Superluminal Frame Adjustments?

[GRDixon]

In theory the set of Inertial Reference Frames could consist of an infinite set of rectangular grids and distributed clocks, overlaid and sliding through one another without interference. Let us say we are initially at rest at the Origin of IRF K. Relative to K, the grid of moving frame K’ will be length contracted, etc.

If we switch our rest frame to K’, then it will be the grid of K that is length contracted, etc. At great enough distances from the Origin of K, this would seem to require parts of the K’ grid to move outward, away from the Origins, at speeds faster than c. (And similarly, from the Origin of K’ it would seem distant parts of the K grid must move closer to the Origins at speeds greater than c.)

How can this violation of the rule, that c is the maximum speed of material objects, be resolved?

 

[matheinste]

In theory the set of Inertial Reference Frames could consist of an infinite set of rectangular grids and distributed clocks, overlaid and sliding through one another without interference. Let us say we are initially at rest at the Origin of IRF K. Relative to K, the grid of moving frame K’ will be length contracted, etc.

If we switch our rest frame to K’, then it will be the grid of K that is length contracted, etc. At great enough distances from the Origin of K, this would seem to require parts of the K’ grid to move outward, away from the Origins, at speeds faster than c. (And similarly, from the Origin of K’ it would seem distant parts of the K grid must move closer to the Origins at speeds greater than c.)

How can this violation of the rule, that c is the maximum speed of material objects, be resolved?

Let the relative velocity of the two frames be v. Every point of the grid at rest in K remains at rest in K and so a constant distance from the origin of the grid in K. Every point of the grid in K' moves at velocity v with respect to the origin of the grid at rest in K. And vice versa. No superluminal speeds required.

Matheinste.

 

[IttyBittyBit]

In theory the set of Inertial Reference Frames could consist of an infinite set of rectangular grids and distributed clocks, overlaid and sliding through one another without interference. Let us say we are initially at rest at the Origin of IRF K. Relative to K, the grid of moving frame K’ will be length contracted, etc.

If we switch our rest frame to K’, then it will be the grid of K that is length contracted, etc. At great enough distances from the Origin of K, this would seem to require parts of the K’ grid to move outward, away from the Origins, at speeds faster than c. (And similarly, from the Origin of K’ it would seem distant parts of the K grid must move closer to the Origins at speeds greater than c.)

How can this violation of the rule, that c is the maximum speed of material objects, be resolved?

This is actually a valid (but somewhat silly, once you realize what's going on) question. What you are thinking of is acceleration from one IRF to another. When we are accelerating, especially if we are accelerating rapidly, we percieve distant parts of the Universe moving around, as if to violate the speed of light limit. But what you are missing is that since we are the one feeling the acceleration, we can't possibly conclude that we are at rest and the Universe is moving. The same thing happens with rotation: Sit down. Look up at the night sky and rotate your head. Sure, you could pretend that your head is stationary and that the cosmos are rotating rapidly around you, but that is obviously false and silly.

In fact, the shift of objects as we accelerate is a kind of rotation. It's called the Penrose rotation.

At any rate, SR does not forbid travel faster than light - it only forbids communication faster than light. So don't try too hard to come up with arguments like 'hey, I just proved that something can travel faster than light, so I disproved SR!' It doesn't work that way.

 

[matheinste]

This is actually a valid (but somewhat silly, once you realize what's going on) question. What you are thinking of is acceleration from one IRF to another. When we are accelerating, especially if we are accelerating rapidly, we percieve distant parts of the Universe moving around, as if to violate the speed of light limit. But what you are missing is that since we are the one feeling the acceleration, we can't possibly conclude that we are at rest and the Universe is moving. The same thing happens with rotation: Sit down. Look up at the night sky and rotate your head. Sure, you could pretend that your head is stationary and that the cosmos are rotating rapidly around you, but that is obviously false and silly.

In fact, the shift of objects as we accelerate is a kind of rotation. It's called the Penrose rotation.

At any rate, SR does not forbid travel faster than light - it only forbids communication faster than light. So don't try too hard to come up with arguments like 'hey, I just proved that something can travel faster than light, so I disproved SR!' It doesn't work that way.

Would it be corrrect to say that if only linear acceleration is involved while moving from being at rest in K to being at rest in K' the accelerating observer will be at rest in a series of comoving inertial frames each of whose velocities relative to the observer's original rest frame is less than c, and so all objects at rest in this series of frames are traveling at less than c relative to the non accelerating observer's rest frame at every stage?

Matheinste.