Time dilation ll

by cos
Tags: dilation, time
P: 801
 Quote by DaleSpam All frames agree that each clock ticks at the rate of 1 s/light-second along their worldline.
I'm sure that's a typo, but that would mean the clock was traveling at c.
 Mentor P: 17,340 That is not a typo. The Minkowski norm of any 4-velocity is c, so a particle at rest can indeed be considered to "travel" at c in the time direction.
P: 212
 Quote by neopolitan If you are not prepared to work through the mathematics which shows how both twins will observe that the other twin's clock appears to run slow, but that after stopping and performing a synchronisation then both will agree that the accelerated twin's clock ran slow, then there is little more to be going on with.
You agree with me as well as with Einstein's comment regarding mathematical 'certainty' and 'reality'!

During his trip the traveling twin calculates ('observes' or 'determines' or 'predicts') that his brother's clock appears to run slow (i.e. appears to be ticking over at a slower rate than his own clock) yet he arrives at B's location to find that, in reality, it was his clock that ran slow.

If the traveler repeats that same journey he could calculate (determine) that his twin's clock appears to be running slow however in accordance with the result of the first experiment he knows that. in reality, it is his clock that is running slow! Of what value his totally contradictory mathematical determination?
 P: 1,060 Hello cos. You seem to be neglecting the comments of DaleSpam and Al68. Matheinste.
P: 212
 Quote by Al68 It seems like you're suggesting that something physically happens to the clocks. This is simply not the case.
"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 .5tv^2/c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be a .5tv^2/c^2 second slow. 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."

In the first paragraph Einstein states -

"...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.

In the third paragraph Einstein states -

"...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."

In other words, according to Einstein, something is physically happening to to the equatorial clock - it is ticking over at a slower rate than the polar clock ("under otherwise identical conditions.")

Perhaps it is your opinion that nothing physically happens to either of the clocks however it is Einstein's opinion to which my posting applies!

 Quote by Al68 And Einstein's 1918 paper does not claim that the time dilation is not reciprocal between inertial frames. It is simply a resolution taking the accelerated frame into account during the turnaround. During each inertial leg, each clock runs slow as observed from the other frame. Only during the turnaround acceleration, the earth's clock runs fast as observed from the accelerated frame.
When the clock in Einstein's 1918 paper decelerates and comes to a stop it is analogous to Einstein's section 4 depiction -

"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."

Having come to a stop (ergo then being in the same reference frame as clock B) clock A can be synchronized with clock B then having accelerated and moved to B's location A will be found to lag behind B on the basis that it must 'go more slowly' (i.e. tick over at a slower rate) than the inertial clock.

According to your depiction that "...during the turnaround acceleration, the earth's clock runs fast as observed from the accelerated frame." the astronaut must be of the opinion that something has physically made the Earth clock run faster than it did before he started accelerating.

Not only is the Earth clock, in his opinion, running fast - time itself, for the Earth must also be 'running fast'. Earth clock seconds, minutes, hours and days 'have' contracted hence the planet would, whilst he is accelerating, be spinning faster on its axis than it was before he started accelerating!

The claim that, during the turnaround acceleration, the Earth clock runs fast is usually accompanied by the claim that when the astronaut stops accelerating Earth time resorts to its normal (some insist slower) rate so at the very instant that the astronaut takes his foot off the gas pedal the Earth's faster axial spin immediately reverts to normal! No gradual slowing down but immediate return to normal!

And it's never a matter of opinion what any clock reads in any frame in SR. Every observer will agree on the facts. No clock is running slower than another in any absolute sense. Which clock runs slower than the other depends on which frame the observation is made from. No observer in any inertial frame ever observes a clock in relative motion to run faster than his own, or his own clock to run slower than one in relative motion.

 Quote by Al68 This is true in Einstein's 1918 paper as well. It is only with respect to the accelerated frame of the ship during turnaround that a clock in relative motion runs fast compared to a clock at rest in that frame, and that's not an inertial frame. During all inertial motion, in each frame, the clock in motion runs slow compared to the clock at rest in that frame. This is reciprocal time dilation.
In Einstein's section 4 he points out that, in each example, when clock A is compared with clock B it is found that A lags behind B.

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.

I am of the opinion that your comment that an astronaut accompanying clock A in Einstein's depictions (of clock A initially accelerating toward clock B) would see clock B 'running faster' is only as a result of Doppler shift however he sees almost precisely the same amount of Doppler shift when he stops accelerating as he did at the very instant that he removes his foot from the gas pedal.

There is, I suggest, nothing in special theory which shows that any action performed by the astronaut - accelerating, decelerating, moving toward or away from another clock at any velocity - will have a physical affect on that other clock - only on what it appears to be doing.

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.
P: 212
 Quote by DaleSpam Whether one clock "physically" ticks at a different rate than normal depends on if you consider experimentally-measurable coordinate-dependent quantities to be "physical".
When Einstein wrote that a clock at the equator 'must go more slowly' than a clock at one of the poles (under otherwise identical conditions) was he indicating that the the equatorial clock physically 'goes more slowly' than the polar clock or was he considering 'experimentally-measurable coordinate-dependent quantities to be "physical."'?
P: 212
 Quote by matheinste Hello cos. You seem to be neglecting the comments of DaleSpam and Al68. Matheinste.
Give me a break!

I do have a life apart from this group furthermore I usually refuse to communicate with fanatics who have, in other postings, applied ad hominem attacks.
 P: 1,060 Hello cos. I do not see where Einstein says or implies that anything physical happens to the clocks. All that clocks do is measure time. In all the examples used in thought experiments the clocks are assumed ideal, that is their physical tmekeeping processes are not affected by their state of motion. As clocks merely measure time and their physical workings are unaffected by motion, it is concluded, as a basic consquence of the postulates of SR that it is time itself which undergoes a change of rate which is reflected in the rate of "ticking" and hence the accumulated time on the clock. As others have made clear, an inertial clock will accumulate more time than a clock that has experienced non inertial motion, in this case having moved around a closed path. Again, as others have said, if we have two observers moving relative to each other with inertial motion, each will see the others clock run slower than his own, having of course discounted any visual effects due to the relative motion. The effect is reciprocal and wll be agreed upon by both observers. Matheinste.
P: 645
 Quote by cos You agree with me as well as with Einstein's comment regarding mathematical 'certainty' and 'reality'!
Probably not since I at no point gave a definition of certainty and reality. I agree that models simple enough to understand are not fully descriptive of reality, and any model which was fully descriptive would be too complex to do much with (except live in, perhaps, since a fully descriptive model of the universe would be .... the universe).

Again, if you refuse to go through the maths, you won't understand.

 Quote by cos During his trip the traveling twin calculates ('observes' or 'determines' or 'predicts') that his brother's clock appears to run slow (i.e. appears to be ticking over at a slower rate than his own clock) yet he arrives at B's location to find that, in reality, it was his clock that ran slow.
Appears only when taking everything into account. Naively, on the way out, both will observe that the other's clock runs slow, because they are separating. Naively, on the way back in, both will observe that the other's clock runs faster, because they are closing on each other.

If you truly want to think about this, rather than push a barrow, then you might want to consider the twin paradox with each twin firing photons at each other during the journey at a rate determined by their on board clock. Consideration of when and where each twin interacts with the incoming photons will show you how it all works out such that both clocks appear to run slow with respect to each other while they are in motion with respect to each other, but the accelerated twin (the one with more than one inertial frame) will experience less elapsed time.

But until you do something like that, you're not learning anything and neither are we.

 Quote by cos If the traveler repeats that same journey he could calculate (determine) that his twin's clock appears to be running slow however in accordance with the result of the first experiment he knows that. in reality, it is his clock that is running slow! Of what value his totally contradictory mathematical determination?
If he is committing to do as much mathematics to arrive at his mathematical determination as you are, no value at all. I keep repeating it, because it's the only way forward for you, do the maths, then come back. There are plenty of people willing to help you work through it, if you need it.

cheers,

neopolitan
Mentor
P: 17,340
 Quote by cos When Einstein wrote that a clock at the equator 'must go more slowly' than a clock at one of the poles (under otherwise identical conditions) was he indicating that the the equatorial clock physically 'goes more slowly' than the polar clock or was he considering 'experimentally-measurable coordinate-dependent quantities to be "physical."'?
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".
P: 212
 Quote by matheinste I do not see where Einstein says or implies that anything physical happens to the clocks.
In section 4 STR Einstein wrote that clock A physically moves to B's location. He also states that a clock that is made to move in a closed curve relative to an 'at rest' clock will 'go more slowly' than the stationary clock. It follows that by 'going more slowly' than the previously synchronous clock that the moving clock is physically 'going more slowly' than it was before it started moving - a rate of operation that is comparable to the stationary clock's rate of operation - whether or not clock A is moving in a polygonal line or in a closed curve.

Having suggested that clock A is then ticking over at a slower rate than it did before it started moving what gives you the impression that Einstein did not imply that something physical happens to clock A?

 Quote by matheinste All that clocks do is measure time. In all the examples used in thought experiments the clocks are assumed ideal, that is their physical timekeeping processes are not affected by their state of motion. As clocks merely measure time and their physical workings are unaffected by motion, it is concluded, as a basic consquence of the postulates of SR that it is time itself which undergoes a change of rate which is reflected in the rate of "ticking" and hence the accumulated time on the clock.
The Hafele-Keating was obviously not a thought experiment and it is said to ratify Einstein's suggestion that a clock that is made to move in a closed path around another clock will tick over at a slower rate than the other clock i.e. at a slower rate than it did before it started moving.

 Quote by matheinste As others have made clear, an inertial clock will accumulate more time than a clock that has experienced non inertial motion, in this case having moved around a closed path.
As Einstein, in my opinion, 'made clear' - a non-inertial clock will 'go more slowly' (i.e. tick over at a slower rate) than an inertial clock (and tick at a slower rate than it was before it started moving). He did not suggest, and I believe would not have tolerated the idea, that the inertial clock will 'accumulate more time' than it would if the other clock had not been made to move. The rate of operation of the inertial clock physically remains unchanged irrespective of the distance traveled through spacetime by another clock.

 Quote by matheinste Again, as others have said, if we have two observers moving relative to each other with inertial motion, each will see the others clock run slower than his own, having of course discounted any visual effects due to the relative motion. The effect is reciprocal and wll be agreed upon by both observers.
An observer accompanying clock A in Einstein's section 4 STR depiction (in accordance with his mathematical calculations) 'sees' (or 'determines') that clock B 'is' ticking over at a slower rate than his own clock yet arrives at B's location to find that B does not lag behind his clock as he calculated (i.e. 'determined' or 'predicted') it will but that his clock lags behind B!

Having arrived at B's location and having determined that his clock lags behind clock B due to the fact that, whilst he was moving, his clock was ticking over at a slower rate than it was before he started moving (i.e. 'going more slowly' than it was before he started moving) A could return to his original location and repeat the experiment during which his calculations will, again, 'show' him that clock B 'is' ticking over at a slower rate than his own clock (i.e at a slower rate than it was before he started moving) however the reality determined by the results of the first leg of the experiment - that his clock was ticking over at slower rate than it was before he started moving - challenges the validity of those calculations (i.e. 'determinations or 'predictions' arrived at via those calculations). They do not refer to reality and that, in my opinion, is what Einstein stated.

Your comment ".. if we have two observers moving relative to each other with inertial motion, each will see the others clock run slower than his own." applies specifically to special theory prior to section 4 which does not refer to those observers moving with inertial motion but to one observer that has (having accelerated) incurred non-inertial motion.

It is, in my opinion, 'misleading' (to say the very least) for anyone to stipulate events depicted in the previous sections of special theory and not to allow for Einstein's comments in section 4.
P: 212
 Quote by neopolitan Probably not since I at no point gave a definition of certainty and reality. I agree that models simple enough to understand are not fully descriptive of reality, and any model which was fully descriptive would be too complex to do much with (except live in, perhaps, since a fully descriptive model of the universe would be .... the universe).
You wrote that the mathematics "...shows how both twins will observe that the other twin's clock appears to run slow, but that after stopping and performing a synchronisation then both will agree that the accelerated twin's clock ran slow."

Are you suggesting that the mathematics are not 'certain' - that they are not self consistent?

Are you suggesting that when they both see that A lags behind B that this is NOT reality?

I made no suggestion whatsoever that you 'gave a definition of certainty and reality' but that, in my opinion, you provided examples OF 'certainty' and 'reality'.

 Quote by neopolitan Again, if you refuse to go through the maths, you won't understand.
Again, on the basis that I am of the opinion that mathematics does not refer to reality what would be the point of my going through the maths when I refuse to believe that what they determine is reality?

Your next comment makes no sense on the basis that you removed my statement -

"During his trip the traveling twin calculates ('observes' or 'determines' or 'predicts') that his brother's clock appears to run slow (i.e. appears to be ticking over at a slower rate than his own clock) yet he arrives at B's location to find that, in reality, it was his clock that ran slow.

[QUOTE=neopolitan;2137819]Appears only when taking everything into account.

There is only one aspect to be taken into account, the astronaut's rate of travel and it's incorporation as 'v' in the Lorentz' transformations.

 Quote by neopolitan Naively, on the way out, both will observe that the other's clock runs slow, because they are separating. Naively, on the way back in, both will observe that the other's clock runs faster, because they are closing on each other.
You wrote, above, that "...both twins will observe that the other twin's clock appears to run slow, but that after stopping and performing a synchronisation then both will agree that the accelerated twin's clock ran slow."

Your "..on the way back in..." is analogous to Einstein's section reference to one clock (A) that is made to move to B's location.

Let us imagine that the journey you depict is the second trip of an astronaut away from and back toward the planet. As a result of the fact that at the conclusion of that first experiment 'both will agree that the accelerated twin's clock ran slow' when it accelerated following turn around would it not be feasible for both observers to realize that precisely the same phenomenon is taking place during the second, identical experiment?

I am of the opinion that whilst the astronaut is 'on the way out' that his clock will also 'go more slowly' than it did prior to his departure in accordance with Einstein's .5tv^2/c^2 equation.

You wrote, above, "...on the way out, both will observe that the other's clock runs slow, because they are separating. Naively, on the way back in, both will observe that the other's clock runs faster, because they are closing on each other." This, I believe, is only due to the Doppler effect wheras the mathematical determinations of both observers is in accordance with the Lorentz transformations which do NOT incorporate or allow for Doppler shift.

The fact that I see the light emitted by a clock toward, or away from, which I am moving blueshifted or redshifted does NOT mean that it IS ticking over at a faster, or slower, rate than it was before I started moving but that it appears to be ticking over at a different rate.

I am of the opinion that Einstein's comment that the accelerated clock ticks over at a slower rate than the inertial clock has absolutely nothing whatsoever to do with Doppler shift!

 Quote by neopolitan If you truly want to think about this, rather than push a barrow, then you might want to consider the twin paradox with each twin firing photons at each other during the journey at a rate determined by their on board clock. Consideration of when and where each twin interacts with the incoming photons will show you how it all works out such that both clocks appear to run slow with respect to each other while they are in motion with respect to each other, but the accelerated twin (the one with more than one inertial frame) will experience less elapsed time.
I find it galling that you continue to resort to snide, belittling remarks.

Each twin firing photons at each other is precisely the same as each of them looking at the other clock i.e. 'receiving photons fired at them' so your depiction is, once again, in relation to the Doppler effect albeit a complicated version of same.

The accelerated twin will, according to Einstein, "...experience less elapsed time." due to the fact that (when he arrives at B's location and finds that his clock lags behind B) he realizes that his clock was, as you have agreed, running slow.
P: 212
 Quote by DaleSpam 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.
 P: 645 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
P: 212
 Quote by 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.
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!

[QUOTE=neopolitan;2138035]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.

 Quote by neopolitan 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.
P: 645
cos,

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

 Quote by cos 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
Mentor
P: 17,340
 Quote by cos 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).
 Mentor P: 11,787 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.

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