Twin Paradox: Einstein's Explanation and Alternative Interpretations

[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.

 

[atyy]

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.

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.

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".

George Jones's post #8 has a rate of change of the proper time of one observer with respect to proper time of another observer (due to gravitational time dilation). What is the equivalent of this in the twin paradox? https://www.physicsforums.com/showthread.php?p=1543402

 

[atyy]

"In other words, Terence computes that Stella's clock is really running slow by a factor of about 7 the whole time, but he sees it running fast during the Inbound Leg because each flash has a shorter distance to travel."
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html

I like the picture with the red lines:
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html

 

[JesseM]

George Jones's post #8 has a rate of change of the proper time of one observer with respect to proper time of another observer (due to gravitational time dilation). What is the equivalent of this in the twin paradox? https://www.physicsforums.com/showthread.php?p=1543402

George Jones' post wasn't comparing the rate of change of each observer's clock in any coordinate-invariant sense though--he specified that he was using Schwarzschild coordinates.

 

[phyti]

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.

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.

If Y and Z have the same speed for the duration of their trips, and they leave and arrive together, their clocks read the same. A difference in clock time would imply one traveled a greater distance before reuniting, which implies a faster speed, which slows clock rate.

 

[cos]

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?

Greater than the “real time” between ticks of A’s clock? Yes.

Before I go into details I again point out that my presentation is specifically in relation to Albert Einstein’s chapter 4 of his 1905 article ‘On the Electrodynamics of Moving Bodies’ depiction.

I have been accused of arguing the validity of the mainstream understanding of relativity however I fail to see why my referring to chapter 4 of relativity could be arguing that mainstream understanding of relativity.

It seems to me that some people are attempting to pretend that chapter 4 of special theory does not exist. If chapter 4 of relativity argues the validity of the mainstream understanding of relativity then I suggest that people should look at chapter 4. It is part and parcel of relativity thus should not be ignored even it is uncomfortable or inconvenient.

In that chapter (paragraph 1) Einstein wrote:- “If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by .5tv²/c² ... t being the time occupied in the journey from A to B.”

In paragraph 3 Einstein refers to a clock that has remained at rest compared with an identical clock that has moved in a closed curve around that clock. I am of the opinion that he implied that clock B in paragraph 1 remains at rest ergo, in that chapter, Einstein does not allow that clock B “moves through spacetime”.

If someone were to draw a diagram of clocks A and B moving through spacetime they would be presenting that phenomenon from the point of view of another reference frame however Einstein specifically pointed out that the event is “viewed in the stationary system” (i.e. clock B’s reference frame).

Although Einstein made no mention of the fact - it is obvious that clock A in paragraph 1 must accelerate in order to move to B’s location. On the basis that the attainment of an instantaneous velocity can be mathematically ‘ratified’ I can only repeat Einstein’s comment that as far as the propositions of mathematics are certain, they do not refer to reality and as far as I am concerned physics should be a study of physical reality thus Einstein’s paragraph 1, chapter 4, clock A must accelerate and as Einstein showed in his 1918 Naturwissenschaften article, it is only the clock that experiences forces of acceleration (clock A) that incurs variations in it’s rates of operation not the clock referred to in his 1918 article which continues to move with uniform velocity (clock B).

In paragraph 3, chapter 4, Einstein wrote:- “Thence we conclude that a balance clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles...”

My interpretation of the phase ‘must go more slowly’ is that the equatorial clock ticks over at a slower rate than (i.e. that it incurs time dilation relatively to) the polar clock.

On the basis that the equatorial clock ‘must go more slowly’ than the polar clock then it must progressively lag further and further behind the polar clock.

I interpret Einstein’s paragraph 1 conclusion that A will lag behind B as being in accordance with his later comment that A (his paragraph 3 equatorial clock) ‘goes more slowly’ (i.e. ticks over at a slower rate) than B (his paragraph 3 polar clock).

I am of the opinion that if Einstein’s paragraph 1 clock A was not located some distance away from B but was initially stationary alongside and synchronous with B then traveled away from B at the same velocity (v) and for the same length of time (t) as does Einstein’s clock A then comes to a stop it will then lag behind B by the same amount as Einstein’s clock A lagged behind B in accordance with his equation .5tv²/c².

This is analogous to an astronaut’s outward bound trip however, having come to a stop and adjusted his clock so that it then indicates the same time as the Earth clock (and, allowing for the fact that the Earth clock’s rate of operation is affected by it’s location in a gravitational tidal area is ticking over at the same rate as the Earth clock), the situation is precisely analogous to Einstein’s paragraph 1, chapter 4 depiction of synchronous clocks located at points A and B of K.

Having synchronized his clock with the Earth clock (having allowed for the time that it takes for light to traverse the intervening distance) the astronaut immediately accelerates and soon attains an instantaneous velocity whereby his clock is ticking over at the same rate as the (gravitationally affected) Earth clock after which his clock starts to progressively ‘go more slowly’ than the Earth clock.

Upon his arrival back at the planet he finds that his clock lags behind the Earth clock whereupon he can either conclude that his clock ‘went more slowly’ than the Earth clock during that trip or that the Earth clock ticked over at a faster rate than his own clock (i.e. the Earth clock incurred time ‘contraction’) yet, in accordance with Einstein’s 1918 article, he knows that his was the reference frame that accelerated.

As as I detailed in another posting - when Galileo wrote his book ‘Two New Sciences’ he was already in trouble with authorities so he presented it as a purely hypothetical discussion between a teacher and two of his students. Einstein also presented his 1918 article as a purely hypothetical discussion - this time between a relativist and a critic.

Having already been criticized for having stated, in his 1916 general theory, that the special theory ‘law’ of the constancy of the velocity of light required modification and, in that same year in his book ‘Relativity’ that this law was not fully valid, it was, perhaps, an attempt on his behalf to avoid further criticisms that he wrote his 1918 article in that format.

In his self-published book ‘Fiction Stranger Than Truth’ Nikolai Rudakov wrote :-

“Very few relativists have actually adopted Einstein’s explanation [of the twin paradox]. Not many authors mention the 1918 dialogue, and some who do imply that Einstein was wrong.”

The simple fact is that that when we are discussing Einstein’s concepts regarding relativity per se (not just his 1905 article) we should, I believe, refer to all of his relevant materiel including his 1918 article as well as his chapter 4 depictions and if any of it ‘argues against the validity of the mainstream understanding of relativity’ then it is Einstein who should be criticized not me! I’m just the messenger.

In my opinion Einstein’s chapter 4 can be shown to describe an out-and-return trip by an astronaut and that the ludicrous claim that the astronaut does not accept that his clock incurs time dilation but insists that the Earth clock incurs time contraction and only during his period of acceleration following turn around does not comply with (argues against) Einstein’s ‘understanding’ of relativity as presented in that chapter.

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?

On the assumption that Z is the astronaut - yes.

(In the first scenario you depicted A and B with B being the astronaut so I assume that when you refer to Y and Z above you are classifying Z as the astronaut.)

On the basis that the astronaut’s clock incurs time dilation (i.e. the “real time” between the ticks of Z’s clock are greater) his rule ‘must’ accordingly incur length contraction (i.e. the “real distance” between the ticks on his rule will be shorter).

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".

My answer to both scenarios is yes.

 

[cos]

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

By 'normal space analogy' I assume that you are talking about a 'real' out-and-return journey.

On the assumption that you suggest that length contraction and time dilation do not take place in reality I can only refer you to the results of the Hafele-Keating experiment as well as similar 'proofs' that time dilation does take place 'in reality'.

 

[JesseM]

have been accused of arguing the validity of the mainstream understanding of relativity however I fail to see why my referring to chapter 4 of relativity could be arguing that mainstream understanding of relativity.

It seems to me that some people are attempting to pretend that chapter 4 of special theory does not exist. If chapter 4 of relativity argues the validity of the mainstream understanding of relativity then I suggest that people should look at chapter 4. It is part and parcel of relativity thus should not be ignored even it is uncomfortable or inconvenient.

In that chapter (paragraph 1) Einstein wrote:- “If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by .5tv²/c² ... t being the time occupied in the journey from A to B.”

Nowhere in this paragraph does Einstein say that A was running slower than B as it approached it in any objective physical sense--he just says it "lags behind", meaning that the time on the A clock is less than the time on the B clock when they meet (which you would predict even if you analyzed the situation in a frame where B was running slower). I would still appreciate a basic yes/no answer to the question of whether you are arguing that A was objectively, physically ticking slower than B as A approached B. I thought you were, which was why I said your arguments conflicted with SR, but I want to be completely sure that I'm not misinterpreting you somehow.

Although Einstein made no mention of the fact - it is obvious that clock A in paragraph 1 must accelerate in order to move to B’s location. On the basis that the attainment of an instantaneous velocity can be mathematically ‘ratified’ I can only repeat Einstein’s comment that as far as the propositions of mathematics are certain, they do not refer to reality

No one denied that clock A had accelerated, I think you're misunderstanding the term "instantaneous velocity"--it does not refer to the idea of a sudden jump in velocity without smooth acceleration! "instantaneous velocity" just refers to the idea that an object has a single well-defined velocity at every instant, even if the velocity is changing continuously. For example, if the velocity of a falling object is given by the continuous function v(t) = (9.8 meters/second^2)*t, then the instantaneous velocity at the precise instant of t=2 seconds would be (9.8 meters/second^2)*(2 seconds) = 19.6 meters/second.

In any case, we are free to imagine that A accelerates for some brief time but after that it moves inertially. So my question, again, is whether during this inertial phase when A and B are approaching one another, do you think there is an objective physical truth about whether A or B is ticking slower, or do you acknowledge that different frames disagree about which is ticking slower, and in relativity no inertial frame is more "correct" than any other?

and as far as I am concerned physics should be a study of physical reality thus Einstein’s paragraph 1, chapter 4, clock A must accelerate and as Einstein showed in his 1918 Naturwissenschaften article, it is only the clock that experiences forces of acceleration (clock A) that incurs variations in it’s rates of operation not the clock referred to in his 1918 article which continues to move with uniform velocity (clock B).

I have no objection to the statement "it is only the clock that experiences forces of acceleration (clock A) that incurs variations in it's rates of operation", since every inertial frame agrees that the clock that accelerates will change its rate of ticking. The issue is just that there are perfectly valid frames where clock A was ticking slower before accelerating than it was after, so although it's an objective fact that A changed its rate of ticking, it's not an objective fact that A's rate of ticking slowed down after it accelerated. So again, I'd like to know whether you are arguing it's an objective truth that A began to run slower than B after accelerating.

Having synchronized his clock with the Earth clock (having allowed for the time that it takes for light to traverse the intervening distance)

But Einstein also points out in chapters VIII and IX here that simultaneity is relative, so two clocks that are synchronized in one frame are out-of-sync in another.

the astronaut immediately accelerates and soon attains an instantaneous velocity whereby his clock is ticking over at the same rate as the (gravitationally affected) Earth clock after which his clock starts to progressively ‘go more slowly’ than the Earth clock.

Do you argue the astronaut's clock starts to "go more slowly" in an objective physical sense, or just that it slows down in the frame of the Earth? This is the only question I'm asking for an answer to, if you don't want to address anything else in my post feel free not to.

 

[atyy]

By 'normal space analogy' I assume that you are talking about a 'real' out-and-return journey.

On the assumption that you suggest that length contraction and time dilation do not take place in reality I can only refer you to the results of the Hafele-Keating experiment as well as similar 'proofs' that time dilation does take place 'in reality'.

No. Since I am unable to communicate what I mean in the "normal space analogy", and it's clearly not being helpful, I withdraw it from discussion with apologies.

 

[cos]

If Y and Z have the same speed for the duration of their trips, and they leave and arrive together, their clocks read the same.

You previously wrote :- “Y flies from Boston directly to San Francisco. Z flies from Boston to Singapore to Japan to San Francisco.”

If “Y and Z have the same speed for the duration of their trips” but Z travels a much greater distance how can they possibly, having left together, arrive together?

A difference in clock time would imply one traveled a greater distance before reuniting...

A trip from Boston to Singapore to Japan to San Francisco IS greater than a trip from Boston to San Francisco!

...which implies a faster speed, which slows clock rate.

In my previous message I wrote:- “their clocks will be ticking over at the same rate as each other during those flights (based on v being identical)”

 

[cos]

No. Since I am unable to communicate what I mean in the "normal space analogy", and it's clearly not being helpful, I withdraw it from discussion with apologies.

That's a refreshing change from some of the messages in this thread - common courtesy. Thank you.

 

[Dale]

No. Since I am unable to communicate what I mean in the "normal space analogy", and it's clearly not being helpful, I withdraw it from discussion with apologies.

Hi atyy, don't give up quite yet.

How about instead of this:

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?

We change it to:

Drivers Y and Z head north from Columbia, SC and eventually meet in Charleston, WV. Driver Y goes through Charlotte, NC and his odometer records 356 miles for the trip. Driver Z goes through Nashville, TN and his odometer records 834 miles for the trip. Does this mean that the real distance between ticks of Y's odometer were 2.3 times greater?

I hope that captures your meaning in a more accessible manner.

 

[atyy]

I hope that captures your meaning in a more accessible manner.

Your version captures my meaning exactly. Thanks!

 

[Dale]

Hi cos,

As you consider the revised example, please remember that atyy is talking only about spatial distances, not time. So the duration and speed of the respective trips are explicitly not considered. This is purely a geometrical question.

Do you think that the distance between the ticks of Y's odometer was 2.3 times greater than the distance between the ticks of Z's odometer?

 

[phyti]

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.

The objective is not to analyze them in another frame. It's to compare the lifetime of the moving group to that of a second group in the lab. The same frame, same observers, the only factor changed is the speed of the group. It's called a controlled experiment. The behavoir of the particles changes as a result of speed. Is that not objective?

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.

Perhaps this presumptive attitude is why some don't respond to you posts.

 

[JesseM]

The objective is not to analyze them in another frame. It's to compare the lifetime of the moving group to that of a second group in the lab. The same frame, same observers, the only factor changed is the speed of the group. It's called a controlled experiment. The behavoir of the particles changes as a result of speed. Is that not objective?

If you're only analyzing them in one frame, then this has nothing to do with the question of which group of muons is "actually, physically" aging slower. It's certainly true that in the lab frame, group A of muons at rest in this frame will decay at an earlier time than the group B of muons moving at relativistic speed in the lab frame. On the other hand, in the rest frame of group B, the group B muons decay at an earlier time than the group A muons. Both frames make exactly the same predictions about physical events like what position on Earth the muons will decay and what the local Earth-clocks at that position will read when they decay.

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.

Perhaps this presumptive attitude is why some don't respond to you posts.

I said if you don't understand, which leaves open the possibility that you do understand, if you do just say so. But our discussion started when you seemed to call into question my statement "As I said, this claim that any clock is 'actually, physically' going more slowly than another contradicts relativity" when you asked "Then what was measured in the prolonged half life of muons?" (and in a later post you also called into question another accepted feature of SR, length contraction) Do you agree that which group of muons decays faster depends on which frame you use, and that all inertial frames are equally valid in SR and all make the same predictions about the results of empirical measurements, so there can be no basis in relativity for saying that either group of muons "actually, physically" decayed more slowly?