It is completely valid. It's just that in large objects, there is often a kind of "averaging" effect taking place that results in the (much more complicated) QM solution giving more or less the same thing as good old classical mechanics. So you could in principle just use quantum mechanics to...
You don't need the Taylor expansion part. You get the masses by looking at the mass terms, ie the ones quadratic in fields. Where did you see that you have to do the Taylor expansion? Perhaps they didn't mean Taylor expansion but rather what you did with the χ field. After all doing a Taylor...
There is no proper framework of quantum mechanics that includes GR. Quantum mechanics is a theory that does not include gravity, except you can try to combine their predictions together. But at any rate it is pointless because the part of your physical argument that is supposed to show how you...
Yes, but the way you determine those "physical grounds" makes no reference to GR, so you can't be using that as an argument to "prove" that yours are valid.
You said that the energy has to be "higher than the classical case" (which doesn't uniquely determine it anyways) because you can't have...
Yes, but you have not given an argument that includes gravity. And as far as I can tell nobody has measured the gravitational field of the ground state of a quantum harmonic oscillator.
But we are talking about the physics predicted by the quantum theory, regardless of general relativity...
Not true, my Hamiltonian has exactly the same physics as your Hamiltonian within the quantum theory, as you can readily check.
Even if we accept this as a physical argument, "higher" just means "higher". How much higher? If you just want it to be higher, why do you not like the anti-Wick...
These things are not incompatible. I have a point of view so far that at this point is very fluid and I am not very confident in it and I am investigating what others have to say about it which goes through asking questions where I would have to advocate for my point of view to see what the...
Maybe, but it does not give a ground state energy that matches the classical case. Also adding a constant to classical potentials is very common, it's what you are doing every time you are setting a specific potential to 0 when solving circuits or chosing a ground potential for problems with a...
I know... We've been talking about that...
I think we are saying kind of the same thing basically. If I understand correctly you are saying the problem is more a fine tuning problem than an inconsistency between predictions. I will have to look into the estimation that was carried out and...
Right, that was my point, I was replying to @Vanadium 50 , they brought it up since they believed we should look at this first and decide whether or not it is physical before looking at the whole universe.
By the way, you varied the energy by adding a constant to the classical Hamiltonian, but...
There is no reason in the classical case why the potential has to be 0 in equilibrium, it is 100% equivalent, and often used in physical problems. There is no reason in the classical theory to prefer one over the other. And even when you do assume that in the classical case, as I showed...
Ah I see. So, if I've got this right, the argument is that the quantum theory doesn't have a unique "recipe" for calculating the stress energy tensor. About the symmetry principle, what exactly do you mean?
I have responded many times but you keep misinterpreting what I said.
Cool, let's go with that, now what is the potential energy and why are you so convinced it is what you are saying it is and not some other, theoretically equivalent version where a constant has been added to it? Why is your...
Or the potential energy could be the same as your potential energy plus whatever constant you want since it doesn't matter, and you haven't given a good theoretical reason why one is better than the other. As I showed even just quantizing the very same Hamiltonian in a slightly different and...
Yes but the point is that if you want to do that, you have to come up with an "official" level, and the entire point is that this choice is arbitrary. There is no theoretical reason why one or the other Hamiltonian is "better" within the confines of the quantum or the classical theory.
Hmm ok, this definitely goes a bit further as far as I can tell to justify the whole idea. But I want to understand here what exactly goes into figuring out that stress energy tensor via the quantum theory.
Hey, if you know an example where it can NOT be eliminated for some reason, I'd love to see it, it's kind of the point of my thread. But the SHO is not such an example for sure.
Yes, but it shows that there is no one "perfect" quantization scheme which would imply it should be preferred. In terms quadratic in x and p, you still have different available schemes, pseudo differential quantization, symmetrized pseudo differential, Wick, anti-Wick, or others for instance the...
Exactly, however I am thinking that maybe we shouldn't even be saying that one is correct and the other isn't, because even when you get back to classical mechanics, adding a constant to the Hamiltonian makes no difference physically.
Not really, because you can add whatever overall constant to the Hamiltonian and the physics does not change. The equations of motion do not care about constants.
Except for when it isn't because it causes problems, for instance in many cases in statistical mechanics, or the quantization of the...
Exactly, I do not want it to be x^2+p^2 in the quantum case. That's my point. That by merely quantizing the classical equation in a different manner (I found out that it actually has a name and it is called Wick and anti-Wick quantization), you get a different quantum Hamiltonian that gets rid...
The point is that @Vanadium 50 said that the matter of the simple harmonic oscillator and its zero point energy should be settled first before tackling something more grandiose, like the entire universe. My conclusion so far in absence of further evidence is that in the case of the oscillator it...
I am correcting my previous post, since I made a small error regarding the definitions of the operators. The ladder operators are (x+ip) and (x-ip). My point still stands as long as we look at the Hamiltonian:
$$ H = (x-ip)(x+ip)/2 $$
...And carry out the same procedure. The end result is indeed...
Check your calculation again, the ladder operators are p-ix and p+ix, both divided by the square root of 2. The number operator N is their product. It is exactly because they don't commute that this result is different from the same result with just p^2 and x^2.
To be more clear:
$$ H =...
There are a lot of papers claiming zero point energy is not required to explain that. I actually found tons of discussion in this forum on the subject, just search for Casimir effect physicsforums and you will see. About Lamb shift etc I don't know much.
To expand on what I was trying to say before about the harmonic oscillator, let's try to quantize the simple harmonic oscillator. The classical hamiltonian is (setting all constants to 1) ##H=p^2/2+x^2/2##. If you try to quantize it now by replacing p and x with the associated quantum...
I'm not at home so I can't check it right now but I remember doing the quantization of the free electromagnetic field via assigning operators to momenta and positions in the classical theory in a slightly different way such that the weird infinite zero point energy of the field disappears. I...
That is what I mean. If the energy of the quantum vacuum or zero point energy or fluctuations or whatever is considered to not be physical, why do people try to make this calculation? Unless it is physical which doesn't seem to be at all universally accepted.
Well, I guess maybe but it seems like there is a lot of emphasis put on that still, and many people still seem to believe they are somehow connected... The Wikipedia article I quoted has some references which seem to imply there is still research claiming that, case in point the paper I...
But then the problem is that we don't know what it is caused by, not the fact that it does not agree with the calculation of vacuum energy, right? I don't see why that calculation is relevant to the problem if we do not expect vacuum energy to be physical and thus have anything to do with the...
Reading the Wikipedia page on it, one reads:
But on the other hand, as far as I know and if I'm not mistaken, zero point energy is not a physical thing, and it is merely a mathematical artifact in QFT. Someone correct me if I'm wrong on that. So if that is the case, then why is it a "problem"...
The question is not about any specific thing. It is about a wide range of similar problems. I could figure out the 5x5 case almost by brute force, however I am more interested in what happens in the general case, or in a 3d case, etc. But yes, you got the conditions right.
Optimally I'd like to...
I was reading about numerical methods in statistical physics, and some examples got me thinking about what seems to be combinatorics, an area of math I hardly understand at all beyond the very basics. In particular, I was thinking about how one would go about directly summing the partition...
For the people talking about bad stat mech books, there is a good couple of stat mech books, Mehran Kardar's books in particular which are accompanied by a free online set of lectures. However they are pretty damn hard. I think Greiner's book is probably alright too but I haven't looked at it in...
I actually don't think these kinds of books are very useful as a first step for similar reasons as BWV described. Economics isn't really a science, so these sorts of books are going to teach you the theory some school of economics has produced but it isn't properly understood unless you look at...
However, asymptomatic patients (in particular never-symptomatic, as opposed to pre-symptomatic) are generally thought to be less infectious than symptomatic people.
I don't know who's biased and who's not, I didn't look that deep into it... The main thing was few reviews and ratings. It was few enough that it's probably just a fluke that they were bad but usually I don't look at books which haven't received many ratings unless someone specifically...
I was put off because that book has few and seemingly pretty bad reviews. Seems to be a theme with books on optics for some reason. Does everyone just use the same horrible Hecht book?