Consequences of the Equivalence Principle

[unchained1978]

I was reading a book on SR and GR and it used the example of a falling elevator with a light beam traveling through it. Considering this setup leads to the conclusion that light bends in a gravitational field. My question is, would light bend as a result of any kind of acceleration given the elevator experiment. For example, if you were to accelerate an elevator magnetically and shine a light beam perpendicular to the direction of motion would not the light beam be curved to an onlooker outside of the elevator?

 

[bcrowell]

Yes.

 

[yuiop]

I was reading a book on SR and GR and it used the example of a falling elevator with a light beam traveling through it. Considering this setup leads to the conclusion that light bends in a gravitational field. My question is, would light bend as a result of any kind of acceleration given the elevator experiment. For example, if you were to accelerate an elevator magnetically and shine a light beam perpendicular to the direction of motion would not the light beam be curved to an onlooker outside of the elevator?

Yes.

No!

To a non accelerating observer outside the accelerating elevator the light beam will appear to follow a straight path whether the source is outside the elevator or attached to the elevator because the observer outside the elevator is in flat space.

To an observer inside the elevator accelerating with the elevator, the light beam will appear to follow a curved path relative to a background grid painted on the walls of the elevator.

 

[bcrowell]

Oops, sorry, yuiop was right and I was wrong. I didn't read the initial post carefully enough.

 

[unchained1978]

No!
To an observer inside the elevator accelerating with the elevator, the light beam will appear to follow a curved path relative to a background grid painted on the walls of the elevator.

How is this? Assuming a constant force is acting on the elevator how would you know if you were accelerating or at rest by the equivalence principle? And therefore, if you were unable to determine if you were accelerating or at rest, how could the light beam be curved inside the elevator but not outside?

 

[Passionflower]

How is this? Assuming a constant force is acting on the elevator how would you know if you were accelerating or at rest by the equivalence principle?

Use an accelerometer.

 

[Al68]

How is this? Assuming a constant force is acting on the elevator how would you know if you were accelerating or at rest by the equivalence principle? And therefore, if you were unable to determine if you were accelerating or at rest, how could the light beam be curved inside the elevator but not outside?

Whether the light beam is curved or not depends on whether the observer is accelerating, not on whether he's inside or outside the elevator. That's why yuiop specified that the observer inside was accelerating with the elevator, while the outside observer was not accelerating.

Basically, light travels in a curved path relative to an accelerating frame of reference, and a straight line in an inertial (non-accelerating) reference frame.

And the distinction is between "accelerating" and "non-accelerating" reference frames. The term "at rest" has no meaning except relative to a particular reference frame.

 

[atyy]

If you accelerate the elevator magnetically, that means there is an accelerated charge, which means it will give off radiation, which means "the" light beam is ambiguous.