1. Oct 4, 2008

### cos

It is my understanding that the twin paradox arose from the fully reciprocal nature of special theory which shows that if a clock is moving past me in outer space that clock is ticking over at a slower rate than my clock but that from the point of view of a person accompanying that clock it is my clock that is ticking over at a slower rate than his clock; the paradox, apparently, being that both clocks cannot be ticking over at a slower rate than the other one (the original ‘clock’ paradox).

In his 1918 Naturwissenschaften article Einstein attempted to negate this paradox insisting that it is only the clock that has been made to move to the other clock’s location that incurs time dilation on the basis that it experiences forces of acceleration however in chapter 4 of his 1905 article ‘On the Electrodynamics of Moving Bodies’ Einstein wrote:-

“If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by ·5tv2/c2.....”

My reason for posting this message is that, having been made to move from A to B clock A (although Einstein does not refer to this fact) must have accelerated.

The alternative is that clock A incurred instantaneous velocity which, I assume, is a concept that Einstein would not have tolerated ergo his chapter 4 depiction effectively provides a similar explanation for the eventual discrepancy between clocks A and B as did his 1918 article.

On the basis that Einstein’s chapter 4 STR clock A accelerated, moved toward B at v then decelerated this is analogous to an astronaut’s return journey following turn-around.

As a result of his outward-bound journey the astronaut’s clock will lag behind his twin’s clock by ·5tv2/c2.. As a result of his inward-bound trip the astronaut’s clock will lag behind the twin’s clock by an additional ·5tv2/c2.

I have read several interpretations of the twin paradox one of which insists that the traveler’s clock does not (as Einstein expressed it in chapter 4) ‘go more slowly’ than the Earth clock but that the Earth clock, from the traveler’s point of view, ticks over at a faster rate than his own clock but only during the astronaut’s period of acceleration following turn-around however it is my understanding that the concept of time contraction was, for Einstein, an anathema.

Although I have included Einstein’s chapter 4 equation it would very much be appreciated if responses did not incorporate mathematical ‘proofs’ or explanations.

I am, as was Faraday, one of those annoying self-taught persons who has no comprehension of mathematics and, like Faraday, prefers simple, every-day language interpretations.

Einstein insisted that as far as the propositions of mathematics are certain, they do not refer to reality and I tend to agree.

2. Oct 4, 2008

### granpa

all of the above

3. Oct 4, 2008

### granpa

seriously, one of them is from the point of view of the stationary twin and the other is from the point of view of the traveling twin. there is no contradiction.

Last edited: Oct 5, 2008
4. Oct 5, 2008

### atyy

I prefer not to think of time dilation, although that is valid. The accumulated proper time of a person is simply the "length" of his trajectory in spacetime.

In normal geometry, a straight line between two points has the shortest length. Still in normal geometry, the edge of a square has a shorter length than the diagonal.

The difference in spacetime geometry is that a straight line has the longest length. If you draw the situations you described in spacetime, and apply this principle, you will reproduce the standard time dilation results.

The reason for defining spacetime length in this somewhat strange way is that it ensures that the speed of light is the same for "normal" observers moving at constant velocity relative to each other, which is an experimental observation.

Although you prefer not to have the equations, here is a link, just in case:

Last edited: Oct 5, 2008
5. Oct 5, 2008

### Fredrik

Staff Emeritus
This is one place where you're going wrong. Not the last part. I agree with that. A theory is a mathematical abstraction. You can think of a theory as an approximate description of our universe or as an exact description of a fictional universe that resembles our own, but not as an exact description of our universe, so you got that part right. Your mistake is to think that there is a non-mathematical answer to this problem.

The reason why there isn't, is that the only way that anyone can believe that the paradox exists in the first place is to use the theory (i.e. the mathematics) incorrectly. No one claims that the twin paradox is something that happens in the real world. The claim is that there's a paradox in the theory. But the "paradox" is just a mistake in a calculation, so there's no way to resolve it without examining the calculation and showing what the mistake is.

So I'm afraid that a resolution is always going to look like e.g. posts #3 and #142 in this thread. They require that you know some mathematics, or that you at least understand simultaneity in the context of inertial frames in special relativity.

6. Oct 5, 2008

### phyti

Aw Freddie, we can at least try.

The fundamental causes of time dilation are the properties of light. [1] It's propagation speed in (matter free) space is constant and independent of its source. Light is the messenger between objects, big and small. Imagine two objects separated vertically or horizontally by a space, and not moving relative to the earth lab. The objects exchange light signals periodically, once per second (1 tick). Then a force is applied to move both to the right. Because of [1], the speed of the objects does not change the speed of light, the objects are moving away from the source, and it takes longer to exchange the signals. Observers in the lab see the tick rate decrease.
Copy these objects, assemble as a clock, put the clock in a capsule with a pilot and launch it into space. As it moves past earth, the lab sees the clock rate slower than the lab clock.
In the capsule, the clock and the pilot are moving, therefore the rate of signal exchange is the same for both, i.e., slower. The pilot is thus not aware of the slower rate and sees his clock as 'normal'. The speed of the capsule alters the perception of the pilot (or device).
Because the capsule is moving at a constant speed (no acceleration), SR allows the pilot to assume he is not moving. If he chooses this option, he will calculate the lab clock rate to be slow. His other option is to accept his motion, adjust his time, and the strange things (anomalies) disappear.
Acceleration definitely makes the twin scenario asymmetrical, but does not explain the time difference, since it's a constant part of the travel time. As the duration of the trip increases, so does the time difference.
Time dilation has been experimentally verified, so it is real and not a mathematical contrivance.
Hope this helps.

7. Oct 5, 2008

### cos

The contradiction, as I see it, is that some people insist that from the point of view of the traveling twin the Earth clock is incurring time contraction as he accelerates toward the planet following turn-around yet it is my understanding that Einstein refused to accept this idea.

It is a ‘contradiction’ of the laws of physics that the astronaut, having accelerated to an instantaneous velocity of close to the speed of light (thereupon generating a gamma factor of 40,000), would be of the opinion that the planet is spinning on its axis at around 64 million k-h.

8. Oct 5, 2008

### cos

In your opinion, does that link show that the traveler truly believes that his clock is not ticking over at a slower rate than it was before he commenced acceleration following turn-around but that it is the Earth clock that is physically ticking over at a faster rate?

In chapter 4 STR, as well as in his 1918, article Einstein effectively wrote that clock A ‘goes more slowly’ than B not that B ‘goes faster’ than A.

In your opinion, does that link show that the traveler truly believes, having accelerated to an instantaneous velocity of (or moving with uniform velocity at) close to the speed of light generating a gamma factor of 40,000, that the Earth is physically spinning on its axis at 64 million k-h?

9. Oct 5, 2008

### cos

There is a non-mathematical solution to this problem (by which I take it you refer to the paradox) and Einstein provided same in chapter 4 as well as in his 1918 article. Observers accompanying both clocks know that they have incurred acceleration thus both of them know that their’s is the moving clock.

The equation provided by Einstein in chapter 4 was not a mathematical solution but a method of determining the amount of lag incurred by clock A.

Doesn’t ‘the theory’ (i.e. the mathematics of chapters 1 through 3) show that the determinations are fully reciprocal? That from A’s point of view B’s clock slows down and from B’s point of view A’s clock slows down?

As far as I’m concerned, Einstein provided a resolution of the twin paradox without requiring any knowledge of mathematics or understanding of simultaneity on my behalf.

My specific interest is in relation to the claim that the traveling twin is not allowed to determine that he is moving (thus that his is the clock that ‘goes more slowly’ than the Earth clock) but determines that the Earth clock incurs time contraction.

10. Oct 5, 2008

### cos

On the basis that the objects exchange light signals it is assumed that they are sources of those signals so I fail to understand why you say that the objects are moving away from the source. They are moving away from the point in space where the source was located at the instant of emission not away from the source.

Your depiction is, of course, a slightly more complicated version of the textbook light clock gedanken.

My specific interest is in relation to the claim that the pilot, having accelerated following turn-around, is of the opinion that it is the Earth clock that is incurring time contraction which is, of course, on the basis that, as you point out, he assumes that he is not moving however, as you also point out, he can accept his motion whereupon the anomaly (that the Earth clock ‘is’ physically ticking over at a faster rate than it was before he started his return trip and that the planet is spinning faster on its axis) disappears. That’s the very point I’m trying to get across.

You have, perhaps albeit unintentionally, ratified my argument.

The pilot, having accelerated away from the planet or following turn-around is fully justified in being of the opinion that he is moving thus that his is the clock A to which Einstein referred in chapter 4 thus that it is his clock which ‘goes more slowly’ than the Earth clock’; that the Earth clock does not incur time contraction.

(As Einstein pointed out in chapter 4.)

It is a primary tenet of physics that whilst a theory, such as STR’s concept of time dilation, can appear to have been experimentally verified on numerous occasions it only requires one experiment to invalidate any theory.

Although it is accepted that time dilation has been experimentally verified it’s absolutely essential counterpart - length contraction - has not!

If the theoretical concept of length contraction does not physically take place (as distinct from ‘mathematically’ or ‘seemingly’) then the concept of the constancy of the speed of light cannot be maintained.

11. Oct 6, 2008

### atyy

No. The traveller believes that everyone has his own clock, which ticks according to his own proper time. His clock has accumulated less time, because he travelled a shorter path in spacetime.

I haven't read the article. In my view, no one's clock ever goes faster or slower, it's just a question of the distance they cover distance in spacetime.

For this paragraph, consider just normal space, not spacetime. A friend and I fly from Boston to San Francisco. He flies directly across the United States. I fly from Boston to London to Singapore to Japan then to San Francisco. My route is obviously longer but that is not because my rulers contracted in length compared to my friend's rulers. That is just nonsensical (actually, it can make sense, but that's another story).

The time dilation comparison only makes sense in the usual, but very special case that one of the twins moves along a straight line in spacetime. In the general case, where both twins travel curly spacetime paths, and meet again, they will have aged by different amounts which is best explained by the different distances they covered in spacetime.

I'm not sure your calculation is right, but I'll answer in the spirit of it - of course not. The twin will feel and be able to measure his acceleration, so he will know that he has changed reference frames, and understanding the theory of relativity he will always be able to correct his measurements to infer what the people on earth are experiencing.

12. Oct 6, 2008

### yogi

Some good observations COS - here is my take on the TP. First Einstein explained things in a way that seemed to make a difference as to which clock was put in motion - then in 1918 he shifted his argument to a pseudo G force - but a correct explanation should be able to resolve which clock logs the most time using an one way trip where there is no acceleration - for example have the A clock already in motion and start it when it passes earth on its way to B clock. When A arrives at B it will have accumulated less time than the earth clock and the B clock (they will read the same since they can by syced and are always in the same frame and not moving wrt to one another). So the whole paradox falls apart in that you are simply measuring one clock traveling between two fixed clocks and that will always lead to an actual difference in the time logged by the single clock when timed by the two clocks - moreover, it doesn't make any difference if the earth and B are moving or if A is moving

13. Oct 6, 2008

### Fredrik

Staff Emeritus
Not quite. In order to be able to say something like that, we have to take "B's point of view" to always be the co-moving inertial frame. (B is the astronaut twin). If we do, then what you said is true at all points on B's world line except the turnaround event. That much is true, but this does not imply that A is younger when they meet again. To see that, you have to understand simultaneity in the context of inertial frames in special relativity. See my spacetime diagram for some of the details. (Use the link in my previous post).

14. Oct 6, 2008

### cos

So you obviously agree with me that the traveler realizes that his clock is ticking over at a slower rate than it was before he started moving regardless of the fact that it appears to him to be ticking over at its normal rate.

15. Oct 6, 2008

### granpa

slower relative to what? to what it was before. suppose the earth is moving at relativistic speed and the traveler is actually slowing down.

16. Oct 6, 2008

### cos

It is imperative that my discussion applies solely to Einstein's chapter 4 depiction as well as an out-and-return journey and that the traveler, or an observer accompanying clock A, be permitted to realize that his clock does incur time dilation (i.e. tick over at a slower rate than it did before he started moving) regardless of the fact that it appears to be ticking over at an unchanged rate.

It does make a difference 'if the Earth and B are moving or if A is moving' on the basis that, according to Einstein's chapter 4 depiction as well as his 1918 article, it is the accelerated clock that incurs time dilation not the unaccelerated clock (i.e. the Earth clock or Einstein's chapter 4 clock B.

17. Oct 6, 2008

### granpa

does or doesnt make a difference?

18. Oct 6, 2008

### JesseM

It is true that, no matter which frame you choose, the average rate of ticking on the clock of the traveling twin must be slower than the average rate on the clock of the Earth twin. But you can find inertial frames where the Earth twin's clock ticks slower than the traveling twin's clock during the trip away from the Earth, then the traveling twin's clock ticks slower than the Earth twin's on the return journey after the turnaround; you can also find frames where the opposite is true, and the traveling twin's clock is slower on the outbound trip but faster on the inbound leg. So, there is no objective truth about whose clock is ticking slower at any given moment, even if the average of the traveling twin's clock is always slower than the Earth twin's clock over the course of the whole trip.

19. Oct 6, 2008

### cos

Suppose the two clocks Einstein referred to in chapter 4 are, initially, moving at relativistic speed and, as Einstein pointed out, clock A moves to B's location; will that have any affect on Einstein's conclusion?

Are you suggesting that Einstein's chapter 4 depiction only applies if the reference frame in which clocks A and B are initially located is stationary - to which I respond - stationary relatively to what?

You wrote "suppose the earth is moving at relativistic speed" to which I apply your question - relative to what?

Are you of the opinion that the Earth could be moving at relativistic speed? Is there any evidence to support such an idea? Is there any evidence which indicates that this could be a valid point of view? Is there any evidence to prove that the tooth fairy does not exist?

In my opinion physics should be a study of reality.

20. Oct 6, 2008

### granpa

it was a hypothetical question.
i believe jesse put it very well in his post. i will leave it at that.