The Twin Paradox: Understanding Time Dilation in Space Travel

[Hurkyl]

only Earth and alpha based observers can measure the proper time in the earth-alpha frame.

Your phrasing sounds awfully like you're assuming a preferred frame.

(1) Anybody can make measurements in any coordinate chart they want. There's nothing stopping the spacebound sibling from using an unusual methodology that produces the exact same picture that the Earthbound sibling would get.

(2) Proper time has nothing to do with coordinate charts -- it is an (invariant) quantity describing a time-like path through space-time. (aka the reading of a clock attached to the path) All observers everywhere will agree on the proper time interval of a time-like path.

The traveler measures an illusory rate when he looks at either the alpha or Earth clock from afar

No more illusory than when Earth looks at alpha's clock from afar. Each traveller determines that rate by comparing the readings of the distant clock to the time coordinate in their coordinate chart.

nor can (acceleration) influence the rate of the stay at home clock

Sure it can. That rate is, by definition, simply the comparison of readings on the stay at home clock with the time coordinate of your coordinate chart, and accelerated frames have different coordinate charts than nonaccelerated frames.

does it not follow that acceleration and turn around have nothing to do with resolving the twin paradox?

I'll say it again, the twin paradox involves doing the analysis in some rest frame of the spacebound traveller. You have never addressed the twin paradox, because all of your analyses have been done with the coordinate chart of Earth's rest frame.


It's as if a student came to you with his homework and said "I did this problem two different ways, and got different answers. What did I do wrong?" And then you only look at his first approach and say "I don't see any problem!", never looking at his second approach.

 

[jdavel]

yogi,

Referring to clock rates in the Earth frame and the "photon frame" you arrived at a conclusion and then said, "...if that is what is observed, it cannot be a real."

It's not observed. Nothing is observed from a "photon frame" because there is no such thing as a phton frame.

 

[yogi]

Huykyl - the only supposition is that the earth-alpha frame is an isotroptic light frame - it may turn out that it is preferred for physical reasons but that is not a part of our discussion. We cannot make the same claim about the travelers frame based upon any experimental evidence - that is, if light is isotroptic in earth-alpha, it is only isotropic in the travelers frame by fiat (Einsteins postulates).

Perhaps the traveler can make measurments in the earth-alpha frame that yield the same time as the proper time measured by Earth clocks - but it will involve some complex relationships that are not part of the present discussion - such diversions simply cloud the issues.

When the Earth and alpha clocks are in sych there is no illusion as between them - knowing their distance L apart either would be able to see that he simply has to subtract L/c from what he sees of the other clock in his own frame - there is no illusion - simply a correction which is immaterial to the discussion

I do not have to do any analysis of what the traveling twin sees to expose the fact that the traveler's clock and the alpha clock have logged different times when the traveler arrives at alpha. You are again trying to derail the implications of the different times measured by the proper clocks in each frame - we are not looking at what moving observers may think of our time as they take notice of our clocks on the fly - it is inconsequential unless they are adjacent to the clocks, and that only occurs at the beginning and end (earth and alpha).

As far as not being able to see another point of view as per your student analogy - I would bounce the ball back into your court. You use the reciprocal frame postulates of SR to justify its validity - but it is these very postulates that the critics of the threory have come to suspect.

Einstein derived his transformations based upon "what is observed in the other frame" ...He then proceeded (without giving a reason) to utilize the transforms to predict actual time discrepancies for moving clocks. But he believed for his own reasons (symmetry of nature maybe) that all inertial frames are equivalent,- so the frames had to be reciprocal - and so what is observed is sometimes taken as real when need be to save the theory (e.g. actual age differences measured for pions and other decay particles) or they are taken as observed, when it is necessary to save reciprocity. I suspect near the end of his life he began to realize his own folly - and much to his credit he so stated ...that probably non of his theories would long last.

 

[Hurkyl]

it is only isotropic in the travelers frame by fiat

Wrong. Once you state the precise procedure by which the traveller makes measurements, the physics of his frame can be mathematically derived from that of the Earth-alpha frame.

but it will involve some complex relationships that are not part of the present discussion - such diversions simply cloud the issues.

I disagree. The very notion of frames and measurement is a central issue to this discussion, and you've been avidly avoiding it. My statement was a response to yet another apparent misconception of yours.

When the Earth and alpha clocks are in sych there is no illusion as between them - knowing their distance L apart either would be able to see that he simply has to subtract L/c from what he sees of the other clock in his own frame - there is no illusion - simply a correction which is immaterial to the discussion

What does it to mean to be in sync? And why would being in sync be a meaningful criterion for not being an illusion? I ask not because I wish to assert that the twin's measurements aren't an illusion, but because I have no idea what you attempt to mean, and that your argument doesn't seem to have any physical meaning -- rather, it appears to be an emotional appeal to discredit the notion of measurement in the twin's frame so you can rationalize ignoring this issue.

I do not have to do any analysis of what the traveling twin sees to expose the fact that the traveler's clock and the alpha clock have logged different times when the traveler arrives at alpha.

Correct. (Depending on how alpha's clock get's set, of course)

If this were a homework problem saying "A twin leaves earth, arrives at alpha, then goes back to earth. Blah blah...", then this is how you should approach the problem.

However, you claim to be addressing the twin paradox, and the very statement of the twin paradox involves analyzing what the traveling twin sees. If you are not doing that analysis, you are not addressing the twin paradox.

You are again trying to derail the implications of the different times measured by the proper clocks in each frame

You cannot even begin speak about the implications of clock measurements in frames until you start to address the notion of frames and measurements. (This is the avoidance I mentioned above)

we are not looking at what moving observers may think of our time as they take notice of our clocks on the fly

What if Earth and alpha were moving observers? This seems to invoke some notion of absolute rest, and there is no justification that such a concept makes sense in the universe -- it's a throwback to geocentricism, that the universe rotates around the Earth.

it is inconsequential unless they are adjacent to the clocks, and that only occurs at the beginning and end (earth and alpha).

And, by the same token, Earth's clock is inconsequential to alpha, because they are not adjacent.

As far as not being able to see another point of view as per your student analogy - I would bounce the ball back into your court. You use the reciprocal frame postulates of SR to justify its validity - but it is these very postulates that the critics of the threory have come to suspect.

I don't think the course of this thread has gotten nearly that far.

I find your rebound irrelevant -- I've not professed to be making any sort of defense of SR, but you've repeatedly stated you are attempting to consider the twin paradox.

Secondly, you have assumed the existence of one frame with an isotropic speed of light. I hinted at this earlier -- that's the only assumption I need to derive the Minowski space-time of Special relativity.

You can't talk about frames until you decide how to define frames. One way any inertial observer can perform a measurement is this: fire a beam of light at an object, and wait for its reflection to return. Then, decide that the beam of light struck the object halfway between when you emitted and received the light, and it struck at a distance ct/2 where t was the round trip time.

Using only your assumption of a single reference frame with an isotropic speed of light, I can mathematically deduce all the geometrical facts about Special relativity, such as time dilation, length contraction, and constancy of the speed of light, are valid for the frames I defined in the previous paragraph.

I don't really know what you mean by "reciprical frame postulates". Do you mean the principle of relativity? (Which, incidentally, was part of physics long before Einstein. He was just the first one bold enough to stop assuming that Maxwell's equations contradicted it)

 

[Hurkyl]

Using only your assumption of a single reference frame with an isotropic speed of light, I can mathematically deduce all the geometrical facts about Special relativity, such as time dilation, length contraction, and constancy of the speed of light, are valid for the frames I defined in the previous paragraph.

Addendum -- I also assumed translation invariance (something true of any theory I know except GR), and I cannot determine the scale of the other frames.

 

[jdavel]

yogi,

This thread is becoming a waste of time.

You told me to "take a look at Zhangs book". I thought we were discussing different interpretations of Einstein's theory which he based on the postulate of constant light speed. Zhang doesn't accept that postulate so anything he says is an ALTERNATE theory, not a different interpretation of Einstein's theory.

On another point, you don't seem to be able to get anyone to understand what you mean by simultaneity. There's a way to describe the trip from Earth to alpha without worrying about simultaneity. Give each observer (T, E and A) a telescope so each of them can compare what their own clock reads with what they see (through their telescope) on the other clocks, any time they want. Try working out what everyone will see at the start of T's trip, along the way, and when he gets there. It's all very continuous, very agreeable, and not at all open to interpretation!

 

[RandallB]

Now let's look at things from the photon frame - no time is logged in the photon frame going out or returning - on the outbound leg the photon must see time in the Earth alpha frame passing more slowly if the situation is reciprocal - but this would mean the Earth time is accumulating at a lesser rate that zero [the proper time measured by the photon clock] Again, if that is what is observed, it cannot be a real.

No fair Yogi – that just a magicians trick of miss-direction!

I enjoy looking in every once in awhile, and yogi you’ve been changing your view to suit yourself unfairly. You can use a “Photon” as a traveler but not so casually as you have.

1)“from the photon frame”
you want us to accept this as being just one frame IT’S NOT the returning frame is much different that the out bound frame! If you can get people to believe this is one frame of course you can trick them disagreeing with SR.

2) “photon must see time in the Earth alpha frame passing more slowly”
No you’ve already agreed in posts long ago when you look across to stations or ships with synced clocks they appear to run FAST. This confirms that the Earth and Alpha are running SLOW as the traveling photon sees Alpha clock stuck on “1 sec”

3) It works
But if the photon uses refection to join a “fellow photon” that started from Beta (at Earth-Alpha-Beta time stamp “0”) on its way to Earth intersecting with Alpha at “1 sec”. Then same rules must apply our fellow photon and it is seeing Earth ‘stuck’ already at “2 sec” as it comes in at v = c over a distance of “0”. Now the traveling photon is going the see the excactly same thing when it reflects, because it's now in the “fellow photon’s” frame going c in the opposite direction. Earth will arrive stuck on a time of “2 sec”. NOT because its clock or distance LURCHED about, like to many folks enjoy saying, but because in the new frame of the fellow proton Earth already was and is that way! The traveling photon has just changed frames that all.

4) “if that is what is observed, it cannot be a real“
It is observed and is real in every test I’ve ever heard of.
In fact I’m finding hard to believe you don’t see it, and are just being contrary for the fun of it.

In SR there is no Paradox:
If you want to convince me that LR is worth looking into at all.
Show me all the times, locations by distances, using two ships passing Earth and Alpha in one direction. The 2nd ship follows the first to pass Earth by a distance in their frame equal to the separation between Earth and Alpha in the Earth frame. Add a third ship going the other way at Alpha when the first ship is at Earth in Earth time. I know anyone here can detail the passing time that with ease for SR. (And of course someone can yell that we’re all wrong) But I’ve never seen detailed what LR says the passing times in the three different frames should be using LR. Can LR even do it? It would at least demonstrate the difference from SR if there is one. If you could do that, I would be impressed. Use you favorite speeds and distances.

 

[Alkatran]

I always think a picture helps with the twin paradox: here's a really bad one.
http://www.vbforums.com/attachment.php?attachmentid=33201&stc=1

The black line is the ship (or ships, whatever)
The green bar is the earth
The blue bar is alpha
The grey bar are 'now' lines for the spaceship: Consider them snapshots of everything happening in the rest frame of the ship
Similarly the blue and green lines are snapshots for Earth and alpha

The red lines are also snapshots for Earth and alpha.

Ignore the picture on the right, it's... umm not consistent at all! (notice how alpha is on the wrong side...)

The main thing to notice is the left picture, how the 'now' lines jump when the ship(s) speed changes.

This isn't a faster than light effect because the ship can't know about this until light reach it from that frame... It's like saying "oh, if I rotate a spotlight, the circle of light can exceed c" but that's because the 'circle of light' isn't a particle... it's an abstract thing.

 

[yogi]

If you don't follow the methodology of reducing the problem to separate frames where all measurements are proper, I cannot think of any other way to get the point across.

There are literally hundreds of articles on the net dealing with these issues - I would guess that everyone who writes on the subject has started out with the same introduction to SR in some book or some course ...and being told that SR is unassailable - but literally thousands have found they cannot accept the smoke and mirrors - back and forth rationale, that attempts to anchor real time dilation to distorted illusions that derive from subjective interpretations of space and time in a relatively moving frame. To many, this isn't physics - its metaphysics.

I can find serious fault with many of the statements that have been made in posts 104 - 107 but to answer them would only proliferate this already too long thread in many different directions.

RandallB - you have asked a question that deserves an answer - While I am not totally sold on LR, I think it may better approximate nature than either SR or MLET. You would get exactly the same answer in the problem you posed as you would get in SR or MLET. So why question SR. Because even though the answers are the same, they come about for different reasons. Theories that depend from a preferred frame say that time flows slow in the frame that is in motion wrt the preferred frame - but unlike SR (which asserts that all inertial frames are equivalent) LR claims that if you were in a frame in motion with respect to the Earth's gravitational field, time on Earth would run faster not slower. In other words, there is no reciprocity between the Earth centered reference frame and the frame of the high speed pion for example. In MLET, the preferred frame is an ether. In one of my earlier posts, I took as the first frame one where light is isotropic (not because of Einstein's postulate) but because it will always be possible to find a frame where that is the case. It might be a frame centered on the G field of the Earth as LR postulates or it might be a frame where the CBR is isotropic.

Hope that helps

 

[ElectroPhysics]

Stop it Please...

 

[JesseM]

RB - In the series of clock(s) systems thought experiments - what results is that each observer, when viewing a single clock in the other frame, will see it going slower - but when viewing a succession of passing clocks the opposite is true - but that doesn't address the problem because we can never have two clocks each running slower than the other - and we can never have a first clock running slower than a second clock w/o some physical reason.

If you have a series of clocks which always show the correct time in some other reference frame, and you fly by them, you will see each clock running at the same rate, slower than your onboard clock. But you will also see that the clocks appear to be out-of-sync relative to your own reference frame, although they are in-sync in the frame whose time they are measuring. So, for example, if I travel at relativistic speeds from one end of the galaxy to another, and pass by a long row of clocks which measure time in the galaxy's rest frame, then each clock will run slower than my onboard clock, but in my frame the clock on the far end of the galaxy may start out hundreds of thousands of years ahead of the clock on the end I start the journey, so that when I arrive on the far end it will be hundreds of thousands of years in the future according to "galaxy time", even if the journey only took a few years for me and every clock I passed by appeared to be running slower than my onboard clock.

 

[Hurkyl]

To restate what JesseM said, the high speed train observes:


If I measure Earth time by looking out the window and observing the time on the nearby clock, then Earth time is running faster than my clock.


If I measure Earth time by focusing on one single Earth clock, and adjust the readings to account for the delay due to light travel, then Earth time is running slower than my clock.


But anyways, the point I want to make clear is this:

LR claims that if you were in a frame in motion with respect to the Earth's gravitational field, time on Earth would run faster not slower.

This statement is absolutely meaningless until you specify how you plan on measuring the time on earth.

SR does say specifically what it's measuring: the second case I gave above.

And, if LR does happen to agree with SR when all measurements are done in Earth's inertial frame, then LR absolutely, positively must agree with SR on the results of that experiment.

You don't even need to assume that the agreement is in Earth's inertial frame -- just that they agree in anyone frame.


Why is this true? Because SR precisely defines a method of measurement, and the results of that measurement can be determined in any frame. Probably the simplest method is this, which I've stated before:


An observer measures the position and time of an event as follows:

(1) It shines a beam of light at time S.
(2) The beam of light is reflected back.
(3) It receives its beam of light at time T.

Then, the observer decides that the beam of light struck the object at time (S + T)/2, and that the object was at a distance of (T - S) c / 2.


This is a well-defined experimental procedure for determining positions and times of events, and the decision made by the observer can be computed in any reference frame.

In particular, if, say, LR and SR agree in your favorite reference frame. Let's call it F. Then, for any observer traveling with a constant speed in F, one can compute, entirely in F, the results that the observer will get for any measurement. Since LR and SR agree in F, they must agree on what this observer measures too.

In other words:

If any theory agrees with Special Relativity for one particular frame of reference, then that theory absolutely, positively, must agree with the predictions of Special Relativity for all reference frames, provided that all observers perform measurements in the way I specified above (or in some equivalent way).

 

[RandallB]

FTL > faster than light
EPR > Einstein, Podelesky and Rosen
GPS > Global Position Satellite
LR > Lorenz Relativity
SR > Special Relativity
GR > General Relativity
MLET> ?
light is isotropic> ?

I agree with the originator of this thread, ElectroPhysics, May be time to stop this one and close it for the archives.

Just - What is “MLET”

Also: Is there such a thing as a “Frame” where Light is isotropic
I don’t understand what that could mean. Is there any realistic way of making measurements from it (Including looking at light going the other way) ?

Yogi
Yes it has been helpful, but I’ve come up with different answers than you.

Your GPS stuff confirm SR when looked realistically
I believe high speed pion example does show ‘reciprocity’ with earth.
And my review of EPR does not show a FTL event.
But still need to work on extracting GR from SR. But I’ll put that in another post.

In time you may learn the same. good luck .

 

[Hurkyl]

Also: Is there such a thing as a ?Frame? where Light is isotropic

I assume yogi meant a coordinate chart in which light would be measured as traveling with constant speed, no matter where it is, when it is, or which direction it travels.

 

[JesseM]

RB - In the series of clock(s) systems thought experiments - what results is that each observer, when viewing a single clock in the other frame, will see it going slower - but when viewing a succession of passing clocks the opposite is true - but that doesn't address the problem because we can never have two clocks each running slower than the other - and we can never have a first clock running slower than a second clock w/o some physical reason.

If you have a series of clocks which always show the correct time in some other reference frame, and you fly by them, you will see each clock running at the same rate, slower than your onboard clock. But you will also see that the clocks appear to be out-of-sync relative to your own reference frame, although they are in-sync in the frame whose time they are measuring. So, for example, if I travel at relativistic speeds from one end of the galaxy to another, and pass by a long row of clocks which measure time in the galaxy's rest frame, then each clock will run slower than my onboard clock, but in my frame the clock on the far end of the galaxy may start out hundreds of thousands of years ahead of the clock on the end I start the journey, so that when I arrive on the far end it will be hundreds of thousands of years in the future according to "galaxy time", even if the journey only took a few years for me and every clock I passed by appeared to be running slower than my onboard clock.

By the way yogi, I just posted this thread with some illustrations of a scenario like this, with two rulers moving in parallel next to each other, and clocks placed at regular intervals along each ruler, sychronized within the ruler's reference frame. You may find it helpful to look at the diagrams and see exactly how things work out consistently in this scenario.

It would be pretty easy to extend this sort of thing to the "triplet paradox" you were describing earlier on this thread. Imagine each triplet is riding along a ruler, and all the rulers are moving at constant velocity relative to one another. We can say triplet A corresponds to the earthbound triplet in your scenario, triplet B corresponds to the one traveling away from earth, and triplet C corresponds to the one traveling towards the earth. At the initial moment when A and B are right next to each other, their clocks read the same time; then we can also specify that at the moment B and C pass next to each other, their clocks must also read the same time. In this case, when C passes A, C's clock will be behind A's clock. In A's frame, the clocks of both B and C are ticking slower than his own, by the same amount; but both B and C see A's clocks ticking slower then their own clocks, also by the same amount. However, B sees all the clocks along A's ruler to be out-of-sync, just like in my illustrations--he sees clocks closer to where A is sitting being behind clocks farther from where A is sitting. On the other hand, C also sees the clocks along A's ruler being out-of-sync, except he sees clocks closer to where A is sitting being ahead of clocks farther from where A is sitting. This is the explanation for why there is no inconsistency in the fact that C's clock will be behind A's clock when they finally pass, despite the fact that both B and C saw A's clocks running slower throughout the journey. If you're still having trouble seeing this, even after looking at the illustrations in my other post, I can make up a more detailed scenario and calculate some numbers explicitly to show how this will work.

note: this discussion is continued on this thread.