Are we wrong to try and unify quantum mechanics and relativity?

[Ken G]

Do you feel the same way about 'Big Bang'? It's terribly inaccurate.

I have no great issue with simple inaccuracy of names, that is something we deal with all the time. It certainly isn't ideal, but it's hard to avoid. But it's not at all hard to avoid names that fool people about what science itself actually is, because that's an issue we grapple with all the time. There are already very strong forces that tend to encourage people to grab onto "magic bullet" kinds of thinking. The last thing science should do is embrace a term that does that-- and none of the other terms you mention do, but "theory of everything" certainly does.

 

[Edward Wij]

in the thread https://www.physicsforums.com/threa...he-wavefunction-is-ontologically-real.795700/
"More evidence that the wavefunction is ontologically real?"

If the wavefunction is indeed ontologically real.. real in the sense the complex numbered hilbert space is real.. what does this constrain on the search for quantum gravity? does the imply the spacetime geometry is ontogically real too. Or if I'm confused.. please enlighten why it is so... especially considering the fact quantum gravity is about quantum spacetime or how matter wave interact with geometry.. so if the wave is ontologically real.. must the geometry too? If not.. please state the reasons and clarify my misunderstandings.. thanks in advance.

 

[Ken G]

The philosophical problem with GR and QM is that we cannot take both the Hilbert space, and the continuous spacetime, to be ontologically real. That's essentially because of the uncertainty relation applied at the Planck scale. If you want to believe either one is ontologically real, that's kind of a personal matter, there's little evidence to draw from the history of science that this will actually be true.

Or perhaps a better way to say something similar is, ontology is not used in physics the same way as in philosophy. In philosophy, it is intended as a claim on what actually exists. In physics, it is never more than a claim on what is demonstrably useful to imagine exists. It seems to me that the various times scientists throughout history have lost track of that distinction, they have wound up with egg on their faces. Even so, the issue "is the wavefunction ontological" is really just the question "is it more useful to imagine it exists, or not to imagine that, regardless of what actually does exist, if indeed anything does."

 

[Edward Wij]

The philosophical problem with GR and QM is that we cannot take both the Hilbert space, and the continuous spacetime, to be ontologically real. That's essentially because of the uncertainty relation applied at the Planck scale. If you want to believe either one is ontologically real, that's kind of a personal matter, there's little evidence to draw from the history of science that this will actually be true.

Or perhaps a better way to say something similar is, ontology is not used in physics the same way as in philosophy. In philosophy, it supposed to be claim on what actually exists. In physics, it is never more than a claim on what is demonstrably useful to imagine exists. It seems to me that the various times scientists throughout history have lost track of that distinction, they have wound up with egg on their faces. Even so, the issue "is the wavefunction ontological" is really just the question "is it more useful to imagine it exists, or not to imagine that, regardless of what actually does exist, if indeed anything does."

To be useful. Let's define real as that existing independently of human observations. Why is uncertainty relation applied at Planck scale makes the Hilbert space and spacetime not ontologically real? Hilbert space and Time + Space has one thing in common.. it has to do with complex numbers. So perhaps we can say the complex numbers are ontologically real in some platonic realm. And in that realm where continuous is not a priori, and smear out positions are the norm... uncertainty relation can occur in Planck scale.. here QM is unified with GR in the ontologically real complex numbers platonic realm. What is wrong with these thoughts?

 

[Ken G]

To be useful. Let's define real as that existing independently of human observations.

It is not obvious that is the useful thing to do-- indeed, I would say usefulness is all about human observations, so let's define real as what humans observe. This difference of opinon shows the problem with thinking that ontology in science is anything more than demonstrable expedience.

Why is uncertainty relation applied at Planck scale makes the Hilbert space and spacetime not ontologically real?

It creates tension between them such that they both cannot be regarded as ontologically real. GR says that the curvature in a region as small as a Planck length depends on the stress-energy tensor that is local to that region, but the uncertainty principle in the Hilbert space says that to be able to assert what is the stress-energy in that small of a region requires consideration of super high frequencies. Since energy comes in tiny quanta of action, to probe the action at such high frequencies requires a very high energy quantum within that spatial domain, and in GR that would cause curvature that would make it impossible to probe that length scale. So the spacetime cannot be meaningful on that scale if QM is correct on that scale. But maybe they could both be ontological on other scales, and just behave differently when it gets to the Planck scale.

So perhaps we can say the complex numbers are ontologically real in some platonic realm.

The issue isn't really with imaginary numbers-- to hold that the wavefunction is ontological is to not be bothered by complex numbers. After all, they are just numbers with magnitude and phase, which could be interpreted as real if you think "phase" is a real thing.

 

[Edward Wij]

It is not obvious that is the useful thing to do-- indeed, I would say usefulness is all about human observations, so let's define real as what humans observe. This difference of opinon shows the problem with thinking that ontology in science is anything more than demonstrable expedience.
It creates tension between them such that they both cannot be regarded as ontologically real. GR says that the curvature in a region as small as a Planck length depends on the stress-energy tensor that is local to that region, but the uncertainty principle in the Hilbert space says that to be able to assert what is the stress-energy in that small of a region requires consideration of super high frequencies. Since energy comes in tiny quanta of action, to probe the action at such high frequencies requires a very high energy quantum within that spatial domain, and in GR that would cause curvature that would make it impossible to probe that length scale. So the spacetime cannot be meaningful on that scale if QM is correct on that scale. But maybe they could both be ontological on other scales, and just behave differently when it gets to the Planck scale.

The issue isn't really with imaginary numbers-- to hold that the wavefunction is ontological is to not be bothered by complex numbers. After all, they are just numbers with magnitude and phase, which could be interpreted as real if you think "phase" is a real thing.

Let's just treat GR as only valid only outside the Planck scale. What is inside Planck scale is not spacetime.. but maybe.. oh.. of course.. strings that vibrate.. why not.. Besides strings.. what else have the quantum gravity guys proposed for what is inside the Planck scale? beside LQG where what is inside it is just unit and nothing more..

 

[Dr Transport]

Try looking at this monograph

https://www.amazon.com/dp/9027722471/?tag=pfamazon01-20

The problem I see is that everyone tries to go from QM to general relativity, I think we need to go the other way... Professor Sachs starts with the quaternion form of GR and takes the linear limit obtaining answers to QM issues.

 

[Mark Harder]

The subject of the relationship between 'lower' and 'higher' levels of explanation in the sciences interests me. Can the theories describing one of these be 'reduced' to the other? That is, does understanding the behavior of lower level systems suffice to understand higher level ones?

Many thoughtful scientists and philosophers disdain what they call 'reductionist' projects. They point out, rightly, that a complex, macroscopic system cannot be fully explained using the rules that the lower ones obey. Many physicists consider Phillip Anderson's 1972 paper "More is Different" a persuasive explanation of the reductionist fallacy in terms of symmetry breaking (not that I understand what is meant by that). My take on the issue is that the motivation for drilling downward to lower level models is that we are trying to find ways of unifying a wider range of phenomena, not reducing one to the rules of the others. A common trend in the broadly defined disciplines of science is the elaboration of new disciplines that knit together lower level and higher level phenomena. Because the higher level phenomena can't be completely explained in terms of the lower ones, new approaches had to be invented.

Examples abound in biology, psychology and scientific fields besides physics. Explaining thermodynamics using the Newtonian physics of atoms and molecules is one such example. In the late 19th and early 20th centuries physicists engaged in this program; and giving birth to statistical mechanics in the process. The Newtonian version did OK under most conditions but the behaviors of black bodies at high temperatures and of metals at very low temperatures could not be adequately explained until quantum mechanical models of the microscopic behaviors were incorporated into the theory. Metaphorically, statistical mechanics is the glue holding atomic physics and thermodynamics together. Another example of a gluing discipline is biochemistry, whose project has been to discover unifying explanations for living structures and processes in terms of molecular structures and dynamics.

Perhaps the way to approach the unification problem is to see gravitation as something that emerges from the other 3 force fields, not equally as fundamental, yet not entirely disconnected either. If so, theoreticians might advance fundamental physics by seeking a new theory, a la statistical mechanics, that glues relativity studies and quantum field studies together. Another benefit of such an approach is that it might unveil new physical fields (dark matter?, dark energy?) that, like gravity, emerge from the 3 quantum fields.

 

[Mark Harder]

Try looking at this monograph

https://www.amazon.com/dp/9027722471/?tag=pfamazon01-20

The problem I see is that everyone tries to go from QM to general relativity, I think we need to go the other way... Professor Sachs starts with the quaternion form of GR and takes the linear limit obtaining answers to QM issues.

Of historical interest: Did Einstein try this approach when he worked on a unified field theory?

 

[bhobba]

Perhaps the way to approach the unification problem is to see gravitation as something that emerges from the other 3 force fields, not equally as fundamental, yet not entirely disconnected either. If so, theoreticians might advance fundamental physics by seeking a new theory, a la statistical mechanics, that glues relativity studies and quantum field studies together. Another benefit of such an approach is that it might unveil new physical fields (dark matter?, dark energy?) that, like gravity, emerge from the 3 quantum fields.

That, and many other directions are being pursued.

But its wise to realize what the problem is - there is no incompatibility between relativity and QM. We have perfectly valid theories up to about the plank scale. Of course we want to peek behind that - but that's the issue - not a fundamental incompatibility.

Thanks
Bill

 

[Ken G]

Another point to bear in mind is that the unification does not require that gravity be treated as a higher order manifestation of the other 3 forces, it could look like all 4 forces looking like higher order manifestations of the same fourth thing. In other words, electroweak and strong unification can be one thing, but unification with gravity could be something quite different. To me that would make sense, because we will always have two separate questions: what does a particle do when nothing is happening to it, and what does a particle do when something happens to it? That basic yin/yang must always be there, because how can we define a happening except in relief against a non-happening? Or put in less philosophical terms, any dynamical theory must make some assumption about the proper dynamical variables to use to describe the dynamics, but where is it written that those dynamical variables cannot exhibit their own dynamics? Or more specifically, in quantum mechanics we are not forced to choose between the Schroedinger picture and the Heisenberg picture, but unification with gravity might require a new theory that does force that choice, and in particular, that requires the Heisenberg picture, where the observables are regarded as dynamical. That would seem to be the key difference needed to go from Newtonian gravity to general relativity, so unification may need to account for that difference.

 

[Mark Harder]

..but the rules differentiating and describing the two games are incompatible... as they stand the rules themselves clash—even though the ball and the pack of cards are made of atoms. ..

Forgive me if my choice of quotes doesn't truly represent what you were saying, but if they do, then aren't the 2 sets of rules incompatible because of the choice of games? Reality doesn't let us choose whatever phenomena we want for it's models. It's quite possible to have different rules in football for what takes place behind the line of scrimmage and on the defense's side There could be some underlying principle of designing the game, or any sport for that matter, that guide the applicability of the rules, like avoiding situations that make it too easy for offense to score, for instance.
In science, there are plenty of examples of theories that are incomplete, in that there are phenomena a theory fails to explain. Professional scientists don't necessarily throw away the theory in those cases

 

[bhobba]

Forgive me if my choice of quotes doesn't truly represent what you were saying,

The tricky part of this is, while it is often said the rules of GR and QM are incompatible, the truth is they really aren't:
http://arxiv.org/abs/1209.3511

Its a modern insight from the effective field theory view of re-normalisation sorted out by Wilson.

Thanks
Bill

 

[Mark Harder]

I may not understand what is implied by the poker-football example, but if I do, then aren't the 2 sets of rules incompatible because of the choice of games? Reality doesn't let us choose whatever phenomena we want for it's models. Instead, might I confine the example to football by itself? There, It's quite possible to have one set legal moves behind the line of scrimmage and another on the defense's side. There could be some underlying principle directing the choice of rules, such as avoiding situations that make it too easy for offense to score, which might make the game less interesting to watch. The different rules aren't contradictory as long as their domains of applicability are carefully defined.

There are some fundamental assumptions in physics that any theory must agree with in order to be valid. Reality is assumed to be objective (I guess some quantum mechanicians take issue with that. IMHO, the issue is far from settled.). Therefore, all observers should observe the same reality, so that well-specified experiments can be reproduced by anyone. Physical laws are valid everywhere in the universe at any time. Since dynamics are given by variational principles, invariant laws imply conservation laws - like conservation of linear momentum and energy. Perhaps these are the true foundation of physics, with which any proposed theory must agree. As long as we have a universe in which GR and QM sit on the same foundation, and where GR doesn't demand behavior from quantum systems that QM rules out, and vice-versa, then the two systems are valid and consistent. It seems to me that the resolution of our problem must lie in experimental observation.

For example, we know that QM accounts for the observed spectra of black bodies. If GR implied that black bodies emit photons with different spectra than those observed, then there's a problem with GR. On the other hand, if we could design a more precise experimental apparatus that revealed spectra that were only approximately described by QM, and they were as far as we could tell exactly described by GR, then QM is not as good a theory as GR. If neither GR or QM predicted the observed spectra, then both are wrong, or at least inaccurate. That would be a really exciting result, since it would open a door into new theories, but a lot of hard work. The most pedestrian result would be that both theories did equally well, and if we wanted to see something more interesting, we would have to move on to different experimental tests.

 

[bhobba]

Reality is assumed to be objective (I guess some quantum mechanicians take issue with that. IMHO, the issue is far from settled.).

Indeed.

Thanks
Bill

 

[stevendaryl]

The tricky part of this is, while it is often said the rules of GR and QM are incompatible, the truth is they really aren't:
http://arxiv.org/abs/1209.3511

Its a modern insight from the effective field theory view of re-normalisation sorted out by Wilson.

I'm not sure that all the problems of reconciling GR and QM are due to non-renormalizability. Certainly that's part of it, and you're probably right, that that part is exaggerated, because nonrenormalizable theories just mean that our theory is incomplete--it's just the low-energy limit of some unknown theory of wider applicability.

But a couple of things about GR seem to call into question some basic fundamental aspects of QM. They are completely over my head, so I can't engage in a meaningful discussion about them, so I'll just mention them.

1. The problem of "time and observables". As I said, this subject is over my head, so my summary is probably misleading or wrong, but as I understand it, the problem is that QM understands dynamics as the evolution of a quantum state as a function of time, while there is no unique, satisfactory time parameter, according to GR. Another, related problem is that QM is about expectation values and eigenvalues for observables, but for the gravitational field itself (or spacetime curvature), there is no obvious notion of "observable" that is local and coordinate-independent.
2. The problem of information. I don't know enough to know whether this is connected with the first problem, or not, but it's easy enough to describe. According to QM, information is never lost, at the microscopic level, since the equations of motion are reversible. In contrast, black hole formation and evaporation through Hawking radiation seems to involve information loss: the information about what went into forming the black hole is gone forever, since regardless of what falls into a black hole, the black is only characterized by total mass, total charge and total angular momentum.

I'm not saying that these two problems are unsolvable, I'm only listing them because they don't immediately seem to be connected to the non-renormalizability of GR.

 

[bhobba]

I'm not sure that all the problems of reconciling GR and QM are due to non-renormalizability. Certainly that's part of it, and you're probably right, that that part is exaggerated, because nonrenormalizable theories just mean that our theory is incomplete--it's just the low-energy limit of some unknown theory of wider applicability.

I am certain you are right.

Thanks
Bill

 

[at94official]

But we can play a game of poker on a football field. Now what rules will you use?

But you can't play football on a poker table, so it will contradict the rules.

 

[DaveC426913]

But you can't play football on a poker table, so it will contradict the rules.

In this analogy, relativity is football, QM is poker. There are, extant, places where they overlap (eg. firing Buckyballs through a double-slit experiment).

So the rules (which nature defines, not us) say that you can play football on a poker table. All we need to do is understand the (unified) rules.

 

[ShayanJ]

I think there is a problem with using the phrase "unified rules", it has two meanings. One meaning is when we use it for e.g. unification of electromagnetic and weak interactions and another is when we put all things in a coherent structure like Standard Model. Unification in its first meaning is not necessary but in its second meaning is!

 

[zonde]

I think there is a problem with using the phrase "unified rules", it has two meanings. One meaning is when we use it for e.g. unification of electromagnetic and weak interactions and another is when we put all things in a coherent structure like Standard Model. Unification in its first meaning is not necessary but in its second meaning is!

I would agree with that and I would say that unification attempts are made for the first type of unification while it would seem more logical to do the unification is second sense first.
But I think that both QM and GR are not unification friendly as they both drag their own philosophical background with them. But you need common philosophical background for any unification.

 

[DaveC426913]

But I think that both QM and GR are not unification friendly as they both drag their own philosophical background with them. But you need common philosophical background for any unification.

Nature does not care about philosophical background, esp. since nature operates just fine billions of light years from where that philosophical bg was invented. It does have rules for how the universe works; it is simply up to us to understand them.

 

[Ilja]

The problem of "time and observables". ... the problem is that QM understands dynamics as the evolution of a quantum state as a function of time, while there is no unique, satisfactory time parameter, according to GR.

Even funnier is the point that even non-relativistic QM treats time very different from other things which are observables. There is no observable for time measurement. And there is even a theorem that every clock has a nonzero probability to go even backward in time.

The problem of information. I don't know enough to know whether this is connected with the first problem, or not, but it's easy enough to describe. According to QM, information is never lost, at the microscopic level, since the equations of motion are reversible. In contrast, black hole formation and evaporation through Hawking radiation seems to involve information loss: the information about what went into forming the black hole is gone forever, since regardless of what falls into a black hole, the black is only characterized by total mass, total charge and total angular momentum.

This problem disappears if quantum theory is treated as an effective field theory, because an effective field theory - which becomes invalid for some small but not astronomically small distance - so, say, with 10^{-50} l_{Planck} being acceptable as a critical length, but not 10^{-10000} l_{Planck} - would not predict any Hawking radiation lasting more than a few hours. This problem is called "trans-Planckian", but this is clearly an euphemism, given the exponential decrease of the critical distance where RQFT has to be assumed as valid with the time the Hawking radiation lasts.

In other words, Hawking radiation is simply not a prediction which could be made in a reasonable way in an effective field theory.

 

[zonde]

Nature does not care about philosophical background, esp. since nature operates just fine billions of light years from where that philosophical bg was invented.

Right.

It does have rules for how the universe works; it is simply up to us to understand them.

It's hard to make sense of this. Do you have some mother's Nature rule book handy so that our main concern should be about understanding the rules?

 

[DaveC426913]

It does have rules for how the universe works; it is simply up to us to understand them.

It's hard to make sense of this. Do you have some mother's Nature rule book handy so that our main concern should be about understanding the rules?

That is, somewhat paraphrased, the definition - and highest purpose - of science.

 

[zonde]

That is, somewhat paraphrased, the definition - and highest purpose - of science.

I disagree with this definition.
Rules are invented by us. We just test them against reality and if they are good to extent we keep them and if not we modify them or throw them out. That's what science is about.

 

[Isaac0427]

In day to day life for example it's quite possible to have two sets of rules that don't overlap. The rules of football and poker for example. They both work and they both explain to an observer what's going on in a game of football and a game of poker, but unification of the two sets of rules is just the wrong way of thinking about it.

Thoughts? Thanks.

A better analogy would be to traffic laws and criminal laws. They both have to work together for the justice system to work, and they many times overlap. For example, it couldn't be legal to hit someone with a car and kill them, because that would make traffic and criminal laws inconsistent. The laws of classical mechanics and quantum mechanics work the same way.

 

[DaveC426913]

I disagree with this definition.
Rules are invented by us. We just test them against reality and if they are good to extent we keep them and if not we modify them or throw them out. That's what science is about.

You're getting hung up on the word 'rule'.

The gist of the assertion here is that nature does have consistent behaviors in how subatomic particles behave does have consistent behaviors in how galaxies behave, and it all occurs on the same universe. So it is up to us to understand how - that is what science is.

To suggest that, essentially, there are two universes - one where QM applies and one where GR applies - is to say we do not understand how nature works.

 

[jedishrfu]

It seems now is a good time to close this thread.

Many good points have been made and we have run out of things to add.

Thank you all for your time and contributions.