Clock postulate and differential aging

[MikeLizzi]

Which one?
In twin paradox astronaut has 2 different diagrams: on the way away and when he returns. You can not have just one, as astronaut changes the frame

Hi Dmitry67,

Thank you for your post. If I may restate what you wrote... (I think english is not your native language)

In the twins paradox (with the astronaut as the observer) one must use 2 different diagrams. One for the case where the Earth is moving away and one where the Earth returning.

OK?

 

[Dmitry67]

yes, correct.

 

[MikeLizzi]

yes, correct.

Hi Dmitry67,

Thank you. I put down some numbers for the first diagram. I assume gamma is 2. The first column is the time on the astronaut's clock. The second column is the calculated time on an Earth clock. OK?

First Diagram:

Astronaut Time____Earth Time
(observer)
0 _______________ 0
1 _______________ .5
2 _______________ 1.0
3 _______________ 1.5
4 _______________ 2.0
5 _______________ 2.5
Turn around

 

[Mentz114]

No single space-time diagram can represent the view-point of the accelerated observer, you need a different one for every instant along the worldline.

But what is the importance of that ? We know that elapsed time is equated with the proper length, so I don't really see that it matters.

 

[Frame Dragger]

No single space-time diagram can represent the view-point of the accelerated observer, you need a different one for every instant along the worldline.

But what is the importance of that ? We know that elapsed time is equated with the proper length, so I don't really see that it matters.

Again, I've been asking this question several times without any meaningful effect. *shrug*

EDIT: Al68: I pointed out 2 pages ago that there is an implied period of accelleration and braking, but it didn't seem to faze him. :/ I'm sticking with my "looking the wrong way through binoculars" metaphor. This is the use of a tool in the manner it wasn't intended, then drawing conclusions that a paradox exists, or a skeptic requires satisfaction in this particular form.

 

[Al68]

Now somebody's clock can go slower or faster than yours but it can't jump...What is really happening is that the astronaut determines the earthbound twin's clock is running FASTER than his during the spaceship turnaround. Skipping that calculation is why this artificial jump needs to be added.

Yep, exactly. Of course time doesn't jump, it only appears to jump as an artifact of the simplifying assumption of instantaneous turnaround, which equally can't happen. In the accelerated frame of the ship, Earth's clock runs fast. The greater the acceleration, the faster Earth's clock runs in the ship's frame. It's only modeled as a jump associated with instantaneous turnaround to simplify the math.

In reality there must be a finite interval for the turnaround acceleration and for Earth's clock to advance. They are both only treated as instantaneous to simplify the math, not to claim it's physically possible.

I've never seen a Minkowski diagram for the ship twin either, but it couldn't be in the standard form. It would have to be modified to allow for gravitational time dilation of clocks in an accelerated reference frame, but I doubt it could then be called a Minkowski diagram.

Einstein's own 1918 Twins paradox resolution is unique in that it does consider the non-inertial reference frame in which the ship is "stationary" the entire trip. It skips the math, presumably because his intended audience wouldn't need it to be shown. You can find it here: http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity

 

[Dale]

Your comment would seem to support my belief that I have not yet see a correct Minkowski diagram with the astronaut as the observer. (In fact I believe it can't be done) The references given by Frame Dragger give the astronaut the orthagonal axis and then offer a kind of compensation for the ensuing contradiction. Yet those references are considered canon.

It is certainly ok to use non-inertial coordinates in which a non-inertial observer is given a constant coordinate position, but then those diagrams are not Minkowski diagrams because the Minkowski metric would not be valid in such coordinates. That would be a more general class of coordinate charts where general metrics are permitted rather than limiting it to the Minkowski metric. You certainly can use such coordinate systems, provided you are careful with your math and if you do so you always get the same result for the twins.

 

[Frame Dragger]

It is certainly ok to use non-inertial coordinates in which a non-inertial observer is given a constant coordinate position, but then those diagrams are not Minkowski diagrams because the Minkowski metric would not be valid in such coordinates. That would be a more general class of coordinate charts where general metrics are permitted rather than limiting it to the Minkowski metric. You certainly can use such coordinate systems, provided you are careful with your math and if you do so you always get the same result for the twins.

...Which brings the whole thing back to... why?! The original statement that a "skeptic" would somehow require a valid reversal of the diagram is still baffling.

 

[MikeLizzi]

Yep, exactly. Of course time doesn't jump, it only appears to jump as an artifact of the simplifying assumption of instantaneous turnaround, which equally can't happen. In the accelerated frame of the ship, Earth's clock runs fast. The greater the acceleration, the faster Earth's clock runs in the ship's frame. It's only modeled as a jump associated with instantaneous turnaround to simplify the math.

In reality there must be a finite interval for the turnaround acceleration and for Earth's clock to advance. They are both only treated as instantaneous to simplify the math, not to claim it's physically possible.

I've never seen a Minkowski diagram for the ship twin either, but it couldn't be in the standard form. It would have to be modified to allow for gravitational time dilation of clocks in an accelerated reference frame, but I doubt it could then be called a Minkowski diagram.

Einstein's own 1918 Twins paradox resolution is unique in that it does consider the non-inertial reference frame in which the ship is "stationary" the entire trip. It skips the math, presumably because his intended audience wouldn't need it to be shown. You can find it here: http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity

Hi Al68,

Yours is the point I was trying to make. Thank you very much for stating it.

To those who think I was being unscientific:

Are you now going to declare Al68 unscientific too?

Just adding the following: I am thu with this thread.

 

[Dmitry67]

Hi Dmitry67,

Thank you. I put down some numbers for the first diagram. I assume gamma is 2. The first column is the time on the astronaut's clock. The second column is the calculated time on an Earth clock. OK?

First Diagram:

Astronaut Time____Earth Time
(observer)
0 _______________ 0
1 _______________ .5
2 _______________ 1.0
3 _______________ 1.5
4 _______________ 2.0
5 _______________ 2.5
Turn around

Yes, then

5 (after turnaround) __ 17.5
6 _______________ 18
7 _______________ 18.5
8 _______________ 19
9 _______________ 19.5
10 ______________ 20

You are probably surprised by the gap in "Earth time"? It is not something really physical. It is just a a position of Earth at 4D miskovski spacetime based on the calculations of the spaceship. When you turn around, you rotate that diagram, and positions of the points change.

 

[George Jones]

You are probably surprised by the gap in "Earth time"? It is not something really physical.

Right. Visual appearances are given by the Doppler effect, so moving clocks can to run fast or slow, depending on the relative direction of travel. I worked a couple of examples in

https://www.physicsforums.com/showthread.php?p=2186296#post2186296.

As the astronaut watches (with a telescope) a clock on Earth, the astronaut does not see the visual image of the Earth clock make a discontinuous jump in time.

 

[MikeLizzi]

Yes, then

5 (after turnaround) __ 17.5
6 _______________ 18
7 _______________ 18.5
8 _______________ 19
9 _______________ 19.5
10 ______________ 20

You are probably surprised by the gap in "Earth time"? It is not something really physical. It is just a a position of Earth at 4D miskovski spacetime based on the calculations of the spaceship. When you turn around, you rotate that diagram, and positions of the points change.

Hi Dmitry67,
Thanks for your reply. No, I am not surprised by the gap. I know about it. And I know that it is not really physical. That's what I wanted to focus on.

If you have a solution that is not physically real then there is one of two possibilities:
1. You solved the problem wrong.
2. The problem is not physically real.

Your solution is correct. So that means the problem, as traditionally described, is not physically real. I tried to get the other members of this forum to recognize that but I was not successfull. Poster "Al68" said the same thing. Since he is a senior member of this forum, other members apparently accepted his statement without challange.

There is more that can be discovered be examining the Twins Paradox but I have accomplished as about as much as I think I can with this thread so I will not bother you anymore.

 

[Dale]

So that means the problem, as traditionally described, is not physically real. I tried to get the other members of this forum to recognize that but I was not successfull.

I don't know what you are talking about. The majority of the regulars on this forum already understand and recognize that. That is why most of us prefer the spacetime geometric approach.

 

[Frame Dragger]

I don't know what you are talking about. The majority of the regulars on this forum already understand and recognize that. That is why most of us prefer the spacetime geometric approach.

I guess he really likes things a particular way?

 

[DanRay]

In a recent thread about differential aging in the archetypal twin scenario, I suggested that the periods of oscillators are affected by accelerations, or in other words that a clock's tick rate is affected by changes in its speed.

Time dilatation is a consequence of Special Relativity where acceleration is not allowed. It is demonstrated by solving the Lorentz Transformation equation specific to time as the unknown when considering extream relative speeds from one frame of reference to another.

The inertial reference systems used in Special Relativity are alway straight line movement at a constant speed. That is the definition of an inertial reference system.

 

[bcrowell]

Time dilatation is a consequence of Special Relativity where acceleration is not allowed.

This is incorrect. Here is a cut and paste that may be useful, from a FAQ I maintain at http://www.lightandmatter.com/cgi-bin/meki?physics/faq .

====

Does special relativity apply when things are accelerating?

Yes. There are three things you might want to do using relativity: (1) describe an object that's accelerating in flat spacetime; (2) adopt a frame of reference, in flat spacetime, that's accelerating; (3) describe curved spacetime. General relativity is only needed for #3. The reason you'll see statements to the contrary is historical. Einstein published special relativity in 1905, general relativity in 1915. During that ten-year period in between, nobody really knew what the boundaries of applicability of special relativity were. This uncertainty made its way into textbooks and lectures, and because of the conservative nature of education, some students are still hearing, a century later, incorrect assertions that SR can't handle #2, or even #1 (which would make SR a useless theory for describing interactions!).

This issue often comes up in discussions of the twin paradox. A good way to see that general relativity is totally unnecessary for understanding the twin paradox is to pose a version in which the four-vector equation a=b+c represents the unaccelerated twin's world-line a and the accelerated twin's world-line consisting of displacements b and c. The accelerated twin is subjected to (theoretically) infinite accelerations at the vertices of the triangle. The triangle inequality for flat spacetime is reversed compared to the one in flat Euclidean space, so proper time |a| is greater than proper time |b|+|c|.

In an accelerating frame (#2), the equivalence principle tells us that measurements will come out the same as if there were a gravitational field. But if the spacetime is flat, describing it in an accelerating frame doesn't make it curved. (Curvature is invariant under any smooth coordinate transformation.) Thus relativity allows us to have gravitational fields in flat space --- but only if the gravitational field is a certain special configuration, such as a uniform field. SR is capable of operating just fine in this context. For example, Chung et al. did a high-precision test of SR in 2009 using a matter interferometer in a vertical place, specifically in order to test whether there was any violation of Lorentz invariance in a uniform gravitational field. Their experiment is interpreted purely as a test of SR, not GR.

Chung -- http://arxiv.org/abs/0905.1929

 

[yuiop]

...
I've never seen a Minkowski diagram for the ship twin either, but it couldn't be in the standard form. It would have to be modified to allow for gravitational time dilation of clocks in an accelerated reference frame, but I doubt it could then be called a Minkowski diagram.

Correct, it would not be a Minkowski diagram. If the ship twin has an initial velocity as he passes the Earth the first time and then decelerates so that he eventually comes to rest wrt the Earth and then continues decelerating until he returns to the Earth, with constant acceleration as measured on the ship throughout the trip, then the path of the Earth could be plotted on a Rindler diagram and the Earth would appear to follow a curved path. However this is a curved path through Rindler spacetime which is different animal from a curved path through Minkowski spacetime. A careful analysis of the elapsed proper time of the Earth would still show that more proper time passes on the Earth than onboard the ship by the time they meet again.

 

[DanRay]

This is incorrect. Here is a cut and paste that may be useful, from a FAQ I maintain at http://www.lightandmatter.com/cgi-bin/meki?physics/faq .

Dear bcrowell,

The scientific world never heard of time dilation until Einstein intorduced it along with his explanations about the consequences of Special Relativity. His explanation is in his book "Relativity" starting with section 7 and continuing through section 17 where he talks about "Minkowski's Four-Dimentional Space." In this section is his first use of the word continuum. But nowhere until Part II which pertains to General Relativity does he deal with anything that includes acceleration. Time dilation was well understood as a consequence of Special Relativity long before he published General Relativity and the Twin Paradox arose before General Relativity as an effort to debunk Special Relativity and Einstein's time dilatation, not to support it.

The most common English translation of Einstein's first Special Relativity Postulate is:
"The laws of physics are the same in all inertial reference systems." The definition of an inertial system is that all motion is in Einstein's own words "in uniform translation " which indisputably disallows acceleration. That doesn't mean that time dilation that includes acceleration can't exist. it simply means you can't atribute that to Special Relativity.

 

[Frame Dragger]

This is incorrect. Here is a cut and paste that may be useful, from a FAQ I maintain at http://www.lightandmatter.com/cgi-bin/meki?physics/faq .

Dear bcrowell,

The scientific world never heard of time dilation until Einstein intorduced it along with his explanations about the consequences of Special Relativity. His explanation is in his book "Relativity" starting with section 7 and continuing through section 17 where he talks about "Minkowski's Four-Dimentional Space." In this section is his first use of the word continuum. But nowhere until Part II which pertains to General Relativity does he deal with anything that includes acceleration. Time dilation was well understood as a consequence of Special Relativity long before he published General Relativity and the Twin Paradox arose before General Relativity as an effort to debunk Special Relativity and Einstein's time dilatation, not to support it.

The most common English translation of Einstein's first Special Relativity Postulate is:
"The laws of physics are the same in all inertial reference systems." The definition of an inertial system is that all motion is in Einstein's own words "in uniform translation " which indisputably disallows acceleration. That doesn't mean that time dilation that includes acceleration can't exist. it simply means you can't atribute that to Special Relativity.

Nothing about TD violates SR's "The laws of physics are the same in all intertial reference systems. If one person is subjected to a force, or not, in one inertial frame, that doesn't require that everyone else be subjected to that force.

Everyone observing the process of the astronaut taking his TD trip would agree on the physics, and causality, and the outcome. That can be formulated within SR. GR extends the concept, but it was there in SR.

 

[Al68]

So that means the problem, as traditionally described, is not physically real. I tried to get the other members of this forum to recognize that but I was not successfull. Poster "Al68" said the same thing. Since he is a senior member of this forum, other members apparently accepted his statement without challange.

That's only because I pointed out that the "impossible time jump" was an artifact of the corresponding impossible instantaneous turnaround.

The fact that an instantaneous turnaround is often stipulated to simplify the math doesn't mean that anyone thinks it's physically possible. Everyone already agreed that an instantaneous turnaround, and therefore the "time jump", couldn't be "physically real". They just thought it was too obvious to be a legitimate point of discussion.

But an apparent time gap could be physically real: Suppose that the turnaround is very short compared to the interval between observations of the Earth clock by the ship twin. In that case, the ship twin would physically observe a "time jump".

Of course that's just the equivalent of "don't blink or you'll miss it".

 

[sylas]

The most common English translation of Einstein's first Special Relativity Postulate is:
"The laws of physics are the same in all inertial reference systems." The definition of an inertial system is that all motion is in Einstein's own words "in uniform translation " which indisputably disallows acceleration. That doesn't mean that time dilation that includes acceleration can't exist. it simply means you can't atribute that to Special Relativity.

DanRay... you can handle acceleration with special relativity just fine. Einstein did this too. An accelerated frame is not inertial, of course, but you can still describe accelerated motions from an inertial frame, and using SR you can find all the time dilations that apply for any motion you like... as long as there's no gravity involved. Accelerations are not a problem.

When Einstein developed general relativity, he did so by generalizing the consequences for an accelerated observer (which can be found using SR) to those of an observer in a gravitational field. He did not need GR to describe accelerated motions, or find the time dilation of accelerated motions.

bcrowell has given some helpful references if this seems confusing, but it is a mathematical fact that you can use special relativity to figure out all the time dilations for any motion you like. You just integrate the proper time c²dτ² = c²dt² - dx² - dy² - dz² along any path given using x,y,z,t co-ordinates in an inertial frame.

Cheers -- sylas

 

[Demystifier]

No.

I had already provided an example:
2 twin scenatio with identical acceleration, with the same distance where second twin is accelerated, but with 2 different "arms" - total travel distance where the accelerated twin is moving without acceleration

Based on your hypotesis, age difference will be the same in both cases (as acceleration is identical), while it is not (in a case with a longer arm there is more difference)

Dmitry is right. See e.g. Eq. (7) in
http://xxx.lanl.gov/abs/physics/0004024 [Found.Phys.Lett. 13 (2000) 595]

 

[ThomasT]

Dmitry is right. See e.g. Eq. (7) in
http://xxx.lanl.gov/abs/physics/0004024 [Found.Phys.Lett. 13 (2000) 595]

The person I was primarily asking (about whether or not we were in agreement) was DaleSpam, who replied that we are in agreement (since we agree on the math and the experimental results) and that the problem (that I was having) was just a semantic one.

OK (or no)?

 

[Al68]

The most common English translation of Einstein's first Special Relativity Postulate is:
"The laws of physics are the same in all inertial reference systems." The definition of an inertial system is that all motion is in Einstein's own words "in uniform translation " which indisputably disallows acceleration..

This just isn't true. An inertial frame means that the reference frame isn't accelerated. Objects may very well accelerate relative to an inertial frame in SR.

In other words, the only thing not allowed to accelerate in (1905) SR is the reference frame. Even that restriction was overcome (by Einstein) around 1907 by defining an accelerated frame by specifying its motion relative to a specified inertial frame.

 

[bcrowell]

This just isn't true. An inertial frame means that the reference frame isn't accelerated. Objects may very well accelerate relative to an inertial frame in SR.

Right.

In other words, the only thing not allowed to accelerate in (1905) SR is the reference frame. Even that restriction was overcome (by Einstein) around 1907 by defining an accelerated frame by specifying its motion relative to a specified inertial frame.

I think it's clear that people eventually worked out all the issues with treating accelerated frames in SR, and that most modern authors consider SR to be defined by flat spacetime, not unaccelerated frames. But does this really go back as far as Einstein in 1907? E.g., I have in front of me a translation of "The foundation of the general theory of relativity," A. Einstein, Annalen der Physik 49 , 1916. In the introduction:

The word "special" is meant to intimate that the principle is restricted to the case when K' has a motion of uniform translation relatively to K, but that the equivalence of K' and K does not extend to the case of nonuniform motion of K' relatively to K."

So it seems to me that as late as 1916, Einstein was defining SR in terms of unaccelerated frames, not flat spacetime.