I think everyone agrees with you on this. The point is that symmetries of particular solutions can lead to preferred choices of coordinates. But this does not say anything about the mathematical structure of the theory.

(And yes, I have had this conversation with students in the past!)

What Andrew says is correct, I would just note that you have to be careful with the word "frame" in this context, specifically the CMB does not define a frame as the term is used in SR. Perhaps foliation would be more appropriate.

George Dishman : Thank you. Let us not discuss about words. You can use any word you want, it will not change the physics.

The name "folliation" may be preferred by mathematicians in some areas, but it has several problems in physics, where one would do better, to be precise, to not abandon frame. There is no new physics that justifies it. The CMB does not introduce new physics, that is the point here.

But a confusion may result, sounding mysterious, if you are not careful to avoid it in physics.

That is, perhaps, why the head of the discussion has to point out that special and general relativity do NOT work on the basis that there is no preferential inertial frame of reference. Try that with "folliation" -- and there is no physical principle to use.

EG: You can use any word you want, it will not change the physics.

Of course, as can you, but "frame" has a specific meaning in SR and I was assuming you were using it that way.

Ed, I basically agree with you on most of the points ... but ... if two objects are each at rest in the same SR frame then they must have a constant separation. If two objects are each "at rest in the CMB" (by which I mean each sees no dipole component) then they are moving apart with the rate determined by the Hubble Law.

A foliation where the spatial surface is everywhere normal to the worldlines of observers "at rest in the CMB" exhibits the symmetry that Andrew mentions so is a preferred coordinate system but is not an SR frame.

George Dishman : You bring an interesting point, that is not a divergence, it is explained in cosmology. If two objects are each at rest in the same SR frame then they must NOT have a constant separation, contrary to usual assumptions, when Hubble flow is introduced.

Only when the Hubble flow is zero, the comoving points may not separate. In short, the Hubble Flow allows comoving observers to separate [1]. I added that reference to the text, to clarify.

Using foliation, in my opinion, does not advance the physics. Not every mathematical idea, though sound, represents physics. For example, STA and Cifford(3,1) are mathematically sound, and complete, but fail in exactly where they aspire to represent -- space time algebra (STA) in physics.

[1] Cosmology, SR, and GR, at http://www.astro.ucla.edu/~wright/cosmo_02.htm

I will argue that space time needs a preferred reference for zero velocity anywhere to reconcile how kinetic energy is used in the Lagrangian function and Lagrangian density. Also Albert Einstein recommended for kinetic energy to be developed as a field in his autobiographical notes as discussed in other threads. Kinetic field energy requires a zero velocity reference available anywhere.

CMB provided a zero velocity reference, but SR and GR do not provide it or recognize it as fundamental. Some famous scientists have declared isotropic CMB to be a fundamental velocity reference.. Others argue that CMB is convenient but not fundamental.

The point is important for the future of space exploration because kinetic field energy opens the possibility of travel among the stars.

I don't support the proposition of special reference frames except as a convenience, when locations and distances are defining the frames. My preference is for reference frames defined by velocities and clocks, because higher dimensional frames can be constructed and tested in ways that promote high speed transport in deep space.

In another thread I ask if CMB has become a fundamental part of relativity, or if it is just a convenience. It is not trivial because a fundamental basis of kinetic field energy allows folding of 4D space time within a higher dimensionality 6D or more in front of a high speed vehicle, while adding a further possibility of wormholes developing short cuts between the folded sheets when kinetic energy exceeds a critical value.

Maybe CMB does introduce new physics, or at least provide a basis for some old science that hasn't been developed beyond the autobiographical notes.

Quantum Field Theory has put the kinetic energy into fields as the inside product of two field vectors. It needs a zero velocity reference that isotropic CMB could provide. So far QFT has not been reconciled with GR but could be reconciled with GR by a fairly simple energy partition. QFT supports CMB as a fundamental reference system based on velocities and clocks, while adding something new in Physics.

EG: If two objects are each at rest in the same SR frame then they must NOT have a constant separation, contrary to usual assumptions, when Hubble flow is introduced.

I think we are saying the same thing in different ways, if you have a Hubble flow in the usual sense, then you can create local SR frames over small regions, but those have relative motion. The only model I know of that bridges the gap is that of Milne which is based on SR purely and assumes no gravity at large scales.

https://en.wikipedia.org/wiki/Milne_model

Given any large scale gravity, and hence a non-zero deceleration parameter, SR can no longer apply.

Maybe you already know Albert Einstein's last definition of SR is it only applies when gravity does not have to be considered.

Jerry Decker : The declaration is different, the condition is free fall, not when gravity does not apply. A body in free fall experiences SR locally.

Only locally though Ed, the volume is restricted to where the effects of gravity can be considered negligible.

it is the Local Lorentz invariance, space-time is supposed to locally Minkowskian (flat space-time)...

The experiences of electrodynamics are supposed to be the same in two satellites at different orbits, none can understand, with measurements within their lab if they are travelling with rectilinear motion in absence of gravitation or not.

But there are some differences....

George Dishman and Stefano Quattrini : Looks like you just restated what I wrote. Thanks sincerely for the support.

But gravity is not annulled in free fall -- if you are in free fall toward the Sun, the Sun gravity does not disappear! It does happen that you experience no gravity, but the entire Sun is still there, 100%, its gravity is still there, 100%, it was not shut-off, even the slightest, it is not negligible at all, spacetime is not even locally flat - someone else certainly experiences gravity at the same point if not in free fall; suppose you just pass by, free falling, not anyone with a rocket, necessarily, but at the same point in spacetime, neglibly close to you in (t, x, y, z) -- just not exactly the same v.

Look at it another way, introducing consciousness, as often done in physics -- without naming the "demonology". The Sun does not know one is in free fall, neither the other planets and bodies. They don't go fly off because you are in free fall, gravity is neither negligible, nor disappears, not even momentarily, not even locally. Spacetime, curved, does not change.

Also, regarding some differences ... when you are in free fall, it is not only relative to the Sun. It is to every gravitational influence, even if the gravity field is dominated by the Sun. Although one could think that the influence of far away planets is not easy to be detected, for example, ignoring just one planet would break conservation of momentum, and cumulatively over billions of years.

Further, two satellites in orbit around the Earth must not be in free fall, they are just following a geodesic dominated by Earth. It is an extended Galileo's inertial principle, also called extended Newton's first law, valid for such non-inertial movement. Another proof, if needed, is also that they do go around, which is not a straight line, which free fall does not do.

Any satellite, also the Earth, is not in free fall -- just non-technically said to be in "free fall". This is demonstrated absolutely, in spacetime terms, not meaning that an absolute reference frame is to be used, by measuring the curvature of the worldline. No curvature means no acceleration, also in flat, Minkowski spacetime.

Motion is, thus, only not detectable if it is inertial. There are no frames in inertial motion where the laws of physics are different to inertial observers.

Free fall in a gravitational field, is not inertial motion and the observer (yourself, falling) is also not inertial, thus it has two "strikes" and is detectable. For example, by that observer in supposed free fall, in local measurements. The laws of physics will be different, even locally.

There are the many other reasons, not all listed above, why free fall in a gravitational field is not undetectable, and the observer is not "at rest," even to the very observer falling.

It is the equivalence principle that does not let you feel it.

Hi Ed,

EG: Looks like you just restated what I wrote. Thanks for the support.

Yes, pretty much, that was the intention.

EG: But gravity is not annulled in free fall .. someone else certainly experiences gravity at the same point if not in free fall, at the same point in spacetime ..

For someone else to be "not in free fall", they have to be accelerating relative to you and that needs some sort of force, the typical example in context being a rocket engine.

The Equivalence Principle says that if you are in free-fall and an accelerometer you carry shows zero reading then it is legitimate to consider yourself at rest and the other observer accelerating through local Minkowski spacetime due to firing the rocket engine.

>

sure it cannot..but local measurements are not able to detect it...

George Dishman and Stefano Quattrini : I replied by editing the answer and question, to make it more complete. Thanks.

In the answer, it is distributed and in the new penultimate line:

There are the many other reasons, not all listed above, why free fall in a gravitational field is not undetectable, and the observer is not "at rest," even to the very observer falling.

The text head has been edidited, hoping to clarify the conditions for the subjects posted here, and including two new Preprints, in ref. [2] and [3]. Thanks sincerely for the cooperation.

"Free fall is to every gravitational influence, even if the gravity field is dominated by the Sun."

It is dominated by Earth if close to earth....Although also the influence of other planets play a role and eventually the influence of sagittarius A (the center black hole) is present but order of magnitudes lower than that..

Although one could think that the influence of far away planets is not easy to be detected, for example, ignoring just one planet would break conservation of momentum, and cumulatively over billions of years.

And, there are the many other reasons, some listed, why free fall in a gravitational field is not undetectable, and the observer is not "at rest," even to the very observer falling.

Ed,

the experiments of twin clocks set in sync then set in radial free fall has not yet been performed...it might be very surprising if they desynch as a function of their distance and distance from the ECI.

Stefano: It is useful to look at nature, we measure that experiment all the time in distant nebulas, galaxies, by measuring the spectra of atoms, molecules, and ions. We do not have to make the experiment ourselves, we can use a lab, such as in the universe, free and unbiased.

But we do not have naturally reliable time counters available other than pulsars...and orbits of planets..but the second are unsuitable for such experiments...so we have to provide reliable local time counters.. to test locally the theories which claim local effects...

Stefano: Thanks for mentioning pulsars. But I said spectra, anywhere we can literally see, we can neasure a time counter, defining time as we define atomic clocks.

Hi Ed,

I think I would agree with almost everything in your question other than perhaps one sentence. You say in the question "Free fall in a gravitational field is not inertial motion" but that is technically not correct. A free-falling object is moving in a fashion which is governed only by it's own inertia, that is there are (by the definition of "free fall") no external forces acting on the object, so the motion should correctly be called "inertial".

You continue "thus it is detectable". GR allows you to define the free-falling object as being at rest and the motion of everything else as being affected by some pseudo-gravitational field. You can detect motion relative to other objects but there remains no absolute frame even in terms of acceleration in GR which is a significant difference from SR.

What can be defined without incurring in level of disagreement is:

A system is not inertial when a acceleration is detected .

Then the redefinition of Inertiality by GR for free falling bodies is not at all a direct consequence of the previous sentence.

If I see a free falling body from outside I can see it accelerating (kinematically) towards the center of gravitation of a celestial body.

Hi Stefano,

Newton's first law defined inertial motion as that which occurs when a body is not being acted upon by an external force. GR simply maintains that. Newton's law effectively predicted that such motion would be at constant velocity in a straight line but both those parameters are coordinate dependent so you can choose a suitable coordinate system such that they are true for any one object.

The only coordinate-free measure of acceleration which cannot result in disagreement is that registered by an accelerometer carried by the body, i.e. proper acceleration, which by its nature is the same in all coordinate systems or for all observers.

Hi George,

George Dishman , Stefano Quattrini and all: Free fall in a gravitational field is not inertial motion, as understood in physics, confirmed. Look for today's formulation of SR and GR, starting with spacetime -- not the Lorentz transformation. You can use Burgess, cited.

You can also use physical arguments, with no maths, SR, or GR -- any non-comoving inertial reference frame cannot be reached at constant velocity, as close as it may be (without being identical -- keeping the non-comoving condition). In other words, your reference frame in free fall would be different in terms of laws of physics, from any inertial reference frame, hence, it is not inertial itself.

Or, one can also use those consequences with students, and use for, hopefully, an illuminating discussion.

Ed Gerck

that would be a step foreward for me....it is a bit against the EEP though...

Burgess...could you provide a link?

Stefano Quattrini : I complemented my answer right above. One can also think physically, no maths, SR, or GR.

The discussion on "free fall" became a bit off-topic here, distracting from CMB, and was moved to a new topic, at

https://www.researchgate.net/post/Free_fall_in_a_gravitational_field_is_not_inertial_motion

A DISCLAIMER is included. All questions are answered in the discussion text.

in regards to free fall...

Preprint Frequency shifts of moving oscillators in gravitational potentials

Stefano Quattrini : Now, since one can differentiate free fall from inertial motion, and names don't matter but meaning does, even though often confused in the literature, you may be able to disambiguate .

Alexandru Szel

I believe your equation has a mismatch of dimensions with dt on right side and h with dimensions of angular momentum. Also your h should be hbar in the context. Then you get uncertainty of momentum and location.

https://www.researchgate.net/post/Can_one_at_the_same_time_accept_special_relativity_SR_by_Einstein_and_non-SR

Dear Ed Gerck , thank you for your question. Additionally, some CMB anomaly about symmetries and inhomogeneity: https://www.researchgate.net/post/CMB_Anomaly_Cosmic_Microwave_Background_Symmetries_and_Inaumogienity Thanks to Alexandru Szel

All: See Deleted research item The research item mentioned here has been deleted

If kinetic energy travels as stress energy wave, as now seems likely, then a zero velocity reference is needed to express the magnitude of curvature around any particular object.

It doesn't need to be a revision of relativity, since relativity allows us to choose any reference we like. Something like this is small to measure, but in principle large objects with much kinetic energy should deflect starlight passing by them, possibly measurable in future. Repeatable observations would decide whether or not CMB is fundamental or only convenient.

JD: Kinetic energy is simply a matter of choosing a reference. It is not intrinsic to the situation. An object can have high kinetic energy to you and yet zero to another observer. In the first case, SR applies to you but does not apply to the comoving (same position and velocity) observer.

EG Einstein thought that kinetic energy should be expressed as a field, in his Autobiographical Notes 1949. He lacked a zero reference frame on which to express the curvature. QFT continues the kinetic field concept, as does the Lagrangian Density. Some researchers are expressing stress energy in terms of Lagrangian which means they have accepted kinetic field energy, without much argument.

Victor Weisskopf and PJE Peebles wrote in books that CMB is a fundamental reference frame of the universe, without discrediting relativity. Others have argued against it. I proposed a test that could eventually prove one way or the other.

In your reply there is no compelling reason for two separate objects not to have equal or unequal stress curvatures representing differences in kinetic energies.

In relativity, energy bends space. Recent work on high speed in deep space is concluding that space has a limit on how much bending can occur before local space experiences a quantum change of state.

The question is important for possibilities of star travel. If a conventional view of space time prevails, star travel will never be practical. On the other hand if new ideas prevail then there is possibility of breakthroughs in deep space transportation.

It can be argued that CMB is fundamental to the stability of our universe, without which a collapse of false vacuum would destroy everything, converting into a burst of light and gamma rays, a new big bang. Passage of time stops, and entropy goes to zero, until the bang cools enough to allow particles of mass. Relativity doesn't say anything about beginning of universe.

Roger Penrose has written much about Cycles Of Time in which energy but no mass passes from one universe to the next. He finds circular patterns in the CMB that are claimed to be the result of exploding super black holes in a previous universe. I agree mostly except in my representation a vehicle with high speed relative to the fading isotropic CMB could have a locally altered space time that survives the destruction.

Implication is that when CMB falls below a critical energy density, our universe comes apart.

Stephen Hawking showed that black holes act like black body radiators, meaning in thermal equilibrium with the CMB, blue shifted for gravity. The CMB stabilizes black holes.

I don't find any reason to object to SR or GR except in highest energy densities, the space time is which they reside may be fundamentally changed.

In my previous comment I suggested the possibility of a test whether CMB is fundamental or just convenient, with far reaching consequences, similar to the observation of light bent by the sun. We just don't have such high speed vehicles yet.

Relativity doesn't speak about CMB, which means it doesn't give a complete model.

JD: The curvature is known intrinsically in GR. The curvature of empty space is zero.

EG Space is never empty of fields and energies. Most of space is nearly flat, slightly curved positive in galaxy clusters, but negative between clusters.

A fast moving vehicle must modify the local space it passes through. Relativity doesn't know about that. Einstein expressed inertia as the reason for assigning properties to space time.

JD: It is a common misconception that energy (such as high-power laser beam) changes curvature, while only mass does. Mass and energy are not the same, energy is the component of 4-vector, mass provides the magnitude. Energy is conserved, mass is not. Mass is invariant, energy is not.

Mass and energy are linked by E=m, but there is no energyless mass but there is massless energy. Mass and energy are not physically equal.