twin paradox

[SamBridge]

 

There is a place where this gets hinky, but it's not the place you're thinking. It mostly has to do with the shape of a gravity field. A gravity field created by a mass is spherical. In real terms, this means, there is in fact an experiment that can tell you if you're accelerating or in a spherical gravity field. It's quite simple: as two objects at the same altitude fall in a real gravity field they move closer together. And this does not happen in an accelerating rocket. You will hear "local" used a lot; this is an acknowledgement of this real difference in the behavior of gravity and acceleration. The key point is, however, if you can imagine a planar instead of spherical gravity field, that planar field would, in fact, be completely indistinguishable from acceleration within the elevator. When relativists talk about a "local experiment," they mean one that doesn't cover enough volume to allow this difference to be measured.

 

It is, BTW, more correct to say "acceleration due to the curvature of spacetime."

 

However, that is a shot in the dark; I'm not entirely clear what you're objecting to so I'm quoting some doctrine that's similar to what I perceive you as talking about, but I'm not confident I'm really answering your questions. However, if I'm not, the above background is necessary to understand the correct answer anyway, so it's not wasted time.

 

The car pushes you forward. This is a real force. You can also define matters (by using the frame in which the car is motionless and accelerates the Earth to its rear) in the opposite direction, and it is this that is called a "pseudo" or "fictitious" force; however, it is always (or, rather, it's components always add up to) Newton's Second Law, as modified by relativity.

 

Later: One of the things that's always gotten my rear end beat by relativists is forgetting that motion and speed/velocity are relative, but acceleration is absolute. You can always perform a local experiment that will tell you if you are accelerating; you can never perform one that will tell you if you are moving.

Ok, so there's some differences, but still to this very minute that you're reading this post, I am not clear on what "causes" the turnaround to have such a great impact and why everything before then is negligible. What is the "fictitious force" that creates the anti-symmetry that resolves the paradox? Is it just that events in time themselves act like a blue-shift, making measured events of the rocket close together which is equivalent to time dilation? But doesn't time dilation and length contraction work the same no matter what direction you're going including tangent to any given direction while you are traveling in a circle? So why would the turn around matter? it's just this tiny part of the entire trip, but somehow that acceleration changes everything?

 

 

You didn't give any details about how such a geometry would exist, but space would have to be curved in that situation, so special relativity would not apply. SR works only in flat space. (another way of saying no accelerations)

It doesn't matter if I give details, the scenario is the same regardless of how I describe it. If I say "return to Earth without turning around," physics doesn't just suddenly not exist, I only used a hyper-doughnut for your sake as piece of mind for how it might work. In reality I really don't care what would explain it, and neither should you. It's no different than saying "suppose we have a perfect sphere," in reality we're never ever ever ever ever going to see a "perfect sphere" at least not on the macroscopic scale, but that doesn't mean you can't apply physics to that situation or pose it as a hypothetical. The question remains the same regardless of how it arises: would anything resembling the twin paradox occur if you could return to Earth without turning around in apparently flat space?

Edited April 6, 2014 by SamBridge

[swansont]

 

It doesn't matter if I give details, the scenario is the same regardless of how I describe it. If I say "return to Earth without turning around," physics doesn't just suddenly not exist, I only used a hyper-doughnut for your sake as piece of mind for how it might work. In reality I really don't care what would explain it, and neither should you. It's no different than saying "suppose we have a perfect sphere," in reality we're never ever ever ever ever going to see a "perfect sphere" at least not on the macroscopic scale, but that doesn't mean you can't apply physics to that situation or pose it as a hypothetical. The question remains the same regardless of how it arises: would anything resembling the twin paradox occur if you could return to Earth without turning around in apparently flat space?

 

 

Actually the details do matter. Physics isn't magic. It's very easy to make a statement that is contradictory to laws of nature ( e.g. let's say I'm traveling at thrice the speed of light) so you can't just make them casually. A hyper-doughnut geometry has certain implications, the most basic one being that the spacetime isn't flat, meaning one of the assumptions of SR is violated. Such an example can't be used to investigate effects of SR. It's an example of begging the question, aka a circular argument (an amusing coincidence), i.e. tacitly assuming SR doesn't apply to show that SR doesn't apply.

[SamBridge]

 

Actually the details do matter. Physics isn't magic. It's very easy to make a statement that is contradictory to laws of nature ( e.g. let's say I'm traveling at thrice the speed of light) so you can't just make them casually. A hyper-doughnut geometry has certain implications, the most basic one being that the spacetime isn't flat, meaning one of the assumptions of SR is violated. Such an example can't be used to investigate effects of SR. It's an example of begging the question, aka a circular argument (an amusing coincidence), i.e. tacitly assuming SR doesn't apply to show that SR doesn't apply.

Then neglect whatever parts of SR that conflict. For all we know we could already be living in a universe where traveling in a straight line get's you to a previous point. Let's say it happens in a hypothetical universe where the inherent curvature of space that causes this looping is too small to be noticed with today's technology, which allows us to say it takes an arbitrarily but still very long distance to make one loop, like 30 billion light years, and everything else about this hypothetical universe is the same as our universe; we still have light as the limit and all the fundamental forces still give us the measurements we currently have in any given local space. There you go. Over light years, space-time can still be approximated as flat because the inherent curvature happens at such a slow rate.

Edited April 6, 2014 by SamBridge

[md65536]

[...]I am not clear on what "causes" the turnaround to have such a great impact and why everything before then is negligible. What is the "fictitious force" in the that resolves the paradox?

The only thing of interest that the turnaround causes is a switch in inertial frames. You're right that it doesn't matter how the turnaround happens.

 

You're looking in the wrong place by focusing on the details of the turnaround, while ignoring the long stretches of relative velocity, where time dilation actually occurs. Before considering the details of the turnaround, consider this: Suppose a twin travels at high constant velocity away from Earth, for one year (by its clock). Then it enters a black box, somehow turns around in the box, and exits at the same speed in the opposite direction and returns to Earth in one year. Say gamma=2 and Earth ages 4 years while the traveling twin ages 2 (while out of the box). All of this will remain true no matter what happens in that box.

 

Also, that twin will really SEE the Earth age 4 years. Using relativistic Doppler shift, the twin sees Earth age .27 years on the first leg, and 3.73 years on the second leg. This is true no matter what happens in the box.

 

Now let's say the box is a billion light years long on all 3 sides, and contains a hyperdoughnut, several Kerr black holes, a Hawking Pretzel, a LaForge Ice Cream Cake, and a zero-point energy singularity. And some regular doughnuts too. Suppose that the twin has enough fuel to make the turnaround itself, or maybe the twin is a neutrino and can be turned around with little energy. Suppose also that the twin ages a million years while in that black box, and you have no idea what complicated manoeuvres took place while it was inside. Also suppose that to the twin, while it aged a million years between entering and exiting the box, it sees that Earth aged only a thousand, or perhaps a billion (it doesn't matter here) between the last image the twin saw while entering the box, and the first image it sees after exiting. Nothing that happens in the box changes the fact that the twin sees Earth age .27 years on the outward journey, and 3.73 years on the inbound journey, for a total of 4 years that Earth has aged while the twin spent 2 years leaving and returned. Whether the twin experienced any proper acceleration, and how much, doesn't change this.

 

IF all those extra details are not so easy to ignore, you can just make the turnaround instantaneous and you get the same result.

 

Once you understand how what happens on the long part of the journey matters, *then* you can look into the turnaround without setting yourself up for so much confusion.

 

 

 

What does this mean, though? If you're doing Doppler shift analysis, very little interpretation is needed. The traveling twin actually sees the Earth age 4 years while itself ages 2. If you're trying to figure it out in terms of inertial frames, it might be something like: the difference in simultaneity between Earth and the twin is already inherent in the difference between the outbound and inbound frames of reference. The change in simultaneity does not need any special causal details; simply having the right velocity and distance from the other observer (Earth) is all that matters.

Edited April 6, 2014 by md65536

[SamBridge]

The only thing of interest that the turnaround causes is a switch in inertial frames. You're right that it doesn't matter how the turnaround happens.

 

You're looking in the wrong place by focusing on the details of the turnaround, while ignoring the long stretches of relative velocity, where time dilation actually occurs. Before considering the details of the turnaround, consider this: Suppose a twin travels at high constant velocity away from Earth, for one year (by its clock). Then it enters a black box, somehow turns around in the box, and exits at the same speed in the opposite direction and returns to Earth in one year. Say gamma=2 and Earth ages 4 years while the traveling twin ages 2 (while out of the box). All of this will remain true no matter what happens in that box.

 

Also, that twin will really SEE the Earth age 4 years. Using relativistic Doppler shift, the twin sees Earth age .27 years on the first leg, and 3.37 years on the second leg. This is true no matter what happens in the box.

 

Now let's say the box is a billion light years long on all 3 sides, and contains a hyperdoughnut, several Kerr black holes, a Hawking Pretzel, a LaForge Ice Cream Cake, and a zero-point energy singularity. And some regular doughnuts too. Suppose that the twin has enough fuel to make the turnaround itself, or maybe the twin is a neutrino and can be turned around with little energy. Suppose also that the twin ages a million years while in that black box, and you have no idea what complicated manoeuvres took place while it was inside. Also suppose that to the twin, while it aged a million years between entering and exiting the box, it sees that Earth aged only a thousand, or perhaps a billion (it doesn't matter here) between the last image the twin saw while entering the box, and the first image it sees after exiting. Nothing that happens in the box changes the fact that the twin sees Earth age .27 years on the outward journey, and 3.73 years on the inbound journey, for a total of 4 years that Earth has aged while the twin spent 2 years leaving and returned.

 

IF all those extra details are not so easy to ignore, you can just make the turnaround instantaneous and you get the same result.

 

Once you understand how what happens on the long part of the journey matters, *then* you can look into the turnaround without setting yourself up for so much confusion.

 

 

 

What does this mean, though? If you're doing Doppler shift analysis, very little interpretation is needed. The traveling twin actually sees the Earth age 4 years while itself ages 2. If you're trying to figure it out in terms of inertial frames, it might be something like: the difference in simultaneity between Earth and the twin is already inherent in the difference between the outbound and inbound frames of reference. The change in simultaneity does not need any special causal details; simply having the right velocity and distance from the other observer (Earth) is all that matters.

See I use to understand that, but somewhere along the line my understanding of why its not symmetrical broke down. So the rocket twin is traveling near the speed of light, their clock slows down from Earth's perspective meaning Earth should see the rocket twin age more slowly, correct?. BUT, as I said, the rocket twin sees Earth leaving them, so from the rocket twin's point of view, it's actually Earth that's traveling near the speed of light away from them, right? And thus the rocket twin should observe the same time dilation of Earth meaning the clocks should still sync up at the end of the trip, and so that's why I can' figure out where the anti-symmetry comes from. But somehow the turn around or journey towards Earth is what "changes inertial frames" even though you say supposedly that the turnaround event doesn't really matter, which is also why I was asking if whether or not time dilation and length contraction work the same whether you are heading towards or away from something.

Edited April 6, 2014 by SamBridge

[swansont]

Then neglect whatever parts of SR that conflict. For all we know we could already be living in a universe where traveling in a straight line get's you to a previous point.

IOW, the laws of physics are different, which makes the whole scenario moot.

 

Let's say it happens in a hypothetical universe where the inherent curvature of space that causes this looping is too small to be noticed with today's technology, which allows us to say it takes an arbitrarily but still very long distance to make one loop, like 30 billion light years, and everything else about this hypothetical universe is the same as our universe; we still have light as the limit and all the fundamental forces still give us the measurements we currently have in any given local space. There you go. Over light years, space-time can still be approximated as flat because the inherent curvature happens at such a slow rate.

Making the effect small but take a long time will still leave you with the same answer, because the two effects compensate for each other. If the geometry isn't flat, then there is an effect beyond SR at play. There are no loopholes here.

[md65536]

See I use to understand that, but somewhere along the line my understanding of why its not symmetrical broke down. So the rocket twin is traveling near the speed of light, their clock slows down from Earth's perspective meaning Earth should see the rocket twin age more slowly, correct?. BUT, as I said, the rocket twin sees Earth leaving them, so from the rocket twin's point of view, it's actually Earth that's traveling near the speed of light away from them, right? And thus the rocket twin should observe the same time dilation of Earth meaning the clocks should still sync up at the end of the trip, and so that's why I can' figure out where the anti-symmetry comes from. But somehow the turn around or journey towards Earth is what "changes inertial frames" even though you say supposedly that the turnaround event doesn't really matter, which is also why I was asking if whether or not time dilation and length contraction work the same whether you are heading towards or away from something.

The details of the turnaround are irrelevant. You still have to get the twins back to the same place to meaningfully compare clocks, you still have to have different spacetime paths to have a difference in aging.

 

Here are a few more details of the Doppler shift analysis to show the asymmetry: I have gamma=2 and proper time tau=1 for each leg of the traveler's journey.

 

Yes, both observers see the other's clock appearing to tick at a relative rate of .27 while receding, and 3.73 while approaching. The traveler sees Earth's clock tick slowly from 0 to 0.27 years (while itself ages 1 year), and fast from 0.27 to 4 years (while itself ages another year). Meanwhile Earth sees the traveler's clock appear to tick slow until it is seen turning around, ie. slow from 0 to 1 year (while itself happens to age 3.73 years), and then fast from 1 to 2 years (while itself ages another 0.27 years). So Earth sees the traveler's clock appear to tick slow for most of the experiment, while the traveler sees it for half of the experiment. Accounting for the delay of light, what they see matches what is calculated by the Lorentz transformation.

Edited April 6, 2014 by md65536

[SamBridge]

The details of the turnaround are irrelevant. You still have to get the twins back to the same place to meaningfully compare clocks, you still have to have different spacetime paths to have a difference in aging.

 

Here are a few more details of the Doppler shift analysis to show the asymmetry: I have gamma=2 and proper time tau=1 for each leg of the traveler's journey.

 

Yes, both observers see the other's clock appearing to tick at a relative rate of .27 while receding, and 3.73 while approaching. The traveler sees Earth's clock tick slowly from 0 to 0.27 years, and fast from 0.27 to 4 years. Meanwhile Earth sees the traveler's clock appear to tick slow until it is seen turning around, ie. slow from 0 to 1 year, and then fast from 1 to 2 years. So Earth sees the traveler's clock appear to tick slow for most of the experiment, while the traveler sees it for half of the experiment. Accounting for the delay of light, what they see matches what is calculated by the Lorentz transformation.

Ok, so what it seems like you're saying is there is in fact a difference in the effects of the Lorentz transformation with different directions which could have been the most important point that was missing from the discussion if that's what you're actually implying. So when the rocket twin is heading towards Earth, Earth sees the rocket twin's clock tick faster, and the rocket twin doesn't see Earth's clock tick faster by the same amount because...you model the frequency that periodic events take place in time in the same way you model relativistic velocity and Doppler shifts, which are asymmetric? Or in other words, you treat events in time like frequency because the distinction of the changes of an object's position in space propagates at the speed of light, which allows events to blue-shift in one direction and redhift in the other?

Edited April 6, 2014 by SamBridge

[md65536]

Ok, so what it seems like you're saying is there is in fact a difference in the effects of the Lorentz transformation with different directions which could have been the most important point that was missing from the discussion if that's what you're actually implying. So when the rocket twin is heading towards Earth, Earth sees the rocket twin's clock tick faster, and the rocket twin doesn't see Earth's clock tick faster by the same amount because...you model the frequency that periodic events take place in time in the same way you model relativistic velocity and Doppler shifts, which are asymmetric? Or in other words, you treat events in time like frequency because the distinction of the changes of an object's position in space propagates at the speed of light, which allows events to blue-shift in one direction and redhift in the other?

The difference isn't in the Lorentz factor (the actual tick rate) but in the apparent tick rate, which is different due to changing delay of light (corresponding to changing distance between the two). The rate at which a clock ticks is a frequency, and the rate that it appears to tick can be Doppler shifted.

 

See again http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html#doppler -- The signals (ticks) leave the source at an even rate, but are received at a lower or higher rate when receding or approaching respectively.

Edited April 6, 2014 by md65536

[Janus]

Ok, so what it seems like you're saying is there is in fact a difference in the effects of the Lorentz transformation with different directions. So when the rocket twin is heading towards Earth, Earth sees the rocket twin's clock tick faster, and the rocket twin doesn't see Earth's clock tick faster by the same amount because...you model the frequency that periodic events that take place in time in the same way you model relativistic velocity and Doppler shifts, which are asymmetric? Or in other words, you treat events in time like frequency because the distinction of the changes of events propagates at the speed of light?

Okay, I think that there's a bit of confusion going on here. when md65536 says "see", they mean actually see, as in light striking the eyeball. This includes the effects of Doppler shift. The Lorentz Transformation excludes the Doppler effect. The Lorentz transformation is direction independent, but the Doppler effect is direction dependent. When you combine the two, you get the Relativistic Doppler effect, which is what md65536 is referring to.

 

When you analyze things using Relativistic Doppler shift, The asymmetry comes in because the rocket twin sees a change in the Doppler shift the instant he turns around, while the Earth twin has to wait for the light carrying the information that the rocket turned around to reach him. (meanwhile the rocket, having turned around, is following close behind this light.) Put another

 

If you want to analyze things just using the Lorentz transformations, you also have to take into account the effects of length contraction and the Relativity of simultaneity. And the point is that the Earth twin remains in a single inertial frame of reference while the rocket twin does not.

 

To use an analogy, imagine two men walking on a featureless plane. they start at the same point, and walk at the same pace but in slightly different directions. As each man walks, he finds that from his perspective, the other man is falling "behind" ( he has to look behind his shoulder to see him and has to crane his neck more and more as he walks to see the other man.)

 

At this point, there is no absolute way of saying which man is "really" behind the other, as both their views are equally valid.

 

Now one man decides to change his direction so that he will now cross the other man's path. As he turns towards the other man's path, he will notice that Other man's position with respect to him changes. He goes from being behind him to being in ahead of him. As he continues to walk, he notes that the other man's progress in the direction he himself is walking is slower than his own. So the degree that the other man is ahead of him shrinks. However, when he finally crosses the other man's path, the other man is still "ahead" of him, and if he now turns to walk in the same direction, he will be walking from behind.

 

From the other man's view, the first man always is lagging behind him and losing ground both before he change direction and after.

 

Note that it depends on which man makes the change in direction that decides which man ends up behind the other at the end.

 

Substitute "having different velocities" for "walking in different direction", "Having a slower time rate" for "not progressing as fast in the direction I'm walking", "changing velocity or switching inertial frames" for "turned in a different direction" and "Shift in simultaneity upon changing frames" for "Shift in the others position when turning", and you pretty much have Special Relativity's description of the Twin Paradox.

[SamBridge]

Okay, I think that there's a bit of confusion going on here. when md65536 says "see", they mean actually see, as in light striking the eyeball. This includes the effects of Doppler shift. The Lorentz Transformation excludes the Doppler effect. The Lorentz transformation is direction independent, but the Doppler effect is direction dependent. When you combine the two, you get the Relativistic Doppler effect, which is what md65536 is referring to.

 

When you analyze things using Relativistic Doppler shift, The asymmetry comes in because the rocket twin sees a change in the Doppler shift the instant he turns around, while the Earth twin has to wait for the light carrying the information that the rocket turned around to reach him. (meanwhile the rocket, having turned around, is following close behind this light.) Put another

 

If you want to analyze things just using the Lorentz transformations, you also have to take into account the effects of length contraction and the Relativity of simultaneity. And the point is that the Earth twin remains in a single inertial frame of reference while the rocket twin does not.

 

To use an analogy, imagine two men walking on a featureless plane. they start at the same point, and walk at the same pace but in slightly different directions. As each man walks, he finds that from his perspective, the other man is falling "behind" ( he has to look behind his shoulder to see him and has to crane his neck more and more as he walks to see the other man.)

 

At this point, there is no absolute way of saying which man is "really" behind the other, as both their views are equally valid.

 

Now one man decides to change his direction so that he will now cross the other man's path. As he turns towards the other man's path, he will notice that Other man's position with respect to him changes. He goes from being behind him to being in ahead of him. As he continues to walk, he notes that the other man's progress in the direction he himself is walking is slower than his own. So the degree that the other man is ahead of him shrinks. However, when he finally crosses the other man's path, the other man is still "ahead" of him, and if he now turns to walk in the same direction, he will be walking from behind.

 

From the other man's view, the first man always is lagging behind him and losing ground both before he change direction and after.

 

Note that it depends on which man makes the change in direction that decides which man ends up behind the other at the end.

 

Substitute "having different velocities" for "walking in different direction", "Having a slower time rate" for "not progressing as fast in the direction I'm walking", "changing velocity or switching inertial frames" for "turned in a different direction" and "Shift in simultaneity upon changing frames" for "Shift in the others position when turning", and you pretty much have Special Relativity's description of the Twin Paradox.

You're analogies don't help, but I was looking for confirmation that the effects of the Lorentz transformation are direction dependent anyway, and that's the key component that wasn't clear because I asked another physicists if it is direction dependent a year ago, a real physicists who teaches at college, and I thought they said it wasn't, which would have made the scenario symmetric. It makes a lot more sense now.

Edited April 6, 2014 by SamBridge

[Janus]

You're analogies don't help, but I was looking for confirmation that the effects of the Lorentz transformation are direction dependent anyway, and that's the key component that wasn't clear because I asked another physicists if it is direction dependent a year ago, a real physicists who teaches at college, and I thought they said it wasn't, which would have made the scenario symmetric. It makes a lot more sense now.

Time dilation is direction independent

Length contraction is direction independent

Relativity of Simultaneity is direction dependent.

[Schneibster]

+1, Janus. I could never figure out what Sam was asking.

 

Let this be a lesson to you Sam: always make sure you bring out all the context and stop trying to trick people. This isn't law, it's physics. We can't answer your questions if we don't know what they are and your assumptions that we would intrinsically link your questions to the subjects you are talking about are incorrect. You're assuming that we know how Clovis points were made because we know the orbit of Mars.

Edited April 6, 2014 by Schneibster

[uncool]

Time dilation is direction independent

Length contraction is direction independent

Relativity of Simultaneity is direction dependent.

Not quite sure I know what you are saying here; length contraction is direction dependent. In the direction of travel, there is contraction, while perpendicular to the direction of travel, there is no contraction.

[SamBridge]

+1, Janus. I could never figure out what Sam was asking.

 

Let this be a lesson to you Sam: always make sure you bring out all the context and stop trying to trick people. This isn't law, it's physics. We can't answer your questions if we don't know what they are and your assumptions that we would intrinsically link your questions to the subjects you are talking about are incorrect. You're assuming that we know how Clovis points were made because we know the orbit of Mars.

If you read my posts, I said multiple times that I had a concern over the direction these relativistic effects were dependent on.

 

Not quite sure I know what you are saying here; length contraction is direction dependent. In the direction of travel, there is contraction, while perpendicular to the direction of travel, there is no contraction.

What he's saying is that the contraction is different if you go directly towards something vs slightly towards something vs completely away from something which makes sense to create a relativistic Doppler shift with events in time since we only find out about events in time from photons and other forces that propagate at the speed of light which of course travel at a finite speed and have specific properties. It seems to suggest information itself has a limit at the speed of light.

Edited April 7, 2014 by SamBridge

[Schneibster]

 

If you read my posts, I said multiple times that I had a concern over the direction these relativistic effects were dependent on.

 

 

The acceleration that makes you go fast enough to see relativistic effects leads to the rotation that makes them inevitable when you reverse direction.

 

In fact, these are both rotations and most of the difficulty you're having is not understanding rotations in four dimensions, as several folks have told you.

 

You are not really to blame; I think the pedagogical technique of "Lorentz boosts" is somewhat to blame. You may or may not have heard of it, but you have clearly, given your questions, read explanations based on it.

 

So everyone knows, a "Lorentz boost" is a truly impossible phenomenon in which an object changes speed without experiencing acceleration. It is used in certain pedagogical techniques for explaining relativity, and is IMO responsible for a great deal of confusion.

 

It is the choice of the direction of acceleration that is responsible for the asymmetry you see, SamBridge. You, by choosing a direction, have fixed a gauge. Now, your twin, BridgeSam, will always be a different age from you unless he, too, accelerates, and furthermore, in that direction, no other. And stops when you do. Your own example fixes the gauge, which creates the asymmetry.

 

Later: Also a note on more relativity: You can either have the little increments all the way along the journey with the big reversal and then unincrements (heh, I made a neologism) all the way back, or you can disperse the reversal along with the increments and unincrements all along the way. It all integrates to the same answer, either way. That's why it's called "relativity."

 

Personally I prefer to use Poincaire hyperbolic geometry rather than Lorentz algebra. It's more graceful when you turn it into scary integrals.

Edited April 7, 2014 by Schneibster

[SamBridge]

 

The acceleration that makes you go fast enough to see relativistic effects leads to the rotation that makes them inevitable when you reverse direction.

 

In fact, these are both rotations and most of the difficulty you're having is not understanding rotations in four dimensions, as several folks have told you.

I don't think that has anything to do with the problem whatsoever, I've been familiar with the Lorentz transformation and the equivalence principal for several years and there's history of me on this forum explaining 4 dimensional rotation. Not that your notion is completely correct anyway, I've had several different physicists tell me that accelerating via change in velocity through space and a gravitational field are not 100% the same. In one instance, the acceleration happens through space with matter, and in the other instance, the acceleration happens within space-time itself, and effects happening within space-time itself can easily yield different results, such as with the ergo-sphere of rotating black holes and the projected expansion of space from dark energy which are predicted to allow super-luminal travel, a phenomena that could not happen via acceleration with the application of constant force into a massive object. As I said, the problem arose from the fact that 1-2 years ago I asked my college professor about a scenario similar to this where I said "the effects must work the other way in the opposite way in the other direction" and he said "no it doesn't it's the same," and I didn't feel like arguing any more with him (wow, NOT arguing was actually worse, who woulda thought...). So obviously there was some kind of misunderstanding because I have multiple people saying otherwise.

 

 

It is the choice of the direction of acceleration that is responsible for the asymmetry you see, SamBridge.

 

Yes I believe we've established that already..........

Edited April 7, 2014 by SamBridge

[Schneibster]

Yes I believe we've established that already..........

 

Then why blame relativity for it?

 

Sam, I'm sorry you're upset but you're still just denying, and you're still not answering the essential question, "What's wrong?"

Edited April 7, 2014 by Schneibster

[SamBridge]

 

Then why blame relativity for it?

Oh, you don't know? That's just another trick relativity likes to play on you.

[Schneibster]

So, again, what's wrong?

 

You're factually incorrect, BTW, my description of rapidity is straight doctrine.

[SamBridge]

So, again, what's wrong?

 

Other than apparently you, I don't think there is anything wrong, my concerns about the paradox seem resolved.

 

 

You're factually incorrect, BTW, my description of rapidity is straight doctrine.

Ok well, do you have evidence that accelerating through space is the very exact same thing as space curving? I brought up two examples where they diverge. As I said, the link is that they both have acceleration, but one instance is that space-time is accelerating via curvature and the other is matter gaining velocity through space, they are different phenomena. With gravitational fields, it doesn't matter what direction you're approaching something or moving away from something, something entering a higher gravitational field will always appear to have a contracting temporal and spacial metric from an outside point of view, whereas with conventional velocity acceleration, you know direction does matter, the clock can speed up or slow down and in different amounts depending on the direction,

 

Unless of course, I'm misunderstanding your ambiguity in which case I have no idea what you're talking about.

Edited April 7, 2014 by SamBridge

[md65536]

What he's saying is that the contraction is different if you go directly towards something vs slightly towards something vs completely away from something which makes sense to create a relativistic Doppler shift with events in time since we only find out about events in time from photons and other forces that propagate at the speed of light which of course travel at a finite speed and have specific properties.

I fear you may be mixing up the relativistic Doppler effect and the Lorentz transformation. Others are right, time dilation and length contraction are the same whether you're receding or approaching. The Doppler effect is different because of the way things change during the travel time of light. The Doppler effect simply shows how it looks, and how the two observers cannot see the described situation symmetrically.

 

You may be satisfied with that --- the outbound and return trip look different --- but that's not describing things according to the Lorentz transformation, independently of how things look from a particular viewpoint within an inertial frame. Once you accept that the situation is not symmetrical, the details still come down to time dilation, length contraction, and relativity of simultaneity. The relativistic Doppler effect includes those, but also includes delay of light, but it doesn't make sense without those first 3 things.

Edited April 7, 2014 by md65536

[SamBridge]

I fear you may be mixing up the relativistic Doppler effect and the Lorentz transformation. Others are right, time dilation and length contraction are the same whether you're receding or approaching. The Doppler effect is different because of the way things change during the travel time of light. The Doppler effect simply shows how it looks, and how the two observers cannot see the described situation symmetrically.

 

You may be satisfied with that --- the outbound and return trip look different --- but that's not describing things according to the Lorentz transformation, independently of how things look from a particular viewpoint within an inertial frame. Once you accept that the situation is not symmetrical, the details still come down to time dilation, length contraction, and relativity of simultaneity. The relativistic Doppler effect includes those, but also includes delay of light, but it doesn't make sense without those first 3 things.

So if they're the same, why did you say the rocket twin's clock is "ticking faster" in post #57 when they head towards Earth if the light delay alone can account for the asymmetry and not time dilation or length contraction? If time dilation was the same in both directions, why didn't you say the clock was still slowing down? I knew I should have brought that up, it still make sense that observers on Earth would see their clock slow down no matter what, every time I decide not to argue some point it creates confusion later on. But either way, the way manner in which photons are measured relativistic-ally with their delay is the most important factor for resolving the paradox is what it seems. If you were trying to equate the measured time dilation with the Doppler effect, that's where I'm confused now, because time dilation works the same in both directions, but the Doppler effect as you put it, doesn't.

Edited April 7, 2014 by SamBridge

[md65536]

So if they're the same, why did you say the rocket twin's clock is "ticking faster" in post #57 when they head towards Earth if the light delay alone can account for the asymmetry and not time dilation or length contraction? If time dilation was the same in both directions, why didn't you say the clock was still slowing down? I knew I should have brought that up, it still make sense that observers on Earth would see their clock slow down no matter what, every time I decide not to argue some point it creates confusion later on. But either way, the way manner in which photons are measured relativistic-ally with their delay is the most important factor for resolving the paradox is what it seems. If you were trying to equate the measured time dilation with the Doppler effect, that's where I'm confused now, because time dilation works the same in both directions, but the Doppler effect as you put it, doesn't.

Sorry for the confusion. There is a difference between what "is" a clocks tick rate and the rate at which one "sees it appear" to tick. I incorrectly assumed that this was well understood and clearly stated.

 

The relativistic Doppler effect and Lorentz transformation agree with each other. If you want to understand why, maybe look to the math.

 

The most important factors are time dilation, length contraction (and thus relative velocity), and relativity of simultaneity (and thus asymmetrical paths). The difference in appearance and any difference in proper acceleration will be there because of the asymmetry, and they *should* by now make it clear that the observers aren't symmetric, but they do not directly show how the paradox is resolved. Time dilation, length contraction, and relativity of simultaneity resolve the paradox. The "paradox" only arises in the predictions of SR, and you really have to look at those details to resolve it, instead of looking for some answer that is not relativity of time, length, and simultaneity.

[SamBridge]

Sorry for the confusion. There is a difference between what "is" a clocks tick rate and the rate at which one "sees it appear" to tick. I incorrectly assumed that this was well understood and clearly stated.

 

The relativistic Doppler effect and Lorentz transformation agree with each other. If you want to understand why, maybe look to the math.

 

The most important factors are time dilation, length contraction (and thus relative velocity), and relativity of simultaneity (and thus asymmetrical paths). The difference in appearance and any difference in proper acceleration will be there because of the asymmetry, and they *should* by now make it clear that the observers aren't symmetric, but they do not directly show how the paradox is resolved. Time dilation, length contraction, and relativity of simultaneity resolve the paradox. The "paradox" only arises in the predictions of SR, and you really have to look at those details to resolve it, instead of looking for some answer that is not relativity of time, length, and simultaneity.

Right, you obviously can't just do away with the relativistic effects, but what I mean is, the thing that makes the difference between being symmetric and asymmetric with different directions is those things but with the added Doppler effect, right? Because otherwise if you don't factor in the delay with light and the seeming delay in the photons you use to measure events, its the same as the scenario I was talking about before where they both see each other's clocks exactly the same.

Edited April 7, 2014 by SamBridge