- #36
ghwellsjr
Science Advisor
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Yes.
This is a meaningless statement. Apply it to lines on a plane, and you see it is meaningless. It reflects one completely arbitrary way of matching two paths against each other. There are infinitely many other ways of matching, all equally justifiable.ghwellsjr said:In my variant it happens that all the acceleration intervals are identical between the twins, not just similar, and the two coasting parts are different between the twins and that is why I say that it is exclusively during the coasting intervals that the aging difference between the twins accumulates.
Because they are irrelevant. We start clocks syncrhonized at zero, for example, when the twins first diverge in path. Again, looking at lines in a plane shows exactly what is meaningful and what isn't.ghwellsjr said:Of course, all intervals contribute to their total ages, including the ones before the scenario began (from the birth of the twins up to the beginning of the scenario and the ones after the scenario ended up to the present moment). Why don't you say they all need to be included, too, to explain the age difference?
ghwellsjr said:If you follow my variant, you will see that the first acceleration, by your definition, is irrelevant, because the twins have not yet diverged in path (as you say), and the time during which the first twin coasts, by your definition, is also irrelevant for the same reason, so why do you insist that these two intervals need to be included in order avoid the "meaningfulness" label?
ghwellsjr said:[...]
Beginners usually have learned that when two people are in relative motion, they can each view the other one as aging at a slower rate than themselves ...
Mike_Fontenot said:They each conclude that the other twin is ageing more slowly, but ONLY during periods of time when the observer isn't accelerating. Whenever the observer IS accelerating, the ageing rate of the other twin (according to the observer) can be higher or lower than the observer's rate. In fact, the other twin can even be getting younger (according to the observer), for scenarios where the observer is accelerating in the direction away from the home twin.
Mike Fontenot
JJRittenhouse said:[...]
...because acceleration means more time dilation, and can be attributed solely to the twin in acceleration?
[...]
Does the twin paradox ignore the effects of gravity on the twin at earth, btw?
ananthu said:Friends,
I will be happy if anybody throws light on the following concepts:
(1). In the case of time dilation it is said that a clock in a moving frame appears to go slow to an observer in a resting frame.It leads to the famous twin paradox in which 'A' who spends some time in a spaceship and returns to the Earth appears younger to 'B' who is his twin and stays on Earth at the time A leaves earth. With respect to B , say, 20 years had passed on the Earth but for A, say, only one year has passed in his ship. Here I don't understand one point.
If the theory of relativity says that A will appear 20 years younger than B, is it just an apparent one or real one? During the journey in the spaceship had the body cells of A really slowed down in its metabolism of aging? This point is highly confusing.
(2). According the theory of relativity, the mass of a body increases with the increase in its velocity. In that case, since a photon behaves like a particle, does it acquire mass because of its velocity?
(3). When the velocity of a body increases its mass increases while its length should decrease. Let us suppose that a rod approaches the velocity of light ( not become equal to it ). Then while its mass approaches infinity its length should approach zero! How is it possible for a body to shrink to an almost zero size but at the same time possesses nearly infinite mass?
I know the theory of relativity is a highly a complex one to comprehend. Still if anybody has simple explanations for my above doubts I will be very happy.
GODISMYSHADOW said:As you know, the double slit experiment shows a photon doesn't have path. Hence, the argument must be invalid. Whether the formula is right or wrong I cannnot say. They just used an invalid argument to reach it.
GODISMYSHADOW said:In the derivation of special relativistic formulas in college textbooks they show a photon bouncing back and forth between two mirrors in a moving spaceship. Then they apply geometry to the photon's path relative to an observer to come up with the formula. Well, I don't like it! As you know, the double slit experiment shows a photon doesn't have path. Hence, the argument must be invalid. Whether the formula is right or wrong I cannnot say. They just used an invalid argument to reach it.
Could you explain this to me?JJRittenhouse said:I know about the doppler effect of flying back, where events on Earth would speed up drastically by his perception
Mentz114 said:No, you just used an invalid argument. Of course light has a path. Shine a laser beam through some smoke or dust and you'll see it with your own eyes. The light clock argument is fine, there are no slits or other weird quantum effects involved.
GODISMYSHADOW said:With the double-slit experiment, they can reduce the intensity of the light to only one photon at a time. Yet they still get an interference pattern on the screen. Could that mean a photon doesn't have path?
JesseM said:The light clock thought experiment doesn't require that any actual particle move at c, even if we come up with some arbitrary function x(t) for position as a function of time that no actual object follows, we can still figure out the velocity of a hypothetical entity moving along this path, and if its coordinate speed is c in one frame it must be c in every other frame.
Yes, but scientific theories aren't like religious revelations, no special precedence is given to the wording of the original paper that stated some theory, later theorists may come to see the original statement as less than ideal and develop more precise ways of defining the "same theory". For example, nowadays I don't think anyone would say SR was falsified if it turned out that photons actually have a tiny mass and move at less than c, provided it was still true that all the fundamental laws of physics are Lorentz-invariant (meaning they obey the same equations in all the different inertial coordinate systems given by the Lorentz transformation). And the Lorentz transformation still says that any path through spacetime with a coordinate speed of c in one frame will have a coordinate speed of c in other frames, regardless of whether any physical object is actually following that path.GODISMYSHADOW said:The postulate Einstein used was that in any inertial reference frame, the observer will always come up with the same value for the speed of light when he tries to measure it.
GODISMYSHADOW said:The postulate Einstein used was that in any inertial reference frame, the observer will always come up with the same value for the speed of light when he tries to measure it.
That being the case, shouldn't the light clock thought experiment be about an actual physical measurement if it's going to use Einstein's postulate in order to prove something?
Mike_Fontenot said:During that first leg of the trip, the two twins are COMPLETELY equivalent. Each can make elementary measurements and simple, first-principle calculations about the current age of the other twin. Each will conclude that the other twin is ageing more slowly. And each of them is correct in their conclusion. Each of their conclusions is as real as anything can be ... it is NOT some kind of illusion.
Mike Fontenot
Where did he state that, in another topic member JesseM stated he implied just the opposite.ghwellsjr said:Einstein stated that you cannot measure the one-way speed of light.
It's in his 1905 paper. In my copy, it's on the second page under the heading "Definition of Simultaneity". He's discussing two observers, A and B separated by a constant distance (they are in the same inertial frame) and how they can each have an identical clock "but it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an 'A time' and a 'B time.' We have not defined a common 'time' for A and B, for the latter cannot be defined at all unless we establish by definition that the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A."Passionflower said:Where did he state that, in another topic member JesseM stated he implied just the opposite.
ananthu said:My confusion has only increased now.
If each looks young to the other, then it means no body has actually aged.
Let us assume A moves away from B and and according to time dilation formula, the clock in the frame of A should appear slower to B and similarly the clock in the frame of B should appear slower to A by the same amount. In this case A and B are moving away from each other. Now take the case of return journey of A. Here both A and B will be approaching each other. Here only I want clarification. When they apporach each other should not the opposite happen ie. the clock the reference frame of A who is actually returning should appear to go fast with respect to that of B and similarly the clock of B should appear faster to A?
So when they meet the time differences that occurred during the forward and return journeys should cancel each other effect and only same time should have elapsed for both of them.
Then it is absurd to say tha when A returns to Earth several years have passed on Earth and B looks older to A and so on.
Can anybody explain this in simple terms?
Note that Mike was talking about the first leg of the journey before either of the twins accelerated or changed direction. While both twins have constant inertial motion relative to each other, a comparison of relative ageing rates is meaningless and it is impossible to determine which twin is really ageing slower than the other, until one of them accelerates and comes to rest in the reference frame of the other twin.ananthu said:My confusion has only increased now.
If each looks young to the other, then it means no body has actually aged.
I think you are getting Doppler shift mixed up with time dilation. In Newtonian physics a clock that emits a light signal once per second will appear to emit a signal at less than once per second when it is going away from the observer and when the clock is coming towards the observer the clock appear to emit signals are more than one per second. However when the moving clock is compared to the stationary clock of the observer in Newtonian physics, the clocks show no difference in elapsed time and the apparent change in clock rate of the moving clock due to Doppler shift is just an illusion caused by light signal travel times. In Special Relativity a comparison of clock rates normally discounts any Doppler shift effects and in the case of the twin's paradox the difference in ageing rates is real.Let us assume A moves away from B and and according to time dilation formula, the clock in the frame of A should appear slower to B and similarly the clock in the frame of B should appear slower to A by the same amount. In this case A and B are moving away from each other. Now take the case of return journey of A. Here both A and B will be approaching each other. Here only I want clarification. When they apporach each other should not the opposite happen ie. the clock the reference frame of A who is actually returning should appear to go fast with respect to that of B and similarly the clock of B should appear faster to A?
ghwellsjr said:It's in his 1905 paper. In my copy, it's on the second page under the heading "Definition of Simultaneity". He's discussing two observers, A and B separated by a constant distance (they are in the same inertial frame) and how they can each have an identical clock "but it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an 'A time' and a 'B time.' We have not defined a common 'time' for A and B, for the latter cannot be defined at all unless we establish by definition that the 'time' required by light to travel from A to B equals the 'time' it requires to travel from B to A."
ananthu said:My confusion has only increased now.
If each looks young to the other, then it means no body has actually aged.
[...]
When they approach each other should not the opposite happen, i.e., the clock in the reference frame of A who is actually returning should appear to go fast with respect to that of B and similarly the clock of B should appear faster to A?