Clocks, rulers... and an issue for relativity

[robinpike]

 

Loses time why? For this essentially instantaneous acceleration/deceleration the two travelling clocks in this scenario are not displaced enough to have a significant change in time...just the rate going forward as measured by each. Compare with respect to the stay at home clock. The greater displacement effects a significant shift to the future through the deceleration.

 

The loss in time refers to after the instantaneous acceleration/deceleration, when the first travelling clock is now stationary with respect to the stay at home clock, and now coasting away from the second travelling clock. At this stage, the first travelling clock is now losing time with respect to the second travelling clock but not losing time to the stay at home clock. For the logical issue to be discussed, it is not necessary to continue with the scenario. Of course if the scenario is completed, then the travelling clock's round trip is continued by further accelerating/decelerating so that it can return to the stay at home clock. But also - and relevant - the first travelling clock could just as easily accelerate back to the second travelling clock to complete a round trip with respect to that clock. Whichever scenario is completed, the 'round trip' clock will have a loss in time to the clock that it returns to.

 

Yes, exactly. In my earlier post that I also linked to, I presented a reference frame according to which the traveling clock ticks faster than the stay at home clock on that part of the trip.

 

 

When an observer sees a clock ticking faster, it is an apparent increase not a real increase in the clock's tick rate.

Edited September 16, 2016 by robinpike

[Endy0816]

Your measurements will agree with that of Earth whenever and wherever you are in the same reference frame.

 

Can we speak in terms of less time passing instead of using the term 'losing time'? One can be fixed, the other cannot.

Edited September 16, 2016 by Endy0816

[J.C.MacSwell]

 

The loss in time refers to after the instantaneous acceleration/deceleration, when the first travelling clock is now stationary with respect to the stay at home clock, and now coasting away from the second travelling clock. At this stage, the first travelling clock is now losing time with respect to the second travelling clock but not losing time to the stay at home clock. For the logical issue to be discussed, it is not necessary to continue with the scenario. Of course if the scenario is completed, then the travelling clock's round trip is continued by further accelerating/decelerating so that it can return to the stay at home clock. But also - and relevant - the first travelling clock could just as easily accelerate back to the second travelling clock to complete a round trip with respect to that clock. Whichever scenario is completed, the 'round trip' clock will have a loss in time to the clock that it returns to.

 

When an observer sees a clock ticking faster, it is an apparent increase not a real increase in the clock's tick rate.

That's not a round trip for either in SR. They will both be displaced in the original frame.

[Tim88]

[..]

 

When an observer sees a clock ticking faster, it is an apparent increase not a real increase in the clock's tick rate.

 

In that post I refer to an inertial reference system, in which from two fast moving clocks, one clock (the "traveler") slows down to zero speed when leaving the Earth. All such determinations are non-absolute in the way as you illustrated.

[Celeritas]

 

At the half-way point, one of the travelling clocks de-accelerates (i.e. reduces its speed with respect to the stay at home clock) to the point where it becomes stationary with respect to the stay at home clock. This means that the travelling clock’s time now runs at the same rate as the stay at home clock’s rate of time.

 

But when the travelling clock de-accelerated, it effectively accelerated away from the second travelling clock (i.e. it increased its relative speed with respect to the second travelling clock). But such an acceleration is just a repeat of the scenario when the travelling clocks first accelerated away from the stay at home clock (although now with respect to different reference frames). This means that the de-accelerated clock’s time has to run slow with respect to the second travelling clock’s rate of time, which already is running slow with respect to the stay at home clock’s rate of time – AND yet the de-accelerated clock’s rate of time has to be at the same rate as the stay at home clock’s rate of time (because they are stationary with respect to each other).

 

If these two conditions were apparent effects – such a scenario would be possible. But the loss in time is real and so these two conditions cannot occur together – hence a logical contradiction has occurred.

 

 

robinpike,

 

I provided an alternate description in my prior post, which you requested.

 

wrt your scenario, you mistakenly presume it reveals an inherent contraction in SR. The contradiction you presume, is only the result of a lack of understand of SR in the very first place, and SR is a kinematic model that does not directly address proper accelerations.

 

Someone could try and answer your questions in brief layman's terms, however this can never satisfy you. You would then need to ask WHY the description explains it. Then, the math would need presented, and possibly some geometric figures in support thereof. That could not possibly satisfy you either, because you are still trying to learn the basic concepts of SR. For example, you are presently trying to learn how POVs properly keep track of the relation between proper lengths and its corresponding contracted-length the length between 2 events per POVs in relative motion. Add, the twins case is very complex, the all inertial case far simpler. You need to focus on the easy challenge first, master it, and then you will possess the tools to understand WHY the twins scenario is no paradox when someone properly explains it.

 

I'll just say this though, wrt the red highlight:

 

during B deceleration at turnabout (thru midpoint of turnabout) ...

 

in the C spacetime system ... the B tick rate slows down, until it matches the A tick rate. The A tick rate remains steady and slower, since inertial.

 

in the A spacetime system ... the B tick rate speeds up, until it matches the A tick rate. The C tick rate remains steady and slower, since inertial.

 

in the B spacetime system ... this is too difficult for you understand at this venture.

 

Since you have declared an inherent contradiction in SR, please explain how your A & C tick rates exist in the B spacetime system during B's deceleration (not just when v=0 wrt A). That should reveal a great deal regarding the source of your belief of a contradiction inherent in SR.

 

Best regards,

Celeritas

Edited September 17, 2016 by Celeritas

[Tim88]

OK finally here's my take on the self contradiction in SR according to you (and as before, bold face mine, with a partial retake):

 

[bold face by tim88]

[..]

the coach and I use our respective measurements before and after my brother ran around the track, to determine only whether my brother’s height got shorter, or got taller, or did not change. So now the coach and I can agree: my brother’s height got shorter and that this change in his height was a real change. This avoids any arguments as to the amount that his height changed, and who has the real measure of feet and inches on their ruler.

 

===============================================================

[..]

To demonstrate the logical contradiction, I will start with the (most) obvious method of how the retardation occurred: the travelling clock’s time runs at a slower rate (overall) during its round trip. Let’s see how this assumed method causes the issue by using one stay at home clock and two travelling clocks.

 

By the way, if you dislike the examples that I have chosen, by all means post an alternative, describing how the travelling clock retards on the stay at home clock and where in its journey that retardation may be deemed to occur, and I will show how the logical contradiction applies to your example.

 

The two travelling clocks C1 and C2 are initially stationary and synchronized against the stay at home clock C0. They start the round trip by accelerating side-by-side away from the stay at home clock (i.e. they increase their relative speed with respect to the stay at home clock). In the following example the assumption is that of the Earth system: half of the retardation is due to the travelling clock’s time running slow during the trip to the half-way point, and consequently both these clocks will now be running slow (with respect to the stay at home clock).

 

At the half-way point, the travelling clock C1 decelerates (i.e. reduces its speed with respect to the stay at home clock) to the point where it becomes stationary with respect to the stay at home clock. This means that the travelling clock’s time now runs at the same rate as the stay at home clock’s rate of time.

 

But when the travelling clock decelerated, it effectively accelerated away from the second travelling clock C2 (i.e. it increased its relative speed with respect to the second travelling clock). But such an acceleration is just a repeat of the scenario when the travelling clocks first accelerated away from the stay at home clock (although now with respect to different reference frames). This means that C1's time has to run slow with respect to the rate of time in S2 (the rest system of C2), which already is running slow with respect to the stay at home clock’s rate of time according to S0 – AND yet C1's rate of time has to be at the same rate as the stay at home clock’s rate of time (because they are stationary with respect to each other).

 

If these two conditions were apparent effects – such a scenario would be possible. But the loss in time is real and so these two conditions cannot occur together – hence a logical contradiction has occurred.

[...]

 

What you describe here is very similar to what I described to you in my earlier post, and there is no contradiction:

 

"From that perspective [of the system S2] the clock rate first is increased to its proper rate, and then on the way back home it is strongly decreased as the traveler tries to catch up with the Earth."

 

The starting assumption of SR is the same as that of Newton's mechanics: any inertial reference system can be chosen for the description of physical phenomena. It's a feature of the Galilean transformations that this works in Newton's mechanics. And it's a feature of the Lorentz transformations that this works in special relativity: if we choose the inertial system S2 for the description of physics, we describe the phenomena somewhat differently (figuratively speaking, "from a different perspective") but we make the same prediction about the clock retardation of C1 on C0 when they are back side by side.

 

I have the impression that we are back to the logically fallacy that I pointed out earlier: the mistake to think that everything must be either "only apparent" or "fully real". In fact, your own type of illustration serves well here. If we have disagreeing measurement tools, or if you see the trajectory of a volleyball from one angle and I see the same from another angle, then we could disagree about the trajectory. But we will still agree if the ball falls through the net or not. Where is the self contradiction?

 

Or maybe you think that the time dilation effect cannot be mutual, so that the clock on Earth cannot be running slow according to the inertial system in which C2 is temporarily in rest?

[..]

Since you have declared an inherent contradiction in SR, please explain how your A & C tick rates exist in the B spacetime system during B's deceleration (not just when v=0 wrt A). That should reveal a great deal regarding the source of your belief of a contradiction inherent in SR.

 

Best regards,

Celeritas

 

Hi Celeritas, I'm still waiting for your comments on my examples in which I illustrated that your presumed "B spacetime system" may be suited for geometrical descriptions, but it's not generally valid for the laws of physics - as you apparently know.

[J.C.MacSwell]

Looking at distant clocks with respect to "B spacetime system" can seem to yield very bizarre results, but they are still valid with respect to causality. The orders of spatially separated events can become reversed but never causally. It may be a very poor choice of frame to analyze events but it is not inherently invalid.

[Celeritas]

Tim88,

 

I had already addressed those posts, so I'll have to go back and see where the breakdown is, if any. I'll have another look-see. Thanx

 

Best regards,

Celeritas

 

 

[koti]

You are comparing a ruler with a clock. You should be comparing a ruler with a metronome and an odometer with a clock.

Could you clarify why we should be using a metronome instead of a clock?

[Celeritas]

Hi Celeritas, I'm still waiting for your comments on my examples in which I illustrated that your presumed "B spacetime system" may be suited for geometrical descriptions, but it's not generally valid for the laws of physics - as you apparently know.

 

Tim88,

 

OK, would it be fair to reduce your point to ... the B system does not measure light speed invariant "throughout his own space" in any duration during his own thruster burns. As such, Einstein's convention-for-simultaneity (used in SR) is an invalid convention for non-inertial POVs. The Einstein convention assumes both the 1-way and 2-way light speed is invariant, isotropic at c, and independent of the motion of the light's source.

 

However, that's why I chose to use the collection of MCCIRF POVs, ie to map all entities within the B system over his proper acceleration in a way completely consistent with inertial POVs (who always concur).

 

I realize that asking michel123456 to explain how the A & C clocks exist in the B system during turnabout, is indeed far over his head at this venture. There are different ways to approach that. And wrt the MCCIRF method i mentioned, one cannot consider that method unless they have first mastered the all-inertial scenarios. However, the MCCIRF method (I used as an example) is a preferred method IMO, because if at anytime B drops into coast-mode, there is no disjunct in his spacetime coordinate predictions for other observers, and no matter where they are or how far their range. It's seamless, and completely consistent with all inertial POVs (who all always concur with each other).

 

The MCCIRF method does not use B's own POV, but rather builds his POV from the collections of MCCIRF infitesimals. Twin B, using Einstein's convention-for-simultaneity (of SR), cannot (while non-inertial) map the heavens in concurrence with all inertial observers. Yet, twin B receives the very same light the MCCIRF observers do. So star maps must be built from inertial POVs, and while properly accelerating, twin B's navigation system would have to dynamically adjust the worldlines of all inertial stars (or bodies), and all steadily accelerating bodies. Then, his own navigation system's current map, could always be completely consistent with maps of all inertial observers.

 

That said, the twin POV is invalid in so far as upholding all the laws of physics, if he uses the convention-for-simultaneity used in SR for all inertial observers, which was ...

 

τ₁ = ½ (τ₀ + τ₂)

 

because the above synchronicity eqn requires that the speed of light be invariant at c, not just locally, but across the all of space in any instant. This fails for non-inertial POVs of relativistic rate, because light's speed is no longer c (per measurement) across an expanse of space in the instant.

 

Best regards,

Celeritas

Edited September 19, 2016 by Celeritas

[imatfaal]

Could you clarify why we should be using a metronome instead of a clock?

 

A clock measures the total elapsed time whereas a metronome merely ticks. A ruler measures length at one moment in time whereas a odometer measures total moved distance.

 

You have to compare like to like; ruler / metronome for instant measurement or odometer / clock for total integrated measurement

[koti]

 

A clock measures the total elapsed time whereas a metronome merely ticks. A ruler measures length at one moment in time whereas a odometer measures total moved distance.

 

You have to compare like to like; ruler / metronome for instant measurement or odometer / clock for total integrated measurement

 

Could you point out where I'm wrong in my babble below because I am clearly missing something? :

 

A clock is a metronome with a display. A metronome is a clock without an apparent display but a metronome gives a ticking sound which we can use as a "display" by counting the ticks. If we set the metronome so it indicates exactly 1 second at each tick (we can use a clock for that) we have oureselves a clock. I don't get it why we should be using a metronome instead of a clock - isn't it the same thing ?

[swansont]

 

Could you point out where I'm wrong in my babble below because I am clearly missing something? :

 

A clock is a metronome with a display. A metronome is a clock without an apparent display but a metronome gives a ticking sound which we can use as a "display" by counting the ticks. If we set the metronome so it indicates exactly 1 second at each tick (we can use a clock for that) we have oureselves a clock. I don't get it why we should be using a metronome instead of a clock - isn't it the same thing ?

 

 

The observation was when comparing this to length contraction of a ruler. A ruler does not have a display to indicate the cumulative distance. The analogue of a ruler undergoing length contraction is a metronome slowing its tick rate. The analogue of a clock measuring a different elapsed proper time is an odometer measuring a different distance traveled.

[robinpike]

To help steer the discussion, if I am reading the counter arguments correctly, then my logical argument is being refuted on the basis that relativity itself has no issue with the scenario under discussion…

 

Summary: When the two travelling clocks are on their journey, coasting side-by-side away from the stay at home clock, their rate of time is seen as slow by the stay at home clock. When the first travelling clock decelerates so that it becomes stationary with respect to the stay at home clock, the stay at home clock sees the first travelling clock’s rate of time return to its own rate of time. At the same time, the second travelling clock sees the deceleration of the first travelling clock as an acceleration away from itself, and so sees the rate of time of the first travelling clock slow down with respect to its (i.e. the second travelling clock) own rate of time.

 

The steps in logic that appear to being used to refute my logical argument being...

• The above scenario is in exact agreement with what relativity predicts and is in exact agreement with what is measured by experiment.

• Therefore relativity is correct.

• Relativity is correct, therefore its premises are correct.

• Using the premises of relativity, robinpike’s steps in logic lead to a logical contradiction.

• Since relativity is correct and robinpike’s logic leads to a logical contradiction, therefore robinpike’s logic is flawed.

• The above logic proves that robinpike’s logic is flawed and therefore it is not necessary to further identify the step in his logic that is flawed.

=========================================================

 

This does not mean that I am not grateful for the examples of relativity that have been provided – I am – but please can the step in my logic that is being refuted be identified. For convenience, here are the steps…

 

1. To demonstrate the logical contradiction, I will start with the (most) obvious method of how time is lost: the travelling clock’s time runs at a slower rate (overall) during its round trip. Let’s see how this assumed method causes the issue by using one stay at home clock and two travelling clocks.

By the way, if you dislike the examples that I have chosen, by all means post an alternative, describing how the travelling clock loses time and where in its journey that loss in time occurs, and I will show how the logical contradiction applies to your example.

 

2. The two travelling clocks are initially stationary and synchronized against the stay at home clock. They start the round trip by accelerating side-by-side away from the stay at home clock (i.e. they increase their relative speed with respect to the stay at home clock). Since the assumption (in this example) is that the real loss in time is due to the travelling clock’s time running slow, during the trip to the half-way point, their clocks will now be running slow (with respect to the stay at home clock).

 

3. At the half-way point, one of the travelling clocks decelerates (i.e. reduces its speed with respect to the stay at home clock) to the point where it becomes stationary with respect to the stay at home clock. This means that the travelling clock’s time now runs at the same rate as the stay at home clock’s rate of time.

 

4. But when the travelling clock decelerated, it effectively accelerated away from the second travelling clock (i.e. it increased its relative speed with respect to the second travelling clock). But such an acceleration is just a repeat of the scenario when the travelling clocks first accelerated away from the stay at home clock (although now with respect to different reference frames). This means that the decelerated clock’s time has to run slow with respect to the second travelling clock’s rate of time, which already is running slow with respect to the stay at home clock’s rate of time – AND yet the decelerated clock’s rate of time has to be at the same rate as the stay at home clock’s rate of time (because they are stationary with respect to each other).

 

5. If these two conditions were apparent effects – such a scenario would be possible. But the loss in time is real and so these two conditions cannot occur together – hence a logical contradiction has occurred.

 

6. You can try to avoid this logical contradiction by explain the travelling clock’s real loss in time by other methods, but I think they will all fail for the same reason.

 

7. For example, try the loss in time is because the travelling clock’s progress through space-time is shorter than the stay at home clock’s progress through space-time. This fails at the turn around point because the decelerated clock’s progress through space-time has to be shorter with respect to the second travelling clock’s progress through space-time, which already is shorter with respect to the stay at home clock’s progress through space-time – AND yet the decelerated clock’s progress through space-time has to be at the same rate as the stay at home clock’s progress through space-time (because they are stationary with respect to each other).

 

If you require more detail on a particular step, please ask. To avoid the temptation of gamesmanship, please, there is no need to suggest that I do not understand relativity, or that the steps are so flawed that it is impossible to comment. If you genuinely feel that is the case, may I suggest that you explain why the first step (for example) is flawed.

 

For example: J.C.MacSwell commented on step 4. With “In this case you are assuming all frames have the same absolute time.”

 

My reply is... that is not the assumption. The assumption in step 4. is that the travelling clocks lose time with respect to the stay at home clock because the travelling clocks are on a round trip away and back to the stay at home clock.

 

=============================================

 

The following may be of interest to those trying to understand flaws in logic and why it is always beneficial to identify the flaw. This one is an example in the fallacy of exclusive premises…

No cats are dogs.

Some dogs are not pets.

Therefore, some pets are not cats. (This is the step with the false reasoning.)

 

If you cannot see why the above step is false reasoning, here is a more obvious example…

No planets are dogs.

Some dogs are not pets.

Therefore, some pets are not planets.

 

In the second example, the physical difference between a dog and a planet has no correlation to the domestication of dogs. The two premises are exclusive and the subsequent conclusion is nonsense, as the transpose would imply that some pets are planets.

 

Here is a link to the Wikipedia article on logic… https://en.wikipedia.org/wiki/List_of_fallacies#Formal_syllogistic_fallacies

Edited September 19, 2016 by robinpike

[Tim88]

Celeritas, I wrote a few days ago:

[..]

My objection, as I tried to illustrate, is really about the phrasing. I gave three illustrations, one of which you apparently interpreted inversely of how I meant it (is the rotating frame according to classical mechanics suited for not just geometrical, but also for physical descriptions?); the other two are in that same post and in a following one.

- post 247, the "PS" http://www.scienceforums.net/topic/97466-clocks-rulers-and-an-issue-for-relativity/page-13#entry942987

- post 251 http://www.scienceforums.net/topic/97466-clocks-rulers-and-an-issue-for-relativity/page-13#entry943345

 

As they were short, I'll now paste them back in here:

 

One more illustration that I thought of, as in this discussion there was a comparison with using maps (e.g. #234 by Mordred).

Imagine the captain of an airplane using a series of country maps (Mercator) when flying around the world. His copilot remarks that coastlines change shape when they are flying over them. Really? Is that a good physical description to explain what is happening?

 

Two men are standing on the ground, and one is asking the other how classical mechanics works, as he has some doubts if the theory is self consistent. The other man explains it as follows: look, he says, if I now turn around then in my reference system the Earth is circling around me, and also the planets are swirling about wildly. I see it and I can plot this in a space-time diagram, so the wild acceleration of the planets is real.

 

Do you think that such is a good physical description of what happens according to classical mechanics, and that it serves to convince the other that classical mechanics is self consistent?

 

and then (red bold face emphasis new)

Hi Celeritas, I'm still waiting for your comments on my examples in which I illustrated that your presumed "B spacetime system" may be suited for geometrical descriptions, but it's not generally valid for the laws of physics - as you apparently know.

 

And you replied:

 

 

Tim88,

 

OK, would it be fair to reduce your point to ... the B system does not measure light speed invariant "throughout his own space" in any duration during his own thruster burns. As such, Einstein's convention-for-simultaneity (used in SR) is an invalid convention for non-inertial POVs. The Einstein convention assumes both the 1-way and 2-way light speed is invariant, isotropic at c, and independent of the motion of the light's source.

 

However, that's why I chose to use the collection of MCCIRF POVs, ie to map all entities within the B system over his proper acceleration in a way completely consistent with inertial POVs (who always concur).

 

I realize that asking michel123456 to explain how the A & C clocks exist in the B system during turnabout, is indeed far over his head at this venture. There are different ways to approach that. And wrt the MCCIRF method i mentioned, one cannot consider that method unless they have first mastered the all-inertial scenarios. However, the MCCIRF method (I used as an example) is a preferred method IMO, because if at anytime B drops into coast-mode, there is no disjunct in his spacetime coordinate predictions for other observers, and no matter where they are or how far their range. It's seamless, and completely consistent with all inertial POVs (who all always concur with each other).

 

The MCCIRF method does not use B's own POV, but rather builds his POV from the collections of MCCIRF infitesimals. Twin B, using Einstein's convention-for-simultaneity (of SR), cannot (while non-inertial) map the heavens in concurrence with all inertial observers. Yet, twin B receives the very same light the MCCIRF observers do. So star maps must be built from inertial POVs, and while properly accelerating, twin B's navigation system would have to dynamically adjust the worldlines of all inertial stars (or bodies), and all steadily accelerating bodies. Then, his own navigation system's current map, could always be completely consistent with maps of all inertial observers.

 

That said, the twin POV is invalid in so far as upholding all the laws of physics, if he uses the convention-for-simultaneity used in SR for all inertial observers, which was ...

 

τ₁ = ½ (τ₀ + τ₂)

 

because the above synchronicity eqn requires that the speed of light be invariant at c, not just locally, but across the all of space in any instant. This fails for non-inertial POVs of relativistic rate, because light's speed is no longer c (per measurement) across an expanse of space in the instant.

 

Best regards,

Celeritas

 

As you see, that was not exactly my point, which was much more general. But I'm glad to see that we are getting nearer as you realize that there can be issues concerning physical description when you do geometrical fitting; only there are more than you here seem to realize. And I suspect that maps of the rest systems of some inertial observers cannot be continuously mapped to your map at all; but that's a side issue.

 

If I do measurements in the lab, I'm required to use consistent measurement tools, calibrated to the same measurement standard.

Now, since you talk just like the copilot in my map example, it appears that you disagree with the standard requirements to measurements; and that you agree with the copilot that it's physically correct to state that in the airplane's frame the coastlines are changing shape while you fly over them.

Edited September 19, 2016 by Tim88

[swansont]

To help steer the discussion, if I am reading the counter arguments correctly, then my logical argument is being refuted on the basis that relativity itself has no issue with the scenario under discussion…

 

Summary: When the two travelling clocks are on their journey, coasting side-by-side away from the stay at home clock, their rate of time is seen as slow by the stay at home clock. When the first travelling clock decelerates so that it becomes stationary with respect to the stay at home clock, the stay at home clock sees the first travelling clock’s rate of time return to its own rate of time. At the same time, the second travelling clock sees the deceleration of the first travelling clock as an acceleration away from itself, and so sees the rate of time of the first travelling clock slow down with respect to its (i.e. the second travelling clock) own rate of time.

 

 

 

The last sentence is (possibly) wrong. The 1st clock will slow down relative to the 2nd, but it is because it is now moving with respect to the 2nd traveling clock. The details of the acceleration are irrelevant.

 

Your "logical contradiction" seems to boil down to the fact that absent any acceleration, time dilation is symmetric. Each clock sees the other as running slow. That's going to be true regardless of any prior history that offsets the time reading, so these increasingly complicated scenarios aren't going to shed light on the issue.

[Tim88]

To help steer the discussion, if I am reading the counter arguments correctly, then my logical argument is being refuted on the basis that relativity itself has no issue with the scenario under discussion…

 

Summary: When the two travelling clocks are on their journey, coasting side-by-side away from the stay at home clock, their rate of time is seen as slow by the stay at home clock. When the first travelling clock decelerates so that it becomes stationary with respect to the stay at home clock, the stay at home clock sees the first travelling clock’s rate of time return to its own rate of time. At the same time, the second travelling clock sees the deceleration of the first travelling clock as an acceleration away from itself, and so sees the rate of time of the first travelling clock slow down with respect to its (i.e. the second travelling clock) own rate of time.

 

The steps in logic that appear to being used to refute my logical argument being...

• The above scenario is in exact agreement with what relativity predicts and is in exact agreement with what is measured by experiment.

• Therefore relativity is correct.

• Relativity is correct, therefore its premises are correct.

• Using the premises of relativity, robinpike’s steps in logic lead to a logical contradiction.

• Since relativity is correct and robinpike’s logic leads to a logical contradiction, therefore robinpike’s logic is flawed.

[..]

 

You did not reply directly to my answer, which does not correspond to your summary. Instead, I pointed out the logical error in your argument. And in what follows after the cited section, you repeat that same logical error.

[robinpike]

 

You did not reply directly to my answer, which does not correspond to your summary. Instead, I pointed out the logical error in your argument. And in what follows after the cited section, you repeat that same logical error.

 

Tim88, sorry - it is not always obvious for me to know which posts to reply to. Let me review your replies and I will get back to you.

And Swansont - I will reply to you as well of course - I'm at work at the moment - so will reply as soon as I can.

Edited September 19, 2016 by robinpike

[koti]

 

 

The observation was when comparing this to length contraction of a ruler. A ruler does not have a display to indicate the cumulative distance. The analogue of a ruler undergoing length contraction is a metronome slowing its tick rate. The analogue of a clock measuring a different elapsed proper time is an odometer measuring a different distance traveled.

So a ticking clock which I always have in mind when babbling about physics would do just as fine as a metronome. Got it, thanks for your answer Swansont.

[J.C.MacSwell]

 

4. But when the travelling clock decelerated, it effectively accelerated away from the second travelling clock (i.e. it increased its relative speed with respect to the second travelling clock). But such an acceleration is just a repeat of the scenario when the travelling clocks first accelerated away from the stay at home clock (although now with respect to different reference frames). This means that the decelerated clock’s time has to run slow with respect to the second travelling clock’s rate of time, which already is running slow with respect to the stay at home clock’s rate of time – AND yet the decelerated clock’s rate of time has to be at the same rate as the stay at home clock’s rate of time (because they are stationary with respect to each other).

....

 

For example: J.C.MacSwell commented on step 4. With “In this case you are assuming all frames have the same absolute time.”

 

My reply is... that is not the assumption. The assumption in step 4. is that the travelling clocks lose time with respect to the stay at home clock because the travelling clocks are on a round trip away and back to the stay at home clock.

After the initial departure of the two traveling clocks...the two clocks run slow in the stay home clocks reference frame - AND the stay at home clock runs slow in the traveling clocks reference frame.

 

So given this...how is the bold a contradiction? One of the traveling clocks simply switched frames (though when it did it changed it's view of what it considers "now" back home with the stay at home clock)

[Celeritas]

PS. One more illustration that I thought of, as in this discussion there was a comparison with using maps (e.g. #234 by Mordred).

 

Imagine the captain of an airplane using a series of country maps (Mercator) when flying around the world. His copilot remarks that coastlines change shape when they are flying over them. Really? Is that a good physical description to explain what is happening?

 

Tim88,

 

As VandD had already pointed out, the time dilation and length contraction of SR are not optical effects. They exist in the spacetime system, and are not the result of visual effects caused by light-transit time after departing distant events. Your statement here, as written, suggests that you are comparing optical geometric effects wrt relativistic effects. However, the LTs define how things exist within the system (at any time), not what they appear to look like later after light's transit (although that is of course always calculable).

 

Navigation systems do not care what things might look like per the pilot. They only care about where things exist right now within the coordinate system, and any predictions as to where they will be later or in the future, also cares only about "where they then exist within the system". The pilot knows that the optical effects he witnesses during flight, do not change "how things actually exist within his navigation system's coordinate system" (his own system). He can just "enjoy the show", while basing his flight decisions on his navigation system readouts.

 

Which brings us back to my prior post here. The MCCIRF method, which is just one method, constructs a map of how things "exist in the system". Twin B cannot apply SR's convention-of-simultaneity directly to his track data while non-inertial, because light's speed is not invariant c across the-all-of-B-space while non-inertial. Preferably, one would desire that twin B (of relativistic rate) use a convention-of-simultaneity of his own (while non-inertial), applied directly to his track data ... that produces spacetime solns "that are always in complete agreement with the predictions of all inertial observers". One then asks, what convention-of-simultaneity would that be?

 

Best regards,

Celeritas

 

Two men are standing on the ground, and one is asking the other how classical mechanics works, as he has some doubts if the theory is self consistent. The other man explains it as follows: look, he says, if I now turn around then in my reference system the Earth is circling around me, and also the planets are swirling about wildly. I see it and I can plot this in a space-time diagram, so the wild acceleration of the planets is real.

 

Do you think that such is a good physical description of what happens according to classical mechanics, and that it serves to convince the other that classical mechanics is self consistent?

 

Tim88,

 

I already addressed this post as well, wrt the twin B. I'll briefly restate it here more generally ...

 

There is no harm whatever, that one models the heavens circling himself as the result of earthly proper-rotation. That, is kinematics. One would have to be a masochist to want to do that, but it is not improper. However, if one is to address energy-considerations, well then energy is absolute. And so if the earth bound observer chooses to make himself the zero reference for all relative motion, he cannot also say that "all of the heavens expended energy to cause the relative motion". He must assign the energy expenditure (that caused the relative motion) to that which in fact experienced the applied force. This is more important in relativity than in classical mechanics, for otherwise the twin B could never accurately predict twin A's clock wrt return. Navigation systems always assign itself the zero reference for motion. For a period of proper-acceleration, a spaceship nav system computes the final location and speed wrt the initial parameters as reference. However, for relativistic rates ...

 

Just before B's virtually-instant turnabout, an inertial phase (v=0.866c so gamma=2) is coming to an end. The location of twin A just before B's proper acceleration is (say) 1 light hr. At the moment halfway thru his turnabout, he is momentarily at rest with earth and twin A, and so twin A "must then be" 2 light hr distant. That happens "in virtually no time at all", because of B's virtually instant turnabout. 2 lt-hr being the proper separation between earth and the turnabout point. Not only that, but with A's wild shift in B-space, comes a wild shift in A-time (in only the B system). Twin A's worldline rapidly rotates in its angular orientation wrt the B worldline, because B's line-of-simultaneity remains always-fixed (since he assumes himself the zero-ref for motion). That rotation also requires twin A to advance wildly along his own worldline (not something that A experiences), but only in the B system, and so (per B) the twin A clock ticks wildly fast during his turnabout. Given such, twin B may accurately predict the twin A clock on return, without any consideration of how A himself experiences it all.

 

Again, this is what the MCCIRF method does. It allows twin B to assign himself the zero reference for all motion, but dynamically adjusts worldlines within B's spacetime system knowing that it was "B himself" who underwent the applied force (causing the change in relative motion). In this way, his spacetime predictions always match that of any inertial observer, who we know all concur with each other using an accepted theory. Twin B's nav system accounts for its own proper acceleration, and adjusts all worldlines in B's own system accordingly. B does not ignore "the consideration of energy-expenditure", but rather accounts for it as necessary.

 

So I"ve already addressed this. If you have a different point that I did not address, maybe just say it, cut to the chase. My point here is that energy considerations are not ignored by twin B using the MCCIRF method. He accounts for it. Twin A knows it was twin B who changed in his own state of motion, because twin A is always inertial and never feels his own inertia. However, the spacetime predictions made by twin A are indifferent wrt who properly accelerated". It matters not, to twin A, because he's always inertial. Twin A knows that for higher relative velocity, the B clock slows down, and that's all A needs. Twin B knows that for higher relative velocity, the A clock slows down, and that's all B needs during his inertial phases of his roundtrip. However during non-inertial phases, twin B "cannot and does not" ignore energy considerations, for otherwise his spacetime predictions of twin A fail.

 

Best regards,

Celeritas

Edited September 19, 2016 by Celeritas

[Tim88]

 

Tim88,

 

As VandD had already pointed out, the time dilation and length contraction of SR are not optical effects.

 

Hi Celeritas,

 

As I have pointed out many times in this thread, time dilation and length contraction of SR are not optical effects. As I stated, my illustration was not about optical effects but about physically correct phrasing when using maps.

 

 

[..] The pilot knows that the optical effects he witnesses during flight, do not change "how things actually exist within his navigation system's coordinate system" (his own system). He can just "enjoy the show", while basing his flight decisions on his navigation system readouts.[..]

 

Which brings us back to my prior post here. The MCCIRF method, which is just one method, constructs a map of how things "exist in the system". Twin B cannot apply SR's convention-of-simultaneity directly to his track data while non-inertial, because light's speed is not invariant c across the-all-of-B-space while non-inertial. Preferably, one would desire that twin B (of relativistic rate) use a convention-of-simultaneity of his own (while non-inertial), applied directly to his track data ... that produces spacetime solns "that are always in complete agreement with the predictions of all inertial observers". One then asks, what convention-of-simultaneity would that be?

 

Best regards,

Celeritas

 

I'll try one last time to clarify the illustration, by putting your words in it. The self made Dynamic Mercator method, which is just one method, constructs a map of how things "exist on Earth". The copilot cannot keep the shape of the coastline on his creatively constructed dynamic map constant, because the Earth's projection is not invariant across the sequential reference maps from which he assembles his dynamic map. But that doesn't matter and it's perfectly correct to say that the coastlines change shape when they are flying over; for that's what his dynamic map shows him; it's simply what his method does. What alternative does he have?

 

 

There is no harm whatever, that one models the heavens circling himself as the result of earthly proper-rotation. That, is kinematics. One would have to be a masochist to want to do that, but it is not improper. However, if one is to address energy-considerations, well then energy is absolute. And so if the earth bound observer chooses to make himself the zero reference for all relative motion, he cannot also say that "all of the heavens expended energy to cause the relative motion". He must assign the energy expenditure (that caused the relative motion) to that which in fact experienced the applied force. This is more important in relativity than in classical mechanics, for otherwise the twin B could never accurately predict twin A's clock wrt return.

[..]

 

I think that here you did understand what I meant: that kind of kinematics language is improper when giving a physical explanation in the context of explaining what "really" happens as a result of you suddenly turning around. However, it appears that you nevertheless deem that it's "no harm"... In view of that, I suppose that we will have to agree to disagree!

 

PS. I insist: especially in this thread the topic is about consistency of physical description. In such discussions it's essential to use a single reference standard per physical description of events, and to correctly describe changes of reference standards as such - not as physical changes to objects that, according to the theory, are unaffected.

Edited September 20, 2016 by Tim88

[robinpike]

 

The last sentence is (possibly) wrong. The 1st clock will slow down relative to the 2nd, but it is because it is now moving with respect to the 2nd traveling clock. The details of the acceleration are irrelevant.

 

Your "logical contradiction" seems to boil down to the fact that absent any acceleration, time dilation is symmetric. Each clock sees the other as running slow. That's going to be true regardless of any prior history that offsets the time reading, so these increasingly complicated scenarios aren't going to shed light on the issue.

 

Describing the whole argument in one post is making the subsequent discussions too difficult for me to ascertain which step(s) in the logic are being refuted.

 

Here are the first steps in the logic. Even at this stage of the discussion I do not know if any of these deductions are being disputed, so continuing in discrete, sequential steps can only help.

 

First statements...

1. When the travelling clock completes its round trip journey, it loses time compared to the stay at home clock.
2. This is a loss in time for the travelling clock (as opposed to a gain in time by the stay at home clock).
3. This loss in time is not an apparent loss - it is a real loss in time.

 

From the above statements the following deductions can be made...

 

1. At some point in the travelling clock's round trip, the travelling clock loses real time with respect to the stay at home clock.
2. It is not necessary to identify at which parts of the travelling clock's journey that real time is lost, or the mechanism as to how that real time is lost, for deduction 1 to be valid.
3. It is not necessary to identify by how much that real time is lost, for deduction 1 to be valid.
4. It is not necessary to include any apparent loss in time (or any apparent gain in time) during the travelling clock's journey for deductions 1, 2 and 3 to be valid.
5. What cannot be deduced from the statements 1, 2 and 3, is whether the travelling clock exclusively loses real time, or whether at any point in its round trip, it gains real time with respect to the stay at home clock. All that can be deduced with those statements is that overall the travelling clock loses real time - and therefore at some point during its journey, it loses real time with respect to the stay at home clock, i.e.deduction 1.

[Tim88]

[..]

Here are the first steps in the logic. Even at this stage of the discussion I do not know if any of these deductions are being disputed, so continuing in discrete, sequential steps can only help.

 

First statements...

1. When the travelling clock completes its round trip journey, it loses time compared to the stay at home clock.
2. This is a loss in time for the travelling clock (as opposed to a gain in time by the stay at home clock).
3. This loss in time is not an apparent loss - it is a real loss in time.

 

From the above statements the following deductions can be made...

 

1. At some point in the travelling clock's round trip, the travelling clock loses real time with respect to the stay at home clock.
2. It is not necessary to identify at which parts of the travelling clock's journey that real time is lost, or the mechanism as to how that real time is lost, for deduction 1 to be valid.
3. It is not necessary to identify by how much that real time is lost, for deduction 1 to be valid.
4. It is not necessary to include any apparent loss in time (or any apparent gain in time) during the travelling clock's journey for deductions 1, 2 and 3 to be valid.
5. What cannot be deduced from the statements 1, 2 and 3, is whether the travelling clock exclusively loses real time, or whether at any point in its round trip, it gains real time with respect to the stay at home clock. All that can be deduced with those statements is that overall the travelling clock loses real time - and therefore at some point during its journey, it loses real time with respect to the stay at home clock, i.e.deduction 1.

 

 

About your deductions:

2. according to SR it is not possible. However if you do not require that, then it's no issue.

3. according to SR all inertial frames agree with that; it's thus maybe not required.

4. on face value that may be correct, but it leads to the erroneous deduction in your foregoing post - the same error as explained earlier:

 

 

5. If these two conditions were apparent effects – such a scenario would be possible. But the loss in time is real and so these two conditions cannot occur together – hence a logical contradiction has occurred.

 

The error was, and still is, that "apparent" does not mean "merely apparent". And I gave the illustration with the apparent trajectories:

 

f we have disagreeing measurement tools, or if you see the trajectory of a volleyball from one angle and I see the same from another angle, then we could disagree about the trajectory. But we will still agree if the ball falls through the net or not. Where is the self contradiction?

Remove the apparent trajectories and the ball cannot really hit the target. Voila, self contradiction!

 

In my analysis - in agreement with Swansont's last analysis - your issue is probably more basic than the twin paradox;

[edit: however you do use the twin paradox to infer that time dilation cannot be merely apparent.]

 

After establishing that time dilation is a physical effect, your issue is with the much simpler mutual time dilation paradox. And that can be understood after understanding measurements of objects in motion, such as started in the spin-off thread on mutual length contraction in http://www.scienceforums.net/topic/98501-lost-in-langevins-language/

Edited September 20, 2016 by Tim88

[robinpike]

 

About your deductions:

2. according to SR it is not possible. However if you do not require that, then it's no issue.

3. according to SR all inertial frames agree with that; it's thus maybe not required.

4. on face value that may be correct, but it leads to the erroneous deduction in your foregoing post - the same error as explained earlier:

 

 

The error was, and still is, that "apparent" does not mean "merely apparent". And I gave the illustration with the apparent trajectories:

Remove the apparent trajectories and the ball cannot really hit the target. Voila, self contradiction!

 

In my analysis - in agreement with Swansont's last analysis - your issue is probably more basic than the twin paradox;

[edit: however you do use the twin paradox to infer that time dilation cannot be merely apparent.]

 

After establishing that time dilation is a physical effect, your issue is with the much simpler mutual time dilation paradox. And that can be understood after understanding measurements of objects in motion, such as started in the spin-off thread on mutual length contraction in http://www.scienceforums.net/topic/98501-lost-in-langevins-language/

 

Thank you Tim88. I think the issue here is a wording one. When I talk about an apparent time loss (or apparent time gain), I am not excluding the presence of a real time loss (or a real time gain if that is appropriate). So if I understand you correctly, I agree with your point.

 

A further conclusion (which please discuss if you disagree), is that it is not necessary to include an apparent time loss in order to deduce the real time loss - they are separate things. When a real time loss occurs, the presence of the real time loss cannot be 'denied' by any particular observer's point of view. Whereas for an apparent time loss, this can be dependent on a particular observer's point of view.

 

So to use the example of two objects in motion, moving at different speeds. This means that the distance between them is changing and thus the change in distance is a real effect. But as to how much that distance is changing, or which one (or both) are moving, or even what their apparent closing speed (or separation speed) is, can be dependent on an observer's point of view.

Edited September 20, 2016 by robinpike