I am reading some book on quantum computing, and it mentions the Clifford group. I understand the Pauli Group and the idea that Clifford group consists of unitaries that map the elements in the Pauli group back to the Pauli group, but what are these unitaries exactly? Can you list some of them...
Thank you Bob, I really now understand what invariance means. But I have one remaining point regarding to covariance
Are you referring here to the fact that the E and B field themselves transforms between a pair of inertial frames? Or are you referring to the Lorentz transformations of the...
Thank you for your reply,
Ok, what do we say about Maxwell's equations, are they Lorentz invariant or Lorentz covariant? And can you please give me examples of Lorentz covariant equations in physics.
Hi, what is the difference between Lorentz Invariance and Lorentz Covariance?
From my lecture note (Group theory course) Invariance and Covariance where defined as follows:
Invariance: refers to the property of objects being left unchanged by symmetry operations.
Covariance: refers to...
Hi,
I am not sure if this post should be in this section. I am currently writing a report and I am using square brackets for my references i.e. [1] [2] and so on. But some of these references are books and I want to refer to a page in the book so do you think its ok to write the reference as an...
m_{1}u_{1}+m_{2}u_{2}=0 can be rearragned to \frac{u_{1}}{u_{2}}=-\frac{m_2}{m_1} and taken the modulus we get \frac{|u_{1}|}{|u_{2}|}=\frac{m_{2}}{m_{1}}
Now, Lets call |u_{1}|+|u_{2}|=x where x is known, and if we divide by |u_{2}| and rearrange we get...
You are absolutely right, sorry about that.
Thank you so much, I worked through it following your steps and I got a very similar answer which is
t=-\frac{1}{\sqrt{2GM}}\int^{x}_{x_{0}}{(\frac{1}{x}-\frac{1}{x_{0}})^{-\frac{1}{2}}}dx= \frac{x_0 \sqrt{x_0}}{\sqrt{2GM}} \left(\frac{1}{2}...
It is simply F=ma, where F=-\frac{GMm}{x^{2}} and ma=m\frac{dv}{dt}
You are definitely right, I was going to get to equation three by using the fact that the total energy is constant, but I decided to start by integrating the e.o.m to show exactly what I mean by integrating the inverse...
Hi, I am trying to solve the following problem (but note you can skip the details and look at the last equation and help me with the integral): a small planet (mass m) is found at rest relative to the Sun (mass M) with a separation distance x_{0}. Consider now the small planet move in response...
I heard this joke on the latest episode of the Big Bang Theory today and I thought I can share it with you. Penny tells the four guys this joke to pull their attention away from a new girl that just moved into a flat above them, and here it is:
(A physicist goes to an ice cream parlour every...
Actually I know that the Dirac equation is invariant under the Lorentz transformation, and I went through the proof. But, the four components of the wave function do not form a 4-vector and so the solutions are not invariant under the Lorentz transformation. However, I know the transformation to...
Hi, I have learned the Dirac equation recently and I managed to solve it for a free particle (following Greiner book “relativistic quantum mechanics” and Paul Strange book “Relativistic Quantum Mechanics”). I was asked to solve the Dirac equation in the stationary frame for a free particle (no...
Thanks jtbell, good hint, I stupidly forgot that it's a dot product.
But I have another problem now and this is what I got
\[
U=\int\mathbf{F}.\mathbf{dr}\]
and in the cartesian form we have \[
\mathbf{r}=x\mathbf{\hat{x}}+y\mathbf{\hat{y}}+z\mathbf{\hat{z}}\]
\[...
Hi, I want to calculate the potential energy between two opposite charges (a dipole) and I know how to integrate Coulomb’s law in the polar form, i.e. in terms of “r”
\[...
Hi, I am having a hard time understanding the Lorentz - Fitzgerald contraction hypothesis (LFCH). I understand that it is a pre-relativity explanation of the null result of Michelson-Morley Experiment. My question is how did Lorentz derive the gamma factor, namely 1/sqrt(1-v^2/c^2), my...
The way you should think about it is that the two observers are sitting at the origins, and the reference frames are their coordinate system. Therefore if the two observers are in a relative motion to each other their coordinate system moves with them, including the origin since they are sitting...