After my colloquium at UC Riverside some weeks back, I was asked an important question I’ve been asked before, and no doubt will be asked again. The same question may have occurred to you given things I’ve written here about the subject of my research concerning applications of string theory (particularly, ideas from quantum gravity) to understanding (relatively) recent experimentally measured phenomena. (The technique of “gauge/gravity dualities”: See also the special Physics Today May issue with articles on all of this. I wrote about that here. It tells you some of what we can and can’t do with the computational technology, and prospects for improvement, etc.)
So the question is “Is it real?”. This is particularly referring to the black hole in the discussion. Recall, one computes properties of new novel liquid phases of matter (that seem to be closely related to what shows up in the lab) by using a toolbox that involves the equations of gravity, in a higher dimensional spacetime, and much of the thermal nature of the system is controlled by a black hole solution of those equations. So people want to know if that black hole is real. A version of the conversation is like this: (Imagine I’ve already introduced the technique, the higher dimensional spacetime, and the black hole…)
Q: Is there a black hole living in the lab somewhere?
A: No, it is in a different place in the extra dimension.
[Wait! Don’t run off, readers. Thinking about an extra dimension is easy. Your coffee cup is on the table, so it shares the same coordinates as the part of the table it is resting on, right? Horizontally, there’s a certain specific amount of left/right-ness and back/forth-ness needed to locate it. But don’t forget that there’s also some up/down-ness (height above the floor) needed too. It is a third dimension that fully locates the cup in its spot on the table. Now raise the cup straight up off the table a little way. It’s not on the table any more. How did you do that? You changed the up/down-ness in such a way that the cup is in a different place. It is off the table because it is in a different place in the extra dimension (height, in this case) that the table top does not care about. Same words (italicized) as for the black hole business up above. It’s no harder than that, conceptually.]
Q: Ah, ok. But do you believe that this higher dimensional spacetime you’re doing the computation in, along with the black hole you put into it to model the phenomena properly, “exist” somewhere? Are they “real”?
A: Ok, interesting question. Here’s an answer…
I got this question in a recent email, and my (slightly edited) reply is below. The short summary is that my answer is two-fold (1) I don’t know what “real” really means, and (2) We should not mix up our computational tools with the thing we are trying to describe (Nature):
[…] You ask if there is anything “real” about the computations or if it is a mathematical technique. I don’t know how to answer that, to be honest. Is QCD [quantum chromodynamics, the theory we use to compute properties of the strong nuclear interactions which quarks, for example, interact with] “real”? Ultimately, I don’t know what real means. You’re wondering about the black hole and the extra dimensions, I imagine. The pragmatic approach is that it does not matter what the nature of the wheels and cogs are going on in the background, as long as they work together to give sensible testable physics. We’ve seen this before. For example QCD has gauge invariance. Is that symmetry “real”. I would say no. Gauge symmetry is a symmetry of the formulation, not of Nature. Everything in the strong interactions is a colour singlet…. In other words, while the theory has red, blue and green quarks on the page, Nature could not care less about red, green and blue quarks, and so forth. Taken literally, there’s an entire internal space that QCD uses in order to work properly, mapped out by the freedom to move around using gauge transformations …. more technically, there’s an SU(3)’s worth of freedom at every point (an eight dimensional space)… But we don’t go around taking that space as seriously existing, although we could do so, along with a long explanation as to why we never see it directly. Same goes, in my opinion, for these gauge/gravity dualities. The gravity theory is a tool for getting the computation done. (There are phenomenological scenarios that use variants of gauge/gravity dualities, branes, and AdS/CFT to discuss extra dimensions and their measurable consequences (examples include ADD and Randall-Sundrum), but it can be thought of as a logically different issue, which I won’t explore further here.)
As for your question about my comment in the colloquium about the non-reality of SU(3) colour (not flavour), see above. This is no more profound than what we already know for electrodynamics. It is a U(1) gauge theory. Formulated in terms of potentials, there’s a freedom to write things in terms of potentials, up to an ambiguity – the gauge transformations. We can use that ambiguity to help our computations, but fundamentally, the physical quantities do not ascribe meaning to the gauge invariance. It simply isn’t there in the physics… it is there in the computational tool – electrodynamics. Same for QCD.
My main point is that it is important at every stage to not mix up our tools with the actual physics, as is so often done.
I hope that helps.
I could go a touch further on the issue of what “real” means if pressed. Let me save that for a possible followup post.