If an observer were to rotate around a point at near light speeds, what sort of length contraction would he observe the universe undergo?

Adelyn Rodriguez
2022-04-06
Answered

If an observer were to rotate around a point at near light speeds, what sort of length contraction would he observe the universe undergo?

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pulpasqsltl

Answered 2022-04-07
Author has **18** answers

The formula for length contraction involves velocity only:

${L}^{\prime}=L\sqrt{1-{v}^{2}/{c}^{2}}.$

Note that acceleration does not contribute. So the answer to your question is obtained by simply taking the instantaneous velocity.

As the object goes around the circle, the length contraction changes according to the change in direction of the velocity.

${L}^{\prime}=L\sqrt{1-{v}^{2}/{c}^{2}}.$

Note that acceleration does not contribute. So the answer to your question is obtained by simply taking the instantaneous velocity.

As the object goes around the circle, the length contraction changes according to the change in direction of the velocity.

Ashley Fritz

Answered 2022-04-08
Author has **5** answers

good answer.

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Relativistic Lagrangian transformations, it's $\text{}L=-m{c}^{2}\sqrt[2]{1-\frac{|u{|}^{2}}{{c}^{2}}}$ I need to study the translation, boost and rotation symmetry. I say it doesn't depend of the position, so it has translation symmetry and the momentum will conserve. It's rotation invariant because depends only of the modulus of the speed $|u|$ (What is the conserved quantity derived by this symmetry?)

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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 2022-05-08

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Now, from what I have understood of special relativity so far, time will flow slower for the astronaut than for the earthlings. Hence, assuming $v=0.8c$, the astronaut will after 30 years have received a video transmission 50 years long!

Is my reasoning correct, that even though the transmission is live, the astronaut would actually be watching things that happened many years ago, while still receiving the "live" feed, which would be stored/buffered in the shuttles memory, thus making it possible for the astronaut to fast-forward the clip to see what happened more than 30 years after passing the earth?

Now, from what I have understood of special relativity so far, time will flow slower for the astronaut than for the earthlings. Hence, assuming $v=0.8c$, the astronaut will after 30 years have received a video transmission 50 years long!

Is my reasoning correct, that even though the transmission is live, the astronaut would actually be watching things that happened many years ago, while still receiving the "live" feed, which would be stored/buffered in the shuttles memory, thus making it possible for the astronaut to fast-forward the clip to see what happened more than 30 years after passing the earth?

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Let's have a definition of massive particle as an irreucible representation of the Poincare group. Then, let's have a spinor field ${\psi}_{\alpha {\alpha}_{1}...{\alpha}_{n-1}\dot{\beta}{\dot{\beta}}_{1}...{\dot{\beta}}_{m-1}}$, which is equal to $(\frac{m}{2},\frac{n}{2})$ representation of the Lorentz group. There is the hard provable theorem:

${\psi}_{\alpha {\alpha}_{1}...{\alpha}_{n-1}\dot{\beta}{\dot{\beta}}_{1}...{\dot{\beta}}_{m-1}}$ realizes irreducible representation of the Poincare group, if

$({\mathrm{\partial}}^{2}-{m}^{2}){\psi}_{\alpha {\alpha}_{1}...{\alpha}_{n-1}\dot{\beta}{\dot{\beta}}_{1}...{\dot{\beta}}_{m-1}}=0,$

${\mathrm{\partial}}^{\alpha \dot{\beta}}{\psi}_{\alpha {\alpha}_{1}...{\alpha}_{n-1}\dot{\beta}{\dot{\beta}}_{1}...{\dot{\beta}}_{m-1}}=0.$

Can this theorem be interpreted as connection between fields and particles?

${\psi}_{\alpha {\alpha}_{1}...{\alpha}_{n-1}\dot{\beta}{\dot{\beta}}_{1}...{\dot{\beta}}_{m-1}}$ realizes irreducible representation of the Poincare group, if

$({\mathrm{\partial}}^{2}-{m}^{2}){\psi}_{\alpha {\alpha}_{1}...{\alpha}_{n-1}\dot{\beta}{\dot{\beta}}_{1}...{\dot{\beta}}_{m-1}}=0,$

${\mathrm{\partial}}^{\alpha \dot{\beta}}{\psi}_{\alpha {\alpha}_{1}...{\alpha}_{n-1}\dot{\beta}{\dot{\beta}}_{1}...{\dot{\beta}}_{m-1}}=0.$

Can this theorem be interpreted as connection between fields and particles?

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${\gamma}^{\mu}{\mathrm{\partial}}_{\mu}={\gamma}^{0}\frac{\mathrm{\partial}}{\mathrm{\partial}t}+\overrightarrow{\gamma}\cdot \overrightarrow{\mathrm{\nabla}}$

where $\overrightarrow{\gamma}=({\gamma}^{1},{\gamma}^{2},{\gamma}^{3})$, but to my knowledge,

${\gamma}^{\mu}{\mathrm{\partial}}_{\mu}={\gamma}^{\mu}{\eta}_{\mu \nu}{\mathrm{\partial}}^{\nu}={\gamma}^{0}\frac{\mathrm{\partial}}{\mathrm{\partial}t}-\overrightarrow{\gamma}\cdot \overrightarrow{\mathrm{\nabla}}$

using the convention ${\eta}_{\mu \nu}=\mathrm{diag}(+,-,-,-)$.

${\gamma}^{\mu}{\mathrm{\partial}}_{\mu}={\gamma}^{0}\frac{\mathrm{\partial}}{\mathrm{\partial}t}+\overrightarrow{\gamma}\cdot \overrightarrow{\mathrm{\nabla}}$

where $\overrightarrow{\gamma}=({\gamma}^{1},{\gamma}^{2},{\gamma}^{3})$, but to my knowledge,

${\gamma}^{\mu}{\mathrm{\partial}}_{\mu}={\gamma}^{\mu}{\eta}_{\mu \nu}{\mathrm{\partial}}^{\nu}={\gamma}^{0}\frac{\mathrm{\partial}}{\mathrm{\partial}t}-\overrightarrow{\gamma}\cdot \overrightarrow{\mathrm{\nabla}}$

using the convention ${\eta}_{\mu \nu}=\mathrm{diag}(+,-,-,-)$.

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