Any resolutions to FTL paradoxes?

[WarpTech]

I do not know of any reason why 2 clocks at rest and separated by a distance (x2 - x1) can't be synchronized by exchanging light pulses.

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.)

No. What "I" am saying is that the EM ZPF defines a zero baseline for the energy content of matter. Matter is in equilibrium with the vacuum it's immersed in. A different zero-point energy in the EM field results in a different equilibrium energy of the matter. As I said previously, you cannot measure velocity relative to the ZPF. The spectrum will Doppler shift and the matter will respond to this increased equilibrium energy. Its length will contract and time will dilate, such that the vacuum will look the same, regardless of the energy content of the object.

...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.

Again, the M-M experiment says nothing about reciprocity. You have not proven to me that it does. It only demonstrates that length contraction prevents it from detecting any change in the speed of light.

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.

No, I'm not saying that, because I know you cannot measure velocity relative to the vacuum. You can, however, measure the energy state by comparing clocks and rulers.

[meberbs]

I do not know of any reason why 2 clocks at rest and separated by a distance (x2 - x1) can't be synchronized by exchanging light pulses.

The problem is the word "at rest" They can be at rest relative to each other, and synchronized in that frame, but in literally every other frame, they will not be synchronized.

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.)

No. What "I" am saying is that the EM ZPF defines a zero baseline for the energy content of matter. Matter is in equilibrium with the vacuum it's immersed in. A different zero-point energy in the EM field results in a different equilibrium energy of the matter. As I said previously, you cannot measure velocity relative to the ZPF. The spectrum will Doppler shift and the matter will respond to this increased equilibrium energy. Its length will contract and time will dilate, such that the vacuum will look the same, regardless of the energy content of the object.

If you cannot measure your velocity relative to it, then your velocity relative to it cannot determine anything about the behavior of objects, otherwise, you could use that effect to determine your velocity relative to it.

Since you cannot measure your velocity relative to it, it can't be a preferred frame, and since it is not a preferred frame, you must have the same laws of physics regardless of your velocity, which is logically equivalent to reciprocity.

...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.

Again, the M-M experiment says nothing about reciprocity. You have not proven to me that it does. It only demonstrates that length contraction prevents it from detecting any change in the speed of light.

No, you still don't understand the M-M experiment. It does not test length contraction, it shows that there is no frame with a special velocity, where the laws of physics change depending on your speed relative to that frame.

The consequence of this is reciprocity. I have already outlined this proof and I am getting tired of of you claiming that I haven't.

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.

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.

No, I'm not saying that, because I know you cannot measure velocity relative to the vacuum. You can, however, measure the energy state by comparing clocks and rulers.

But you keep claiming that reciprocity is wrong based on claiming that one moving object's velocity relative to the vacuum is different than another's.

You still haven't answered how to tell which clock is the one that accelerated, and some of your comments seem to be backtracking and agreeing with the point that you cannot tell which one is moving relative to the vacuum, but that is the definition of reciprocity being true.

[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.

What is non-symmetric here isn't the speed of light.  Both planes would record a light beam as moving at c but with various Doppler shifts so that isn't the issue (except for maybe the specifics of the light changing vacuum frames leading to Doppler shifts).  What is non-symmetric is the passage of time as in the Minkowski_diagram.  https://en.wikipedia.org/wiki/Minkowski_diagram  where one persons time space axis tilts while the others does not (non-symmetric).  Here we have the very non-symmetric effect which leads to one twin more rapidly ageing while the other doesn't. 

Knowing what your moving with respect to is detectable by the passage of time not the speed of light.  This is exactly what they detected.  This is why I stated, "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."

It is also one of the reasons I have speculated that the vacuum might be considered to flow into a gravity well such that the vacuum reaches the speed of light at an event horizon where time stops and light can't escape.  Faster your moving with respect to this speculated vacuum the slower time appears to pass.  There might also be something to this imaginary time as another dimension where objects become timeless or some transition between that slows time.  Not really sure about the last idea. 

Frame dragging is another aspect I suspect to be an example of a flow in vacuum.

[meberbs]

What is non-symmetric here isn't the speed of light.  Both planes would record a light beam as moving at c but with various Doppler shifts so that isn't the issue (except for maybe the specifics of the light changing vacuum frames leading to Doppler shifts).  What is non-symmetric is the passage of time as in the Minkowski_diagram.  https://en.wikipedia.org/wiki/Minkowski_diagram  where one persons time space axis tilts while the others does not (non-symmetric).  Here we have the very non-symmetric effect which leads to one twin more rapidly ageing while the other doesn't. 

Knowing what your moving with respect to is detectable by the passage of time not the speed of light.  This is exactly what they detected.  This is why I stated, "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."

The passage of time demonstrated in a Minkowski diagram is symmetric though. The assymmetry in this experiment purely comes from the fact that all of the clocks (including the one on the ground due to earth's rotation) have a constantly changing velocity vector. This causes (for the special relativistic portion) the "bent" spatial axis, and the direction of the bend of the time axis to be constantly changing. This changing of the spatial axes is what produces the measured effects and it is possible to directly measure they are changing. This is similar to how "fictitious" forces need to be accounted for in classical physics when using a rotating reference frame. You mentioned this with the changing frames leading to Doppler shifts.

The calculations being done next to the non-rotating earth center frame are just for convenience. You could do all of the same calculations from the sun's inertial frame where all of the clocks are moving in a spiral, and you get consistent results showing that there is no need to consider the earth frame as special.

[WarpTech]

I'll get back to what we were discussing later. Right now, let's consider Frame Dragging.

The Hafele–Keating experiment,
https://en.wikipedia.org/wiki/Hafele–Keating_experiment

has both Kinematic and Gravitational time dilation at work. The Kinematic time dilation stands out because;

"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]"

There is an alternate interpretation of this. If there were a gravitomagnetic potential, A_G has units of velocity, m/s, it is essentially the cause of frame dragging. One could draw the conclusion that the field (space-time) rotates in the direction of the earth's rotation. Flying eastward, the clock is moving faster than the field, A_G-v < 0. Flying westward, the clock is moving slower than the field, A_G - v > 0. This would imply that there is a preferred reference frame that is "at rest" relative to the rotating field A_G. They used the center of the earth as the reference, which would also be the center of the rotation, A_G => 0 as the flux through the loop, Φ_G => 0 at the singularity r=0.

The 3 clocks run at different rates. They are not reciprocal. The field A_G provides a background velocity field relative to which they are moving.

Possible or no?

[meberbs]

I'll get back to what we were discussing later. Right now, let's consider Frame Dragging.

Please do get back to it, because frame dragging seems to be an additional complication that you are bringing up to try and avoid the fact that you can't consistently explain simple situations in a non-reciprocal way.

The Hafele–Keating experiment,
...

First frame dragging typically refers to rotational frame dragging from a spinning massive object. Linear frame dragging is also a thing and is a consequence of the fact that for consistency, gravity must look different from a moving frame, since gravitational influences only propagate at the speed of light, and the additional kinetic energy the object has in a frame moving relative to it increases its relativistic mass.

Rotational frame dragging is a negligible effect in the Hafele-Keating experiment.

There is an alternate interpretation of this. If there were a gravitomagnetic potential, A_G has units of velocity, m/s, it is essentially the cause of frame dragging. One could draw the conclusion that the field (space-time) rotates in the direction of the earth's rotation. Flying eastward, the clock is moving faster than the field, A_G-v < 0. Flying westward, the clock is moving slower than the field, A_G - v > 0. This would imply that there is a preferred reference frame that is "at rest" relative to the rotating field A_G. They used the center of the earth as the reference, which would also be the center of the rotation, A_G => 0 as the flux through the loop, Φ_G => 0 at the singularity r=0.

To reiterate, frame dragging is a measured effect, but much smaller than the results of this experiment could measure, so your explanation already fails. Even more so, your conclusion breaks down when you instead look at things from the perspective of the sun's inertial frame. This is a complicated situation to do that for, which is why a simpler example would be better, but you cannot claim non-reciprocity just because there is a frame where the calculations are easier.

The 3 clocks run at different rates. They are not reciprocal. The field A_G provides a background velocity field relative to which they are moving.

Possible or no?

Referring to the field of the object to define a special frame is like referring to the rest frame of a charged object as special because you don't have to calculate the magnetic field. The fact is that physics has forces that are a function of the relative velocity between 2 objects, but the underlying physics does not define any kind of "absolute" velocity.

No, they are reciprocal (at least for the portion that doesn't depend on depth in a gravitational well). Asymmetries arise from the fact that they are accelerated differently as their directions change relative to each other, but the same math that correctly calculates how much time delta changes between them also requires that changing your mind halfway through the trip on what path you are taking, or by moving the "stationary" clock would change the results. A theory that claims that there is an absolute measure at all times of which clock is slower or faster would simply produce different results.

Rather than sort this out for a complicated experiment with multiple overlapping effects, wouldn't it be easier to go back to the simple example we were talking about with separated clocks?

[dustinthewind]

I will refer to this paper here http://www.cellularuniverse.org/R2SpeedParadox.pdf (How DSSU Relativity Resolves the Speed Paradox  Measurable Absolute Motion Resolves a Paradox in Einstein’s Special Relativity by Conrad Ranzan)

It seems to also predict a variable non-local speed of light will locally making it measurably invariable.  I think it mentions the effect of the vacuum on the local ruler, the twin paradox and asymmetry in time travel.   

Below they touch on the vacuum flow being related to gravity ( http://cellularuniverse.org/Th6EnergyProcess-Part1_Ranzan.pdf )

The DSSU gravitational field is fundamentally
different. Instead of a force field it is a dynamic aether
“field” —an active region which can be divided into two
functional components.
The first is the aether flow field. Surrounding any
gravitating body there is a bulk flow of aether —a
continuous streaming into the central mass body. The
speed of the aether flow increases with proximity to the
surface of the central body. 

A book with a short explanation of DSSU or Dynamic Steady State Universe
Google books Astronomy, Cosmology and Fundamental Physics: Proceedings of the ESO/CERN ...

I am not endorsing it just that it is interesting.  Pondering if it holds out in all circumstances.  Havn't really found any papers contradicting it yet.  A paper in favor it seems here: Google shcholar A Strange Detail
Concerning the Conceptualization of the
Hubble Constant


Edit: some more I found later, (another article I have yet to find also - never found it something about the quantum vacuum falling in a gravity well.)

Of course, the most striking aspect of the above
equation is that <rho> is negative. It is therefore interesting
to understand the origin of the minus sign in more details
...
where ... are the particle
and anti-particle number operators respectively. Of
course, their mean value vanishes in the vacuum state
which contains no particle. The zero point energy is thus
given by the formally infinite term δ(0). Since this term
appears with a minus sign in the Hamiltonian, the corresponding
energy density is indeed negative. The origin of
this minus sign is the anti-commuting properties of the
creation and annihilation operators. We conclude that
the vacuum energy density is negative because we deal
with fermions which are anti-commuting objects.
...
we estimate the vacuum energy and find a value
very far from the often quoted “122 orders of magnitude”.
...
4. Schr¨odinger Equation in an Accelerated Frame
It is also frequent to refer to the weak equivalence principle
as the property stating that, locally, the effect of a
constant gravitational field can be mimicked by an accelerating
frame. Therefore, it is interesting to study
whether this claim holds in quantum mechanics. This
question has been studied in Refs. [146, 150, 151]. Here,
we follow the treatment of Ref. [146].
Let us consider the free Schr¨ondinger equation (in one
dimension to simplify the problem).
...
 we find that the equivalence between a constant
gravitational field and an accelerated frame propagates
to quantum mechanics.

https://arxiv.org/pdf/0705.2611.pdf (How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy Kimball A. Milton,∗ Prachi Parashar,† K. V. Shajesh,‡ and Jef Wagner§)

https://arxiv.org/pdf/cond-mat/9711071.pdf (The ‘Friction’ of Vacuum, and other Fluctuation–Induced Forces
Mehran Kardar , Ramin Golestanian)

In a previous paper we have shown it is possible to build alternative versions of Special Theory of Relativity only considering homogeneity of space, of time and Relative Principle without invoking the postulate of invariance of light velocity in all the inertial frames. Within these alternatives, space and time transformations different than the Lorentz ones like, in particular, the Selleri inertial transformations, are possible. This has many important consequences as, for example, the need for the distinction between physical time as duration of change in space and mathematical time as a parameter quantifying this change as well as the anisotropy of one-way velocity of light. ...

[dustinthewind]

A test I believe might indicate a relative velocity with respect to such a frame would be to measure the static dipole electric field of a magnetic field.  In the lab frame.  If there is no difference in clock rates for the individual charges in the lab frame no dipole electric field should form in the lab frame. 

However if for some reason the clock of a charge sped up moving in some particular direction in the lab, as opposed to another direction, there should be a corresponding dipole electric field to go with it. 

Such an experiment with sufficient sensitivity, I believe could determine velocity relative to a local field that determines the clock rate.

I suspect existing in a gravity field may induce some effect but I would be curious of it's exact orientation of the lab frame dipole electric field.  Parallel or perpendicular to Earth's surface.

[WarpTech]

Getting back to it...

There are two identical clocks, at rest wrt each other and synchronized at the same place, at the same time.

My hypothesis is; that if you accelerate either one of these clocks, "work" is performed on that clock that is not performed on the other clock. It is the work performed that makes that clock run "slower" because it now has a higher energy content, its T^uv has changed. The situation is not symmetrical, since no work was done to the other clock. It's rate isn't affected and it's energy-momentum tensor is unchanged.

However, given the previous example where one of the clocks was put into orbit at the same altitude as the other clock. Work was done to the clock in orbit, and now it is in free-fall, where there are no forces and no proper acceleration in the frame of the orbiting clock. The clock in orbit runs slower than the clock that is hovering at the same altitude. Even though the hovering clock feels a force supporting it, no work has been done to it because it hasn't moved anywhere. In this scenario, the clocks do not tick at the same rate, their T^uv's are different, AND observers with each clock will agree on whose clock is running faster or slower. It is not reciprocal.

This non-reciprocity cannot be demonstrated with Lorentz transformations because they are inherently reciprocal. The fact that the observer and the source are moving toward or away from each other changes the situation, such that the changing time delay between them gives the "illusion" of reciprocity. I say it is an illusion because it is not present in the orbital scenario where it can be tested. The issue is that the differences in the T^uv of each clock is ignored, because the work done is not taken into consideration.

Are we clear up to this point?

[meberbs]

Getting back to it...

There are two identical clocks, at rest wrt each other and synchronized at the same place, at the same time.

My hypothesis is; that if you accelerate either one of these clocks, "work" is performed on that clock that is not performed on the other clock. It is the work performed that makes that clock run "slower" because it now has a higher energy content, its T^uv has changed. The situation is not symmetrical, since no work was done to the other clock. It's rate isn't affected and it's energy-momentum tensor is unchanged.

How does some observer passing by (moving at some arbitrary velocity) know which clock was accelerated? Your hypothesis is meaningless if you cannot answer this question. If the answer is "they can't" then you are left with a perfectly symmetrical situation.

However, given the previous example where one of the clocks was put into orbit at the same altitude as the other clock. Work was done to the clock in orbit, and now it is in free-fall, where there are no forces and no proper acceleration in the frame of the orbiting clock. The clock in orbit runs slower than the clock that is hovering at the same altitude. Even though the hovering clock feels a force supporting it, no work has been done to it because it hasn't moved anywhere. In this scenario, the clocks do not tick at the same rate, their T^uv's are different, AND observers with each clock will agree on whose clock is running faster or slower. It is not reciprocal.

We already had this conversation, and your description here does nothing to change what I already said:

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.

The key is that the one with the slow clock is experiencing a constantly changing metric.

This non-reciprocity cannot be demonstrated with Lorentz transformations because they are inherently reciprocal. The fact that the observer and the source are moving toward or away from each other changes the situation, such that the changing time delay between them gives the "illusion" of reciprocity. I say it is an illusion because it is not present in the orbital scenario where it can be tested. The issue is that the differences in the T^uv of each clock is ignored, because the work done is not taken into consideration.

You also cannot consistently describe simple situations without the Lorentz transformations. No matter how many times you call it an "illusion" the fact is that you need to accept reciprocity to come to a consistent conclusion regarding the "twin paradox" and similar situations. Your "work done" hypothesis still makes no sense, because how do you know they didn't both start in orbit, and the work was done on the one that ends up hovering. You are also still simply ignoring the perspective of a distant observer that is moving at a constant velocity relative to the central mass.

Are we clear up to this point?

The only thing clear at this point is that you are determined to ignore everything I say, and have not answered a single one of my questions.

Despite starting your post with "getting back to it," you did nothing in this post to address the post you had previously said that you would get back to which ended with the following question to you:

You still haven't answered how to tell which clock is the one that accelerated, and some of your comments seem to be backtracking and agreeing with the point that you cannot tell which one is moving relative to the vacuum, but that is the definition of reciprocity being true.

[WarpTech]

Getting back to it...

There are two identical clocks, at rest wrt each other and synchronized at the same place, at the same time.

My hypothesis is; that if you accelerate either one of these clocks, "work" is performed on that clock that is not performed on the other clock. It is the work performed that makes that clock run "slower" because it now has a higher energy content, its T^uv has changed. The situation is not symmetrical, since no work was done to the other clock. It's rate isn't affected and it's energy-momentum tensor is unchanged.

How does some observer passing by (moving at some arbitrary velocity) know which clock was accelerated? Your hypothesis is meaningless if you cannot answer this question. If the answer is "they can't" then you are left with a perfectly symmetrical situation.

Simple! The random "inertial" observer passing by, would need to use his sensors (telescope) to read the face of both clocks as the two clocks pass each other. He would need to observe 1 or more complete orbits (2 readings) to acquire the data to compare the time elapsed on each clock. The one that is running slower is the one that was accelerated in the past. He doesn't need to assume anything, and his velocity is irrelevant when doing the comparison, because he is not comparing to his own clock.

Also, if both clocks were synchronized while in orbit, work had to be done to both clocks to get them there in the first place, the work increased the energy content of both clocks. Therefore, work must also be done to restore it to its hovering platform, but this work is in the opposite direction and therefore removes the energy that was previously given to it when it was put into orbit. In other words, this work lowers its energy content by removing what was previously added. No one would argue the fact that the clock in orbit has a higher kinetic energy than the one on the platform.

Work done in the past is part of the system as a whole, it can't be ignored. There is no such thing as a reference frame where the clocks are in orbit but have "never" been accelerated to get to that frame of reference at some time in the past.

[meberbs]

Getting back to it...

There are two identical clocks, at rest wrt each other and synchronized at the same place, at the same time.

My hypothesis is; that if you accelerate either one of these clocks, "work" is performed on that clock that is not performed on the other clock. It is the work performed that makes that clock run "slower" because it now has a higher energy content, its T^uv has changed. The situation is not symmetrical, since no work was done to the other clock. It's rate isn't affected and it's energy-momentum tensor is unchanged.

How does some observer passing by (moving at some arbitrary velocity) know which clock was accelerated? Your hypothesis is meaningless if you cannot answer this question. If the answer is "they can't" then you are left with a perfectly symmetrical situation.

Simple! The random "inertial" observer passing by, would need to use his sensors (telescope) to read the face of both clocks as the two clocks pass each other. He would need to observe 1 or more complete orbits

What orbits? Nothing is orbiting anything in the described situation.

[WarpTech]

Getting back to it...

There are two identical clocks, at rest wrt each other and synchronized at the same place, at the same time.

My hypothesis is; that if you accelerate either one of these clocks, "work" is performed on that clock that is not performed on the other clock. It is the work performed that makes that clock run "slower" because it now has a higher energy content, its T^uv has changed. The situation is not symmetrical, since no work was done to the other clock. It's rate isn't affected and it's energy-momentum tensor is unchanged.

How does some observer passing by (moving at some arbitrary velocity) know which clock was accelerated? Your hypothesis is meaningless if you cannot answer this question. If the answer is "they can't" then you are left with a perfectly symmetrical situation.

Simple! The random "inertial" observer passing by, would need to use his sensors (telescope) to read the face of both clocks as the two clocks pass each other. He would need to observe 1 or more complete orbits

What orbits? Nothing is orbiting anything in the described situation.

I thought we were getting back to my previous example, where one clock is in free fall (orbit) and the other is hovering on a platform. That's where I'm at.

[meberbs]

What orbits? Nothing is orbiting anything in the described situation.

I thought we were getting back to my previous example, where one clock is in free fall (orbit) and the other is hovering on a platform. That's where I'm at.

The quoted section of your post did not mention orbiting. The post of mine that you previously said that you would get back to and I quoted/linked at the end of my previous post was This post. We were not discussing anything orbiting there either.

For convenience, that example started with your image here  which discusses 2 clocks in free space with no description of being in orbit of anything. Also, I don't care if you had meant to imply them being in orbit of something, but never said so for multiple posts in a row. What we need to discuss right now is clocks in free space with no nearby gravity wells.

You keep using objects being in orbit to add confusion by ignoring the difference between moving in a circle/helix and moving in a straight line, misusing the equivalence principle, and creating the illusion of a preferred frame, since there is one frame that is much easier to do calculations in. The inherent contradictions in your claims will be much more obvious if we stop talking about orbits for now.

[dustinthewind]

Are there any example of real experiments being performed in deep space away from gravity wells?  Some deep space probes not moving in circular orbits.  It seems nature conspires in a rotating frame to give the illusion of absolute motion but we need a test of non rotating frames in deep space.  Wonder if some of the probe anomalies could be connected.

[WarpTech]

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.

For me, it comes down to this quote "energy is frame dependent". Obviously, in an orbital situation, the kinetic energy makes a big difference. A clock that has it, stays in orbit. A clock that doesn't, falls to the ground. This perspective comes from choosing the center of mass frame.

If you eliminate the center of mass frame, I have no solution. On the other hand, there is nowhere in our entire galaxy that is not relative to some center of mass object. Be it the earth, the sun or Sagittarius A. So what is the point of discussing a situation where there is no gravitational potential as is done in SR? There is nowhere in our galaxy where it would apply, except as an approximation to a larger model. I can choose any center of mass I want, but it have to have a center of mass relative to which, a gravitational potential can be established in order to know the rate at which clocks "actually" tick. Not the rate they are perceived to tick by a moving observer.

[meberbs]

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.

For me, it comes down to this quote "energy is frame dependent". Obviously, in an orbital situation, the kinetic energy makes a big difference. A clock that has it, stays in orbit. A clock that doesn't, falls to the ground. This perspective comes from choosing the center of mass frame.

I have said this repeatedly, yet you still have not acknowledged it:

You can pick a frame where the large mass is moving, then you can do so in a way that the "hovering" object has more kinetic energy than the orbiting one (at least some of the time)

If you eliminate the center of mass frame, I have no solution.

The universe does not have a center of mass frame. As far as we know, the universe may contain an infinite amount of mass across an infinite amount of space. I don't have to remove a frame that doesn't exist in reality.

On the other hand, there is nowhere in our entire galaxy that is not relative to some center of mass object. Be it the earth, the sun or Sagittarius A. So what is the point of discussing a situation where there is no gravitational potential as is done in SR?

There are countless situations where gravitational potentials are irrelevant and space is essentially flat. You can imagine a couple of clocks halfway between here alpha centuari, and you would be able to have them move around at relativistic speeds for a few light weeks in any direction without having to worry about any gravity wells, and motion relative to the center of the galaxy would be negligible on that scale, so any effects from changing gravitational potential or such would be negligible.

There is nowhere in our galaxy where it would apply, except as an approximation to a larger model.

As I said, for all meaningful purposes there are such places, and general relativity says that you get special relativity in them. You are the one missing the big picture, because if your model does not reduce to this in these cases, then your model is simply inconsistent. If your model was consistent, then you would have no problem answering what happens in the simplest cases.

I can choose any center of mass I want, but it have to have a center of mass relative to which, a gravitational potential can be established in order to know the rate at which clocks "actually" tick. Not the rate they are perceived to tick by a moving observer.

Except, your model is now dependent on the choice of center of mass (earth, sun, center of galaxy, etc.) so it gives different results for each situation and is inconsistent.

[WarpTech]

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.

For me, it comes down to this quote "energy is frame dependent". Obviously, in an orbital situation, the kinetic energy makes a big difference. A clock that has it, stays in orbit. A clock that doesn't, falls to the ground. This perspective comes from choosing the center of mass frame.

I have said this repeatedly, yet you still have not acknowledged it:

You can pick a frame where the large mass is moving, then you can do so in a way that the "hovering" object has more kinetic energy than the orbiting one (at least some of the time)

You could, but it would be wrong to do so. The resulting frame would not be an inertial frame, it would have forces acting on the observer at all times.

If you eliminate the center of mass frame, I have no solution.

The universe does not have a center of mass frame. As far as we know, the universe may contain an infinite amount of mass across an infinite amount of space. I don't have to remove a frame that doesn't exist in reality.

I couldn't care less about the rest of the universe. Our galaxy is big enough to explore for the next few millennia, at least! Sagittarius-A would be the center of mass until we are half-way to Andromeda. The space between the Sun and Alpha Centauri still has a gravitational potential relative to the Sag-A that can be used to set the baseline for the rate at which a clock will tick. It is also there to set the baseline to compare which clock has a kinetic energy content and which does not, relative to this CM. From that, the difference in the rate of the two clocks can be determined.

On the other hand, there is nowhere in our entire galaxy that is not relative to some center of mass object. Be it the earth, the sun or Sagittarius A. So what is the point of discussing a situation where there is no gravitational potential as is done in SR?

There are countless situations where gravitational potentials are irrelevant and space is essentially flat. You can imagine a couple of clocks halfway between here alpha centuari, and you would be able to have them move around at relativistic speeds for a few light weeks in any direction without having to worry about any gravity wells, and motion relative to the center of the galaxy would be negligible on that scale, so any effects from changing gravitational potential or such would be negligible.

The gravitational potential is only irrelevant if you don't care about comparing the rate at which clocks tick. If that is the goal, then gravity can't be ignored anywhere in the Universe.

[meberbs]

You could, but it would be wrong to do so. The resulting frame would not be an inertial frame, it would have forces acting on the observer at all times.

The frame of a distant observer moving at constant speed is an inertial frame.

I couldn't care less about the rest of the universe.

If your theory is inconsistent anywhere in the universe then it is wrong.

The space between the Sun and Alpha Centauri still has a gravitational potential relative to the Sag-A that can be used to set the baseline for the rate at which a clock will tick. It is also there to set the baseline to compare which clock has a kinetic energy content and which does not, relative to this CM. From that, the difference in the rate of the two clocks can be determined.

So at some point when leaving the solar system, the Voyager clocks will suddenly start ticking slower because the center of mass frame changed? Either there is one and only one rest frame for the whole universe that determines this, or there is no universal rest frame and all frames are equally valid, no jumping to only "center of mass" frames. You can't have it both ways, and experimental data supports the second one.

There are countless situations where gravitational potentials are irrelevant and space is essentially flat. You can imagine a couple of clocks halfway between here alpha centuari, and you would be able to have them move around at relativistic speeds for a few light weeks in any direction without having to worry about any gravity wells, and motion relative to the center of the galaxy would be negligible on that scale, so any effects from changing gravitational potential or such would be negligible.

The gravitational potential is only irrelevant if you don't care about comparing the rate at which clocks tick. If that is the goal, then gravity can't be ignored anywhere in the Universe.

For the described situations, the gravitational potential would be essentially constant, therefore it has the same effect on all of the clocks. You can't talk about orbits when the scenario is measured in weeks and the orbit is similar to the sun's around Sagittarius-A.

Now are you going to attempt to answer the question of how to tell apart 2 clocks at the same gravitational potential that are moving relative to each other or are you going to keep making excuses and avoiding the question?

[WarpTech]

The gravitational potential is only irrelevant if you don't care about comparing the rate at which clocks tick. If that is the goal, then gravity can't be ignored anywhere in the Universe.

For the described situations, the gravitational potential would be essentially constant, therefore it has the same effect on all of the clocks. You can't talk about orbits when the scenario is measured in weeks and the orbit is similar to the sun's around Sagittarius-A.

Now are you going to attempt to answer the question of how to tell apart 2 clocks at the same gravitational potential that are moving relative to each other or are you going to keep making excuses and avoiding the question?

Constant or not, the gravitational potential sets the baseline for the rate at which the clock ticks. That gravitational potential has a source, assumed to be at the center of mass of whatever field(s) created that potential. Kinetic energy must be measured relative to that, regardless of where in the universe the clock is located.

In regards to your question, here is the procedure:
The observer who comes onto the scene where there are 2 clocks in motion relative to each other, and relative to him.

1. He must first determine where is the center of gravity for region of space, and then adjust his position and speed to match that frame.
2. Then measure the rate of each clock by comparing their rates and kinetic energy, in this frame.

It doesn't have to be a universal rest frame. It only has to be a gravitational field from which to derive a baseline. The spectral energy density of the vacuum is free to be different from place to place in space-time, and any matter will conform (scale) itself to establish equilibrium with that local density. That kinda makes it difficult to measure!