Rockinghorse on SR and GR (Split from 'Answer to the Twin Paradox')

[Rockinghorse]

Any objections so far?

This applies only when the curvature of space-time is Euclidian. In real universe however there is no flat geometry anywhere in the universe, therefore this symmetry is always broken. And twins can always synchronize their clocks in real time and they can observe whose clock is slowing down due to uniform motion.

 

More clear example is that GPS satellite can always synchronize its atom clock with Big Ben and therefore we can say that the clock of GPS satellite is slowing in real time. GPS satellite is in uniform motion, but it travels in curved space-time.

[swansont]

This applies only when the curvature of space-time is Euclidian. In real universe however there is no flat geometry anywhere in the universe, therefore this symmetry is always broken. And twins can always synchronize their clocks in real time and they can observe whose clock is slowing down due to uniform motion.

At the moment it's a thought experiment, but in practicality one can investigate under conditions where this symmetry is broken at a level too small to affect the results.

 

More clear example is that GPS satellite can always synchronize its atom clock with Big Ben and therefore we can say that the clock of GPS satellite is slowing in real time. GPS satellite is in uniform motion, but it travels in curved space-time.

The GPS satellite is also undergoing an acceleration; one could concoct a scenario where such motion was in flat spacetime and look only at the kinematic effects. This was done in a fashion similar to the Pound-Rebka experiment but with a rotating system.

[Rockinghorse]

The GPS satellite is also undergoing an acceleration.

According to general relativity GPS satellite is not accelerating, but it is in uniform motion at curved space-time.

 

The broken symmetry in twin paradox is important, because it implies the physical reality of time dilatation. This is especially important question when we start pondering the nature of simultaneity in non-local quantum systems. It turns out that if symmetry is anyway broken, there is no need to object non-local nature of quantum systems. E.g. Lee Smolin has therefore concluded that hidden variables are plausible, because the symmetry of special relativity is by definition broken. I personally do not believe hidden variables, but I do believe in non-local quantum systems and simultaneity due to broken symmetry of relativity.

[swansont]

According to general relativity GPS satellite is not accelerating, but it is in uniform motion at curved space-time.

The context of the OP is special relativity. In SR, the GPS satellite is accelerating.

[Rockinghorse]

The context of the OP is special relativity. In SR, the GPS satellite is accelerating.

The context of special relativity is irrelevant, because it does not refer to the real physical world, but it is refering to purely non-existing imaginary world.

[swansont]

The context of special relativity is irrelevant, because it does not refer to the real physical world, but it is refering to purely non-existing imaginary world.

Welcome to the world of physics problems and gedanken experiments. Frictionless surfaces that support sliding elephants whose mass may be ignored do not exist in the real physical world, either, but it doesn't stop us from investigating the impact of specific physics phenomena.

[Greg H.]

I don't often use frictionless surfaces, but when I do, I support elephants with them.

[Rockinghorse]

Welcome to the world of physics problems and gedanken experiments. Frictionless surfaces that support sliding elephants whose mass mass may be ignored do not exist in the real physical world, either, but it doesn't stop us from investigating the impact of specific physics phenomena.

This has nothing to do with idealized models. The point is that Twins can always communicate in real time and synchronize their clocks, so there is no such thing as relative motion, but time dilation is always physical phenomena and it can always be measured.

 

This is extremely hard thing to understand, because laypersons typically do not understand special and general relativity and they fail to visualize when it is required to comprehend more than three dimensions.

[swansont]

This has nothing to do with idealized models. The point is that Twins can always communicate in real time and synchronize their clocks, so there is no such thing as relative motion, but time dilation is always physical phenomena and it can always be measured.

 

This is extremely hard thing to understand, because laypersons typically do not understand special and general relativity and they fail to visualize when it is required to comprehend more than three dimensions.

"No such thing as relative motion"? Seriously?

[Rockinghorse]

"No such thing as relative motion"? Seriously?

The principle of relativity (the Galilean relativity) requires euclidian spacetime. This is dead serious, because this is the most common misconception of theory of relativity.

 

You can understand this if you think that time is physically real. The time dilatation of GPS satellite is real and it can be measured in real time in all frame of references without twin paradoxes.

 

Of course if it is only looked Newtonian physics and the Einsteinian relativity is ignored, then of course it makes sense to talk on relative motion. But in the context of general relativity there is no such thing as relative motion.

[hypervalent_iodine]

!

Moderator Note

I've split this tangent off into its own thread as they were a little off topic in the other one.

 

 

(Sorry I couldn't think of a better title; I'm open to suggestions if anyone feels it should be changed.)

[swansont]

 

Of course if it is only looked Newtonian physics and the Einsteinian relativity is ignored, then of course it makes sense to talk on relative motion. But in the context of general relativity there is no such thing as relative motion.

 

The context of the discussion was SR, not GR. Relative motion is not limited to Galilean coordinates.

 

The clocks in the twin paradox can't be synchronized. They can only be set to agree to one time. Afterwards, they will disagree.

[Rockinghorse]

The clocks in the twin paradox can't be synchronized. They can only be set to agree to one time. Afterwards, they will disagree.

But in real physical world clocks can always be synchronized. This is hard for people to understand that in real world there is no such thing as twin paradox. Edited December 6, 2013 by Rockinghorse

[swansont]

But in real physical world clocks can always be synchronized. This is hard for people to understand that in real world there is no such thing as twin paradox.

 

It's not generally true in the real world, either, but this misses the whole point (in a seemingly obtuse way) of doing a thought experiment. If I put a really good clock in a van, synchronize it with a reference and drive it somewhere, it will not be synchronized once I start moving. Even along a route that has no elevation change, and is along a N-S axis so there is no Sagnac term to worry about.

[Rockinghorse]

Saying that "the context of discussion was SR", is pretty much the same as saying that "Let's assume that the laws of physics do not apply in our thought experiment."

Edited December 6, 2013 by Rockinghorse

[swansont]

Saying that "the context of discussion was SR", is pretty much the same as saying that "Let's assume that the laws of physics do not apply in our thought experiment."

 

Not at all. You can apply the laws but not have gravity present, or not have a change in gravitational potential.