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We know that Quantum Theory should be considered as a framework in which all other theories/forces (Strong, Weak, EM and Gravity) exist.

For example, we have the Quantum Chromodynamics, Quantum Flavordynamics (Electroweak), Quantum Electrodynamics (but still no Quantum GR).

When I think about this, it then strikes me why gravity, and specifically special relativity, is part of the framework itself (because QFT is based on QM and SR). Why would a theory like SR (and maybe in future GR) be part of the framework? This looks like a circular logic.

I would appreciate it if someone can explain?

My understanding is that gravity is different because it exist everywhere, and are not a result of a charge (electric, color or flavor). That's why we cannot speak about a quantum theory of EM without considering gravity, but we can do it without considering strong or weak force. Is this correct?

EDIT: it would make more sense to me to see Gravity/GR considered only as a framework (a geometric one) rather than a force, or it can be considered a fictitious force, as with the centrifugal force. see first paragraph of first answer here.

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  • $\begingroup$ Gravity is (in the weak-field limit) not fundamentally different from the other interactions, to the contrary of what you seem to believe. It is the result of a charge (called "mass"), and the only reason it "exists everywhere" and EM doesn't is that EM charges can be positive or negative, thus canceling out each other's effects. The only difference is that the coupling constant of gravity (Newton's constant) has positive mass dimension, leading to a non-renormalizable theory when quantized naively. (Naive QGR makes perfect sense in the effective field theory interpretation, though.) $\endgroup$ – David Vercauteren Nov 11 '13 at 19:52
  • $\begingroup$ It's important to make it clear that there is no gravity in special relativity. If what you mean by "we cannot speak about a quantum theory of EM without considering gravity" is that any quantum theory of EM must include special relativity, then your statement is incorrect. $\endgroup$ – Emilio Pisanty Nov 11 '13 at 20:12
  • $\begingroup$ @DavidVercauteren, I got your point about why Gravity exist everywhere, but still this isn't the main question, I am still confused about why SR (a special case of GR/Gravity) is a part of the framework although it is just a force/interaction. $\endgroup$ – student1 Nov 11 '13 at 22:16
  • $\begingroup$ @EmilioPisanty, but indeed QED include SR, If I understand correctly. $\endgroup$ – student1 Nov 11 '13 at 22:17
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/6980/2451 , physics.stackexchange.com/q/10088/2451 , physics.stackexchange.com/q/52211/2451 and links therein. $\endgroup$ – Qmechanic Nov 11 '13 at 22:42
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Special relativity and general relativity are quite different beasts. SR is a group of symmetries that get embedded in the quantum theory, and gives us RQFT. Thus, you can have a field and therefore a quantum field theory on top of SR with no need to quantize SR. You can do quantum mechanics of EM, for instance, with no need to talk about gravity (remember, SR is a group of symmetries only).

General relativity / gravity adds dynamical degrees of freedom, and while you can do quantum field theory on top of GR (e.g., hawking radiation), it is necessarily incomplete.

Here's a previous question on why gravity needs to be quantized

Long story short: imagine doing a double-slit experiment with very heavy particles. Since the particles couple to gravity, we would expect their gravitational back-reaction to exhibit quantum behaviour, and, therefore, gravity itself.

Unfortunately, just adding gravity as another field and plodding along doesn't work. There has been a lot of promising progress in string theory though. Some would say too much progress ;)

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  • $\begingroup$ But SR is indeed a special case of GR (non accelerating frames). Thus if SR is part of the framework, so should GR, which means, again, that GR should be treated as framework rather than force/theory. $\endgroup$ – student1 Nov 11 '13 at 22:10
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    $\begingroup$ Fish swim. I swim. Therefore I am a fish? Don't take this as gospel, but rather a way of thinking about the problem. SR is a global symmetry. GR is theory of gravity that has the same symmetry locally. If space is not curved, then the two look the same. But GR has degrees of freedom that SR does not, and so it's more along the lines of "force/theory". Btw you can have accelerating frames in SR and while you can use the tools of GR to study it, unless space is curved, I would argue that you are still doing SR. $\endgroup$ – lionelbrits Nov 12 '13 at 1:39
  • $\begingroup$ Alright, that makes sense. So we can say that QFT is really a merge of two sub-frame works, so to speak, one is SR the other is QM. All other forces exist within this QFT framework (not yet for GR). $\endgroup$ – student1 Nov 12 '13 at 4:37
  • $\begingroup$ Roughly. QFT is a tool for studying fields. Thus far we've managed to fit all our fields in there except for gravity (and dark energy and dark matter and whatnot). Don't confuse the tool with the physics, though. For example, the 0-dimensional quantum mechanics of infinite dimensional matrices is thought to be equivalent to all of string theory. Wrap your head around that. $\endgroup$ – lionelbrits Nov 12 '13 at 11:41

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