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

[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.

 

[stevendaryl]

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.

Well, in that sense of "unify", it's not clear why we need for the various forces to be unified. If there are 16 or 32 types of forces, that's a pain, but there is nothing inconsistent about it. But if we have two theories that work fine in their own domain of applicability, but contradict each other when applied outside of those domains, that means that the two can't be the final story. There must be a type of unification to resolve the inconsistency.

 

[Ken G]

Well, in that sense of "unify", it's not clear why we need for the various forces to be unified. If there are 16 or 32 types of forces, that's a pain, but there is nothing inconsistent about it. But if we have two theories that work fine in their own domain of applicability, but contradict each other when applied outside of those domains, that means that the two can't be the final story. There must be a type of unification to resolve the inconsistency.

I agree, but note that when there was a weak force, and an electric force, there was not an inconsistency between them-- nevertheless, it was realized that there would be value in unifying them into electroweak. Buoyed by that success, the idea was floated that all forces should be the same thing-- that's what "unification" really means, not just that we can describe them all with different but consistent theories. So in that light, the key question is, if all forces are the same thing, is gravity a force, or isn't it? That's where I point to the differences between Newton's first and second laws as evidence that perhaps gravity is not a force, it is the "default" answer to what happens when there are no forces. Of course, maybe that is not what gravity is, that is what something else is that we don't even have a name for because Galileo got it right the first time.

 

[stevendaryl]

I agree, but note that when there was a weak force, and an electric force, there was not an inconsistency between them--

Actually, the very first attempt to develop a theory of weak interactions was inconsistent. It worked as an approximate theory, but it led to incurable divergences if you tried to be more accurate. That was Fermi's theory. To make it consistent, it had to be made into a gauge theory. I don't know whether it was necessary for consistency that it be unified with QED.

 

[Ken G]

Actually, the very first attempt to develop a theory of weak interactions was inconsistent. It worked as an approximate theory, but it led to incurable divergences if you tried to be more accurate. That was Fermi's theory. To make it consistent, it had to be made into a gauge theory. I don't know whether it was necessary for consistency that it be unified with QED.

I was wondering that-- so you are saying the primary motivation to unify it with electromagnetic forces was simply that we already had a theory that worked well, so why not try to piggyback on that? But even QED has its region where it cannot be used, so even piggybacking on that was accepting some inconsistency with reality. Do you think the main motivation to fix Fermi's theory of the weak force came from a desire to make it more general, or from a desire to make it the same force as electromagnetic? I could see both arguments, but it seems to me that there is some kind of philosophical drive to find unity here-- not just an effort to make more general predictions for more different forces.

 

[Stephen Tashi]

If they were both correct, then they wouldn't contradict each other, and they wouldn't contradict experiments.

They can both be correct and give different predictions. If one theory's prediction is "If A then B " and another theory's prediction is "If C then not B" then these theories are different but not necessarily contradictory. For example, to make a prediction in General Relativity, how much information must you have in the If... part of the statement? Does an equivalent "If...then..." statement in the context of Quantum Mechanics even permit specifying this amount of information?

To do an experiment that shows the contradiction between two theories you need to set up conditions where both theories agree on the conditions of the experiment. So to settle "If A then B" vs "If C then not B" you need a situation such that both A and C precisely describe it. Is there a valid set of rules to translate a description A in the language of Quantum Mechanics to a description C in the language of General Relativity - and vice versa?

 

[stevendaryl]

I was wondering that-- so you are saying the primary motivation to unify it with electromagnetic forces was simply that we already had a theory that worked well, so why not try to piggyback on that? But even QED has its region where it cannot be used, so even piggybacking on that was accepting some inconsistency with reality. Do you think the main motivation to fix Fermi's theory of the weak force came from a desire to make it more general, or from a desire to make it the same force as electromagnetic? I could see both arguments, but it seems to me that there is some kind of philosophical drive to find unity here-- not just an effort to make more general predictions for more different forces.

Fermi's theory was not renormalizable, so perturbation theory using his theory produced nonsense if you went beyond the lowest-order terms. So I think that the biggest motivation was to make a renormalizable theory.

You're right, though, that QED has other problems, besides being nonrenormalizable (for example, the Landau pole). I don't know whether the electroweak theory fixes these problems, or not.

 

[Ken G]

That's a good question, because if it does fix the Landau pole problem, we can certainly say that unifying those two forces gave us something that was significantly better than the pieces that went into it. But if it did not fix that problem, we must probably conclude that we have an essentially philosophical advance there-- we have achieved a subjective goal of science, to unify what can be unified, but we have not actually used the unification to remove all the problems, which opens the possibility that a theory that does remove the remaining problems might be required to disunify them!

 

[Ilja]

Both GR (general relativity) and QM(quantum mechanics) are logically self consistent and work at the scale of their domain.

Hm, is it justified to name a theory with singularities logically self-consistent? I doubt.

 

[jerromyjon]

Hm, is it justified to name a theory with singularities logically self-consistent? I doubt.

Everything in physics endures the same inability to completely describe anything that occurs. From any reference model there are drawbacks or limitations but it does not preclude the evidentiary consistency for which they are known. The fact that nature insists on being evenly random at heart and constructively massive upon implication defies unification philosophically. Singularities are a mathematical problem obviously not a natural one.

 

[Ilja]

That

Singularities are a mathematical problem obviously not a natural one.

That's my point. Mathematics is, essentially, extended logic, thus, singularities can be considered as a logical problem. On the other hand, when an infinity starts to become so obviously wrong that one should reject the theory as logically inconsistent? Not every infinity is problematic, good old Euclidean space is infinite too.

 

[Ken G]

I would say infinities in physics are not logical problems, they are problems with logic, which is a bit different. In some ways, the relationship of mathematics and physics is like the relationship between the clothes and the Emperor who is not wearing any. At some point, you need a child to say "but the universe isn't really doing that, that's just how you are thinking about it." Then the Emperor says, "I know child, but that's what we adults mean by the universe."

 

[martinbn]

But having singular space-times is not the same as having infinities. Lorentzian geometry is self consistent mathematical subject. So why can't it be a description of reality?

 

[Quds Akbar]

Well I do know that Quantum mechanics cannot be the ultimate T.O.E yet because it does not have an agreed-on and unified theory of gravity .

 

[the_pulp]

Im not an expert, just an amateur, but here is my view on the subject, not very mainstream, maybe because of my ignorance, but as there is a tiny chance that my ignorance is not contaminated with mainstream physics, perhaps I can make an useful point. If that is not the case, Sorry!
I think that the main issue is that the theories proposed, from what I understood, take QM for granted. I mean, complex numbers mixed with superposition principle and such. And I think that it is not clear that QM principles rule in the Planck Energy regime. In fact, there are many papers that state that the use of complex numbers is a consequence of Continuity, but, as in this levels the continuity of spacetime is no clear / understood or whatever you may call, the use of complex numbers is not granted. My (ignorant) opinion is that there is a chance that in this regime we should use some sort of algebra that, in the particular case that we are dealing with a system with a lot of objects, should converge to the complex numbers, the use of the Born Rule, etc.
Sorry for posting just an especulation, but I always wanted to say that! I promise it would be the last time!

 

[Ken G]

There is nothing more unscientific than the concept of a theory of everything. That is the granddaddy of all unscientific beliefs, for the following reasons:
1) there is no way to test if it is actually a theory of everything
2) it would not even be able to predict a small fraction of the things we already observe
3) for a century after a theory like that is created, life will change on Earth not one iota
4) good science is based in skepticism and critical investigation, never acceptance
It's fine to look for more unifying theories, but to cast them as anything but that does science a disservice by mischaracterizing what it is. The only thing worse than saying that gravity and quantum field theories have to be unified (because saying that misses the possibility that they might have to be separate) is saying that doing so would create a theory of everything (because there have been many times in the history of science where it did not present obvious contradictions, even though it could not predict everything we observe, and these should never be characterized as theories of everything).

 

[DaveC426913]

There is nothing more unscientific than the concept of a theory of everything. That is the granddaddy of all unscientific beliefs, for the following reasons:

I believe you are taking it far too literally, as in The Theory of Everything. The common concept for the theory of everything (note: sans caps) is simply the unification of the 4 fundamental forces. While, in principle, that could be extrapolated to explain everything we so far see (because, as far as we understand, all physical principles can be deduced from the 4 fundamentals) , there is no explicit - and certainly no scientific - imperative that it will, indeed, describe everything

1) there is no way to test if it is actually a theory of everything

As above, no one who uses the term, including scientists believes that it is actually a Theory of Everything.

2) it would not even be able to predict a small fraction of the things we already observe

Who said anything about predict? But, in principle, the universe could be deduced from it.

3) for a century after a theory like that is created, life will change on Earth not one iota

Of what relevance is this to 'being unscientific'? It sounds a lot more like a 'what use is it in feeding the hungry' comment.

4) good science is based in skepticism and critical investigation, never acceptance

This sounds like a 'deepity'. Who said nobody was being skeptical? Who said anything about acceptance?

 

[Ken G]

I believe you are taking it far too literally, as in The Theory of Everything. The common concept for the theory of everything (note: sans caps) is simply the unification of the 4 fundamental forces. While, in principle, that could be extrapolated to explain everything we so far see (because, as far as we understand, all physical principles can be deduced from the 4 fundamentals) , there is no explicit - and certainly no scientific - imperative that it will, indeed, describe everything

Yes, it is a rather unfortunate label because it is disingenuous.

Who said anything about predict? But, in principle, the universe could be deduced from it.

That has never been shown to be true. It is really just a belief that this would hold "in principle", meaning, that it is just a problem in doing the calculation that prevents us, because since we cannot do the calculation, we cannot check this belief! Indeed, I would say that it actually doesn't hold, not even in principle, because solving the equations is only a small part of what physics requires, in order to describe the behavior of something. The parts we don't give as much press to (boundary conditions, geometry, context, etc.) may be just as important as the fundamental laws, but require a lot of manual manipulation on the part of the physicist. So on the topic of "unification", here's one that no one ever talks about: unifying the equations and the boundary conditions and other external constraints around which they are solved.

Of what relevance is this to 'being unscientific'? It sounds a lot more like a 'what use is it in feeding the hungry' comment.

I said it was not unscientific to look for such a theory, what is unscientific is calling it a theory of everything. I realize it's just a name, so what's in a name? Well, quite a lot, actually, when most people are never going to get much past the name anyway.

This sounds like a 'deepity'. Who said nobody was being skeptical? Who said anything about acceptance?

All good questions, and I will happily answer them. When you try to explain to people what science is, and why it belongs in classrooms where religious dogma does not belong, you teach them (hopefully) that what defines science is that it is never satisfied it has found the truth-- it is always looking under the hood of what is widely believed. So if you do that, and then turn around and say "now scientists are looking for the theory of everything," you completely undercut everything important that you just tried to tell them about what science is, and what it isn't.

 

[DaveC426913]

Yes, it is a rather unfortunate label because it is disingenuous.

No more or less so than 'black hole' (which is neither black nor a hole) or 'wormhole'. But you wouldn't claim they are unscientific concepts. No one expects that a 2-4 word phrase could possibly describe such concepts without a massive degree of misdirecting symbolism. How is tToE any different?

 

[Ken G]

Not at all the same, those terms don't undercut the core principle of science, which is what "theory of everything" does do. The label blurs the important distinction between what we are allowed to discover, versus what we simply choose to believe because we like the idea.

 

[DaveC426913]

undercut the core principle of science, which is what "theory of everything" does do.

It's four words. It's a label, not a treatise. You give it far, far too much power.

The name itself is steeped in history and evolved organically. It was merely a riff off the names that went before it: notably GUT, which unified 3 of the 4 forces.

The common names of things (like the aforesaid black hole and wormhole and many others) are not obliged to be accurate. They're just ... monikers, popularizations. Scientific labels are a reflection of their formation through science history, not a 4-words-or-less synopsis of the theory.

Do you feel the same way about 'Big Bang'? It's terribly inaccurate.
String theory? Atomic theory ('atom' means 'indivisible')?

Anyway, you're certainly entitled to your viewpoint, and it's not my place to try to overwhelm yours with mine. It just seems kind of ... arbitrary to me.