Why do people talk as if the Twin Paradox is problematic?

[syano]

I have read a few threads that talk about scientist having to “solve” the twin paradox as if there is a problem with it… What is it that I am misunderstanding?

Since time and length contractions have been verified with multiple experiments then what is the problem with the twin paradox?

At the end of the journey one twin is younger then the other… Is there some problem with this that I am unaware of? Why do people talk about a problem within the twin paradox?

Thank you,

 

[jdavel]

syano asked, "Why do people talk about a problem within the twin paradox?"

For one (or both) of two reasons:

1) They don't understand SR

2) They've read in books, by authors whose credentials as physicists seem sufficient, that the twin paradox can only be explained with GR because it involves acceleration. This is nonsense, but as late as the 1960s it was still showing up in physics textbooks, written by PhD physicists, teaching at major universities.

 

[kurious]

I can't see a problem with it either.
I can understand people trying to find a cause for relativistic effects but not why they argue with experimetally verified equations and the predictions that come from them.

 

[pmb_phy]

Is there some problem with this that I am unaware of? Why do people talk about a problem within the twin paradox?

It depends on which frame of reference you wish to describe events from. But to give a precise answer you'd have to state where you read this and what the context was. It might have been something as simple as a statement of something to solve and thus any such "something to solve" might be called a "problem". Otherwise I'm not sure where you heard that and what context it was stated in. There is really no problem inherent to relativity. There is at best some misunderstanding of the physics.

syano asked, "Why do people talk about a problem within the
twin paradox?"
...

2) They've read in books, by authors whose credentials as physicists seem sufficient, that the twin paradox can only be explained with GR because it involves acceleration. This is nonsense, but as late as the 1960s it was still showing up in physics textbooks, written by PhD physicists, teaching at major universities.

That is incorrect. It is far from nonsense. At best it is a difference of opinion of how "GR" is defined. As defined by Einstein GR is physics in non-inertial frames. As such the traveling observer, i.e. the observer who turns around and comes back, uses GR to explain what he observers. The temporal effects can then be explained in terms of gravitational redshift.

And this has zero to do with how old a text was. Even some modern texts explain the events as observed by the traveling twin in terms of gravitational redshift. In fact one such text is Cosmological Physics, John A. Peacock, Cambridge University Press, (1999) . In fact the portion of that text which explains this in terms of GR is located online at

http://assets.cambridge.org/0521422701/sample/0521422701WS.pdf

Pete

 

[OneEye]

From a tyro's point of view:

The twin paradox is, simply stated, that in SR the time dilation can be attributed to either twin, and so there should be no age difference between the twins should their inertial, non-accelerated courses bring them back in contact with each other.

I probably really hacked that up. Sorry if it's obscure. Let me put this another way: Unless you have one twin accelerate, travel a distance at a significant fraction of the speed of light, decelerate, turn around, accelerate again, travel back to the starting point, decelerate, and meet the other twin, then there is a paradox involved.

In SR, time dilation is attributed to velocity. But, the time dilation works in both directions; observers in both inertial reference frames see the other as experiencing a time dilation. So, since the time dilation is complementary, then if the only effect we were considering was velocity (as opposed to acceleration/gravity), then each twin would see the other as aging more slowly than himself as they traveled away from each other, and so if it were possible for the two twins to meet again without decelerating or accelerating, we would have to explain how the apparent time dilation is "undone" when the two inertial frames again syncrhronize.

I'm sure someone else can add some more information to clear this up. I've probably muddied the waters rather than helping. I welcome the assistance of anyone who can spot my inadequacies and clear them up.

But I hope this helps somewhat.

(BTW, if I understand it correctly, there is a triplets paradox, wherein two of the three triplets hop into spaceships, accelerate in opposite directions, achieve near-light speeds, slow down, turn around, come back, and meet up, all together again. If I am not mistaken, the two traveling triplets out to be different ages, but will not be, while both of the travelers will have the same age difference from the homebody triplet.)

 

[yogi]

I will add a little to one eye's post. The so called paradox comes about because the situation starts out symmetrical. Two twins pass each other at velocity v, but neither can determine which one is moving (at this point). The argument the proceeds that as they depart each sees the other twins clock running slow. Well, that is usually based upon signals being sent from one to the other (they don't really see the other twin's clock running slow - so the statement is misleading) ... what they see is that the signals received by the other are separated by a greater period because they are receding from one another - then the jump to the paradox is made, specifically that it is impossible for both clocks to be running slow with respect to each other.

Now Einstein predicted that if one of the clocks were decelerated and brought back (reunited with the other clock) the two clocks would not read the same. To avoid the paradox he postulated that the turn around clock had to have experienced a force (an acceleration) but the other did not - therefor since SR only deals with inertial systems (those that do not undergo acceleration) there is no paradox

The problem however, gets more intriguing - if time dilation is real, there is no need to ponder the effect of an acceleration at the turn around point. (For example, if the outbound twin, instead of turning around and undergoing an acceleration, simply transfers his clock reading to an inbound 2nd traveler, when the 2nd traveler encounters the first twin, there will be a time discrepency. This is known as the triplet scenaro - it does not appear to be resolvable unless time dilation is actual - not apparent. As near as can be determined, Einstein considered time dilation as apparent, and therefore, to arrive at a time loss for the traveler, something else, such as acceleration, was required to avoid the paradox.

 

[Janitor]

I was a little gradeschool pipsqueak when an older kid down the block borrowed a laser overnight from his high-school physics class. It was a large, boxy affair back in those days, not like the modern battery-powered laser pointers. I think he even had to have an extension cord running from inside his house to the laser which was mounted on a tripod. At any rate, I watched him goof around with the laser, and we got to talking about physics. He told me, as best he could, about the twin paradox. My kneejerk reaction was: ah come on, time does not work like that. They've got to be wrong.

Humans evolved in a world where a kind of Galilean/Newtonian intuition was good enough for us to kill bison and to drive the poor sabre-toothed tiger to extinction, so I guess we ought to be pretty proud of even our naive intuition about physics.

 

[Janus]

I will add a little to one eye's post. The so called paradox comes about because the situation starts out symmetrical. Two twins pass each other at velocity v, but neither can determine which one is moving (at this point). The argument the proceeds that as they depart each sees the other twins clock running slow. Well, that is usually based upon signals being sent from one to the other (they don't really see the other twin's clock running slow - so the statement is misleading) ... what they see is that the signals received by the other are separated by a greater period because they are receding from one another -

Wrong, The time delay caused by the increasing distance is factored out and is not considered a part of time dilation. Time dilation is the time rate difference left over after you've accounted for said signal delay.

then the jump to the paradox is made, specifically that it is impossible for both clocks to be running slow with respect to each other.

Now Einstein predicted that if one of the clocks were decelerated and brought back (reunited with the other clock) the two clocks would not read the same. To avoid the paradox he postulated that the turn around clock had to have experienced a force (an acceleration) but the other did not - therefor since SR only deals with inertial systems (those that do not undergo acceleration) there is no paradox

Wrong, SR can deal with acceleration.

The problem however, gets more intriguing - if time dilation is real, there is no need to ponder the effect of an acceleration at the turn around point. (For example, if the outbound twin, instead of turning around and undergoing an acceleration, simply transfers his clock reading to an inbound 2nd traveler, when the 2nd traveler encounters the first twin, there will be a time discrepency. This is known as the triplet scenaro - it does not appear to be resolvable unless time dilation is actual - not apparent. As near as can be determined, Einstein considered time dilation as apparent, and therefore, to arrive at a time loss for the traveler, something else, such as acceleration, was required to avoid the paradox.

I've already in another thread showed you how SR deals with the triplet scenerio and how it predicts a difference in the clocks, without relying on absolute time dilation.

 

[OneEye]

Janus,

Wrong, The time delay caused by the increasing distance is factored out and is not considered a part of time dilation. Time dilation is the time rate difference left over after you've accounted for said signal delay.

Well, perhaps you can help me, then: The Microsoft Encarta article on Special Relativity posits a Gedanken wherein a spaceship passes by a "stationary" observer. The article reads thus:

"A consequence of [the constancy of c] is that there must be no such thing as absolute time either. Inside the red ship we have a clock that uses light to measure time. A pulse of light strikes a mirror, and returns to its source. The light travels .6 meters in two nanoseconds. In the astronaut's frame of reference, the pulse travels a total distance of one meter [v=240,000 km/s] along a diagonal path. The astronaut observed the light travel the same speed as always -- .3 meters per nanonsecond. According to his watch, the pulse takes 3.3 nanoseconds to make the trip. The astronaut concludes correctly that the clock on the moving ship runs slowly." ((c) 1999 Microsoft.)

This appears to disagree with what you are saying. The Encarta article seems to say that the apparent time delay is exactly and only the result of increasing distance. (Which would make sense, since time delay is a direct result of and proportional to v.)

Maybe I mistook you. Would you please apply yourself to this? Thanks.

 

[quartodeciman]

Maybe it would be better if the term "paradox" were removed from this and another title given, like "spacetime asymmetry consequences" of the relativity theories instead. Then it would merely be a matter of experimental confirmation or disconfirmation of the theories, rather than having to carry the stigma of being some kind of dysfunction of thought.

 

[robphy]

The argument the proceeds that as they depart each sees the other twins clock running slow. Well, that is usually based upon signals being sent from one to the other (they don't really see the other twin's clock running slow - so the statement is misleading) ... what they see is that the signals received by the other are separated by a greater period because they are receding from one another - then the jump to the paradox is made, specifically that it is impossible for both clocks to be running slow with respect to each other.

Each observer will see (with his eyes) that the face of the distant clock is running at a slower rate than that of his local clock. This is the Doppler Effect. (Clock ticks separated by a lightlike vector.) I don't feel this is so paradoxical. Each observer equipped with an identically constructed light source will see the light from the other observer to be redshifted, indicating that they are separating from each other.

What could be regarded as paradoxical (of time dilation) involves the comparison of clock ticks that are simultaneous according to an observer. (Here, the clock ticks are separated by a spacelike vector orthogonal to the observer.)

Now Einstein predicted that if one of the clocks were decelerated and brought back (reunited with the other clock) the two clocks would not read the same. To avoid the paradox he postulated that the turn around clock had to have experienced a force (an acceleration) but the other did not - therefor since SR only deals with inertial systems (those that do not undergo acceleration) there is no paradox

The resolution should read
"the turn around clock had to have experienced a force (an acceleration) but the other did not - therefore since the situation is no longer symmetrical there is no paradox"

 

[jdavel]

pmb_phy said, "That is incorrect. It is far from nonsense."

You misread my post. What I said was that claiming GR is NECESSARY to explain the twin paradox, is nonsense. The fact that it's POSSIBLE to explain it with GR should come as no surprise (after all, GR includes SR). But it's not necessary. The apparent symmetry leading to this so called paradox is easily broken with arguments base purely on SR.

As to the link you gave me where the paradox is explained using GR, it uses an approximation (the traveler's speed is much less than c) to arrive at exactly the result predicted using SR and ignoring the acceleration. Not too impressive!

 

[Janus]

Janus,


Well, perhaps you can help me, then: The Microsoft Encarta article on Special Relativity posits a Gedanken wherein a spaceship passes by a "stationary" observer. The article reads thus:

"A consequence of [the constancy of c] is that there must be no such thing as absolute time either. Inside the red ship we have a clock that uses light to measure time. A pulse of light strikes a mirror, and returns to its source. The light travels .6 meters in two nanoseconds. In the astronaut's frame of reference, the pulse travels a total distance of one meter [v=240,000 km/s] along a diagonal path. The astronaut observed the light travel the same speed as always -- .3 meters per nanonsecond. According to his watch, the pulse takes 3.3 nanoseconds to make the trip. The astronaut concludes correctly that the clock on the moving ship runs slowly." ((c) 1999 Microsoft.)

This appears to disagree with what you are saying. The Encarta article seems to say that the apparent time delay is exactly and only the result of increasing distance. (Which would make sense, since time delay is a direct result of and proportional to v.)

Maybe I mistook you. Would you please apply yourself to this? Thanks.

Read the article again. It deals with a light beam that bounces back and forth between a lightsource and mirror that is traveling with the ship. For an observer in the ship the light travels straight back and forth. For an observer that the ship is traveling relative to, the light has to travel a diagonal path to strike the mirror and return. This has nothing to do with any increase of distance between the ship and the outside observer. It would be just as true if the distance between the ship and observer were decreasing or remained constant (such as when the ship is traveling in a circle around the observer).

Yogi's statement implies that time dilation is the product of the increasing distance between the observers. While this effect is real, it is due to Doppler shift and not due to Relativistic time dilation. While in real life you would see a combination of both, in most Gedankens dealing with Relativity we ignore the Doppler effect because it is not the point of interest.

 

[yogi]

Yes Janus - there is the Doppler shift - but read what I said - it is not correct to interpret the increased spacing between the received pulses as indicative of the fact that the other clock is running slow - that is the common bogus approach given by most of those who publish simple explanations - the fact of the matter is, if you simply start with the statement that two twin pass each other at velocity v, there is no basis for assuming either clock is running faster than the other - how could there be - the fallacy is in asserting that there is something left over after you have factored out the Doppler - which one is running faster?

I would also take direct issue with you Janus on when the symmetry is broken - it is at the beginning - when one twin takes off and the distance traveled by him is measured in the Earth rest frame - we now have two terms that are proper in the Earth frame - the proper time as measured by an Earth clock and the proper distance as measured in the Earth frame to the turn around point. If we specify a third data point - e.g., the time lapsed by the clock which escorts the traveling twin when he arrives, then there is only one factor left to calculate - that is the effective distance as measured by the traveling twin. While we all agree that the interval is invarient, the space term and the time increment as measured by the traveling twin to the turn around point in the frame of the traveling twin will be different from the space term and the time increment as measured in the Earth frame. The symmetry is broken as soon as you identify the proper distance that is traveled in the Earth system.

I have never seen you explain the triplet paradox - when I have raised this issue before you have not answered it directly (at least I never saw your post if you did - and the last time the subject got interesting, you locked the thread)

 

[yogi]

Let me ad a little more - I do not now, nor have I ever considered the signaling method of resolving SR problems as being either useful or correct - I couldn't care less what the Earth observer might deduce from getting a squint at a passing clock or signals sent from afar - So tell me Janus, or anyone else, will the traveling twin's clock have accumulated less time that the Earth clock when the twin reaches the turn around point. If the answer is yes - there is no need to consider forces, GR, changing inertial system - whatever. The problem is resolved because time loss is actual, not apparent, and upon returning home the lost time will simply be double that accrued at the turn around post. Ok Posters - here is you chance to commit... Yes if the clock in the Earth frame reads different at the time the turnaround is commenced... No if you agree with Einstein, that time dilation is apparent and some other factor(s) such as acceleration, forces, GR, different inertial system, etc must be involved to explain the time difference upon reunion.

 

[Hurkyl]

there is no basis for assuming either clock is running faster than the other

Exactly right. In fact, relativistically speaking, it doesn't even make sense to say one clock is running faster than another.

Such statements only make sense relative to a frame of reference, and there most certainly is a basis for stating that each clock is running slow in the rest frame of the other clock.

So tell me Janus, or anyone else, will the traveling twin's clock have accumulated less time that the Earth clock when the twin reaches the turn around point.

This question does not make sense... until you specify in which reference frame you want to compare.

I have never seen you explain the triplet paradox

The triplet paradox (that I'm familiar with) is only confusing if you've already been confused by the twin paradox and are trying to salvage the paradoxical nature.

The asymmetry is much more apparent in the triplet "paradox"; the earthbound path consists of a single clock in a single reference frame, and the spacebound path consists of two distinct clocks in two different reference frames.

 

[selfAdjoint]

The turnaround twin accumulates less proper time on his total journey - out and back. Think of a spacetime diagram with time vertical and the relevant space direction horitzontal. Let it be taken relative to the nonturning twin's restframe, so his worldline will appear as a vertical line along the time-axis - conveying that he let time pass without (relative to his own rest frame) moving any distance.

Now the worlline of the other twin will appear as two slanted lines; one going out from the origin to the turn around point, and the other slanting back from the turn around point to the time-axis at the point where the twins meet again. Together with the length on the time-axis between the start and finish events (which is the nonturning twin's worldline) , these two lines form a triangle. Now you have to know that in relativity, the direct path through time is LONGER in proper time than the indirect or partly spatial one. Just the opposite of what you would think of course, but it's a solid result of relativity. So it's the fact that the turnaround twin took a partly spacelike excursion while the other twin didn't that makes the difference in their ages, which is just the proper time that each has incurred along their respective worldlines.

 

[jdavel]

yogi said, "So tell me Janus, or anyone else, will the traveling twin's clock have accumulated less time that the Earth clock when the twin reaches the turn around point."

hurkyl replied, "This question does not make sense... until you specify in which reference frame you want to compare."

Why? An event occurs: traveler arrives at distant planet. That event has spacetime coordinates in both frames. yogi's question is, "Are the time coordinates of that event the same in both frames, or are they different?"

 

[Janus]

Yes Janus - there is the Doppler shift - but read what I said - it is not correct to interpret the increased spacing between the received pulses as indicative of the fact that the other clock is running slow - that is the common bogus approach given by most of those who publish simple explanations - the fact of the matter is, if you simply start with the statement that two twin pass each other at velocity v, there is no basis for assuming either clock is running faster than the other - how could there be - the fallacy is in asserting that there is something left over after you have factored out the Doppler - which one is running faster?

Read the article posted by OneEye. The fact that the bouncing light as measured in the ship's frame travels a shorter distance than that as measured by the external observer, yet both observers measure the light as moving at c means that the same light takes longer to reflect back and forth as measured by the outside observer. Thus if the light takes 1 sec according to the ship's time, it takes more than one sec by the external observer's time, and time progresses more slowly for the ship as measured by this observer. None of these observations rely on Doppler shift, and still occur even if you ignore the Doppler effect.

I have never seen you explain the triplet paradox - when I have raised this issue before you have not answered it directly (at least I never saw your post if you did - and the last time the subject got interesting, you locked the thread)

The reply is here. It is the reply right after it and you acknowledeged it:

https://www.physicsforums.com/showthread.php?t=17141&page=4&pp=15

I very carefully show how, when you take all the triplet's measurements into account, they all agree as to the time difference between the Earth clock and the clock that had the time transferred to it from the outbound triplet's clock. There is no paradox, and no reason to assume absolute time.

 

[syano]

Thank you for all of the explanations.

The differences of thought you guys mention in this post has caused some confusion for me.

There are three parties of thought here right? One, are folks like Janus who sees no paradox in the “Twin Paradox” and is a firm believer in relativity. Two, are folks like Yogi who are skeptical of relativity and sees problems within the Twin Paradox. And three, are folks like Jdevel who are just trying to get a clearer picture. Am I correct on this?

Allow me to explain my thoughts on the subject please.

It seems simple to me. But I am thinking my logic may be way off because of the simplicity of it.

Analogy:
Say a certain type of house takes 64 man hours to build. And you hire 2 workers who can each work 8 hours a day. So it will take 4 days to build the house. I am sure no one disagrees with this. Now say the house is built in 2 days. If the house is built in 2 days then something had to change. Either there were more workers added, or the 2 original workers worked more then 8 hours a day.

That’s very simple to understand. My understanding of relativity’s time contractions is very similar to that.

Simple explanation I have read:
(I’m sure you guys have read this too)
A train traveling 40 feet per second has a man on it that throws a ball 30 feet per second towards the other side of the cart he is on. The man on the train threw the ball at the precise time he passed another man standing outside of the train. The man on the train saw the ball move at 30 feet per second while the man outside the train saw the ball moving 70 feet per second.

This is easy to understand as well. One man sees the ball flying at one speed and the other man saw the ball flying at a different speed.

The speed of a ball is not constant. But the speed of light is constant. So if you take the same example but use a flashlight, instead of a ball, then each man will see the light move at 186,000 miles per second.

Since the man standing outside of the train did not see the light travel at 186,000 miles per second plus 40 feet per second then something had to change (just like something had to changes with the analogy of workers building the house). Either the distance the ball traveled or the time interval.

So if the speed of light is constant then time dilation and length contraction is neat little phenomenon.

So why is there a problem with this phenomenon when talked about in terms of the Twin Paradox? And is there anything wrong with my logic on the examples I mentioned above?

Thanks again,

 

[yogi]

O yes Janus - I misspoke myself - I do recall that you posted your numerical solution to the triplet problem - what I wanted was not a numerical solution, but rather an answer to the critical question as to whether the lost time was real or apparent. I recall finding interesting is that your triplet analysis is (was) in my view, inconsistent with what I viewed your position to be as to the twin caper - i.e., specifically what do the times at the halfway (turn around point) mean.

You state in that treatise that triplet 2 takes 11.55 years as measured by a clock in the Earth frame (the stay at home triplet 1 frame) to travel out to the turn around point (10 light years distance) and that when he reaches that point triplet Two's clock will only read 5.77 light years. Ergo, doesn't it follow that time dilation is real, and that the clock discrepency has already been accounted for. If that is your position, fine - you would be a "yes" voter - that is, we don't need anything extra to explain why the two clocks have logged different amounts of time when they are ultimately reunited (we just double the difference for the one way trip.

Specifically, on your other posts re the twin caper, you have referred to the force felt by the deceleration - so perhaps you can enlighten me as to why you believe it is necessary in the twin situation and not in the triplet situation.

 

[Janus]

O yes Janus - I misspoke myself - I do recall that you posted your numerical solution to the triplet problem - what I wanted was not a numerical solution, but rather an answer to the critical question as to whether the lost time was real or apparent.

It is real and relative. The trouble is your use of 'real', you seem to want to make equal in meaning to 'absolute'. I.E. if a measurement isn't absolute, then it isn't "real". By that definition, according to Relativity, Time and Space themselves aren't "real". If that is the case, then the word "real" has no meaning in our universe.

That is only a problem if you tie 'real' to 'absolute'. Once you acknowledge that measurements can be relative and still be "real", then the problem goes away.

The "lost time" is "real", it is also relative.

 

[OneEye]

Yogi's statement implies that time dilation is the product of the increasing distance between the observers. While this effect is real, it is due to Doppler shift and not due to Relativistic time dilation. While in real life you would see a combination of both, in most Gedankens dealing with Relativity we ignore the Doppler effect because it is not the point of interest.

Thanks for the reply. I was taking "increasing distance" to mean "distance traveled over time" - velocity. But I see that you are using the phrase "increasing distance" to mean "growing displacement between the object and the observer." I mistook your meaning. But I hope that you can forgive my mistake as at least somewhat understandable.

 

[Janus]

You state in that treatise that triplet 2 takes 11.55 years as measured by a clock in the Earth frame (the stay at home triplet 1 frame) to travel out to the turn around point (10 light years distance) and that when he reaches that point triplet Two's clock will only read 5.77 light years. Ergo, doesn't it follow that time dilation is real, and that the clock discrepency has already been accounted for.

Triplet 1 determines that triplet's 2 clock reads 5.77 yrs because of time dilation in Triplet 2's frame. Triplet two determines that his own clock reads 5.77 yrs because Triplet 1's frame undergoes length contraction, and so to reach 10 lys separation as measured by frame 1, the separation has to be only 5 ly in his frame. (Triplet 1 and 2 separate to a distance of 5 ly at a relative velocity of .866 c, which takes 5.77 yrs.)

The time dilation triplet 2 is aware of is that occurring to frame 1, meaning that triplet 1's clock at this time according to triplet 2 reads 2.885 yrs.

Specifically, on your other posts re the twin caper, you have referred to the force felt by the deceleration - so perhaps you can enlighten me as to why you believe it is necessary in the twin situation and not in the triplet situation.

In the twin scenerio you have one twin that changes frames during the exercise. (first he is in a inertial frame, then an acclerated frame, and then a different inertial frame) You have to take all theses frames into account when determining the outcome according to him. In the outbound and inbound inertial frames, Earth's clock runs slow. During the accelerated frame Earth time runs fast.

From the Earth frame his clock always runs slow.

Thus while both twin's agree as to the end result, They do not agree as whose clock ran slow when.

In the triplet scenerio you have three different observers who stay in three different inertial frames without change. There are no accelerated frames, so there is no need to consider one. You just determine whether all three observers agree as to the end result of the exercise (the time difference between the returned clock and Earth clock.)

From the Earth frame, the 2's clock runs slow while outbound, and the clock to which the outbound clocks reading is transferred to runs slow while inbound.
Meaning that after 23.1 yrs of Earth time, the clock returns reading 11.55 yrs

From the outbound twin's frame, Time runs slow for the Earth frame and even slower for the inbound frame. When he transfers his time to the inbound frame, less time will have passed on Earth than for him. the Instant he makes the transfer, he notes that the clock he tranfered the time to runs slower than his and slower than the Earth's. Because of the relative velocity between the inward bound clock and the Earth as measured by the outbound triplet, by the time that the inbound triplet reaches Earth, 46.2 yrs will have passed for him, meaning 23.1 yrs passes on Earth (due to time dilation of the Earth frame.) Since he also determines that the inbound clock runs slower than Earth time, he will note that 5.77 years is added to the clocks reading, in addition to the 5.77 yrs he transferred to it. for a total of 11.55 yrs.

From the inbounds triplet's frame, The Earth clock runs slow, but the out bound clock runs even slower. When he passes the outbound clock he receives the transferred time (5.77 yrs) he is 5 ly distant from the Earth at this time by his measure so it takes 5.77 yrs for the distance to close to zero and the clock reads 11.55 yrs when he reaches Earth. During this time 2.885 yrs passes on Earth according to triplet three. But, According to triplet three, Triplet two left Earth while Triplet three was much further from Earth than he was according to Earth or triplet two.(Relativity of Simultaneity) Such that when triplet three received the time transfer, 40.43 yrs has passed for him since triplet two left Earth. This equates to 20.215 yrs in Earth time. Plus the 2.885 yrs passed on Earth since the transfer equals 23.1 yrs.

Note again, that while all three triplets agree to the end result, none agree as to who's clock ran slow.

The two scenerios involve different dynamics and so involve different analyses.

 

[yogi]

janus - Wait - this is where the issue gets obscured - go back to what the triplet 2 clock has logged when T-2 reaches the turn around point - Don't talk about anything other that what the T-2 clock reads at this event - is that 5.77 years?

Now - when this event occurs, what does the T-1 clock read? (I don't want to know what triplet 1 determines triplet two's clock to read and I don't want to know what triplet two calculates for triplet one). Does triplet one's clock read 11.55 years or not?

 

[Janus]

janus - Wait - this is where the issue gets obscured - go back to what the triplet 2 clock has logged when T-2 reaches the turn around point - Don't talk about anything other that what the T-2 clock reads at this event - is that 5.77 years?

Since this is a space time event that everyone agrees on, it reads 5.77 years, but for different reasons for each of the triplets.

Now - when this event occurs, what does the T-1 clock read? (I don't want to know what triplet 1 determines triplet two's clock to read and I don't want to know what triplet two calculates for triplet one). Does triplet one's clock read 11.55 years or not?

11.55 years according to frame 1
2.885 years according to frame 2
20.215 years according to frame 3

What does it really read?

11.55 years according to frame 1
2.885 years according to frame 2
20.215 years according to frame 3

Asking what the clock reads without specifying from which frame of reference it is being read is a meaningless question. And none of the frames holds priority over the others.

 

[yogi]

Janus - no - it is not at all meaningless, and that is the point I am trying to resolve with you. Triplet 2 has carried a clock with him and he can read it when he reaches the turn around point (before he decelerates) and Twin 1 has kept time with his own pocket watch that records proper time in the Earth frame (which also includes the turn around point since the turn around point is a fixed distance from the earth) So do you agree that at this event, twin 2's clock will read 5.77 years when twin two views it and twin 1's pocket watch will have logged 11.55 years when he (twin 1) peaks at it.

Please - yes or no

 

[rtharbaugh1]

Hi all,

Usual apollogies and explanations inserted here (I have no credentials and do not understand mathematics, etc.)

However, my poor attempt to understand the twinship problem in another thread in this forum led me to some unexpectedly dark and mysterious places. Ok, here it is.

The rocket twin leaves Earth and accelerates at one G force. After traveling a few years, calculations show that everyone on Earth is dead and gone to dust. A few more years and the planet and good old Sol are extinguished by old age. A few more years and the milky way galaxy has spun down to a few grumbling creaky old black holes. A few more years and the whole universe has met up with Father Time, the old guy with the shifting sand and the rusty scythe. The universe itself no longer exists! The bumbling branes have met and departed. Yet our twin in her puttering little one G elevator to the stars seems unaffected, dragging her little one G bubble of a reference frame along with her. Does the magic of the hyperbolic tangent make this possible? Are we so close to achieving immortality, if only at the cost of eternal exhile?

Well not quite. It seems to me now that there is a problem with forces lateral to the direction of travel. The force required to achieve any tiny motion right or left or up or down onboard ship becomes large. Our poor twin soon reaches a condition of being unable to lift a spoon or take a breath of air. Every particle under such acceleration becomes linear, and a test of Euclid's fifth postulate. Do they remain parallel or do they finally crunch together? I don't think I want to volunteer to find out, even for the immortality reward.

Now I have recently been reading An Imaginary Tale The Story of \sqrt(-1) by Paul J. Nahin, and have new confusions to confess, but will not belabor them here. However, there are one or two remaining puzzles in my finite capacity of wonder. How is it we can continue to accelerate indefinately under one G on Earth's surface and not experience the lateral force difficulties that beset our astronautical sister? Also, if she goes on a dozen or so of her years, and the universe we know has gone still and the branes have ceased to collide, where, exactly, is she? Even if she cannot move at all under the tidal forces, she ought to still be someplace.

I admire the courage and wisdom of our intrepid pf mentors and send them my thanks. For the rest of us, fools rushing in, tally-ho!

Regards,
Richard T. Harbaugh

 

[yogi]

Janus - there is a question pending:

"Janus - no - it is not at all meaningless, and that is the point I am trying to resolve with you. Triplet 2 has carried a clock with him and he can read it when he reaches the turn around point (before he decelerates) and Twin 1 has kept time with his own pocket watch that records proper time in the Earth frame (which also includes the turn around point since the turn around point is a fixed distance from the earth) So do you agree that at this event, twin 2's clock will read 5.77 years when twin two views it and twin 1's pocket watch will have logged 11.55 years when he (twin 1) peaks at it.

Please - yes or no

 

[Janus]

Janus - there is a question pending:

"Janus - no - it is not at all meaningless, and that is the point I am trying to resolve with you. Triplet 2 has carried a clock with him and he can read it when he reaches the turn around point (before he decelerates) and Twin 1 has kept time with his own pocket watch that records proper time in the Earth frame (which also includes the turn around point since the turn around point is a fixed distance from the earth) So do you agree that at this event, twin 2's clock will read 5.77 years when twin two views it

Yes, because that's how long it would tke for twin1 and twin 2 to separate by 5 lys (the proper distance to twin1 in twin 2's frame) at .866c

and twin 1's pocket watch will have logged 11.55 years when he (twin 1) peaks at it.

Yes, because that's how long it would take for twin1 and twin 2 to separate by 10 lys (the proper distance to twin2 in twin one's frame) at .866c

 

[yogi]

Janus - thanks for your response. Ok - good - you answered both questions "yes" so each twin has a clock that belongs to a different reference frame, and each can read his own clock at the event where the turnaround post is arrived at. So since the two clocks have recorded different amounts of time in their own reference frames (their own proper times that have nothing to do with how they could or would be viewed by the other twin at this event), why is it necessary to explain why the traveling twin will have a different age upon returning because he has undergone an acceleration, or a change in reference frame - whatever? We already have a reading that confirms actual relative time dilation (or time loss, depending upon how one describes the difference). Don't we already (upon reaching the turn around point) have the necessary asymmetry to conclude that the time loss difference is simply doubled when the traveling twin rebounds off the turn around point and returns home at the same velocity to be reunited. Why does one need to invoke acceleration? ... changing reference frames? ... GR... etc. Have we not already created an inherent asymmetry by specifying the distance traveled in the Earth frame (10 light years proper distance) and the lapsed proper time (11.55 years) vs the 5 light years distance perceived by the traveling twin and 5.75 accumulated clock time?

 

[Janus]

Janus - thanks for your response. Ok - good - you answered both questions "yes" so each twin has a clock that belongs to a different reference frame, and each can read his own clock at the event where the turnaround post is arrived at. So since the two clocks have recorded different amounts of time in their own reference frames (their own proper times that have nothing to do with how they could or would be viewed by the other twin at this event), why is it necessary to explain why the traveling twin will have a different age upon returning because he has undergone an acceleration, or a change in reference frame - whatever? We already have a reading that confirms actual relative time dilation (or time loss, depending upon how one describes the difference). Don't we already (upon reaching the turn around point) have the necessary asymmetry to conclude that the time loss difference is simply doubled when the traveling twin rebounds off the turn around point and returns home at the same velocity to be reunited. Why does one need to invoke acceleration? ... changing reference frames? ... GR... etc. Have we not already created an inherent asymmetry by specifying the distance traveled in the Earth frame (10 light years proper distance) and the lapsed proper time (11.55 years) vs the 5 light years distance perceived by the traveling twin and 5.75 accumulated clock time?

Because you would not be taking all the relevant observations into account. You can't just ignore the fact that from twin 2's frame when he hits the turn around, the Earth clock only reads 2.875 yrs. This reading on Earth's clock is just as real and actual to twin 2 as the reading on the clock he carries with him.

It is not enough for Twin 1 to say 23 yrs passed on his clock, while 11.5 yrs passed on twin 2's clock after the round trip and for twin 2 to agree that 11.5 years passed for him. Twin 2 must also agree that, by his observations, 23 yrs passed on Earth.

And you cannot say that Twin 2's observation of Earth time is less valid than the other observations because it is arrived at by the same rules as the other observations.

 

[yogi]

Janus - your quote:

Because you would not be taking all the relevant observations into account. You can't just ignore the fact that from twin 2's frame when he hits the turn around, the Earth clock only reads 2.875 yrs. This reading on Earth's clock is just as real and actual to twin 2 as the reading on the clock he carries with him."

There is no reading on any Earth clock that says 2.875 years - there is only one Earth clock and it reads 11.55 years.

 

[yogi]

Let me embellish further. Assume a clock is placed at the turn around post and it is sync(ed) with the time when the twin's clocks are set to zero at beginning of the voyage (we can do this with a light signal sent from twin 1's location - it takes 10 years to arrive, so the operator at the remote clock starts it running when he receives the signal from twin 1 and adds 10 years to the dial reading - so when twin 2 arrives, he sees the clock on the turn around post reading 11.55 years. There is no other communication between the frames - twin 2 reads the proper time on the clock which escorts him and twin 1 reads proper time on the Earth clock. Any other times that are calculated are not real - they are apparent - just as is length contraction - a fictitious time calculated from the relative velocity between the two frames.

 

[Janus]

Let me embellish further. Assume a clock is placed at the turn around post and it is sync(ed) with the time when the twin's clocks are set to zero at beginning of the voyage (we can do this with a light signal sent from twin 1's location - it takes 10 years to arrive, so the operator at the remote clock starts it running when he receives the signal from twin 1 and adds 10 years to the dial reading - so when twin 2 arrives, he sees the clock on the turn around post reading 11.55 years.

But that does not represent the present time on Earth from twin 2's frame. There is Relativity of Simultaneity. Simultaneous events in one frame are not simultaneous in a frame moving relative to the first. So while for twin one the events of his clock and the turnaround post's clocks reading 11.55 yrs are simultaneous events, this is not true for Twin 2, for him, when the turnaround clock reads 11.55 yrs, Twin 1's clock will read 2.875 yrs.

There is no other communication between the frames - twin 2 reads the proper time on the clock which escorts him and twin 1 reads proper time on the Earth clock. Any other times that are calculated are not real - they are apparent - just as is length contraction - a fictitious time calculated from the relative velocity between the two frames.

No, all the times are real for each frame discussed. For Twin 2 when he reaches the turn around point the real time on Earth is 2.875 yrs. The length contraction is real also. It is just as real as the fact that for The operator at the turnaround point adding 10 yrs to his clock synchronizes his clock to twin one's clock.

 

[yogi]

Janus - how can different times in the same frame at the same point both be real. The real time on Earth could not be 2,875 years when Twin 2 reaches the turn around point - he would have had to travel faster than the velocity of light in the Earth frame. The real time on Earth is that read by a proper clock in the Earth frame - and the clock at the turn around can be sync(ed) with the Earth clock since they are both in the same frame and not moving with respect thereto.

In the problem posed, there are only two events and two times - you agreed that the 11.55 years measured in the Earth frame was a proper real time and that the 5.77 years in the twin 2 frame is a proper real time (at least I think you agreed to these statements). Event 1, the beginning of the trip all clocks read zero - event 2, the turn around point, the proper time accumulated by the Earth clock and the post clock will both be 11.55 years but the proper time accumulated by the twin 2 clock will be less (5.77 years)

How can length contraction be real in SR - that idea belongs in Lorentz Ether Theory. Eddinton said straight out - length contraction is not real - so have many other authors of relativity texts. Twin 2 cannot make proper distance measurements in the Earth frame because he is moving wrt the Earth frame - any calculation he makes will be fictitious - it may seem that he has traveled less miles because his clock is running slow - but the miscalculation is due to the fact that he uses the clock reading in his own frame to calculate a distance in another frame

 

[Janus]

Janus - how can different times in the same frame at the same point both be real.

Because time is Relative. The time on Earth depends on who you ask. Do not confuse 'real' with 'absolute' or 'universal'.

The real time on Earth could not be 2,875 years when Twin 2 reaches the turn around point - he would have had to travel faster than the velocity of light in the Earth frame.

I'll touch on this later.

The real time on Earth is that read by a proper clock in the Earth frame - and the clock at the turn around can be sync(ed) with the Earth clock since they are both in the same frame and not moving with respect thereto.

again, you are trying to make "real" mean 'absolute', Time is relative. they are only in sync when viewed from the frame they are in

In the problem posed, there are only two events and two times - you agreed that the 11.55 years measured in the Earth frame was a proper real time and that the 5.77 years in the twin 2 frame is a proper real time (at least I think you agreed to these statements). Event 1, the beginning of the trip all clocks read zero - event 2, the turn around point, the proper time accumulated by the Earth clock and the post clock will both be 11.55 years but the proper time accumulated by the twin 2 clock will be less (5.77 years)

The term "proper time" only means "time as measured by a clock that is not moving relative to the frame of reference". This is to distinguish it from time as read by a clock moving with respect to the frame of reference. "proper time is no more "real" than any other time.

How can length contraction be real in SR - that idea belongs in Lorentz Ether Theory. Eddinton said straight out - length contraction is not real - so have many other authors of relativity texts.

Again, confusion of "real" with "absolute".

Twin 2 cannot make proper distance measurements in the Earth frame because he is moving wrt the Earth frame - any calculation he makes will be fictitious - it may seem that he has traveled less miles because his clock is running slow - but the miscalculation is due to the fact that he uses the clock reading in his own frame to calculate a distance in another frame

If twin 2 were to trail a measuring tape behind him, he would note that at the instant he reached the turn around point, the Earth would be exactly opposite the 5 ly mark on his tape. He would also note that if a measuring tape were stretched out from the Earth, that he would be at the 10 ly mark of it when he reaches the turn around point.

Now, the Earth being next to the 5 ly mark of twin 2's tape and twin two being next to the 10 ly mark of the Earth's tape are "space time events".
These space time events provide the markers we need to determine what happens from each frame.

According to twin 2, he reaches the turn around point when his 5 ly mark aligns with the Earth. Now, on Earth, when does the Earth align with the 5 ly mark on twin 2's tape? Well, since from the Earth frame Twin 2's measuring tape undergoes length contraction, this happens when twin 2 is 2.5 ly away. How much time passes on Earth while twin twin moves out to 2.5 ly? 2.875 yrs. So no, twin 2 does not appear to travel faster than c as you implied earlier.


The whole problem is that you are having trouble coming to terms with the idea of time being Relative.

An analogy:

At one time, a large percentage of the world's population held the world to be flat. As a result they came to the conclusion that "down" was a universal and absolute direction. When confronted with the idea of a spherical world, it made no sense. After all, if they were standing upright, people on the other side must be hanging head down. What kept them from falling off?

Even once the force of gravity, and how it worked towards the center of the Earth was explained, some still refused to give up their idea of universal "down" and would ask, "Then what holds the Earth up?" They might accept that gravity towards the center of the Earth could create a "fictitious down" , but the "real" direction of down was still a universal direction. They refused to accept that the very notion of "down" was defined by gravity.

And you have to learn to accept that the very notion of "time" is defined by observation. And observers moving relative to each other will have different observations.

 

[yogi]

Janus - I have no trouble at all distinquishing between relative and absolute - the times referred to in our story are of course relative - they are not defined with respect to a universal reference frame if there is one - the two times are exactly what is prescribed by the invarience of the interval in SR - the Earth time as measured by a clock at rest in the Earth frame is what determines how fast change is taking place in the Earth frame - and likewise for the twin 2 frame - change occurs slower for twin 2 - RELATIVE TO THE pace at which change is measured in the Earth frame. I fail to see how you could deduce that I am talking absolute(s). There may be an absolute where an observer measures no CBR asymmetry, but it is not part of this query.

What I have tried to do is pin you down as to two simple events in two relatively moving reference frames. You perpetually introduce how the other guy views the other frame and from there you invoke arguments that may be consistent with some interpretations of the LT, but to me they simply obscure the focus.

As most text(s) state - the proper quantities represent "invarient quantities" and that is why I have formulated the problem without using improper lengths and improper times which you claim are as equally real as proper times and proper lengths.

 

[yogi]

janus - again - as to your statement about the reality of length contraction, here is quote I have posted before by Eddinton - and the message is clear:

With regard the actuality of length contraction, Eddington had this to say:

"You receive a balance sheet from a public company ... it is certified by a chartered accountant. But is it really true? Many questions arise; the real values of items are often very different from those that figure in the balance sheet...There is a blessed phrase "hidden reserves" and generally speaking the more respectable the company the more widely does its balance sheet deviate from reality. This is called sound finance ... the main function of the balance sheet is to balance and everything else has to be subordinated to that end. The writing down of lengths for balance sheet purposes is the FitzGerald Contraction. The shortening of the moving rod is true, but it is not really true. It is not a statement about reality (the absolute) but it is a true statement about appearances.

 

[Chronos]

GR explains local relativistic effects nicely. SR gives the illusion that that acceleration is relative to a local reference frame [lorentzian thing]. GR changes the equation using time based topological reference frames.

 

[rtharbaugh1]

The Many Times Interpretation

The desire for an absolute seems to be part of the human condition. We need one thing, just one lousy thing, that doesn't move, isn't broken, and can be relied upon to always be there every time we look.

Children as they grow up have to learn what it is that is reliable about experience, and what it is that changes. A small infant attracted by a shiny toy will reach for it even though it is too far away, not having learned about the limits of arms and fingers. A slightly older child will still say that a tower in the distance is on the right side of the road, and then be astounded and insist that the tower has moved when, on coming closer, the road curves so that the tower passes on the left. How can a tower jump over the road? The child still has to learn about curves, and how they affect our perception.

As recently as Gallileo people didn't understand how a ship in the distance would drop below the horizon. It seemed as if the ship were sinking. Two ships moving apart on the ocean would each see the other sink, and a novice sailor might be surprised to meet up with that same ship again in another port. The other ship always seems to sink over the horizon, shrink in the distance, change sides of the path we are on, yet we learn that there is symetry and these effects are illusions, not "real." Not absolute, but relitive somehow to our own position.

Now in special relativity we learn that there is a curve in time. Things that are moving very fast compared to our own movement seem to change shape, shrink over some horizon. Only this time, it is possible using space-like curves for the shrinking object to remain nearby, as in DW's counter-rotating frames example in another thread in this forum. An object moving very fast seems to shrink, even though it is passing close by us. We are surprised to learn that from the point of view of the object, it is we who have shrunk. This is new. Usually things we know about that seem to shrink are far away, and we have become familiar, as adults, with the idea that things far away only seem smaller. In near space, we have come to assume that the balance sheet requires that if you shrink, I will seem bigger to you, and if you grow, I will seem to become smaller. As growing children and as young adults we are surprised to see our parents get smaller, and our children get large. How many times have you said to a child or heard from an adult, the phrase "My, how you have grown!"

Now we have to get our minds around the idea that time is curved, and objects still very close to us in space can seem to shrink in a way that has to do with their being "far away" in some time sense. Usually things far away in time are in the past or the future, and we do not expect to see them sharing our bit of space, but we have to adjust our idea again. THere is a far-away sense in time that is not far away in the past or future or far away in space. This new direction in time is orthagonal, at right angles, to everything we think we know. There is not just one direction in time, there are at least two. There is not just past and future, there is also fast and slow. There may even be other orthagonalities in time, more time dimensions, and we have trouble fitting more ninety degree angles into three dimensional space, so we find this difficult to model in our mind's eye. Yet the evidence is impossible to deny. Time is multidimensional. It curves. There is not just a single straight path from the past through the present into the future.

We deal with the effect of time curvature every day in our ordinary experience. We move. If time were not curved, it could not be so, and the universe would be unitary indeed, not allowing for time or change. There is no great mystery here. We are growing up as a species, and have to get around this new curve. There are more directions than three in space and one in time. We access other directions in time by making choices, that is, by changing our velocities. If we had made the other choice, gone the other way or gone there faster or slower, we would be in a different universe.

We have to accept then that there is not just one universe, which is difficult because the very word "universe" seems to insist that there is just one. That at least seems absolute, unchangeing, reliable. Every time we look, there is only one. But it seems to me now that we must give up even this idea of constancy.

Some have a problem with multiple universes because it seems to them untidy, and anyway, if there are so many universes, what does that say about the total sum of energy? Isn't energy additive and so if there are many universes doesn't this mean that the total sum of energies explodes into unwieldy and embarrassing infinities? I think these arguments are shown to be specious, and it is time to grow up. The Universe, meaning the total sum of everything that is, was, and ever can be, is much bigger than we can imagine.

Let us cease arguing about what is real and what is not real. Your god or my God, and if there is only one God, which of the two should be capitalized? It is a schoolyard fight that will never be settled by bullies. Instead, we need to think about how to accept our own greatness without insisting that others must be diminished.

Thanks for Being,

rth

 

[yogi]

rthar - the issue is not nitpicking - it is fundamental to explaining the nature of the universe - if the classical paradox can be resolved w/o resort to ancilliary accelerations - then the time differential between two moving systems is "real" ..it must be consequent to a physical cause.

Janus - here is quote from Robert Resnick's book - introduction of SR at page 93:

At page 93 of his book “Introduction to Special Relativity, Resnick analogous length contraction to Doppler shift: “ Is the frequency, or wavelength, shift in the Doppler effect real or apparent. ...When the source and observer are in relative motion, the observer definitely measures a frequency (or wavelength) shift. Likewise the moving rod is definitely measured to be contracted. The effects are real in the same sense that the measurements are real. We do not claim that the proper frequency has changed because of our measurement shift. Nor do we claim that the proper length has changed because of our measurement contraction. The effects are apparent (i.e., caused by the motion) in the same sense that proper quantities have not changed."

 

[SuperKamiokande]

I couldn't really be bothered reading everything everyone had to say but i got the gist of it from the beginning. It is possible to solve the twins paradox in terms of SR. Instead of taking a laser light, take pulses of laser light released from each twin.

Now consider the twin on Earth, he will be receiving a pulses of laser light at a lower frequency than he is sending them due to the absolute velocity of light and the near light speed at which the other twin travelling. However, the traveling twin will be receiving signals at a slower rate than that twin on Earth because his spaceship is moving at near light speed away from the earth. This is where the age difference occurs because one twin receives more signals than the other.

Now because we are in SR we just turn the spaceship around and head to earth. Suddenly the traveling twin is receiving much more frequent signals while the twin on Earth receives none until he/she gets a whole bunch of signals at once. But the number of signals sent and received during this part of the travel should be the same.

So overall we have one twin who has received fewer signals than the other twin despite both signals having sent (relative to themselves) the same number of signals. Job done I feel.

 

[yogi]

Signaling gets the right answer (ostensibly) because each twin assumes that the received frequency of transmission is altered from the proper frequency measured in the transmitting frame (by the Doppler effect). So one twin ages more than the other, but we all agree on that (I guess), so that is not the issue. SR predicts that each observer will see the other clock running slow consequent to relative motion.