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

[gerbilmore]

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.

 

[dextercioby]

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

 

[gerbilmore]

Thanks, yes. Post edited.

 

[mfb]

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.

 

[stevendaryl]

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.

Well, GR says that gravity is spacetime curvature due to the presence of matter. QM says that matter is described by a wave equation. So figuring the effect of matter on gravity in detail would certainly involve both GR and QM. So at some level, there has to be a unification. In practice, unification doesn't matter very much because at the microscopic level (particle, atoms and molecules), the effects of GR are negligible, and at the macroscopic level (stars, galaxies), the effects of QM are negligible. But in theory, both apply at all times.

 

[bhobba]

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?.

Not all physicists think there is one set of rules governing everything. I believe there is because I suspect there is some startling symmetry waiting for us to discover. But that is just opinion. Nature may be such as you peel away each layer there is another layer.

But regards to General Relativity and Quantum Mechanics the situation is more subtle thatn popularisations would have you believe:
http://arxiv.org/abs/1209.3511

Thanks
Bill

 

[WannabeNewton]

Hi,
Why do physicists make the assumption that there is one set of rules governing everything?

Because we can easily quantize general relativity in the low energy regime, wherein the metric tensor is just a spin 2 tensor field propagating on flat space-time, and compute tree-level Feynman diagrams and loop corrections for graviton interactions just like with photons in electromagnetism with no issues whatsoever. There must exist some high energy theory of quantum gravity which reduces to this low energy 'effective field theory' of gravitons.

That being said, there do exist arguments for why a quantization of GR is not necessarily the right way to go. Most of these arguments rely on showing in one sense or another that GR is an emergent theory much like statistical thermodynamics. C.f. http://arxiv.org/abs/gr-qc/9504004

 

[DaveC426913]

...it's quite possible to have two sets of rules that don't overlap.

But they do overlap.

Where would you draw the line between them? Atoms? Molecules? Cells? Volvos?

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.

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

 

[gerbilmore]

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

I think I understand what you mean, and yes, ultimately the playing field (atoms, laws of nature etc) is the same (being equivalent to the laws of QM and general relativity applying in the same universe) but the rules differentiating and describing the two games are incompatible. Being offside means nothing in the game of poker. We can make new rules, to integrate the two games, but as they stand the rules themselves clash—even though the ball and the pack of cards are made of atoms. The rules sit above the 'stuff' governed by those rules. Does that make sense?

 

[mfb]

The rules sit above the 'stuff' governed by those rules.

And that tells you they are not the fundamental rules governing the games. There has to be something more fundamental, some set of rules that allows to describe what a poker table on a football field would lead to.

 

[DaveC426913]

Yes, mfb has hit it on the head.

Our current rules are incompatible. Since the universe obviously does work with both QM and GR, we know that the rules we currently have are incomplete.

It is important that you recognize that there are places in our universe where both QM and GR do come into play at the same time. Our current rules for QM and GR do not cover those scenarios. We call it a singularity - meaning, literally, that our rules stop working.

 

[gerbilmore]

And that tells you they are not the fundamental rules governing the games. There has to be something more fundamental, some set of rules that allows to describe what a poker table on a football field would lead to.

But even if we did find one set of rules governing the universe, it is still possible to have other sets of rules (society laws, poker, football, etc) that work within that universe, and only overlap in the sense that the stuff governed by the second set of laws is ultimately governed by the fundamental set of laws. What if QM is the most fundamental set of rules for the universe, and GR is another set of rules that that sits on top of those rules.

 

[gerbilmore]

It is important that you recognize that there are places in our universe where both QM and GR do come into play at the same time.

Just as there are in poker and football ... the cards physically move around the table according to the same fundamental laws governing the physical movement of the ball. It seems to me that two sets of laws can exist which overlap in some areas, but not others. Both are right, even though they cannot be entirely unified.

 

[DaveC426913]

What if QM is the most fundamental set of rules for the universe, and GR is another set of rules that that sits on top of those rules.

That would be just fine. That's still one set of rules that explains both the quantum and cosmological universes.

 

[gerbilmore]

That would be just fine. That's still one set of rules that explains both the quantum and cosmological universes.

My point exactly. It works and it's fine ... so why assume we can unify them any further?

 

[DaveC426913]

My point exactly. It works and it's fine ... so why assume we can unify them any further?

Because they are currently inadequate to describe our universe! We don't have a model that fully describes what we see.

 

[gerbilmore]

We don't have a model that fully describes what we see.

Correct me if I'm wrong—we don't have one, but we do have two models (QM AND GR) which describe things very precisely at different scales, each of which is incomplete, but both of which may turn out to be correct and complete—aside from the fact that they are not unified. What I'm trying (perhaps not very well) to say is that aren't we imposing our own expectations on nature by trying to find one complete set of all encompassing laws to describe the universe, when, actually, two sets of laws may be the answer—as bizarre and counter intuitive as it may seem (remembering that bizarre and counter intuitive arguably describes QM, which is well established and verified).

Thanks for your patience :)

 

[gerbilmore]

To put it another way, what if all these problems were solved individually:

http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics

... and the resulting outcome was two sets of laws. We could either conclude that we seriously messed up somewhere along the line and go back to the drawing board, or we could accept that nature is just plain weird.

 

[stevendaryl]

Correct me if I'm wrong—we don't have one, but we do have two models (QM AND GR) which describe things very precisely at different scales, each of which is incomplete, but both of which may turn out to be correct and complete—aside from the fact that they are not unified.

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.

 

[gerbilmore]

So we have two descriptions of their interactions, and those two descriptions can't possibly both be right.

Why not? Simply because that's counterintuitive?

 

[stevendaryl]

Why not? Simply because that's counterintuitive?

If two theories make contradictory predictions, then one or the other prediction is wrong. It's not just not counter-intuitive.

 

[gerbilmore]

If two theories make contradictory predictions

Is this the case? Are there any examples you could quote? That may answer my question in some ways, although I still feel my reasoning stands.

 

[stevendaryl]

Is this the case? Are there any examples you could quote? That may answer my question in some ways, although I still feel my reasoning stands.

I gave you a specific example. What happens if you have two identical particles of mass M and charge Q and release them near each other? QM predicts that they repel each other (reflected in the fact that the probability of the particles being found close together gets smaller and smaller as time increases). GR predicts that if the masses are great enough, then they will be attracted to each other. Those are contradictory predictions.

 

[gerbilmore]

Those are contradictory predictions.

Thanks for explaining that example.; very useful.

I do still feel that in some ways this says something about our willingness to accept contradictory findings. But arguably that's also how we describe something as 'wrong'! :) Not that I'm suggesting I'm right by any means of course, but I would just cite the many occasions in the history of science where something that seemed wrong was actually right, ultimately highlighting the durability of our preconceptions.

 

[jerromyjon]

QM accurately predicts what naturally occurs which defies logical causal-realistic relativity. No mass exists until you weigh it and QM ignores the minuscule influences in its realm where it has unobservable physical impact.

 

[DaveC426913]

Why not? Simply because that's counterintuitive?

No, because - and I'll say it again - there are scenarios where both QM and GR need to apply. We do not have a description for these scenarios. We call them singularities because our models (both of them) break down.GR requires a smooth continuous field of space-time. QM requires quantified units.

GR uses zero-dimensional point for particles (if they're not zero-dimensional then it doesn't work). What happens when two aero-dimensional particles collide? You get an energy transfer over zero distance. This results in an energy transfer of, essentially an infinite amount.

This is super-simplified, but there are multiple similar examples. If you try to apply GR to QM, what you keep getting are infinities.

 

[jerromyjon]

Gravity and common sense fails in subatomic physics. EMR which behaves spooky at a distance in light physics causes the same phenomenon in matter so there is a conflict where QED is right and relativity says nothing or classical EM and physics are your options.

 

[gerbilmore]

Thanks for your answers; very useful for further reading, although something still niggles. I'm struggling to think of another way to accurately describe what I mean (probably because I'm wrong!) but how about this example:

x + y = z (representative of GR)
y + x = z (epresentative of QM)

Two sets of rules that look different (in that the sequential order of x and y is different) but that are both correct and ultimately describe the same thing. If you know the value, but choose not to give it a number, of the first number in each equation (x in GR; y in QM), then your predictions of the second number (y in GR; x in QM) would be different, so you could be forgiven for thinking there was something wrong, especially if the result (described as z) is the same. But both are correct set of rules, both allow for different predictions (the value of the second number in sequence based on knowing, although not explicitly as a number, the first) and both describe the same result.

I guess that requires some additional thinking outside of the rules of maths, but while still in the confines of a mathematical equation.

That makes some sense to me ;-)

 

[gerbilmore]

If you try to apply GR to QM, what you keep getting are infinities.

I realize that a result of infinity suggests something has gone wrong, but why? Why is infinity an unacceptable answer? It seems very beautiful.

Perhaps a separate thread. I find this all fascinating.

 

[DaveC426913]

Why is infinity an unacceptable answer? It seems very beautiful.

These aren't abstract things we're talking about; they're real phenomena. As in my example, infinity might apply to the amount of energy transferred between two particles. This cannot be true. You cannot have an infinite amount of energy in a finite interaction - it is literally more energy than the entire universe.

 

[gerbilmore]

You cannot have an infinite amount of energy in a finite interaction

Understood. However, to flip that around with an example, if our universe is flat (which is seems to be by my understanding) then that suggests it may be infinite—infinity is therefore posited as a possible real phenomena. We could have an infinite universe made up of a finite amount of energy (based on the first law of thermodynamics). It could then also be argued that infinity is a finite value, but I won't even go there...!

 

[DaveC426913]

Understood. However, to flip that around with an example, if our universe is flat (which is seems to be by my understanding) then that suggests it may be infinite—infinity is therefore posited as a possible real phenomena. We could have an infinite universe made up of a finite amount of energy (based on the first law of thermodynamics).

But that's just word salad. I'm not talking about abstracts you can dance around.

I listed a specific example of a physical interaction between a pair of particles - they could be particles in the hair on your nose - transferring an infinite amount of energy.

 

[gerbilmore]

I listed a specific example of a physical interaction between a pair of particles

Understood. So am I right in saying that in that example an infinite result or proposition would be incorrect, but in other examples (infinite universe, perhaps not described mathematically?) it may not? I guess I'm trying to understand why infinity seems to be plausible (accepted?) in some instances but not others.

Trying to keep on topic here ... both aspects of discussion seem to follow my same line of thinking ... are our ways of describing things insufficient to actually describe the thing we're trying to describe; similar to Heisenberg's quote: "We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning."

 

[Nugatory]

Understood. So am I right in saying that in that example an infinite result or proposition would be incorrect, but in other examples (infinite universe, perhaps not described mathematically?) it may not? I guess I'm trying to understand why infinity seems to be plausible (accepted?) in some instances but not others.

You've been tricked by common but sloppy informal language here. The statement "the universe is infinite", whether true or not, would be more precisely phrased as "the distance between us and any other object in the universe at any moment is finite, just as would be in a non-infinite universe, but there is no upper bound on the distances that we might observe". infinite or universe or no, there are no infinite distances.

We have, however, strayed far from your original question...

 

[gerbilmore]

You've been tricked by common but sloppy informal language here. The statement "the universe is infinite", whether true or not, would be more precisely phrased as "the distance between us and any other object in the universe at any moment is finite, just as would be in a non-infinite universe, but there is no upper bound on the distances that we might observe". infinite or universe or no, there are no infinite distances.

That gives me a much clearer sense of an infinite universe, and actually shows how a finite and an infinite universe are, arguably, quite similar. It suggests something finite but limitless as opposed to something stretching into the distance for an eternity. It's amazing how just a difference of a few words can make such a difference to such a baffling concept!

 

[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.