EM Waves in a Rotating Frame: Questions & Answers

In summary, in Case 1, the observers see themselves rotating while the other observer seems to have stopped. In Case 2, the observers see each other tilted at an angle after they start rotating.
  • #1
Xynon
6
1
Hello there,

I have a question (two very similar questions) about the time and phase delay between rotating objects. I want to describe two extreme cases here: I would appreciate any helps.

Case 1
Imagine two observers (people with telescopes maybe) in space that are standing thousands of kilometers apart and directly facing each other in free space.

At time t0 they are standing still. At t1 they start rotating about the axis between them (their centers of bodies) with let's say 360 degrees/second in the same directions. And after a time delay, at t2 , the "news that the other observer had started rotating" arrives to each observer.

What would an observer see after t1 and t2 ?

My guess is that;
during from t1 to t2, an observer would see him/herself rotating relative to the other one. In other words, s/he would see the other one starting to rotate in the opposite direction.

But at t2, the other observer would seem to have stopped rotating relative this one. However, s/he would look standing tilted with an angle of maybe like 10-20 degrees.

Case 2

Same as in the Case 1 but let's replace the observers with huge horseshoe magnets, poles directly facing each other, looking like this:
< ....... >

(pulling or pushing orientation doesn't matter). Let's say at t0, they were pushing each other with F0.

Between t1 and t2, would the force start decreasing?

After t2, would they reach a stable force F2 which is smaller than F0? (Due to them "seeing" each other tilted with an angle)

I know the examples here are too extreme to be realistic but in order to render any other factors uneffective, I needed to exaggerate. Thank you for your time.
 
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  • #2
For Case 2, for the very long distances you specify, we must assume that the static magnetic field is negligible. However, an accelerating magnet can radiate an EM wave, so the second magnet will respond to an EM wave radiated by the first. But the radiated field depends on acceleration, not on velocity, so at t2 the second magnet will receive a sudden kick as a consequence of the start of movement of the first magnet.
 
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  • #3
tech99 said:
an accelerating magnet can radiate an EM wave
Is it easy deriving general equations for the magnitude, etc of such EM wave?
 
  • #4
davidge said:
Is it easy deriving general equations for the magnitude, etc of such EM wave?
No.
For an accelerating electric charge, there is the Lamour Equation (Wiki) which gives the radiated power, but I have never seen the equivalent equation for an accelerating magnet. There is always that niggling doubt in my mind about radiation by a magnet! After all, a magnet consists of moving charges anyway.
 
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  • #5
tech99 said:
No.
For an accelerating electric charge, there is the Lamour Equation (Wiki) which gives the radiated power, but I have never seen the equivalent equation for an accelerating magnet. There is always that niggling doubt in my mind about radiation by a magnet! After all, a magnet consists of moving charges anyway.
Oh, ok. Thanks.
 
  • #6
Xynon said:
Case 1 ...

Case 2 ...
If they saw each other through a telescope before they started rotating, they will see nothing after they started due to aberration of light, I am afraid to say. Aberration of light changes apparent position of illuminated object. I think they must tilt telescopes forward at corresponding to their velocity angle so as a ray of light could pass through the telescope. At least, they can find this angle by trial and error.
Related article: R C Jennison. Ray path in a rotating system 1963 Nature No 4895 p. 739
 
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Related to EM Waves in a Rotating Frame: Questions & Answers

What are EM waves in a rotating frame?

EM waves in a rotating frame refer to electromagnetic waves that are observed in a reference frame that is rotating or moving at a constant velocity. This phenomenon is known as the Sagnac effect and can have significant implications in the field of physics and engineering.

What is the cause of EM waves in a rotating frame?

The cause of EM waves in a rotating frame is the rotation of the reference frame itself. This rotation leads to a change in the propagation speed of the electromagnetic waves, resulting in a phase difference between the waves that leads to interference patterns.

How does the Sagnac effect affect measurements of EM waves?

The Sagnac effect can affect measurements of EM waves by causing a shift in the measured frequency of the waves. This shift is known as the Sagnac frequency shift and is proportional to the angular velocity of the rotating frame and the area enclosed by the path of the waves.

What are the applications of understanding EM waves in a rotating frame?

Understanding EM waves in a rotating frame is crucial in various fields such as navigation, geophysics, and optical communication. It allows for accurate measurements and corrections for the Sagnac effect, which is essential for the proper functioning of devices such as gyroscopes and interferometers.

What are some challenges in studying EM waves in a rotating frame?

One of the main challenges in studying EM waves in a rotating frame is the complexity of the mathematical equations involved. It requires a deep understanding of special relativity and differential geometry. Another challenge is the accurate measurement and correction of the Sagnac effect, which can be affected by factors such as temperature and vibrations.

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