Frequency shifts in rotating frames

[PeterDonis]

I used that phrase as careless shorthand for the 'coordinate basis vectors' are rotating.

But if you're using an inertial frame, the coordinate basis vectors are not rotating. So I'm confused about what frame you're using.

 

[Mentz114]

But if you're using an inertial frame, the coordinate basis vectors are not rotating. So I'm confused about what frame you're using.

Peter, I've tried hard to distinguish between the elevator whose worldline is given above, and the center observer whose worldline is the elevator worldline where ##r=0##, which gives ##u_C^\mu=\partial_t##, which is at rest in the Minkowski chart.

The problem is that if there is no frequency shift, then there can be no deflection. Ehlers&Rindler show that a beam of light traveling across the gravitational field gradient will fall. And so it must have a frequency shift. If we shone a light across the room we're in, it would fall, wouldn't it ?

Maybe that's where I'm going wrong.

 

[jartsa]

Why bring the energy absorbed by the wall into this. It's not relevant surely.

I don't see how this can be correct. I'm talking about kinematics and Doppler shifts.

"careful thinking" is fine, but how about some calculation ?

Well here's one calculation that ignores time dilation, as the speed is quite low:

A laser gun moving at speed 0.1 c shoots forwards a laser pulse whose duration is 1 s.

Observer whose speed is zero says the length of the beam is 0.9 light-seconds. (because the front of the beam is 0.9 c * 1 s away when the rear of the beam leaves the laser gun). Now this observer calculates how long it takes for the pulse to be absorbed by an absorber that is co-moving with the laser gun.

It takes 1 s, because at closing speed 0.9 c, a 0.9 light-seconds long beam disappears into the absorber in 1 s. (I mean, a 0.9 light-seconds long thing dives into another thing at closing speed 0.9 c)

Observer calculated that co-moving observer received the wave crests at equally quick succession as they were created, because the wave crests were created in one second and absorbed in one second.

 

[Mentz114]

Well here's one calculation that ignores time dilation, as the speed is quite low:

A laser gun moving at speed 0.1 c shoots forwards a laser pulse whose duration is 1 s.

Observer whose speed is zero says the length of the beam is 0.9 light-seconds. (because the front of the beam is 0.9 c * 1 s away when the rear of the beam leaves the laser gun). Now this observer calculates how long it takes for the pulse to be absorbed by an absorber that is co-moving with the laser gun.

It takes 1 s, because at closing speed 0.9 c, a 0.9 light-seconds long beam disappears into the absorber in 1 s. (I mean, a 0.9 light-seconds long thing dives into another thing at closing speed 0.9 c)

Observer calculated that co-moving observer received the wave crests at equally quick succession as they were created, because the wave crests were created in one second and absorbed in one second.

Yes, thank you. I drew myself a diagram with spherical wave fronts and they are squeezed on emission and then stretched again on reception. I can't work out the deflection though. It looks as if the inertial frame would see deflection.

 

[A.T.]

he problem is that if there is no frequency shift, then there can be no deflection.

If the beam arrives at the same height in the box frame, then there is not frequency shift, even if the beam is bent. The inertial frame just sees the beam going straight.

 

[harrylin]

[..] The problem is that if there is no frequency shift, then there can be no deflection. Ehlers&Rindler show that a beam of light traveling across the gravitational field gradient will fall. And so it must have a frequency shift. If we shone a light across the room we're in, it would fall, wouldn't it ?

Maybe that's where I'm going wrong.

Perhaps - it depends on what frequency shift you are thinking of. The equivalence principle is about predicted observations; interpretation is a different matter.

Einstein as well as Okun explained that in vacuum in a gravitational field in rest, the number of wave crests must be conserved. A predicted frequency shift due to Doppler effect from acceleration in an accelerating frame without gravitation, must therefore in an equivalent gravitational field in rest be interpreted as due to difference in reference frequencies (clock frequencies).

PS. it was that insight that led to the first prediction of gravitational time dilation.

 

[Mentz114]

If the beam arrives at the same height in the box frame, then there is not frequency shift, even if the beam is bent. The inertial frame just sees the beam going straight.

I now take the view that there is no deflection of frequency shift. See Below.

Perhaps - it depends on what frequency shift you are thinking of. The equivalence principle is about predicted observations; interpretation is a different matter.

Einstein as well as Okun explained that in vacuum in a gravitational field in rest, the number of wave crests must be conserved. A predicted frequency shift due to Doppler effect from acceleration in an accelerating frame without gravitation, must therefore in an equivalent gravitational field in rest be interpreted as due to difference in reference frequencies (clock frequencies).

PS. it was that insight that led to the first prediction of gravitational time dilation.

The Einstein elevator differs from the elevator on a string in a crucial way. If the EE is not in a gravitational field it moves in the same direction as the 'field' gradient ( up-down). The rotating elevator moves sideways in relation to the field. So one would not expect the same phenomena for the transverse light beam., viz deflection and frequency shifts.

 

[A.T.]

it moves in the same direction as the 'field' gradient ( up-down). The rotating elevator moves sideways in relation to the field.

The proper acceleration of the box is relevant here.

So one would not expect the same phenomena for the transverse light beam., viz deflection and frequency shifts.

They will differ quantitatively if the box is large enough. But for small enough boxes they are very similar. In both cases Light rays (send perpendicular to the proper acceleration of the box) will be curved in the frame of the box. But if received at the same height (along the proper acceleration of the box) as emitted there will be no frequency change.