Thank you very much @vanhees71 : That gives me peace of mind. It will probably be covered later in the text I am following, but when I saw this example I was troubled :)
I didn't know about canonical transformations. But I thought that by making the coordinate transformation ##Q=q-Ut##, I had changed my frame of reference, so that U loses its meaning and should not be part of the Lagrangian at all.
ok,
$$ L = \frac{m}{2}(U+\dot{Q})^2 - \frac{1}{2}kQ^2$$
$$ p = m\dot{Q} + mU $$
$$ H = \dot Q p - L = ...= \frac 1 2 p^2/m+U p+\frac 1 2 kQ^2 $$
If we ignore U completely, Kinetic Energy is simply ## KE = \frac{m}{2}\dot{Q}^2 ##. Therefore
$$ P = \frac {\partial L} { \dot Q} = m \dot Q $$...
In a classical example, for a system consisting of a mass attached to a spring mounted on a massless carriage which moves with uniform velocity U, as in the image below, the Hamiltonian, using coordinate q, has two terms with U in it.
But if we use coordinate Q, ##Q=q−Ut##, which moves with the...
Please help me confirm that I understand this correctly.
Imagine a system comprised of two black holes orbiting each other, which will eventually merge. At any point in time we describe the stress-energy tensor of the system. Assume that we could solve the EFE's for every point (t,x,y,z). This...
I think this demonstrates a complete lack of understanding, which is not surprising being, as it is, a language model. If I am not mistaken the Wolfram Alpha plugin intends to make life easier for the user when expressing the problem that they want Wolfram Alpha to solve, not to enhance the...
Hi guys,
I have heard a lot of claims about ChatGPT and how it is going to put a lot of people out of work. I have a friend who is a teacher of humanities and he is fearful of losing his job in the long term. People seem to be in awe at the thing and think it understand what is saying. So I...
That paragraph is indeed in the 1st edition at section 2.3 (Cosmological observations). But, given that his book is titled 'A First Course in General Relativity', he could not possibly assume that the reader would understand that recession speeds >c are possible, especially after the quote I...
In the last chapter of Schutz devoted to Cosmology, Schutz writes
So it seems that in 1985 it was assumed as obvious that the recession speed could not exceed ##c##.
The consensus seems to have swiftly changed. When did that happen? Was it debated at all?