As a new member, I'm not allowed to make a post here linking elsewhere, so I cannot give you a link in the text. Fortunately, the software does not object against an URL in the signature.
Interested in your objections.
At last, my paper is finished, my new ether theory can be studied and criticized.
As a new member, I'm not allowed to make a post here linking elsewhere, so I cannot give you a link in the text. Fortunately, the software does not object against an URL in the signature.
Interested in your objections.
As a new member, I'm not allowed to make a post here linking elsewhere, so I cannot give you a link in the text. Fortunately, the software does not object against an URL in the signature.
Interested in your objections.
Page 2 : What exactly is A(3)? Is it a standard group of some kind (I'm not aware of it)?
Page 2 : If fermion doubling gives 4 if you're in 3+1 dimensions, why is it only 2 in 3 dimensions?
Page 2 : How can you justify quantising only part of space-time?
Page 2 : You don't reduce from R to Z_2, you work R/Z_2, the quotient space.
Page 3 : You talk about E(3) symmetries applies to A(4). Firstly, by the sound of it A(4) is not a group, it's a multiplet representation. A group is a specific mathematical/physical thing. Secondly, you claim it doesn't apply to the right handed neutrinos, but since you never lay out specifically this action, by giving an example, such a claim is completely unjustified. You're claiming to have solved some major thing and yet you give absolutely no explaination of how you did it in any concrete manner. The bigger the 'result', the more explaination and detail it needs.
Infact, that seems to be the general jist of your 'paper'. You sort of tip toe around using a lot of the same very basic notation and algebra you'd find in introductory chapters to quantum mechanics, but you never actually prove anything with it. You'll fill a page with menial algebra about commutator relations (something anyone even vaguely familiar with quantum mechanics will know in their sleep) and then just say "And this gives up the reason the neutrino is electromagnetically neutral". How precisely do you excluse SO(10)? Go through it in detail.
You completely skim over gauge groups. You write down the definition for how a 'Wilson link' works and then announce it explains SU(3) etc. No, you just say it does. You'll find pages and pages and pages of discussion about Wilson loops and gauge links in books and they do a hell of a lot more work than just write down the definition of U and then say "Thus we get the Standard Model".
Then when it comes to relativity, you seem to just be trying to redress the derivation of the Einstein Field Equations for a perfect fluid in the guise of ether. You initially equate your metric entries with some fluid properties and then forget about it, just working with the metric and pretty much postulating the answer you expect to get!
Errors you've made including thinking that in a discrete space, the continuous symmetry of E(3) will be valid. No, it won't. You also say that renormalisation is a next step in your research. You've quantised your space-time, you have an natural energy scale at which to cut off your physics, you don't need to renormalise. But you'd know this if you knew about quantisation of space-time methods.
Generally the entire paper seems to be paying a bit of lip service to very basic equations in both quantum mechanics and relativity and then utterly glossing over the derivation of any important claimed result, as if they follow trivially from commutator relations.
Page 2 : If fermion doubling gives 4 if you're in 3+1 dimensions, why is it only 2 in 3 dimensions?
Page 2 : How can you justify quantising only part of space-time?
Page 2 : You don't reduce from R to Z_2, you work R/Z_2, the quotient space.
Page 3 : You talk about E(3) symmetries applies to A(4). Firstly, by the sound of it A(4) is not a group, it's a multiplet representation. A group is a specific mathematical/physical thing. Secondly, you claim it doesn't apply to the right handed neutrinos, but since you never lay out specifically this action, by giving an example, such a claim is completely unjustified. You're claiming to have solved some major thing and yet you give absolutely no explaination of how you did it in any concrete manner. The bigger the 'result', the more explaination and detail it needs.
Infact, that seems to be the general jist of your 'paper'. You sort of tip toe around using a lot of the same very basic notation and algebra you'd find in introductory chapters to quantum mechanics, but you never actually prove anything with it. You'll fill a page with menial algebra about commutator relations (something anyone even vaguely familiar with quantum mechanics will know in their sleep) and then just say "And this gives up the reason the neutrino is electromagnetically neutral". How precisely do you excluse SO(10)? Go through it in detail.
You completely skim over gauge groups. You write down the definition for how a 'Wilson link' works and then announce it explains SU(3) etc. No, you just say it does. You'll find pages and pages and pages of discussion about Wilson loops and gauge links in books and they do a hell of a lot more work than just write down the definition of U and then say "Thus we get the Standard Model".
Then when it comes to relativity, you seem to just be trying to redress the derivation of the Einstein Field Equations for a perfect fluid in the guise of ether. You initially equate your metric entries with some fluid properties and then forget about it, just working with the metric and pretty much postulating the answer you expect to get!
Errors you've made including thinking that in a discrete space, the continuous symmetry of E(3) will be valid. No, it won't. You also say that renormalisation is a next step in your research. You've quantised your space-time, you have an natural energy scale at which to cut off your physics, you don't need to renormalise. But you'd know this if you knew about quantisation of space-time methods.
Generally the entire paper seems to be paying a bit of lip service to very basic equations in both quantum mechanics and relativity and then utterly glossing over the derivation of any important claimed result, as if they follow trivially from commutator relations.
..so do they get a B minus?.. 
QUOTE
Page 2 : What exactly is A(3)? Is it a standard group of some kind (I'm not aware of it)?
The three-dimensional affine group (linear transformations + translation in R^3).
QUOTE (->
| QUOTE |
| Page 2 : What exactly is A(3)? Is it a standard group of some kind (I'm not aware of it)? |
The three-dimensional affine group (linear transformations + translation in R^3).
Page 2 : If fermion doubling gives 4 if you're in 3+1 dimensions, why is it only 2 in 3 dimensions?
Each discrete direction gives a factor 2. Naive fermion doubling gives factor 16.
Staggered fermions have one complex number on each lattice node, so that the 16 is obtained by 4 x 4 complex fields = 4 fermions.
Discretization in space only gives factor 8, which is 2 x 4 fields = 2 fermions.
QUOTE
Page 2 : How can you justify quantising only part of space-time?
Quantizing? An ether consists of discrete parts in space (ether constituents). But they change their state continuously in time. Thus, the description is discrete in space, but continuous in time.
Of course, the whole theory is quantized as a whole. Canonical quantum theory is a theory with continuous time.
QUOTE (->
| QUOTE |
| Page 2 : How can you justify quantising only part of space-time? |
Quantizing? An ether consists of discrete parts in space (ether constituents). But they change their state continuously in time. Thus, the description is discrete in space, but continuous in time.
Of course, the whole theory is quantized as a whole. Canonical quantum theory is a theory with continuous time.
Page 2 : You don't reduce from R to Z_2, you work R/Z_2, the quotient space.
No. The theory splits into two parts - a boson with large mass, and a Z_2 field with small mass. It is my choice to consider only the low energy regime.
QUOTE
Page 3 : You talk about E(3) symmetries applies to A(4). Firstly, by the sound of it A(4) is not a group, it's a multiplet representation. A group is a specific mathematical/physical thing.
???? Some confusion. A(4) I never use, I use A(3), which is the denotation I know for the three-dimensional affine group.
QUOTE (->
| QUOTE |
| Page 3 : You talk about E(3) symmetries applies to A(4). Firstly, by the sound of it A(4) is not a group, it's a multiplet representation. A group is a specific mathematical/physical thing. |
???? Some confusion. A(4) I never use, I use A(3), which is the denotation I know for the three-dimensional affine group.
Secondly, you claim it doesn't apply to the right handed neutrinos, but since you never lay out specifically this action, by giving an example, such a claim is completely unjustified. You're claiming to have solved some major thing and yet you give absolutely no explaination of how you did it in any concrete manner. The bigger the 'result', the more explaination and detail it needs.
I see. Its hard to tell what is obvious for the reader. In my opinion, the three-dimensional affine group is much more elementary than commutation relations in quantum theory.
QUOTE
Errors you've made including thinking that in a discrete space, the continuous symmetry of E(3) will be valid. No, it won't.
Sorry, but space is not discrete. I have a discrete ether (consisting of elementary cells), but it moves in continuous space R^3.
QUOTE (->
| QUOTE |
| Errors you've made including thinking that in a discrete space, the continuous symmetry of E(3) will be valid. No, it won't. |
Sorry, but space is not discrete. I have a discrete ether (consisting of elementary cells), but it moves in continuous space R^3.
You also say that renormalisation is a next step in your research. You've quantised your space-time, you have an natural energy scale at which to cut off your physics, you don't need to renormalise. But you'd know this if you knew about quantisation of space-time methods.
If I consider the long distance continuous limit, it is, of course, very interesting to consider renormalization and renormalization group equations. I don't need renormizability, I know. But that's another question. And, again, it is not spacetime which is quantized or discretized. Spacetime remains the fixed, continuous framework, R^3 x R, for canonical quantization.
QUOTE
Then when it comes to relativity, you seem to just be trying to redress the derivation of the Einstein Field Equations for a perfect fluid in the guise of ether. You initially equate your metric entries with some fluid properties and then forget about it, just working with the metric and pretty much postulating the answer you expect to get!
In some sense, the postulates are, of course, obtained by reverse design, to obtain the result I want. And the derivation is not very complicate.
But what I "pretty much" postulate are axioms which are perfectly reasonable for an ether theory: That the Noether conservation law - in some special form - should give continuity and Euler equations of the ether. Nothing in this axiom seems to suggest that it is constructed to derive the GR Lagrangian in harmonic gauge.
QUOTE (->
| QUOTE |
| Then when it comes to relativity, you seem to just be trying to redress the derivation of the Einstein Field Equations for a perfect fluid in the guise of ether. You initially equate your metric entries with some fluid properties and then forget about it, just working with the metric and pretty much postulating the answer you expect to get! |
In some sense, the postulates are, of course, obtained by reverse design, to obtain the result I want. And the derivation is not very complicate.
But what I "pretty much" postulate are axioms which are perfectly reasonable for an ether theory: That the Noether conservation law - in some special form - should give continuity and Euler equations of the ether. Nothing in this axiom seems to suggest that it is constructed to derive the GR Lagrangian in harmonic gauge.
You'll fill a page with menial algebra about commutator relations (something anyone even vaguely familiar with quantum mechanics will know in their sleep) and then just say "And this gives up the reason the neutrino is electromagnetically neutral". How precisely do you excluse SO(10)? Go through it in detail.
Adding a constant vector to a field should commute with the gauge action. That's possible only if the direction remains unchanged by the gauge action. I thought it is sufficiently obvious. But you may be right here, I have to write this down in more detail.
But in this case I have to write down much more things which "anyone even vaguely familiar with math will know in their sleep".
Thanks very much for your remarks.
QUOTE (AlphaNumeric+Sep 27 2007, 08:49 PM)
What exactly is A(3)?
I would assume it's referring to the affine Weyl group. At least in the study of some algebraic aspects of Painlevé Equations, that's the notation employed - see here for example.
I would assume it's referring to the affine Weyl group. At least in the study of some algebraic aspects of Painlevé Equations, that's the notation employed - see here for example.
QUOTE (Euler+Sep 27 2007, 08:44 PM)
I would assume it's referring to the affine Weyl group. At least in the study of some algebraic aspects of Painlevé Equations, that's the notation employed
I see that A(n) for the affine group is, indeed, seldom used, see gr-qc/9402012 or
www.maths.gla.ac.uk/~wws/cabripages/klein/affine0.html, but not much more.
Aff(n) seems more common.
Improved version on the page.
I see that A(n) for the affine group is, indeed, seldom used, see gr-qc/9402012 or
www.maths.gla.ac.uk/~wws/cabripages/klein/affine0.html, but not much more.
Aff(n) seems more common.
Improved version on the page.
Also, primary objections are never addressed.
Conclusion: This paper would not pass peer review even if all your reviewers were engineers.
- Why is this trip necessary? There's no discussion of motivation.
- This lattice is not Lorentz-invarient, so why do the laws of the universe we measure obey local Lorentz-invariance at the low-energy scale?
- There is just one t in your equations. How then to explain gravitational time dilation?
- You don't have enough free-parameters to fit the standard model and you don't have enough calculations to demonstrate you do replicate the standard model.
- Section 1 is not connected with the rest of the paper by any math at all. a, b, x, and y just disapper. The rest of the sections has no foundation. It looks like wishful thinking rather than logic.
Conclusion: This paper would not pass peer review even if all your reviewers were engineers.
QUOTE
[*] This lattice is not Lorentz-invarient, so why do the laws of the universe we measure obey local Lorentz-invariance at the low-energy scale?
[*] There is just one t in your equations. How then to explain gravitational time dilation?
[*] There is just one t in your equations. How then to explain gravitational time dilation?
The theory of gravity follows the EEP, as proven. This includes local Lorentz invariance. And it also gives gravitational time dilation.
QUOTE (->
| QUOTE |
| [*] This lattice is not Lorentz-invarient, so why do the laws of the universe we measure obey local Lorentz-invariance at the low-energy scale? [*] There is just one t in your equations. How then to explain gravitational time dilation? |
The theory of gravity follows the EEP, as proven. This includes local Lorentz invariance. And it also gives gravitational time dilation.
[*] You don't have enough free-parameters to fit the standard model and you don't have enough calculations to demonstrate you do replicate the standard model.
It is clear that I don't compute the mass terms, because they require symmetry breaking. That this symmetry breaking requires additional research is clearly said.
The paper is named "giving SM fermions, gauge fields", not "giving the SM".
QUOTE
[*] Section 1 is not connected with the rest of the paper by any math at all. a, b, x, and y just disapper. The rest of the sections has no foundation. It looks like wishful thinking rather than logic.
Ok, the a,b,x,y, have been introduced yesterday evening to explain the affine group.
The purpose of the introduction is, AFAIU, to describe what is presented in the remaining part of the paper, not to present math. I'm wrong here?
What do you mean with "no foundation"? Ok, some more formulas in the gauge field section, I will do it.
QUOTE (->
| QUOTE |
| [*] Section 1 is not connected with the rest of the paper by any math at all. a, b, x, and y just disapper. The rest of the sections has no foundation. It looks like wishful thinking rather than logic. |
Ok, the a,b,x,y, have been introduced yesterday evening to explain the affine group.
The purpose of the introduction is, AFAIU, to describe what is presented in the remaining part of the paper, not to present math. I'm wrong here?
What do you mean with "no foundation"? Ok, some more formulas in the gauge field section, I will do it.
[*] Why is this trip necessary? There's no discussion of motivation.
IMHO the line "This makes it a candidate for a theory of everything." gives sufficient motivation. Not?
QUOTE
Conclusion: This paper would not pass peer review even if all your reviewers were engineers.
I'm sure that an ether paper will not pass peer review. The use of the e-word is almost sufficient to reject it today. At least this is my experience.
In the worst case, "not of interest for the readers of this journal" is certainly correct (there is no scientific journal with readers interested in ether theories) and sufficient for rejection (no journal in the world is obligued to publish things not of interest for the readers, except by laws of various states). I have reached this state with gr-qc/0205035 and, after this, given up to submit it.
But it is, of course, interesting to see the objections.
Thank you too.
Two weeks later.
There have been two critical postings, but IMHO I have been able to answer the objections. At least, there have been no second reply by these posters.
The main problem of the first critique, by AlphaNumeric, was a confusion about the meaning of A(3). Of course, if somebody does not understand that it is the affine group Aff(3), it is clear that some simple things (like the action of E(3) on it) seem undefined and not clear.
The main problem of the second critique was relativistic symmetry, despite my proof of the Einstein Equivalence Principle.
The claims about an error ("Errors you've made including thinking that in a discrete space, the continuous symmetry of E(3) will be valid. No, it won't. You also say that renormalisation is a next step in your research. You've quantised your space-time, you have an natural energy scale at which to cut off your physics, you don't need to renormalise. ") has been answered.
Some general argumentation of type "It looks like wishful thinking rather than logic" or "Generally the entire paper seems to be paying a bit of lip service to very basic equations in both quantum mechanics and relativity and then utterly glossing over the derivation of any important claimed result, as if they follow trivially from commutator relations." remains, its hard to argue against such claims.
Anyway, the only surviving criticism is directed against my presentation of the results, not against the theory itself. (Of course, the presentation needs some improvement, especially the gauge field part.)
Nonetheless, I wonder why I don't see more replies here.
OK, I see, there are much more important and interesting things to discuss, like "Discovered Gold As The Ultimate Heat Source" or "THE GREAT ERROR OF EINSTEIN (The proof) "
There have been two critical postings, but IMHO I have been able to answer the objections. At least, there have been no second reply by these posters.
The main problem of the first critique, by AlphaNumeric, was a confusion about the meaning of A(3). Of course, if somebody does not understand that it is the affine group Aff(3), it is clear that some simple things (like the action of E(3) on it) seem undefined and not clear.
The main problem of the second critique was relativistic symmetry, despite my proof of the Einstein Equivalence Principle.
The claims about an error ("Errors you've made including thinking that in a discrete space, the continuous symmetry of E(3) will be valid. No, it won't. You also say that renormalisation is a next step in your research. You've quantised your space-time, you have an natural energy scale at which to cut off your physics, you don't need to renormalise. ") has been answered.
Some general argumentation of type "It looks like wishful thinking rather than logic" or "Generally the entire paper seems to be paying a bit of lip service to very basic equations in both quantum mechanics and relativity and then utterly glossing over the derivation of any important claimed result, as if they follow trivially from commutator relations." remains, its hard to argue against such claims.
Anyway, the only surviving criticism is directed against my presentation of the results, not against the theory itself. (Of course, the presentation needs some improvement, especially the gauge field part.)
Nonetheless, I wonder why I don't see more replies here.
OK, I see, there are much more important and interesting things to discuss, like "Discovered Gold As The Ultimate Heat Source" or "THE GREAT ERROR OF EINSTEIN (The proof) "
If you're after a more specific critique, please explain precisely how you've quantised gravity. You have done nothing more than use the GR equations for a perfect fluid (which is, literally, the textbook way to derive the Einstein Field Equations in a simple system), without reference to your ether you outline in the first part of the paper. Everything in section 4 is just usual GR but you're claiming it's an aether, your aether.
You certainly do not approach the issue of quantising it, you just work out some classical equations of motion (or rather, you just state them). Previously you'd written out mode operators for the quantum fields, why don't you do this for gravity? You can't claim to have used your ideas to 'solve problems with quantising gravity' when you never address it!
As I said, you seem to just be skimming off the results of mainstream physics, ignoring all the actual details and now and again saying "And this is from the aether" for various things. If you continue down the road you appear to be on, ie just rehashing mainstream work in a very naive way, you'll find that you're unable to quantise gravity because of renormalisation issues. Even with the notion of a lattice to quantise on, it's not immediately trivial, since lattice methods are common place in mainstream QFT and they don't help with gravity.
You certainly do not approach the issue of quantising it, you just work out some classical equations of motion (or rather, you just state them). Previously you'd written out mode operators for the quantum fields, why don't you do this for gravity? You can't claim to have used your ideas to 'solve problems with quantising gravity' when you never address it!
As I said, you seem to just be skimming off the results of mainstream physics, ignoring all the actual details and now and again saying "And this is from the aether" for various things. If you continue down the road you appear to be on, ie just rehashing mainstream work in a very naive way, you'll find that you're unable to quantise gravity because of renormalisation issues. Even with the notion of a lattice to quantise on, it's not immediately trivial, since lattice methods are common place in mainstream QFT and they don't help with gravity.
QUOTE (AlphaNumeric+Oct 10 2007, 09:35 PM)
If you're after a more specific critique, please explain precisely how you've quantised gravity.
I don't claim to have finished quantization of gravity.
Instead, my "to do" list contains "The connection between the SM ether model and the ether theory of gravity, which are metaphysically compatible but mathematically yet unrelated theories;" The SM ether model is already a quantum theory, but the theory of gravity not yet.
The claims "The ether approach
to gravity solves many quantization problems of GR quantization: The notorious
problem of time [10] simply disappears. Together with the black hole collapse
the related information loss problem [13] disappears too."
are sufficiently obvious even without finishing quantization if you know the mentioned problems, for more details see gr-qc/0205035.
Especially I quote a paper about the problem of time with "``... in quantum gravity, one response to the problem of time is to `blame' it on general relativity's
allowing arbitrary foliations of spacetime; and then to postulate a
preferred frame of spacetime with respect to which quantum theory
should be written.'' My ether theory obviously follows this way.
Sorry, but that's simply false. The continuity and Euler equations, as I use them, are classical fluid equations, with partial instead of covariant derivatives, and have nothing to do with GR equations for some fluid on some curved background or so. It is certainly not the textbook way to derive the EFE, already because I do not derive the EFE. Instead I derive the EFE with some additional term.
The additional term is not "just usual GR", it prevent black hole and big bang singularities and enforces harmonic coordinates.
It holds for all ether theories which fulfill the axioms. If such a Lagrange formalism exists for the continuous limit of my SM model is an open question. I can hardly answer it without having found the general Lagrangian for the SM model. (Which requires symmetry breaking + continuous limit.)
Sorry, but that's simply false. The continuity and Euler equations, as I use them, are classical fluid equations, with partial instead of covariant derivatives, and have nothing to do with GR equations for some fluid on some curved background or so. It is certainly not the textbook way to derive the EFE, already because I do not derive the EFE. Instead I derive the EFE with some additional term.
The additional term is not "just usual GR", it prevent black hole and big bang singularities and enforces harmonic coordinates.
It holds for all ether theories which fulfill the axioms. If such a Lagrange formalism exists for the continuous limit of my SM model is an open question. I can hardly answer it without having found the general Lagrangian for the SM model. (Which requires symmetry breaking + continuous limit.)
You certainly do not approach the issue of quantising it, you just work out some classical equations of motion
Indeed.
I postulate classical continuity and Euler equations, and their connection with the Lagrange formalism (a form of the Noether theorem). What follows is a derivation of the most general Lagrangian.
I postulate classical continuity and Euler equations, and their connection with the Lagrange formalism (a form of the Noether theorem). What follows is a derivation of the most general Lagrangian.
Previously you'd written out mode operators for the quantum fields, why don't you do this for gravity? You can't claim to have used your ideas to 'solve problems with quantising gravity' when you never address it!
Quantization of gravity consists of two parts: Defining a quantum theory, and to show that the classical continous limit of this theory is, in some limit, GR.
I have defined now the quantum theory. There are some open problems with the connection between the ether model and the continuous theory of gravity (I need a very special form of the Lagrange formalism for the continuous limit of my model), but, assume they can be solved on the classical level.
Then, there is no need for writing down quantum operators for gravity. It is already defined. The continuous limit of the quantum theory may be full of technical problems. But these are problems of derivation of continous limits of well-defined quantum theories, not problems of defining quantum gravity.
In gr-qc/0205035 I have addressed some quantization issues. And what I have done after this, working on my SM model, was the following point in that quantization program:
"Next, we have to find atoms, that means, to discretize the
problem. The density $\rho$ should be identified with the number of
nodes inside a region,..."
It may be, indeed, that the situation with various types of hierarchy problems (smallness of the cosmological constant) is not better in my approach. This is left to future research. But, even in the worst case, the result will be a well-defined theory with some fine-tuning problem. Or what else do you expect?
It may be, indeed, that the situation with various types of hierarchy problems (smallness of the cosmological constant) is not better in my approach. This is left to future research. But, even in the worst case, the result will be a well-defined theory with some fine-tuning problem. Or what else do you expect?
Even with the notion of a lattice to quantise on, it's not immediately trivial, since lattice methods are common place in mainstream QFT and they don't help with gravity.
I agree.
But note that a whole direction of research - LQG - want's much more, namely to derive the dimensionality of spacetime from some foam-like background-free lattice.
That's not what I have to do. In my approach, the background R^3 x R is already given from the start.
Note also that non-renormalizability is not an issue.
The only issue related with renormalization are various fine-tuning problems. I acknowledge their importance, but, nonetheless, having a well-defined unitary and so on theory with some fine tuning problems is much better than having no such theory at all.
I don't claim to have finished quantization of gravity.
Instead, my "to do" list contains "The connection between the SM ether model and the ether theory of gravity, which are metaphysically compatible but mathematically yet unrelated theories;" The SM ether model is already a quantum theory, but the theory of gravity not yet.
The claims "The ether approach
to gravity solves many quantization problems of GR quantization: The notorious
problem of time [10] simply disappears. Together with the black hole collapse
the related information loss problem [13] disappears too."
are sufficiently obvious even without finishing quantization if you know the mentioned problems, for more details see gr-qc/0205035.
Especially I quote a paper about the problem of time with "``... in quantum gravity, one response to the problem of time is to `blame' it on general relativity's
allowing arbitrary foliations of spacetime; and then to postulate a
preferred frame of spacetime with respect to which quantum theory
should be written.'' My ether theory obviously follows this way.
QUOTE
You have done nothing more than use the GR equations for a perfect fluid (which is, literally, the textbook way to derive the Einstein Field Equations in a simple system), without reference to your ether you outline in the first part of the paper. Everything in section 4 is just usual GR but you're claiming it's an aether, your aether.
Sorry, but that's simply false. The continuity and Euler equations, as I use them, are classical fluid equations, with partial instead of covariant derivatives, and have nothing to do with GR equations for some fluid on some curved background or so. It is certainly not the textbook way to derive the EFE, already because I do not derive the EFE. Instead I derive the EFE with some additional term.
The additional term is not "just usual GR", it prevent black hole and big bang singularities and enforces harmonic coordinates.
It holds for all ether theories which fulfill the axioms. If such a Lagrange formalism exists for the continuous limit of my SM model is an open question. I can hardly answer it without having found the general Lagrangian for the SM model. (Which requires symmetry breaking + continuous limit.)
QUOTE (->
| QUOTE |
| You have done nothing more than use the GR equations for a perfect fluid (which is, literally, the textbook way to derive the Einstein Field Equations in a simple system), without reference to your ether you outline in the first part of the paper. Everything in section 4 is just usual GR but you're claiming it's an aether, your aether. |
Sorry, but that's simply false. The continuity and Euler equations, as I use them, are classical fluid equations, with partial instead of covariant derivatives, and have nothing to do with GR equations for some fluid on some curved background or so. It is certainly not the textbook way to derive the EFE, already because I do not derive the EFE. Instead I derive the EFE with some additional term.
The additional term is not "just usual GR", it prevent black hole and big bang singularities and enforces harmonic coordinates.
It holds for all ether theories which fulfill the axioms. If such a Lagrange formalism exists for the continuous limit of my SM model is an open question. I can hardly answer it without having found the general Lagrangian for the SM model. (Which requires symmetry breaking + continuous limit.)
You certainly do not approach the issue of quantising it, you just work out some classical equations of motion
Indeed.
QUOTE
(or rather, you just state them)
I postulate classical continuity and Euler equations, and their connection with the Lagrange formalism (a form of the Noether theorem). What follows is a derivation of the most general Lagrangian.
QUOTE (->
| QUOTE |
| (or rather, you just state them) |
I postulate classical continuity and Euler equations, and their connection with the Lagrange formalism (a form of the Noether theorem). What follows is a derivation of the most general Lagrangian.
Previously you'd written out mode operators for the quantum fields, why don't you do this for gravity? You can't claim to have used your ideas to 'solve problems with quantising gravity' when you never address it!
Quantization of gravity consists of two parts: Defining a quantum theory, and to show that the classical continous limit of this theory is, in some limit, GR.
I have defined now the quantum theory. There are some open problems with the connection between the ether model and the continuous theory of gravity (I need a very special form of the Lagrange formalism for the continuous limit of my model), but, assume they can be solved on the classical level.
Then, there is no need for writing down quantum operators for gravity. It is already defined. The continuous limit of the quantum theory may be full of technical problems. But these are problems of derivation of continous limits of well-defined quantum theories, not problems of defining quantum gravity.
In gr-qc/0205035 I have addressed some quantization issues. And what I have done after this, working on my SM model, was the following point in that quantization program:
"Next, we have to find atoms, that means, to discretize the
problem. The density $\rho$ should be identified with the number of
nodes inside a region,..."
QUOTE
If you continue down the road you appear to be on, ie just rehashing mainstream work in a very naive way, you'll find that you're unable to quantise gravity because of renormalisation issues.
It may be, indeed, that the situation with various types of hierarchy problems (smallness of the cosmological constant) is not better in my approach. This is left to future research. But, even in the worst case, the result will be a well-defined theory with some fine-tuning problem. Or what else do you expect?
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| If you continue down the road you appear to be on, ie just rehashing mainstream work in a very naive way, you'll find that you're unable to quantise gravity because of renormalisation issues. |
It may be, indeed, that the situation with various types of hierarchy problems (smallness of the cosmological constant) is not better in my approach. This is left to future research. But, even in the worst case, the result will be a well-defined theory with some fine-tuning problem. Or what else do you expect?
Even with the notion of a lattice to quantise on, it's not immediately trivial, since lattice methods are common place in mainstream QFT and they don't help with gravity.
I agree.
But note that a whole direction of research - LQG - want's much more, namely to derive the dimensionality of spacetime from some foam-like background-free lattice.
That's not what I have to do. In my approach, the background R^3 x R is already given from the start.
Note also that non-renormalizability is not an issue.
The only issue related with renormalization are various fine-tuning problems. I acknowledge their importance, but, nonetheless, having a well-defined unitary and so on theory with some fine tuning problems is much better than having no such theory at all.
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