Twin Paradox: Einstein's Explanation and Alternative Interpretations

[cos]

(continued from previous post)Again, in relativity it is quite meaningless to talk about how fast any clock is ticking "physically" in a frame-independent sense.

So I assume that it is quite meaningless for someone to claim that the astronaut is of the opinion that the Earth clock is physically ticking over at a faster rate than it was before he started moving?

I am of the opinion that this claim is quite meaningless.

No matter what clock you are dealing with, different frames assign it different rates of ticking, and for any pair of clocks, different frames will disagree about whose rate of ticking is slower (since different frames will disagree about which clock's speed is greater).

I assume that by ‘different frames’ you are referring to frames other than those of the astronaut however I reiterate that I am not in the slightest bit interested in what ‘different frames’ agree or disagree about but purely and simply what the astronaut determines.

Einstein makes it quite clear that there is no reason to prefer one inertial frame's perspective over any other, and any relativity textbook you might care to look at should make this clear as well.

The claim by the astronaut that his clock is ticking over at its normal rate thus that the eventual time variation between his clock and his twin’s clock can only have occurred as a result of the Earth clock ticking over at a faster rate than it was before he started moving indicates that he is giving preference to his reference frame over that of the Earth.

On the basis that he determines that every other reference frame in the universe is moving relatively to him he is of the opinion that his is the only reference frame in the entire universe that is ‘at rest’.

"a velocity of close to the speed of light" relative to what?

Duh; relative to what it was before he started moving?

If the astronaut is moving at close to the speed of light in the rest frame of the Earth, then in the astronaut's own inertial rest frame the astronaut is at rest and the Earth has a velocity close to the speed of light.

A brilliant young student living in a small town is selected for astronaut training however as the aeroplane taking him on his very first flight lifts off he starts screaming “The sky is falling! The sky is falling!” What promised to be a very exciting career ends up in a rubber room.

An astronaut is in a ship prior to takeoff. He hears the command “ignition” and feels a tremendous force of acceleration pushing him back into his seat.

He keeps accelerating and having attained an instantaneous velocity of close to the speed of light sees the universe appearing to flash past his window in a blur.

He takes his foot off the gas pedal but according to the way of thinking that you presented he is then of the opinion that he is, at that very instant, no longer moving but that it is the universe that has incurred instantaneous acceleration and is now moving past him at close to the speed of light.

He carries out internal dynamic experiments involving “the phenomena of electrodynamics as well as of mechanics” but achieves no result that permits him to determine if his ship is moving with uniform velocity or if it is ‘at rest’ so by giving preference to his reference frame over that of the universe he determines that the universe must have incurred instantaneous acceleration and is now moving past him at that velocity.

It is my understanding that the Galilean principle of relativity showed that a state of rest or of uniform motion cannot be detected without reference to an outside point! i.e. without the astronaut being able to look out of his window.

On the basis that the astronaut is of the opinion that he has stopped moving and that it is the universe that is now moving past him he must also be of the opinion that it has taken a force of energy that was greater than the infinite mass of the universe to make it move!

Not only that, but the universe has instantaneously accelerated to near-light speed! What effect could that near-infinite force of acceleration have had on his twin?

If, at the very instant that he lifts his foot off the gas pedal, everything in the universe has been made to instantaneously accelerate to near-light speed why wasn’t his ship affected by that greater-than-infinite force?

Could it have been the infinitesimally weaker force generated by his ship’s engine which overcame that greater-than-infinite force of energy?

"According to his calculations"? If the astronaut is moving inertially, then in his own rest frame, it is the Earth that has the large velocity while he is at rest, and the time dilation formula must work the same way in every inertial frame according to the first postulate of relativity, so he must calculate that the Earth's clock is ticking 40,000 times slower than his own if he does the calculations relative to his own inertial rest frame, not 40,000 times faster.

The last few lines are my very argument!

The claim to which my posting refers is that the astronaut insists that his clock is not ticking over at the rate of 40,000 seconds for each Earth second but that the Earth clocks are ticking over at the rate of 40,000 seconds for each of his seconds!

You appear to have badly misunderstood the principle that the laws of physics work the same in all inertial reference frames, which was one of the two basic postulates of SR that Einstein put forward in his 1905 paper. Every frame must predict that clocks moving in that frame slow down, not speed up. Two observers moving inertially relative to one another will each calculate that the other one's clock is running slower than their own.

However, in his chapter 4 Einstein points out that, irrespective of the fact that clocks A and B are, effectively (ignoring the fact that in order to move to B’s location clock A must have incurred acceleration) “moving inertially relative to one another” an observer accompanying clock A, regardless of his calculations that B is running slower than his clock, finds upon his arrival at B’s location that B was not running slower than his own clock as predicted by his calculations but that his own clock was running slower than clock B (alternatively, according to some people, that B was running faster than his clock) resulting in A lagging behind B not B lagging behind A.

Your comment that “Two observers moving inertially relative to one another will each calculate that the other one's clock is running slower than their own.” is, of course, the origin of the clock paradox that Einstein sought to overcome with his 1918 article wherein he insisted that the only way those clocks can be accurately compared is if one of them is made to move to the other clock’s location which requires the former to undergo several periods of acceleration.

That relocated clock is, in my opinion, analogous to Einstein’s chapter 4 clock that follows a polygonal path.

It is interesting to note that when Galileo wrote his book ‘Two New Sciences’ he was already in trouble with authorities so he presented it as a hypothetical discussion between a teacher and two of his students.

Einstein similarly wrote his 1918 article in the form of a purely hypothetical conversation (this time between a relativist and a critic) perhaps in order to prevent criticism from his opponents, colleagues and authorities for his application of an aspect of general theory (gravitational acceleration) as a solution to a special theory related paradox.

He had already been criticised by his associates (particularly Max Abrahams) for suggesting, in the introduction to general theory, that the special theory law of the constancy of the speed of light required modification and, in his 1916 book ‘Relativity, the Special and General Theory’ that the law of the constancy of the speed of light was not valid.

And despite this seemingly counterintuitive result, all frames will nevertheless get identical predictions about all local events like what two clocks read at the moment they pass next to one another...

In chapter 4 Einstein makes no suggestion that clocks A and B are inertial reference frames that pass next to one another but points out that clock A is made to move toward, and come to a stop, alongside clock B as does his 1918 depicted clock!

As far as I am concerned, Einstein’s chapter 4 depictions (specifically his reference to a clock that is made to move in any polygonal path) is directly equivalent to his 1918 attempted negation of the twin paradox.

Relativity deals with plenty of instantaneous quantities such as instantaneous velocity, as do all dynamical theories of physics expressed using calculus.

The fact that the mathematical propositions of relativity and all dynamical theories of physics expressed using calculus deal with plenty of instantaneous quantities such as instantaneous velocity does NOT prove that they are reality!

“As far as the propositions of mathematics are certain, they do not refer to reality.” (A. Einstein)

So do you agree that if the astronaut is moving inertially, then in his inertial rest frame he is at rest while the planet is moving towards him at high speed, therefore in this frame his own clock is ticking at the normal rate while the planet's clock is ticking slower?

NO! I most certainly do NOT!

I do not believe that an intelligent astronaut would adopt a Henny Penny attitude.

I believe that an intelligent astronaut, having accelerated to a relativistic velocity and having taken his foot off the gas pedal, would realize that he is still moving - either away from, or toward, the planet.

I believe that an intelligent astronaut would be of the opinion that there is no such thing as a force of energy that is greater than infinite that could cause the Earth, and the entire universe, to suddenly - instantaneously - start moving at close to the speed of light when he takes his foot off the gas pedal.

Conversely - I assume that somebody would be able to provide a mathematical proposition which ‘proves’ the idea of a force that is greater than infinite and that the Earth, along with the universe, could physically cope with being instantaneously accelerated to near-light speed.

Having initially set out to establish the infallible nature of mathematics Bertrand Russell was reluctantly forced to admit that “Mathematics may very well be a subject in which we never know what we are talking about nor that what we are saying is true.”

Furthermore, as I have pointed out several times, the claim to which I refer is not that the astronaut believes that “his own clock is ticking at the normal rate while the planet’s clock is ticking slower” but insists that his own clock is ticking at the normal rate while the planet’s clock is ticking FASTER!

He claims that this is the reason why his clock lags behind the Earth clock upon his return.

The astronaut, being of the opinion that, during his return journey, the Earth clock is ticking slower than his own clock would be surprised to find, upon his return the the planet, that his clock lags behind the Earth clock whereas, according to his calculations, it should be the Earth clock that (having, as you point out, ticked over at a slower rate than his clock) should lag behind his clock - but it doesn’t!

This is why the claim is that he finds that his clock lags behind the Earth clock due to the ‘fact’ that it is the Earth clock that has ticked over at a faster rate than his clock - not at a slower rate.

 

[cos]

I don't think you can break down the total time dilation into a linear sum of SR velocity-based time dilation and GR gravitational time dilation in the way you're suggesting.

I didn’t suggest that - Clifford Will did! Take up your argument with him.

I think the only way to calculate the total time elapsed on the clocks is to do an integral over the path of each clock in curved spacetime;

I’m not suggesting that we “calculate the total time elapsed on the clocks.”

Einstein pointed out that the total time elapsed is not ‘calculated’ but is observed!

So are you saying you do think he meant "more slowly at every instant in an objective frame-independent sense"? If so, what you're saying goes against the basics of relativity, and is objectively wrong, it's not just a matter of opinion. On the other hand, if you don't mean to imply that one clock is going more slowly than another at every moment in a frame-independent sense, then please spell out explicitly what you do mean.

What I mean is that in my opinion when Einstein wrote that a clock at the equator “must go more slowly” than a clock at one of the poles he meant that the equatorial clock will continuously tick over at a slower rate than the polar clock.

But as I said, visual appearances are completely different than time dilation. If you talk about what would be happening in the inertial rest frame of the observer at the pole, in this case it's true that the clock at the equator is ticking slower than his own clock. However, there are other equally valid inertial frames where at certain times the clock at the pole is ticking slower than the clock at the equator (because the clock at the pole has a higher speed at those times in that frame).

On the basis that despite my requests you continue to waste my time talking about other inertial frames that have absolutely no relevance whatsoever to the matter on hand this discussion is terminated.

 

[matheinste]

cos .

Quote:-

--I believe that an intelligent astronaut, having accelerated to a relativistic velocity and having taken his foot off the gas pedal, would realize that he is still moving - either away from, or toward, the planet.----

Yes,he can look and see the Earth moving relative to him (or vice versa ), but he cannot determine if he is "moving" in an absolute sense. For all he knows he and the Earth may have initially been "moving" and his acceleration may have brought him to "rest" while the Earth carries on "moving".

This is absolutely fundamental in SR.

Matheinste
-

 

[JesseM]

So I assume that it is quite meaningless for someone to claim that the astronaut is of the opinion that the Earth clock is physically ticking over at a faster rate than it was before he started moving?

I already said that this was not what I was claiming.

I assume that by ‘different frames’ you are referring to frames other than those of the astronaut however I reiterate that I am not in the slightest bit interested in what ‘different frames’ agree or disagree about but purely and simply what the astronaut determines.

The astronaut can "determine" the coordinates of events in any frame he wants, there is no physical reason he must use his own rest frame.

Einstein makes it quite clear that there is no reason to prefer one inertial frame's perspective over any other, and any relativity textbook you might care to look at should make this clear as well.

The claim by the astronaut that his clock is ticking over at its normal rate thus that the eventual time variation between his clock and his twin’s clock can only have occurred as a result of the Earth clock ticking over at a faster rate than it was before he started moving

An inertial frame is a system of coordinates that covers all of spacetime, and where any fixed coordinate position has been moving inertially. There is no inertial coordinate system where the "Earth clock is ticking over at a faster rate than it was before he started moving". If the astronaut chooses to use a coordinate system where he is at rest as the Earth approaches him, then in this coordinate system the astronaut was not at rest before he accelerated, only after accelerating. And in this inertial coordinate system the Earth was always moving inertially, it never changed velocities.

indicates that he is giving preference to his reference frame over that of the Earth.

"Preference" means saying that statements made in one coordinate system are somehow more physically correct than statements made in another coordinate system. I never said that the astronaut should say anything like that about statements in his frame. The astronaut isn't saying that his own clock is ticking at a normal rate while the Earth's clock is ticking slower in any objective, frame-independent sense; he's just saying it's what's happening in one particular inertial frame, the frame where he is at rest during the journey (but not before). The astronaut would certainly acknowledge that in the frame where the Earth is at rest, it is his clock that's ticking slower than the Earth's clock. So, he is not "preferencing" either frame, he's just acknowledging that in relativity neither statement is more physically correct than the other, they are both just the perspectives of two different equally valid inertial reference frames.

On the basis that he determines that every other reference frame in the universe is moving relatively to him he is of the opinion that his is the only reference frame in the entire universe that is ‘at rest’.

Not in any objective sense, just from the perspective of that frame. Do you acknowledge that in relativity there can be no single "real truth" about what object is at rest, that different frames treat different objects as being at rest and it's understood that all statements about rest are frame-dependent?

A brilliant young student living in a small town is selected for astronaut training however as the aeroplane taking him on his very first flight lifts off he starts screaming “The sky is falling! The sky is falling!” What promised to be a very exciting career ends up in a rubber room.

If both the Earth and the aeroplane are moving inertially, in relativity there is no objective truth about whether the ground is at rest and the aeroplane is moving up or the the aeroplane is at rest and the ground is moving down. But since you seemed to be confused about this point earlier, this does not mean there is any valid inertial frame where the ground was at rest while the aeroplane was on the ground, then suddenly started moving downward. An inertial frame is moving at the same velocity for all time, so in the frame where the aeroplane was at rest before taking off and the ground was moving downward, it must have been true that the ground was always moving downward at the same constant velocity (again, assuming for the sake of the argument that the Earth is moving inertially), and the aeroplane was originally moving downward along with it until it accelerated and came to rest.

An astronaut is in a ship prior to takeoff. He hears the command “ignition” and feels a tremendous force of acceleration pushing him back into his seat.

He keeps accelerating and having attained an instantaneous velocity of close to the speed of light sees the universe appearing to flash past his window in a blur.

He takes his foot off the gas pedal but according to the way of thinking that you presented he is then of the opinion that he is, at that very instant, no longer moving but that it is the universe that has incurred instantaneous acceleration and is now moving past him at close to the speed of light.

Again you are repeating the same confusion as above. Inertial frames move at constant speed for all time, so if the stars around him are moving inertially, there is no valid inertial frame where the stars were originally at rest and then suddenly accelerated to relativistic speed. But there is a valid inertial frame where these stars have been moving at the same relativistic speed for all time, and the astronaut was originally moving along with them, but then when he accelerated he came to rest in this frame. This frame is just as good as the frame where the astronaut was originally at rest and then moving at relativistic speed after acceleration, the first postulate of relativity says that we have no grounds for saying either perspective is more physically "true" than the other.

He carries out internal dynamic experiments involving “the phenomena of electrodynamics as well as of mechanics” but achieves no result that permits him to determine if his ship is moving with uniform velocity or if it is ‘at rest’ so by giving preference to his reference frame over that of the universe he determines that the universe must have incurred instantaneous acceleration and is now moving past him at that velocity.

Nope, this is just confused reasoning. If he felt the G-forces when accelerating, then all inertial frames agree it was him that accelerated, not the stars around him. They disagree about his original velocity before accelerating, and whether his speed increased or decreased after the acceleration, but they all agree that the inertial stars maintained a constant velocity throughout. If you try to construct a non-inertial frame where the astronaut was at rest both before and after accelerating, the first postulate does not apply to this frame, and indeed he could do experiments during the accelerating phase which would have different results than they would when he was moving inertially, so the laws of physics don't appear to work the same way in this non-inertial frame.

It is my understanding that the Galilean principle of relativity showed that a state of rest or of uniform motion cannot be detected without reference to an outside point! i.e. without the astronaut being able to look out of his window.

Your understanding is incorrect, the principle of relativity says that the whole idea of distinguishing "rest" from "uniform motion" is meaningless. Different inertial frames disagree about which objects are at rest and which are in motion, and all inertial frames are on equal footing as far as relativity is concerned.

"According to his calculations"? If the astronaut is moving inertially, then in his own rest frame, it is the Earth that has the large velocity while he is at rest, and the time dilation formula must work the same way in every inertial frame according to the first postulate of relativity, so he must calculate that the Earth's clock is ticking 40,000 times slower than his own if he does the calculations relative to his own inertial rest frame, not 40,000 times faster.

The last few lines are my very argument!

The claim to which my posting refers is that the astronaut insists that his clock is not ticking over at the rate of 40,000 seconds for each Earth second but that the Earth clocks are ticking over at the rate of 40,000 seconds for each of his seconds!

Either one can be true depending on which inertial frame you use--in the rest frame of the Earth, 40,000 seconds go by on the Earth clock for every one second that goes by on the astronaut's clock, while in the inertial frame where the astronaut is at rest during the journey, 40,000 seconds go by on the astronaut's clock for every one second that goes by on the Earth's clock. As always, there is no reason to say one inertial frame's perspective is more physically true than another's.

However, in his chapter 4 Einstein points out that, irrespective of the fact that clocks A and B are, effectively (ignoring the fact that in order to move to B’s location clock A must have incurred acceleration) “moving inertially relative to one another” an observer accompanying clock A, regardless of his calculations that B is running slower than his clock, finds upon his arrival at B’s location that B was not running slower than his own clock as predicted by his calculations but that his own clock was running slower than clock B (alternatively, according to some people, that B was running faster than his clock) resulting in A lagging behind B not B lagging behind A.

Einstein only says that clock A will be behind clock B when they meet, but this does not prove that clock A was running slower. Do you understand what is meant by the phrase "relativity of simultaneity"? Do you understand that if two clocks are synchronized in their own rest frame, that means that in other inertial frames they'll be out-of-sync? There are perfectly valid frames where clock B was running slower, but in these frames B's time was already well ahead of A's time at the moment A accelerated, so because of this "head start" B is still ahead of A's when A meets it, despite the fact that B was ticking slower. If I place a clock 1 mile away from you that reads 5 PM when you start to walk towards it, and that clock is also running at half the correct rate, and if your clock reads 3 PM at the moment you start walking towards it, and your clock is ticking at the normal rate, then if it takes you half an hour to reach the other clock, your clock will read 3:30 and the other clock will read 5:15. In this example it's clear that despite the fact that the other clock was running slower than yours, it's still ahead of yours when you meet because it was already ahead by a lot when you started out.

Your comment that “Two observers moving inertially relative to one another will each calculate that the other one's clock is running slower than their own.” is, of course, the origin of the clock paradox that Einstein sought to overcome with his 1918 article wherein he insisted that the only way those clocks can be accurately compared is if one of them is made to move to the other clock’s location which requires the former to undergo several periods of acceleration.

No, you missed the point of the thought-experiment, Einstein certainly wasn't saying that bringing the two clocks together would settle the question of which was "really" ticking slower during the initial phase when they were moving apart inertially, that would contradict the first postulate of relativity. It is true that the fact that one clock has to accelerate explains why one clock has elapsed less time in total when they reunite, but different frames can disagree on which clock was ticking faster during the initial phase when they were moving apart, yet they'll still all make the same prediction that the clock that accelerates will have elapsed less time in total when they reunite.

In chapter 4 Einstein makes no suggestion that clocks A and B are inertial reference frames that pass next to one another but points out that clock A is made to move toward, and come to a stop, alongside clock B as does his 1918 depicted clock!

I don't know what "no suggestion that clocks A and B are inertial reference frames" means. A clock is a physical object, an inertial reference frame is a coordinate system.

The fact that the mathematical propositions of relativity and all dynamical theories of physics expressed using calculus deal with plenty of instantaneous quantities such as instantaneous velocity does NOT prove that they are reality!

First of all, we're dealing with thought-experiments here. Second of all, if space and time are continuous, and an object has a definite position x(t) at all times, the instantaneous velocity is just defined as dx/dt. If you're arguing that maybe space and time are not infinitely divisible, feel free to just talk about the nearly instantaneous velocity defined as (change in position)/(change in coordinate time) for the smallest possible time-interval you're willing to accept, and likewise we can talk about nearly instantaneous rate of clock ticking defined as (time elapsed on clock)/(change in coordinate time).

So do you agree that if the astronaut is moving inertially, then in his inertial rest frame he is at rest while the planet is moving towards him at high speed, therefore in this frame his own clock is ticking at the normal rate while the planet's clock is ticking slower?

NO! I most certainly do NOT!

I do not believe that an intelligent astronaut would adopt a Henny Penny attitude.

I believe that an intelligent astronaut, having accelerated to a relativistic velocity and having taken his foot off the gas pedal, would realize that he is still moving - either away from, or toward, the planet.

There is no such thing as absolute motion in relativity. If you want to argue that relativity is wrong and that there is some objective truth about whether an object is moving or at rest, this is not the forum to do so--see the thread IMPORTANT! Read before posting

I believe that an intelligent astronaut would be of the opinion that there is no such thing as a force of energy that is greater than infinite that could cause the Earth, and the entire universe, to suddenly - instantaneously - start moving at close to the speed of light when he takes his foot off the gas pedal.

Again, this is a misunderstanding of yours. There is no inertial frame where the astronaut is at rest both before and after the acceleration, I was talking only about a frame where the astronaut was at rest after accelerating, while the planet he took off from was moving inertially at the same speed both before and after.

Furthermore, as I have pointed out several times, the claim to which I refer is not that the astronaut believes that “his own clock is ticking at the normal rate while the planet’s clock is ticking slower” but insists that his own clock is ticking at the normal rate while the planet’s clock is ticking FASTER!

There is no frame where the rate the planet's clock is ticking changes when the astronaut accelerates. It is true, though, that in the planet's own rest frame the astronaut's clock is ticking slower than the planet's clock after the astronaut accelerates, which is the same as saying that in this frame the planet's clock is ticking faster than the astronaut's after the astronaut accelerates, though this is not to say the planet's clock is ticking faster than it was before the astronaut took off in this frame.

The astronaut, being of the opinion that, during his return journey, the Earth clock is ticking slower than his own clock would be surprised to find, upon his return the the planet, that his clock lags behind the Earth clock whereas, according to his calculations, it should be the Earth clock that (having, as you point out, ticked over at a slower rate than his clock) should lag behind his clock - but it doesn’t!

If the astronaut calculates things from the perspective of the inertial frame where he is at rest during the return trip, then again this is a matter of the relativity of simultaneity--in this frame the Earth's clock is already well ahead of his own at the moment the astronaut begins the journey, so even though the Earth's clock is ticking slower than his throughout the journey, it will still be ahead of his clock when he reaches the amount. If you factor in both the relativity of simultaneity and the time dilation factor, you'll get exactly the same prediction in this frame about how much the Earth clock is ahead as you would if you calculated things in the Earth's rest frame.

 

[JesseM]

On the basis that despite my requests you continue to waste my time talking about other inertial frames that have absolutely no relevance whatsoever to the matter on hand this discussion is terminated.

I continue to bring it up because you are explicitly contradicting basic principles of SR by saying there is a definite truth about which of two clocks is ticking slower in thought-experiments like the one where the astronaut travels from a distant planet to Earth, and my point is that different inertial frames disagree about which of two clocks is ticking slower, yet they all make the same predictions about physical events (like what two clocks read when you bring them together) and it's a basic principle of SR that all inertial frames are equally valid. If you continue to talk as though there is an objective truth about which clock is ticking slower without being willing to listen to counterarguments explaining your error (and these counterarguments necessarily require you to look at the same situation in multiple inertial frames), then you are violating the rules of this forum as laid out in the IMPORTANT! Read before posting thread.

 

[cos]

cos; The dilation only applies to the ship and its contents, thus the pilot cannot detect the difference within his frame.

In paragraph 1, chapter 4, Einstein wrote that clock A - moved to clock B’s location - will lag behind B. In paragraph 2 Einstein extended this event to clock A moving in any polygonal line then, in paragraph 3, he again extended the phenomenon to a clock that is moving in a closed curve around another clock then that a clock at the equator “must go more slowly” than a clock at one of the poles.

It is my understanding that by the term “must go more slowly” Einstein was suggesting that clock A ticked over at a slower rate than (i.e. incurred time dilation relatively to) clock B.

I believe, although he did not state this, that Einstein was of the opinion that clock A (in paragraph 1) “must go more slowly” (i.e. tick over at a slower rate than) clock B.

An observer accompanying clock A who has read and fully accepts Einstein’s paragraph 1, chapter 4, could take Einstein’s word for it and realize that his clock is ‘going more slowly’ (ticking over at a slower rate) than B irrespective of the fact that his clock (A) appears to have remained unchanged.

Although applicable to general theory - a person at sea level should determine that an identical clock at that location is ticking over at the same rate as his own clock. If he moves to the top of a nearby mountain he could insist (on the basis that a clock at that location is also ticking over at the same rate as his clock) that time does not vary depending on a clock’s location in a gravitational tidal area (as GR shows) on the basis that both clocks tick over at the same rate as his clock OR he could apply his knowledge of the Wallops Island experiment and realize that his watch has also been affected by its location in a different gravitational tidal area irrespective of the fact that it’s rate of operation appears to have remained unchanged.

When Hafele and Keating conducted the first leg of their experiment they could either assume (having returned to Washington to find, as Einstein predicted, that their clocks lagged behind the clocks that had remained ‘at rest’ and having taken into account and eliminating any variations due to gravitational time distortion effects) that the laboratory clocks physically ticked over at a faster rate than they did prior to the flight commencing OR that their clocks physically ticked over at a slower rate than they did prior to the commencement of the flight as per Einstein’s chapter 4.

I am of the opinion that Hafele and Keating (et al) would have accepted the latter explanation irrespective of the fact that, during the flight, their clocks appeared to them to be ticking over at an unchanged rate in the same way that an observer at the top of a mountain could insist that his clock is ticking over at an unchanged rate compared to when he was at sea-level.

Confucius wrote:-

“Knowledge is one-dimensional, the proper application of knowledge is multi-dimensional. Only the extremely wise, and the exceptionally foolish, are not prepared to change.”

Assuming that the mountain-ascending observer is aware of, and fully accepts, the results of the Wallops Island experiment he could (and should) apply that knowledge thus realize that although his clock appears to have remained unaffected it is actually, physically, ticking over at a faster rate than it was when he was at sea-level.

Although an observer accompanying Einstein’s chapter 4 clock A could be of the opinion that his clock’s rate of operation remains unchanged he could also (assuming that he has read and accepted Einstein’s chapter 4 thought experiment as well as Einstein’s 1918 negation of the twin paradox and the reports pertaining to the HKX) realize that his clock is actually, physically, ‘going more slowly’ (ticking over at a slower rate) than it was before he started moving.

You may, perhaps, have missed my original posting which included the reason for that submission:-

“I have read several interpretations of the twin paradox one of which insists that the traveler’s clock does not (as Einstein expressed it in chapter 4) ‘go more slowly’ than the Earth clock but that the Earth clock, from the traveler’s point of view, ticks over at a faster rate than his own clock but only during the astronaut’s period of acceleration following turn-around however it is my understanding that the concept of time contraction was, for Einstein, an anathema.”

If he looks out, he should see a polarized universe, events forward happening faster and events rearward happening slower, a scenario which is not normal.

This, of course, is a result of Doppler shift which some postings regarding the twin paradox dismiss retaining the relativistic time dilation effect however I fully appreciate that during acceleration following turn-around an astronaut would observe that the Earth clock appears to be ticking over at a proportionally increasing faster rate however for him to insist that what he sees is reality - that the Earth clock is physically ticking over at a faster rate than it was before he started accelerating is, in my opinion, asinine!

It is to be noted that this ludicrous claim insists that the variations in the rate of operation of the Earth clock only takes place as the astronaut accelerates however the Doppler shift that the astronaut observes at the instant that he starts to take his foot off the gas pedal is precisely the same as it is when he has removed his foot.

In correspondence at that time (about the mid-90s) the author of that claim responded to my question about what happens when the astronaut stops accelerating and is moving with uniform velocity insisting that the astronaut’s clock is then ticking over at the same rate as the Earth clock! He also insisted that there is no variation in the rates of operation of those clocks as the astronaut moves away from (or, with uniform velocity) toward the planet and continued to insist that the total amount of the eventual discrepancy between the two clocks all takes place during acceleration following turn around.

When I asked him what would happen if the astronaut is transporting a light clock and, in lieu of landing back on the planet, traveled past same and his response was that the light clock would not necessarily be ticking over at a slower rate than an Earth-bound light clock.

One of my reasons for submitting the original posting was to see if anyone in this group agreed with such nonsense.

Of course there is the remote possibility that the author of that nonsense and his supporting cronies may have realized their error as the result of my arguments and have dropped the idea - but I doubt it.

All other clocks do not change rates, because the astronaut initiated the motion

That’s what I said; thank you for agreeing with me.

 

[JesseM]

Although an observer accompanying Einstein’s chapter 4 clock A could be of the opinion that his clock’s rate of operation remains unchanged he could also (assuming that he has read and accepted Einstein’s chapter 4 thought experiment as well as Einstein’s 1918 negation of the twin paradox and the reports pertaining to the HKX) realize that his clock is actually, physically, ‘going more slowly’ (ticking over at a slower rate) than it was before he started moving.

As I said, this claim that any clock is "actually, physically" going more slowly than another contradicts relativity (because all inertial frames are equally valid, and different inertial frames disagree about which clock is ticking more slowly), and if you aren't willing to listen to people explain your error, you're violating the rules of the forum, which is not meant to be a place for people to promote ideas that go against mainstream physics. Here again is my explanation of why you are free to use an inertial frame where A is at rest and B is moving, in which case B is ticking more slowly than A, but B will still be ahead when they meet because of the relativity of simultaneity:

Einstein only says that clock A will be behind clock B when they meet, but this does not prove that clock A was running slower. Do you understand what is meant by the phrase "relativity of simultaneity"? Do you understand that if two clocks are synchronized in their own rest frame, that means that in other inertial frames they'll be out-of-sync? There are perfectly valid frames where clock B was running slower, but in these frames B's time was already well ahead of A's time at the moment A accelerated, so because of this "head start" B is still ahead of A's when A meets it, despite the fact that B was ticking slower. If I place a clock 1 mile away from you that reads 5 PM when you start to walk towards it, and that clock is also running at half the correct rate, and if your clock reads 3 PM at the moment you start walking towards it, and your clock is ticking at the normal rate, then if it takes you half an hour to reach the other clock, your clock will read 3:30 and the other clock will read 5:15. In this example it's clear that despite the fact that the other clock was running slower than yours, it's still ahead of yours when you meet because it was already ahead by a lot when you started out.

If you continue to repeat these sorts of claims that one clock is "physically" ticking slower, and ignore explanations of why this is incorrect according to SR, I'll report your posts to the moderators.

 

[cos]

cos .

Quote (cos):-

--I believe that an intelligent astronaut, having accelerated to a relativistic velocity and having taken his foot off the gas pedal, would realize that he is still moving - either away from, or toward, the planet.----(unquote)

Yes,he can look and see the Earth moving relative to him (or vice versa ), but he cannot determine if he is "moving" in an absolute sense. For all he knows he and the Earth may have initially been "moving" and his acceleration may have brought him to "rest" while the Earth carries on "moving".

This is absolutely fundamental in SR.

Matheinste
-

"...he and the Earth may initially been 'moving'" relatively to what? The CBR? Newton's absolute rest?

On the basis that "This is absolutely fundamental in SR" what does SR suggest the Earth could have been moving relatively to?

I see absolutely no difference whatsoever to the astronaut (having come to a stop) moving toward the Earth and Einstein's paragraph 1, chapter 4, reference to clock A being made to move to clock B's location.

Is it possible that Einstein's clocks A and B could also have initially been moving relatively to some form of fundamental reference frame thus that whilst clock A is moving toward B with uniform velocity it would have been 'at rest' relatively to that FRF thus that it would not, as Einstein posited, eventually be found to lag behind clock B on the basis that it was clock B that "carried on moving" thus that B would be found to lag behind A?

Are you of the opinion that Einstein was wrong in suggesting that A will lag behind B on the basis that they could both have initially been moving thus that A came to 'rest'?

 

[JesseM]

"...he and the Earth may initially been 'moving'" relatively to what? The CBR? Newton's absolute rest?

Pretty sure that was matheinste's point, that there can be no evidence for any absolute notion of motion in relativity, and similarly no evidence for any objective truth about which of two clocks is ticking more slowly in an absolute sense.

On the basis that "This is absolutely fundamental in SR" what does SR suggest the Earth could have been moving relatively to?

What's fundamental is that there is no absolute truth about how fast an object is moving; your comment that the astronaut "would realize that he is still moving" seemed to say otherwise (it is perfectly valid to use an inertial frame where the astronaut comes to rest after finishing his acceleration, so in this frame he is not moving after that, and this inertial frame's perspective is no more or less valid than any other's).

Are you of the opinion that Einstein was wrong in suggesting that A will lag behind B on the basis that they could both have initially been moving thus that A came to 'rest'?

As I keep saying, if A and B initially had synchronized clocks in their mutual rest frame before A accelerated, then in a different frame where A was at rest after accelerating, B's clock was already significantly ahead of A's before A accelerated, so even though B ticks more slowly in this frame as it approaches A, it will still be ahead of A when they meet. This inertial frame's perspective is no more or less valid than any other's, therefore it is just as valid to say B was running slower than A as they approached each other as it is to say A was running slower than B as they approached each other.

 

[atyy]

I see absolutely no difference whatsoever to the astronaut (having come to a stop) moving toward the Earth and Einstein's paragraph 1, chapter 4, reference to clock A being made to move to clock B's location.

Referring to your first post, clocks B and A are specified to be "synchronous", a technical term. Is the astronaut, having come to a stop, also "synchronous" with the non-rotating non-gravitating Earth? (Non-gravitating since only special relativity is being discussed, and non-rotating to save the Earth twin from being spun off into space without gravity.)

 

[matheinste]

Hello cos

Quote:-

----"...he and the Earth may initially been 'moving'" relatively to what? The CBR? Newton's absolute rest?----

Relative to any non-accelerating object.

Matheinste

 

[cos]

Referring to your first post, clocks B and A are specified to be "synchronous", a technical term. Is the astronaut, having come to a stop, also "synchronous" with the non-rotating non-gravitating Earth? (Non-gravitating since only special relativity is being discussed, and non-rotating to save the Earth twin from being spun off into space without gravity.)

Let us imagine that the astronaut's outward journey is directly away from the South Pole and, having come to a stop, he is now looking back at a very large clock at that location which is mounted on a platform that allows it to remain stationary from the traveler's point of view (i.e. it is not spinning around with the planet).

According to my interpretation of Einstein's chapter 4, paragraph 1, his clock (Einstein's clock A) will then lag behind the Earth clock (Einstein's clock B) by .5tv²/c2. When he determines a lag created by the time that it takes that light to reach him as well as any gravitational time dilation created by the Earth's mass he can calculate the exact amount of that lag however his clock will then be ticking over at the same rate as the Earth clock on the basis that they are Einstein's paragraph 1, chapter 4, 'points A and B of K.

He then adjusts his clock so that it reads the same time as the Earth clock so yes, the astronaut's clock is (temporarily) synchronous with the Earth clock and whilst the Earth clock's rate of operation is affected by it's location in a gravitational tidal area the astronaut attains Einstein's chapter 4 (purely hypothetical) instantaneous velocity (of near-light speed for the astronaut) ergo his clock is then 'going more slowly' than the Earth clock by a factor of .5tv²/c2 and he will arrive back on the planet with his clock lagging behind the Earth clock by the same amount as it did at the end of his outward-bound trip.

Alternatively, if the astronaut (in a suitably equipped ship), accelerates at perhaps 100g his clock will very soon be 'going more slowly' than the gravitationally affected Earth clock.

A version of your depiction is that Einstein's paragraph 1, chapter 4, clocks A and B are twin astronaut's each in identical ships that, unlike Einstein's clocks A and B, are initially stationary alongside, and synchronous with, each other whereupon A moves in Einstein's paragraph 2 polygonal path (i.e. away from then back to B's location).

At the end of his 'outward-bound' trip A's clock, although lagging behind, is ticking over at the same rate as B's clock so A adjusts his clock in accordance with the calculated lag factor and they are once again synchronous.

 

[atyy]

Let us imagine that the astronaut's outward journey is directly away from the South Pole and, having come to a stop, he is now looking back at a very large clock at that location which is mounted on a platform that allows it to remain stationary from the traveler's point of view (i.e. it is not spinning around with the planet).

According to my interpretation of Einstein's chapter 4, paragraph 1, his clock (Einstein's clock A) will then lag behind the Earth clock (Einstein's clock B) by .5tv²/c2. When he determines a lag created by the time that it takes that light to reach him as well as any gravitational time dilation created by the Earth's mass he can calculate the exact amount of that lag however his clock will then be ticking over at the same rate as the Earth clock on the basis that they are Einstein's paragraph 1, chapter 4, 'points A and B of K.

He then adjusts his clock so that it reads the same time as the Earth clock so yes, the astronaut's clock is (temporarily) synchronous with the Earth clock and whilst the Earth clock's rate of operation is affected by it's location in a gravitational tidal area the astronaut attains Einstein's chapter 4 (purely hypothetical) instantaneous velocity (of near-light speed for the astronaut) ergo his clock is then 'going more slowly' than the Earth clock by a factor of .5tv²/c2 and he will arrive back on the planet with his clock lagging behind the Earth clock by the same amount as it did at the end of his outward-bound trip.

Alternatively, if the astronaut (in a suitably equipped ship), accelerates at perhaps 100g his clock will very soon be 'going more slowly' than the gravitationally affected Earth clock.

A version of your depiction is that Einstein's paragraph 1, chapter 4, clocks A and B are twin astronaut's each in identical ships that, unlike Einstein's clocks A and B, are initially stationary alongside, and synchronous with, each other whereupon A moves in Einstein's paragraph 2 polygonal path (i.e. away from then back to B's location).

At the end of his 'outward-bound' trip A's clock, although lagging behind, is ticking over at the same rate as B's clock so A adjusts his clock in accordance with the calculated lag factor and they are once again synchronous.

So which twin is older when they reunite?

 

[phyti]

JesseM;

As I said, this claim that any clock is "actually, physically" going more slowly than another contradicts relativity

Then what was measured in the prolonged half life of muons?

 

[JesseM]

Then what was measured in the prolonged half life of muons?

The muons have a slowed rate of decay in our frame where they are moving at relativistic speed, but they aren't slowed down in any objective, frame-independent sense. You can analyze the behavior of muons perfectly well in a frame where the muons are at rest and the Earth is moving at relativistic speed, and you get the exact same prediction about the point on Earth where they decay. Have a look at this page which analyzes muons created in the upper atmosphere in both the Earth frame and the muon frame; in the Earth frame, the muons are able to make it to the surface because their decay is slowed down, while in the muon frame, they decay at the normal rate but they are able to make it to the surface because the distance from the upper atmosphere to the surface is shrunk due to Lorentz contraction.

If you don't understand that any situation in special relativity can be analyzed in any inertial frame using precisely the same laws of physics (so in each frame you assume clocks moving faster in that frame are slowed down by a greater amount) and you'll always get all the same predictions about local physical events (like whether a muon reaches the surface, or what two clocks read at the moment they pass next to each other), you've missed one of the most central conceptual ideas of SR--this is the meaning of the first postulate.

 

[phyti]

JesseM;

in the Earth frame, the muons are able to make it to the surface because their decay is slowed down,

Here you gave a good answer.

while in the muon frame, they decay at the normal rate but they are able to make it to the surface because the distance from the upper atmosphere to the surface is shrunk due to Lorentz contraction.

Here you'll have to explain what physical process shrinks space!
To my knowledge, it has never been experimentally verified.

 

[JesseM]

Here you'll have to explain what physical process shrinks space!

What do you mean by "shrinks space"? It's just a fact about the coordinate systems given by the Lorentz transformation that objects have a shorter coordinate length in a frame where they're moving than in their rest frame, this has nothing to do with physics, it would be true even if you used these coordinate systems in a universe governed by Newtonian laws, for example. Where physics enters into it is that the equations of all known fundamental laws have the property of being invariant under the Lorentz transform, which means they'll look the same in all the different inertial coordinate systems given by the Lorentz transform--this means that if two observers construct physical rulers at rest in their own frame using identical procedures, then the coordinate distance between ends of these identically-constructed rulers will be identical in the rulers' rest frame (this would not be true in a universe with Newtonian laws), and from there it's just a property of the coordinate transformation that if you have two objects moving relative to one another that have the same coordinate length in their own rest frame, in each one's own rest frame the other one will have a shorter coordinate length.

To my knowledge, it has never been experimentally verified.

It's just a mathematical matter to check if some equations of physics are Lorentz-invariant, if they are that means they will be the same in different frames given by the Lorentz transform, and everything I said above will apply. So, to the extent that the equations we have for quantum field theory are Lorentz-invariant and all the tests have supported the idea that systems obey these equations, this is a form of indirect evidence for Lorentz contraction. The page on evidence for special relativity lists another form of evidence for length contraction:

A current-carrying wire is observed to be electrically neutral in its rest frame, and a nearby charged particle at rest in that frame is unaffected by the current. A nearby charged particle that is moving parallel to the wire, however, is subject to a magnetic force that is related to its speed relative to the wire. If one considers the situation in the rest frame of a charge moving with the drift velocity of the electrons in the wire, the force is purely electrostatic due to the different length contractions of the positive and negative charges in the wire (the former are fixed relative to the wire, while the latter are mobile with drift velocities of a few mm per second). This approach gives the correct quantitative value of the magnetic force in the wire frame. This is discussed in more detail in: Purcel, Electricity and Magnetism. It is rather remarkable that relativistic effects for such a tiny velocity explain the enormous magnetic forces we observe.

 

[cos]

Hello cos

Quote:-

----"...he and the Earth may initially been 'moving'" relatively to what? The CBR? Newton's absolute rest?----

Relative to any non-accelerating object.

Matheinste

So when he is, as you expressed it, at ‘rest’ this only applies to the reference frame of a non-accelerating object relatively to which the Earth was moving at the velocity that the astronaut attains at the end of his period of acceleration?

It seems that you are depicting a reference frame (an object) relatively to which the Earth was moving at near-light speed. The astronaut aims his ship at that object and accelerates until he attains a velocity whereby he is moving away from the Earth at near-light speed and is then at rest in that object’s reference frame.

So the only reference frames relatively to which he could be ‘at rest’ at the end of that period of acceleration are those that, before he started accelerating, the Earth was moving relatively to at near-light speed and only in the opposite direction to the astronaut’s planned route not to any (i.e. all) non-accelerating object’s reference frame?

So your response “Relative to any non-accelerating object.” combined with your comment that “his acceleration may have brought him to ‘rest’” does not, as you point out, apply to any ‘non-accelerating object’ but only to a non-accelerating object that was located in the direction of the astronaut’s route and only relatively to which the Earth was moving at near-light speed.

Having accelerated to near-light speed away from the Earth the astronaut could be ‘at rest’ in the reference frame of another (or even several) non-accelerating objects however he is also moving relatively to the ‘non-accelerating’ reference frame that is the planet Earth.

On the basis of your comment that the Earth could have been moving “relative to any non-accelerating object” is it possible that Einstein's clocks A and B could also have initially been moving relatively to some non-accelerating object thus that whilst clock A is moving toward B with uniform velocity it would have been 'at rest' relatively to that non- accelerating object thus that it would not, as Einstein posited, eventually be found to lag behind clock B on the basis that it was clock B that "carried on moving" thus that B would be found to lag behind A?

Are you of the opinion that Einstein was wrong in suggesting that A will lag behind B on the basis that they could both have initially been moving relatively to any non-accelerating object thus that A came to 'rest' in that object’s reference frame whilst B kept moving?

I am of the opinion that Einstein’s paragraph 1, chapter 4 depiction of clocks A and B was in relation to the fact that clock A was moving relatively to the non-accelerating object clock B and that Einstein’s conclusion that A lags behind B is from the point of view of clock B’s reference frame not from the point of view of any other non-accelerating object.

 

[cos]

So which twin is older when they reunite?

At the end of his outward-bound trip the astronaut's clock lags behind his Earth-bound twin's clock and when he returns to the planet his clock lags even further behind his twin's clock in accordance with Einstein's paragraph 1, chapter 4 depiction ergo, according to that depiction, the astronaut will have aged at a slower rate than his twin thus the Earth-bound twin will be the elder.

 

[JesseM]

On the basis of your comment that the Earth could have been moving “relative to any non-accelerating object” is it possible that Einstein's clocks A and B could also have initially been moving relatively to some non-accelerating object thus that whilst clock A is moving toward B with uniform velocity it would have been 'at rest' relatively to that non- accelerating object thus that it would not, as Einstein posited, eventually be found to lag behind clock B on the basis that it was clock B that "carried on moving" thus that B would be found to lag behind A?

As always, the relativity of simultaneity explains why, even if you look at a frame where A is at rest after accelerating and B is in motion, A's time will still be behind B's when they meet even though B was ticking slower as they approached each other in this frame. Einstein specified that A and B were synchronized in the frame where they were both at rest before A accelerated, which means that in the other frame where A is at rest after it accelerated, B's clock-reading was already well ahead of A's clock-reading before A accelerated.

(by the way, it's pretty hypocritical that you stopped responding to my posts because you didn't like my discussing other reference frames, and yet here you are asking matheinste about a different reference frame where A is at rest after accelerating, which is precisely what I had been talking about in relation to this problem)

 

[matheinste]

Hello cos.

I am not talking about anything as complicated as clocks lagging or leading or out of synch. I am just pointing out one of the absolute basic tenets of SR that all inertial motion is relative and the terms rest and motion have no meaning in isolation. Until that general principle is accepted there is no point in discussing clocks.

And yes the Earth is moving at near light speed to some objects in the universe. And yes the Earth is moving at any speed you care to name relative to some object in the universe but not, as you may think i meant, the same object.

Matheinste.

 

[atyy]

At the end of his outward-bound trip the astronaut's clock lags behind his Earth-bound twin's clock and when he returns to the planet his clock lags even further behind his twin's clock in accordance with Einstein's paragraph 1, chapter 4 depiction ergo, according to that depiction, the astronaut will have aged at a slower rate than his twin thus the Earth-bound twin will be the elder.

When you say the Earth-bound twin will be the elder, this means he will have accumulated a greater proper time. What do you mean by "the astronaut will have aged at a slower rate"? Does this mean the temporal intervals between ticks of the astronaut's clock were greater?

Consider normal spatial geometry now. Y flies from Boston directly to San Francisco. Z flies from Boston to Singapore to Japan to San Francisco. This means that Z accumulates a greater spatial distance. Does this mean that the spatial intervals between ticks on Y's ruler were greater?

 

[cos]

(by the way, it's pretty hypocritical that you stopped responding to my posts because you didn't like my discussing other reference frames, and yet here you are asking matheinste about a different reference frame where A is at rest after accelerating, which is precisely what I had been talking about in relation to this problem)

I was not "asking matheinste about a different reference frame where A is at rest after accelerating." but was responding to his argument in that respect.

Had he not responded to my question similar to my several requests to you to stop saying the same thing over and over again but had effectively repeated his reference to 'any non-accelerating object' I would, as I will now - as a result of his last message wherein he ignored my questions - sever further communication.

 

[matheinste]

Hello cos.

Please accept my apology. It is quite wrong of me to think i am correct just because i agree with the concepts of SR.

Mathienste.

 

[JesseM]

I was not "asking matheinste about a different reference frame where A is at rest after accelerating." but was responding to his argument in that respect.

So do you agree that a discussion of an inertial reference frame where A is at rest after accelerating has some possible relevance to the question of whether there is an objective truth about whether A or B is ticking slower after the acceleration?

Had he not responded to my question similar to my several requests to you to stop saying the same thing over and over again

Of course I only repeated the point about multiple reference frames because you never actually addressed this point, and you also never addressed my arguments about why they are relevant to the question of whether there's a physical truth about which of two clocks ticks slower. In a debate it is not legitimate to simply ignore an argument that tries to show why you are incorrect about something, and then to fault the person for repeating this argument when you continue to repeat the incorrect claim!

Again, if you aren't willing to actually address such arguments, any further posts in which you repeat the incorrect claim that there is some objective physical truth about which of two clocks is ticking slower should be reported to the moderators, as it is against the rules here to argue the validity of the mainstream understanding of relativity.

 

[cos]

When you say the Earth-bound twin will be the elder, this means he will have accumulated a greater proper time. What do you mean by "the astronaut will have aged at a slower rate"? Does this mean the temporal intervals between ticks of the astronaut's clock were greater?

According to Einstein's chapter 4, STR, if clock A moves in any polygonal line to B's location (in the same way that the astronaut makes an out-and-return journey) clock A will "lag behind" clock B.

For clock A (the astronaut's clock) to lag behind clock B (the Earth clock) 'the temporal intervals between ticks of the astronaut's clock' (clock A) were, according to Einstein, greater i.e. the temporal intervals expand (dilate) ergo, according to Einstein's chapter 4, the astronaut (clock A) will have aged at a slower rate than his Earth-bound twin (clock B).

Consider normal spatial geometry now. Y flies from Boston directly to San Francisco. Z flies from Boston to Singapore to Japan to San Francisco. This means that Z accumulates a greater spatial distance. Does this mean that the spatial intervals between ticks on Y's ruler were greater?

(Typo? 'ruler' or 'clock'?) Assuming you obviously meant 'clock' then - no.

According to Einstein's paragraph 2, chapter 4 description - if a clock is made to move in a straight line (eg. Boston to San Francisco) or any polygonal line (eg. Boston to Singapore to Japan to San Francisco) those clocks will lag behind an identical clock that has remained 'at rest' (eg. in San Francisco) and the amount of lag will be determined in accordance with the equation .5tv²/c² v being, of course, the velocity at which A (Y and Z) moves so on the assumption that their aircraft move at the same velocity as each other then the spatial intervals between ticks on Y's clock will be the same as those for Z's clock.

Einstein's equation refers to t which is the total elapsed time for each of the trips so although their clocks will be ticking over at the same rate as each other during those flights (based on v being identical) the amount by which Z's clock lags behind the clocks in San Francisco will be greater than the amount by which Y's clock lags behind those clocks.

 

[atyy]

(Typo? 'ruler' or 'clock'?) Assuming you obviously meant 'clock' then - no.

I meant ruler. So that accumulated proper time for the twins in spacetime analogous to accumulated spatial distance for X and Y in normal spatial geometry.

Edit: I edited the typo originally in this post, not the other - it should be 'ruler'.

 

[cos]

Again, if you aren't willing to actually address such arguments, any further posts in which you repeat the incorrect claim that there is some objective physical truth about which of two clocks is ticking slower should be reported to the moderators, as it is against the rules here to argue the validity of the mainstream understanding of relativity.

If pointing out that in paragraph 3, chapter 4, of his article 'On the Electrodynamics of Moving Bodies' Albert Einstein wrote "A balance-clock at the equator must go more slowly than a precisely similar clock at one of the poles under otherwise identical conditions." is arguing "the validity of the mainstream understanding of relativity" then so be it.

If Einstein pointed out in paragraph 3, chapter 4, of his article 'On the Electrodynamics of Moving Bodies' "that there is some objective physical truth about which of two clocks is ticking slower" then I suggest that your argument is with paragraph 3, chapter 4, OEMB!

 

[JesseM]

According to Einstein's chapter 4, STR, if clock A moves in any polygonal line to B's location (in the same way that the astronaut makes an out-and-return journey) clock A will "lag behind" clock B.

For clock A (the astronaut's clock) to lag behind clock B (the Earth clock) 'the temporal intervals between ticks of the astronaut's clock' (clock A) were, according to Einstein, greater i.e. the temporal intervals expand (dilate) ergo, according to Einstein's chapter 4, the astronaut (clock A) will have aged at a slower rate than his Earth-bound twin (clock B).

And do you assert that not only will the astronaut's clock have elapsed less time in total than the Earth clock if the astronaut leaves Earth and later returns, but also that the astronaut was aging at a slower rate (in a real, physical sense rather than a frame-dependent sense) than the Earth-bound twin during a single phase of the trip in which the astronaut was moving inertially--say, from the moment after the astronaut accelerated to turn around to the moment the astronaut reached Earth (with this phase being similar to A moving towards B in section 4 of Einstein's 1905 paper)? Or are you backing away from this second claim, which as I have said is incorrect according to the mainstream understanding of SR? If you don't want to engage in discussion with me that's your choice, but I'd appreciate a clear yes/no answer to this question.

 

[cos]

I meant ruler. So that accumulated proper time for the twins in spacetime analogous to accumulated spatial distance for X and Y in normal spatial geometry.

Edit: I edited the typo originally in this post, not the other - it should be 'ruler'.

The message in respect to which I hit the 'quote' button stated 'clock' this one says 'ruler'. In either case, I can't understand the above sentence. Is it a question? If it is - I can't understand it.

 

[JesseM]

If pointing out that in paragraph 3, chapter 4, of his article 'On the Electrodynamics of Moving Bodies' Albert Einstein wrote "A balance-clock at the equator must go more slowly than a precisely similar clock at one of the poles under otherwise identical conditions." is arguing "the validity of the mainstream understanding of relativity" then so be it.

If Einstein pointed out in paragraph 3, chapter 4, of his article 'On the Electrodynamics of Moving Bodies' "that there is some objective physical truth about which of two clocks is ticking slower" then I suggest that your argument is with paragraph 3, chapter 4, OEMB!

The balance clock does go more slowly on average over a full rotation, and it also goes more slowly at every moment in the frame of the Earth, and as I said it is plausible that Einstein might have meant either of these. It's not correct that it's going more slowly at every moment in any objective physical sense though. However, you have said you don't like to talk about instantaneous quantities like "rate of ticking at a single moment", so let's stick to a situation where the two clocks are moving at constant velocity for an extended period of time, like the scenario where the clock A accelerates towards B and then moves inertially towards it until it reaches B. Do you assert that in this situation, there is an objective physical truth about whether A or B is ticking slower during the time period when both are moving inertially relative to one another?

 

[atyy]

The message in respect to which I hit the 'quote' button stated 'clock' this one says 'ruler'. In either case, I can't understand the above sentence. Is it a question? If it is - I can't understand it.

Sorry! I confused myself totally too.

Anyway, my post 92 has no typo. I wanted to draw an analogy between accumulated proper time in spacetime for the twins, and accumulated spatial distance for X and Y in normal space. If the analogy holds, then if we conclude that the time between ticks on the astronaut's clock is greater, shouldn't we also conclude that the distance between ticks on Y's rulers is also greater by analogy?

Edit: Riddled with typos - I meant Y and Z.

 

[atyy]

The message in respect to which I hit the 'quote' button stated 'clock' this one says 'ruler'. In either case, I can't understand the above sentence. Is it a question? If it is - I can't understand it.

OK, let me try state my question more clearly.

As a preliminary, the twins are earth-bound A and astronaut B. Although A stays at the same "place", he moves through "time", and so moves through spacetime. Here's the analogy:

In the twin paradox, A and B start off at the same point in spacetime, then both of them move through spacetime in different paths, eventually meeting at another point in spacetime. At that point, they find that they have accumulated different amounts of ageing or "real time". Does this mean that the "real time" between ticks of B's clock were greater?

In the normal space analogy, Y and Z start at the same point in space, then both of them move through space in different paths, eventually meeting at another point in space. At that point, they find that they have accumulated different amounts of "real distance". Does this mean that the "real distance" between ticks of Y's rulers were greater?

Given the analogy, I suggest that if the answer is "no" for the second scenario, it must also be "no" for the first scenario. If so, then we can ask if it makes any sense to say that "time" goes more slowly for B. If it is to make sense, then "time" in that statement cannot be "real time".

 

[cos]

Anyway, my post 92 has no typo. I wanted to draw an analogy between accumulated proper time in spacetime for the twins, and accumulated spatial distance for X and Y in normal space. If the analogy holds, then if we conclude that the time between ticks on the astronaut's clock is greater, shouldn't we also conclude that the distance between ticks on Y's rulers is also greater by analogy?

On the basis of the concept of length contraction - although the time between ticks on the astronaut clock should be greater shouldn't the distance between 'ticks' on his rule be shorter?

 

[atyy]

On the basis of the concept of length contraction - although the time between ticks on the astronaut clock should be greater shouldn't the distance between 'ticks' on his rule be shorter?

The normal space analogy takes place in normal space and time - no length contraction, no time dilation, just an analogy from everyday life.