Why is this necessary?It makes no sense that a conventional calculation of a transition probability gives you an infinite result. What craziness lead to it, a division by zero?
>>16146996it's just the visual equivalent of a taylor series
>>16146996It's a way for physicists to make a numerical computation while pretending that their solutions are still closed form analytical models (they aren't).
>>16146996The idea is pretty simple, it's just the observation that things which happen on a small scale don't have much effect on things which happen on a very big scale, so you kind of "smooth out" those divergences.
>>16147077I dont follow you but.. why is it needed to smooth out anything? Transition probabilities are calculated by evolving forward some initial state, until it reaches some final state. This is done with an unitary operator that changes a state but not the norm, so states ought to keep their norm at 1.But the calculations give out infinity. This is like rotating a unitary 3D vector by some angle and instead of a change of direction you get a change in length.. to infinityhow?
>>16147050>it's just the visual equivalent of a taylor seriesthats just what a feynman diagram is and they have nothing to do with renormalization
>>16146996There's nothing wrong with it. Surprisingly someone else beat me to the punchline here >>16147077Basically the divergences are coming about because you are taking your field theory to be valid up to arbitrarily small scales, but continuum quantum fields are very ill-behaved objects. You can see this even for free quantum fields which from the path integral point of view involves rough Brownian motion-like field configurations (from the mathematical point of view this is related to all the difficulties in defining the Ito integral in stochastic calculus).But the physics point of view is that we don't know whether the continuum quantum field description is valid up to arbitrary small scales. Perhaps for instance spacetime is discrete at some very small scale (who knows?). If spacetime is discrete, then the integrals of QFT aren't really divergent, they just depend on the size of this smallest length scale. The point of renormalization is everything depends on that smallest length scale, including physical parameters like coupling constants, and when you take that into account, all dependence on the smallest length scale (which we don't really know) cancels.This is all basically the statement that the large scale physics doesn't depend on whatever is going on at the smallest scales, and whatever is going on there is just already taken into account in our parameters.
>>16147152Im talking about mathematics, i dont care if some theory describes reality. When you have a theory that is essentially some hamiltonian that defines evolution, one expects changes in states that are just going from one state in hilbert space to another state.Both states connected with an unitary operator, by definition doesnt change the norm.Yet the mathematical result is infinite. Why is that?
>>16147135>>16147283your operator is only properly defined in the first place when you have nicely defined fields, and you don't have nicely behaved fields below a certain length scale (a cutoff)
>>16147305>when you have nicely defined fields,Explain what you mean by this. Im 90% convinced you dont know what the fuck you are talking about
>>16147283>Im talking about mathematics, i dont care if some theory describes reality.I am too. If you are talking about quantum fields on a discrete spacetime lattice there are no divergences in perturbation theory. This is a completely mathematically well defined theory and everything if finite, but depends on the scale of your lattice. But if you calculate large scale physical things much bigger than the lattice you find that the scale of the lattice doesn't matter at the end of the day. We are pretending that everything is continuous and that the integrals are infinite, but this is just a shorthand and the regularization needs to be there for the theory to make sense.If you are skeptical look at all the discussions about the continuum limit for brownian motion in a course on stochastic pde. From a physicists perspective this is just a free QFT, 'but there are already issues with the continuum limit.>Both states connected with an unitary operator, by definition doesnt change the norm.Yet the mathematical result is infinite. Why is that?There are two issues. The more mundane one that has nothing to do with infinities is simply that the integrals calculated in QFT have to do with perturbation theory, and taking the perturbation series at some finite order spoils unitarity if you are not careful. This is true in ordinary quantum mechanics too and it is easy to work around.The other issue that has to do with renormalization is simply that the results weren't really infinite at all. The are infinite in the shorthand that you ignore the regulator (the lattice scale in my example). If you explicitly include the lattice scale, everything is finite and at the end of the day the lattice scale drops out of your final answer.
>>16147321>Im 90% convinced you dont know what the fuck you are talking aboutI'm the other guy, but he knows what he is talking about, and you are taking a stupid approach to learning something. Lose the Dunning-Kruger syndrome sooner rather than later.
>>16147324>If you are talking about quantum fields on a discrete spacetime latticeIm not. Stop changing the topic>>16147324>There are two issues. The more mundane one that has nothing to do with infinities is simply that the integrals calculated in QFT have to do with perturbation theory, and taking the perturbation series at some finite order spoils unitarity if you are not careful. This is true in ordinary quantum mechanics too and it is easy to work around.Explain what you mean by this. >>16147324>The are infinite in the shorthand that you ignore the regulator (the lattice scale in my example).Renormalization has many such tricks, the issue is that there should be no need for any of that.I get the idea that many infinities could cancel out so you get a finite results. Boo hoo. That doesnt always work. Dont pretend that renormalization is some kind of 0/0 limits problem.Tell you what, your style of writing and explaining things sucks ass. I can only sort of follow you because i have studied renormalization, without understanding much but i sort of follow you. You are vomiting a word salad that is much worse than anything i can read in a textbook. You offer zero insight, your "answers" have nothing to do with any question i have posed here.What do i need you for when i can just open a book? idiot.
>>16147338Ok I'm done with you
>>16147340Suck my dick nigger
>>16147321I’m saying that your issue is that, like the other anon said, your theory isn’t valid down to infinitesimally small scales, but when you’re doing these calculations you’re talking about, you’re implicitly assuming it is when you do these calculations without renormalisation.If you were talking about fluid mechanics instead, then you know that certain quantities don’t make sense if you apply them to very small length scales because you know that the fluid is actually just a larger scale phenomenon and in reality it’s made up of lots of discrete molecules smacking into each other. At the Planck scale we have good reasons to suspect something similar happens with QFT, e.g. maybe spacetime behaves completely differently or something like that. So you need that cutoff in the same way we need the cutoff in fluid mechanics so we don’t start applying fluid calculations on the molecular scale. Most operators aren’t defined for arbitrarily high energies in the same way that e.g. kinematic viscosity isn’t defined for arbitrarily small length scales of a fluid, because eventually the fluid is no longer a reasonable definition.The only way we could possibly do without regularisation is therefore if we had a theory which were somehow valid at all length scales, but this is obviously a dream.>>16147324Actually explains all of this very accurately so I recommend being more patient, or clarifying something specific you want answered so that you get your confusion sorted out.
>>16147993This is non-sense. Define the fluid effect that isn't occurring at a small scale and explain how it can thereby exist at large.
>>16148006You can’t define any of the bulk quantities down to small scales. You can’t apply any of your fluid formulae to the molecular scale because nearly none of the assumptions behind them are still valid. This should be emphasised in every basic QM course too, because that’s exactly what went wrong with classical mechanics. People assumed it held at all length scales, did some calculations with that assumption, and got infinite results. Then we figured out energy was discretised at smaller length scales. So we now think of classical mechanics as only being valid down to some rough level where energies start to become of the order of hbar. The critical point is that these are only apparent infinities that were coming up in the calculations, in other words that they’re only there because we are applying the theory in regimes where the assumptions behind it are not true. No actual infinities are physically there.In the same way, applying QFT without introducing these cutoffs is committing exactly the same error that we did with classical mechanics before we got to quantum mechanics, giving us artificial infinities, and for the exact same reason, that there is a length scale where these assumptions do not make sense anymore. So we do the same thing, and restrict ourselves to talking about where we know the theory does make sense.
And strictly speaking that’s only regularisation, but if you don’t really get why regularisation is absolutely vital then that’s a big part of why renormalisation won’t make any sense to you. Having said that, I would’ve thought the importance of regularisation should be very clear from other physics courses so that should probably be cleared up before you continue with renormalisation.
>>16148021Those bulk forces don't exist if they don't have a mechanism for existence at the small scale.
>>16148032Yes, that’s right. But that does not mean your large scale theory can be applied at the smaller length scales. Otherwise you’re arguing like people did to wind up with the UV catastrophe. This was surely covered before a QFT course.
>>16148105Such a large scale theory doesn't exist if it doesn't have a small scale explanation. There is nothing to explain. It would be just pseud screeching about things they call laws, founded on nothing. The building blocks of the large scale must precisely match the small scale.
>>16147993>your theory isn’t valid down to infinitesimallyThis isnt even defined. What the fuck do you mean by "not valid"? We are talking about symbols on a blackboard. It isnt relevant if the theory describes or not reality, thats not the issue here but that a completely theoretical calculation gives out an absurd result. Absurd not because it calculated a wrong probability, but an infinite one, which cant happen no matter how wrong a model is.
>>16148149>The building blocks of the large scale must precisely match the small scale.what
>>16148149You understand that physics is just an inferential discipline right? It's not the source code to the universe. It is the best approximation that we have right now with the limited knowledge we have right now.
>>16148029I understand the difference between carefully evaluating a limit and literally evaluating a function at infinite. Its calculus 1, i know what a limit is. But that isnt the problem
>>16148203Apparently you don't understand, because that's not regularisation. Why do you on one hand ask someone to explain something, admitting you don't understand it, but then insist you really do know what's going on? You will never learn anything like this.>>16148149As I said, this is exactly the logical mistake that led to UV catastrophe. >>16148159>we are talking about symbols on a blackboardThat doesn't change anything, but if you want to play it like that, we can rephrase it as "the assumptions which set the rules for how these symbols work do not hold at infinitesimally small length scales. Therefore if you insist on using these symbols in cases where those assumptions are not true, you should expect to get wrong answers."Your issue is logically equivalent to arguing that classical mechanics is nonsense because if we apply it to small enough things then we wind up with infinite results as well. Except I doubt you'd say that unless you wanted to look completely ridiculous.So in a similar vein, there's no sense in saying "QFT doesn't make sense because if I apply it to situations where the assumptions that we use to build the model don't hold, I get nonsense answers." If you accept that classical mechanics shouldn't be applied to very tiny things, then you accept the exact same logic that justifies regularisation. From there, you proceed to the rest of renormalisation. But arguing against regularisation at all is just wilful ignorance and contrarianism, because I bet you don't apply the same logic to plainer things like classical mechanics.
>>16148219>but then insist you really do know what's going on?Because you idiot think that spitting out some buzzword is explaining things. Retard poser
>>16148219>That doesn't change anything,This nigger doesnt understand the difference between physical reality and some mathematical model
>>16148228I've used very little technical language with you. You haven't really explained why you think you should be able to apply a QFT to any length scale at all, while we know that doesn't work for other physical theories.Also, if you're asking about renormalisation in the first place, none of this should be complicated to you. You get an answer in plain English, and you say that's not technical enough. You get multiple answers in technical language, and then you complain that you don't understand the words, even when the earlier anon gave you a perfectly good explanation of the issue.You complain you don't even understand "buzzwords" when the only even half-technical language I used were "UV catastrophe" (one of the first things you learn about in QM), "cutoff" (a prerequisite for you even getting to renormalisation in the first place, not to mention common sense if you already covered basic QM), and what else?The issue is pretty clear: You're not even close to having a good enough foundation in physics to cover renormalisation. You haven't addressed anything anyone has said with a remotely coherent reply and everything anyone says to you goes in one ear and out the other.
>>16148242>I've used very little technical language with you.Spitting a buzzword isnt technical language. You are basically saying nothing.
>>16148242>ou haven't really explained why you think you should be able to apply a QFT to any length scale at all,I also have not explained why water is wet. Your comments are absurd and unrelated to anything that is being talked about in this thread.
You don't actually study physics, do you OP?
