
#37
Mar2909, 07:43 PM

P: 645

"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 travelling twin turned around later than travelling twin calculated. This is totally in agreement with the fact that the travelling twin's clock ran slow compared to the stationary twin. So if you like, both clocks really ran slow, the travelling 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 



#38
Mar2909, 07:51 PM

P: 212

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 noninertial observer with his previously depicted inertial observer. Albert Einstein's 1905 article 'On the Electrodynamics of Moving Bodies' is said to be the foundation of modernday 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! 



#39
Mar2909, 08:41 PM

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#40
Mar2909, 08:49 PM

P: 1,060

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 



#41
Mar2909, 10:18 PM

P: 212

He is an astronaut returning to the planet following turnaround; 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 noninertial 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 noninertial 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. 



#42
Mar2909, 10:22 PM

P: 212





#43
Mar2909, 10:29 PM

P: 212

In section 4 he wrote  "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." 



#44
Mar2909, 10:38 PM

P: 645

cos,
I assume that you are refering to the section titled "Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks" since that section ends with: 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 travelled 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: [tex]\gamma ( t  x.v / c^{2} ) = \gamma ( t  t.v^{2} / c^{2} ) = \gamma t (1  v^{2} / c^{2} ) = t / \gamma [/tex] The difference is therefore [tex]\Delta = t  t' = t ( 1  1 / \gamma) \approx 1/2t . v^{2} / c^{2} [/tex]. When that moving clock stops, there are a number of ticks from the "stationary" clock still travelling to catch up, x/(cv) = vt/(cv) 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 



#45
Mar2909, 10:55 PM

P: 645

Einstein's paper was written in German. The original text can be seen here. 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 



#46
Mar2909, 11:50 PM

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P: 16,476

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



#47
Mar3009, 02:31 AM

P: 212

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



#48
Mar3009, 03:17 AM

P: 212

The concept of a 'fictitious force' is in my opinion a desperate grasping at straws analogous to the 'parallel universes' escapeclause, suitably impossibletodisprove, 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 nonmaterial 'force' can result in an equal and opposite reaction provided the results supply the solution they seek. 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! 



#49
Mar3009, 03:43 AM

P: 645

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 



#50
Mar3009, 03:53 AM

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#51
Mar3009, 06:21 AM

P: 801

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. 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. 



#52
Mar3009, 06:53 AM

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#53
Mar3009, 04:10 PM

P: 801

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. 



#54
Mar3009, 04:25 PM

P: 801

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. 


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