because one of them (clock A in his section 4 depiction) has undergone acceleration!

You may have your own interpretation of why those clocks ar no longer in synch however I'm referring to Einstein's explanation.

[cos]Having, during his trip, 'determined' that B is, as you say, running slow compared to his clock that is at rest in his frame he arrives at B's location to find that B does not lag behind (having 'run slower' than) his clock but that his clock lags behind B.

No. The ship's twin knows 2 things during the outbound inertial part of the trip:
1. Earth's clock runs slower than the ship's clock in the ship's frame.
2. The ship's clock runs slower than Earth's clock in Earth's frame.

I find it particularly galling that some people take phenomenon out of context.

In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.

When he stops at the turnaround, the ship's twin doesn't "find" that his clock ran slower than Earth's clock,

Having come to a stop (analagous to Einstein's section 4 clock A moving to B's location) his clock will, according to Einstein, lag behind the previously synchronous Earth clock.

He allows for light travel time whereupon he eventually notices that the Earth clock is ahead of his own clock (although now ticking over at the same rate as his own clock).

He can either assume that the Earth clock ticked over at a faster rate than his own clock (and at a faster rate than it did before he started accelerating) NOT at a slower rate as 'determined' by his calculations OR he can conclude, in agreement with Einstein, that his clock 'went more slowly' (i.e. ticked over at a slower rate) than it did before he started moving.

Alternatively, there could be a clock located at the point where he comes to a stop that is synchronous with the Earth clock (it's mechanism compensates for it's location in a much weaker gravitational tidal area) whereupon he finds that his clock lags behind that clock. He can either assume that this clock physically ticked over at faster rate than it did before he started moving toward it (in total contradiction of what his calculations 'showed' him is taking place) OR that, as Einstein suggested, his clock was 'going more slowly' than it was before he left the planet ergo is ticking over at a slower rate than this clock.

he knew all along that the ship's clock ran slower than Earth's clock in Earth's frame.

Assuming that he has read and understands STR specifically section 4 he could (and in my opinion should) be of the opinion, during that flight, that his clock - having incurred acceleration - is 'going more slowly' than it did before he started accelerating thus he will know (or at least be able to assume) that Einstein was right - that his clock was 'going more slowly' than it did before he started accelerating.

The relative ticking rate of clocks is frame-dependent, not absolute. Nothing changed with Earth's clock during the turnaround, the relative speed of the ship changed. Earth's clock didn't change its ticking rate, we changed which frame we're referring to, and the ticking rate of a clock is frame dependent.

The relative rate may well be 'frame-dependent' on the basis of the calculations made by observers in those frames however the physical rate of clocks is not frame-dependant. All clocks will tick over at their own rate regardless of the opinions expressed, or determinations arrived at, by other frames.

Nothing changed with Earth clock during the turn-around nor when the astronaut previously accelerates away from the planet nor when he was moving away at uniform vleocity nor when he slows down nor when he turns his ship around nor when he accelerates back to the planet nor when he moves with uniform velocity nor when he decelerates prior to landing!

Nothing the astronaut does has any physical affect whatsoever on the physical rate of operation of the Earth clock!

It seems that you're ignoring Einstein's most important contribution to modern physics, that the rate that any clock runs is dependent on the relative speed of the observer. That means that if someone changes his speed relative to a given clock, the rate of that clock will be different. Not because the clock changed, but because the reference frame of the observer changed.

That's precisely what I'm saying!

That clock's rate of operation does not change!

Ergo when a traveler 'determines' that the inertial clock 'is' running slower or faster than his own clock he is deluding himself if he believes that the inertial clock's rate of operation has physically changed in lieu of accepting that it is his clock's rate of operation that has changed.

When observer A in Einstein's section 4 depiction arrives at clock B's location to find that it lags behind his clock he could assume that B has, overall, ticked over at a faster rate than his own clock (i.e. at a faster rate than it did before he started moving on the basis that, in his opinion, his clock's rate of operation 'has remained unchanged') or he could agree with you that the rate of operation of that clock has not changed.

 

[JesseM]

In the previous sections of STR Einstein pointed out that an observer accompanying a clock that is moving relative to another clock will be of the opinion that the other clock 'is' ticking over at a slower rate than his own clock however in section 4 (as well as in his 1918 article) Einstein pointed out that a clock that has incurred acceleration (i.e. the astronaut's clock - having blasted off from the planet) will 'go more slowly' (i.e. tick over at a slower rate) than a clock that has remained 'at rest'.

He is obviously not saying that the accelerated clock is ticking more slowly at every instant, since at any given instant you can pick an inertial frame where the accelerated clock has a smaller velocity and thus is ticking faster. Presumably in section 4 he's talking about something like the average rate of ticking of the accelerated clock, either between the time it departs from and returns to a non-accelerating clock, or over the course of a complete orbit in the case of the clock which is accelerating because it's at the equator of a rotating sphere. All inertial frames will agree in these cases that the average rate of ticking of the accelerated clock is slower, even though in a given inertial frame there may be periods of time where it is ticking faster.

 

[cos]

[cos]My references are to reality and I am of the opinion that fictitious forces do not come under that category.

That is fine by me, but then neither should coordinate time (and therefore the rate of a clock wrt coordinate time). Again, I don't care how you use the words "physical" or "real" but you need to be consistent.

Does your comment "That is fine by me." mean that you agree with me that fictitious forces do not come under the heading of reality?

[cos]The concept of a 'fictitious force' is in my opinion a desperate grasping at straws analogous to the 'parallel universes' escape-clause, suitably impossible-to-disprove, concept.

This is also fine, but if you do not like fictitious forces then you cannot do any analysis in any non-inertial frame. You must stick exclusively to inertial frames. As I mentioned previously, all inertial frames agree on the results also.

In my opinion this means that unless I accept the 'reality' of purely hypothetical, non-existent, fictitious forces I cannot, in a non-inertial frame, do any analysis.

[cos]It has been pointed out in relation to my previous thread in this forum that there could be third observer, C, relative to whom A and B were initially moving at v. When A accelerates he, from C's point of view, decelerates and comes to a stop in C's reference frame (thus ticks over at the same rate as C's clock) whereas B keeps moving relative to C at v thus from C's point of view clock B is ticking over at a slower rate than his own clock ergo also at a slower rate than clock A so when A 'accelerates' back to B's location (in B's reference frame, decelerates and comes to a stop alongside B) it is, in C's opinion, clock B that will lag behind A.

No, you have forgotten that A is moving at 2v/(1+v²/c²) on the second leg of the trip. Since A travels at a faster speed than B, A experiences more time dilation than B. Also, that second leg lasts for a longer coordinate time in C's frame. Because of that, C is of the (correct) opinion that A will lag behind B when they meet and that A was "physically" slower than B on average. Again, all frames agree on this result.

What 'second leg of the trip'?

A accelerates toward and comes to a stop alongside B. There is only one leg of that trip unless of course you are referring to periods of acceleration as being 'legs' of that trip.

A does not, from C's point of view 'travel at a faster speed than B'.

In C's frame A decelerates and comes to a stop alongside C whilst B keeps moving at it's original speed ergo B is moving whilst A has 'come to a stop'.

On the basis that A has come to a stop alongside C it cannot, from C's point of view, be experiencing any time dilation! A is then ticking over at the same rate as C!

 

[cos]

Having calculated that B 'is' ticking over at a slower rate than his own clock, observer A 'determines' or 'predicts' that when he arrives at B's location he will find that it lags behind his clock yet he learns that it does NOT!

This is not true. Observer A makes no such prediction. Each twin will make the same prediction. That is that when they reunite, A's clock will read less elapsed time than B's clock.

A calculates that clock B is ticking over at a slower rate than his own clock. What stops him from believing that when he arrives at B's location that B's clock will not - having ticked over at a slower rate than his own clock - lag behind his clock?

Does he believe that B's slower rate of operation is reality or does he realize that it is an illusion!

What might be a source of confusion is that the fact that time dilation is symmetrical, but proper elapsed time is not.

According to Einstein's section 4 STR depiction (and to his 1918 article) time dilation is not symmetrical!

According to Einstein the non-inertial clock ticks at a slower rate than it did before it started moving whilst the inertial clock continues to tick over at the same rate as it did before A started moving.

According to Einstein in his 1918 article it is only the clock that has incurred acceleration (i.e. his 1905 section 4 depicted clock A) that undergoes time dilation not the clock that has remained at rest.

 

[cos]

Recently Mentz114 told someone not to write in capitals because it is indicative of an unhinged mind -

In my case it is a result of sheer frustration.

Correspondence terminated.