Physical Review Letters has changed their sections around. Previously, quantum information was in the last section “Interdisciplinary Physics: Biological Physics, Quantum Information, etc.” For the more fundamental oriented papers, one would sometimes also submit to “General Physics.” Now quantum information has been moved to the new first section “General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.”
Is this a good thing? Since I am nothing if but a bag of poorly thought out opinions I will spew out some here. (1) It is nice to see that quantum information is consider a part of “General Physics.” “Interdisciplinary physics” seems a way to say, well there were these good physicists, and then they took interest in this other field which has overlap outside of physics, and since we liked these physicists we let them publish here. If I look at this move as acknowledging that quantum information has intrinsic value to physics, then I get goosebumps all over (sadly doubling the amount of stimulation I’ve had all day.) (2) The old “General Physics” section was notoriously harder to get papers accepted into if they had a quantum information tilt. Generally (err) this was because the papers submitted there were of a more foundational nature, and well, let’s not even go there. Will the movement of quantum information to general physics make it easier for foundational people to get published?
Stop! Right There at the Beginning!
There is no concept more evil, more corrupting than that of the continuum. Why at the very bottom of physics do we bury the most unprovable of assertions. All science is counting. No science counts for ever. Real numbers can never be more than conjecture.
But of course, you answer: it works so well! The conjecture has withstood ages, from Newton to Einstein to (fill in modern genius here.) Sure we can never prove the conjecture, but if it continues to serve us in building models of the world why should we get rid of it. Why, for that matter, should the dictates of science lead to dictates about physical reality?
The only crack we see in the idea of the continuum comes from quantum theory. Here, if the circumstances are right, we get discrete answers for different configurations. So, as many have suggested, when we try to construct a quantum theory of spacetime, perhaps there will be a discretization.
But even hear we come of short of ridding physics from the unprovable assertion. Even here we find, when we use the rules of quantum theory, that all probabilities are allowable. Again real numbers find themselves at the center of the theory.
Remarkably, there are ways in which one can get rid of both of these continuums (at least in a limited sense.) These are Roger Penrose’s spin networks. For sufficiently complicated spin networks, the networks posses two properties: they approximate directions and the approximate quantum probabilities. Combinatorial rules give rise to quantum probabilites and the full real span of probabilities is not postulated a priori. Combintaroial rules give rise to quantum probabilities which describe an object with with discrete degrees of freedom which approximate direction in three dimensional space. Funny but that they remain no more than a curiousity, or a way to find orthogonal sets of states in loop quantum gravity.
Real numbers. Bah. I’d rather believe in fairies. Us of the digital era, we are such pains in the rear.
The Superphysicist Myth
Physicist like to boast that a main benefit of their curriculum is that it teaches “problem solving skills” and that this means that a physicist can jump into just about any field and quickly get up to speed, cut to the heart of the problem, and then solve the problem. So why do so many theoretical physicists become so specialized?
Moore's Law
Our universe is expanding. Not only that, but this expansion is probably accelerating. Now two authors, Lawrence Krauss and Glenn Starkman, have proposed that a consequence of this acceleration is that in such a universe only a finite amount of information processing can be performed: astro-ph 0404510. This means, according to the authors, that the total amount of information process can be at most 10^(120) bits. A consequence of this is that Moore’s law can last for at most 600 years in any civilization!
Data and Program
A most powerful idea in computation is that the program and the data can be one and the same. (That this distinction is often lost in higher level programming languages is a shame.) Thus a program which is some form of data can manipulate the data which is itself part of the future program. We often like to speculate that the universe may act like some form of a (possibly quantum) computer. What is interesting, then, about this “universe computer” is that it does not appear to be merging program and data in any way. The machine language of the universe does not manipulate its own program. Sure, at some higher level the universe does have the ability to manipulate its own program (for the universe does allow for us to build a computer!), but at its most fundamental level, there is not manipulation of the program. Or at least this is the fashion in which we think about the physics of the universe: there are laws which are the fundamental program and there is data which is the state of the universe. The program then acts to change this state of the universe over and over again, producing the evolution of the universe. But what if this is not the way the universe works? What if there is no distinction between the data and and the program in the universe? There can still be a state, and there can still be evolution of this state, but the laws of this evolution will depend on the past executed program. The laws in there most general form can not only change in time, but they will be a function of the past history (past program) of the universe.
Just as Reimann’s realization that we can define curved spaces without reference to any higher dimensional space into which this space curves, perhaps the lesson of computer science should be that we can think about a computer without a physical device to carry out the computation. We can think of the universe as a von Neumann computer in all its abstract glory of such a machine without actually believing that such a universe computer exists.
OK, I’ve clearly stumbled into crank land with this “creature of eager speculation.” But damn straight I’ve stumbled into crank land.
Silly Questions
The number one most irritating question I was asked during my faculty interviews was “what will you do if quantum computation doesn’t pan out?” At first glance this question seems perfectly valid: a department should concern itself with whether they are hiring someone whose work will quickly become irrelevant. But I’ve got news for you all, quantum computing’s not going away! Why? Well not for the reason the question askers are thinking: what happens if a quantum computer can’t be built? No, quantum information science will stick around because it has an intrinsic intellectual value. And this is what makes the question so irritating: it implies that quantum information science is a fad with no intrinsic intellectual value. Do you ask string theorists whether what they do will be experimentally testable and if not what will they do? Do you ask astrophysicists whether studying cosmology will have any significant impact on society? No. But because these are part of a long tradition of theoretical physics they are acceptable intellectual persuits, whereas quantum information science, being new and getting too much press is most definitely suspect.
There is, of course, great irony in this situation. Theoretical physics has always justified a large portion of it’s work as for the greater intellectual good (holier-than-thou-physics.) But mention the word “quantum” all of a sudden normally elitist physicists turn into engineers. The psychology behind this is pretty simple in my opinion (wait this whole thing is my opinion!): physicists have yet to actually accept quantum theory. They don’t want to think about it because it’s strange. The fact that it’s current position is basically to serve as the operating system of the universe doesn’t help at all. Because we can separate the axioms of quantum theory nicely from the physics of the fundamental forces most physicists can spend their entire life living, breathing, and calculating classically. Rather embarrasing for a group which seeks to understand the fundamentals of our universe.
Pondering physics as an art business
If physics is an artform, then what would be in a physicist’s studio? How can we sell physics like artists sell their works of art? What is the business of physics as art. Most of a theorist’s art is knowledge. Maybe physics is more like poetry. So does that mean we have to write books? Is that our art?
Two Papers
Sometimes you slog through tons of papers and wonder how much the whole huge mess really matters. But then there are days like today where I found two papers which I think completely and totally rock. Maybe they don’t really matter, but they are really interesting. The first paper appear on the arXiv today, so I really didn’t have to dig for it, but the other paper I just stumbled upon and somehow missed it when it came out in 2002.
Paper 1: quant-ph/0401137
“Fast simulation of a quantum phase transition in an ion-trap realisable unitary map” by J.P. Barjaktarevic, G.J. Milburn, Ross H. McKenzie. The idea in this paper is very beatiful. Consider a system with a Hamiltonian which posses a quantum phase transition. On a quantum computer it is possible to simulate the dynamics of this Hamiltonian. Suppose that your Hamiltonian is a sum of two noncomuting terms H_1 and H_2 and that you can easily implement evolution according to each of these terms separately, i.e. you can do exp(iH_1t) and exp(iH_2t). One way to then simulate the full Hamiltonian is to “trotterize” the evolution and perform alternating infinitesimal exp(iH_1 dt) exp(iH_2dt) exp(iH_1 dt) exp(iH_2 dt)… =exp(i(H_1+H_2)t)+small error. But suppose that you don’t do this (because, for example you can’t really do good infinitesimal evolutions in the real world!) So instead you use “big” steps exp(iH_1T)exp(iH_2T)… Now you can ask, does this system have a quantum phase tranisition! So in what sense does the “big” evolution model have the same properties as the “infinitesimal” evolution mode? In this paper the authors address this issue for the ising model with a transverse field. And indeed, the authors present strong evidence that there is a quantum phase transition in the behavior of this “big” model! A summer student and I worked a bit on this problem for a different decomposition of the same Hamiltonian. As a nice summer project the summer student, Jaime Valle, wrote code to simulate this evolution. In this model we indeed did see evidence of the phase transition. And now we see that for the decomposition choosen by these authors there is direct analytic evidence of the quantum phase transition!
The second paper that I discovered which I loved was quant-ph/0206016, “The Dirac Equation in Classical Statistical Mechanics” by G.N. Ord. Now this paper, and a series of other papers by this author and coworkers, rocks! What they show is that there is a microscopic statistical mechanical model for the Dirac equation in one dimension! There is a famous prescription for obtainin the Dirac equation in one dimension which is due to Feynman. Basically this prescription works as follows. Consider a particle which moves either forwards or backwards at the speed of light. If you want to calculate the amplitude for the particle to go from spacetime point A to spacetime point B, you simply take all paths for such a particle and associate with it an amplitude which is (im)^(# corners) where m is an infinitesimal parameter, i is the square root of minus 1 and the # corners it the number of times the particle switches directions in the path. If you use this to calculate the amplitudes for all of the paths between A and B and add up all of these amplitudes, you get the kernel for the Dirac equation in one dimension!
What Ord talks about is similar to Feynman’s prescription but what Ord shows how it is possible to construct a model where the statistics of the dirac equation fully explained by a microscopic classical model. One of his version of this model has some very nice properties, like being a beautiful nonlocal hidden variable model of the Dirac equation (it is interested that even for one particle, one gets a nonlocal hidden variable model)
Some Wine
Sputnik = 1957, but the boom in Physics PhDs peaked in 1970, with a second peak in the mid 90s (from the aps):
So those 1970 PhDs are now in their late 50s. And, of course, everyone knows that physicists always do their best work when they are much younger. So, logically, these 1970 PhDs should retire. Right? Right?
Clockwork Universe
To the question “Is the universe a computer?” many today might answer “Yes…a quantum computer!” The first comment I want to make about this is that this is a kind of funny answer. The reason this answer is funny is that when we refer to a quantum computer we are usually refering to a machine with a finite language. So what many people mean by this is that one could set up a quantum computer which runs a program which simulates the physics of our universe. Of course there are all sorts of issues with the fact that this will be some sort of approximation of the universe. Another interesting fact is that what we probably mean by the universe is a quantum computer is we are thinking about a grid of quantum computers each executing local evolutions which give us the full evolution of the universe. So we might be better of saying the universe is well approximated by a bunch of quantum computers.
In comparison to the question “Is the universe a computer?” if we ask people “Is the universe a classical computer?”, we will universally get the response that the universe is not a classical computer. The first reason for thinking that the universe is not a classical computer is that we think that quantum computers are more powerful than classical computers. Thus we might think that if the universe is a classical computer, then it is very inefficient. Well you might not care that it is inefficient! Well, OK, but what about the nonlocality in quantum mechanics. Bell’s theorem tells us that in a real way, the universe is not a bunch of local computers which only talk to their neighbors. Quantum nonlocality challenges the notion of local realistic descriptions of nature.
What has begun to intrigue me lately is the question of whether the issue of programming languages has much to say about the question of whether the universe is a classical computer. To explain this I’d like to explain a bit about the difference between an imperitive programming language and a declaritive programming language. Imperitive programming languages are the ones most of us are used to (like C++, assembly language, etc.) In imperitive languages, one provides a list of instructions to execute in a particular order. The computer has a state which is updated according to the next instruction to be updated. Declaritive languages are used less frequently. The prototypical example of such a language is Prolog. In declarative languages one gives the computer a set of conditions (relationships between variables) and the computer then applies a fixed algorithm to these relations to produce a result.
So the question I want to ask is whether thinking about the universe as a classical computer with an imperitive versus a declaritive language helps clear up this whole bloody issue of quantum nonlocality? The basic idea for why this might help is that the declaritive languages are much more like path integrals in quantum theory. What I’m imagining is not local computers executing declaritive languages, but that the universe a computer which can execute a nonlocal declaritive language. In many ways this reminds me of those who delude themselve into believe quantum logic is the solution to all interpretive problems in quantum theory, but maybe casting the question in terms of the programming language helps overcome some of these interpretive questions.