
#1
Mar2509, 01:47 AM

P: 212

In my previous thread ‘Time dilation’ dated Mar2209 I wrote 
In section 4 STR Einstein wrote  "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 balanceclock 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." What do people think he meant by the phrase "...must go more slowly..."? Does anyone agree that he meant that the moving clock will tick over at a slower rate than (i.e. incur time dilation relatively to) the other clock? ******************** On the (probably erroneous) basis that some people may agree that he did I follow that up with the question  On the basis of his depiction of a clock that is made to move in a closed curve around another clock is it correct for me to assume that Einstein meant that the clock that is moving in a closed curve will “go more slowly”(i.e. tick over at a slower rate) than the clock “which has remained at rest.”? Pretty obvious questions  I know  however they are leading to a conclusion but my previous attempt started at the wrong end of Einstein’s section 4 STR depictions leading to confusion. 



#2
Mar2509, 02:33 AM

P: 645

A spinning mass is not spherical. It is fatter at the equator than at the poles. The clock at the pole at sea level will be closer to the centre of mass of the earth than a clock on the equator at sea level is. I am pretty sure that the overall effect is that when comparing clocks at sea level, all clocks will run at the same rate. I wouldn't like to have to do the maths, perhaps someone else can If the earth was a perfect sphere, then yes, the clock at the equator would run slow compared to the clock at the pole (but the rotation of this perfectly spherical earth would be terribly unstable). neopolitan 



#3
Mar2509, 08:03 PM

P: 212

Furthermore, the argument you present has no relevance to his previous depiction "...one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A..." which is analogous to an astronaut making an outandreturn trip into space. Having stated (albeit perhaps erroneously) that an equatorial clock will 'go more slowly' than a polar clock i am of the opinion that the clock that is made to travel in a closed curve around another clock will similarly 'go more slowly' than the 'stationary' clock. We assume, theoretically, that both systems are in an otherwise empty space whereby there is no question that the central clocks are moving as there is nothing with which a state of motion can be determined. I am of the opinion that his comment "must go more slowly" means that the equatorial clock and the clock that is moving in a closed curve will respectively be ticking over at slower rates than (i.e. incurring time dilation relatively to) the 'stationary' polarcentral clocks. An astronaut blasts off from the planet and travels out into space continuously firing a lateral rocket and moves in a closed curve returning to the planet. According to Einstein's section 4 STR depiction his clock (A) 'must go more slowly' than his twin's clock (B) and upon arriving home he finds that his clock lags behind his twin's clock. Having read and accepted special theory (in particular section 4) as well as Einstein's 1918 Naturwissennschaften article (in which he stated that it is only the clock that incurs acceleration that ticks over at the slower time not the 'stationary' clock) the astronaut should be entitled to conclude that his clock lags behind clock B because, whilst he was moving, his clock went more slowly (i.e. ticked over at a slower rate than) his twin's clock regardless of the fact that his clock appears to be ticking over at it's 'normal' rate. The alternative is that he is of the opinion that, whilst he was traveling, the Earth clock (and the entire universe) ticked over at a faster rate than his own clock. I am of the opinion that the idea that a clock can be made to tick over at a faster rate than it was before another clock started moving (i.e. universal time contraction)was an anathema to Einstein and it is his work to which my postings apply not interpretations of same. 



#4
Mar2509, 09:08 PM

P: 645

Time dilation ll
Nowhere in my post did I say SR is wrong in any section. Nothing in my post should be taken as suggesting that SR is wrong is any section.
Setting up two towers, so that a clock is at the same separation from the centre of mass of the earth has the same effect as placing two clocks on a rotating perfect sphere, without the issue of rotational instability. Highlighting words will not change what I have written above. In light of your clarification, ie your interpretation of "under otherwise identical conditions" to mean "with same separation from the earth's centre of mass" rather than "at sea level", then I would answer your question, viz: Similarly, if you are inertial and have a clock in orbit around you, or moving in a closed curve around you, then that clock would run more slowly than any identical clock that you held. Furthermore, if you are essentially in orbit around a point mass (stand on the surface of the Earth and that is what you are doing  you are in geosynchronous orbit around the Earth, normally referred to as "standing still") and there is a clock on a tower above you, that clock will be affected by the greater effective orbital velocity relative to you, and as a result it will run slower than an identical clock held by you. That effect must, however, be considered together with the effect of your being deeper in the gravity well, which means that your clock is running slower than clocks less deep in the gravity well. These effects are considered in the calculations required to make GPS work (because GPS works on triangulation performed by comparing the times on clocks)  check wikipedia if you don't believe me. Note that this third scenario is generalised version of the second scenario, whereas in the third scenario the radius of the closed curve is r=R, in the second scenario r=0. The first scenario is also a generalised version of the second scenario, but there is a lateral offset of the closed curve which is zero in the second scenario and R in the first. R is the radius of the Earth. cheers, neopolitan 



#5
Mar2609, 02:25 AM

P: 212





#6
Mar2609, 02:50 AM

P: 645





#7
Mar2609, 07:53 PM

P: 212

According to Einstein, a clock at the equator will go more slowly than a clock at one of the poles (under otherwise identical conditions ergo there is no reason whatsoever to refer to any tower). Why would the person at the equator disagree with Einstein insisting that his clock is not 'going more slowly' (i.e. ticking over at a slower rate) than a clock at one of the poles? On what basis would that person insist that Einstein was wrong? A person who is, in accordance with Einstein's section 4 depiction, moving in a closed curve around another clock knows that his is not an inertial reference frame and that the clock which has, in Einstein's terms, remained at rest is inertial and because of that fact his clock will, as Einstein pointed out, 'go more slowly' than the inertial clock. That person is, in my opinion, entitled to agree with Einstein thus realize that his clock is ticking over at a slower rate than it was before he started moving. 



#8
Mar2609, 08:32 PM

P: 645

Are you going to get towards a situation where the planet is in empty space but still rotating, with nothing to reference against and claim that it is impossible to judge which is moving in a closed curve around the other? In that instance, you will still have one clock experiencing centripetal acceleration and the other one not. They are distinguishable. If you try taking the planet away, you will have taken away too much, since your mechanism for one clock moving around the other in a closed curve was the planet and will have to be replaced. Whatever mechanism you replace it with will give one clock centripetal acceleration and not the other (unless you make them coorbit something, in which case they both experience centripetal acceleration, but the situation is no longer analogous). cheers, neopolitan 



#9
Mar2609, 09:24 PM

P: 1,060

Matheinste. 



#10
Mar2609, 11:31 PM

P: 212

I have no reason whatsoever to suggest that if the planet was in empty space that it is impossible to judge which is moving in a closed curve around the other. The planet is, although spinning, not moving in a closed curve! "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." If you do respond in the positive to the question, above, asking if you accept that the person at the equator is allowed to know that his clock is, as Einstein stated, running more slowly than it would if he were located at one of the poles do you also accept that the person traveling in a closed curve around another clock is entitled to insist that his clock is, as Einstein suggested, ticking over at a slower rate than the 'at rest' (inertial reference frame) clock? 



#11
Mar2609, 11:47 PM

P: 212

My next question is  on the basis that a clock at the equator is (according to Einstein's section 4 STR presentation) ticking over at a slower rate than a polar clock  is a person located at the equator entitled to be of the opinion that, as Einstein suggested, his clock is physically ticking over at a slower rate than it would be if he were at one of the poles? Alternatively, if he were originally located at one of the poles and moved to the equator would he be entitled to realize that his clock is then physically ticking over at a slower rate than it was before he made that trip? 



#12
Mar2709, 12:03 AM

P: 645

Perhaps if you say what it is that you are actually aiming towards, you might be able to get your concern resolved. cheers, neopolitan 



#13
Mar2709, 01:46 AM

P: 212

Unlike his later depictions of a clock that is moving in a closed curve around another clock there is, in this polygonal line trip, no continuous acceleration as A moves toward B with uniform velocity as intimated by the factor 'v' in his equation ergo, during that trip, is an observer accompanying clock A entitled to be of the opinion that, as indicated by Einstein's equation, his clock is physically ticking over at a slower rate than it was before he started moving? Einstein's section 4 depiction of a clock that is made to move toward another clock is, in my opinion, analogous to his 1918 Naturwissenschaften article wherein he stated that it is only the clock that experiences a force of acceleration that physically incurs time dilation whilst the other clock (the stationary, inertial, clock B) does not incur variations in it's rate of operation ergo it does not, as some people insist, tick over at a faster rate than it did before A started moving. 



#14
Mar2709, 06:58 AM

P: 645

cos,
This is analogous to the twin paradox. The accelerated twin, I believe is justified in thinking that his clock has slowed. His observations while in the inertial phase will not conform to that since other clocks which were previously synchronised will now appear to run slow. However, if the travelling twin stops (after a deceleration) and performs a synchronisation with the stationary twin, the travelling (accelerated) twin will find that it was his clock that ran slow. It's reasonably simple to do the maths to show how all the observations match up as long as you use the right equations. Neither of the twins will observe the other's clock speed up. The only way you could do that, to my knowledge, is to put one twin into orbit, moving him out from the gravity well and reducing the GR effect of gravity. But I think that is outside your scenario. cheers, neopolitan 



#15
Mar2709, 05:50 PM

P: 212

He described, in that article, two clocks that are moving past each other and pointed out that the only way that the time indicated by those clocks can only be accurately compared would be if they were stationary alongside each other and for this to take place one of them would have to decelerate, come to a stop and accelerate toward the other clock, again coming to a stop. Einstein insisted that it is only the clock that experiences forces of acceleration that incurs time dilation not the 'at rest' clock. The second leg of that journey  the clock accelerating toward the other one and coming to a stop alongside it  is precisely the same phenomenon as Einstein described in section 4 where clock A moves to B's location ergo, in my opinion, his 1918 article was effectively a reiteration of what he had previously indicated in section 4. I feel that it is interesting to note that when Galileo prepared his book 'Two New Sciences' he had already been castigated by authorities as a result of his support for the nongeocentric universe thus wrote that manuscript in the form of a 'purely hypothetical' dialogue between a teacher and two of his students. Having apparently been castigated by his colleagues for suggesting  in the introduction to general theory  that the law of the constancy of the speed of light required modification  I am of the opinion that Einstein similarly wrote his 1918 article in the form of a 'hypothetical' discussion between a relativist and a skeptic perhaps (having referred to acceleration in order to 'justify' his argument) in an attempt to prevent additional criticism. You wrote "...other clocks which were previously synchronised will now appear to run slow." Run slow relatively to what? To the accelerated twin's clock? On the basis that the accelerated twin is justified in thinking that, as Einstein suggested, his clock is now ticking over at a slower rate than it was before he started moving how can his 'observations' (calculations) show him that the previously synchronized inertial clock B is also running slow (presumably compared to his clock)? "As far as the propositions of mathematics refer to reality, they are not certain. And as far as they are certain, they do not refer to reality." Observer A moves to B's location in a polygonal line and arrives to find that his clock lags behind B. He is, apparently, permitted to realize that, whilst he was moving, his clock was ticking over at a slower rate than it was before he started accelerating (and at a slower rate than clock B) irrespective of the fact that it 'appeared' to have been ticking over at its normal rate but when he 'does the math' involving the 'certain' (i.e. fully selfconsistent) Lorentz transformations he 'determines' that B is ticking over at a slower rate than his own clock. One interpretation that I read several years ago showing "how all the observations match up as long as you use the right equations." insisted that when an astronaut is returning to the planet he can 'do math' which 'shows' him that his twin sister is, by his judicious application of the accelerator, physically retroaging by a factor of sixty years! When I argued that the sister could have died during that period  thus his calculations would 'show' him that she came back to life and, along with millions of other people, emerged from her grave  that author insisted that the astronaut could be of that opinion on the basis that this is what his math shows him is taking place. I'm afraid that I have little faith in such 'certainties'. A worthy opponent in this group in response to my previous thread pointed out that from the point of view of a third observer (C) clocks A and B could, initially, have been moving past him at v thus when A accelerates then moves with uniform velocity it would be stationary alongside C whilst, from his point of view, B continues to move past him at v so in his opinion B is ticking over at a slower rate than A. He would thereby determine that when A pulls up alongside B it will not lag behind B but B will lag behind A! It is my belief that 'reality' is determined in the reference frame where the event takes place so if C accelerates toward and comes to a stop alongside B he will see that B does not lag behind A as indicated by his 'internally balanced' mathematical equations but that A lags behind B. Of what value his 'determinations' or 'predictions'? He should be allowed to realize that what he assumed to be taking place was not taking place in reality thus that his observations, determinations, predictions, were affected by his relative rate of travel. "Knowledge is onedimensional, the proper application of knowledge is multidimensional. Only the extremely wise, and the exceptionally foolish, are not prepared to change." (Confucius) 



#16
Mar2709, 09:06 PM

P: 645

And that is what this is. A misuse of logic. As soon as you mention "worthy opponents" the misuse of logic makes more sense. 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. Using the correct frames and equations, all the predictions and determinations made by either twin will be reconcilable with those of the other. Throwing more words at the "problem" won't make it a real problem. As for Einstein, I suspect a quotation taken out of context, but even if he was wrong that is no great issue, he was a man as subject to error as the rest of us. It's just that the things he was right about were of such great consequence. cheers, neopolitan 



#17
Mar2709, 10:27 PM

P: 801

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. 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. 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. 



#18
Mar2809, 12:47 AM

Mentor
P: 16,485

Whether one clock "physically" ticks at a different rate than normal depends on if you consider experimentallymeasurable coordinatedependent quantities to be "physical". 


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