All Questions
64
questions
1
vote
1
answer
144
views
Physical intuition for the Minkowski space?
As the title suggests, I am looking for physical intuition to better understand the Minkowski metric.
My original motivation is trying to understand the necessity for distinguishing between co-variant ...
- 11
0
votes
1
answer
71
views
On covariant form of Lorentz equation
The non-relativistic version of Lorentz equation has the form
$$m\frac{d\vec{v}}{dt}=q(\vec{E}+\vec{v}\times\vec{B}) $$
Where $\vec{v}, \vec{E}, \vec{B}$ refers to the velocity of charged particle, ...
- 1,752
3
votes
0
answers
68
views
Counting independent components of Lorentz tensor
Say I have Lorentz tensors $A^{\mu\nu}$ and say this Lorentz tensor is symmetric under $\mu \Leftrightarrow \nu$ and there are only $p^\mu$ and $q^\mu$ as the physical Lorentz vectors involved. If so, ...
- 857
0
votes
1
answer
209
views
Formulation of the Bianchi identity in EM
I'm trying to understand, as a self learner, the covariant formulation of Electromagnetism. In particular I've been stuck for a while on the Bianchi identity. As I've come to understand, when we ...
- 540
0
votes
0
answers
50
views
How is tensor analysis useful to Relativity? [duplicate]
How does the knowledge of tensor analysis and Differential Geometry help us understand the equations of General and Special Relativity?
0
votes
1
answer
486
views
Show that the contraction of a covector and a vector is Lorentz invariant
I just got Sean Carroll's Spacetime and Geometry: An Introduction to General Relativity a couple of weeks ago, and I have resolved to go through the entire book. In the first chapter, he prompts the ...
- 187
0
votes
1
answer
80
views
About general covariance
\begin{equation} u^{\mu}=\frac{d}{d\tau}x^{\mu} \end{equation}
\begin{equation} \partial_{\lambda}(u_{\nu} u^{\nu}) = (\partial_{\lambda}u_{\nu}) u^{\nu} + u_{\nu}(\partial_{\lambda}u^{\nu}) = 0 \end{...
- 31
4
votes
1
answer
235
views
Understanding tensor and covariance
I'm really struggling to understand the use of tensors when we want to have a covariant equation.
From what I understand, if we write an equation using tensors only, then the physics behind it will be ...
- 41
2
votes
1
answer
850
views
Raised index of partial derivative
I am having a really hard time wrapping my head around component notation for tensor fields. For example, I do not know exactly what the following expression means
$$\partial_\mu\partial^\nu \phi, \...
- 133
0
votes
1
answer
63
views
Explanation of an equation in special relativity
$$
{\partial (0.5 (\partial_{\mu} A^{\mu})^2) \over \partial(\partial_{\mu} A_{\nu})} = {(\partial_{\rho} A^{\rho}) g^{\mu \nu} }
$$
Can somebody explain why this is true?
1
vote
2
answers
1k
views
Lorentz invariance of the Lorentz force law
I'm self-studying Friedman and Susskind's book Special Relativity and Classical Field Theory. The following question popped up while reading section 6.3.4 Lorentz Invariant Equations.
In this Lecture, ...
- 1,951
2
votes
1
answer
430
views
How to be sure that a law is invariant under Lorentz's Transformation?
For starters let's talk about Maxwell's Equations; we know that Maxwell's Equations are invariant under Lorentz's Transformation, after all this is why all the relativity business got started. To ...
- 4,577
5
votes
4
answers
3k
views
Is the Four-gradient of a Scalar Field a Four-Vector?
Consider a scalar field $\phi$ as a function of spacetime coordinates $x^\mu$. The four-gradient of $\phi$ is given by
\begin{equation}
\frac{\partial \phi}{\partial x^\mu} = \left( \frac{\partial \...
- 1,290
0
votes
0
answers
211
views
What are covectors in special relativity?
In special relativity the purpose of vectors makes fairly intuitive sense, they represent a point in spacetime:
$$x^{\mu}=\begin{pmatrix}x^0 \\ x^1 \\ x^2 \\ x^3\end{pmatrix}$$
and we can define the ...
- 6,963
3
votes
1
answer
7k
views
What is the difference between invariance and covariance? [duplicate]
In relativistic physics, paricularly in General Relativity and Quantum Field Theory, we often find the use of the two terms 'invariance' and 'covariance'. But I couldn't find any mention of the ...
- 115