In this paper, they are studying the decay of a particle of a scalar field into two particles of two other scalar fields. I have two questions.
(1) In textbook QFT, we would treat the incoming states and outgoing states as free particles (or plane waves). Also, total energy is conserved through the process. Hence, we would have that the "free" energy of the initial particles is equal to the "free' energy of the final particles.
however, in (3.8) we evidently have this $e^{i(m_\Phi - E_\chi(p) - E_\psi(p))}$ which is not taken to just be $e^{i0} = 1$
so it seems that we are not assuming that energy is conserved in our decay process?
I mean the final "physical" result (3.11) turns out to be energy conserving, but it is not clear that energy is conserved before that point
(2) Here, the $t \to \infty$ limit is being taken. it seems like a not-well defined quantity is hiding in the $\mathcal{P}$ of (3.10), is that right? It seems like $\mathcal{P} = \lim_{t\to\infty} e^{it\eta}$ for some constant $\eta$...
@SillyGoose this is nothing special. conservation of energy and momentum is only enforced at infinitely far away from each other. In between, the vacuum state has all kinds of spurious nonsense; that is why we have no choice but to only ever talk about infinite past and future, never anything in-between.
@SillyGoose no, that P should be the Cauchy's principle value
I have made video for 1st law of motion. I will share you. It is basically in my language. But i have written everything in English. You will understand it what i am trying to say.
But i am very excited to make 3rd and 2nd law. Those are technical.
@MoreAnonymous according to one, there is a universe which is made of consciousness substance and it has mathematical properties dissolved in it, which we discover as physics
according to the other, there is a universe made of consciousness. it's just one thing. but sometimes, a part of it disassociates from the rest, and it emerges as a first person perspective like yours or mine. And then, from this perspective, the universe's properties manifest as physics
so the disassociated part is looking at the rest of it, from its disassociated perspective
@MoreAnonymous this seems like they're trying to have some meta laws
laws which explain the laws we know
@MoreAnonymous Bernardo Kastrup believes that the wavefunction of QM is the state of knowledge, that a disassociated form of consciousness holds, about the rest of the universe
@MoreAnonymous so when the friend does the observation, the wavefunction relative to the friends perspective becomes : up or down. but wrt to Wigner, it becomes $|\text{friend saw up}\rangle |up\rangle + |\text{friend saw down }\rangle |down\rangle$
and when Wigner subsequenly measures the system, the state relative to him becomes $|\text{Wigner saw up, friend saw up, up}\rangle$ or the corresponding state for down (depending on what Wigner observes)
@naturallyInconsistent Hi, I have one question regarding transitions between states, where the initial state of the system is an arbitrary one, an eigenstate $|m\rangle$ and after the turning on of some sort of disturbance, we want to find the probability of the system ending up in an eigesntate $|n,t\rangle$
I don't know if you are familiar with what I am talking or if you need for details about it
which I can provide if necessary
But the idea was that the probability of transition was: $P_{m,n}=t\frac{2\pi}{\hbar}\delta(E_n-E_m)|\langle n|V|m\rangle|^2$, where V is the potential, which we take it as time idependent
This expression though, indirectly says that as time passes, the probability increases. And of course it can't be correct
So what is the interpretation here
Because, from that expression, dividing by t, one gets the transition rate, or fermis golden rule (for stationary states):$\Gamma_{mn}=\frac{P_{mn}}{t}=\frac{2\pi}{\hbar}\delta(E_n-E_m)|\langle n|V|m\rangle|^2$
youtube.com/watch?v=cBIvSGLkwJY What do you guys think about this recent YouTube video? In short, she rants that physicists have wasted away decades working on things that they know are useless and/or completely incorrect and false.
is logic an empirical finding some philosophers say that logical truths must be valid in every possible world e.g. if A --->B and A then B then this is not an empirical law. it must hold in every conceivable world
it would mean laws of logic are necessary true, instead of possibly true a possible truth is something that happens to hold in our universe. and a necessary truth is something that must hold in every world
@Sahaj i think it's false accusations. string theorists def believe in their ideas
A string theorist is kissing his secretary when his wife walks in. She bursts into tears and turns to run out. The string theorist yells, "Wait! I can explain everything!"
Progress in physics: Newtonian mechanics can't solve the 3 body problem Relativistic mechanics can't solve the 2 body problem Quantum mechanics can't solve the 1 body problem String theory can't solve the vacuum
The problem with physics jokes is that you don’t know whether they’re funny until you observe them.
