Understanding Time Dilation in Einstein's Special Theory of Relativity

[cos]

Einstein didn't use the word "physical" to describe time dilation, but if I had to guess then I would guess that at that time he considered such experimentally-measurable coordinate-dependent quantities to be "physical".

I did not suggest that he did, however, thank you for that agreement.

 

[neopolitan]

cos,

I don't know what you are after. I have made plenty of snide and belittling comments in my time, but what you claim was snide and belittling wasn't intended to be.

Your position is inconsistent since in part it is based on maths and then you say maths doesn't reflect reality. Additionally, what you are arguing seems to be based on an appeal to authority (Einstein said something, so what I interpret him to have said must be true). I don't think that Einstein expected to be believed just because he said something.

He'd probably suggest that you work through the maths, which he certainly didn't reject as you seem to.

cheers,

neopolitan

 

[cos]

cos,

I don't know what you are after. I have made plenty of snide and belittling comments in my time, but what you claim was snide and belittling wasn't intended to be.

I was, for 30 years, married to an alcoholic who constantly belittled me and the next day tearfully insisted that she didn't intend to but, that same evening, did the same thing. This caused me to suffer from chronic and severe reactive depression however I put up with it on the basis of my marriage vows but I will not tolerate such behavior from anyone!

Your position is inconsistent since in part it is based on maths and then you say maths doesn't reflect reality. Additionally, what you are arguing seems to be based on an appeal to authority (Einstein said something, so what I interpret him to have said must be true). I don't think that Einstein expected to be believed just because he said something.

My 'position' is not, in any part, based on maths but is based solely on Einstein's section 4 STR comments in which he based his depictions on maths.

I am of the opinion that clock A ticks over at a slower rate than it did prior to it's acceleration NOT because that's what the maths shows but that the slower rate of operation is, according to Einstein, in accordance with that equation.

He'd probably suggest that you work through the maths, which he certainly didn't reject as you seem to.

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

I do NOT reject mathematics on the basis that it is an absolutely indispensable aspect of science and, indeed, of everyday life however I do NOT accept that what it shows is reality.

Where 'reality' indicates that a mathematical proposition does not take place as indicated by an equation I am of the opinion that reality takes precedence.

 

[neopolitan]

cos,

It appears that you have had some misfortune, but it is 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.

So, I put it to you again, try the maths. The maths worked for Einstein. In 1918, to be honest, his attitude about what "must be right" wasn't working. He later called his search for a cosmological constant his greatest blunder.

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

cheers,

neopolitan

 

[Dale]

I did not suggest that he did, however, thank you for that agreement.

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.

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).

 

[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?