The Twin Paradox: Understanding Time Dilation in Space Travel

[Hurkyl]

If the alpha clock is synchronized with the Earth clock,

Don't forget -- you mean to determine this using Earth's rest frame.

 

[jdavel]

Hurkyl,

"Don't forget -- you mean to determine this using Earth's rest frame."

Correct.

 

[jdavel]

yogi,

"Would you then permit me to claim that if T immediately turned around at alpha and returned to Earth at the same speed, the total time difference would be double that measured for the one way excursion?"

Yes. On T's return to earth, the Earth clock will read 2L/v and T's clock will read (2L/v)/gamma.

 

[yogi]

djavel - Wonderful - we agree upon that - so can we now say that neither acceleration nor turn around is significant in explaining the clock paradox. In other words, while the traveler's return to the starting point is part of the journey, the Earth is really a convenience point for measuring the age difference ---the turn around and the consequent changing of frames occassioned thereby does not play a role per se in the age difference upon arrival back on earth.

Hurkyl - when I refer to sync for one instant - I am saying that if T and S clocks both read 12:00 at the time of passby, then since alpha reads the same as S, all three clocks will read the same initially - and for one instant only.

 

[Hurkyl]

alpha reads the same as S, all three clocks will read the same initially

And I am saying that, until you state how you are comparing spatially separated clocks, these two statements are pure nonsense.

One such way is to select a coordinate chart, such as an inertial reference frame from SR, and then compare readings that occur at the same coordinate time.

so can we now say that neither acceleration nor turn around is significant in explaining the clock paradox ... the turn around and the consequent changing of frames occassioned thereby does not play a role per se in the age difference upon arrival back on earth.

As I've mentioned before, the "clock paradox" arises when you also do the analysis in the rest frame of the spaceship -- the turn around is crucial to explaining why that analysis doesn't predict that Earth clock doesn't read less than the space clock.

 

[yogi]

Hurkyl - I thought you agreed that the two clocks read differently at the halfway point (when T reached alpha).

Clocks can be compared in a common frame and they can be compared in relatively moving frames when they are adjacent - this does not violate any tenant of SR - It is not necessary to specifically set out a particular means of reading a clock or of setting it so long as they both read the same in the same frame - we simply say two clocks in the same frame are in sync - you can use Einstein's method if you like - but this is just another example of your introducing a SR bias into the thought experiments - the very purpose of which is to examine whether the theory comports with the real world in every case - as I have repeatedly stated, Einstien's derivation started with observing events in a moving frame - all measurements were "as viewed from the other frame" as Einstein said 3 times in the first paragraphs of the derivation in his 1905 paper - then w/o reason or explanation, he applies these transforms to predict that clocks will experience actual time differences (loss of sync) when moved apart and returned. It is the propriety of this shift from observation to reality that is at root - so what I was attempting to do was to confine all measurements to those which are proper and those which are adjacent. I know you can always pull yourself up by the bootstraps and use the same shifting methodology to show SR is correct. But if I define as true 1 + 2 = 4 , I can also prove 2 + 2 = 5

 

[Hurkyl]

Hurkyl - I thought you agreed that the two clocks read differently at the halfway point (when T reached alpha).

Only on the condition that I had correctly guessed how alpha's clock is set.

you can use Einstein's method if you like - but this is just another example of your introducing a SR bias into the thought experiments

I've asked you plenty of times to specify what method you intended to use. Einstein's method, incidentally, conforms to that of any (flat-space) preferred frame theory I know, when done done relative to that preferred frame.

 

[jdavel]

yogi,

"when I refer to sync for one instant - I am saying that if T and S clocks both read 12:00 at the time of passby, then since alpha reads the same as S, all three clocks will read the same initially - and for one instant only."

Not true. If T and S are synched and S and alpha are synched, then T and alpha won't be synched.

 

[Hurkyl]

Again, you have to be careful about what you mean by "synced". For instance, if S and T coincide when they both read zero, and if S and alpha read 0 simultaneously in Earth's rest frame, then T and alpha will read 0 simultaneously in Earth's rest frame. Of course, in the ship's rest frame, alpha will have some positive reading when S and T are both zero.

 

[ElectroPhysics]

Thanks and just continue your discussion. You guys are really Physicists :)

 

[ElectroPhysics]

and Happy New Year...

 

[yogi]

ElectroPhysics - If there is anything to be learned by all this...it is that there is more than one interpretation of both the theory and the experiments. Ultimately I would assume that all but one view will be relegated to the waistbasket.

 

[jdavel]

yogi,

"ElectroPhysics - If there is anything to be learned by all this...it is that there is more than one interpretation of...the theory..."

But only one is correct.

"Ultimately I would assume that all but one view will be relegated to the waistbasket."

They already have by everyone who understands the theory.

 

[Garth]

The paradox and its resolution depends on the concept of what we think of as 'now', not here where that is obvious, but 'over there'. At distance those events that we think of as happening 'now' are selected according to our frame of reference. Two close observers moving relative to each other would select a different set of contemporary events; simultaneity is relative, or 'frame dependent'.

This is particularly important for the non-inertial twin. As she reversed her course her own timing of events back home would suddenly change. Those distant events back home that she thought of as in her future would suddenly become in her past, so when she arrived back home she would realize that her twin was actually older than herself.

I hope this helps.

Garth

 

[yogi]

djavel "They already have by everyone who understands the theory"

- your statement is totally incorrect - acknowledged and respected relativity authors take entirely different approaches to explaining the twin and triplet paradox - Read Professor Robert Resnick's book and compare his treatment of the twin paradox to the treatment of Max Born - the relativist views are almost as diverse as the antagonist's views (but not quite).

Garth - what is at issue is not whether SR offers an explanation of some sort or the other - SR has a built-in self consistency which prevents it from being falsified by thought experiments. Relativity always gives an answer - but does it give the right answer for the right reasons? In the posts above - I attempted to reduce the experiment to proper measurements made within the confines of the proper frame of each participant. - while there may be minor errors induced at the time of initial readings (e.g., if all clocks are initially set to read the same in the Earth frame - and then the traveler takes off (introducing a small error) we then ask a question - do the eart-alpha clocks run at the same rate as the travelers clock so that all three read the same at the turn around point? If the answer is yes - then all of the age discrepancy that we assume will be measured after the parties are reunited, must be do to something physical that occurs at turn around - while the traveler may observe the Earth clock to be changing at turn around - he can also observe the nearby alpha clock (which is in sync with the Earth clock) as not changing. Therefore what is observed by the traveler at the time of turn around (for the rapid change in the Earth clock reading) must be an illusion. An illusion cannot affect the time on the Earth clock - only something physical can cause identical clocks to run at different rates - SR does not provide any inkling as to what causes the age difference - what you have cited is one explanation adopted by some relativity authors - In the triplet problem from which this long thread derived, there is no acceleration at turn around ...simply a reading of the outbound siblings clock by the inbound sibling. Does that make the Earth clock rush forward in time?

 

[Chronos]

Clocks tick at the same rate in both frames, relative to their own. Both sisters age differently than the other. But, neither sister will agree upon how old the other is relative to herself. In a sense, they are in different universes. The implications of relativity and quantum physics are both profound. They are not mutually compatible. The effects on both levels of reality are too small to be measurable. The more important point is to measure where they meet. This may not be an important discovery, but may be important to the discovery process,

 

[Garth]

yogi Clocks always tick "at the same rate" - one second per second - in their own frame, it is how they tick as observed by another frame that is the issue. The twin sisters have no way of comparing their clocks, except by light signal, until they meet again.
The traveling sister, i.e. the one who has changed her own frame of reference by accelerations, will find her clock has ticked less than the inertial sister.

Garth

 

[Hurkyl]

but does it give the right answer for the right reasons?

An interesting philosophical question -- there's a good argument that getting the right answers (in advance) is all that matters. The "right reasons" are only an explanation made up after the fact to help understand, and be able to make even more predictions.

if all clocks are initially set to read the same in the Earth frame - and then the traveler takes off (introducing a small error) we then ask a question - do the eart-alpha clocks run at the same rate as the travelers clock so that all three read the same at the turn around point?

During the outbound trip:

In the Earth frame, the traveller's clock run slow, and the Earth and alpha clocks do not.
In the outbound frame, the clocks on Earth and alpha run slow, and the spaceship clock does not.


If alpha and Earth's clocks always agree in Earth's frame, then the clock on alpha will read more than that of the spaceship when it arrives.

If alpha and Earth's clocks always agree in the outbound frame, then the clock on alpha will less than that of the spaceship when it arrives.


Other comments:

"which is in sync with the Earth clock" -- only according to Earth's frame.

"SR does not provide any inkling as to what causes the age difference" -- would you also say that Euclidean geometry doesn't provide any inkling as to what causes one side of a triangle to be less than the sum of the other two sides? It is fairly directly analagous.

In a sense, they are in different universes.

Or, more accurately, each twin is merely using a different coordinate chart. Geometrically speaking, it's no more mystifying than, why the apparent width of a piece of paper is different when you look at its edge or its front.

The implications of relativity and quantum physics are both profound. They are not mutually compatible.

Partially incorrect -- special relativity and quantum physics are quite compatable. You're thinking of general relativity.

 

[jdavel]

yogi,

djavel: They already have by everyone who understands the theory

jogi: ...your statement is totally incorrect - acknowledged and respected relativity authors take entirely different approaches...

No they don't. They DID, but not anymore; the issue was settled over thirty years ago.

Anyone who thinks that relative simultaneity or (equivalently) constant light speed, or (again, equivalently) the Lorentz transforms can't account for what everyone sees on everyone's clock, in any reference frame, doesn't understand this theory.

 

[pervect]

"Why" questions generally do not have any unique answer in science - if they are even addressed at all. Somewhere around 4 years old, most everyone learns that they can always ask "why", and in a short amount of time arive at a point where there is not any answer to their questions. Science is ultimately concerned with "what" rather than "why". This is why scientific questions generally have nswers, even if they are hard to find - as opposed to philosophical questions, which tend to spawn endless debates, with no ultimate resolution.

On a slightly more advanced note, classical Newtonian mechanics has many alternate formulations - the typical "f=ma" introductory formulation, and the more advanced Lagrangian and Hamiltonian formulations. I see very few people criticising Newtonian mechanics because of the fact that alternative mathematical formulations of the theory exist. Most people seem to be quite content with the fact that all valid formulations of Newtoian mechanics give the same results. I would urge people to apply the same standards to relativity theory and quantum theory. Of the two, quantum theory has by far the biggest issue with "interpretations". Ultimately, though, it is the agreement of final results which is important.

 

[yogi]

pervect - Newton didn't say F = ma ... he said F = rate of change of momentum. That is valid as far as we know in any framework notwithstanding the later developments of Lagrange and Hamilton.

Questions of "why" have to do with pushing the goal post back a few more feet in our attempt to understand nature - there will always be one more question to answer - the question of "why" relates to finding an interpretation that betters our understanding of the next level - if we adopted your position we would still believe that Zeus was the cause of lightning. There is a great story told by Feynman in his chapter on lightning - and the Persian king who sought advice before invading Greece.

 

[yogi]

Hurkyl - "If alpha and Earth's clocks always agree in Earth's frame, then the clock on alpha will read more than that of the spaceship when it arrives."

I would agree with that - as for your next statement:

"If alpha and Earth's clocks always agree in the outbound frame, then the clock on alpha will less than that of the spaceship when it arrives."

Yes - that is so according to the LT (we don't ever really make this measurement, but assuming arguendo it is true, it is not part of the analysis I have set out in the above posts... I have repeatedly stated that it is of no moment what the moving observer measures in the Earth frame - only Earth and alpha based observers can measure the proper time in the earth-alpha frame. The traveler measures an illusory rate when he looks at either the alpha or Earth clock from afar - but he can read the clock on the church tower on alpha when he arrives - and he can compare it to his own clock at that time because there is no vx/c^2 time slip when the two clocks are adjacent .

 

[yogi]

djavel - Take a look at Zhangs book - quoted with authority in FAQ in Physics. "There are no experiments that verify the one way speed of light is isotopic" If it is not, then any number of different transforms can be used to explain all of the known experiments. All of the alternative theories are based upon some difference between an isotropic frame and a frame that moves relative thereto. They all predict the same time dilation as Lorentz's transformations - and consequently all of the other predictions that flow therefrom - SR has been a successful theory - but the other theories make the same predictions w/o relying upon one way isotropy - a postulate that was unnecessary to explain MMx

 

[yogi]

Garth - I agree that the traveling sibling ages less - you say because of acceleration - but there are many authors that argue otherwise (usually they simply invoke a path integral approach using signaling techniques) Since acceleration does not affect local clock rate - nor can it influence the rate of the stay at home clock, how can it add time to the Earth system? The temporal influences that are posited to occur due to acceleration or changing frames can only be observational illusions - recall that this whole thread originated with triplets where there is no acceleration at any time - not at the start - nor at turn around (because there is no turn around).

 

[pervect]

pervect - Newton didn't say F = ma ... he said F = rate of change of momentum. That is valid as far as we know in any framework notwithstanding the later developments of Lagrange and Hamilton.

AFAIK what Newton orginally said (as nearly as exactly as a websearch can find, this may not be perfect) is:

1: A body remains in a state of rest or a state of motion unless a force acting upon it compels it to change.

2: Change occurs in proportion to the force applied and in the same direction.

3: For every action there is an equal and opposite reaction

Formulations of this as "F=ma" and F=dp/dt are all "different" than Newton's original formulation.

As I mentioned, there are additional formulations, such as the principle of least action which are entirely equivalent to Newton's laws.

In spite of the fact that the wording was different in Newton's time, I do not see people claiming that

1) We don't really understand Newton's laws
2) Physics is changing, explanations of Newton's laws are inconsistent
3) Respectable physicists all have "different" interpretations of Newton's laws

all things you've said about SR. In fact, most people (including you, I presume) seem to realize that "different" formulations of Newton's laws are not "different" if they lead one to the same identical results. Including, as I mentioned, the Hamiltonian or Lagrangian formulations (the former, in terms of the principle of least action, is quite elegant).

BTW, if you wish to distinguish Newtonian physics from relativity, you need to specify that momentum=mv, which implies that f=ma. If you don't make this assumption, you have implicitly allowed "Newtonian physics" to include relativistic physics, where p = mv/sqrt(1-(v/c)^2).

 

[pervect]

On isotropy:

Suppose an airplane leaves Los Angeles, Calif, at noon, and arives at Chicago, Ill at 5:40 pm, nonstop. Suppose the same plane leaves Chicago, Ill, at noon on the next day, and arrives at LA at 2:12 pm nonstop. And suppose Chicago and LA are 1749 miles apart. Is it physically meaningful to say that the plane flew at a speed of 308 mi/hr on the first trip, and 795 mi/hr on the trip back? Why or why not?

 

[yogi]

pervect:

1) We don't really understand Newton's laws
2) Physics is changing, explanations of Newton's laws are inconsistent
3) Respectable physicists all have "different" interpretations of Newton's laws

I have made no such statements about SR - if SR is incomplete or wrong it was just as wrong in 1905 as it is today. There were competing theories at the time - but there was no way to verify time dilation until we begin observing the lifetimes of muons and pions.

The reason no one is criticizing Newton's Laws is because they don't lead to paradoxical interpretations. And I don't need to write p = mv to know what is meant by rate of change of momentum - d/dt(mv). This impliedly takes into account the fact that mass may not be constant.

 

[pervect]

Well, your'e at least partially consistent then, Yogi, I suppose. Since we don't really understand Newton's laws after all these years, perhaps we should just give up science and become monks? I mean, what's the point, after all?

:-) for the humor impaired

 

[yogi]

Lets substitute a photon for the traveling twin - we will put a mirror on alpha and assume that alpha is 3 x 10^8 meters from earth. Clocks at Earth and alpha are in sync and the time read when the photon passes the Earth clock is zero. A clock in the photon frame logs "0" when the photon strikes the alpha mirror - the Earth and alpha clocks both read one second - upon return the photon clock still reads "0" but the Earth clock reads 2 seconds. Time passage in the two frames is not equal - half the time is accumulated in the earth-alpha frame on the outbound journey and half is logged on the inbound leg. How does acceleration (reflection) explain the difference between the time lost in the one way trip (between 1 second vs 0)? If the time lost is truly one second on the one way trip, does it not follow that acceleration and turn around have nothing to do with resolving the twin paradox?

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.

 

[yogi]

Pervect - I was merely copying your statement from post 95 - forgot to put in quote marks - as I said - the interesting issue(s) with SR is whether two frames in relative motion can be treated as truly reciprocal as Einstein hypothesized - didn't mean to infer anything about Newtonian Physics.

 

[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.