# Does Relativity and Quantum Mechanics NEED to be reconcile?

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## Main Question or Discussion Point

One of the greatest quest in physics is to reconcile Relativity with QM. But is this reconciliation really necessary? They both work quite well in their respective fields so why not just leave it at that? The only issue I can see is the problem of the singularity but can't that be solved by finding a theory of Quantum Gravity?

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jedishrfu
Mentor
Its a good question however how else would you discover the theory of quantum gravity? Only by trying to preserve GR and QM while at the same time building a bridge between them that we may in fact discover the theory of QG.

According to the GR theory, when a particle and its antiparticle collide they should form a body with double their mass, which at least for particles without internal structure should be a black hole. Yet particle+antiparticle tend to just give off 2 other particles (photons) which fly away. That is something that GR cannot explain. I think QM can because the wave nature of particles and the uncertainty relations mean that a particle is not situated in a point in space, but is somewhat spread out.

the wave nature of particles and the uncertainty relations mean that a particle is not situated in a point in space, but is somewhat spread out.
A better rephrasing would be that it is undetermined in space, not spread out.

Demystifier
One of the greatest quest in physics is to reconcile Relativity with QM. But is this reconciliation really necessary? They both work quite well in their respective fields so why not just leave it at that? The only issue I can see is the problem of the singularity but can't that be solved by finding a theory of Quantum Gravity?
This doesn't make sense because it is not clear what do you mean by "Relativity". Do you mean special relativity or general relativity? If you mean special relativity, then it is already reconciled with QM (even though there are some unsolved issues related to the measurement problem and non-locality). If you mean general relativity, then reconciling relativity with QM is the same as finding the theory of quantum gravity.

This doesn't make sense because it is not clear what do you mean by "Relativity". Do you mean special relativity or general relativity? If you mean special relativity, then it is already reconciled with QM (even though there are some unsolved issues related to the measurement problem and non-locality). If you mean general relativity, then reconciling relativity with QM is the same as finding the theory of quantum gravity.
Well since I'm asking about gravity it's obviously GR we are discussing here. Even if we do find a theory of Quantum Gravity how would that necessarily reconcile with GR? Suppose the hypothetical graviton is detected GR will still fail to describe what it is since according to GR gravity is not quantized.

mathman
A major problem area requiring reconciliation is: what is going on inside a black hole?

Nugatory
Mentor
Well since I'm asking about gravity it's obviously GR we are discussing here. Even if we do find a theory of Quantum Gravity how would that necessarily reconcile with GR?
Reconciling two conflicting theories means finding a way that they can both be right. A successful theory of quantum gravity will be equivalent to general relativity when the distances involved are large compared with the Planck length. It has to, because GR already works at those distances - therefore any theory that doesn't agree with GR in that domain cannot be right.

This is analogous to the way in which special relativity has already been successfully reconciled with quantum mechanics. Quantum field theories, and especially quantum electrodynamics, unite quantum mechanics and SR. The measure of their success is that they reduce to ordinary SR when the distances involved are large enough that the quantum mechanical effects are negligible.

Suppose the hypothetical graviton is detected GR will still fail to describe what it is since according to GR gravity is not quantized.
It's just as true that special relativity fails to describe the photon because according to SR electromagnetic fields are not quantized. To describe photons we need quantum electrodynamics which unifies SR and QM. That doesn't make either SR or QM wrong, it means that QED would be a non-starter if it didn't agree with both of them in their respective domains of validity.

bhobba
Mentor
One of the greatest quest in physics is to reconcile Relativity with QM.
That's a misconception, although a very very common one even in professional literature:
http://arxiv.org/abs/1209.3511

They are reconciled, but the combined theory is only valid to a cutoff about the plank scale. The same with QED for that matter - it has this thing called a Landau pole that means the theory is not valid beyond a certain cutoff. And indeed we know that's true - well before the Landau pole is reached the electro-weak theory takes over. It is now thought all our usual theories, and that includes gravity, are low energy approximations to some more fundamental theory - String Theory maybe?

Thanks
Bill

Nugatory
Mentor
According to the GR theory, when a particle and its antiparticle collide they should form a body with double their mass, which at least for particles without internal structure should be a black hole.
We don't even need to collide a particle and an anti-particle to create a problem for GR - a point particle of non-zero mass is already an impossible black hole unless we ignore gravitational effects. The key phrase here is "according to the GR theory" - the moral of the story is that we cannot trust GR at these distance scales, and that's why we need a theory that reconciles GR (applicable when gravitational effects cannot be neglected) and QM (applicable when distances are small enough that quantum effects cannot be neglected).

bhobba
Mentor
We don't even need to collide a particle and an anti-particle to create a problem for GR - a point particle of non-zero mass is already an impossible black hole unless we ignore gravitational effects. The key phrase here is "according to the GR theory" - the moral of the story is that we cannot trust GR at these distance scales, and that's why we need a theory that reconciles GR (applicable when gravitational effects cannot be neglected) and QM (applicable when distances are small enough that quantum effects cannot be neglected).
Just to expand a little in light of the paper I posted on the effective field theory that reconciles QM and GR up to a cutoff, what we need is a theory that does that beyond the plank scale - we already have one up to then. That is the key problem.

We cant trust anything in the standard model at the plank scale anyway so gravity is hardly alone on that score.

It of course makes the problem of doing it none the easier - all it does is change how the problem is viewed. But it is a very interesting new perspective.

Thanks
Bill

Reconciling two conflicting theories means finding a way that they can both be right. A successful theory of quantum gravity will be equivalent to general relativity when the distances involved are large compared with the Planck length. It has to, because GR already works at those distances - therefore any theory that doesn't agree with GR in that domain cannot be right.

This is analogous to the way in which special relativity has already been successfully reconciled with quantum mechanics. Quantum field theories, and especially quantum electrodynamics, unite quantum mechanics and SR. The measure of their success is that they reduce to ordinary SR when the distances involved are large enough that the quantum mechanical effects are negligible.

It's just as true that special relativity fails to describe the photon because according to SR electromagnetic fields are not quantized. To describe photons we need quantum electrodynamics which unifies SR and QM. That doesn't make either SR or QM wrong, it means that QED would be a non-starter if it didn't agree with both of them in their respective domains of validity.
Great post this is actually starting to make some sense to me. But didn't the photoelectric effect shown that EM can be quantized before QED came along? I believe Planck's formula was involved somewhere but correct me if I'm wrong.

So was this a precursor to QED or did QED resolve some kind of paradox? Or rather the photoelectric effect provided the experimental evidence and that QED was the theory behind it? I feel like I'm on the right track here but I also feel like I'm missing a lot.

bhobba
Mentor
But didn't the photoelectric effect shown that EM can be quantized before QED came along?
Sure - but it was hardly a fully blown theory applicable to all situations and the whole issue of if its even required just for that is debateable (I side with Arnold on this - photons are not required - but it is something that creates some debate):
http://physics.stackexchange.com/questions/68147/can-the-photoelectric-effect-be-explained-without-photons

Dirac gave EM a quantum injection when he quantised the EM field:
https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field

That predicted photons from a more fundamental theory. That became part of QED when it was combined with the electron. Trouble is it had these horrid infinities that required quite a while to sort out. The key thing from the modern viewpoint is the theory (in its usual perturbative form - but that is a whole new thread) requires a cut-off to make sense and some of the quantities in the theory were in fact cutoff dependent. The moral is - don't push theories beyond their domain of applicability.

Same with gravity actually. If we don't push it beyond about the Plank scale there is no problem. But of course we all want to peek behind that veil.

Thanks
Bill

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Nugatory
Mentor
Great post this is actually starting to make some sense to me. But didn't the photoelectric effect shown that EM can be quantized before QED came along? I believe Planck's formula was involved somewhere but correct me if I'm wrong.
The photoelectric effect was observational evidence that we needed a theory that quantized the electromagnetic field, that the classical electromagnetic theory of Maxwell was inadequate when it came to the interaction of electromagnetic fields and electrons. However, it didn't come anywhere near supplying that theory - Einstein's explanation of the photoelectric effect (1905), Bohr's electron model (1913), and Planck's theory of blackbody radiation (1900) were all ad hoc efforts to explain observations that were inconsistent with classical theory. It took another decade to work out non-relativistic quantum mechanics in the 1920s and put a theory behind Einstein's, Bohr's, and Planck's brilliant intuitive leaps.
So was this a precursor to QED or did QED resolve some kind of paradox? Or rather the photoelectric effect provided the experimental evidence and that QED was the theory behind it? I feel like I'm on the right track here but I also feel like I'm missing a lot.
Quantum mechanics as it was initially formulated (the only kind you're likely to encounter as an undergraduate) is not a relativistic theory. It works only when the speeds are small compared with the speed of light and the energies are small compared with the $E=mc^2$ energy of the particles involved; clearly neither condition applies to photons. Quantum field theories in general and QED in particular were developed over several decades starting in the late 1920s as a relativistic quantum theory - this was the reconciliation of QM and SR that Demystifier mentioned above.

Demystifier
Quantum gravity in the limit $\hbar \rightarrow 0$ must give classical gravity, and classical gravity is (at least approximately) given by GR.