All Questions
13
questions
0
votes
1
answer
173
views
Can momentum exist in a null direction?
CONTEXT (skip to "my question is"):
As I understand it, and correct me if I'm wrong, an orbit trades momentum between the X and Y directions. But spacetime can have negative and even null ...
- 278
3
votes
1
answer
64
views
Proportional null vectors [closed]
the past few days I've been studying special relativity and was just now making some exercices on it. One exercice was the following:
Let $U$ and $V$ be two null vector is a $d$-dimensional Minkowski ...
- 29
2
votes
3
answers
276
views
Deriving the norm of four-velocity from the definition of a time-like interval
I am going through Sean Carroll's Spacetime and Geometry, trying to learn GR. On page 31, he introduces the concept of the four-velocity $U^\mu$ as $$U^\mu = \frac{dx^\mu}{d\tau}$$ where $\tau$ is the ...
- 187
0
votes
1
answer
155
views
Is the zero 4-vector lightlike? [closed]
I'm not sure whether the zero 4-vector can be considered lightlike, spacelike, or timelike in special relativity. Can anybody give me some insight?
- 468
1
vote
2
answers
261
views
Scaling of null vectors
By definition any vector with $g_{\mu\nu}n^\mu n^\nu = 0$ is a null vector.
For simplicity let's look at flat spacetime. Is there any physical difference between two null vectors like these two?
\...
- 123
0
votes
0
answers
66
views
Is the space and time dimensions in Schwarzschild metric orthogonal?
Schwarzschild metric does not contain any cross-terms such as $dtd\phi$, does that mean that space and time coordinates are orthogonal to each other?
Should the dot product of any time vector with ...
- 11
0
votes
2
answers
83
views
Is a still object in 4D spacetime lightlike?
Every particle in the universe is moving in spacetime: a massive "still" one (in the 3D sense) is moving in a purely timelike direction, a massive "moving" one in a direction with ...
- 5,931
0
votes
0
answers
79
views
Why is "time orthogonal to space" in inertial reference frames?
I'm reading about the geometry of spacetime in special relativity (ref. Core Principles of Special and General Relativity by Luscombe). Here's the relevant section:
Minkowski space is a four-...
- 1,051
2
votes
0
answers
323
views
Spacelike, timelike, lightlike vectors and the light-cone structure
Consider a semi-Riemannian manifold which of these statements is false:
All vectors on the light-cone are light-like, all vectors in the interior of the light-cone are time-like and all vectors in ...
- 305
6
votes
2
answers
1k
views
Physical Motivation for Four-Velocity definition
I'm bothered with the motivation behind defining a four-velocity. In Schutz's A First Course in General Relativity, he uses the concept of a tangent vector at each point of a worldline of a particle ...
- 1,290
1
vote
1
answer
201
views
Quadrivectors in relativity
This is what I understood about 4-vectors in relativity.
We define the contravariant and covariant vectors like this :
$$
A^\mu=\begin{bmatrix}
A^0 \\
A^1 \\
A^2 \\
...
- 1,450
1
vote
2
answers
538
views
Motivation for usage of 4-vectors in special relativity
I understand that if one considers a 4-dimensional space-time from the outset then 4-vectors are the natural quantities to consider (as opposed to 3-vectors as in Newtonian mechanics), since the ...
- 3,207
2
votes
4
answers
10k
views
Question about dot product of four vectors?
I am looking back over some old notes and see that I have written
$\bar{p}=\left(\overset{E}{\vec p}\right)$ and $\bar{x}=\left(\overset{t}{\vec x}\right)$
(using Planck units)
And then $\bar{p} \...
- 3,997