You are correct. What I imagined was to evaluate the action at the different points on the manifold. If the action remains invariant under translation along the direction described by x -> x' so that is takes the same value at those different points. Then this is a symmetry transformation. Is...
Not sure I understood really. But what are you actually doing when you make a coordinate transformation of the fields $$ \phi(x) $$ in general in the context of Noethers theorem? What I imagine is you just take your field evaluated at x on the manifold and you evaluate the same field it at some...
I'm so confused here. If we make the transformation of the coordinates x -> x', are we not suppose to consider the transformation of the coordinates only
$$ \phi(x) \rightarrow \phi(x') $$ ? Then why are they writing $$ \phi(x) \rightarrow \phi'(x') $$ ? If $$ \phi(x) $$ is a scalar function...
No we are not assuming a Minkowski metric or any other metric. (cdt)^2 - (dx)^2 is just a quantity that we are calculating. The space could be cartesian or any other space, we can calculate any quantity we want from the coordinates between two point in the space. But we have showed using the...
I thought I was clear. We are not assuming the underlying space is Minkowski, we are going to derive it. We can derive from the relation s=s' which states that (cdt)^2-(dx)^2 = (cdt')^2 - (dx')^2. We can prove that this relation holds when (cdt)^2-(dx)^2 = (cdt')^2 - (dx')^2 = 0 by considering...
We haven't made any assumptions about the underlying geometry. We have only assumed that the speed of light is invariant. From this assumption we can prove that s=s'=0 for two event separated by a light pulse. But how does it extend to the case when s differs from 0?
Yes of course, that would be trivial. But circular reasoning as I see it, because I want to use the invariance of the interval to derive the Lorentz transformations. The case s=s'=0 for a light pulse traveling between point A and B follows from the principle that the speed of light is invariant...
Two inertial frames of reference. "The interval is invariant because it is invariant". What kind of explanation is that? Then why did we use the invariance of the speed of light to prove that s=s' in the case when s=0? Would it not also be true because an invariant is an invariant because of...
If we use a light pulse that is emitted at A and absorbed at B. The spacetime interval between these two events are s'=s=0 in both frames of reference. But how does this invariance between s and s' extend to cases where s is not zero? Then we cannot measure the distance between the events using...
The quantum number n determines the energy, and for each n the allowed values for the angular momentum quantum number are -(n-1),...,(n-1).
This doesn't seem resonable to me. Classically increasing the orbital angular momentum will result in an increase in the energy of the system. But why is it...
"Second, it suggests that quantum mechanics can be thought of as a local theory, because the Einstein–Podolsky–Rosen (EPR) criterion of reality can be rejected."
From Wikipedia Quantum_Bayesianism
So supposedly, they claim QBism to be a local theory and at the same time claiming that the...
Quantum Bayesianism takes the view that the there are no quantum states in the objective sense and that the probabilities should only be interpreted as what information an agent has about the system. Isn't this the same as claiming that there are hidden variables, and that probabilities arises...