Relativity+

[BenTheMan]

I'm glad to hear that you agree, because your remarks taken at face value looked false to me. It appeared as though your position was that time is not treated differently from space in any respect in modern physics. But of course, it is treated differently in certain respects in SR, and even moreso in QM.

Certainly time is treated differently. But not in this manner:

And while the past is the integral of all nows, now lasts for no time at all. Because time needs events, and if there were only intervals and no events, there wouldn’t be any time. When you take away the events and the motion, you take away the time.

This is incredibly wrong on so many levels. "Time" is not a property of the events in the universe, it is a property of the universe itself---we have time because we live on a Lorentzian manifold, just as Einstein told us. Farsight seems to think there can be space-time without time. Treating time differently in THIS manner is basically trashing ALL of Lorentz Invariance.

This whole thread needs to be moved into the pseudo-science forum.

 

[Farsight]

Einstein also said:

In his response to Godel's paper in the Schilpp volume, Einstein acknowledged that "the problem here disturbed me at the time of the building up of the general theory of relativity." This problem he described as follows: "Is what remains of temporal connection between world-points in the theory of relativity an asymmetrical relation (like time, intuitively understood, and unlike space), or would one be just as much justified to assert A is before B as to assert that A is after B? The issue could also be put this way: is relativistic space-time in essence a space or a time."

I've said repeatedly that Lorentz Invariance isn't broken: we will always measure c at 300,000km/s and the same laws of physics will apply. I also quoted this in my post 28:

Relativity has been one of the most successful theories of the last century and is a cornerstone of modern physics. This review focuses on the modern experimental tests of one of the fundamental symmetries of relativity, Lorentz invariance. Over the last decade there has been tremendous interest and progress in testing Lorentz invariance. This is largely motivated by two factors. First, there have been theoretical suggestions that Lorentz invariance may not be an exact symmetry at all energies. The possibility of four-dimensional Lorentz invariance violation has been investigated in different quantum gravity models (including string theory [185, 107], warped brane worlds [70], and loop quantum gravity [120]), although no quantum gravity model predicts Lorentz violation conclusively. Other high energy models of spacetime structure, such as non-commutative field theory, do however explicitly contain Lorentz violation [98]. High energy Lorentz violation can regularize field theories, another reason it may seem plausible. Even if broken at high energies, Lorentz symmetry can still be an attractive infrared fixed point, thereby yielding an approximately Lorentz invariant low energy world [79]. Other ideas such as emergent gauge bosons [54, 189, 161, 80], varying moduli [93], axion-Wess-Zumino models [30], analogues of emergent gravity in condensed matter [40, 238], ghost condensate [34], space-time varying couplings [177, 50], or varying speed of light cosmologies [219, 209] also incorporate Lorentz violation. The ultimate fate of Lorentz invariance is therefore an important theoretical question.

And whilst I'm not querying Lorentz Invariance, other establised and reputable physicists are. Which means your Lorentz Invariance objection is invalid.

 

[BenTheMan]

True or false. This quote comes from "Time Explained".

And while the past is the integral of all nows, now lasts for no time at all. Because time needs events, and if there were only intervals and no events, there wouldn’t be any time. When you take away the events and the motion, you take away the time.

This quote, if written by you, betrays your ignorance of Lorentz Invariance. Lorentz Invariance is more than just having c measured the same in every frame---this is only the naive interpretation.

 

[Farsight]

I said that, it's in the essay. I also know what Lorentz Invariance is. What's the problem? Would you prefer it if I refined my clean crisp layman's wording somehow? You seem to be trying to make a meal out of thin gruel here.

How many times have I got to say it: Lorentz invariance still holds, and even if it didn't, that's insufficient cause to disregard the essay. See my post above. And look at your justification involving rotation in Minkowski "space". Your objection uses an axiomatic time is a Dimension argument to try to refute my challenge to the time is a Dimension axiom that you hold dear. Let me make it clear: we measure time, therefore it is a dimension, a measure. We treat it like a Dimension as per space where we have freedom of movement, but not as a Dimension. The difference between the d and the D and between the like and the as is crucial, and you're overlooking it.

And saying "it destroys GR" is no argument either. String theory isn't about strings any more. And you said the maths is ten years behind remember? If this destroys General Relativity, your String Theory get shredded twenty years ago.

 

[BenTheMan]

I said that, it's in the essay. I also know what Lorentz Invariance is. What's the problem? Would you prefer it if I refined my clean crisp layman's wording somehow? You seem to be trying to make a meal out of thin gruel here.

Farsight---this quote is not "thin gruel". In some sense it sumarizes your argument. You have imposed an interpretation on time that is not consistent with the idea of Lorentz Invariance.

How many times have I got to say it: Lorentz invariance still holds, and even if it didn't, that's insufficient cause to disregard the essay.

This is not an admission from you, this much is clear. But also simply saying "Santa Clause is real" doesn't make it so. You are interpretting time in a manner that is not consistent with Lorentz Invariance. Specifically, there CAN be time in an otherwise empty universe. Time is NOT defined by events. Time is a measure of one of the dimensions of a four dimensional Lorentzian manifold. It is not merely the "integral of all nows", as you put it.

And look at your justification involving rotation in Minkowski "space". Your objection uses an axiomatic time is a Dimension argument to try to refute my challenge to the time is a Dimension axiom that you hold dear.

I am trying to clarify to you the reason why we believe that time is a dimension, which you obviously do not know. And because you do not understand WHY physicists believe that time is a dimension, you have no basis whatsoever to criticize this concept. Show me how your ideas can possibly be consistent with the idea of Lorentz Invariance.

Let me make it clear: we measure time, therefore it is a dimension, a measure. We treat it like a Dimension as per space where we have freedom of movement, but not as a Dimension. The difference between the d and the D and between the like and the as is crucial, and you're overlooking it.

Perhaps you would care to explain this further, as every time I have tried to read it, it has made my head hurt.

And saying "it destroys GR" is no argument either.

I would concede this point if you hadn't started your post with "I have always held Einstein in high regard...". The worst thing about all of this is that you don't even understand that you are basically shitting on Einstein's ideas.

String theory isn't about strings any more. And you said the maths is ten years behind remember? If this destroys General Relativity, your String Theory get shredded twenty years ago.

If you would like to quote me out of context, then so be it. If you would like to make an indictment of string theory in another thread, then start one. However, you are even less qualified to make these statements about string theory than you are to talk about time.

Your ideas kill Lorentz Invariance, which is the essence of General Relativity. String Theory correctly reproduces general relativity in the IR limit, and is manifestly Lorentz Invariant. There are people who are paid to research string theory (I am one of them), but I have never been to a conference or read a serious scientific article on "RELATIVITY+". We could start a thread called "String Theory vs. RELATIVITY+", if you like.

 

[Farsight]

The interpretation I'm putting on time is the one Einstein eventually reached during his Princeton years with Godel. It's different to the Minkowski block universe and worldlines. These are still usable, but need to be taken less literally, with clear distinction made between mathematical space and real space. Re your request for further explanation:

The word dimension used to mean measure. You could measure the height, width, and depth of an object. You could also measure its mass and its temperature. Temperature used to be thought of as a dimension, and mass is still generally considered rather fundamental. But we'd doubtless agree that temperature isn't a "Dimension" because it's a derived effect of atomic or molecular motion, be it the kinetic motion of the atoms of an ideal gas, or the various motions within bonds. What I'm saying is that time is similar. It's a derived effect of motion, or change, or events. We compare motions using a scale we call time, but we can't move through this measure of motion, so it's different to the space dimensions where we can. Yes, we can treat the time dimension like the space dimensions, but not the same as the space dimensions. Einstein wondered if spacetime was a space, I think he was right.

My ideas don't kill Lorentz Invariance. It's just a subtle shift in interpretation. If that makes you feel the maths is wrong, the maths can catch up, it's not a problem for string theory so why is it a problem for relativity? General Relativity didn't "destroy" Special Relativity. General Relativity wasn't destroyed by the realisation that The Principle of Equivalence does not apply to a proper gravitational field, which is the only sort there is. Theories grow, evolve, improve, they move on.

Now can you move on and actually read the essays to give that rational feedback you said you'd give?

PS: Of course you've never been to a conference on RELATIVITY+. This is the start of it. You're privileged to be here. Make the most of it. If you wait until there are conferences on it you'll be kicking yourself for wasting even more years on String Theory instead of getting in on the ground floor of 21st Century physics.

 

[Farsight]

Can we try to keep this an alpha thread please? Pete, can you assist by changing the title?

 

[BenTheMan]

Can we try to keep this an alpha thread please? Pete, can you assist by changing the title?

Farsight you are not sticking to the alpha rules yourself. You attacked string theory, which has nothing to do, and will never have ANYthing to do, with your theory.

 

[BenTheMan]

The interpretation I'm putting on time is the one Einstein eventually reached during his Princeton years with Godel.

1. Why would I care what Einstein thought in 1950?
2. Reference? It was Minkowski who showed Einstein how to formulate his ideas on a Lorentzian manifold, and I was never aware that Einstein changed his mind.

Yes, we can treat the time dimension like the space dimensions, but not the same as the space dimensions. Einstein wondered if spacetime was a space, I think he was right.

This is the only thing that you've said so far that I've agreed with. Space-time IS a space, and we have known that for a long time---if this is all that RELATIVITY plus is, then you are about 90 years late. Minkowski showed Einstein how to do all of this on a manifold in 1919, I think. But this is not consistent with the other quote of yours that I cut and paste.

Specifically (this is me pointing out the flaws in your logic), IF space-time is a space, the time is a property independant of any matter that you may put in that space. If there was a universe that had no matter, it could still have time because time is a dimension. Time is a property of space-time.

If that makes you feel the maths is wrong, the maths can catch up, it's not a problem for string theory so why is it a problem for relativity?

There is no way that you can justify your position using this quote. The only reason you think the maths are behind your theory is because they specifically disprove it.

If you wait until there are conferences on it you'll be kicking yourself for wasting even more years on String Theory instead of getting in on the ground floor of 21st Century physics.

I'd rather shoot myself in the head.

 

[BenTheMan]

Now can you move on and actually read the essays to give that rational feedback you said you'd give?

Why read your whole essay if I can find one scentence that is patently wrong?

 

[temur]

Let me list some points of Relativity+ and give comments to each.

+ Time is not space. It is true not only in R+.

+ We compare motions using a scale we call time, but we can't move through this measure of motion, so it's different to the space dimensions where we can. The same as the above point.

+ Time is a dimension, but not a Dimension. The same as the above, assuming that Dimension means that we can "move through it".

I don's understand why this makes R+ different from GR, since GR also treats space and time differently. Correct me if I am wrong, but you only changed some wordings, like introducing dimension and Dimension.

Is Relativity+ merely a shift in interpretation or does it have a potential to make predictions different than GR?

 

[Farsight]

I'd say it's a shift in interpretation, temur, but it does rather depend on who's doing the interpreting. If you read BenTheMan's posts, he seems to consider the time dimension to be very close to the space dimensions, whilst perhaps yourself and pryzk don't. And from what I've read, it's a shift in interpretation that takes us closer to Einstein's own eventual interpretation in the fifties.

One prediction that's interesting concerns black holes. Rather than having a central singularity with infinities that "blow up" the GR maths, c is zero at the event horizon, and the black hole is returned to the earlier Russian interpretation of a "frozen star". This means it can have no charge and no spin, and is the closest you can get to "pure energy". Obviously this isn't a particularly good prediction because we can't test it directly.

Another predicition is no gravity waves. The stress + tension "toy model" which depicts gravity as tension opposing mass/energy stress means a travelling stress like a photon is accompanied by a tension wave, but you can't have a tension wave on its own. If you could move a planet very quickly you'd see a gravity change, but not a gravity wave. This means gravitons are definitely out. But again, these are a negatives, and not ideal.

 

[Farsight]

1. Why would I care what Einstein thought in 1950?

Because he was the originator of General relativity and a smart guy. I care what he thought.

2. Reference? It was Minkowski who showed Einstein how to formulate his ideas on a Lorentzian manifold, and I was never aware that Einstein changed his mind.

He was unhappy about it at the time, but accepted the value when formulating GR, then had doubts again later in life. Like in 1950. But you don't care.

This is the only thing that you've said so far that I've agreed with. Space-time IS a space, and we have known that for a long time---if this is all that RELATIVITY plus is, then you are about 90 years late. Minkowski showed Einstein how to do all of this on a manifold in 1919, I think. But this is not consistent with the other quote of yours that I cut and paste.

I don't think you do agree actually. Spacetime is a space. By this Einstein meant a real space. Not a mathematical space. There are no actual world lines, there is no actual block universe. These are mathematical abstractions with no actual existence in the real space that's out there.

Specifically (this is me pointing out the flaws in your logic), IF space-time is a space, the time is a property independant of any matter that you may put in that space. If there was a universe that had no matter, it could still have time because time is a dimension. Time is a property of space-time.

Your argument here is still axiomatic. You're saying I'm wrong to say time isn't a Dimension because time is a Dimension. And your logic is badly flawed. Come on, if spacetime is a space it has no property of time. You can introduce as much matter as you like, but if it's fixed, unmoving, there is nothing that you can call time. It's not until you also introduce some events or change or motion that you then obtain the derived effect that you call time.

There is no way that you can justify your position using this quote. The only reason you think the maths are behind your theory is because they specifically disprove it.

I do justify my position. You criticise me on the maths, but you're doing string theory even though you yourself said the maths is ten years behind.

Why read your whole essay if I can find one sentence that is patently wrong? ...I'd rather shoot myself in the head.

Your attitude is unscientific. You should read all the essays and see if they offer anything of value. To be so hostile when you haven't read them just isn't sensible. And RELATIVITY+ isn't patently wrong. You are.

 

[przyk]

Imagine you've got twins A and B standing at your desk laden with their rulers and clocks and video recorders and other equipment. They each go off to their assigned black-box space capsules, and return much later.

Twin A is noticeably older now, with grey hairs and creases round his eyes. He demonstrates to your satisfaction that according to his measurements seven years have elapsed, during which time he has continuously measured c to be 300,000km/s. He therefore calculates that since you were all last together light has travelled seven lightyears.

Twin B however is not noticeably older. But he can demonstrate to your satisfaction that according to his measurements, only one year has elapsed, during which time he has continuously measured c to be 300,000km/s. He therefore calculates that since you were all last together light has travelled one lightyear.

At this point an argument breaks out between the twins. One insists that light has travelled seven lightyears, the other insists that light has travelled one lightyear. They say they can't both be right, because the speed of light is constant. They ask you to reveal which one is right, and wonder if you'll say that Twin B was sent on a fast round trip at .99c and didn't notice the acceleration because of the drugs. You say no, and explain that even if this were so, the explanation would employ the current mutually-shared reference frame as a preferred or absolute reference frame, and would say that both lightpaths were actually seven light years long.

Instead you reveal that twenty years have elapsed, and you're on a space station in a parking orbit around Cygnus X1. Each twin has been on a ride round the hole. And on Earth, a hundred years have elapsed.

There can be no preferred frame, not this one, not Earth's. There is no definitive lightpath length. And that means c varied across those frames, even though inside them it never did.

No-one ever said the path taken by light was invariant - just that the ratio (distance travelled)/(time taken) was constant across all frames. Twins A, B, and the station commander could all very well have witnessed the same particle travel (say between a source and detector) a distance of seven, one, and a hundred light years in their respective rest frames in seven, one, and a hundred years respectively. If the people involved understood relativity, they would not make such simplistic claims as "light has travelled X distance, period", as if this wasn't frame dependent.

I guess we'll have to agree to differ on that. The Lorentz invariance is still there. It's not a fundamental law, it's just the postulate that got SR going, and describes how you see the world through your reference frame. When you step back from the reference frames and see them all together, you get the big picture and you see why you always measure c to be 300,000km/s.

See them all together and you get the Poincaré group.

Because light defines your time.

What is that supposed to mean?

Because spacetime is a space.

What is this supposed to tell me?

Then you get to the real heart of relativity.

The heart of relativity is Lorentz invariance, and it explains the observed invariance of c. I've made this claim a few times but you've never asked me to justify or otherwise responded to it.

It's like the Principle of Equivalence that gave Einstein the idea for GR. It doesn't hold, but it doesn't break GR.

The equivalence principle doesn't hold? This is news to me.

IMHO Einstein knew all this stuff but was somewhat marginalised later in life. Maybe if he'd been younger he might have made more of it. I can't be sure.

Do you have references for this?

Not quite. Opinions tend to vary, but a common theme is that we move forwards through time at one second per second and can increase this via relativistic effects, but we can't or don't as yet know how to move backwards through time.

Then they're keeping their minds open, and you were arguing about little more than the terminology.

Trust me on this. If you want an IT disaster on your hands just give your variables, subroutines, functions, programs, files and tables meaningless names.

Because names have intrinsic meaning, or because humans get confused if names, once agreed upon, are not used consistently or at all?

Actual as opposed to mathematical, I guess. In physics we're trying to understand how the world works, what's there.

Physics is about modelling reality.

Look at the opening paragraphs of TIME EXPLAINED where I talk about our senses and how I'm trying to "look beyond" what we see or hear or smell.

Science does not deal with the undetectable.

I'm trying to see what's there, and I can't see any time there. The block universe isn't there.

And you were just going on about looking beyond what your senses detect? No-one ever claimed "time" was a physical object that could emit or reflect light.

Reference frames are abstract things, we might look through them, but they aren't actually there either.

Reference frames are very real things in the sense they can be mapped out with clocks and metre sticks.

Nor I suspect are gravitons, or Higgs bosons. Current physics just doesn't explain what's there. Not enough. Otherwise we wouldn't be here talking about it.

I don't know where the story will go for gravitons, but I have no problems with the way physics is done by physicists today.

 

[Pete]

Can we try to keep this an alpha thread please? Pete, can you assist by changing the title?

No... you have to specify Alpha rules when you make the thread.

 

[BenTheMan]

Because he was the originator of General relativity and a smart guy. I care what he thought.

I'm sure Einstein was a smart guy. You certainly won't find any arguments here. But the fact is that Einstein was mistaken about many things, and we respect Einstein because he wrote down General Relativity, not the other way around.

He was unhappy about it at the time, but accepted the value when formulating GR, then had doubts again later in life. Like in 1950. But you don't care.

Yes. Fine. This does not constitute a reference. Please justify the statement you made, or withdraw it.

I don't think you do agree actually. Spacetime is a space. By this Einstein meant a real space. Not a mathematical space. There are no actual world lines, there is no actual block universe. These are mathematical abstractions with no actual existence in the real space that's out there.

What's the difference? This is very confusing to me.

Your argument here is still axiomatic. You're saying I'm wrong to say time isn't a Dimension because time is a Dimension. And your logic is badly flawed. Come on, if spacetime is a space it has no property of time.

Specifically, the onus is on you to show that time isn't a dimension. And you'll have to be a bit more sophisticated than saying "Time travel is impossible". Also, I am not sure we are working from the same definition of "space".

You can introduce as much matter as you like, but if it's fixed, unmoving, there is nothing that you can call time. It's not until you also introduce some events or change or motion that you then obtain the derived effect that you call time.

This is where you break Lorentz Invariance. Time is a property of the manifold, not of the stuff ON the manifold. I don't know how else to tell you that you are wrong about this.

I think I know what your confusion is. You have confused the concepts of Euclidean space and Minkowski space.

I do justify my position. You criticise me on the maths, but you're doing string theory even though you yourself said the maths is ten years behind.

Of course you DO justify your position, that doesn't change the fact that your position is unjustified. The math is here, and was there in 1919 when Minkowski showed Einstein how to do differential geometry. The math is there and it proves you wrong. In ten years you will be just as wrong as you are now.

Your attitude is unscientific. You should read all the essays and see if they offer anything of value. To be so hostile when you haven't read them just isn't sensible.

First of all, I am not being hostile. I am telling you that your ideas are wrong. If you take this personally, perhaps you shouldn't be a scientist. Being hostile would be resorting to calling you names. And you haven't frustrated my that much yet.

Second of all, I will continue reading your essay when you sufficiently address the Lorentz Invariance arguments I have made.

And RELATIVITY+ isn't patently wrong. You are.

Ooh. So instead of refuting my arguments about Lorentz invariance, you want a pissing contest.

 

[Farsight]

I had guests over Easter, and I've got to go away for three days tomorrow, and may be offline. I'll get back to you in detail later.

 

[Farsight]

I'm sure Einstein was a smart guy. You certainly won't find any arguments here. But the fact is that Einstein was mistaken about many things, and we respect Einstein because he wrote down General Relativity, not the other way around.

He had plenty of time to think about it afterwards, and it wouldn't be right to brush it all off.

Yes. Fine. This does not constitute a reference. Please justify the statement you made, or withdraw it.

I've already given you one on another thread. It's “A World Without Time: The forgotten legacy of Godel and Einstein” by Palle Yourgrau. This is a rather philosophical book, if you feel it's not adequate do note that it references other sources.

Farsight: I don't think you do agree actually. Spacetime is a space. By this Einstein meant a real space. Not a mathematical space. There are no actual world lines, there is no actual block universe. These are mathematical abstractions with no actual existence in the real space that's out there. What's the difference? This is very confusing to me.

The mathematical space is employed in a model intended to give grasp of how the world works. We can hopefully use it to make predictions that we can then test via experiment to advance our knowledge, perhaps refining the model as we go along, so that in the end we understand the world, and can explain things like gravity - perhaps in some "theory of everything". If we find we can't make progress, maybe it's because the model is in some way misleading. I think the Minkowski mathematical model of "spacetime", or its interpretation, falls into this category. It employs a four dimensional mathematical space, but the space I actually see has three dimensions. Things move through it, and we use "time" to compare and measure these motions. But the space itself has no identifiable inherent property called time, and whilst we infer this fourth "dimension" using our records and our memory, we cannot actually observe it directly. What we actually observe are things moving through three dimensional space, not "through" time, and not "through" four dimensional spacetime.

Specifically, the onus is on you to show that time isn't a dimension. And you'll have to be a bit more sophisticated than saying "Time travel is impossible". Also, I am not sure we are working from the same definition of "space".

I don't know what more I can say above and beyond the TIME EXPLAINED essay. Maybe we aren't using the same definition of space. I'm trying to think in ontological terms of what's actually there, the thing that gives us space to move around in.

This is where you break Lorentz Invariance. Time is a property of the manifold, not of the stuff ON the manifold. I don't know how else to tell you that you are wrong about this.

We'll have to agree to differ on the Lorentz Invariance. Can't you at least park it for a while? As regards the manifold, see GRAVITY EXPLAINED for where I end up - in a world that is "painted in light". It's Einstein's pure marble geometry achieved via a variable vacuum impedance within Euclidean space. However I haven't explained how this variation occurs, so I can't confidently say what should be included in "the manifold".

I think I know what your confusion is. You have confused the concepts of Euclidean space and Minkowski space.

Please elaborate.

Of course you DO justify your position, that doesn't change the fact that your position is unjustified. The math is here, and was there in 1919 when Minkowski showed Einstein how to do differential geometry. The math is there and it proves you wrong. In ten years you will be just as wrong as you are now.

Obviously I don't think so. Time will tell.

First of all, I am not being hostile. I am telling you that your ideas are wrong. If you take this personally, perhaps you shouldn't be a scientist. Being hostile would be resorting to calling you names. And you haven't frustrated me that much yet.

Just read the essays properly first, that's all I ask.

Second of all, I will continue reading your essay when you sufficiently address the Lorentz Invariance arguments I have made.

No. You've raised this repeatedly and I've replied adequately. You shouldn't use this as a reason not to read the essays.

Ooh. So instead of refuting my arguments about Lorentz invariance, you want a pissing contest.

No. I just want you to do what you said you'd do, which is read through all the essays properly and give considered feedback. If you'd prefer to carry on thinking you can judge an essay from its title, or if you feel you can declare an axiom-challenging model "patently wrong" for an axiomatic reason after reading a few paragraphs, that's up to you.

 

[BenTheMan]

Maybe we aren't using the same definition of space. I'm trying to think in ontological terms of what's actually there, the thing that gives us space to move around in.

If this is the case then there is no physics in your essays.

We'll have to agree to differ on the Lorentz Invariance. Can't you at least park it for a while?

No. I will not concede this point and unless you can tell me why you DON'T break Lorentz Invariance, or why the Lorentz violating effects are confined to a very high scale, then your ideas are wrong.

Lorentz Invariance is an idea that we know to be right. And if it isn't right, then you have to explain to me both why it's wrong and why I would be fooled into thinking that it's right.

Unless you can do that, then there is no point in continuing this discussion.

 

[Farsight]

If this is the case then there is no physics in your essays.

There's plenty of physics in my essays. And you haven't read them remember? You were calling them pseudoscience when you'd only read the title. The lack of physics, and the lack of scientific objectivity, of rationality, lies with you.

No. I will not concede this point and unless you can tell me why you DON'T break Lorentz Invariance, or why the Lorentz violating effects are confined to a very high scale, then your ideas are wrong. Lorentz Invariance is an idea that we know to be right. And if it isn't right, then you have to explain to me both why it's wrong and why I would be fooled into thinking that it's right. Unless you can do that, then there is no point in continuing this discussion

Bah. You dredge this up as an irrelavent pretence, a feeble excuse to dismiss these essays because you can't find fault with my impeccable logic. Here, I'll reiterate what I've said umpteen times before:

I don't break Lorentz invariance. We will always measure c at 300,000km/s because light defines our time. And everything else follows suit - we can expect no observational differences when we change our frame, the laws of physics will remain the same. But the deeper truth is that gravity is a variation in c. The speed of light is constant in all frames, because light defines our time, but gravitational time dilation tells us c varies across frames. Your use of Lorentz Invariance as a brick wall "law" to disqualify this understanding of gravity is not a rational argument, it's a facile artifice to dress up an axiomatic denial that says "c is not variable because c is constant QED hence I've proved you wrong". And even if I had broken Lorentz Invariance, that's no reason to not read RELATIVITY+ because it's challenged elsewhere:

"Relativity has been one of the most successful theories of the last century and is a cornerstone of modern physics. This review focuses on the modern experimental tests of one of the fundamental symmetries of relativity, Lorentz invariance. Over the last decade there has been tremendous interest and progress in testing Lorentz invariance. This is largely motivated by two factors. First, there have been theoretical suggestions that Lorentz invariance may not be an exact symmetry at all energies. The possibility of four-dimensional Lorentz invariance violation has been investigated in different quantum gravity models (including string theory [185, 107], warped brane worlds [70], and loop quantum gravity [120]), although no quantum gravity model predicts Lorentz violation conclusively. Other high energy models of spacetime structure, such as non-commutative field theory, do however explicitly contain Lorentz violation [98]. High energy Lorentz violation can regularize field theories, another reason it may seem plausible. Even if broken at high energies, Lorentz symmetry can still be an attractive infrared fixed point, thereby yielding an approximately Lorentz invariant low energy world [79]. Other ideas such as emergent gauge bosons [54, 189, 161, 80], varying moduli [93], axion-Wess-Zumino models [30], analogues of emergent gravity in condensed matter [40, 238], ghost condensate [34], space-time varying couplings [177, 50], or varying speed of light cosmologies [219, 209] also incorporate Lorentz violation. The ultimate fate of Lorentz invariance is therefore an important theoretical question..."

But you're right. There is no point continuing this discussion. In fact, it's never been a discussion. It started with your irrational crackpot rant, and you haven't met my challenge to be rational and study the model I offer. You never intended to. And since you think the best physicists are mathematicians, I was foolish to expect anything scientific and objective from you.