
#19
Mar2809, 01:18 AM

P: 801





#20
Mar2809, 09:22 AM

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P: 16,489

That is not a typo. The Minkowski norm of any 4velocity is c, so a particle at rest can indeed be considered to "travel" at c in the time direction.




#21
Mar2809, 07:02 PM

P: 212

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? 



#22
Mar2809, 07:16 PM

P: 1,060

Hello cos.
You seem to be neglecting the comments of DaleSpam and Al68. Matheinste. 



#23
Mar2809, 08:28 PM

P: 212

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 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." 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 balanceclock 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! "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. 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. 



#24
Mar2809, 08:38 PM

P: 212





#25
Mar2809, 08:43 PM

P: 212

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. 



#26
Mar2809, 09:02 PM

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. 



#27
Mar2809, 09:50 PM

P: 645

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



#28
Mar2809, 10:18 PM

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P: 16,489





#29
Mar2809, 11:48 PM

P: 212

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? 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 noninertial 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. 



#30
Mar2909, 12:55 AM

P: 212

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'. 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. 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! 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. 



#31
Mar2909, 12:58 AM

P: 212





#32
Mar2909, 02:08 AM

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 



#33
Mar2909, 02:51 AM

P: 212

[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. 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. 



#34
Mar2909, 06:20 AM

P: 645

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



#35
Mar2909, 08:10 AM

Mentor
P: 16,489

However, since your opinion appears to be firm that framedependent 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 framevariant "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). 


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