Secondly, mathematicians doing physics sometimes overlook the quirks and shortcomings of mathematical syntax.

We believe with good reason that it shouldn't be possible for someone to be able to travel faster then their own light (along the same path, at the same time), because, if they did, all sorts of craziness happens. For starters, it's difficult to see how their atoms could remain in equilibrium if signals travelling across their structure had no legal return path.

So we have the statement "you cannot travel faster then the speed of light", and an associated mathematical expression, "vv", "the speed of light is always faster than the speed of an object".

This statement implies that lightspeed is not fixed but variable, that the velocity of a body is the dominant quantity, and that c, lightspeed, is expected to adjust itself accordingly.

With the first statement we tend to get an assumed fixed global speed of light and a lightspeed barrier, with the second we tend to get a variable c, with no limits on velocity.

While we can say that actually, particle accelerators do show a lightspeed limit, ruling out c>v, there is a third option for which there is no obvious corresponding math notation, the idea that there's a mutual interplay between lightspeeds and object velocities.

With Option One we tend to end up with a fixed lightspeed barrier, special relativity and a Minkowski metric, with Option Three, we instead get a relativistic acoustic metric. With the acoustic metric approach we get proximity-dependent lightspeed dragging and "hybrid" behaviour: a particle accelerator can only directly accelerate a particle to a speed less than cACCELLERATOR, but cPARTICLE is greater, and the particle itself can then throw off a daughter particle that (initially, at least) travels at less than the local velocity of light, but more than the background velocity and speed of light. The daughter-particle radiation then shows up in descriptions as Hawking radiation.

The problem with the poverty of conventional mathematical syntax is that it encourages the casual physicist to write "v

Hi,

GR is not limited to the use SR, it extend SR. For example Minkowskian spacetime is just used locally to solve problems with closed form. But the GR spacetime is not globally Minkowskian. SR can be viewed as a particular case of GR, where frames of reference are inertial and in flat spacetime.

So GR is "build" with the c limit. It is not possible to reach c in GR, except for light that can have only speed c (it can't go slower).

If an information is able to go faster than c, it will violate the causality principle. So there have been proposals for particules that live beyond c, but can't "cross" c, and don't carry information, the tachyon. It is highly speculative. It may even have been refuted, I don't remember. Within GR, only the light can live at c.

So if there is a possibility to cross c limit, the GR will be refuted and we'll need another theory. But for 100 years, the GR predictions has been correct and highly accurate, even on extreme conditions for wich it has not been "developped" at the beginning.

Arnaud

Dear Ed,

if I have understood you correctly, you are asking whether relative speeds in GR which are greater than c are allowed. Is my understanding correct?

If so, the answer is as follows: velocities are measured locally. The whole concept of measurement is always local, and for a local velocity v is always

Arnaud Dion , Oliver Tennert , Mohamed Hassani

In the same way, mutatis mutandis, one could consider that, independent of cosmology, GR can support v >c while SR is confirmed. There is an extra degree of freedom when going from SR to GR -- even though, locally, a body in free fall in a gravitational field obeys SR.

We cannot use quotes of others as elements of proof in science. That, as the question says, «In Special Relativity (SR) as formulated by Minkowski using spacetime, even arbitrary motion is always within c, the speed of light in vacuo.», is sufficiently explained in the literature cited, and by experiments, that it should not be doubted at this level, as it is too elementary in current times (2019).

Dear Ed,

EG: How about GR? As GR is defined using SR spacetime description, c is also the maximum speed in GR.

That is correct but in GR the equations are derivatives so only apply locally (at a point). Intrinsic curvature alters the relationships for remote measurements.

My "belief" or I would rather say "impartial assessment" is that evidence like this confirms SR to the limit of our ability to test it:

https://phys.org/news/2015-09-precise-lorentz-symmetry-photon-constant.html

Numerous other experiments and observations do the same for GR, there is no case of anything showing any repeatable error up to the boundary of the limited data available from LIGO to date.

Where I think we may have scope for new results is in the detail of BBH merger waveforms where there seems to be a hint of possible deviations in the form of "echoes" or "correlated backgrounds". These are very tentative at the moment and may vanish with better statistics and better SNR but the hope is there that we can get some subtle pointer to new physics beyond GR.

Dear Ed Gerck,

You ask what is our belief. My belief is that space is flat as can be described in Minkowski space. Lambda-CDM, based on GRT describes that space is expanding and it takes galaxies with it in the Hubble flow. There velocities v>>c are common. So why do I disagree with that? Let me explain. In the old time it was assumed that we were the centre of the universe. In that view, that also is a valid reference frame in GRT, the universe revolves around the earth. We need complex mathematics to explain why all the solar system objects have their strange orbits. But there is something interesting in this view. The orbital velocity of the universe is constant and objects have a tangential velocity that only is a function of the distance. So similar to the Hubble flow we have a tangential 'Hubble' flow. With the Hubble flow it is space that moves and the objects go with space. In the rotation flow it is space that rotates and the objects go with space. In both cases we see that we have velocities v>>c.

For the rotation we came to the conclusion that not space rotates but that the Earth rotates. It was a big step in science. Now suddenly there is no tangential velocity of any object that exceeds the speed of light. But we still assume that space expands. Out of similarity we can decide that space should also not expand but that the observations of cosmological redshift originate in from the fact that matter shrinks. With rotation we first assumed that the passive object was the earth and the active object was space. We changed that to the passive object to be space and the active object, the rotating object, to be Earth. For the scale change, expansion, we still assume the passive object Earth and the active object space. We are stuck with recession speeds v>>c in this case. When we change it to the active object is the Earth, matter, atoms, and the passive object space, then we have no more recession speeds v>>c but only the observation that older matter, from greater distance, emitted their characteristic EM at a larger wavelength than we have now.

When the observer has a reference stick, the distance between two lines on a rod, that is build of matter that shrinks, then it looks as if with that reference space expands. When space really expands then we have to explain why it expands by having equations that describe the scale of the universe as a function of its contents. When matter shrinks then we need equations why matter has to lose energy. The space equations have in my analysis problems of consistency. The LIGO results, for me, seem to show that space never expanded. These results also seem to show that whatever matter is moving with respect to other matter is emitting GWs. Looking to a presentation of Lawrence Krauss for the Nobel comity I find that it is acceptable to assume that a proton mass by more than 90% originates from the creation and annihilation of particles inside envelope of the proton. This means that the mass of a proton is a dynamic average. Thus it can be seen as a variating mass. This has to emit GWs, time dependent gravity.

So, I believe that we live in a Universe where mass shrinks and space is flat. The shrinking mass towards the future originates from a larger mass in the past. With larger mass goes larger units of time. The BB event can be expanded back to infinite past and the hyper inflation is the extreme slow start.

I hope that you understand what I write. If you agree is your part.

Regards,

Paul Gradenwitz

Dear Paul,

PG: You ask what is our belief. My belief is that space is flat as can be described in Minkowski space.

In that case the question you need to address is why apples fall off trees and accelerate towards the ground. In the flat space of SR, there would be no gravity. You need something additional to SR to explain gravitational acceleration so, in relation to the question Ed asked, what theory do you believe models that and what is your evidence supporting it?

Paul Gradenwitz and George Dishman : Thank you. Belief is a claim that needs trustworthy evidence, and is measured by the probability of that evidence, following DS. Trustworthiness, however, does not have to be measured with probabilities. A certain, deterministic, event does not have probability 1.

Probability is is an open range, excluding 0 and 1, by definition, in frequency or Bayes. That said, cooking, finance, and chemistry cannot be random --- we need a model, a most probable model. All certain, deterministic, models have failed, including Black-Scholes (in finance, investment models).

Determinism has failed in physics, as well. The GR is just a model using geometry, it does not tell us what gravity is but models it using extrinsic curvature and is our most probable model, not the only one.

We have belief, based on nature, that a body does not move intrinsically --- even a rocket --- something outside must act. If an apple falls, and we exclude all other external sources, what is left we call gravity... and model by Newtonian mechanics in first approximation, Einstein equations in second, X in the future.

But we can retain the first approximation, and calculate the others as corrections. This might be be a litmus test of Paul's assertions, towards belief.

Dear George Dishman,

George>: In that case the question you need to address is why apples fall of trees and accelerate towards the ground. In the flat space of SR, there would be no gravity. You need something additional to SR to explain gravitational acceleration so, in relation to the question Ed asked, what theory do you believe models that and what is your evidence supporting it?

All of SRT is about light; EM radiation. Electric charge and magnetic forces don't need explanation in SRT, am I right? With our latest discussions about gravitational waves, GWs, I came to the conclusion that I only can explain how the LIGO observatories could get a signal if the mirrors don't move. If the distance between the mirrors remains constant then the only way to change the arrival time of light is to slow down and speed up the light in the orthogonal directions. Closer to mass the speed of light is slower. As a result there has to be a gradient in the speed of light. This gradient in the speed of light will have an effect on every object of matter since an orbit of an electron in an environment where the speed of light changes over the position it has with respect to the nucleus has to make it drift unbalanced. That drift will make the mass move towards other mass. You might then think that a neutron should be without mass but when you think this consisting of subatomic particles that have mass but cancel it out then we still end up with sensitivity to a gradient in the speed of light.

GRT models this with the assumption that the speed of light is constant thus then space has to distort. It is the normal solution where GRT distorts space to make curved fields appear straight. When you look into a distorting mirror and suddenly you see your belly disappear then that does not mean that space around your body bulges and that in that bulged space your body only appears fat, like I see it when I look down my body.

So, my evidence supporting it is the results of LIGO that detect only the differential effects and not any large scale movements. This only can happen if there are no large scale space movements and no expansion and contraction of space. We don't have space racing around us with superluminal tangent speed and we don't have space evading from us in superluminal speed. We rotate and we shrink.

Regards,

Paul Gradenwitz

Hi Paul,

PG: All of SRT is about light; EM radiation.

No, SR was all about changing our understanding of the nature of time, the elimination of absolute simultaneity. Time is not a universal background as was thought, it is a measurement made along the worldline of a specific clock. "At the same time" is then a surface normal to the worldline at a specific event. That has a major effect on the way you convert coordinates in one inertial frame to another.

PG: Electric charge and magnetic forces don't need explanation in SRT, am I right?

Not at all. The whole of electromagnetism is still needs an explaination and that is provided by Maxwell's equations (in the classical approach, or possibly Kalusa-Klein theory), and we have a relativistic version taking what we learned about time into account.

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

However, we have come a long way since then and light today is really understood through quantum field theory. That predicts all sorts of behaviour that is inexplicable by classical means, single photon interference and quantum entanglement for example, which have been comprehensively proved by experiment and are the basis of some amazing new technologies.

[Edit - I missed a comment]

PG: This gradient in the speed of light will have an effect on every object of matter since an orbit of an electron in an environment where the speed of light changes over the position it has with respect to the nucleus has to make it drift unbalanced.

Why? I see no logic to that. You didn't accept what I said about stress between atoms where they are bound by Coulomb force and the change in the speed of light must alter the equilibrium separation, but here you want to have a force when there is no other particle involved.

PG: You might then think that a neutron should be without mass ...

I wouldn't think that at all.

PG: .. but when you think this consisting of subatomic particles that have mass.

Why is that even relevant.

What I would point out though is that an electron is a solitary fundamental particle, it doesn't have structure so I wouldn't expect it to be affected by any gradient.

In SR, magnetic and electric fields are not independent. Magnetism is caused exclusively by motion of charges, where motion is relative -- could be both charge and observer, or either.

Dear George Dishman,

I understand what you state about time, but it is closely interwoven with the speed of light. Also relativity of simultaneity is what is assumed about events that are at the moment of their assumed simultaneity on spacelike distance and thus without relation. Only after their information has reached the observer will he select those as simultaneous that appear to him as such. Send a command from the Earth to Mars, then you can tell everybody in the room that, after the time it needs for this command to travel with the speed of light to there, the rover will perform a certain task. But if at that moment a meteorite hits the rover, then you might find out about that only when there is a response back. So between sending and receiving the status of the rover is a complete unknown where only in back sight can be decided what happened simultaneously. SRT works fine. But it is a mathematical description of reality. Only if gravity really is the curvature that GRT describes then gravity has no room in SRT.

Why do electrons and protons attract each other? Does Newton explain why mass attracts? I think no and Neither does GRT. They describe in a mathematical way what is observed. That is no explanation

Maxwells equations don't explain electromagnetism. They describe them. With these equations we have great tools to predict experimental results. They don't make nature to follow the numbers crunched in the computer to solve the equations.

Remember the biggest misfit in physics. QM assumes the energy density of the vacuum to be 10120 times larger than cosmology assumes it to be. When space doesn't care about how much is in it, then QM could be right. But what is vacuum? that is the space between boundaries of matter. The larger that space the more possible modes of EM waves can exist. This means that the larger the volume of emptiness the higher the energy density of the vacuum should be. In a volume with a given energy level of the vacuum we can imagine 2 objects at a given distance. Between them the energy density has to be smaller than outside. That gradient will push them together. Can this be step to an explanation of gravity?

Regards,

Paul Gradenwitz

In SR and quantum mechanics (QM), there is no loss, also when matter can be created and destroyed. This introduced a new thinking, that even two photons (but not only one) can have mass and that mass can have physical significance -- as a new particle, for example.

Surprisingly, Newtonian gravity still applies, as a zeroth-order approximation. This, for example, leads one to hope that, in physics, that GR can be mathematically inserted, also when a new particle is not created, but the two photons exist. Every two different photons have mass, but not every mass appears as a new particle. What makes mass appear? QM is a potential new factor in GR, it seems. Other new factors may exist.

Dear Ed Gereck,

Before I pondered on that gravity could be the push in a gradient of quantum vacuum energy density levels. Electromagnetic waves interact with boundaries like mirrors. If a set of EM waves curls them self so that a boundary is created then the object is a boundary condition in the energy density configuration. With that a certain set of EM modes are restricted. This influences the gradient configuration and changes thus gravity.

In this consideration the creating EM waves, photons, have no mass, but once they have interacted to create an object with a boundary, then that object has mass and reacts to gravity.

Changes in the level of the vacuum energy density can change the propagation speed of light. This makes light bend along mass. Injecting at the boundary of a conic cylinder a lot of different frequencies thus could explain the impossible drive Chinese reported and Nasa is testing.

Regards,

Paul Gradenwitz

Paul Gradenwitz : Thank you. Two different photons, in a colision course or not, have mass that may not become matter. This fact (true) has to be explained and accounted for, gravity-wise. Reactionless drives deserve an explanation within the SM. Still, v < c.

Dear Paul,

PG: I understand what you state about time, but it is closely interwoven with the speed of light.

Light, or any massless particle, travels at the maximum speed allowed by the geometry so light is a useful probe of that but it isn't the cause, it's an effect.

PG: Also relativity of simultaneity is what is assumed about events that are at the moment of their assumed simultaneity on spacelike distance and thus without relation.

Not at all, it applies to the coordinates of all events whether spacelike separated or not, it is purely a consequence of rotating the coordinate scheme.

PG: Only after their information has reached the observer ..

Coordinates values don't depend on the transfer of information.

PG: SRT works fine. But it is a mathematical description of reality.

A mathematical description is an effective form of language, it lets us talk about the reality of the geometry in a quantitative way.

PG: Only if gravity really is the curvature that GRT describes then gravity has no room in SRT.

There is no curvature or any other description of gravity in SR, and the speed of light has the same value everywhere and at all times. To introduce gravity, as I said before, you need something extra beyond SR. Newton's force at a distance was an example but as you know it doesn't work. Curvature of the geometry does.

PG: Why do electrons and protons attract each other?

Electrostatic force which is an exchange of virtual photons. If you want to extend that approach to gravity then you would say the static force could be an exchange of virtual gravitons while a gravitational wave is a flux of real gravitons.

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

• "Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to the stress–energy tensor in the same way that gravitational interactions do."

PG: Does Newton explain why mass attracts? I think no

Yes, it explains it by "instantaneous force at a distance", but that conflicts with SR as nothing can be instantaneous, that's why Einstein set out to find a relativistic alternative.

PG: Neither does GRT.

Of course it does, it explains that the geometry is curved by the presence of mass and matter follow geodesics as in SR or deviates from a geodesic at a rate determined by the force applied to it.

PG: They describe in a mathematical way what is observed.

Exactly, and 'describing what is observed in a mathematical way' is a good definition of physics

PG: Maxwells equations don't explain electromagnetism. They describe them.

Maxwell's equation explain the macroscopic behaviour, photons explain the quantised behaviour. Both are purely mathematical.

PG: The larger that space the more possible modes of EM waves can exist. This means that the larger the volume of emptiness the higher the energy density of the vacuum should be.

A larger number in a larger space implies the same density.

PG: In a volume with a given energy level of the vacuum we can imagine 2 objects at a given distance. Between them the energy density has to be smaller than outside. That gradient will push them together. Can this be step to an explanation of gravity?

No, it is the explanation of the Casimir Effect.

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

Dear George Dishman,

Thank you for your patient answers. I think we have a different opinion about cause and effect. I state that the behaviour of nature is the cause and that the mathematical description is the effect. If nature would have behaved different, or happens to behave different than expected, then the description of nature and the mathematics that goes with it are adapted to nature.

PG: I understand what you state about time, but it is closely interwoven with the speed of light.

George>: Light, or any massless particle, travels at the maximum speed allowed by the geometry so light is a useful probe of that but it isn't the cause, it's an effect.

The behaviour of light is the test to prove SRT and not SRT the judgement if light did listen to the university lectures of how it should behave.

PG: Also relativity of simultaneity is what is assumed about events that are at the moment of their assumed simultaneity on spacelike distance and thus without relation.

George>: Not at all, it applies to the coordinates of all events whether spacelike separated or not, it is purely a consequence of rotating the coordinate scheme.

SRT describes it in that way and is very successful. But the observation of nature is first. And only after observing that you can describe nature the simplest way like that you can continue to accept the theory.

PG: Only after their information has reached the observer ..

George>: Coordinates values don't depend on the transfer of information.

A theory has predictive value once we understand how nature works. But the simultaneity of an event only can be observed if it happens at one point in spacetime. Any other simultaneity observation is assumed under the assumption that its information traveled at the same speed.

PG: SRT works fine. But it is a mathematical description of reality.

George>: A mathematical description is an effective form of language, it lets us talk about the reality of the geometry in a quantitative way.

Yes, I support that. It describes nature, it does not force nature. It is extracted out of the behaviour of nature and will change when better observations lead to an improved description.

PG: Only if gravity really is the curvature that GRT describes then gravity has no room in SRT.

George>: There is no curvature or any other description of gravity in SR, and the speed of light has the same value everywhere and at all times. To introduce gravity, as I said before, you need something extra beyond SR. Newton's force at a distance was an example but as you know it doesn't work. Curvature of the geometry does.

That is what I said in more words than mine. Curvature works in differential form. Integration of these differential equations seems not possible. You need to make a boost. But added to that I also imply that if there is a different description of gravity then it could be that this could have room in SRT.

PG: Why do electrons and protons attract each other?

George>: Electrostatic force which is an exchange of virtual photons.

It is never exchange of virtual particles because that is a mathematical construct. It can be described as such but virtual reality is virtual reality and not reality. In Electronics you use eiω and other imaginary numbers. Electrons never have entered imaginary number space. Extremely effective description of nature with the toolset of mathematics does not make these imaginary spaces real. Again you exchange a mathematical way to describe nature as the cause of nature to follow.

George>: If you want to extend that approach to gravity then you would say the static force could be an exchange of virtual gravitons while a gravitational wave is a flux of real gravitons.

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

• "Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to the stress–energy tensor in the same way that gravitational interactions do."

That all is an attempt to describe gravity.

PG: Does Newton explain why mass attracts? I think no

George>: Yes, it explains it by "instantaneous force at a distance", but that conflicts with SR as nothing can be instantaneous, that's why Einstein set out to find a relativistic alternative.

That was an attempt to describe it. Postulate an instantaneous force at a distance. You repeat that nothing can be instantaneous but that is the core of our dispute about gravity. I state that the cause of a gravity effect never can be on a spacelike separated distance. You disagree with that.

PG: Neither does GRT.

George>: Of course it does, it explains that the geometry is curved by the presence of mass and matter follow geodesics as in SR or deviates from a geodesic at a rate determined by the force applied to it.

It describes how it can be seen as. But if space would curve in reality then the mirrors would have moved by 0.6mm. They didn't. So in the relation between length and speed, GRT assumes the length to change and light speed to be constant where it seems to be a better description if light speed changes and length remains constant. One description is virtual the other description is reality. The theory has to follow nature even if the physicists have problems to understand why and how.

PG: They describe in a mathematical way what is observed.

George>: Exactly, and 'describing what is observed in a mathematical way' is a good definition of physics.

You seem to get it here. It is a definition of physics, not of nature.

PG: Maxwells equations don't explain electromagnetism. They describe them.

George>: Maxwell's equation explain the macroscopic behaviour, photons explain the quantised behaviour. Both are purely mathematical.

They describe things so that they can be used and predicted. They don't explain why. They only explain how they can be described.

PG: The larger that space the more possible modes of EM waves can exist. This means that the larger the volume of emptiness the higher the energy density of the vacuum should be.

George>: A larger number in a larger space implies the same density.

In a volume of 1m3 we can have all the wave modes that fit within the walls. In a volume of 8m3 we can have the wave modes that fit in the 1m3 plus those that fit within 2m length. It is not linear and it results in a nearly square law of gravity.

PG: In a volume with a given energy level of the vacuum we can imagine 2 objects at a given distance. Between them the energy density has to be smaller than outside. That gradient will push them together. Can this be step to an explanation of gravity?

George>: No, it is the explanation of the Casimir Effect.https://en.wikipedia.org/wiki/Casimir_effect

The Casimir effect is the deviation from the gravitational expectation. With the energy density as predicted by Cosmology it is not easy to explain as gravity. With an energy density that is in the order of 10120 higher the view can be different. Coming closer together it seems that there is some quantum effect where gravitational effects stop to be continuous.

Regards,

Paul Gradenwitz

Paul Gradenwitz, George Dishman and all: Teleological (the end justifies the means), teological (god justifies the means), deus ex machina (appears and justifies the means), Platonic models, and other models, have always being used by humans to justify to themselves what they think is seen.

But physics says otherwise, neither we actually see nor we need to justify it -- it is what it is. Also in maths.

It is a habit from too much humanities, as if history could be a good teacher. Well, the E and B fields are not independent, all accelerated particles (charged or not) have a motion that can be transformed to uniform, that can be transformed to a stationary point, so that any arbitrary motion is in SR, not just inertial.

Physics assumes natural causes for everything, to finer and finer detail, as well as bigger. So, in that search, we have to assume that we don't know what we don't know.

There is always the certainty on physics that we are leaving something out, but that this is what we could explain, and other will continue. It is naive to think that we can explain correctly, in a few 100 or even 10,000 years, what nature took tens of billions of years to build, and before, and after. Physics can, and there are models even for before the big-bang, and after, but we must keep the certainty that we are leaving something out, in our human view, whatever we call it, or don't.

Dear Ed Gerck,

That also is about what I wanted to convey to George Dishman. The Gravitational Wave observatory results have shown me that GRT is not correct in how they try to describe gravity. Already in the terminology of their measurement data: strain, they show that they think in length variation per unit of length. But all I can conclude is that the results only are in agreement with mirrors that don't move and light speed that is different in orthogonal directions. Although that is in agreement with the differential description of GRT it is in disagreement with the assumption that space changes shape.

Regards,

Paul Gradenwitz

Paul Gradenwitz: All the assumptions have to agree, and it is highly unlikely that LIGO or Caltech would make an error there. There are other arguments regarding an interferometer as well, such as modes of the field. Everything is open for another interpretation, but the subject is very old, and tried by different groups, in different countries, while there is no disagreement of note.

Hi Ed,

EG: it is highly unlikely that LIGO or Caltech would make an error there.

It's more to do with the outreach versions presented to the public. I'm intending to write something regarding the transverse traceless gauge which I think is favoured by those working in the field and another conversation has veered into that topic, but it's quite complex and too hard to explain in a few posts.

George Dishman : Outreach versions can never be right, can at most be motivational for high school audiences, which is the public they write for. RG discussions seem to fit in the middle.

Dear Ed Gerck,

Ed>: All the assumptions have to agree, and it is highly unlikely that LIGO or Caltech would make an error there. There are other arguments regarding an interferometer as well, such as modes of the field. Everything is open for another interpretation, but the subject is very old, and tried by different groups, in different countries, while there is no disagreement of note.

Results of GRT should be valid in every coordinate system. When you sit in the train and see the station move backwards, then that observation is as valid as that you assume that you move forward and the station remains at rest. When two observers see the station moving, one forward and one backward, and a third observes it moving downward from an elevator, then it becomes more logical to agree among the observers that not the station moves but each of the three observers moves in a different direction.

The GRT equations are differential equations. The calculated strain is a correct solution of these equations. Only, is the coordinate frame where the mirrors keep their distance, or the frame where the mirrors change their distance, during GW passage the more logical correct representation. The outreach information is that space expands and contracts. That is in agreement with the outreach that space expands since the Big Bang. For me the interpretation where space remains constant and the speed of light changes and where space never expanded but matter shrinks is closer to reality. Both can be described by the same GRT equations.

Regards,

Paul Gradenwitz

Ed, I agree entirely. My paper would be a cautionary tale in respect of taking the material as gospel and extrapolating it too far. It also has the effect of showing that the common concept of there being a "fabric of space" is a coordinate artefact, again produced by treating helpful visualisations as reflecting reality.

Dear George Dishman,

George>: It also has the effect of showing that the common concept of there being a "fabric of space" is a coordinate artefact, again produced by treating helpful visualisations as reflecting reality.

Do you think that space expands and that in the Hubble flow the galaxies retreat from our position with a velocity higher than the speed of light and that light, traveling towards us from far redshift distances in its path first moved away from us before it started to close in on us? Or is that only helpful visualisation?

Regards,

Paul Gradenwitz

Dear Paul,

PG: Do you think that space expands ..

That is a layman description which may sometimes be useful but often causes problems, it implies that "space" has properties like a substance.

PG: in the Hubble flow the galaxies retreat from our position with a velocity higher than the speed of light

Again, the terms invoke images that may be inappropriate, such as motion of the galaxy through the 'substance' of space. Instead I always say that the proper distance to such such galaxies is increasing at a rate greater than 1 light year per year which emphasises that the change is occurring throughout the intervening gap, and I state the rate of increase as "1% per 140 million years" to emphasise that it isn't a speed, it doesn't even have the right units.

PG: and that light, traveling towards us from far redshift distances in its path first moved away from us before it started to close in on us?

For a galaxy far enough away, the expansion means that the light is moving towards us by 1 light year per year but after each year it has farther still to travel. Plot the proper distance versus time and you get the usual "peardrop" locus.

PG: Or is that only helpful visualisation?

All of those are only visualisations and dependent on the choice of coordinates. The actual scientific description is the FLRW metric. Look at Ned Wright's tutorial and see how different conformal coordinates look compared to proper coordinates, yet they describe the same universe:

http://www.astro.ucla.edu/~wright/cosmo_03.htm#MSTD

There's a lot more on this in this classic paper:

Article Expanding Confusion: Common Misconceptions of Cosmological H...

Dear George Dishman,

I agree with you that the expansion of space is a matter of coordinate choice. I know the peardrop locus of the lightcone with proper distance. Why you call it in units of time where you have time as a length axis related to the speed of light and then tell me the units are not correct?

In the proper distance coordinate system the distance of objects increases. In the comoving coordinate system the distance remains constant. What is important is in the proper distance coordinate system what happens with the distance of the mirrors. You emphasise that the change is in between the objects. Space is added in between. But we know that the proper distance between galaxies in galaxy clusters is not altered. The gravity there keeps them at a proper distance. So I would assume that the same is valid for the atoms of earth. The added space in between them does not change their distance. But the mirrors are free to follow and the added space between them would make the mirrors move away from their mean position.

So, in the same coordinates where space is seen as expanding the mirrors should swing by the strain amount out of their resting position. They didn't do that.

George>: I state the rate of increase as "1% per 140 million years" to emphasise that it isn't a speed, it doesn't even have the right units.

Compare that with the quote of your linked paper:

If recession velocity were meaningless we could not refer to an “expanding universe” and would have to restrict ourselves to some operational description such as “fainter objects have larger redshifts”. However, within general relativity the relationship between cosmological redshift and recession velocity is straightforward. Observations of SNe Ia apparent magnitudes provide independent evidence that the cosmological redshifts are due to the general relativistic expansion of the universe. Understanding distance and velocity is therefore fundamental to the understanding of our Universe.

(15) (PDF) Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe. Available from: https://www.researchgate.net/publication/1794580_Expanding_Confusion_Common_Misconceptions_of_Cosmological_Horizons_and_the_Superluminal_Expansion_of_the_Universe [accessed Apr 03 2019].

Regards,

Paul Gradenwitz

Comparison of New and Old Thermodynamics

1. Logic of the Second Law of Thermodynamics: Subjectivism, Logical Jump, Interdisciplinary Argumentation.

2. New thermodynamics pursues universality, two theoretical cornerstones:

2.1 Boltzmann formula: ro=A*exp(-Mgh/RT) - Isotope centrifugal separation experiments show that it is suitable for gases and liquids.

2.2. Hydrostatic equilibrium: applicable to gases and liquids.

3. The second and third sonic virial coefficients of R143a derived from the new thermodynamics are in agreement with the experimental results.

3.1. The third velocity Virial coefficient derived is in agreement with the experimental data, which shows that the theory is still correct when the critical density is reached.

4. See Appendix Pictures and Documents for details.

Arnaud,

There are two main problems with mathematical physics (that occur to me at the moment).

Firstly, mathematicians are often keen to be able to produce "bombproof" proofs of their results. They want their results to be elevated to the status of theorems, on the assumption that if something is a theorem, it's mathematically proved and therefore can't be wrong.

Unfortunately, in their quest to be able to claim a proof of a result, they sometimes have to change the initial assumptions so far away from physical reality (the "spherical chicken" problem), that the final result becomes dependent on the form of the initial unrealistic idealisations, and disappears or changes form when we use more realistic assumptions.

This can produce the slightly perverse situation that in some branches of mathematical physics, the easier it is to elevate a result to the status of a theorem that can't possibly be wrong, the less likely it is to be correct physics. In some cases, the dependency on unrealistic idealisations ("X is true only if unrealistic idealisations are made") means that the proof of a result inadvertently amounts to a proof that the result cannot be correct physics. (for instance with SR, SR is provably the only relativistic answer to inertial physics if spacetime is flat and particles are assumed to have zero curvature ... but since the proof requires particles to have zero curvature, and the principle of equivalence says that massed particles cannot have zero curvature, the proof works in reverse as a proof that real-world physics cannot exactly conform to the SR equations but must obey Something Else).

When it comes to questions of "can you go faster than the speed of light" under general relativity, while you shouldn't (on principle) be able to overtake your own light along the same path "from behind", it seems perfectly possible to travel faster than background lightspeed.

This would in fact appear to be the default behaviour it you throw yourself into a black hole. If the gravitational differential gives you an inward velocity of v=c when you reach the horizon, and horizon physics is not locally singular, and you have an even greater inward velocity once you have passed through the horizon, then you will be successfully travelling at more than background lightspeed. However, you will not be overtaking your own light, whose inward velocity is even greater.

The reason people get this stuff confused is because for convenience, we tend to talk about the speed of light, and we define that speed as a round-trip quantity ... whereas if you want to work on metric engineering problems, you have to ditch the idea of round-trip speeds and go back to using proper one-way velocities for lightsignals. To ask, "is it possible to travel faster than background c?" in a given situation, you normally have to deal with light-velocities, and accept that a given point in spacetime supports multiple light velocities depending on signal direction (the nominal velocity of light travelling into a black hole is not the same as the nominal velocity of a signal at the same position aimed outwards).

But this makes it more difficult to generate proofs, so mathematicians tend to fall back on the simpler concept of c="round-trip speed". If you say that c=lightspeed, then you can prove all sorts of things ... but many of them will not be physically correct. For instance with c as an averaged direction-independent property that has a single value at each point in spacetime, the speed of light at a black hole horizon becomes zero, and we can "prove" that since nothing can travel faster than c, that nothing can ever really fall into a black hole.

In a more realistic model, things should find it very easy indeed to fall into black holes!

What's gone wrong with the logic here is that people have recognised that if spacetime is flat, relativity does not allow us to physically identify offsets in the speed of light, so there's then no such thing as an offset in light velocity (it's no longer considered a physics "thing"), and we then go on to reject the very concept of a one-way velocity and replace it with the idea of a round-trip speed, and GR then inherits some of the resulting SR conventions.

Trouble is, in curved spacetime, variations in one-way light velocities are physically identifiable. If you move a star, it should exert a gravitomagnetic dragging effect, and if you move a block of perspex, you can race two parallel beams of light and physically measure the one-way difference between the SoL in a moving black and the corresponding SoL in a stationary block alongside. The lightbeam in the block travelling towards the target reaches its destination first.

So beware mathematical proofs based on over-idealisations, and on known behaviour and principles that later turned out to be wrong (like SR's "law" of global c-constancy - it's not real).

The mathematician dabbling in physics may be more interested in provability than truth. Some things may be true but not provable; in physics, others are provable but not true. SR and a load of related proofs fall into the "provable but not true" category, as the "proofs" often depend on counterfactuals, or on simplifying assumptions that violate other fundamental principles that we rely on.

Secondly, mathematicians doing physics sometimes overlook the quirks and shortcomings of mathematical syntax.

We believe with good reason that it shouldn't be possible for someone to be able to travel faster then their own light (along the same path, at the same time), because, if they did, all sorts of craziness happens. For starters, it's difficult to see how their atoms could remain in equilibrium if signals travelling across their structure had no legal return path.

So we have the statement "you cannot travel faster then the speed of light", and an associated mathematical expression, "vv", "the speed of light is always faster than the speed of an object".

This statement implies that lightspeed is not fixed but variable, that the velocity of a body is the dominant quantity, and that c, lightspeed, is expected to adjust itself accordingly.

With the first statement we tend to get an assumed fixed global speed of light and a lightspeed barrier, with the second we tend to get a variable c, with no limits on velocity.

While we can say that actually, particle accelerators do show a lightspeed limit, ruling out c>v, there is a third option for which there is no obvious corresponding math notation, the idea that there's a mutual interplay between lightspeeds and object velocities.

With Option One we tend to end up with a fixed lightspeed barrier, special relativity and a Minkowski metric, with Option Three, we instead get a relativistic acoustic metric. With the acoustic metric approach we get proximity-dependent lightspeed dragging and "hybrid" behaviour: a particle accelerator can only directly accelerate a particle to a speed less than cACCELLERATOR, but cPARTICLE is greater, and the particle itself can then throw off a daughter particle that (initially, at least) travels at less than the local velocity of light, but more than the background velocity and speed of light. The daughter-particle radiation then shows up in descriptions as Hawking radiation.

The problem with the poverty of conventional mathematical syntax is that it encourages the casual physicist to write "v

Oops, stupid typos! you probably spotted them, corrections here in bold text:

" If we say "AA", it implies instead that A is the known or dominant quantity, and that it is now B's responsibility to adjust it's own possible range of values to accommodate A's value or range. "

That makes more sense. Apologies for any confusion.

I explained here and elsewhere on the danger, such as confirmation bias, of following one's opinion, or what one can imagine -- that it is better to focus on questions than (supposed) facts or (outdated) quotes. I give an example that seems far removed, but harbors the same issue.

It comes from the theory and the practice of tri-state logic design and as taught in EE in good universities. And, in Physics, let us remind ourselves that there is a notion of right and wrong --- it it agrees with Nature, it is right; but wrong otherwise. Opinions and voting do not matter in Physics, Maths, EE, and son on.

Everyone should know this, and it can change lives, can bring in new sound ideas, did influence logic, all as explained below, in different logic levels, as well.

In RG, for example, we can use it. Some answers are YES, some NO, and some are DON'T CARE. You have three logical states, but RG gives a point for any answer!

Is RG one state? Always YES? No, it's a multi-state computation, where each answer is counted according to different values, and any answer has more than three states it can be found, but RG shows only one, a point.

Go get your point, now, carelessly -- one might think, any anwer is a point -- and a disagreement gives me more points, more answers, more traffic. But, in reality, RG is part of life and life is a school. Being an RG-whale does not make one better, it actually can disqualify -- as all one can do... in life, evaluation follows several logic states, not just Boolean YES and NO.

Same with a tri-state IC. The final state of each chip IC is not just YES and NO, it can also be X. And all is computed in tri-state, one can't mix-in two-state chips, and just imagine that the end is somehow tri-state because the last chip is tri-state.

If you are paying attention, the array of tri-state chips can connect to another tristate device, compatibly. In EE, one can use even 12 states, or more, consult the IEEE for information and standards.

Silicon Valley would not exist otherwise, literally, and tri-state is a TM. It changes lives, and give sound ideas one can follow, and trade-mark, and advance technology along a more sure path -- that Physics also follows -- that of the unknown.

Boolean logic is two centuries behind, cannot compete? No, it just doesn't agree with Nature, as already measured in Physics, EE, Maths, and so on. Time to catch-up, why it makes sense in Physics, for example, to follow Minkowski SR --- that it agrees with Nature more completely, and avoids "paradoxes."

Deleted research item The research item mentioned here has been deleted

I tend to see things through QM as a litmus test.

Reality is observer-dependent, in QM. Starting with the Heisenberg principle, observer and experiment cannot be dissociated. There is no objectivity in QM (objectivity would be observer-independent, contradicting QM).

Above we show, however, that there is a common coherent abstract view one can pursue in QM, and how it EXPANDS EM, SR, GR and other areas, even no SR, with logical VALIDITY.

If you want to explore spacetime curvature via QM, you might like to look at Khavtgain Namsrai's paper:

Article Space-time structure near particles and its influence on par...

also published as a section in his 1985 book:

Book Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics

Namsrai uses a stochastic approach to QM to model the position of an object as a cloud of potential positions, with the cloud density naturally varying with the probability of finding that location for the particle.

As we increase the number of samples, the cloud builds up into an increasingly accurate representation of a classical field around the particle's centre-of-probability. This classical field represents that field shape that, when quantised, would give the QM statistics. It gives the apparent classical shape of spacetime around a massed particle that would quantise to give QM behaviour, and therefore the properties of classical field theory that would be required for classical field theory to agree with quantum field theory. It's a way of reverse-engineering classical field theory from QM.

In Namsrai's exercise, the shape of spacetime around a moving particle looks like a "Witches Hat" with a tilted rounded peak, , smoothly transitioning from a tilted conical sort of throat to a "brim" that's more in accordance with the background shape of spacetime in the region.

The field expresses the extension of the particle's mass and momentum into the surrounding region, and since it expresses the particle's mass and momentum (mass-field plus momentum-field), it's technically a gravitational field (the overall gravity-well shape), with a gravitomagnetic field component (the tilt of the throat, or "hat" peak).

So a QM-compatible description of classical physics requires particles to have associated gravity-wells, and also associated gravitomagnetic curvature when they have relative motion.

This is in broad agreement with the principle of the equivalence of inertial and gravitational mass, but disagrees with the simplifying assumption used by special relativity that particles have zero associated curvature and that their relative motion has zero effect on the shape of spacetime. Both QM and physical experiment (Fizeau, etc.) say otherwise, that the motion of particles should (and according to experiment, does) drag nearby light, warping the lightbeam geometry.

The QM-based approach gives a classical theory in which the shape of spacetime varies dynamically with the presence and motion of matter, which gives an interactive "relativistic acoustic metric" instead of the fixed "Minkowski metric" of special relativity.

So, if you want to apply a QM-compatible approach to classical relativistic field theory, you probably shouldn't be trying to make it fit special relativity.

SR is not fundamental (except as an idealisation), and Minkowski spacetime disagrees with both QM, the PoE, the GPoR, and with long-standing experimental data. It's a simplified "flat" approximation, but it isn't, and logically can't be, the correct geometry.

Ed Gerck: " I explained here and elsewhere on the danger, such as confirmation bias, of following one's opinion, or what one can imagine -- that it is better to focus on questions than (supposed) facts or (outdated) quotes. "

Okay, I'll play: Here's a fun question: Given that SR/Minkowski spacetime assumes a geometry in which the presence and relative motion of particles have zero effect on light propagation ... and that the principle of equivalence and the general principle of relativity both say that this shouldn't be true, and that experimental evidence seems to confirm that it's not true ...

... if we tentatively try assigning non-zero curvature to particles, in accordance with the PoE, the GPoR and experimental evidence ...

In other words, what is the relationship between an assumed amount of particle curvature and the resulting calculated divergence (if any) from SR?

All: First, I suggest to see the video by Robbert Dijkgraaf in https://www.youtube.com/watch?v=6oWLIVNI6VA

For a metaphor, a finger may type D on a keyboard, but G was meant. The D was an illusion, but made real by the keyboard. Error-correcting codes may encode all possible futures as the one real possibility, e.g., forming a n-step circle of maximum probability around each letter on a QWERTY keyboard, so that for a 2-step circle if one types D then it is correctable to G, but if one types L it is NOT correctable to G.

This can prevent "microscopic" folding of past, present, and future from "macroscopically" affecting reality, and is represented in reverse by a large number of birds doing a macroscopic pattern in the sky, albeit microscopically avoiding it.

The B field in EM, is another example -- it is in all cases generated by movements of charges, using SR as fundamental, so that macroscopically we do "see" an external magnetic field B, while there is no internal magnetic monopole or dipole, intrinsically.

All: A block may be our non-constructive idea of mathematics. See

Deleted research item The research item mentioned here has been deleted

I allow myself to enter in this discussion :

"on the possibility of v > c in Einstein General Relativity".

I have developped a new theory of gravitation called "Dynamic Medium of Reference" --> see my project "A new theory of gravitation" and my article on my profile.

In the frame of my theory the gravitational waves propagate at the speed of light BUT the gravitational field propagates much faster than the speed of light.

Best regards,

OP