Dear Niels,

If my understanding is correct, may be the D0-branes are the point particles of Quantum Theory that you are asking about.

Regards,

Rajat

Dear Rajat,

Thank you for your reply. If D0-branes are point particles then what are all the higher dimensional branes? The idea of the Standard Model (SM) is that is gives us the basic building blocks out of which everything is built right? If we then say that everything in SM corresponds to D0-branes then do the other branes not imply additional building blocks?

Regards,

Niels

Thanks for your answer Mohamed. I do not see how your answer is related to the question however.

No-a point particle, with finite mass would be a black hole-more precisely it would be a naked singularity.(Incidentally, while there doesn't, yet, exist a well-defined theory of quantum gravity, the term *means* that quantum effects and gravitational effects are both relevant.) This illustrates that, when gravitational effects become relevant, the notion of a massive point particle, that isn't a test particle, leads to inconsistencies-at, both classical and quantum levels of description. How these can be resolved isn't, yet, known. D0-branes don't make sense by themselves-they are the endpoints of strings and are, also, related to other branes in string theory. However their quantitative description isn't, yet, completely worked out. 

Good question. And at least in one set of quantum gravity theories the answer is they are indeed compatible but in a "dual" sense. In AdS/CFT and BFSS/M-theory examples, which are believed to be fully non-perturbative formulations, there exists a dual local quantum field theory definition i.e. point particles moving on a "holographic screen". However because of holography the projections of these point particles in the target space are non-local i.e. not point like in general. They do become sharply local(point) at some  large value of some discrete parameter, say "N", the rank of the color group on the holographic screen. Hope this helps.

The AdS/CFT correspondence relates the description of quantum effects of particles and fields, with *non-gravitational* interactions on the boundary to the description of *classical* effects of the gravitational interactions of particles and fields in the bulk, in certain classes of gravitational backgrounds. In the dual description, when quantum effects and gravitational effects both become relevant, the appropriate description is in terms of strings and branes, not point particles. However the quantitative description in this case isn't, yet, known in full detail. So, once more, when quantum effects and gravitational effects become relevant, the notion of a point particle isn't appropriate. 

Who knows for sure what it will be the situation in the Quantum Gravity regime? Everything may turn purely classical even ! Just think of asymptotic freedom-- A very strong attractive force at short range becomes ineffective at very short ranges and the quarks behave like free particles!

The concept of a massive point particle leads to inconsistencies already in classical gravity-i.e. beyond the test particle approximation (cf. previous message).  Quantum dynamics of point particles doesn't resolve these issues and can't. So their resolution can only be found in a theory that describes consistently quantum and gravitational effects.  Asymptotic freedom isn't a property of classical, but of quantum fields: in classical field theory the coupling constant doesn't depend on the scale. And while the coupling constant does decrease in value at high energies, the scaling behavior isn't that of classical fields. In fact, it's the *bare* coupling constant that vanishes in the scaling limit for asymptotically free theories: in the scaling limit the physical coupling constant is not zero. Asymptotic freedom means that perturbation theory is  a reliable approximation at high energies, not that the fields are classical. 

Thank you Stam Nicolis for your clear and insightful answers. You seem very knowledgeable about this topic.

One part of the question hasn't been addressed. Are the discrete spectra of the area and volume operators in loop quantum gravity  compatible with point particles? Or, do they imply particles cannot be pointlike?

That certain operators have a discrete spectrum doesn't, by itself, imply anything about whether the dynamical degrees of freedom are point-like or not. For example, in quantum mechanics, the phase space volume is always quantized, but the spectrum of the Hamiltonian of a point particle can be continuous or discrete, depending on the potential and the boundary conditions. So what matters is what precisely is the area or volume these operators measure. 

Dear Stam,

My point was to propose that it may be drastically different in QG regime from what we think it should be on the basis of low-energy theories. A very strong field at small separations vanishing at very small separations is, to say the least a reversal of expected behaviour. It is surprising to say the least. So it may surprise us by becoming classical.

The D0 brane DOF on the surface are for all purposes point particle DOF and that is all there is to it when for an outside observer calculating entropy etc.

Regards,

Rajat

``Quantum gravity'' is different from general relativity. While we don't know what it is in detail, we do know something. We know, in particular, that it can't be described by a ``very strong'' field at ``small'' separations that vanishes at ``very small'' separations, because it is known, from general relativity, that this leads to the formation of black holes. And certain properties of black holes, when quantum effects can be consistently taken into account, are known. (And if black holes *can't* be formed, at all, this is in contradiction to known properties of general relativity.)

(There's no point talking about D0-branes in this context, absent any technical framework. It's just name-dropping.)

A quantum theory of gravity is expected to describe the evolution of black holes, in particular their radiation. This is not possible in classical terms and, indeed, doesn't even make sense in those terms. It isn't, yet, known, how to do this in any known framework, for arbitrarily long times.  How to describe, consistently, the finite entropy of certain classes of black holes is, however, already, known and cannot be described in classical terms either, since, classically, the entropy of any black hole is infinite-and the reason can be understood within general relativity.

You could probably ask whether the concept of point particle (as an absolute idea, not as an approximation) makes sense in any quantum field theory. at all. As you point out, it is even more questionable in quantum gravity. However, the more interesting question in my opinion is whether the concept of a continuous space-time makes sense in a quantum gravity theory, where space-time is becoming dynamical. Then, the concept of almost vanishing separation might not make sense either.

As for D0-branes, the fact that the "coordinates" they define tend to become non-commutative on a non-trivial brane also suggests that these are not classical point-like coordinates. As for loops in loop quantum gravity, they are not representing matter particles, but rather some kinds of "local" measurement of space-time curvature and topology, akin to a gravitational instanton.