I General Relativistic Quantum Theory?

[PeterDonis]

the 120 order of magnitude difference is between what QFT appears to predict and what we actually observe.

This article by John Baez might be helpful:

https://math.ucr.edu/home/baez/vacuum.html

 

[jake jot]

See the bolded addition above. GR already solves the problem of how to have classical matter and spacetime evolve dynamically together. The only part of the problem that isn't (yet) solved is how to do that for cases where the matter has to be described using quantum mechanics.

However, in a practical sense, that problem is a non-problem, because there are no practical cases where we need to describe the interaction between matter and spacetime geometry using quantum mechanics. The problem is purely a theoretical one. And it's not 100 percent certain even that it is a theoretical problem; some physicists (for example, Freeman Dyson) have proposed that maybe there is no such thing as a "quantum" theory of gravity, that quantum fields on a classical curved spacetime really is as deep as we need to go.
You don't. All efforts to do that other than QFT failed back in the 1920s and 1930s.
He never proposed anything along these lines at all. The unification he was preoccupied with for most of his life after discovering GR was a classical unified theory of gravitation and electromagnetism. He was never convinced that QM was a necessary part of a fundamental theory.
String theory. String theory is a quantum field theory of strings instead of point particles.
LQG wasn't even begun as a research program until well after Einstein's death. I don't think it's fruitful to speculate about what he would have thought of it.

I meant LQG could or might (?) be what Einstein wanted even though LQG was discovered much later after he died (I Know Einstein and Smolin belong to different generations).

No. It's a different kind of framework. The only connection between the two is that LQG will need to show why QFT works in the regime in which it works--i.e., that a QFT like our Standard Model emerges from LQG in some appropriate limit.
No, that's not correct.

First, the actual observed value for the cosmological constant (aka dark energy) is 120 orders of magnitude smaller than the theoretical value, not larger.

I just wrote "The vacuum is said to have 120 magnitude more energy than predicted by GR." Why did you attribute what I wrote to cosmological constant? I meant by vacuum as the ground state of QFT. Why. If one wrote "vacuum", it refers to cosmological constant. And if one wrote "quantum vacuum", it refers to the ground state of QFT? So I can be more careful with words next time.

Second, the 120 order of magnitude difference is between what QFT appears to predict and what we actually observe. GR makes no prediction whatsoever about the value of the cosmological constant; it just says that you can have a cosmological constant term in the field equation and the theory will still work.

What "QFT appears to predict" is related to quantum vacuum. So can't we think of nature as actually having quantum vacuum which is the ground state of the quantum fields? So there is a distinction between "quantum vacuum" and "cosmological constant" (which perhaps one refers simply as "vacuum"?)?

Also what we observe has to do with GR. If we ignore or don't use GR, the 120 magnitude problem predicted by QFT is still a problem or it goes away since if we don't use GR, spacetime doesn't bend?

 

[PeterDonis]

I just wrote "The vacuum is said to have 120 magnitude more energy than predicted by GR." Why did you attribute what I wrote to cosmological constant?

Because that's what "vacuum energy" means. "Vacuum energy", "cosmological constant", and "dark energy" are all just different names for the same thing.

I meant by vacuum as the ground state of QFT.

Yes. That is the meaning I understood you to be using. It doesn't change anything I said. The fact that "vacuum energy" ultimately comes from the ground state of QFT doesn't mean it can only be described in a quantum theory. The cosmological constant is how that same vacuum energy appears in GR.

what we observe has to do with GR.

What we observe of the accelerated expansion of the universe, which is how we know there is a nonzero cosmological constant/vacuum energy/dark energy, requires GR for its analysis, yes.

If we ignore or don't use GR

Then we would be doing an incorrect analysis of cosmological observations.

the 120 magnitude problem predicted by QFT is still a problem

The "problem predicted by QFT" is a problem in other contexts than cosmology, yes. If the energy of the vacuum were what QFT predicted, everything we observe would be very, very different. (It might even be impossible for creatures like us to exist at all.)

if we don't use GR, spacetime doesn't bend?

You are confused. You can't change what spacetime does by not using some particular theory developed by humans.

 

[PeterDonis]

So there is a distinction between "quantum vacuum" and "cosmological constant" (which perhaps one refers simply as "vacuum"?)?

I strongly suggest reading the Baez article I linked to. I think it will help you to overcome some evident confusions that you have.

 

[Fra]

So there is a distinction between "quantum vacuum" and "cosmological constant" (which perhaps one refers simply as "vacuum"?)?

Not sure if this makes it more clear?

1) The cosmological constant is the classical term in the classic GR equations.
In GR is interpreted as a energy density of empty space. (ie. empty classical space).
In principle this has nothing to do with quantum mechanics framework.

2) The other value is the "expectations values" as per QM/QFT of the energy density of the lowest energy levels in the quantum fields. As fields fluctuates with particle-antiparticle creations, the consequence is that even empty space - on average - contains energy. The problem is the formal computations typically diverge and are infinite. Sometimes one can make it finite be renormalization procedures, but its still HUGE, like discussed. In principle this has nothing to do with GR.

Its when you try to merge the two theories and think they are the same, that it doens't add up. But in principe, energy in GR and energy in QM is defined differently.

I personally think this will be solved automatically along with the progress of unification, so it is IMO not a "primary conceptual problem", I see it it's more symptomatic problem of a deeper issue.

Divergent formal expressions is abundant in QM, while renormalization helps tame it in a mathematical sense, it is IMO not a satisfactory way of handling it; its more an engineering trick of curing formal problems, than fundamentally fixing it. One could argue that the divergences are related to the background depencens as well. As the "expectations" actual refer to background structures, that are FIXED. And understanding constructing principles of GR the association "FIXED background ~ infinite inertia" seems natural. But these external backgrounds make no sense in GR. So the problem is not unexpected.

/Fredrik

 

[jake jot]

Peterdonis and others,

Related to this thread. I'm reading the great relativist John Stachel book Einstein from B to Z.

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

In it is said that "Even relativists have not yet fully adopted the point of view, "no metric, no nothing". As relativists, why have you guys adopted the "no metric, no nothing" view. What is your problem with it?

In the next page where it wasn't shown above is written these:

"space shows. But one does not start out with global topology and then look for all the metrics solving the field equations that are compatible with it. The important point is that if one wants to consider all solutions to the field equations - or even a subclass wide enough to include solutions on topologically inequivalent manifolds - one must have a mathematical structure that allows this to be done.

Although the two ideas are not exactly the same, the moral I want to draw from this final point may be related to something that Chris Islam talked about. Supposed you take really seriously the point of view that there is something fundamentally local about the way general relativity approaches a problem. Then there is another fundamental tension between the basic approaches of general relativity and of quantum mechanics since quantum mechanics, in a deep sense, is fundamentally global in its approach to problems. It doesn't make much sense to talk about the wave function in one path of space-time, or the sum over all paths on one path of space-time. In solving a quantum-mechanical problem, you have to consider the whole manifold from the beginning. The conventional mathematical approach to general relativity, which starts with a manifold, masks this tension. If we develop a mathematical formulation of general relativity that emphasizes the element of locality from the beginning, it would emphasize this contrast more sharply. Such an emphasis on the tension may be a necessary stage in finding its ultimate resolution.

Indeed, this way of thinking also suggests new possibilities. Perhaps the existence of a global manifold is just a special case. Maybe in the ultimate theory all the patches won't always fit together to form a manifold, except in the classical limit. Here is where my point of view may connect some of Isham's ideas. If you don't build in a global manifold at the beginning, perhaps you are better off, because you may have to get rid of it in the end anyway.

What does these lines mean "The conventional mathematical approach to general relativity, which starts with a manifold, masks this tension.", why does it mask the tension?

And continued "If we develop a mathematical formulation of general relativity that emphasizes the element of locality from the beginning, it would emphasize this contrast more sharply." What would it take to emphasize element of locality from the beginning in GR?

And lastly. Concerning the last paragraph and all. It was written in 2000. Are there developments that already disprove some of the ideas?

In the last sentence " If you don't build in a global manifold at the beginning, perhaps you are better off, because you may have to get rid of it in the end anyway."
Can this be made for the case of QM where you don't consider the whole manifold from the beginning?

I want to see ideas where both QM and GR are just effective field theories that you can override in the more fundamental theories. Meaning you are not bounded (binded or whatever) by QM or GR in the ultimate framework.

 

[PeterDonis]

As relativists, why have you guys adopted the "no metric, no nothing" view.

I assume you mean why haven't relativists adopted this view? The answer is simple: they have. Stachel's claim is wrong.

Even on the basis of what Stachel himself says further down on the same page, his claim is at least questionable. After describing the way he claims GR is taught in textbooks (the way that he says does not adopt the "no metric, no nothing" view), he goes on to say that nobody actually does GR that way in practice--the way people actually do GR in practice is the "no metric, no nothing" view. So he's contradicting himself.

Further, I'm not sure even the way GR is taught in textbooks is as Stachel describes. The GR textbooks I'm most familiar with are MTW and Wald; I'm also fairly familiar with Carroll's online lecture notes. None of those sources present GR the way Stachel describes it. A more detailed discussion of why I think that would probably be too technical for an "I" level thread. But suffice it to say I don't agree with Stachel's claims in this regard.

 

[jake jot]

I assume you mean why haven't relativists adopted this view? The answer is simple: they have. Stachel's claim is wrong.

Even on the basis of what Stachel himself says further down on the same page, his claim is at least questionable. After describing the way he claims GR is taught in textbooks (the way that he says does not adopt the "no metric, no nothing" view), he goes on to say that nobody actually does GR that way in practice--the way people actually do GR in practice is the "no metric, no nothing" view. So he's contradicting himself.

Further, I'm not sure even the way GR is taught in textbooks is as Stachel describes. The GR textbooks I'm most familiar with are MTW and Wald; I'm also fairly familiar with Carroll's online lecture notes. None of those sources present GR the way Stachel describes it. A more detailed discussion of why I think that would probably be too technical for an "I" level thread. But suffice it to say I don't agree with Stachel's claims in this regard.

You mentioned above that a more detail discussion would probably be too technical for an "I" level thread, that's why I created an "A" thread in the relativity forum.

But without discussing the technical details (I opened that new thread for the relativity discussion without all this BSM stuff). I think here is the way to resolve the seemingly conflicts. Remember this passage by Einstein himself in 1954.

"It required a severe struggle to arrive at the concept of independent and absolute space, indispensable for the development of theory. It has required no less strenous exertions subsequently to overcome this concept - a process which is by no means as yet completed (Einstein 1954b)"

Looking at background of John Stachel. He was born in 1928, so maybe his statement is because he lived those years Einstein was contemplating it.

https://www.encyclopedia.com/arts/educational-magazines/stachel-john-jay-1928

"Lehigh University, Bethlehem, PA, instructor in physics, 1959-61; https://www.encyclopedia.com/social-sciences-and-law/education/colleges-us/university-pittsburgh, Pittsburgh, PA, instructor in physics, 1961-62, research associate, 1962-64; Boston University, Boston, MA, assistant professor of physics, 1964-69, associate professor, 1969-72, professor, 1972-97, professor emeritus, 1997—, Center for Einstein Studies, director, 1985—. Visiting research associate, Institute for Theoretical Physics, Warsaw, Poland, 1962; visiting professor, King's College, London, 1970-71, University of Paris, 1990-91, https://www.encyclopedia.com/people/science-and-technology/physics-biographies/max-planck Institute for History of Science, Berlin, 1994—, and https://www.encyclopedia.com/social-sciences-and-law/education/colleges-us/california-institute-technology, 1998; visiting senior research fellow, Department of Physics, https://www.encyclopedia.com/social-sciences-and-law/education/colleges-us/princeton-university, 1977-84; editor, Einstein papers, 1977-89; research associate, https://www.encyclopedia.com/social-sciences-and-law/education/colleges-us/university-california—Berkeley, 1994. "

"As director of Boston University's Center for Einstein Studies, Stachel conducts conferences on general relativity with other leading scholars, and with Don Howard edits the resulting collections of papers in the "Einstein Studies" series. In reviewing Volume One in this series, Einstein and the History of General Relativity, Wolfgang Drechsler wrote in Physics Today that the volume "is a true and valuable source of information on the origin and development of Einstein's theory. The reader may only wonder why such a book had not been written decades ago." "

So the answer is after 70 years, with new generations born, the no metric, no geometry is already not doubted.

Going to Einstein United Field Theory. You wrote in message #50

He never proposed anything along these lines at all. The unification he was preoccupied with for most of his life after discovering GR was a classical unified theory of gravitation and electromagnetism. He was never convinced that QM was a necessary part of a fundamental theory.

But at that time, there was already the electron. How come Einstein didn't add electron to unification of gravity and electromagnetism? Whereas in our present String Theory, the electron is included along with gravity, electroweak, and strong force, and matter particles like quark?

Whatever. I know GR and QFT explain our world. And the ultimate framework is only said to be valid at higher energies (like Planck scale), right? But why is it impossible to have the ultimate theory occurring right at the low energy scale, where with another mode. GR and QFT theories are not used by a more powerful theory? The physicists reasonings might be that they are no phenomena at low energy not explainable by our GR and QFT (even dark matter). I couldn't state the reasons why they are wrong, But just theoretically. Is it not at all impossible to formulate a theory where the ultimate framework can also occur at low energy by bridging some kind of barrier whereby GR and QFT are just effective field theory at a patch. Here the last two paragraphs of Stachel passages may be relevent.

(others, kindly give models where the ultimate framework occurs at low energy, and not the Planck scale)

 

[PeterDonis]

You mentioned above that a more detail discussion would probably be too technical for an "I" level thread, that's why I created an "A" thread in the relativity forum.

As I noted in that thread, though, I'm not sure you have the background for an "A" level discussion. You would probably be better served by taking the time to study some GR textbooks or course notes first. Then you might be able to evaluate for yourself whether Stachel's description is accurate. Sean Carroll's lecture notes on GR are freely available online:

https://arxiv.org/abs/gr-qc/9712019

 

[PeterDonis]

How come Einstein didn't add electron to unification of gravity and electromagnetism?

It's right there in what you quoted from me: "He was never convinced that QM was a necessary part of a fundamental theory." He thought a classical unified field theory was the way to go, so that's what he worked on.

 

[PeterDonis]

The physicists reasonings might be that they are no phenomena at low energy not explainable by our GR and QFT

Exactly.

kindly give models where the ultimate framework occurs at low energy

There aren't any, for the very reason you gave and I said "exactly" to above.

 

[jake jot]

It's right there in what you quoted from me: "He was never convinced that QM was a necessary part of a fundamental theory." He thought a classical unified field theory was the way to go, so that's what he worked on.

But there was already an electron. What is Einstein thought of electron classically? Even if he was not convinced of QM. Still the electron exists. How would he embed electrons in the unified field theory? Maybe electron as some kind of geometry? What is it?

 

[PeterDonis]

But there was already an electron.

That was true even in 1905 when Einstein published his original paper on special relativity. (The electron was discovered in 1897.) That doesn't mean Einstein was required to produce a theory of it.

What is Einstein thought of electron classically? Even if he was not convinced of QM. Still the electron exists. How would he embed electrons in the unified field theory?

I don't know if Einstein considered the electron or any charged particles specifically in his unified field theory work. I think he had a very general idea that a charged "particle" would be described as a solution of the classical field equations that looked like a dense bundle of energy in a very small volume. I don't think he ever actually found such solutions mathematically, however.

 

[bhobba]

What is Einstein thought of electron classically?

I do not think he had any specific ideas, except maybe as part of some unified theory he was working on at the time (he worked on a few). Actually Dirac discovered classically the electron had its problems:
https://cds.cern.ch/record/419756/files/9912045.pdf

He fully believed in QM, except at the beginning where his famous debates with Bohr were part of the reason he, and every other physicist I am aware of, came to believe in QM. I have posted it before, but here is his interpretation of QM:
https://www.informationphilosopher.com/solutions/scientists/ballentine/AJP72.pdf

It is still around today, being called the Ensemble Interpretation. It is the interpretation in one of the most respected modern QM books:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

The only real issue Einstein had was till his dying day he believed it incomplete, and part of a more classical unified field theory he spent the latter part of his life working on. In fact, for what it's worth, so do I, except I do not think it is likely 'classical'.

Thanks
Bill

 

[atyy]

He fully believed in QM, except at the beginning where his famous debates with Bohr were part of the reason he, and every other physicist I am aware of, came to believe in QM. I have posted it before, but here is his interpretation of QM:
https://www.informationphilosopher.com/solutions/scientists/ballentine/AJP72.pdf

It is still around today, being called the Ensemble Interpretation. It is the interpretation in one of the most respected modern QM books:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

Ballentine's ensemble interpretation is not Einstein's interpretation. Ballentine's textbook has many fundamental errors and cannot be recommended except to experts.

 

[atyy]

It's right there in what you quoted from me: "He was never convinced that QM was a necessary part of a fundamental theory." He thought a classical unified field theory was the way to go, so that's what he worked on.

But there was already an electron. What is Einstein thought of electron classically? Even if he was not convinced of QM. Still the electron exists. How would he embed electrons in the unified field theory? Maybe electron as some kind of geometry? What is it?

Couldn't he have used a classical Dirac field? Or would that not count that as having an "electron" since there is no quantization?

This has nothing to do with Einstein's classical unification efforts, but here's an interesting reference for the classical Einstein-Maxwell-Dirac equations:

The Einstein-Dirac-Maxwell Equations - Black Hole Solutions
Felix Finster, Joel Smoller, Shing-Tung Yau
https://arxiv.org/abs/gr-qc/9910030

 

[PeterDonis]

Ballentine's textbook has many fundamental errors

Can you give some specific examples?

 

[PeterDonis]

Couldn't he have used a classical Dirac field?

In principle he could have considered that, but I don't know of any evidence that he did. AFAIK the only fields he was considering were the metric tensor $g_{\mu \nu}$ and the EM field tensor $F_{\mu \nu}$.

 

[atyy]

Can you give some specific examples?

Ballentine lacks a clear statement of collapse or state reduction. He misrepresents the Copenhagen interpretation, and suggests that the Copenhagen interpretation is in conflict with experiment (Chapter 9). Ballentine's lack of collapse makes him give the wrong result in conflict with experimental outcomes on the "watched pot" experiment.

 

[jake jot]

It depends on what you call "spacetime". If you call all 10 (or 11) dimensions postulated by string theory "spacetime", then 6 of those dimensions are the ones in the Calabi-Yau spaces, yes. But if you only call the 4 dimensions we actually observe "spacetime", then no, the 6 dimensions in the Calabi-Yau spaces are different from those.

My understanding (which might possibly be mistaken; perhaps other experts on this forum can weigh in here) of how "spacetime emerges" in string theory is that the string mode that looks like a massless spin-2 field at low energy only affects the 4 dimensions we actually observe, not the others. If that is correct, then the dimensions contained in the Calabi-Yau spaces do not emerge that way; and that was what you were asking about.
No. You have our normal spacetime of 4 dimensions, and then 6 (or 7) other dimensions that are compactified.
Yes.
Not the EFE of GR, no. That EFE is specifically for 4 dimensions.

About the "That EFE is specifically for 4 dimensions.". Does it mean whenever there are 4 dimensions, there is automatically GR? Or are there 4D worlds that are not described by GR? If so, what would change if the world is 4D but doesn't have Equivalence principle and if you put feather and iron core, they don't fall at same time?

In LQG, there is always the comment it can't recreate GR. So I wonder if LQG can somehow create 4D world but not described by GR.

Also Hossenfelder wrote in Sabine Hossenfelder: Backreaction

"Personally, I find it misleading to say that in this case, time is not real. It’s like claiming that because our theories for the constituents of matter don’t contain chairs, chairs are not real. That doesn’t make any sense. But leaving aside that it’s bad terminology, is it right that time might fundamentally not exist?

I have to admit it’s not entirely implausible. That’s because one of the major reasons why it’s difficult to combine quantum theory with general relativity is that… time is a dimension in general relativity. In Quantum Mechanics, on the other hand, time is not something you can measure. It is not “an observable,” as the physicists say. In fact, in quantum mechanics it is entirely unclear how to answer a seemingly simple question like “what is the probability for the arrival time of a laser signal”. Time is treated very differently in these two theories. "Is it possible Quantum Mechanics lives not in the 4D spacetime of GR but it has its own space where time is different?

All this is to prepare for reading Julian Barbour new book "The Janus Point" (which she mentioned at the end).

The Janus Point: A New Theory of Time: Barbour, Julian: 9780465095469: Amazon.com: Books

In a review

"In his radical new book, Julian Barbour argues that...time flows in not one, but two ways... Such an argument might seem overly technical, but it's explained simply and accessibly for all to understand."
―BBC Science Focus

But a reader has this to say:

"Left me baffled
Reviewed in the United Kingdom on December 29, 2020

I found this book incomprehensible - even with a strong science background. The explanations given for the Janus point and the diagrams illustrating it are not well explained and the text left me totally baffled in too many places.".

This thread can prepare or make me see even slightly or catch a glimpse through the cloudy dense veil of Julian Barbour uncanny ideas. Thank you.

The paper isn't investigating when "GR is no longer applicable". It is investigating how large the compactified dimensions could be without conflicting with observations. That has nothing to do with GR not being applicable. See below.
Not as geometry, no. As above, GR describes only the geometry of the 4 ordinary spacetime dimensions we observe. As far as GR is concerned, these "extra dimensions", or more precisely their effects as manifested in things like new particles or fields beyond the ones we already know of (in the Standard Model of particle physics) would appear as part of the stress-energy tensor not the spacetime geometry. That doesn't mean GR is "not applicable"; it just means GR doesn't describe the "extra dimensions" as spacetime geometry.
There isn't one. Why do you think there is? I don't see anything saying this in the paper you linked to.

 

[PeterDonis]

About the "That EFE is specifically for 4 dimensions.". Does it mean whenever there are 4 dimensions, there is automatically GR?

No. Mathematically, you can have 4-dimensional manifolds that don't even have a metric.

what would change if the world is 4D but doesn't have Equivalence principle and if you put feather and iron core, they don't fall at same time?

Such questions are meaningless unless you give us a specific alternative theoretical model to GR to use when answering them.

In LQG, there is always the comment it can't recreate GR.

This tells us nothing without a specific reference.

Is it possible Quantum Mechanics lives not in the 4D spacetime of GR but it has its own space where time is different?

This is personal speculation and is off topic for this forum.

All this is to prepare for reading Julian Barbour new book "The Janus Point"

If you want to discuss one of Barbour's models, you need to look at his peer-reviewed papers and start a separate thread on one of them.

 

[PeterDonis]

This thread has run its course and is now closed.