BenTheMan

ashes---was this explanation good enough or do you want me to clarify anything?

I wasn't aware that there was a theory of consciousness, or that it was considered science.

Come on man give me some credit! Sure the spectrum can be in principle infinite (or semi-infinite), but the dimensionful parameter is the Planck Volume---like hbar in quantum mechanics. This means the lowest lying states in the Hilbert space are of order the Planck volume, up to possibly some numerical factors. The faulty logic of...dimensionful analysis? In the past few posts, I haven't really made any arguments for or against any other approaches to gravity---I've only asked questions based on dimensionful parameters. The point is that your volume operator gives back discrete values, as you have admited. This means that in your path integrals, you have a hard, Lorentz Violating cutoff at the Planck length (whether you like it or not) because the phase space doesn't exist above the Planck scale---they don't live in your Hilbert Space. In this sense you are trying to solve gravity by discretizing the path integral, an approach that doesn't always work. You can see this if you try to regularize QED with a hard UV cutoff---it doesn't really work. This was Nima's argument, as I understood it. Martin---I don't care about the competition. They are not competing for the jobs that I want, I promise you. If I never learn another thing about Loop Quantum Gravity, I will be able to sleep at night. I posted this argument of Nima's to start a discussion, and I was under the illusion that there were people here who could discuss these things with me. If this is not the case, then perhaps I am in the wrong place. This place seems to have more than a few people who think string theory is wrong, whether they want to admit it or not (cf---The Trouble with Physics is STILL the book of the month, even though it looks like the discussion thread has been locked and no one actually read the book to start with), despite the fact that there doesn't really appear to be any discussion on the topic. What I really want is to have (semi-)technical answers to questions, so that I can learn (or at least get a flavor for) the physics. I don't have the money or the time to go attending Loops conferences (I don't even plan to attend the Strings conference, unless they invite me or it's within driving distance). I don't really care to be told how miguided I am, or how short-sighted I am, or how I really need to read more papers or attend more conferences.

Ok, perhaps we are talking past each other a bit. The point I wanted to make was that one expects the eigenvalues of the volume operator to be on the order of the Planck scale, just by dimensional analysis. Maybe there are some factors of pi or root two or something floating around, but at the end of the day the Planck length should dictate the size of these eigenvalues. I'm game as long as you are I'm always game to talk about physics. Before we move on---I think we've agreed that the volume operator should give eigenvalues that are Planck Length cubed, wether or not we can actually calculate the exact values...yes or no?

Clearly this is what I meant. The potentials are both inversely proportional to distance. The forces are incerse squared. I still don't understand what pioneer is confused about. Gravity can be thought of electromagnetism with ``mass'' as the charge. All of the calculations are the same, except you use different numbers.

But if you dropped something from an infinite height, it would take an infinite amount of time to get to the horizon, right?

Ummm kinetic energy? [math]T=\frac{1}{2}mv^2[/math]. Gravity is really no different at long scales than electromagnetism, other than the numbers are different.

It probably isn't unreasonable to assume that the volume eigenvalues are in units of the Planck Length? Just by naive dimensional analysis---there aren't any other scales in the problem, are there? I disagree. You always know the scales in the problem, so at the very least you can ballpark it. Just like the QED thread in another sub-forum---the guy wanted to know how QED treated the diffraction of light. The answer is that it doesn't---the scale of QED (i.e. the only dimensionful parameter in the theory) is the electron's mass (which is about a fifth of the Bohr radius), so QED effects become important at the Compton wavelength of the electron, which is MUCH smaller than any diffraction grating you'll ever be able to build. I may be missing something, and please point me to a counter-example if I am wrong. But in gravity the only dimensionful parameters we have are the Planck parameters---this means that the relevant time, distance, energy, and length scales are all in Planck units. This means that all of your operators have to give you eigenvalues in those units, UNLESS you introduce another scale or parameter into the problem. In string theory, there is the string coupling. Come on Martin---the scale is important. Sure you could shove me and give me Planck energy, but I'm also made of 10^25 ish particles. A counter example---each proton in the LHC beam has an energy of 14 TeV or so. Individually, that's about the equivalent of a paperclip. But all of the protons put together have as much kinetic energy as a fully loaded air craft carrier moving at 40 knots. I don't buy it. This is like saying that one can measure energies smaller than hbar. Isn't there some analogue of the uncertainty principle at work here? And besides, you seem to be ignoring the scale of the problem again. Absolutely:) Plus, it's a tremendous rush to imagine calculating something that someone will actually MEASURE some day.

Ahh farsight---there you go again...misunderstanding physics and breaking Lorentz Invariance. This is only relative to an observer at infinity. I had a discussion about this with some graduate students last week when I was at Princeton. The time dilation is infinite only when compared to a frame that is infinitely far away. Otherwise the time dilation is large but non-infinite. This means that a nearby observer (i.e. Chandra) can see a black hole form, but asymptotic observes never see such events. (This is at the heart of Hawking's new ideas about information loss---locally it is a fact, but asymptotically observers never see a black hole form, so there can be no information loss.) Patently false for a plethora of reasons. just look at the potential. At least classically, one expects potentials to be smooth functions, which contrasts what you say. Sure, this is old news---quantum gravity effects take over at the planck scale. But classically, it's quite clear that there is a singularity. And if you're not willing to accept string theory or loop quantum gravity, then you'd better have something good to motivate this statement. This pretty much sums up Farsight's work.

I think also somewhere I saw a proof that any worm-holes had to be behind horizons. (I could be mistaken, though.) But if this IS the case, you could go into a worm hole, but you could never get out.

noob--- Are you talking about the Schroedinger equation or the wave equation? Because the Schroedinger equation isn't a wave equation, it's a dispersion (i.e. heat) equation. This is kind of trivializing some pretty brilliant work. I think it was a gradual realization, as opposed to ``fiddling around with numbers untill it worked''. Presumably you mean ``What IS the Schroedinger equation?'' The Schroedinger equation describes the time evolution of a probability density. When you know the initial conditions of the system, you know the probabilities at all future times that the system will be in a given state.

So you can't measure kinetic energy? Doesn't your car have a spedometer?

Well the asymptotic states in QED are plane waves, so it explains refraction in the same way that electromagnetism does. The scale of the problem is ALWAYS important. So here goes---a lesson in the power of dimensional analysis. If you KNOW the QED lagrangian, let me ask you---how many dimensionful parameters does it have? Just one---the mass of the electron. So where do you expect the theory to be important? Well, mass is the same as inverse length (using God's units), so the length that you expect to see QED effects become important is 1/m, or about 10^-12 meters. So you would only expect QED to be important on those length scales. AND, seeing as how 10^-12 meters is about a tenth the Bohr radius, you're not likely to ever build a diffraction grating this small. For all other lengths, QED effects aren't important. ashes---if you're interested in physics, it is very important to know how to use these naive dimensional analysis arguments. They seem stupid, I know, but they are right almost all of the time---at the very least, they can give you bounds on things that you wouldn't have otherwise been able to calculate! Also, you should learn your orders of magnitude too http://www.matpack.de/Info/Tables/meter.html You would be surprised at how much physics is actually done this way.

You're thinking classically. The electrons live in clouds, not orbitals. They are also negatively charged, so they repell each other. If you're familiar with classical mechanics, this is what causes the normal force usually---the electrostatic repulsion between, say, your ass molecules and the chair molecules prevents you from falling to the floor, where the repulsion between your ass molecules and the molecules that make the Earth keep you from falling to the center of the Earth, where gravity wants to pull you. You could do the calculation, you know Here's the formula. Put in the mass of the atom and find out what the Schwarzschild radius is. Then look up the average radius of the atom and see if it's bigger or smaller. Be sure to convert everything to kilograms and meters, and let me know what you find. http://en.wikipedia.org/wiki/Schwarzschild_metric Sometimes---they are produced in beta decay. They only live untill they find an electron.

The point was that people have been getting very realistic phenomenology from string theory since the mid eighties, when the heterotic string was discovered. As far as I know, these ``sanity checks'' aren't as easy in LQG, but I could be mistaken about this. (And, to be fair, I never claimed that string theory gave testable predictions.) I'm not sure what you're talking about here---let me look at the copy of Martin's paper I have in my office.

Inasmuch as I understand GR, I think you are mistaken. There are gravity wave solutions of Einstein's equations, independant of curvature solutions. What you are describing is gravity waves, which is something very different from, say, curvature caused by a very massive body. We fully expect to see gravity waves coming from quasars and such, and we expect them to have all of the same properties of electromagnetic waves, in terms of interference patterns and such. The current round of experiments don't directly see gravity waves (google search LIGO), though the next generation space experiments (goggle ``LISA'') should have no problems. Note that we've also seen indirect evidence of gravity waves from looking at binary pulsars---work which received a Nobel Prize: http://nobelprize.org/nobel_prizes/physics/laureates/1993/illpres/discovery.html. Further, the waves (again, inasmuch as I understand GR) don't cause attraction. The bug analogy you made is good for demonstrating this---the bugs are not drawn towards the basketball in the center of the pond, they only move up a little, then down a little. Gravity waves have pretty much the same effect: Again, read the LISA or LIGO stuff on the web, and this picture may make more sense. Either way, there is no need to ``add'' anything to GR to get this behavior out.

When I have a free hour that I wish to fill with new physics, then I will listen to his talk. And one day when I no longer have several projects to work on I will try to actually read some LQG papers. Untill then, I would like to ask questions to people who know more about the field than I do, when I have ten or fifteen spare minutes to read answers and construct responses. I was under the impression that that was what this thread was.

Martin--- Don't mistake this for an attack on non-string QG---firstly, I want to provide a counterargument in as many places as possible to people who claim that string theory is wrong, with little or no knowledge of the subject. Like it or not, Lee Smolin cast non-string QG as an underdog in his book, the media siezed on this, and now there are people all over these discussion boards parroting the arguments that they read but don't understand. Internet discussion fora are full of people who are willing to eat whatever the media feeds them, instead of trying to understand the whys of the thing. The irony, of course, is that I have done the same thing in another thread, which leads me to the second reason for trying to discuss this---I don't really understand the edifice that is non-string QG. Well, sure---on large scales. What if we find a large extra dimension at LHC---will that alter any of the QG conclusions? Or can you fiddle around with equations to get any number of space-time dimensions. Has anyone ever tried picking a differnet dimension (like 10 or 11 or 350) to see what happens? So, in one approach---this doesn't seem like a robust feature of quantum gravity. But I do agree that the number of dimensions should be a prediction of any approach to QG. (This is one of the best arguments, in my opinion, for strings---this and the natural appearance of space-time symmetries and chiral fermions. These things almost come for free.) I would have to say that it also never did anyone any good to nourish the illusion that there are real competitors when there aren't any. Can Loop Quantum Gravity give the standard model? Three generations? A heavy top? No experimental signatures that should have already been seen by now? Gauge coupling unification? There are several string models which satisfy these constraints, and there have been since the early days of string model building (c. 1987), WAY before Witten's 1995 paper. Your reply will doubtless be something like ``We just haven't studied it enough, but look at these papers''. Also, these successes came relatively quickly after string theory's birth in 1985. Perhaps this is a social thing though---most string theorists worked on particle physics before they took up strings, and most non-stringy QG people seem to be gravity guys. From what it sounds like, though, the field is very dispersed. Perhaps this is analagous to the pre-duality situation in string theory, where there were five consistent string theories? Right---I realized my mistake after I read this... Gauge invariance in GR is diffeomorphism invariance, which is COORDINATE invariance, not background independance. The metrics are the fields in the Einstein-Hilbert action, which is where I screwed up.

It's really not debatable. The fact that there are people (like me) getting very realistic low energy phenomenology out of string theory (three generations, heavy top, realistic higgs sector...) says quite a bit. This is actually something I've in mind to look at. The usual calculations of these threshold effects only give small contributions to the runnings below the threshold. The consensus is that corrections of about 1% are expected---this is why unification in the standard model was so hard to get. ====\begin{edit} http://arxiv.org/PS_cache/hep-ph/pdf/0411/0411057v1.pdf I just looked at a Graham Ross paper, perhaps not the one that you were talking about, where he concludes that the threshold corrections improve unification, when starting with the weakly coupled heterotic string. But the consensus among traditional GUT physicsts (i.e. my advisor) is that the threshold corrections won't screw up unification. ====\end{edit} This is also interesting, and another thing I'd like to look at. Maybe I should stop talking to you before I give away all of my research ideas:)

I'm not sure if I understand the question properly. Electrons, for example, do not experience the strong force. So, suppose you send an electron through an electric field---the electron carries electric charge, so in a sense it ``feels'' the electric field. Now send an electron through a strong force field (i.e., a field of the strong force). The electron doesn't ``feel'' the strong force because it doesn't carry strong charge. Is this answering your question at all?

I think you are reading too much into this. A good percentage of the string graduate students I have met don't really care about the ultimate fate of the string theory edifice---they think it is interesting enough to write a PhD on it. It is quite clear to everybody that I have talked to, though, that there are no real competitors, at least at this point in the game of quantizing gravity. IS the number of dimensions derived from first principles, or put in by hand? Also, it's not clear to me how important background independance actually is. The example I can think of is that we generally have to introduce gauge invariance to do calculations in quantum field theory. But in order to get sensible results out, we have to pick a gauge, because our hilbert space gets messed up with things like states of negative norm. So we introduce gauge invariance, and then gauge fix the theory, which makes it no longer gauge invariant. Just like in GR---the gauge invariance in GR translates as diffeomorphism invariance. In order to get numbers out of GR, one has to pick a metric (i.e. Schwarzchild metric), which makes the theory no longer background independant. So why is background dependance so important? You have to pick a gauge to do calculations anyway, right?

Martin--- Thanks for the history of the LQG revolutions, but I really want to know the physics of what is happening here. So, you're telling me that dimensional analysis fails in quantum gravity? So the Smolin quote is wrong, where he explicitly says that the spectra of the two operators is discrete, and that it can be seen as a prediction of the theory? Sorry if these questions are circular, but I'm just looking for some simple answers about quantum gravity outside of strings. I understand some of the rudiments of string theory (think: volume one of Polchinski modulo chapter 2, which I am assured that nobody understands), but don't really understand anything about other approaches to QG. Don't be affraid to get technical---I probably won't be convinced otherwise.

A few things tim--- First of all, I take exception to you stating that strings was a mistake (if you will) in physics. The story is far from complete, and I don't really think you are in a position to make such judgements. I always get pissed when people bash string theory just because they read Peter Woit's or Lee Smolin's book, or for some other unknown reason. The fact is that string theory is the most studied way to understand what happens to gravity at high energies---successes have been made in strings that other approaches to the question cannot claim. Secondly, in regards to unification it is well known that the strengths (except for gravity) of the foces change with energy. So, depending on the energy at which you do your scattering experiments, the relative strengths of the forces that you'll measure are different. From all of the data we've gathered, the forces are all very close together at high energies---if you include something like supersymmetry, the unification is precise to within 1% or so. So you have to ask yourself---if the unification works so well, can it be a coincidence? Or, stated another way, suppose you draw three lines on a piece of paper. Is there any reason that those three lines should meet at exactly one point? This doesn't explain why gravity would be so much weaker than the other forces. For example, gravity is pulling you towards the center of the earth, right? Well, why don't you fall into the Hell? The reason is that there is another force that is much stronger than gravity---namely electromagnetism. Electromagnetic repulsion, which is 10^30 or so times stronger than gravity saves you.

Well, for example, if length is quantized, and energy is 1/L, the energy should also be quantized. Right?