
#163
Feb2012, 04:22 AM

Sci Advisor
P: 4,491

Here is my (very very rough) estimate.
Assume that there are 1000 scientists in the world working on string theory. If each costs 100.000 $ per year, this gives 100 millions $ per year. Applying this number to the last 20 years gives 2 billions $. If half of that money is payed by USA, then it is 1 billion $ in last 20 years payed by USA. 



#164
Feb2112, 08:30 PM

Sci Advisor
PF Gold
P: 2,040

Thanks Bill 



#165
Feb2112, 10:31 PM

P: 381





#166
Feb2212, 12:06 AM

P: 381





#167
Feb2212, 10:48 AM

Sci Advisor
P: 1,663

I realize that certain people on this forum have a tendency to get ahead of themselves, but I really don't think its ok to throw technical words together willy nilly if you don't understand what they mean.
The renormalization group is not an 'effective field theory'. It's not really a group at all! Its a set of partial differential equations (technically 'flow' equations) that explains the scaling behaviour of certain quantities in quantum field theory. More to the point.. Before you can understand advanced topics like string theory, quantum gravity, and so forth, it really behooves posters to first learn some modicum of basic physics first! I assure you, none of the advanced material can possibly make sense unless you get the logic, ideas and preferably the mathematics of the introductory material first. 



#168
Feb2212, 11:34 AM

P: 407





#169
Feb2212, 01:17 PM

Astronomy
Sci Advisor
PF Gold
P: 22,792

I think I see what you are driving at (the unaccustomed use of some technical terms doesn't bother me in this case as long as the intuition comes thru.) I think there is a kernel of insight. The RGbased approach (Asym. Safety) might be limited in its ability to resolve certain classical singularities and nevertheless it might be nearly righteffectively right within certain limits. Let's imagine, just for the sake of illustration, that AS works as long as the underlying manifold which it requires is not going to develop singularities or defectsa topological condition. AS requires you to set out some prior metric on the smooth manifold you plan to be working with, for starters, so that scale can be defined in the first place. then it has some key numbers change with scale and run to a happy conclusion. But in its present form AS seems to be having trouble resolving the big bang singularity. We can't use the word "effective" because that word is owned by people who do conventional perturbation theorya type of math where you have a long series of numbers describing a blip on a flat background, and stuff like that. Each number is calculated according to its own elaborate formula and a theory is "effective" if you can just consider the low energy terms and it works OK. We don't want to offend these gentlemen, so we need a new word like, say, "quasiexcellent" to describe what Asymptotic Safety might achieve. It might be effectively successful as a basis for quantizing gravity EXCEPT for not resolving the big bang singularity. Because of the breakdown of conventional topology itself or some damn reason like that, so what's a poor theory supposed to do? if it's defined on a smooth manifold model continuum. It is effectively right except it doesnt quite make it where the basic topological or else smoothness assumption breaks down. So we call it "quasiexcellent" I'm only half serious here, trying to imagine what you are driving at, by attempting a speculative illustration of what might be. So then you say (to generalize a bit) suppose SOME quantum theory of geometry, Loop or some other, turns out to reproduce Gen Rel. Then (I hear you reasoning) since Gen Rel is asymptotically safe, then that QG theory, Loop say, must be asymptotically safe. So it would be not only quasiexcellent, it would also resolve the singularity, so it would be fully excellent. It would complete the picture, geometrywise. And then you'd have to see if you could build satisfactory matterfields on it. It could be very convenient if Loop or some such QG turned out to underly and complete AS, then one could use AS, which is continuumbased and has a conventional manifold, all the way back in time to very near start of expansion and then seamlessly shift theoretical gears and continue on. But that's just speculation. People are only just getting started implementing RGtype stuff in Loop. Maybe some other related QG (like Oriti GFT or Livine's approach) is farther along. I dont have a complete picture, by far. One extremely nice thing is the recent Cai Easson paper indicating that AS could give inflation "for free" just by the running of the couplings and without a madeup "inflaton" field having to be added on and finetuned. This is the nicest thing I've seen this year. Maybe someone will tell me why it doesn't work. To me this makes it seem almost imperative that Loop should embrace and encompass AS, to acquire that yummy feature. Anyway waterfall, I see sense in your post, rebounding off of the Atyy post you copied. IMO there's a valuable kernel of insight. 



#170
Feb2212, 04:47 PM

P: 381

http://www.physicsforums.com/showthr...=579379&page=2 where science advisor atyy (in message #20) replied: "Renormalization has nothing to do with infinities. QED is renormalizable and it has a cutoff  it is not a true theory valide at all energies, it is only an effective theory like gravity, valid below the Planck scale. Once you have a cutoff, there are no infinities. Sometimes you are lucky and you get a theory where you can remove the cutoff, like QCD. But in QED, as far as we know, the cutoff probably cannot be removed." 



#171
Feb2212, 07:23 PM

Sci Advisor
PF Gold
P: 2,040

Anyway I did join this thread later because I only just saw the message asking me to contribute so I want to get a bit of a feel for those issues people are concerned about before saying anything else. Thanks Bill 



#172
Feb2212, 07:35 PM

Sci Advisor
PF Gold
P: 2,040

Also I am very glad to see gravity is mentioned as a quantum theory. Too many people believe gravity has problems with Quantum Theory  that is false  if you impose a cutoff about the plank scale it is a perfectly valid quantum theory  its no different than QED. http://arxiv.org/pdf/grqc/9512024v1.pdf The conventional wisdom is that general relativity and quantum mechanics are presently incompatible. Of the “four fundamental forces” gravity is said to be diﬀerent because a quantum version of the theory does not exist. We feel less satisﬁed with the theory of gravity and exclude it from being recognized as a full member of the Standard Model. Part of the trouble is that we have tried to unnaturally force gravity into the mold of renormalizable ﬁeld theories. In the old way of thinking, only the class of renormalizable ﬁeld theories were considered workable quantum theories. For this reason, general relativity was considered a failure as a quantum ﬁeld theory. However we now think diﬀerently about renormalizability. Socalled nonrenormalizable theories can be renormalized if treated in a general enough framework, and they are not inconsistent with quantum mechanics[1]. In the framework of eﬀective ﬁeld theories[2], the eﬀects of quantum physics can be analyzed and reliable predictions can be made. We will see that in this regard the conventional wisdom about gravity is not correct; quantum predictions can be made. Thanks Bill 



#173
Feb2212, 07:48 PM

P: 381

http://groups.google.com/group/sci.p...known+strings# > But in string theory, spacetime still has curvature. You (Bill) replied: "No it doesn't. It emerges as a limit  but the underlying geometry of spacetime  if it has one  is not known." This statement has perplexed me for 5 years already. I didn't have the chance to ask you there because you no longer participate there. But what do you mean by that. I know that the spin2 field + flat spacetime can be equal to curved spacetime in what atyy mentioned as described by harmonic coordinates. But in convensional string theory, they assume spacetime has curvature and the gravitons just quantized modes of it. So you are assuming the spin2 field + flat spacetime as being more primary? or just alternative way of thinking it. If alternative, then you can't say spacetime has no curvature. Second, you said the underlying geometry of spacetime  if it has one, is not known. I assume you were talking about spacetime inside the planck scale. But isn't it that the spacetime inside the planck scale are those 6 dimensional compactified dimensions? So what do you mean it is unknown? Hope to get these things clear up after 5 long years of thinking it. Thanks. 



#174
Feb2212, 07:59 PM

Sci Advisor
PF Gold
P: 2,040

In string theory its about many more dimensions than we currently perceive  some are suspected to be curled up and the latest thinking seems to be the precise nature of that curling up determines the physics we see ie the standard model. What I probably was referring to is the emergence form that curling up. Yes I was referring to the geometry and physics below the Plank scale is not known  it may not even be based on what we generally think of as geometry. Thanks Bill 



#175
Feb2212, 08:39 PM

P: 381

Also I think it's better to think string theory has spacetime curvature outside the planck scale. The alternative about using spin2 field over flat spacetime is just an alternative. It doesn't have to be a priori.. unless you have reason to think it can be more primary than spacetime curvature? At sci.physics.relativity, you were one of the few authorities, the others are crank up to now which is much worse so PF is the last and only sensible physics site. The following conversation may make you remember. From time to time, I read it again and again to get some perspective and didn't really understand it well. So please clear it up once and for all. In the conversation when someone asked: > You said that GR, with its geometrical interpretation, emerges as a > limit. This means GR with spacetime curvature, emerges as a limit. > But then you replied that "No it doesn't" to the statement "But in > string theory, spacetime still has curvature.". So make up your mind. You replied: "I suggest you think a bit clearer. A membrane as a continuum and treated by the methods of continuum mechanics emerges as a limit from the atomic structure of an actual membrane  yet does not imply it is a continuum at the level of individual atoms. The same with GR. Gravity as spacetime curvature emerges from spin two gravitons when the underlying geometrical background is not known, but usually assumed to be Minkowskian flat, so the methods on QFT theory can be applied." Aren't you mixing two concepts above, one below and above the planck scale? This spin two gravitons thing causing spacetime curvature is outside the planck scale. Or are you saying the gravitons exist inside the planck scale and somehow it can cause spacetime curvature outside? This is also a question to others. Do gravitons exist inside or outside the planck scale? 



#176
Feb2212, 09:57 PM

Sci Advisor
PF Gold
P: 2,040

Thanks Bill 



#177
Feb2212, 10:11 PM

P: 381

1. Are you saying that spin 2 gravitons can produce GR even if the background is not flat? Because Carlip and even Feynman were simply referring to existing flat spacetime with spin 2 gravitons producing spacetime curvature. But you added the planck scale thing or issue. 2. Are you saying unknown physics inside planck scale first produce flat spacetime, then later it goes into spin 2 mode and produce curvature from that flat spacetime to produce gravity? 3. How did the flat spacetime arise from the planck scale? Is this a valid question? 



#178
Feb2312, 03:53 AM

Sci Advisor
PF Gold
P: 2,040

As I said before once you feel comfortable with single variable Calculus  get Boas. If you study a bit each day you will be surprised what you learn over time  an understanding those who just read popular accounts like Hawking can never appreciate. Thanks Bill 



#179
Feb2312, 04:29 AM

P: 407

Why don't you study an easier example, namely classical electromagnetic fields, before trying to understand gravity? Perhaps there it is easier to understand the difference between a classical field configuration, and small oscillations around them, which are called photons when quantized. Then you see that it is a misguided question to ask how a nonperturbative field configuration is made out of "spin 1 photons". At best, it can be viewed as coherent superposition of an infinite number of field quanta, but that viewpoint is not really helpful here. It is by definition not possible that by adding single photons one after the other you can build up a nonperturbative field configuration (with nontrivial, macroscopic curvature = field strength). A photon is a single particle, perturbative concept and this can capture only physics that is close to a given macroscopic background. Sometimes it is possible to resum infinitely many contributions, eg one can show how the classical potential between two charges can be obtained by summing virtual photons. But that won't work for nonperturbative configurations like instantons.
This applies analogously to gravity and gravitons. 



#180
Feb2312, 04:32 AM

P: 381

Speaking of calculus. Reminds me of the virtual particles. You know what. Perturbation theory is not something permanent like the Diract Equation, it's only because we don't know the interacting theory. Therefore remembering that virtual particles corresponds to each term of the power series of the Perturbation Theory and PT is only a temporarity math rule. Then virtual particles don't exist. We don't even need Neumaier arguments that everything is field. So what if there is effects in the casimir plates, etc. They can be explained by others because simply of the fact that virtual particles being a symptoms of perturbation theory being a symptoms of noninteracting theory is just a math artifact. I think you agree with this. 


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