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

[Nugatory]

It's amazing how just a difference of a few words can make such a difference to such a baffling concept!

This is why people say that "mathematics is the language of science." A corollary is that if you're not reading the math itself, it's like trying to study the literature of another culture in translation - there's nothing wrong with doing so as long as you remember that you're at the mercy of the translator, and you aren't studying the real thing.

That applies to this discussion as well - at best, I've just given you a more careful translation for this particular situation.

 

[bhobba]

each of which is incomplete, but both of which may turn out to be correct and complete

?

They can't both be correct and complete because their combination leads to a theory only correct to a certain cut-off.

Thanks
Bill

 

[gerbilmore]

The second bit is correct - not the first.

How so? My understanding is that there are many things not fully understood in QM and GR.

 

[bhobba]

How so? My understanding is that there are many things not fully understood in QM and GR.

I expressed it incorrectly and changed it - you got the old post.

Your second bit contradicts the first. QM (in the form of QFT) and GR can't both be correct to all energies as explained in the paper I linked to. If string theory is correct GR is incorrect and QFT correct - but they both can't be correct.

But it's not surprising - even QED is incorrect and replaced by the electroweak theory.

Thanks
Bill

 

[brianhurren]

I have always thought that part of the problem of unification is because we asume that gravity is a quantum field, GM says it isn't and that it is a result of the geometry of space time. would things work out better if we were to just accept this?

 

[stevendaryl]

I have always thought that part of the problem of unification is because we asume that gravity is a quantum field, GM says it isn't and that it is a result of the geometry of space time. would things work out better if we were to just accept this?

I would say that we don't know how to "just accept" it. You're proposing dividing the world into two domains, the domain of matter/energy, which is described by quantum field theory, and the domain of spacetime geometry, which is described by General Relativity. That sounds great, but how do the two interact? I believe that it is not too difficult to figure out how spacetime geometry affects quantum fields, but we don't know how quantum fields should affect spacetime geometry, if the latter is treated classically. If a particle only has a probability of being here or there, then how does that particle warp spacetime? The most straightforward assumption is that if the particle has a probability of being here or there, then that spacetime has a probability of being warped this way or that way. In other words, spacetime has to be in a superposition of configurations, as well. So spacetime has to be treated quantum mechanically. There is no consistent way (as far as I know) to have a quantum field affect a classical object.

I suppose that one possibility is to let the source of gravity be the expectation value of the momentum/energy. Even if momentum/energy itself is a quantum operator, the expectation value is just a number. So maybe that would work. But it seems a little strange---it means that there is a possibility of a particle being found at one point, while its gravitational field is centered on a completely different point.

The other possibility, which was suggested by Penrose (in a book about minds, of all things), is that quantum mechanics should be modified to include gravitationally-induced wave function collapse. So particles would have definite positions, after all.

 

[bhobba]

I have always thought that part of the problem of unification is because we asume that gravity is a quantum field, GM says it isn't and that it is a result of the geometry of space time. would things work out better if we were to just accept this?

GR does not say gravity is not a quantum field - whatever gave you that idea?

The issue is its non-renormalisable and needs a cutoff as an effective field theory to work in the usual way we quantize fields.

EM, while renormaliseable, doesn't work beyond a certain cutoff either eg the issue of the Landau pole.

So what's new?

Thanks
Bill

 

[brianhurren]

you are right it doesn't say that it isn't. it does say that it is a distortion in space time geometry though.

 

[bhobba]

it does say that it is a distortion in space time geometry though.

GR is based on the idea of no prior geometry and geometry is itself a dynamical variable.

The details are technical, and can be found in the following reference:
https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

But here is the gist. Starting from the most general formulation of geometry, namely Riemannian geometry, locally its euclidean. We can consider quantum particles of spin 2 using ordinary QFT formulated in flat space-time, which is perfectly OK since its locally euclidean. We then see this field classically, in the non relativistic limit, is exactly the same as Newtonian gravity. Another interesting property is particles move as if space-time had an infinitesimal curvature. Then we have the issue that the source of the field is the stress energy tensor - but gravity itself has energy - this means except for small fields where this energy can be neglected it wrong. To fix it up we simply insist whatever the real equations are they must not depend on the coordinate system. Lo and behold, if you do that, GR inevitably results. In that sense it is thought space-time geometry is determined by spin 2 particles.

The big issue is its only valid to a cutoff.

Thanks
Bill

 

[WannabeNewton]

There is no consistent way (as far as I know) to have a quantum field affect a classical object.

Actually quantum fields do affect curved backgrounds due to back reaction. C.f. section 12.1.7. of "Introduction to Quantum Effects in Gravity"-Mukhanov et al for a calculation of the back reaction.

 

[Ken G]

We then see this field classically, in the non relativistic limit, is exactly the same as Newtonian gravity. Another interesting property is particles move as if space-time had an infinitesimal curvature

And isn't this the rub? You make the nice point that under some circumstances, a spin-2 quantum field can cause particle motions that could be mistaken as being due to an infinitesmal curvature of spacetime. But of course we can turn that around, and say that under some circumstances, an infinitesmal curvature of spacetime could be mistaken as being due to a spin-2 quantum field. It seems to me the OPer is basically asking, how do we know that we need to unify the extrapolations of those conditions just because they are unified at the scales you describe? Perhaps they are just different, and the fact that they can be made to look similar on some scale is not surprising. (Note I do not mean that we don't need a theory that can allow for us to include both at the same time, I mean the theory that does that might not treat gravity as a quantum field.)

Another way to frame the question, it seems to me, is which should we regard as more fundamental-- the field or the geometry it lives on? If we think everything has to be quantum fields, then when we see a geometrical effect mimic a quantum field effect on some scale, and our current way to extrapolate those effects is by manipulating the geometry, we ask if there is not some way to get the same result with a field theory that does not need to manipulate the geometry. But, if we think geometry is just as fundamental as quantum fields, then we are not bothered that we need both fields and geometry to be able to extrapolate to other scales, we are always expecting to need to be able to do both. That the infinitesmal curvatures can be treated as quantum fields might just be due to the flexibility of quantum fields, and not necessarily an indication that it's all about quantum fields.

I am not knowledgeable in quantum field theories, but I do see some justification for taking a two-stroke approach to GR and QM, which comes from Newton's first two laws. It is sometimes claimed that the first law is covered by the second, in that, if there is zero force, there is zero acceleration. But it seems to me the first law is not so much the statement that you will have zero acceleration, it is the decription of what zero acceleration is in the first place. Newton agreed with Galileo that zero acceleration is something we can know when we see it, it is motion at a constant speed in a straight line through a pre-ordained geometry. Einstein's GR holds that we need a dynamical theory just to even know what zero acceleration is, and a second dynamical theory to know what accelerations we will get when it is not zero. There's a certain sense to that system, because even though of course physics always tries to unify wherever it can, there might be a philosophical justification for expecting that the processes responsible for determining the meaning of acceleration might be different from the processes that determine what the acceleration is.

 

[bhobba]

It is sometimes claimed that the first law is covered by the second, in that, if there is zero force, there is zero acceleration. But it seems to me the first law is not so much the statement that you will have zero acceleration, it is the decription of what zero acceleration is in the first place.

The first law follows from the second and the second is really a definition of force - its physical content lies in the third. A careful analysis of Newtons laws show they are really a prescription on how to analyse mechanical problems that says - get thee to the forces.

Thanks
Bill

 

[Ken G]

The first law follows from the second and the second is really a definition of force - its physical content lies in the third. A careful analysis of Newtons laws show they are really a prescription on how to analyse mechanical problems that says - get thee to the forces.

Yet I don't agree-- even if you know all the forces, all you can ever get from them is an acceleration. Acceleration relative to what? All you can predict is what an accelerometer will measure, you could never predict the motion without an independent law that tells you what acceleration is, i.e., what it means to have zero acceleration. That's why I'm saying the important thing in the first law is not the claim that you'll get zero acceleration when the forces are zero, that's the second law. The key part of the first law is what is sometimes explicitly included in it: that zero acceleration means motion in a straight line at constant speed. Note the crucial implication that we must be able to know what those things mean.

 

[bhobba]

Yet I don't agree-- even if you know all the forces, all you can ever get from them is an acceleration. Acceleration relative to what?

Acceleration relative to the inertial FOR you are solving the problem in.

Thanks
Bill

 

[Ken G]

Acceleration relative to the inertial FOR you are solving the problem in.

Of course-- but what law tells you what an inertial frame is? If I'm in a space station near Earth, is the inertial frame the one in which the Earth just hangs there in the distance against a fixed background of stars, or the one where the Earth is coming at me faster and faster? Being able to predict my accelerometer reading does not tell me which one of those to expect to see, so I'm going to need two independent laws there-- two laws that are not obviously unifiable.

 

[atyy]

But, if we think geometry is just as fundamental as quantum fields, then we are not bothered that we need both fields and geometry to be able to extrapolate to other scales, we are always expecting to need to be able to do both.

It is very difficult to regard the geometry as classical, because the matter fields that make up the stress-energy of the classical Einstein equation are quantum. On the other hand, we can consistently regard the geometry as quantum, as consistently as we can regard electromagnetism as quantum. There are problems with both, but since electromagnetism is already problematic at high energies, we don't bring in any new problems by treating gravity as a quantum field, whereas we do get new problems by treating gravity as classical geometry, ie. we unify our problems if gravity is quantum :)

Whether the solution to our unified problem is classical or quantum remains to be seen.

 

[Ken G]

It is very difficult to regard the geometry as classical, because the matter fields that make up the stress-energy of the classical Einstein equation are quantum. On the other hand, we can consistently regard the geometry as quantum, as consistently as we can regard electromagnetism as quantum. There are problems with both, but since electromagnetism is already problematic at high energies, we don't bring in any new problems by treating gravity as a quantum field, whereas we do get new problems by treating gravity as classical geometry, ie. we unify our problems if gravity is quantum :)

Perhaps the only options are not classical vs. quantum. Certainly classical represents outdated thinking, and quantum represents modern thinking. But what kind of thinking will allow us to treat gravity and other interactions at the same time? Certainly we have three possibilities:
1) the quantum approach will unify them
2) some new kind of thinking will unify them
3) some new kind of thinking will allow us to treat them both by recognizing their fundamental differences that are not supposed to be unified, differences such as the difference between knowing how an inertial frame will act, and knowing how forces generate noninertial frames.
I think the OP is basically asking, how do we know which of these will work? Logically, we should try them all, though of course every individual theorist is welcome to put their own investment in whichever course matches their intuition. The order is more or less the order of how nice it would be for us, so it makes sense to try them in that order, but it does not make sense to bang our heads on any walls. I don't know when we can say we are banging our head, and when we are just noticing the problem is difficult.

Whether the solution to our unified problem is classical or quantum remains to be seen.

Indeed.

 

[bhobba]

Of course-- but what law tells you what an inertial frame is?

Its a definition - like many things in physics.

The definition is a frame such that all points, directions, and instants of time are equivalent. Its utility is such frames exist to a high degree of accuracy.

Thanks
Bill

 

[WannabeNewton]

The first law follows from the second and the second is really a definition of force - its physical content lies in the third.

The first law does not follow from the second. The first law is what defines an inertial frame. The second law then formulates dynamics in inertial frames.

 

[Mark Harder]

We know there are situations where both are relevant at the same time - notably black holes, (theoretical) ultra-high-energetic particle collisions and probably the big bang. They have to work together in some way, we just don't know how.

If you try to start a poker session in a football match, something will happen, and you need rules that go beyond the two separate cases to describe it.

Neat analogy.

 

[Mark Harder]

If they aren't unified, then they can't be complete. Consider two identical particles of mass $M$ and charge $Q$. If we ignored quantum mechanics, we could describe their interaction using GR and electromagnetism. If we ignored gravity, we could describe their interaction using QM. So we have two descriptions of their interactions, and those two descriptions can't possibly both be right. Presumably, their actual interaction involves both quantum mechanics and gravity, so neither theory by itself is correct.

OK. But suppose we decide that both theories are equally incomplete? The project then would be to correct each one so that they would make the same predictions separately. I don't know what the results of such a project would imply about physical reality, though. The project would be futile, however, if one could show that the extensions of the 2 theories actually contradicted each other.

 

[Ken G]

Its a definition - like many things in physics.

The definition is a frame such that all points, directions, and instants of time are equivalent. Its utility is such frames exist to a high degree of accuracy.

Here I agree with WannabeNewton, and let me explain why. It doesn't matter how we define inertial frames, what matters is what laws we need to account for all the observations we see. So let's say you are in a universe you know nothing about, except that Newton's second and third laws should apply, and you know all the force laws in some grand unification sense. You notice the forces on you, and calculate what your accelerometer should read. You check your accelerometer, and you got the right answer-- you understand the working of Newton's second law in this universe.

Let's also say that as it happens, the net force was zero, and that's what your accelerometer reads. Now you look out the window of your spaceship, and see a huge body looming in front of you, stationary against the background stars. You also notice that this huge body has no forces from the grandly unified menu of forces on it, so it should also be an inertial frame. Now here's the key question: tell me how, without invoking any new laws beyond Newton's second and third, how you know if that large body will just stay hanging there in front of you, or will move toward you faster and faster and faster with time?

 

[Mark Harder]

Why not? Simply because that's counterintuitive?

Exactly. As Einstein said, science can prove nothing; it can only disprove ideas. If you have a theory that explains all pertinent phenomena and is not logically incompatible with any results, then that theory is acceptable. But these results in no way prove that there are NO OTHER theories that would do just as well as, or even better than the conventional wisdom. Perhaps our understandings of GR and QM are BOTH incomplete and another framework would work better than everything we have. Now that possibility should cause all of us who care about such things to lose sleep. ;)

 

[Ken G]

Perhaps our understandings of GR and QM are BOTH incomplete and another framework would work better than everything we have. Now that possibility should cause all of us who care about such things to lose sleep. ;)

Don't lose sleep, because that is almost certainly true, given the history of science, but you have to sleep anyway.

 

[Ilja]

For the record, special relativity and quantum mechanics have been 'unified' since the end of the 1920s. The problem is with general relativity.

Hm, only if you forget about Haag's theorem.

What we know as QFT makes, in the light of Haag's theorem, sense as an effective field theory, but not more. But as an effective field theory quantum gravity is not a problem too.

 

[bhobba]

The first law does not follow from the second. The first law is what defines an inertial frame. The second law then formulates dynamics in inertial frames.

Some define it that way - but more advanced texts, correctly IMHO, define it by symmetry principles - see page 3 Landau - Mechanics. It travels at constant velocity in an inertial from the symmetry of the Lagrangian - see page 5 Landau. But regardless Newtons laws are assumed to apply in inertial frames.

The real essence of Newtons Laws is actually the PLA which follows immediately from the sum over histories approach to QM - ie the laws of QM.

Thanks
Bill

 

[jerromyjon]

PLA

What is that?

sum over histories approach to QM

http://muchomas.lassp.cornell.edu/8.04/Lecs/lec_FeynmanDiagrams/node3.html
Renormalization just scales fundamental processes to large "chunks" of histories and you get probability from P²?

 

[bhobba]

What is that?

Principle Of Least Action.

It has nothing to do with renormalisation - without getting into exactly what it is about.

Thanks
Bill

 

[atyy]

Hm, only if you forget about Haag's theorem.

What we know as QFT makes, in the light of Haag's theorem, sense as an effective field theory, but not more. But as an effective field theory quantum gravity is not a problem too.

As I understand, Haag's theorem is not a problem. It just means the right equations have been derived the wrong way :) So for example, there are rigourous relativistic quantum field theories in 2 and 3 spacetime dimensions, where the usual sloppy equations can be properly derived. There are probably problems with the most physically relevant quantum field theories in 4 spacetime dimensions, which are probably only effective field theories, but I don't think the obstacle is Haag's theorem.

 

[Ken G]

My point from before was, whether one uses Newton's approach, Hilbert's, Einstein's, or Feynman's, the essential point remains: one has two separate issues to resolve, so one's formalism will require two different elements to resolve them. Those two separate elements come down to the questions, what happens when there are no forces or interactions, and what kind of forces or interactions are there which change that. You can take any of those formalisms and see how each approaches those two questions, and in none of them, are they unified into the same question. This means that making gravity a field theory will also not unify those issues, so it is a kind of illusion that those two questions can be unified. Since Einstein's main insight in GR is to provide a separate dynamical approach to answering the first question from the second question, it is arguable that this disunification was actually the step forward there. If so, attempts to unify gravity and quantum fields are in effect an effort to sweep under the rug that fundamental disunity-- it places all the emphasis on the second question, and treating the first question as if it was too trivial to merit its own dynamical treatment. In short, the fact that quantum mechanics treats the answer to the first question as if it does not require anything more than the treatment Galileo gave it four centuries ago may be a bug rather than a feature of quantum mechanics, and if that is true, then efforts to unify GR and QM are actually efforts to ossify that bug.

 

[Fredrik]

What if both sets of rules are correct and cannot be combined?

If they were both correct, then they wouldn't contradict each other, and they wouldn't contradict experiments. Classical GR says that matter behaves in a classical way. That contradicts QM and experiments. So there's a good reason to look for a way to replace GR with something better.

The replacement may or may not be a way to incorporate the spacetime of GR into the framework of QM. My understanding of this is rather poor, but I think the jury is still out on whether that can be done. The alternatives include the possibility that QM needs to be changed as well, and the possibility that unification will forever be beyond the reach of experimental science.

 

[Clayjay]

Hi,

We're still seeking a satisfactory way to unify quantum mechanics and general relativity together, correct? Why do physicists make the assumption that there is one set of rules governing everything? Is it because that's what we tend to see in nature? Or because it's just a nice idea? Is it a desire, an expectation or a prediction? What if both sets of rules are correct and cannot be combined? 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.

 

[Ken G]

It seems we might need to clarify a bit more what we mean by "unify." To unify two things does not just mean to have a single physics theory that incorporates both without contradicting each other, it means more than that. We could say that Newton's laws already incorporated gravity with the other forces, but none of them were unified in the sense that they could not have been viewed as different aspects of the same thing. So when GR further distanced gravity from the other forces, it wasn't a case of introducing disunity where there was unity, it was introducing more disunity where there was already considerable disunity. So even had we never needed quantum mechanics, we still might have made it a goal to unify gravity with the other forces. Hence, the question of unification is not just how can we get a single theory that can handle in complete generality either gravity or the other forces, it is also how can we get a theory where gravity does not behave fundamentally differently from the other forces.

It is that latter mission that I am not so sure can be accomplished, but more to the point, I'm not so sure it should be accomplished-- we tend to think the more you can unify the better you understand, but perhaps there is a point where fundamental differences are what need to be understood.

 

[Clayjay]

Both GR (general relativity) and QM(quantum mechanics) are logically self consistent and work at the scale of their domain. However, their domains do not overlap. When theoritical predictions are tested and proven by experimental results the Theory is supported. That is the classical way of doing science. However classical physics was not ready to explain why electron orbits did not decay. QM bypassed an explanation of why electrons have discrete orbits and simply stated that atomic orbits are discrete.

 

[Clayjay]

I was composing a reply and somehow it got posted. My mistake but I was just getting started. And I had to stop to take care of something else. I have not even read your reply yet but I wanted you to know what happened. I will eventually complete my first posting. I a'm sure her message will be helpful.