Is it allowed to have the zeroth-component of a four-velocity be negative?

This is referring to $V^0$ for a curved space metric with signature $-+++$.

This is referring to $V^0$ for a curved space metric with signature $-+++$.

motsetjela
2022-08-12
Answered

Is it allowed to have the zeroth-component of a four-velocity be negative?

This is referring to $V^0$ for a curved space metric with signature $-+++$.

This is referring to $V^0$ for a curved space metric with signature $-+++$.

You can still ask an expert for help

asked 2022-09-26

Lorentz Boosts in the same direction should form a group. Two boosts along the x axis should produce another boost along the x axis. Is that correct?

asked 2022-07-16

Why do we say that irreducible representation of Poincare group represents the one-particle state?

Only because

1. Rep is unitary, so saves positive-definite norm (for possibility density),

2. Casimir operators of the group have eigenvalues ${m}^{2}$ and ${m}^{2}s(s+1)$, so characterizes mass and spin, and

3. It is the representation of the global group of relativistic symmetry,

yes?

Only because

1. Rep is unitary, so saves positive-definite norm (for possibility density),

2. Casimir operators of the group have eigenvalues ${m}^{2}$ and ${m}^{2}s(s+1)$, so characterizes mass and spin, and

3. It is the representation of the global group of relativistic symmetry,

yes?

asked 2022-05-19

Looking for specific Relativity example

The example had to do with two people walking along a sidewalk in opposite directions, and an alien race on a planet millions of light-years away planning an invasion of the Solar System. The example showed that in one walker's reference frame the invasion fleet had departed, but in the other reference frame the fleet had not.

At the time, the explanation made perfect sense, but I have forgotten the details and have never run across this example again.

Does anybody know where this was, or have the text of the explanation?

The example had to do with two people walking along a sidewalk in opposite directions, and an alien race on a planet millions of light-years away planning an invasion of the Solar System. The example showed that in one walker's reference frame the invasion fleet had departed, but in the other reference frame the fleet had not.

At the time, the explanation made perfect sense, but I have forgotten the details and have never run across this example again.

Does anybody know where this was, or have the text of the explanation?

asked 2022-08-11

Manipulating an $n\times n$ metric where $n$ is often $>4$, depending on the model. The $00$ component is always $\tau $*constant, as in the Minkowski metric, but the signs on all components might be $+$ or $-$ , depending on the model. Can I call this metric a Minkowski metric? Or what should I call it?

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Does a relativistic version of quantum thermodynamics exist? I.e. in a non-inertial frame of reference, can I, an external observer, calculate quantities like magnetisation within the non-inertial frame?

asked 2022-08-11

If some kind of source was able to supply an infinite amount of energy, does that imply that it also must have an infinite mass? Is the contrary also true?

asked 2022-08-21

The perimeter is moving at a speed such that the acceleration is $g=9.81\text{m/s^2}$. Combining $g={\frac{{v}^{2}}{R}}_{s}$ with $\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}$ gives dilation factor

$\sqrt{1-\frac{g\phantom{\rule{thinmathspace}{0ex}}{R}_{s}}{{c}^{2}}}$

Assuming the radius ${R}_{s}$ of the space station is $500$ meters, a perimeter clock would lose about $1e-6$ seconds per year with respect to a clock in the center axis.

Now since the clock at the perimeter is subject to acceleration g, by the equivalence principle it would seem that the gravitational time dilation would apply, which is

$\sqrt{1-\frac{2{R}_{e}g}{{c}^{2}}}$

where ${R}_{e}=6.38\times {10}^{6}\text{m}$. This would make the perimeter clock slow by about $0.02$ seconds per year.

$\sqrt{1-\frac{g\phantom{\rule{thinmathspace}{0ex}}{R}_{s}}{{c}^{2}}}$

Assuming the radius ${R}_{s}$ of the space station is $500$ meters, a perimeter clock would lose about $1e-6$ seconds per year with respect to a clock in the center axis.

Now since the clock at the perimeter is subject to acceleration g, by the equivalence principle it would seem that the gravitational time dilation would apply, which is

$\sqrt{1-\frac{2{R}_{e}g}{{c}^{2}}}$

where ${R}_{e}=6.38\times {10}^{6}\text{m}$. This would make the perimeter clock slow by about $0.02$ seconds per year.