Interesting. But then I wouldn't want to do it cheaply like, just set the $t$ values of 4-vectors to be negative to make up for that and preserve lorentz invariance. That's cheating lol
After all what does lorentz invariance says, that if a massive thingy chases a light beam, no matter who's measuring how close he gets, they all get the same result right
I always get a feeling that a lot of QM was developed still with a vague hope that "okay it's all crazy now, but if we make it just a bit more crazy so that we can calculate better, it'll all become clear physically..."
Kind of like accepting having to pass a dark tunnel to reach the light lol
Yes because it may be true that we will get a better picture just by making our calculations more accurate. On the other hand, at what point do we say that the model has become so mathematical that we have no idea how to even ask about the physics of what it models
Something like the Feynman rules say, I think everyone kind of admits that what's going on physically is not what the diagrams represent. Yet, it's clear that something is going on that these diagrams are modelling, and we don't exactly know what that is
@ACuriousMind What happened is that I didn't know the exact derivation of Coulomb's law using scattering. But I knew that the 2-p function was the Coulomb potential
The calculation involved in Feynman diagrams is something like : G(x, x1) G(x1, x2) G(x2, y). Here, see that x1 and x2 are repeating indices. This means they r integrated over @ACuriousMind
oh, you just mean that when you have to diagrams with external legs and you connect the legs you integrate over the variable associated with the legs in the same way you sum over the indices of two tensors when you contract them
Hello. I need to know how to calculate SPL change from a sound source to the listening position at a distance. Please help me find this out it's so important and urgent! thank you.
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Since many topics of Physics and Biology tend to intersect with Chemistry, is it possible that a question might be called a duplicate for being asked on anot...
finding spl at the listening position, not the source
@amit I already know the sound pressure the speaker is producing, but I wanna see, in the distance the listener has to the speaker, how the spl changes, how would it be at the listening position.
@Amit On the PDF I have, the information consists of a "SPL at the membrane of speaker" and also "Virtual point Distance". Does this mean that the SPL at the membrane is measured at Virtual point distance?
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There are:
Bertrand’s theorem, which says that the isotropic oscillator and Kepler potentials are the only analytic radial ones all of whose nonrectilinear bounded orbits are closed. (Recommendation: Albouy - Lectures on the two-body problem. But he says: “The proof of this theorem provides ver...
So M is the matrix I am trying to determine if can have a degenerate spectrum, and so I am trying to see if there is a way to check this while avoiding explicitly defining the matrix :P
like maybe there is a list of properties like: If your matrix has X characteristic, its spectrum is degenerate
well i think it is easiest to think of the exponential as its taylor series. so the action of the exponential (to the power of hte hamiltonian) on the density matrix amounts to considering the action of the hamiltonian on the density matrix which in general is not trivial
but i think i got the wrong idea of what to ask :). i think my question should have been in general can matrices of the same dimension have the same maximum eigenvalue, which I think is quite plausible to be true
i mean in linear algebra you do have a spectral radius, but since you constrain apparently two matrices to have the same one it must be due to physical reasons right
but this project is quite cool :D. it is about trying to factor some Hilbert space into system and environment based on quasi-classical criteria. So for each factorization, we assign a score by computing the linear entropy (computationally nice way to measure the likelihood of a state to entangle) of some candidate quasi-classical state(s). Then we search for the space with the smallest score.
well there is no constrain per se, but having two matrices with the same maximum eigenvalue in my context corresponds to two factorizations being equally good
@SillyGoose for such questions, just remember that the diagonal matrix with diagonal entries $\lambda_i$ trivially has eigenvalues $\lambda_i$. So there are infinitely many operators/matrices with the same highest eigenvalue - their diagonalisations just differ in the lower $\lambda_i$
well actually i know how to classify them, but i think implementing it into code will be a bit difficult because there are infinitely many
well so I have a 4-dimensional Hilbert space factored into the tensor product of 2 2-dimensional spaces. I am starting with an initial candidate pointer state which is [[1,0],[0,0]] \otimes (maximally mixed state), where the first tensor factor is the system.
I also have a Hamiltonian which is the 1D ising model hamiltonian. Everything is already put into the tensor product factorization such that this initial candidate pointer state when time evolved has no entanglement entropy.
