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

[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.