General Relativistic Quantum Theory?

[jake jot]

Is it possible to have some kind of General Relativistic Quantum Theory without passing through the stage of Quantum Field Theory (where Quantum Theory is married to Special Relativity)?

Einstein attached primary significance to the concept of general covariance as shown in this letter in 1954. You can google these letter to see they are really from Einstein:

"You consider the transition to special relativity as the most essential thought of relativity, not the transition to general relativity. I consider the reverse to be correct. I see the most essential thing in the overcoming of the inertial system, a thing that acts upon all processes but undergoes no reaction. This concept is in principle no better than that of the center of universe in Aristolian physics (Einstein to Georg Jaffe, January 19, 1954)"

This implies that the class of global inertial frames singled out in the special theory of relativity can have no place in the relativistic theory of gravitation. Is this true in general (pun unintended)?

It seems he felt a quantum theory constructed on the basis of Galilean or even special-relativistic space-times could not consititute a satisfactory foundation of physics. What do you think?

"Contemporary physicists do not see that is hopeless to take a theory that is based on an independent rigid space (Lorentz-invariance) and later hope to make it general-relativistic (in some natural way) (Einstein to Max von Laue, September 1950)"

Einstein admitted though he may be mistaken:

"I have not really studied quantum field theory. This is because I cannot believe that special relativity theory suffices as the basis of a theory of matter, and that one can afterwards make a non-generally relativistic theory into a generally relativistic one. But I am well aware of the possibiity that this opinion may be erroneous (Einstein to K. Roberts September 6, 1954. "

But still, please tell me why Einstein (at one time) couldn't believe that special relativity theory suffices as the basis of a theory of matter, and that one can afterwards make a non-generally relativistic theory into a generally relativistic one.
This is puzzling considering he discovered both SR and GR.

 

[PeterDonis]

Is it possible to have some kind of General Relativistic Quantum Theory without passing through the stage of Quantum Field Theory (where Quantum Theory is married to Special Relativity)?

It depends on what you mean by "General Relativistic Quantum Theory". If you mean something like quantum field theory but based on general relativity instead of special relativity, nobody has come up with such a theory. If you mean something else, I don't see how your question can be answered unless you are able to describe more specifically what you mean.

please tell me why Einstein (at one time) couldn't believe that special relativity theory suffices as the basis of a theory of matter

It's impossible to tell from the quote you give.

and that one can afterwards make a non-generally relativistic theory into a generally relativistic one

That's not what he did in going from SR to GR. You can use general curvilinear coordinates in SR, and transform between them and standard inertial coordinates, just fine. That's not what differentiates SR from GR.

What differentiates SR from GR is that in SR, spacetime must be flat, but in GR, spacetime is allowed to be curved. Quantum field theory can be done in curved spacetime, but it raises a number of issues that present problems for physical interpretation. If Einstein was able to foresee such problems, that might explain why he was skeptical about quantum field theory, since he would have known that any QFT based on special relativity would be limited to flat spacetime and so could not include gravity.

 

[jake jot]

It depends on what you mean by "General Relativistic Quantum Theory". If you mean something like quantum field theory but based on general relativity instead of special relativity, nobody has come up with such a theory. If you mean something else, I don't see how your question can be answered unless you are able to describe more specifically what you mean.

In the quotes, Einstein seemed to say that general covariance and inertial systems were not compatible. He felt a quantum theory constructed on the basis of Galilean or even special-relativistic space-times could not constitute a satisfactory foundation of physics.

Therefore I didn't use the words "General Relativistic Quantum Field Theory". Instead I used "General Relativistic Quantum Theory" that doesn't include Special Relativity in QFT, but directly using General Covariance. See reference here (page 417):

Einstein from 'B' to 'Z' - John Stachel - Google Books

It's impossible to tell from the quote you give.



That's not what he did in going from SR to GR. You can use general curvilinear coordinates in SR, and transform between them and standard inertial coordinates, just fine. That's not what differentiates SR from GR.

What differentiates SR from GR is that in SR, spacetime must be flat, but in GR, spacetime is allowed to be curved. Quantum field theory can be done in curved spacetime, but it raises a number of issues that present problems for physical interpretation. If Einstein was able to foresee such problems, that might explain why he was skeptical about quantum field theory, since he would have known that any QFT based on special relativity would be limited to flat spacetime and so could not include gravity.

 

[PeroK]

In the quotes, Einstein seemed to say that general covariance and inertial systems were not compatible. He felt a quantum theory constructed on the basis of Galilean or even special-relativistic space-times could not constitute a satisfactory foundation of physics.

Therefore I didn't use the words "General Relativistic Quantum Field Theory". Instead I used "General Relativistic Quantum Theory" that doesn't include Special Relativity in QFT, but directly using General Covariance. See reference here (page 417):

Einstein from 'B' to 'Z' - John Stachel - Google Books

I'm not convinced that any book written in 1951 has much relevance to what may or may not be the fate of the quantum theories of gravity. The past 80 years have provided so much experimentally and theorectically that anything dating from 1951 can only be looked at in a historical persepective.

You've put this post in "Beyond the standard model"; but actually it should be "Before the standard model". Einstein may well be greatest physicist ever, but he lived before the standard model was developed.

 

[jake jot]

I'm not convinced that any book written in 1951 has much relevance to what may or may not be the fate of the quantum theories of gravity. The past 80 years have provided so much experimentally and theorectically that anything dating from 1951 can only be looked at in a historical persepective.

You've put this post in "Beyond the standard model"; but actually it should be "Before the standard model". Einstein may well be greatest physicist ever, but he lived before the standard model was developed.

The author was like describing that by using Special Relativity in QFT, we may not derive at any General Relativistic QFT. We have none now. So I was just asking what would happen if we go directly from plain Schroedinger Quantum Theory to General relativistic quantum theory without passing through QFT (and special relativity). Who knows. This might be the only viable road to quantum gravity. All possibilities must be tried.

 

[PeterDonis]

In the quotes, Einstein seemed to say that general covariance and inertial systems were not compatible.

No, he wasn't saying that at all. He was only saying that general covariance requires that the laws of physics must be written in such a way that they work in any valid coordinate system, not just an inertial one. That does not make inertial coordinates invalid; it just means they're not the only valid ones and don't have any special physical meaning.

Therefore

Your "therefore" is based on an incorrect premise and is wrong. It is impossible to have general covariance without inertial coordinates being included as one of the possible kinds of coordinates. And it is impossible to have General Relativity that does not include Special Relativity as a special case (the special case in which the spacetime curvature is zero).

See reference here

The Einstein quotes given in the reference are not talking about what you think they are talking about.

The key is this sentence in the first quote you give in the OP:

"I see the most essential thing in the overcoming of the inertial system, a thing that acts upon all processes but undergoes no reaction."

What he means by this is that, in special relativity, the spacetime geometry is fixed: it must be flat. (This fixed flat geometry is what Einstein means by "the inertial system" that "acts upon all processes but undergoes no reaction".) In general relativity, the spacetime geometry is not fixed: it can change depending on the matter and energy that is present, and the Einstein Field Equation, the central equation of General Relativity, describes how the spacetime geometry changes as the matter and energy present changes. (In Einstein's terminology, the spacetime geometry in GR "undergoes reaction" from matter and energy even as it "acts upon" matter and energy. A common layman's description of this is that in GR, "spacetime tells matter how to move, and matter tells spacetime how to curve".)

Quantum field theory, at the time Einstein was writing, had only been done in the fixed flat spacetime of special relativity; but quantum field theory describes matter and energy, and that matter and energy should affect the spacetime geometry, as it does in general relativity, but does not in special relativity. So Einstein was basically saying that QFT based on SR could not be right because it left out the "reaction" of the spacetime geometry to matter and energy.

Even today, when we know how to do quantum field theory in curved spacetime, we have not fully solved this problem. The best we can do is to use what is called a "semiclassical" analysis, which assumes that the spacetime geometry is changing much more slowly than the quantum field theory processes we are studying, so that we can approximate the matter and energy content described by the QFT by its expectation value, and use that as the description of the matter and energy in the GR equations. I don't know what Einstein would have thought of that; this approach still has many limitations.

 

[PeterDonis]

I was just asking what would happen if we go directly from plain Schroedinger Quantum Theory to General relativistic quantum theory without passing through QFT.

The answer to this is simple: won't help. The problem is not what you think it is. See my previous post.

 

[PeroK]

So I was just asking what would happen if we go directly from plain Schroedinger Quantum Theory to General relativistic quantum theory without passing through QFT (and special relativity).

The Schroedinger equation (SDE) is manifestly non-relativistic: there is no possibility of starting with that. What you have to do is start somewhere else and re-derive the SDE in the approriate approximation.

This might be the only viable road to quantum gravity. All possibilities must be tried.

Maybe and maybe not. If I were a professional physicist about to embark on my life's work, I might not share your faith in eighty-year-old ideas.

You say "all possibilities must be tried", but I assume you're not the one dedicating your life to a long-shot!

 

[Fra]

So Einstein was basically saying that QFT based on SR could not be right because it left out the "reaction" of the spacetime geometry to matter and energy.

Even today, when we know how to do quantum field theory in curved spacetime, we have not fully solved this problem...

If I may suggest the generalisation of this:

Quantum Mechanics as it stands leaves out the full "reaction" of the observer side to the inteactions. This IMO the natural generalisation. Einsteins might have seem part of if, but it seems there is more to the "observer side" than spacetime geometry. But it is too much to ask for someone, prior to development of QFT to see this, especially given Einsteins scepsism of the probabilistic foundations.

Today, the reaction implicit in QM is quite simple and assumes we stay in the one and same linear space. Ie. the observer revises his information in the light of new information - but it never evolves the state space itself. This is also related to all the weird conservation and p-conservation issues you run into.

And to realize the full "reaction", it seems likely that the foundations of QM need deep revision, which of course is an open issue.

That QFT works flawlessly (besides lacking Planck scale unification) seems to be no coincidence, as when you study a small subatomic system, from a distance, ie a laboratory, you HAVE the solid classical SR spacetime there; to attach QM. This (QM constructions) breaks down in a fully relativistic scenario.

/Fredrik

 

[mitchell porter]

There's no doubt that over the years, people have tried out this starting point. There are decades of formal speculations recorded in journals like "Foundations of Physics". You could find some by googling "general relativistic quantum". But once you decide to start this way, it's still only the beginning. You then have to decide what aspects of GR and QM you will consider fundamental.

For example, whether you implement GR in a space-time or pre-space-time way. Assuming the use of operators and observables, the former might mean that you assume observables based on space-time points, and then seek a diffeomorphism symmetry; while the latter approach might mean observables that are not a-priori connected to space or time at all - thus immediately avoiding the problem of coordinate system dependence - with the aim then being to have space-time emerge somehow.

Christopher Isham might be the best writer for an overview of the theoretical options, e.g. see his gr-qc/9510063... This kind of deeply speculative, first principles approach is somewhat out of fashion, since we now have a variety of concrete frameworks in which quantum gravity can be studied (string theory, Hartle-Hawking wavefunction, etc). But it still has a place even in these frameworks - their conceptual foundations are often obscure and might be clarified by this perspective.

 

[Fra]

Thanks for the link, that's a good overview! He highlights some of the important things.

One that myself feel is one key and will not let pass is this one:

In particular, how justified is
(i) the concept of a ‘ spacetime point’;
(ii) the assumption that the set M of such points has the cardinality of the continuum
(iii) giving this continuum set the additional structure of a differentiable manifold.

Christopher Isham might be the best writer for an overview of the theoretical options, e.g. see his gr-qc/9510063... This kind of deeply speculative, first principles approach is somewhat out of fashion

Note sure when deep thinkers started to care about what's in fashion, but Chris comes with some honest carrier advice on "Transcendental quantisation".

Transcending classical categories in this way is a fascinating idea, but it is also very iconoclastic and—career-wise—it is probably unwise to embark on this path before securing tenure!

Wether its wise to stay fashionable is the question? I think the diffuculty is that we we talked too far down a successful path, that the idea that we MIGHT need to go back and find another route so solve this problem is depresseing and overwhealming. But I can not stand the idea of keep walking along a path in the wrong direction that i am convinced is wrong, I prefer to stay out of fashion.

/Fredrik

 

[Fra]

Just to comment on another important point.

In particular, how justified is
(i) the concept of a ‘ spacetime point’;

If one considers the generalisation of a "spacetime point" to rather be an abstract "label" for a distinguishable event - from the perspective of an observer(which is of course matter). To assign a metric, toplogy etc to this set is a higher construct.

In this perspective, its easier to see that spacetime could be just a part of the wholed index where all the observers happens to "hold an equivalent map" of relations to each other. As Rovelli argues in LQG, spacetime is defined as relations between observers, and relations are defined by means of communication.

And where are these relations encoded? In a spacetime substance? - obviosly not, right? So maybe in the observers themselves? And the observer is of course nothing but matter. Its just that we need to explain how come everyone happens to be in agreement, of part of the index, and see how the whole index separates into spacetime, and other internal structures. It seems quite reasonable to expect an explanation of why 4D+X? Why not 5D+X?

/Fredrik

 

[bayakiv]

Try to write a paper...

[Moderator's note: Invalid reference deleted.]

Better watch the thread Geometry of matrix Dirac algebra

 

[PeterDonis]

there is nonsense written about gravity, and I am lazy to write a new article

Sorry, but this is simply not acceptable as a reference. You have now been banned from further posting in this thread. Members who are interested can follow the link you give to the other thread.

 

[PeterDonis]

Moderator's note: A number of off topic posts have been deleted.

 

[bhobba]

The author was like describing that by using Special Relativity in QFT, we may not derive at any General Relativistic QFT. We have none now.

Not quite:
https://blogs.umass.edu/donoghue/research/quantum-gravity-and-effective-field-theory/

We have a perfectly good theory up to the Planck scale. Also I do not know of any physicists that believe the standard model holds beyond the Planck scale. In fact our modern view of renormalisation takes the cutoff seriously ie the standard model has a cutoff beyond which it is thought to not be applicable:
https://quantumfrontiers.com/2013/06/18/we-are-all-wilsonians-now/

Again that is thought to be at about the Planck scale. So all our theories really have the same problem - what is going on below the Planck scale?

To be more specific one assumes a flat space-time, and spin 2 particles. Low and behold Einstein's Field Equations result (see Feynman's famous Lectures on Gravitation for the detail). So is space-time curved, or flat and the gravitational field just makes everything act as if it is curved? There is no way to tell the difference. This is an example of science being stranger than many think.

Thanks
Bill

 

[jake jot]

There's no doubt that over the years, people have tried out this starting point. There are decades of formal speculations recorded in journals like "Foundations of Physics". You could find some by googling "general relativistic quantum". But once you decide to start this way, it's still only the beginning. You then have to decide what aspects of GR and QM you will consider fundamental.

For example, whether you implement GR in a space-time or pre-space-time way. Assuming the use of operators and observables, the former might mean that you assume observables based on space-time points, and then seek a diffeomorphism symmetry; while the latter approach might mean observables that are not a-priori connected to space or time at all - thus immediately avoiding the problem of coordinate system dependence - with the aim then being to have space-time emerge somehow.

Christopher Isham might be the best writer for an overview of the theoretical options, e.g. see his gr-qc/9510063... This kind of deeply speculative, first principles approach is somewhat out of fashion, since we now have a variety of concrete frameworks in which quantum gravity can be studied (string theory, Hartle-Hawking wavefunction, etc). But it still has a place even in these frameworks - their conceptual foundations are often obscure and might be clarified by this perspective.

I tried to read Isham paper and something confused me. What is the main difference between Quantum Gravity without using QFT and one that uses QFT? (By QFT is meant quantum theory with SR) He didn't state it directly. In page 8 Isham stated:

B. The four types of approach to quantum gravity

The four major categories in which existing approaches to quantum gravity can be classified are as follows.

1. Quantise general relativity. This means trying to construct an algorithm for actively quantising the metric tensor regarded as a special type of field. In practice, the techniques that have been adopted fall into two classes: (i) those based on a spacetime approach to quantum field theory—in which the operator fields are defined on a four-dimensional manifold representing spacetime; and (ii) those based on a canonical approach—in which the operator fields are defined on a three-dimensional manifold representing physical space.

2. ‘General-relativise’ quantum theory. This means trying to adapt standard quantum theory to the needs of classical general relativity. Most work in this area has been in the context of quantising a matter field that propagates on a fixed, background spacetime (M, γ), where M denotes the manifold, and γ is the spacetime metric.

3. General relativity is the low-energy limit of a quantum theory of something quite different. The most notable example of this type is the theory of closed superstrings.

4. Start ab initio with a radical new theory. The implication is that both classical general relativity and standard quantum theory ‘emerge’ from a deeper theory that involves a radical reappraisal of the concepts of space, time, and substance.

Which of them unites the Quantum and General Relativity without using Special Relativity in QFT? What is the major or distinguishing difference between quantum gravity that uses SR and those that don't?

 

[bhobba]

I tried to read Isham paper and something confused me. What is the main difference between Quantum Gravity without using QFT and one that uses QFT?

Using spin 2 quantum particles and a flat space-time, curvature effectively energes. Space-time in that view is still flat - but acts as if it is curved.

Normal GR can be done that way as well - see:
https://www.amazon.com/gp/product/1107012945/?tag=pfamazon01-20

Thanks
Bill

 

[jake jot]

There's no doubt that over the years, people have tried out this starting point. There are decades of formal speculations recorded in journals like "Foundations of Physics". You could find some by googling "general relativistic quantum". But once you decide to start this way, it's still only the beginning. You then have to decide what aspects of GR and QM you will consider fundamental.

For example, whether you implement GR in a space-time or pre-space-time way. Assuming the use of operators and observables, the former might mean that you assume observables based on space-time points, and then seek a diffeomorphism symmetry; while the latter approach might mean observables that are not a-priori connected to space or time at all - thus immediately avoiding the problem of coordinate system dependence - with the aim then being to have space-time emerge somehow.

"Pre-space-time way" and "have space-time emerge somehow" smell like Loop Quantum Gravity. I wonder if LQG has special relativity built-in?

Using spin 2 quantum particles and a flat space-time, curvature effectively energes. Space-time in that view is still flat - but acts as if it is curved.

Normal GR can be done that way as well - see:
https://www.amazon.com/gp/product/1107012945/?tag=pfamazon01-20

Thanks
Bill

But is it not using spin 2 quantum particles or linearized gravity still uses QFT? Einstein ideas may be more radical. Again he proclaimed.

"Contemporary physicists do not see that is hopeless to take a theory that is based on an independent rigid space (Lorentz-invariance) and later hope to make it general-relativistic (in some natural way) (Einstein to Max von Laue, September 1950)"

 

[PeterDonis]

We have a perfectly good theory up to the Planck scale.

Note that this claim depends on two things being true that we cannot check experimentally:

(1) That the "effective field theory" approach, as applied to the field theory of a massless spin-2 field (which leads to the same field equation as GR), remains valid up to the Planck scale, i.e., that no new physics that cannot be described by an effective field theory appears before that scale is reached.

(2) That the non-renormalizability of the field theory of a massless spin-2 field does not cause any issues before the Planck scale is reached--in other words, that the coefficients of the non-renormalizable terms in the theory are small enough for those terms to remain negligible up to the Planck scale.

Our current experiments are still about 20 orders of magnitude short of the Planck scale.

 

[PeterDonis]

"Contemporary physicists do not see that is hopeless to take a theory that is based on an independent rigid space (Lorentz-invariance) and later hope to make it general-relativistic (in some natural way) (Einstein to Max von Laue, September 1950)"

See my comments on this in post #6. As I said there, Einstein was not talking about what you think he was talking about. Nothing he said invalidates QFT as an effective field theory, which is how it is viewed today.

 

[jake jot]

See my comments on this in post #6. As I said there, Einstein was not talking about what you think he was talking about. Nothing he said invalidates QFT as an effective field theory, which is how it is viewed today.

Yes. QFT is an effective field theory. Maybe Einstein meant that to create the full theory without any back reaction thing. One doesn't start from the effective field theory. But different formulation where matter and spacetime evolve. Anyway i wonder if Loop Quantum Gravity is it. It has no backreaction. But unfortunately it has no other forces. So maybe a full fledged LQG with forces is Einstein dream too.

 

[bhobba]

But is it not using spin 2 quantum particles or linearized gravity still uses QFT? Einstein ideas may be more radical. Again he proclaimed.

Read the book I gave by O'hanian. The way it's done is simply to note that EM is linear. Now a very important theorem by Wigner says in any relativistic field theory the field must be a tensor. A 4 tensor leads to EM. Write down a general linear theory in a 4x4 tensor and you get linearised gravity. But one notes that in linearised gravity spacetime acts as if it has an infinitesimal curvature. It can't of course because you have assumed it is flat. But it acts like it is curved. OK this is just for an infinitesimal curvature. But due to an interesting phenomena sometimes called gravity gravitates it should be generalised to any curvature:
https://www.physicsforums.com/insights/does-gravity-gravitate/

What would a theory look like if the curvature was arbitrary? Low and behold you find that only one set of equations, the EFE's, reduce to linearised gravity. It is a rather strange mathematical property - but it is true. Probably related to Lovelock's theorem - but that's another story - see Lovelock and Rund:
https://www.amazon.com/dp/0486658406/?tag=pfamazon01-20

Thanks
Bill

 

[PeroK]

Low and behold ...

Isn't it "lo and behold"?

 

[bhobba]

Isn't it "lo and behold"?

Of course

Thanks
Bill

 

[Fractal matter]

Is it possible to have some kind of General Relativistic Quantum Theory without passing through the stage of Quantum Field Theory (where Quantum Theory is married to Special Relativity)?

I think you may be interested in articles by Thomas Andersen. I suggest you to check them out.

 

[Fra]

Is it possible to have some kind of General Relativistic Quantum Theory without passing through the stage of Quantum Field Theory (where Quantum Theory is married to Special Relativity)?

Einstein attached primary significance to the concept of general covariance as shown in this letter in 1954. You can google these letter to see they are really from Einstein:

"You consider the transition to special relativity as the most essential thought of relativity, not the transition to general relativity. I consider the reverse to be correct. I see the most essential thing in the overcoming of the inertial system, a thing that acts upon all processes but undergoes no reaction. This concept is in principle no better than that of the center of universe in Aristolian physics (Einstein to Georg Jaffe, January 19, 1954)"

This implies that the class of global inertial frames singled out in the special theory of relativity can have no place in the relativistic theory of gravitation. Is this true in general (pun unintended)?

It seems he felt a quantum theory constructed on the basis of Galilean or even special-relativistic space-times could not consititute a satisfactory foundation of physics. What do you think?

Hard to imagine how Einsten was thinking at the time. But it seems plausible to think that the core guiding principle of the time - common to both SR and GR, is that the laws of physics must be the same to every possible observer.

Two key differences between GR and QFT(SR+particle physics):

(1) GR is a larger equivalence class of observers than SR - but the constructing principle is the same.

(2) QFT is constructed for small subsystems, from the perspective of an effectively external observer (scattering measurements) where the "references" of the measurements are never influenced by the measurements. In GR there is no such thing as and external observer. Any measurements must be constructed from withing the system of study, possibly having its very references beeing affected by the measurements themselves.

In classical physics, with realism in mind, the assymmetry in 2 can be dismissed as of pratical matter only.

In this view (ignoring 2) enforcing the diffeomorphism invarance, may seem in principle no different than enfording poincare invariance. Thus the conclusion that constructing a theory of measurement, based on a special case (SR) can not possibly be right.

But taking (2), and the process of measuremeent and inference more serious and paramount than a minor practical matter, actually suggests that there is something wrong with (1) - it contains assumptions that are far too strong. But their strenght is also its power, but the same power can lead us wrong.

Its the classic choice here, which guiding principe is "more important", observer equivalence or onstructability from a given observer? There are good arguments for both sides, and analysing this in depth actually takes us down to the foundations of the scientific method. This is why a lot of physicists, stubbornly refuse to accept the fuzzy stuff about evolution of law, because they think it makes not sense as science. I can follow both arguments. But discussing this takes us outside physics, and many physicists will refuse to stay in discussion.

/Fredrik

 

[jake jot]

Hard to imagine how Einsten was thinking at the time. But it seems plausible to think that the core guiding principle of the time - common to both SR and GR, is that the laws of physics must be the same to every possible observer.

Two key differences between GR and QFT(SR+particle physics):

(1) GR is a larger equivalence class of observers than SR - but the constructing principle is the same.

(2) QFT is constructed for small subsystems, from the perspective of an effectively external observer (scattering measurements) where the "references" of the measurements are never influenced by the measurements. In GR there is no such thing as and external observer. Any measurements must be constructed from withing the system of study, possibly having its very references beeing affected by the measurements themselves.

In classical physics, with realism in mind, the assymmetry in 2 can be dismissed as of pratical matter only.

In this view (ignoring 2) enforcing the diffeomorphism invarance, may seem in principle no different than enfording poincare invariance. Thus the conclusion that constructing a theory of measurement, based on a special case (SR) can not possibly be right.

But taking (2), and the process of measuremeent and inference more serious and paramount than a minor practical matter, actually suggests that there is something wrong with (1) - it contains assumptions that are far too strong. But their strenght is also its power, but the same power can lead us wrong.

Its the classic choice here, which guiding principe is "more important", observer equivalence or onstructability from a given observer? There are good arguments for both sides, and analysing this in depth actually takes us down to the foundations of the scientific method. This is why a lot of physicists, stubbornly refuse to accept the fuzzy stuff about evolution of law, because they think it makes not sense as science. I can follow both arguments. But discussing this takes us outside physics, and many physicists will refuse to stay in discussion.

/Fredrik

Let's connect what you said to Bhobba linearized gravity.

I think linearized gravity is saying that massless spin-2 field implies gravity, that if your theory contains such a field, then the only consistent way for it to interact is as gravity. But this is valid only up to the Planck scale.

So below Planck scale physics may not be string theory or loop quantum gravity. Whatever. It may still have spin 2 particles. And I guess spin 2 particles can't handle back reaction?

Einstein preference seemed to be to have general covariance and quantum particles without back reaction?

Didn't Einstein know about spin 2 particles implied GR and about linearized gravity?
Unless Einstein wanted to do away with spin 2 particles? Does Loop quantum gravity lack any spin 2 particles? Does it mean Einstein was looking for some kind of LQG?

It's sad that in spite of being year 2021 already. We were still discussing old 1950s physics. The last quantum revolution occurred in 1927. Hope in 2027 we will have another revolution. We are long overdue for it.

 

[PeterDonis]

Write down a general linear theory in a 4x4 tensor and you get linearised gravity. But one notes that in linearised gravity spacetime acts as if it has an infinitesimal curvature. It can't of course because you have assumed it is flat. But it acts like it is curved.

Sort of. This description might be misleading, though.

A better way to describe the situation, IMO, would be as follows:

(1) You decide to write down the field theory of a massless spin-2 field. To linear order, this field is described as a symmetric 2-index tensor on flat Minkowski spacetime.

(2) You then notice that this theory is not consistent: looked at one way, it predicts that freely falling objects should follow geodesics of the flat Minkowski spacetime, but looked at another way, it predicts that freely falling objects should follow geodesics of a curved spacetime, whose metric tensor is the metric of flat Minkowski spacetime plus the tensor you wrote down to describe the massless spin-2 field.

(3) The only way to resolve this inconsistency in the theory is to go beyond linear order. Once you have carried that out completely, what you end up with is the nonlinear Einstein Field Equation--in other words, General Relativity. You can still view the metric tensor you end up with as being the metric of flat Minkowski spacetime plus a "correction" due to a massless spin-2 field, but now the theory is no longer linear and it now consistently predicts, no matter which way you look at it, that freely falling objects follow geodesics of the curved spacetime described by the full metric tensor.

 

[PeterDonis]

I think linearized gravity is saying that massless spin-2 field implies gravity

Sort of. See my post #29 just now in response to @bhobba's earlier post.

I guess spin 2 particles can't handle back reaction?

Sure they can. Just not at linear order. See my post #29.

Einstein preference seemed to be to have general covariance and quantum particles without back reaction?

Einstein, AFAIK, never considered what a quantum theory of gravity might look like. Most of the work on the QFT of a massless spin-2 field, including figuring out what I described in post #29, was done after he died, in the 1960s and early 1970s.

Didn't Einstein know about spin 2 particles implied GR and about linearized gravity?

AFAIK nobody knew about that until after Einstein died. Einstein did not develop GR by the route I described in post #29. When he developed GR, quantum field theory didn't even exist at all; non-relativistic QM was still in its infancy.

 

[jake jot]

Sort of. See my post #29 just now in response to @bhobba's earlier post.



Sure they can. Just not at linear order. See my post #29.

When I wrote "I guess spin 2 particles can't handle back reaction?" What I meant was "I guess spin 2 particles can't handle the symptoms of QFT that can't not take into account back reaction?". I know we so far do not have a version of QFT in which we can dynamically solve for the QFT and the background spacetime at once. And this includes spin 2 particles. But then spin 2 particles were not proven to exist so far yet. In case they exist. I was asking (asking for confirmation) we can't still dynamically solve for the QFT and the background spacetime at once even with spin 2 particles?

In String theory. We have spin 2 particles and this gives rise to GR by some kind of linearized gravity tricks? meaning the GR is not fundamental in string theory but emergent from the behavior of spin 2 particles? If so, then spin 2 particles were the fundamental. And there is nothing that would prevent the existence of anti-spin 2 particles or other modes of strings. This means GR not being fundamental can be over ridden by whatever string modes would produced particles or forces that would counter spin 2 particles? Just asking.

Einstein, AFAIK, never considered what a quantum theory of gravity might look like. Most of the work on the QFT of a massless spin-2 field, including figuring out what I described in post #29, was done after he died, in the 1960s and early 1970s.



AFAIK nobody knew about that until after Einstein died. Einstein did not develop GR by the route I described in post #29. When he developed GR, quantum field theory didn't even exist at all; non-relativistic QM was still in its infancy.

 

[PeterDonis]

I know we so far do not have a version of QFT in which we can dynamically solve for the QFT and the background spacetime at once. And this includes spin 2 particles.

No, that's not correct. The QFT of a massless, spin-2 field is General Relativity in the classical limit. That means it is a QFT that dynamically gives you a curved spacetime geometry. It's just not renormalizable.

What we don't have is a way of combining the QFT of a massless, spin-2 field with a QFT containing other fields that are not spin-2, such as the Standard Model of particle physics (which contains spin-1/2 and spin-1 fields), to get a self-consistent model that dynamically determines both the spacetime geometry and the "matter" content. So the problem is that the QFT that tells us the "matter" content does not include a massless, spin-2 field; that QFT can only be solved if we first assume a fixed, background spacetime.

Note, btw, that the above does not mean "back reaction" can't be included at all. One can still include, for example, the expectation value of the stress-energy tensor associated with the "matter" fields in the Einstein Field Equation that you then solve for the background spacetime geometry. What one can't do is have a fully quantum theory including both the "matter" content and the spacetime geometry, in which, for example, we could have a superposition of different spacetime geometries corresponding to a superposition of different matter field configurations.

GR is not fundamental in string theory but emergent from the behavior of spin 2 particles?

More precisely, it's emergent in string theory from the fact that one of the fundamental string modes appears as a massless, spin-2 field in the low energy limit.

there is nothing that would prevent the existence of anti-spin 2 particles or other modes of strings

What do you mean by "anti-spin 2 particles"? The graviton (the massless, spin-2 field) is its own antiparticle, since it does not carry any conserved charges.

As for other modes of strings, yes, string theory has lots of them. Too many, in fact; that's one of the major problems with string theory, that nobody knows how to write down a string theory that just contains the string modes that would produce the actual Standard Model particles we see. (In fact, nobody knows for sure that there even are string modes that would produce the actual Standard Model particles we see.)

 

[jake jot]

No, that's not correct. The QFT of a massless, spin-2 field is General Relativity in the classical limit. That means it is a QFT that dynamically gives you a curved spacetime geometry. It's just not renormalizable.

What we don't have is a way of combining the QFT of a massless, spin-2 field with a QFT containing other fields that are not spin-2, such as the Standard Model of particle physics (which contains spin-1/2 and spin-1 fields), to get a self-consistent model that dynamically determines both the spacetime geometry and the "matter" content. So the problem is that the QFT that tells us the "matter" content does not include a massless, spin-2 field; that QFT can only be solved if we first assume a fixed, background spacetime.

Note, btw, that the above does not mean "back reaction" can't be included at all. One can still include, for example, the expectation value of the stress-energy tensor associated with the "matter" fields in the Einstein Field Equation that you then solve for the background spacetime geometry. What one can't do is have a fully quantum theory including both the "matter" content and the spacetime geometry, in which, for example, we could have a superposition of different spacetime geometries corresponding to a superposition of different matter field configurations.



More precisely, it's emergent in string theory from the fact that one of the fundamental string modes appears as a massless, spin-2 field in the low energy limit.



What do you mean by "anti-spin 2 particles"? The graviton (the massless, spin-2 field) is its own antiparticle, since it does not carry any conserved charges.

Since GR is emergent in string theory. By other string modes I meant just like we have Pauli Exclusion principles that prevent matter from occupying same space. It is not impossible to have string modes that can shield against spin 2 particles? This is just asking.

As for other modes of strings, yes, string theory has lots of them. Too many, in fact; that's one of the major problems with string theory, that nobody knows how to write down a string theory that just contains the string modes that would produce the actual Standard Model particles we see. (In fact, nobody knows for sure that there even are string modes that would produce the actual Standard Model particles we see.)

Maybe (just for sake of arguments) one can just think of string theory as programmable, meaning you can input any arbitrary constants of nature? We will don't know where our constants of nature comes from so we may have to think of string theory as the numbers put it. At least we have the device (string theory) to make it happen.

 

[PeterDonis]

By other string modes I meant just like we have Pauli Exclusion principles that prevent matter from occupying same space.

First, that's not what the Pauli Exclusion principle says. It says no two fermions can be in the same quantum state, but what spatial region the particle occupies is not all there is to the quantum state.

Second, the Pauli Exclusion principle doesn't tell you anything about which particular types of fermions can exist. That's just as true if you think the fermions are "string modes".

It is not impossible to have string modes that can shield against spin 2 particles?

I don't know what you mean by "shield against". If you mean "not interact with", the answer is no: anything that has energy interacts with the massless spin-2 field. That's just as true in string theory.

Maybe one can just think of string theory as programmable, meaning you can input any arbitrary constants of nature?

I don't know what would make you think this. String theory only has one constant whose value can be chosen, the string tension. Everything else is a prediction of the theory, not an input to it. That includes all of the things that in our current theories we call "constants of nature" and have to put in values for from experiments.

 

[Fra]

I would be careful still to mix discussions of conceptual structures and founding principles, with mathematical methods, such are perturbation theory. For this reasons, perturbative approaches to gravity is of course interesting, as i provides a probe, but I do not consider terms popping out from such expansions to necessarily have any profound meaning beyond a mathematical tool.

/Fredrik