A Theory of "Everything"

[Anjelus]

Hello! I'm trying to think of a (relatively) simple way to explain this issue to someone. Don't worry, I'm not interested in "magic" talk about free will or anything of the sort, just a clarification of terms. Is it fear to break down the, completely hypothetical, "theory of everything" as so:

 

 

1. General Relativity is (seems to be?) determinate.

 

2. Quantum Mechanics is (seems to be?) indeterminate. The Uncertainty Principle means not only that we can't determine QM through observation, but that the system seems to be fundamentally indeterminate.

 

3. Einstein, to the end of his days, insisted that we're missing variables that would remove the apparent uncertainty in QM, but my understanding is that the Uncertainty Principle is inherent to QM. This is the source of the Einstein/Bohr debates, and the common consensus is now that Einstein was wrong to insist QM can't be indeterminate. Is this a fair description of events?

 

4. The "holy grail" Theory of Everything would unify GR & QM because, from what we know, they cannot both be simultaneously true. And they cannot both be simultaneously true... because the determinism & indeterminism cannot co-exist? Is that the core reason for non-compatibility?

 

Is that a fair way of describing the issue? Further clarification/discussion/recommended readings would be great too.

 

Dankeschön!

[ajb]

1. General Relativity is (seems to be?) determinate.

Yes general relativity is determinate in the classical sense that we do not have to resort to probabilistic methods to understand the observables.

 

 

 

2. Quantum Mechanics is (seems to be?) indeterminate.

Yes and no.

 

Given a state at a given time, I can calculate the time evolution of that state exactly (in principle). So the theory is determinate, I know the time evolution of the system.

 

However, when we calculate observables we have to discuss this all in terms of probabilities. In this sense the theory is indeterminate.

 

 

The Uncertainty Principle means not only that we can't determine QM through observation, but that the system seems to be fundamentally indeterminate.

Well, we still compare what the mathematical models based on quantum mechanics state with experiment. We have generally good agreement. So we do determine quantum mechanics though observations.

 

What the uncertainty principle really says its that we cannot exactly know the position of a particle if we know its momentum (velocity) and vice versa.

 

3. Einstein, to the end of his days, insisted that we're missing variables that would remove the apparent uncertainty in QM, but my understanding is that the Uncertainty Principle is inherent to QM. This is the source of the Einstein/Bohr debates, and the common consensus is now that Einstein was wrong to insist QM can't be indeterminate. Is this a fair description of events?

We know that Einstein was not happy with quantum mechanics, this is clear. The reason is probabily due to his geometric way of thinking which was so important in developing relativity.

 

Anyway, Bell in 1964 showed that (local) hidden variable theories cannot reproduce what quantum mechanics predicts.

 

 

4. The "holy grail" Theory of Everything would unify GR & QM because, from what we know, they cannot both be simultaneously true. And they cannot both be simultaneously true... because the determinism & indeterminism cannot co-exist? Is that the core reason for non-compatibility?

That could be one way of looking at the issue.

 

There are other ways that are probably more technical. In short, one would expect gravity to also be quantised as all the other forces we know of are. That is we have a quantum description of these forces. However, the standard methods of quantisation (what ever that is) fail for general relativity.

 

So either we need to modify general relativity or quantum mechanics, or maybe both.

 

Is that a fair way of describing the issue? Further clarification/discussion/recommended readings would be great too.

As for further reading, I am not sure. Smolin's three roads book I like. Not so much his later books.