Light in an accelerated elevator

In summary: The problem with that is that you don't have a static situation. If the proper acceleration doesn't vary along the height of the lift then the length of the lift is varying in its own rest frame. And you still need to choose what coordinates to work in, because you can't avoid relativity when you are asking about light.
  • #1
John Mcrain
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Elevator (2m height) is accelerate upward, light is at the top pointed toward flor of elevator.
Is time t=2m/c to light pass from top to bottom?

Bottom moving toward light,so time would be smaller then t=2m/c?
 
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  • #2
John Mcrain said:
Bottom moving toward light,so time would be smaller then t=2m/c?
In an inertial frame, yes.
 
  • #3
Dale said:
In an inertial frame, yes.
How explain smaller t, c increase(impossible), elevator become shorter then 2m ?

In frame of elevator t is also smaller then t=2m/c, once when light leave top it is not part of elevator and flor coming toward light?
 
  • #4
John Mcrain said:
How explain smaller t, c increase(impossible), elevator become shorter then 2m ?
The speed of light is only invariant in inertial frames of reference. It can differ in other classes of frame.

I'm not sure who is measuring what in your scenario, so it's difficult to know how to answer exactly. But note that, as measured in an inertial frame, the rate of a clock in the lift is varying, as is the length of the lift. This will have consequences for the speed of light as measured by an observer in the lift.
 
  • #5
John Mcrain said:
How explain smaller t, c increase(impossible), elevator become shorter then 2m ?
Obviously, the explanation is that the elevator is moving in the inertial frame. You already gave that explanation in your OP so I am not sure why you seem to be ignoring your own statements now.

John Mcrain said:
In frame of elevator
Before you ask any questions about the frame of the elevator you will need to define what you mean. Common choices would be Kottler Moeller, Rindler, or Lass coordinates.

See https://en.m.wikipedia.org/wiki/Rindler_coordinates

Once you choose the coordinates you choose to represent the frame of the elevator then the remainder of your questions can be answered
 
  • #6
Dale said:
Obviously, the explanation is that the elevator is moving in the inertial frame. You already gave that explanation in your OP so I am not sure why you seem to be ignoring your own statements now.

Before you ask any questions about the frame of the elevator you will need to define what you mean. Common choices would be Kottler Moeller, Rindler, or Lass coordinates.

See https://en.m.wikipedia.org/wiki/Rindler_coordinates

Once you choose the coordinates you choose to represent the frame of the elevator then the remainder of your questions can be answered
So I cant use same formulas as instead light is ball?
 
  • #7
Ibix said:
The speed of light is only invariant in inertial frames of reference. It can differ in other classes of frame.

I'm not sure who is measuring what in your scenario, so it's difficult to know how to answer exactly. But note that, as measured in an inertial frame, the rate of a clock in the lift is varying, as is the length of the lift. This will have consequences for the speed of light as measured by an observer in the lift.
light can be faster then c in non inertial frame?

Men in elevator meassure with stopwatch how long take the light to hit the flor.
 
  • #8
John Mcrain said:
So I cant use same formulas as instead light is ball?
Not if you want it to be relativistically correct. Of course, if you just want a rough approximation then that would be fine.

John Mcrain said:
light can be faster then c in non inertial frame?
Yes

John Mcrain said:
Men in elevator meassure with stopwatch how long take the light to hit the flor.
You still have to choose your coordinates for that.
 
  • #9
Dale said:
Of course, if you just want a rough approximation then that would be fine.
Ball in my video has a=10m/s2, what is acceleration of light?
 
  • #10
John Mcrain said:
Ball in my video has a=10m/s2, what acceleration I must use for light?
The problem is not the value of ##a##. You have to choose a coordinate system for the accelerated frame to get relativistically accurate results.

Why are you so resistant to making this choice?
 
  • #11
Dale said:
The problem is not the value of ##a##. You have to choose a coordinate system for the accelerated frame to get relativistically accurate results.

Why are you so resistant to making this choice?
I ask for non relativistic case, case where I use formula as in my video with ball
 
  • #12
John Mcrain said:
I ask for non relativistic case, case where I use formula as in my video with ball
The problem with that is that you don't have a static situation. If the proper acceleration doesn't vary along the height of the lift then the length of the lift is varying in its own rest frame. And you still need to choose what coordinates to work in, because you can't avoid relativity when you are asking about light.

The point that @Dale is making is that the answer you will get depends on the choice of coordinate system you choose. You don't know which to choose because you don't have a practical reason for doing the analysis, so there's no particular advantage to one over another. So flip a coin or whatever and pick one.
 
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  • #13
Ibix said:
And you still need to choose what coordinates to work in, because you can't avoid relativity when you are asking about light.
That mean I cant use formula from my video with ball.
 
  • #14
John Mcrain said:
I ask for non relativistic case, case where I use formula as in my video with ball
For a non relativistic case you can use the approach in the video, but that would be best in a different sub forum. The relativity sub forum is for relativity
 
  • #15
Dale said:
The relativity sub forum is for relativity
To be fair, this is in Classical. But it's relativity anyway if we need to discuss light in accelerating frames.
 
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  • #16
Ibix said:
To be fair, this is in Classical. But it's relativity anyway if we need to discuss light in accelerating frames.
Oops, that’s embarrassing.

@John Mcrain please decide if you want to discuss balls or light. If you want to discuss light then I will move this to the relativity forum. If you want to discuss balls then I will close this thread and you can start a new one focused on balls.
 
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  • #17
Dale said:
For a non relativistic case you can use the approach in the video,
How can I use this approach for light, if I dont know what is acceleration of light?
Dale said:
@John Mcrain please decide if you want to discuss balls or light. If you want to discuss light then I will move this to the relativity forum. If you want to discuss balls then I will close this thread and you can start a new one focused on balls.
I didnt know when I write my first post that belong to relativity..I think I wont go to relativity forum for now, it is too complicated..
And with ball answer is in my video...
 
  • #18
John Mcrain said:
How can I use this approach for light
You cannot. Balls are non relativistic. Light is the most relativistic thing there is.

John Mcrain said:
I think I wont go to relativity forum for now, it is too complicated..
And with ball answer is in my video...
Sounds good. I will close the thread then. When you are ready to discuss light please post in the relativity sub forum.
 
Last edited:

FAQ: Light in an accelerated elevator

What happens to light inside an accelerated elevator according to general relativity?

According to general relativity, light inside an accelerated elevator will appear to bend due to the equivalence principle. This principle states that the effects of acceleration are indistinguishable from those of a gravitational field. Therefore, an observer inside the elevator would perceive the light as bending, similar to how light bends in a gravitational field.

How does the frequency of light change in an accelerated elevator?

The frequency of light will experience a shift due to the Doppler effect. If the elevator is accelerating upwards, the frequency of light traveling upwards will appear to increase (blue shift), while the frequency of light traveling downwards will appear to decrease (red shift). This is analogous to the gravitational redshift and blueshift observed in a gravitational field.

Can the speed of light change in an accelerated elevator?

No, the speed of light remains constant at approximately 299,792,458 meters per second in a vacuum, even in an accelerated elevator. This constancy is a cornerstone of both special and general relativity. However, the path of the light and its frequency can be affected by the acceleration.

How does an observer inside the elevator measure the bending of light?

An observer inside the elevator can measure the bending of light by using a reference frame fixed to the elevator. By shining a beam of light horizontally and observing its trajectory, the observer will notice that the light beam curves downward, similar to how it would in a gravitational field. This curvature can be quantified to understand the effects of acceleration.

What experimental evidence supports the bending of light in an accelerated frame?

Experimental evidence supporting the bending of light in an accelerated frame comes from tests of the equivalence principle and observations of light bending in gravitational fields. One of the most famous pieces of evidence is the observation of starlight bending around the Sun during a solar eclipse, which confirmed predictions made by general relativity. Laboratory experiments with accelerating systems also support these predictions by demonstrating similar effects on light.

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