What is the rationale behind gravitons?

[Eelco]

A test particle propagates on a fixed background.

I understand such is customary in real analysis, yeah. That is a limitation of the mathematical tools you are using. Why does everyone insist on confusing that with something physical?

 

[Finbar]

Yes, i realize that, but these dependencies seem conceptually very different to me. Since when are a source term and a metric interchangable concepts?


Yeah, but they are mathematically and physically different dependencies. Space is space and matter is matter.

If gravitons seek to dissolve the distinction between space and matter, that's an ambitious goal, and I am surprised i havnt seen it stated like that: ill believe it works when someone does a simulation involving gravitons, that doesn't depend on arguments such as 'yeah it reduces to the einstein field equations because of this general abstract nonsense, so actually, we are solving that instead. The linearized variant, yeah.'

No your still confused. The metric tensor isn't spacetime. Its a function of spacetime. The metric has a value at each point in spacetime. The same goes for the EM potential. These are fields. What exists as absoloute concepts are the fields. We can make a general coordinate transform and change the spacetime coordinates so spacetime isn't an absolte concept.

Look both the EM field(U1 gauge field) and the gravitational field have geometic interpretations. In fact gravity is a gauge theory aswell. Yes gravity is a theory of the metric and therefore defines lengths and yes this leads to many conceptual and mathematical problems. But despite this you have to agree that the gravitational field created by a body A will transfer momentum to a body B. Momentum is consvered and according to general pricplies of QM comes in discrete packets. Therefore we can interprete the exchange of this momentum as a "particle". Buts its just an interpretation. Nobody starts off with the idea of a gravition and produces a quantum theory of gravity. It's just a useful concept when dealing with QM where quantities such as momentum do not take continuous values and when also using relativity when means that momentum must travel between two points in spacetime ie there is some notion of propagation.

 

[Eelco]

No your still confused. The metric tensor isn't spacetime. Its a function of spacetime. The metric has a value at each point in spacetime. The same goes for the EM potential. These are fields. What exists as absoloute concepts are the fields. We can make a general coordinate transform and change the spacetime coordinates so spacetime isn't an absolte concept.

You are arguing over real analysis, not over physics. In Regge calculus, id definitely say the metric is spacetime.

Look both the EM field(U1 gauge field) and the gravitational field have geometic interpretations. In fact gravity is a gauge theory aswell. Yes gravity is a theory of the metric and therefore defines lengths and yes this leads to many conceptual and mathematical problems. But despite this you have to agree that the gravitational field created by a body A will transfer momentum to a body B. Momentum is consvered and according to general pricplies of QM comes in discrete packets. Therefore we can interprete the exchange of this momentum as a "particle". Buts its just an interpretation. Nobody starts off with the idea of a gravition and produces a quantum theory of gravity. It's just a useful concept when dealing with QM where quantities such as momentum do not take continuous values and when also using relativity when means that momentum must travel between two points in spacetime ie there is some notion of propagation.

I agree, a non-gravitonic spacetime seems hard to reconcile with discrete energy quanta.

That said: why should i care about conservation laws in anything but a time averaged sense, when wavefunction collapse does not either?

 

[Finbar]

You are arguing over real analysis, not over physics. In Regge calculus, id definitely say the metric is spacetime.


I agree, a non-gravitonic spacetime seems hard to reconcile with discrete energy quanta.

That said: why should i care about conservation laws in anything but a time averaged sense, when wavefunction collapse does not either?

What is real analysis? the metric tensor g_ab defines a length ds^2 = dx^a dx^b g_ab(x). So it defined a infintessimal length ds in spacetime. Saying "the metric is spacetime" is totally meaningless.

Energy conservation is always obeyed in physics. Its just a common misconception that QM or the uncertainty principle does't conform to it.

 

[atyy]

Isn't Regge calc the motivation behind CDT?

CDT may be a computational version of either Asymptotic safety or Horava-Lifschitz - both of which have gravitons.

 

[Haelfix]

Regge calculus is about the earliest form of spacetime discretization that I am aware off that was also solutions of the field equations of GR. So yes, it is a precursor to dynamic triangulations, random triangulations, and so forth. Its heavily used in numerical approximations for hard problems in GR (the aforementioned black hole collisions for instance).

Later people tried to get it to work as a quantum gravity or quantum cosmology programs (not to be confused with the original intent). Like most such work, before CDT arrived, the problem was that all the various primordial simplexes would have a tendency to crumble up in numerical simulations and the classical flat limit was never achieved.

 

[Eelco]

What is real analysis? the metric tensor g_ab defines a length ds^2 = dx^a dx^b g_ab(x). So it defined a infintessimal length ds in spacetime. Saying "the metric is spacetime" is totally meaningless.

Real analysis is most of mathematics, including the calculus of real variables you are talking about here.

Even if you implicitly assume a flat spacetime, you are assuming a metric. When you propose a function of three variables, you are implicltly assuming a metric. There is no spacetime without a metric.

Energy conservation is always obeyed in physics. Its just a common misconception that QM or the uncertainty principle does't conform to it.

Dunno, there are published papers on the subject.

My understanding: The expectation value of energy is conserved. Then your wavefunction collapses, at some arbitrary point, without further particle exchange. Does that state it collapses to not affects its energy?

 

[Eelco]

Regge calc does not have gravitons.

The QG variants thereof might; depending on your interpretation. I don't mind thinking of space in terms of superpositions, and if youd want to call that gravitons, fine. My problem is with propagating the defining property of spacetime, over spacetime. How do you cut that knot? What do you start with? A flat spacetime is no less arbitrary than any other, and the only reason you are picking it, is because otherwise the real analysis gets too complicated.

 

[tom.stoer]

How do you formulate energy conservation in gravity theories?
- there is a locally conserverd energy momentum tensor in GR - fine
- if you enlarge your theoretical framework and introduce torsion, this conservation law vanishes
- I do not see how you can define a globally conserved energy (as a volume integral transforming as the zeroth component of a four vector)
- I do not see how you can define energy in QG theories (LQG, CDT, ...)

So we should restrict ourselves to talk about local symmetries; energy conservation may be a concept that works only in certain scenarios with appropriate symmetries, asymptotic conditions etc.

(is there an expert in this forum who can talk about quasi-local mass and things like that?)

 

[fleem]

Can someone explain the rationale behind gravitons to me?

My background is computational physics, and as such i may be biased towards physics that is actually computable, such as LQG and regge calc. I have some clue what this is all about, but i have some questions:Is there any reason (beyond aestetics which i disagree with anyway) to favor a particle over a geometric explanation? Any sort of empirical matter gravitons may help explain?

We know that energy stored in a gravitational system can be converted to energy stored in other kinds of systems. all those other kinds of systems require that energy be quantized. If energy in a gravitational system were not quantized, then how could it smoothly flow into another type of system which accepted energy in packets? So this is why gravitational energy must be quantized.

How is something like gravitational lensing explained in a flat spacetime with gravitons? Are there force-carrier-to-force-carrier interactions in such a model? I have a hard time imagining how youd explain bending of light with gravitons. It seems likea pressing question to me, but no one else seems to care, as far as i can tell.

SR and GR, space-time, continuums, manifolds, dimensions, and Newtonian mechanics are descriptions of the large-scale behavior of many individual machines (particle interactions). You are right, there is no reasonable merging with the behavior of individual particle interactions for any of those large-scale theories. Scientists continue to erroneously presume theories developed solely to describe the average behavior of many simple machines will also be the founding theories in describing the behavior of each of those machines. There is no reason to believe that.

 

[Eelco]

We know that energy stored in a gravitational system can be converted to energy stored in other kinds of systems. all those other kinds of systems require that energy be quantized. If energy in a gravitational system were not quantized, then how could it smoothly flow into another type of system which accepted energy in packets? So this is why gravitational energy must be quantized.

Yup, that makes sense to me.

Yet in general, I don't think it is a good thing to get too hung up on things like invariants, or even conservation laws. Yeah, they seem to hold. As far as we can tell, which is only to limited resolution.

If your model can explain all observations, it is good to me. To convince me it can, you need to actually compute stuff with it, and compare it side by side with observations. To me, juggeling mathematical theorems is a means to an end, not a goal in itself.

SR and GR, space-time, continuums, manifolds, dimensions, and Newtonian mechanics are descriptions of the large-scale behavior of many individual machines (particle interactions). You are right, there is no reasonable merging with the behavior of individual particle interactions for any of those large-scale theories. Scientists continue to erroneously presume theories developed solely to describe the average behavior of many simple machines will also be the founding theories in describing the behavior of each of those machines. There is no reason to believe that.

Yeah, we completely agree here.