Speed of Point on Expanding Sphere

[Ad VanderVen]

TL;DR

Suppose we have an expanding sphere. That means that the surface $4 \Pi r^{2}$ is getting bigger and bigger. For example, suppose the area expansion rate is $b r$. Does this limit the speed at which a point can move on the surface?

Reference: https://www.physicsforums.com/forums/special-and-general-relativity.70/post-thread

Suppose we have an expanding sphere. That means that the surface $4 \pi r^{2}$ is getting bigger and bigger. For example, suppose the area expansion rate is $b \, r$. Does this limit the speed at which a point can move on the surface?

 

[PeroK]

Limit in what way? In SR the speed of a particle as measured in an IRF is limited by $c$. Having an expanding physical object, if that is what you mean, doesn't change that.

 

[PeroK]

PS the link in the OP doesn't lead anywhere.

 

[Ad VanderVen]

PS the link in the OP doesn't lead anywhere.

I do not know how to re-edt the summary.

 

[Ad VanderVen]

Limit in what way? In SR the speed of a particle as measured in an IRF is limited by $c$. Having an expanding physical object, if that is what you mean, doesn't change that.

I mean it purely mathematically.

 

[Ad VanderVen]

I mean it purely mathematically.

I mean $r(t) \, = \, b \, t$ where $t$ represents time and $0 \, < \, b$..

 

[Nugatory]

I mean $r(t) \, = \, b \, t$ where $t$ represents time and $0 \, < \, b$..

And $r$ is the distance from the center of the sphere to a particle on the surface of the sphere (using an inertial frame in which the center of the sphere is at rest)?

Then $\frac{dr}{dt}=b$ is the speed of that particle using that frame. It will of course be less than $c$.

 

[Nugatory]

I do not know how to re-edt the summary.

Report your post, include the correct link in your report, and one of us mentors can fix it for you.

 

[PeroK]

I mean it purely mathematically.

There's no purely mathematical limit on the speed of a particle. But, if you apply the theory of SR, then there is a limit.

 

[jbriggs444]

TL;DR Summary: Suppose we have an expanding sphere. That means that the surface $4 \Pi r^{2}$ is getting bigger and bigger. For example, suppose the area expansion rate is $b r$. Does this limit the speed at which a point can move on the surface?

Reference: https://www.physicsforums.com/forums/special-and-general-relativity.70/post-thread

Suppose we have an expanding sphere. That means that the surface $4 \pi r^{2}$ is getting bigger and bigger. For example, suppose the area expansion rate is $b \, r$. Does this limit the speed at which a point can move on the surface?

So you are asking about the idea of an object that is confined to the expanding surface but which may be moving across that surface?

If the object is "coasting" across the surface, what happens to its speed as the surface expands? Does it retain its original tangential velocity? Or is its tangential velocity amplified by the expansion of the surface?

Neither physics nor mathematics can answer that question. Only clarification on the setup of the situation can answer it.