Any resolutions to FTL paradoxes?

[meberbs]

You were claiming that it only shows time dilation relative to the center of gravity. If you want to say the results are valid regardless of reference frame, you are accepting reciprocity. Choice of reference frame makes no difference in the M-M experiment under special relativity, but if you reject reciprocity, choice of reference frame matters.

This only proves that if the M-M experiment is done at the surface of the Earth, or where ever. The outcome is independent of what frame I observe it from. It says nothing about reciprocity.

I honestly can't tell which statement in my post the word "that" (bolded above) is referring to. (I am assuming the word "this" refers to the M-M experiment, but maybe you meant something else)

Whatever you were trying to say though, your last 2 sentences are contradictory. Being independent of frame leads directly to the Lorentz transforms, which are inherently reciprocal. Your previous attempts to explain how the experimental results don't show reciprocity included marking the rest frame of the local large mass as "special," despite the fact that this is inconsistent with the actual experimental results. You seem to have taken this back, so you now have no remaining arguments supporting your claim that the experiments that demonstrate reciprocity don't do so.

To repeat clearly, non-reciprocity by definition means that there is some special frame defined by some speed and velocity where time dilation is always relative to that frame. Without such a frame, there would be no way for everyone to agree on which clock is faster or slower, so you end up with reciprocity, where 2 observers moving separately each see the other's clock as moving slower. Experiments show that there is no such frame, so reciprocity holds.*

Rather than continuing to assert contradictory things, could you respond to at least one of the following?
-ppnl's suggestion to describe the concrete scenario of the "twin paradox" and how that can be consistent under non-reciprocity (just don't repeat your description from earlier in the thread that I showed to be inconsistent)
-The description of an experiment that could be used to demonstrate reciprocity to you.
-An actually consistent non-reciprocal explanation for existing experiments. (You recently tried and failed at this, so I recommend not this option.)

* There is a special position (the location of the mass for the example of the Schwarzschild solution) so that the gravitational portion of time dilation is non-reciprocal, everyone agrees on how deep they are in the gravity well, but this does not introduce a special frame for velocity.

[WarpTech]

You were claiming that it only shows time dilation relative to the center of gravity. If you want to say the results are valid regardless of reference frame, you are accepting reciprocity. Choice of reference frame makes no difference in the M-M experiment under special relativity, but if you reject reciprocity, choice of reference frame matters.

This only proves that if the M-M experiment is done at the surface of the Earth, or where ever. The outcome is independent of what frame I observe it from. It says nothing about reciprocity.

I honestly can't tell which statement in my post the word "that" (bolded above) is referring to. (I am assuming the word "this" refers to the M-M experiment, but maybe you meant something else)

The word "that" is being used as a conjunction, not a pronoun. Have you ever watched the show "Monk"? You remind me of that guy. (Now I used "that" as a pronoun.) 

You obsess over precision in language and misinterpret anything that doesn't meet your expectations. You do this to everyone and it's very annoying.

I'll get to the rest of this later...

[meberbs]

You were claiming that it only shows time dilation relative to the center of gravity. If you want to say the results are valid regardless of reference frame, you are accepting reciprocity. Choice of reference frame makes no difference in the M-M experiment under special relativity, but if you reject reciprocity, choice of reference frame matters.

This only proves that if the M-M experiment is done at the surface of the Earth, or where ever. The outcome is independent of what frame I observe it from. It says nothing about reciprocity.

I honestly can't tell which statement in my post the word "that" (bolded above) is referring to. (I am assuming the word "this" refers to the M-M experiment, but maybe you meant something else)

The word "that" is being used as a conjunction, not a pronoun. Have you ever watched the show "Monk"? You remind me of that guy. (Now I used "that" as a pronoun.) 

You obsess over precision in language and misinterpret anything that doesn't meet your expectations. You do this to everyone and it's very annoying.

I'll get to the rest of this later...

I had considered that use of "that" as well, but "if the M-M experiment is done at the surface of the Earth" is a condition under which the experiment is performed, not something proven by anything, so I still have no idea what you are trying to say with that sentence. If you consider that sentence important you are going to have to explain it.

I am specifically trying to not misinterpret you which is why I stated exactly what I didn't understand. If you want me to understand what you are saying regardless of the words you write you are going to have to explain to me how to acquire psychic powers. If you are annoyed by me trying to have clear communication and avoid misunderstandings, then I have to ask if you care about clear communication. (You are simultaneously accusing me of misinterpretations and getting annoyed that I request clarification, so I really don't know what you expect.)

[WarpTech]

I had considered that use of "that" as well, but "if the M-M experiment is done at the surface of the Earth" is a condition under which the experiment is performed, not something proven by anything, so I still have no idea what you are trying to say with that sentence. If you consider that sentence important you are going to have to explain it.

Rewrite: "The outcome of the M-M experiment is independent of the frame of reference from which it is observed."

Likewise, what is happening on earth "now" is independent of the frame of reference from which it is observed.

[meberbs]

I had considered that use of "that" as well, but "if the M-M experiment is done at the surface of the Earth" is a condition under which the experiment is performed, not something proven by anything, so I still have no idea what you are trying to say with that sentence. If you consider that sentence important you are going to have to explain it.

Rewrite: "The outcome of the M-M experiment is independent of the frame of reference from which it is observed."

Likewise, what is happening on earth "now" is independent of the frame of reference from which it is observed.

Thank you for the clarification.

Yes, and combined with the fact that the M-M results are constant regardless of time of day, season, etc. the results show that reference frames are all equivalent, which means Lorentz transformations, which means reciprocity. Therefore the experiment demonstrates reciprocity.

[WarpTech]

I had considered that use of "that" as well, but "if the M-M experiment is done at the surface of the Earth" is a condition under which the experiment is performed, not something proven by anything, so I still have no idea what you are trying to say with that sentence. If you consider that sentence important you are going to have to explain it.

Rewrite: "The outcome of the M-M experiment is independent of the frame of reference from which it is observed."

Likewise, what is happening on earth "now" is independent of the frame of reference from which it is observed.

Thank you for the clarification.

Yes, and combined with the fact that the M-M results are constant regardless of time of day, season, etc. the results show that reference frames are all equivalent, which means Lorentz transformations, which means reciprocity. Therefore the experiment demonstrates reciprocity.

False. The M-M experiment can be done at different gravitational potentials, and this will not affect the outcome. Gravitational fields are not reciprocal. Therefore, as I said... The M-M experiment says nothing about reciprocity. Reciprocity has never been tested.

[meberbs]

False. The M-M experiment can be done at different gravitational potentials, and this will not affect the outcome. Gravitational fields are not reciprocal. Therefore, as I said... The M-M experiment says nothing about reciprocity. Reciprocity has never been tested.

See my above post with the difference between reciprocity of velocity while position is non-reciprocal.

The M-M experiment includes rotating the apparatus such that the arms have different orientations with respect to the current velocity relative to the sun/center of galaxy. For the same test with gravitational potential, you would need to change the gravitational potential applied to each arm. If you did so you would find the effective arm length changes and therefore be able to tell the existence of the gravitational potential gradient.

[WarpTech]

False. The M-M experiment can be done at different gravitational potentials, and this will not affect the outcome. Gravitational fields are not reciprocal. Therefore, as I said... The M-M experiment says nothing about reciprocity. Reciprocity has never been tested.

See my above post with the difference between reciprocity of velocity while position is non-reciprocal.

The M-M experiment includes rotating the apparatus such that the arms have different orientations with respect to the current velocity relative to the sun/center of galaxy. For the same test with gravitational potential, you would need to change the gravitational potential applied to each arm. If you did so you would find the effective arm length changes and therefore be able to tell the existence of the gravitational potential gradient.

Sorry, I was specifically thinking of the experiment as it is done on the surface of the earth, where the gravitational acceleration is down, orthogonal to the plane of the experiment. Such as, testing at the top of Mt. Everest vs at the bottom of Death Valley. The outcome will be unaffected.

Reciprocity plays no role in the experiment. The outcome will be the same, regardless if Lorentz transforms are reciprocal or not. Therefore, the experiment doesn't test reciprocity at all.

[meberbs]

False. The M-M experiment can be done at different gravitational potentials, and this will not affect the outcome. Gravitational fields are not reciprocal. Therefore, as I said... The M-M experiment says nothing about reciprocity. Reciprocity has never been tested.

See my above post with the difference between reciprocity of velocity while position is non-reciprocal.

The M-M experiment includes rotating the apparatus such that the arms have different orientations with respect to the current velocity relative to the sun/center of galaxy. For the same test with gravitational potential, you would need to change the gravitational potential applied to each arm. If you did so you would find the effective arm length changes and therefore be able to tell the existence of the gravitational potential gradient.

Sorry, I was specifically thinking of the experiment as it is done on the surface of the earth, where the gravitational acceleration is down, orthogonal to the plane of the experiment. Such as, testing at the top of Mt. Everest vs at the bottom of Death Valley. The outcome will be unaffected.

Yes I understood that, and as I stated, the reason the results do not change is because you are not doing a test where the arms are at different gravitational potentials. Your argument that it does not test reciprocity because it doesn't detect the non-reciprocity of gravitational wells is invalid.

If there was non-reciprocity with velocity a single run of the M-M experiment would show it, the multiple runs to show reciprocity are to make sure you didn't get "lucky" the first time.

Reciprocity plays no role in the experiment. The outcome will be the same, regardless if Lorentz transforms are reciprocal or not. Therefore, the experiment doesn't test reciprocity at all.

The outcome shows that inertial reference frames are equivalent regardless of velocity, this directly leads to the Lorentz transformations, which are inherently reciprocal. It does not matter how many times you claim otherwise, you have no supporting argument, and are just ignoring what the results say.

Now, rather than continuing to repeatedly make the same incorrect claim as if it will become true through repetition, I had another post that you said you would get to later, how about you respond to that one, it would probably be more productive.

[WarpTech]

I will respond to this.

* There is a special position (the location of the mass for the example of the Schwarzschild solution) so that the gravitational portion of time dilation is non-reciprocal, everyone agrees on how deep they are in the gravity well, but this does not introduce a special frame for velocity.

Consider a gravity well. It doesn't have to be a black hole, but whatever. There are twins hovering at the gravitational potential, Φ(R₀) in separate identical ships.

One of the twins receives an impulse which imparts a momentum p, such that it's kinetic energy now equals its gravitational potential energy. In other words, he shuts down his engine and enters orbit around the center of gravity, at the radius R₀. The twin in orbit is now following a geodesic path, so there is no force and no acceleration in this twin's frame of reference. The ship and the twin are in freefall.

This situation continues for who knows how long, and each time the two twins pass each other, they compare clocks. The one that is hovering is ageing faster than the one that is in orbit. There is no reciprocity in this situation. They both agree the one hovering is ageing faster than the one in orbit.

By the typical response to the twin paradox, the one accelerating should be younger. Here, the opposite is true. Why? Becuase it is the relative damping that determines the rate at which clocks tick. Since they are at the same gravitational potential, the field has the same density and at rest, it has the same damping factor. But the one who is in orbit now has a higher damping factor due to the added kinetic energy (velocity) imparted to it by the initial impulse, therefore the twin in orbit ages slower. To be accurate, it's not the velocity that matters but the "Jerk", which is approximated by; frequency squared times the velocity, which results in damping of the quantum oscillators. It's proportionality to velocity is inherent, but it's the Jerk term doing the damping. See Milonni sec. 5.4, last paragraph.

PS: I added Grammarly to my browser. Maybe it will help. 

[meberbs]

I will respond to this.

* There is a special position (the location of the mass for the example of the Schwarzschild solution) so that the gravitational portion of time dilation is non-reciprocal, everyone agrees on how deep they are in the gravity well, but this does not introduce a special frame for velocity.

Consider a gravity well. It doesn't have to be a black hole, but whatever. There are twins hovering at the gravitational potential, Φ(R₀) in separate identical ships.

You know that the Schwarzschild solution applies to non-black holes too right? I never mentioned anything being a black hole.

One of the twins receives an impulse which imparts a momentum p, such that it's kinetic energy now equals its gravitational potential energy. In other words, he shuts down his engine and enters orbit around the center of gravity, at the radius R₀. The twin in orbit is now following a geodesic path, so there is no force and no acceleration in this twin's frame of reference. The ship and the twin are in freefall.

This situation continues for who knows how long, and each time the two twins pass each other, they compare clocks. The one that is hovering is ageing faster than the one that is in orbit. There is no reciprocity in this situation. They both agree the one hovering is ageing faster than the one in orbit.

By the typical response to the twin paradox, the one accelerating should be younger. Here, the opposite is true.

No, the one that is accelerating is the one that is in orbit, and this is still consistent with the standard version of the twin paradox. The stationary twin is stationary because he has 2 forces applied to him, gravity and the rocket keeping him up. The other one can see that he is moving in a circle around the massive object, because his velocity (direction) is changing relative to it. This is not the closed elevator thought experiment, he can look and see the source of the gravitational field. He knows about being in a gravitational field and is accounting for it.

Lets consider another situation that we have actual data for, the GPS constellation. Using purely the time dilation due to gravitational potential, you can calculate that a clock at GPS altitude would run about 0.53 ns/s fast. If you calculate the expected clock slowdown due to special relativity, you get 0.08 ns/s. This totals 0.45 ns/s which matches what you calculate if you just use the full Schwarzschild metric to begin with.

You can try calculating what would be observed from the frame of an object in orbit, or from the frame of a distant observer whose relative velocity with respect to the massive object matches that of the instantaneous velocity of the object in orbit, but such calculations are difficult since they result in time dependent metrics. If you did all the work, you would be able to show that the velocity portion is reciprocal. The easiest way to see this is to take the case where you have a frame where the velocity relative to the massive object is sufficiently close to c that the time dilation from the gravity well is negligible in comparison. In this case, you simply recover special relativity with all of its symmetry.

PS: I added Grammarly to my browser. Maybe it will help. 

You might want to check if it is working, my browser pointed out a typo in your post ("becuase") I would be making such typos constantly if my browser didn't have auto spell check, and I still miss some. Also if it doesn't get confused by you using the technical definition of the word jerk I will be impressed.

[dustinthewind]

Here is an actual experiment with relativity that shows it is non symmetric.  https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment

Considering the Hafele–Keating experiment in a frame of reference at rest with respect to the center of the earth, a clock aboard the plane moving eastward, in the direction of the Earth's rotation, had a greater velocity (resulting in a relative time loss) than one that remained on the ground, while a clock aboard the plane moving westward, against the Earth's rotation, had a lower velocity than one on the ground.

2 aircraft flying in opposite directions on earth.  Aircraft one, flying in the direction of the rotation of earth has its clock slowed the greatest.  The clock on the ground is not as slow as aircraft 1 but is slower than aircraft 2.  Aircraft 2's clock is the fastest as it moves the counter the earths rotation.  Now take this path and reduce it to an instant in time with the two aircraft passing each other.  One aircraft clock is running fast w.r.t. one plane while the other plane should see the others as slow.  They quickly land and measure the smaller change in time via the shorter trip. 

This appears to me to be non-symmetric.  Oddly with respect to something that doesn't rotate and seems to be with respect to the earth center if this article is correct.

[WarpTech]

I will respond to this.

* There is a special position (the location of the mass for the example of the Schwarzschild solution) so that the gravitational portion of time dilation is non-reciprocal, everyone agrees on how deep they are in the gravity well, but this does not introduce a special frame for velocity.

Consider a gravity well. It doesn't have to be a black hole, but whatever. There are twins hovering at the gravitational potential, Φ(R₀) in separate identical ships.

You know that the Schwarzschild solution applies to non-black holes too right? I never mentioned anything being a black hole.

Obsessing over minutia again? It's insulting.

One of the twins receives an impulse which imparts a momentum p, such that its kinetic energy now equals its gravitational potential energy. In other words, he shuts down his engine and enters orbit around the center of gravity, at the radius R₀. The twin in orbit is now following a geodesic path, so there is no force and no acceleration in this twin's frame of reference. The ship and the twin are in freefall.

This situation continues for who knows how long, and each time the two twins pass each other, they compare clocks. The one that is hovering is ageing faster than the one that is in orbit. There is no reciprocity in this situation. They both agree the one hovering is ageing faster than the one in orbit.

By the typical response to the twin paradox, the one accelerating should be younger. Here, the opposite is true.

No, the one that is accelerating is the one that is in orbit, and this is still consistent with the standard version of the twin paradox. The stationary twin is stationary because he has 2 forces applied to him, gravity and the rocket keeping him up. The other one can see that he is moving in a circle around the massive object, because his velocity (direction) is changing relative to it. This is not the closed elevator thought experiment, he can look and see the source of the gravitational field. He knows about being in a gravitational field and is accounting for it.

You have a strange notion of how the EEP works!  The twin in orbit is in free fall. By definition he is following a geodesic through space-time. There are no forces, no accelerations acting on him. He is in an inertial reference frame and he doesn’t need to close his eyes for this to be true. This is what the Math says under GR. This is where moving in a circle is equivalent to moving in a straight line in curved space-time.

"In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it."

The twin in orbit was only accelerating for a tiny instant of time when the initial impulse gave his ship the kinetic energy and momentum to go into orbit at the same altitude as his brother. They don’t need to take the gravitational potential into account because they are both at the same potential. The only thing causing their clocks to disagree is the additional kinetic energy that was imparted to the orbiting twin, and it is inherently not reciprocal. It depends on the history. It was the orbiting twin that received the impulse and was raised to a higher energy state. Therefore his clock runs slower than his hovering twin. The twin that is hovering has been in a non-inertial reference frame the whole time, and his clock is running faster. The act of "turning around" that is usually credited as the solution to the twin paradox is inapplicable, and yet we have twins ageing at different rates in a steady state.

Lets consider another situation ...

Let's not. It doesn't help to complicate things. See the post above regarding the Hafele–Keating experiment. It supports the non-reciprocity of time dilation, though I don't think it's definitive. It would be better if they were orbiting clocks rather than aeroplanes. Then the two clocks flying in each direction would be in free fall.

[meberbs]

Consider a gravity well. It doesn't have to be a black hole, but whatever. There are twins hovering at the gravitational potential, Φ(R₀) in separate identical ships.

You know that the Schwarzschild solution applies to non-black holes too right? I never mentioned anything being a black hole.

Obsessing over minutia again? It's insulting.

You brought up black holes for some reason, either you didn't know that the Schwarzschild solution covers planets and stars too, and I was providing information to make sure you knew what I was talking about, or you did know (and apparently thought I didn't) and I was letting you know that I was on the same page. So where exactly is the insult?

You have a strange notion of how the EEP works!  The twin in orbit is in free fall. By definition he is following a geodesic through space-time. There are no forces, no accelerations acting on him. He is in an inertial reference frame and he doesn’t need to close his eyes for this to be true. This is what the Math says under GR. This is where moving in a circle is equivalent to moving in a straight line in curved space-time.

I thought that your theory included interpreting the cause of GR effects as damping rather than space time curvature (And I do think that a non-curvature based interpretation of GR may aide creating a theory of quantum gravity) This is somewhat irrelevant pedantry though, so I'll try to restate the important point that I wanted to communicate:

The way gravity is treated in GR makes it easy to miscommunicate meaning when talking about words like acceleration. In the standard "twin paradox" it is the one that accelerates that ages slower. In the situation that you are describing, it seems clear that the definition of "one that accelerates" is "one with a non-constant velocity vector relative to a distant observer who is moving at constant velocity." The constantly changing velocity vector is the equivalent of turning around in the standard twin paradox, but the situation as described doesn't have any "non-accelerating" portions to clearly show the reciprocity.

The time dilation is purely related to the velocity, and the situation is replicated in special relativity by one person at rest, and another who flies in a big circle, but with no gravity present. It seems that you may be trying to apply the equivalence principle inside out, which is easy to do by accident. We agree on the answer though, and nothing about the situation you have described invalidates that relativity works and includes reciprocity.

Let's not. It doesn't help to complicate things.

I tried to give an example to show how general relativity has both gravitation potential and velocity based effects. if you think that complicates things, why don't we simplify things and you try to provide a consistent non-reciprocal explanation of what happens when you act out the twin paradox.

See the post above regarding the Hafele–Keating experiment. It supports the non-reciprocity of time dilation, though I don't think it's definitive. It would be better if they were orbiting clocks rather than aeroplanes. Then the two clocks flying in each direction would be in free fall.

I think I may understand the problem with your line of reasoning now. It seems like you think things are either reciprocal or non-reciprocal. If things were purely non-reciprocal then everyone would agree on the rate of time passing on everyone else's clocks. So if A thinks B's clock is at half speed, then B thinks that A's clock is at double speed. You keep taking any evidence that differs from perfect symmetry and jumping to this case.

The problem is that things don't have to be perfectly symmetric to include some reciprocity. A can think B's clock runs at half speed, while B thinks that A's clock runs at 2/3rds speed. (relative to each other, not to some distant observer)

The FTL resulting in time travel still happens in this scenario, and for the examples of paradox situations in this thread, gravitational wells involved produce very little time dilation compared to the velocities, to the extent they shouldn't have significant effect, maybe 50% vs 49% if that.

[RSE]

Meberbs, I would like to “show my work” in my analysis.

Your work is irrelevant, because as I already stated, you are not discussing a paradox causing situation, and I never stated that anything was wrong with your answers. I will use a couple things you mention to clarify some misunderstandings you seem to have.

2. At earth time “t prime”,

Please call this t2. When discussing special relativity, the prime notation is used for indicating a different reference frame, not time coordinates in the same reference frame. This is just for clarity in communication.

Under Relativity, where did this data come from?

4.  From Sirius's reference frame, under Relativity, it could have only come from the future.

No. It came from a spacelike separated point that is undefined as being the past or future. Using the Earth's reference frame it came from 0.7 years in the past.

5. Here is where it gets tricky. Where is the future starting point? From Sirius's reference frame, it is 8 years in the future from the point where the ship, bearing the data, arrived.

No, Sirius (for purposes relevant to this example) is moving at the same speed as Earth, so Sirius's frame and the Earth frame are the same frame as far as relativity is concerned. You can define a frame with the same speed and a new origin at the ship's arrival at Sirius, which would just be a linear transformation of t' = t-0.7 years, x' = x - 8 light years. No special relativity involved.
The rest of your description is just you agreeing with this until you say:

Note, 8 years in the “future”, from Sirius's reference frame, coincides with the departure of the ship, minus the transit time, in earth's reference frame.

Which doesn't make sense, because as you just explained, the ship came from Sirius's past, not future.

7. On the return to earth, everything applies the same way. The ship leaves Sirius, (with the Sirius's data transcripts) and returns to earth. It takes .7 years transit time. The ship is now perceived from earth's reference frame as returning from “the future”, coming backwards in time,

No, that is not what relativity says. The ship is still starting from a frame with the same velocity, so it is still travelling forward in time just like it was during the journey out. To see travelling backwards in time, you would have to look at it from a frame that is travelling at some speed relative to the Earth.

Meberbs, I went to all this detail to try to determine exactly where the “point of asymmetry” between the two viewpoints arises. Thank you for your time.

The "point of asymmetry" as you call it arises from the problems that occur when you look at things from the perspective of some frame with a different relative velocity. As long as you don't consider a different rest frame, you are not actually applying relativity. Look at the examples I discussed early in this thread for how to do that.

“The purpose of answers is to help us refine our questions.”

Meberbs, according to what you are saying, time at various FTL velocities (should they exist), causes a jump backwards in time, from almost the entire duration of the FTL trip, (at velocity just above c), and steadily dropping as the FTL velocity approaches infinity (instantaneous).

This strikes me as a strange discontinuity. (Graphing it also looks strange.)

Granted that for the purpose of Relativity there needs to be a negative sign, why must it be assigned to the time component? Could it not be assigned to the mass component? At this stage, with no way to experiment, why is there a preference?

[meberbs]

Meberbs, according to what you are saying, time at various FTL velocities (should they exist), causes a jump backwards in time, from almost the entire duration of the FTL trip, (at velocity just above c), and steadily dropping as the FTL velocity approaches infinity (instantaneous).

That doesn't sound like anything I have said.

What I said is that for an FTL jump that results in forward in time motion in the Earth frame will result in backwards in time motion in a reference frame moving sufficiently fast with respect to Earth. The closer to instantaneous the jump is from Earth's perspective, the more backwards in time it will appear to be from the same alternate reference frame. Similarly, the faster the FTL jump, the slower the other frame can be to see the jump as backwards in time motion.

It seems like you are making an assumption that "simultaneous" is something that doesn't change between reference frames. Observers moving at different velocities relative to each other do not ever agree on whether 2 events are simultaneous (unless the events are also co-located, but for the purpose of special relativity, that would make them the same event.).

Granted that for the purpose of Relativity there needs to be a negative sign, why must it be assigned to the time component? Could it not be assigned to the mass component? At this stage, with no way to experiment, why is there a preference?

Component of what with a negative sign? There is a negative sign attached to time in the metric, but there is no mass component in the metric to shift it to.

[WarpTech]

You have a strange notion of how the EEP works!  The twin in orbit is in free fall. By definition, he is following a geodesic through space-time. There are no forces, no accelerations acting on him. He is in an inertial reference frame and he doesn’t need to close his eyes for this to be true. This is what the Math says under GR. This is where moving in a circle is equivalent to moving in a straight line in curved space-time.

I thought that your theory included interpreting the cause of GR effects as damping rather than space-time curvature (And I do think that a non-curvature based interpretation of GR may aide creating a theory of quantum gravity)

Interpreting is the keyword... Remember, any quantum gravity solution must be able to be interpreted as space-time curvature. The two interpretations are interchangeable.

This is somewhat irrelevant pedantry though, so I'll try to restate the important point that I wanted to communicate:

The way gravity is treated in GR makes it easy to miscommunicate meaning when talking about words like acceleration. In the standard "twin paradox" it is the one that accelerates that ages slower. In the situation that you are describing, it seems clear that the definition of "one that accelerates" is "one with a non-constant velocity vector relative to a distant observer who is moving at constant velocity." The constantly changing velocity vector is the equivalent of turning around in the standard twin paradox, but the situation as described doesn't have any "non-accelerating" portions to clearly show the reciprocity.

No, you're overthinking it. It is the one that has a higher energy content whose clock runs slower. Whatever frame you choose, the twins started in the same frame, at the same energy and "one" was given additional kinetic energy making his clock run slow. There is no reciprocity because the history of the situation is apparent and their clocks confirm it.

The time dilation is purely related to the velocity, and the situation is replicated in special relativity by one person at rest, and another who flies in a big circle but with no gravity present. It seems that you may be trying to apply the equivalence principle inside out, which is easy to do by accident. We agree on the answer though, and nothing about the situation you have described invalidates that relativity works and includes reciprocity.

I'm glad we agree. However, the situation is not the same as what you describe. Flying in a big circle requires forces acting on the ship/twin for the whole trip. This is equivalent to the twin hovering in my experiment. In your situation, the other twin at rest would age faster. In the situation which I described we have the opposite. It is the twin in the inertial frame in free fall that ages slower and the one accelerating (forces present) that ages faster.

See the attached image below. This is the crux of the issue I have with reciprocity.

The image shows in red, two clocks separated by some distance, (x2 - x1).
The clocks are at rest relative to each other and were synchronized in the past.
As long as nothing changes, (t = t' = Now) at both locations.
At any moment, an impulse is imparted to the clock at x2, causing it to move away from x1 at a constant velocity. These are the blue lines.

From your previous statements, you believe that after this impulse the situation is reciprocal. I say reciprocity in this situation is an illusion. It is not reciprocal because only the clock at x2 received an impulse.
After receiving the impulse, in the rest frame of the clock that started at x2. Looking behind it, it's x' axis (blue) which represents "Now" is directed into the past of the clock at x1. The longer the distance (x2 - x1), the farther into the past the axis extends. I say this is an illusion because the clock (and ruler) which started at x2 has been changed by the impulse it received. The clock at x1 didn't change and the impulse didn't suddenly give us access to the past, if and when FTL is possible.

 

[meberbs]

No, you're overthinking it. It is the one that has a higher energy content whose clock runs slower. Whatever frame you choose, the twins started in the same frame, at the same energy and "one" was given additional kinetic energy making his clock run slow. There is no reciprocity because the history of the situation is apparent and their clocks confirm it.

Except energy is frame dependent. In a frame based on a distant observer that is moving at the same instantaneous velocity as the orbiting twin, the orbiting twin is the one with less (0) kinetic energy. Your claim of "no reciprocity" ignores the existence of this frame.

The time dilation is purely related to the velocity, and the situation is replicated in special relativity by one person at rest, and another who flies in a big circle but with no gravity present. It seems that you may be trying to apply the equivalence principle inside out, which is easy to do by accident. We agree on the answer though, and nothing about the situation you have described invalidates that relativity works and includes reciprocity.

I'm glad we agree. However, the situation is not the same as what you describe. Flying in a big circle requires forces acting on the ship/twin for the whole trip. This is equivalent to the twin hovering in my experiment. In your situation, the other twin at rest would age faster. In the situation which I described we have the opposite. It is the twin in the inertial frame in free fall that ages slower and the one accelerating (forces present) that ages faster.

In both situations it is the twin that is moving in a circle as seen by a distant observer that ages slower. The situations are mathematically equivalent, yet you are insisting on defining your terms in such a way as to get an apparent contradiction.

See the attached image below. This is the crux of the issue I have with reciprocity.

The image shows in red, two clocks separated by some distance, (x2 - x1).
The clocks are at rest relative to each other and were synchronized in the past.
As long as nothing changes, (t = t' = Now) at both locations.

All of these statements are only true in one, ultimately arbitrary frame.

At any moment, an impulse is imparted to the clock at x2, causing it to move away from x1 at a constant velocity. These are the blue lines.

From your previous statements, you believe that after this impulse the situation is reciprocal. I say reciprocity in this situation is an illusion. It is not reciprocal because only the clock at x2 received an impulse.

And how would an observer coming in later know that that was the case and not that they had both started moving and the first clock had been slowed to a stop? Or if the observer who looks later happens to be moving with the same speed as the second clock, it is the first clock that they would see as moving and slowed.

After receiving the impulse, in the rest frame of the clock that started at x2. Looking behind it, it's x' axis (blue) which represents "Now" is directed into the past of the clock at x1. The longer the distance (x2 - x1), the farther into the past the axis extends. I say this is an illusion because the clock (and ruler) which started at x2 has been changed by the impulse it received. The clock at x1 didn't change and the impulse didn't suddenly give us access to the past, if and when FTL is possible.

Except there is nothing different between the 2 clocks, everything is exactly identical, and all of your conclusions are based on picking a preferred frame, but if you pick a preferred frame, you will no longer see the speed of light as constant in all frames.

[WarpTech]

Except energy is frame dependent.

All energy gravitates. In that sense, it cannot be frame dependent when in a gravitational field because one clock/twin has the extra kinetic energy imparted to it and the other does not. Their gravitational attraction to the center of gravity will be different. Therefore, KE is not frame dependent when considering the gravitational effects of that energy. Time dilation is a gravitational effect based on the absolute energy content wrt the vacuum ZP energy, i.e., the gravitational field.

...In the situation which I described we have the opposite. It is the twin in the inertial frame in free fall that ages slower and the one accelerating (forces present) that ages faster.

In both situations, it is the twin that is moving in a circle as seen by a distant observer that ages slower. The situations are mathematically equivalent, yet you are insisting on defining your terms in such a way as to get an apparent contradiction.

See the attached image below. This is the crux of the issue I have with reciprocity.

The image shows in red, two clocks separated by some distance, (x2 - x1).
The clocks are at rest relative to each other and were synchronized in the past.
As long as nothing changes, (t = t' = Now) at both locations.

All of these statements are only true in one, ultimately arbitrary frame.

How can there be more than one true "now"? One is true, the rest are illusions.

At any moment, an impulse is imparted to the clock at x2, causing it to move away from x1 at a constant velocity. These are the blue lines.

From your previous statements, you believe that after this impulse the situation is reciprocal. I say reciprocity in this situation is an illusion. It is not reciprocal because only the clock at x2 received an impulse.

And how would an observer coming in later know that that was the case and not that they had both started moving and the first clock had been slowed to a stop? Or if the observer who looks later happens to be moving with the same speed as the second clock, it is the first clock that they would see as moving and slowed.

After receiving the impulse, in the rest frame of the clock that started at x2. Looking behind it, it's x' axis (blue) which represents "Now" is directed into the past of the clock at x1. The longer the distance (x2 - x1), the farther into the past the axis extends. I say this is an illusion because the clock (and ruler) which started at x2 has been changed by the impulse it received. The clock at x1 didn't change and the impulse didn't suddenly give us access to the past, if and when FTL is possible.

Except there is nothing different between the 2 clocks, everything is exactly identical, and all of your conclusions are based on picking a preferred frame,...

No, from a QM perspective, the clock that received the impulse was Doppler shifted into a higher energy ZP spectrum, i.e, a higher energy state wrt the vacuum ZP field. They are not exactly identical anymore at the QM scale or gravitationally. An observer coming in would not know this so an experiment would have to be conducted carefully, as was the Hafele-Keating experiment. The Lorentz transformations make the assumption that they are identical, it's built into the derivation but nobody has tested it!

but if you pick a preferred frame, you will no longer see the speed of light as constant in all frames.

This is a false assumption. As in the PV Model, everyone sees the same value c "locally". Time dilation and length contraction at higher energy states relative to the vacuum, assure that the rulers and clocks are scaled to always give "c" as the local value. It's NOT an aether.

[meberbs]

Except energy is frame dependent.

All energy gravitates. In that sense, it cannot be frame dependent when in a gravitational field because one clock/twin has the extra kinetic energy imparted to it and the other does not. Their gravitational attraction to the center of gravity will be different. Therefore, KE is not frame dependent when considering the gravitational effects of that energy. Time dilation is a gravitational effect based on the absolute energy content wrt the vacuum ZP energy, i.e., the gravitational field.

Moving objects have more energy, and therefore gravitate more, but the gravitational field is not simply a moving Schwarzchild solution with increased mass. Because of this, there is no contradiction between kinetic energy being different in different frames, and in fact it would not work if kinetic energy did not vary between frames. You still are simply ignoring the fact that general relativity has no problem looking at things from the perspective of a distant observer that is moving relative to the mass. This frame is still equally valid.

How can there be more than one true "now"? One is true, the rest are illusions.

I am not sure how you can ask that question. It is answered in every single book that discusses introductory relativity. The short version is that the concept of "one true now" does not make any sense given that spacelike separated events by definition cannot be put into a chronological order that everyone agrees on.

Except there is nothing different between the 2 clocks, everything is exactly identical, and all of your conclusions are based on picking a preferred frame,...

No, from a QM perspective, the clock that received the impulse was Doppler shifted into a higher energy ZP spectrum, i.e, a higher energy state wrt the vacuum ZP field. They are not exactly identical anymore at the QM scale or gravitationally.

What you are saying is that the quantum vacuum defines a universal rest frame, so as I said, you are just defining a preferred frame. This means that you should be able to measure your velocity relative to it. How would you do so? (And no, Hafele-Keating does not show a difference, you are going to state exactly what you are going to measure, and how 2 observers, one that comes in and is moving at the same velocity as clock 1 and one moving the same as clock 2, would agree on which clock was accelerated.)

An observer coming in would not know this so an experiment would have to be conducted carefully, as was the Hafele-Keating experiment. The Lorentz transformations make the assumption that they are identical, it's built into the derivation but nobody has tested it!

Except you just named a test of it. That experiment showed that relativity with its built in reciprocity makes the correct predictions. The M-M experiment clearly demonstrates that the speed of light is invariant between reference frames demonstrating that there is no difference between frames based on their velocity, which requires reciprocity to work.

You continue to claim that this has not been tested when you have been given evidence, and every counterargument you have made I have shown to be either contradictory or irrelevant. You continuing to claim this is simply ignoring everything I have written so far.

but if you pick a preferred frame, you will no longer see the speed of light as constant in all frames.

This is a false assumption. As in the PV Model, everyone sees the same value c "locally". Time dilation and length contraction at higher energy states relative to the vacuum, assure that the rulers and clocks are scaled to always give "c" as the local value. It's NOT an aether.

It is a preferred frame, you are claiming that the velocity measured relative to the vacuum matters. If that is true, then there must be a measurable difference based on this. This would be counter to the most fundamental principles that relativity is derived from, so you would simply not get the same results.