The discussion centers on the twin paradox in special relativity, specifically addressing the aging differences between two twins, Bob and Alice, when one travels at high speed. Bob's frame of reference is non-inertial due to acceleration, while Alice remains stationary, leading to Bob experiencing time dilation and returning younger than Alice. The key conclusion is that the twin who accelerates (Bob) takes a different path through spacetime, resulting in a measurable difference in aging when they reunite. The discussion emphasizes that biological aging is not merely a mechanical clock but is influenced by the relativistic effects of motion and acceleration.
PREREQUISITESStudents of physics, educators teaching relativity, and anyone interested in the implications of special relativity on time and aging.
Ok, but how Bob/Alice/any clock are physically affected by the "path through spacetime"? In the odometer analogy we know how "the path" (the road) makes the odometer to record more/less kilometers, but how does the spacetime actually affect the clocks/people?PeterDonis said:Everyone ages at one second per second along their own path through spacetime. The difference between the two twins is that Bob follows a shorter path through spacetime--one that has fewer total seconds along it--than Alice does. That is why Bob is younger when they meet up again.
Different paths through spacetime have different lengths, and the length of a timelike path through spacetime is the amount of time that a clock moving along that path ticks off. We use clocks to measure "distances" in spacetime the same way we use odometers to measure distances in space.DanMP said:Ok, but how Bob/Alice/any clock are physically affected by the "path through spacetime"? In the odometer analogy we know how "the path" (the road) makes the odometer to record more/less kilometers, but how does the spacetime actually affect the clocks/people?
This is more like a definition than an explanation. It does not explain the action, if any, made by the spacetime to affect the "ticking" of the clock. For odometers we have such an action: the road makes the wheels turn/rotate due to friction. How is spacetime affecting the clocks/people?Nugatory said:Different paths through spacetime have different lengths, and the length of a timelike path through spacetime is the amount of time that a clock moving along that path ticks off. We use clocks to measure "distances" in spacetime the same way we use odometers to measure distances in space.
For every clock we have such an action too. For an atomic clock the energy level difference for the hyperfine transition makes the oscillator oscillate at a specific frequency.DanMP said:For odometers we have such an action: the road makes the wheels turn/rotate due to friction. How is spacetime affecting the clocks/people?
Time is inherently a part of space-time and clocks measure the time part of space-time. That's all there is to it. Time is what clocks measure. All clocks tick at one second per second in their own frame of reference. There is no other "action" performed by space-time on time. What matters is, as Nugatory pointed out, the path through space-time. This is exactly analogous to a space path where distance is measured in meters instead of seconds. Don't be confused by the action of an odometer --- there are other ways to measure distance but they all measure the same distance (assuming they are working correctly).DanMP said:This is more like a definition than an explanation. It does not explain the action, if any, made by the spacetime to affect the "ticking" of the clock. For odometers we have such an action: the road makes the wheels turn/rotate due to friction. How is spacetime affecting the clocks/people?
That is an excellent point. It isn’t about the odometer, it is about the geometry.phinds said:Don't be confused by the action of an odometer --- there are other ways to measure distance but they all measure the same distance (assuming they are working correctly).
DanMP said:Ok, but how Bob/Alice/any clock are physically affected by the "path through spacetime"? In the odometer analogy we know how "the path" (the road) makes the odometer to record more/less kilometers, but how does the spacetime actually affect the clocks/people?
You have two men, they start off walking from the same point but in slightly different directions. They have the same stride. At some point, one of the men turns and changes the direction he is walking in so that he is now headed back towards the other man's path. Once he crosses it, bot men measure their present distance from the starting point. The man who changed direction will be shorter distance from the starting point. This was not caused by anything affecting him or the pace at which he walked, just the fact that he took a different route.DanMP said:This is more like a definition than an explanation. It does not explain the action, if any, made by the spacetime to affect the "ticking" of the clock. For odometers we have such an action: the road makes the wheels turn/rotate due to friction. How is spacetime affecting the clocks/people?
Yes, I know that, but still, where is the role of spacetime in that energy level difference and/or in the oscillation?Dale said:For every clock we have such an action too. For an atomic clock the energy level difference for the hyperfine transition makes the oscillator oscillate at a specific frequency.
How exactly they do that? According to Dale, clocks are counting oscillations. I can't see the direct connection between that and the spacetime, or "the time part of space-time".phinds said:Time is inherently a part of space-time and clocks measure the time part of space-time.
The geometry is good in explaining how to understand and apply the theory, but it is as good in "explaining" what is really happening as contour lines in a topographical map: we can say that we get more tired walking between A and B because we cross contour lines (climbing a hill), but we need to explain why/how contour lines are responsible for this. The same is valid, in my opinion, for world lines / paths through spacetime: we need to show the direct connection, if there is any, between them and the clocks.Dale said:Yes, friction rolls the wheel and yes the hyperfine transition has a specific energy, but the point is that the geometry makes it so that a bent path in space always requires more wheel rotations and a bent path in spacetime requires fewer hyperfine transitions.
That is not explained by the physical mechanisms since, as you point out, we can replace them with any other mechanisms. It is explained by the geometry.
No, I'm pretty sure that this is "the best tree", if we want to solve the mystery of dark matter and to finally/really understand relativity.Janus said:As long as you keep looking for something that "affects" the ticking of clocks as the cause for time dilation, you are barking up the wrong tree.
Dude, you are SERIOUSLY barking up the wrong tree. I am constantly astounded by the patience of the mentors here but I predict that this thread has run its course.DanMP said:No, I'm pretty sure that this is "the best tree", if we want to solve the mystery of dark matter and to finally/really understand relativity.
I think that my questions are legitimate and deserve to be answered.phinds said:Dude, you are SERIOUSLY barking up the wrong tree. I am constantly astounded by the patience of the mentors here but I predict that this thread has run its course.
This analogy is wrong. The relevant one is why is it a longer distance over the hill than through a straight tunnel. What answer would you consider acceptable to that question?DanMP said:The geometry is good in explaining how to understand and apply the theory, but it is as good in "explaining" what is really happening as contour lines in a topographical map: we can say that we get more tired walking between A and B because we cross contour lines (climbing a hill), but we need to explain why/how contour lines are responsible for this.
Wow. That came from nowhere. Are you really telling all these scientists how to do their job?DanMP said:No, I'm pretty sure that this is "the best tree", if we want to solve the mystery of dark matter and to finally/really understand relativity.
My analogy is not wrong, because it is about causality. The one with the tunnel is, again, just geometry.Ibix said:This analogy is wrong. The relevant one is why is it a longer distance over the hill than through a straight tunnel. What answer would you consider acceptable to that question?
You are confusing doing work against gravity (countours) with traveling a further distance (route).DanMP said:My analogy is not wrong, because it is about causality. The one with the tunnel is, again, just geometry.
But they have BEEN answered. You just don't seem to LIKE the answers.DanMP said:I think that my questions are legitimate and deserve to be answered.
So "it's just geometry" is, to you, an acceptable answer for "why are the distances different", but not for "why are the times different". Do I understand you correctly?DanMP said:My analogy is not wrong, because it is about causality. The one with the tunnel is, again, just geometry.
You're fixated on the idea of objects interacting with space(/time) probably because most of our experiences happen on Earth, where we are physically attached to an object with a certain geometry, so it makes for a convenient example. Please understand: this analogy is leading you astray because you are not, in fact, interacting with space (you are not interacting with geometry) you are interacting with an object.DanMP said:How exactly they do that? According to Dale, clocks are counting oscillations. I can't see the direct connection between that and the spacetime, or "the time part of space-time".
The geometry is good in explaining how to understand and apply the theory, but it is as good in "explaining" what is really happening as contour lines in a topographical map: we can say that we get more tired walking between A and B because we cross contour lines (climbing a hill), but we need to explain why/how contour lines are responsible for this. The same is valid, in my opinion, for world lines / paths through spacetime: we need to show the direct connection, if there is any, between them and the clocks.
No, I'm pretty sure that this is "the best tree", if we want to solve the mystery of dark matter and to finally/really understand relativity.
No. I obtained interesting results doing that, so I offered a hint. Nothing more. Take it or leave it (to me) :-)m4r35n357 said:Are you really telling all these scientists how to do their job?
Yes. Distances in space are easy to deal with, but with time is different:Ibix said:So "it's just geometry" is, to you, an acceptable answer for "why are the distances different", but not for "why are the times different". Do I understand you correctly?
Why (if I understand correctly) a clock measures less time in a bent (longer) path in spacetime? This (at least) requires an explanation, but also:Dale said:the geometry makes it so that a bent path in space always requires more wheel rotations and a bent path in spacetime requires fewer hyperfine transitions.
DanMP said:clocks are counting oscillations. I can't see the direct connection between that and the spacetime, or "the time part of space-time".
It really isn't.DanMP said:Yes. Distances in space are easy to deal with, but with time is different:
Because Minkowski geometry does not work like Euclidean geometry. Rather than having the Pythagorean theorem ##c^2 = a^2 + b^2##, you have the corresponding relation ##(c\tau)^2 = (ct)^2 - x^2##. This geometry is required in order for the speed of light to be invariant.Why (if I understand correctly) a clock measures less time in a bent (longer) path in spacetime? This (at least) require an explanation, but also:
DanMP said:Why (if I understand correctly) a clock measures less time in a bent (longer) path in spacetime? This (at least) requires an explanation
Ok, so one question was answered. Thank you!Orodruin said:... Minkowski geometry does not work like Euclidiean geometry. Rather than having the Pythagorean theorem ##c^2 = a^2 + b^2##, you have the corresponding relation ##(c\tau)^2 = (ct)^2 - x^2##. This geometry is required in order for the speed of light to be invariant.
To measure distance you see how many times a thing of known constant length fits between point A and point B. To measure duration you see how many times a thing of known constant time fits between event A and event B. We call the first thing a ruler and the second a clock.DanMP said:This (at least) requires an explanation, but also:
We can measure the distance along a path in space with meter sticks: place the meter sticks end to end and then count the number of meter sticks needed. Equivalently we can use just one meter stick, repeatedly picking it up and putting it down again with the near end where the far end had been, and count the number of times we placed the stick before we reached the end of the path.DanMP said:How exactly they do that? According to Dale, clocks are counting oscillations. I can't see the direct connection between that and the spacetime, or "the time part of space-time".
Your post only contained one question.DanMP said:Ok, so one question was answered. Thank you!
What about the other one?
Yes, this is a nice explanation. I like it. Thank you!Ibix said:To measure distance you see how many times a thing of known constant length fits between point A and point B. To measure duration you see how many times a thing of known constant time fits between event A and event B. We call the first thing a ruler and the second a clock.
Another very nice explanation. Thank you!Nugatory said:We can measure the distance along a path in space with meter sticks: place the meter sticks end to end and then count the number of meter sticks needed. Equivalently we can use just one meter stick, repeatedly picking it up and putting it down again with the near end where the far end had been, and count the number of times we placed the stick before we reached the end of the path.
Counting oscillations is the analgous procedure for measuring the interval along a timelike path through spacetime.
Let me ask you a closely related question here. If we draw a triangle on a piece of paper and then measure the length of one side with a ruler and compare it to the length of the other two sides measured with similar rulers, then we always find that the two sides together are longer than the one side. How would you explain that?DanMP said:The geometry is good in explaining how to understand and apply the theory, but it is as good in "explaining" what is really happening as contour lines in a topographical map: we can say that we get more tired walking between A and B because we cross contour lines (climbing a hill), but we need to explain why/how contour lines are responsible for this. The same is valid, in my opinion, for world lines / paths through spacetime: we need to show the direct connection, if there is any, between them and the clocks.
Dale said:Let me ask you a closely related question here. If we draw a triangle on a piece of paper and then measure the length of one side with a ruler and compare it to the length of the other two sides measured with similar rulers, then we always find that the two sides together are longer than the one side. How would you explain that?
The reason I ask is because I think that the geometry is a complete answer, but you do not. So if I can understand what sort of answer you would find satisfying for the triangle question then I can probably make a similar answer for time that would be satisfying for you.