The Response of chat-GPT, about Michelson-Morely Experiment

However according to special relativity, the maximum speed is the speed of light, and this violates the fringe shift expectation. I mean, is the assumption wrong, and can fringe shift not prove the non-existence of any medium or ether?

ChatGPT said:

ChatGPT

You’re absolutely correct in pointing out that special relativity places constraints on the assumptions underlying the Michelson-Morley experiment. Let’s analyze this step by step to reconcile these ideas and address your question about whether the experiment can truly prove the non-existence of a medium or ether.

1. Fringe Shift Expectation and the Classical Assumption

The Michelson-Morley experiment was originally based on classical physics, which assumed:

1. Light propagates through a medium called the ether (similar to how sound propagates through air).
2. The speed of light would depend on the motion of the observer or apparatus relative to this ether, using vector addition: c′=c±vc' = c \pm vc′=c±v where vvv is the relative velocity of the apparatus to the ether.

Under this assumption, a fringe shift was expected because the light traveling parallel to the ether wind would take longer to traverse the arm of the interferometer compared to the perpendicular arm.

2. Special Relativity: Challenging the Assumption

Einstein’s special relativity fundamentally changed the framework:

1. Speed of Light is Constant: The speed of light is invariant and does not depend on the motion of the source or observer.

c′=cc' = cc′=c

regardless of vvv.

1. No Vector Addition of Light Speeds: Velocities in relativity combine via the relativistic velocity addition formula, ensuring that no object or signal can exceed the speed of light:

u′=u+v1+uvc2u' = \frac{u + v}{1 + \frac{uv}{c^2}}u′=1+c2uvu+v

For light (u=cu = cu=c), this simplifies to u′=cu' = cu′=c, irrespective of the relative velocity vvv.

1. Relativistic Effects: Special relativity introduces effects like: Length contraction: L′=L1?v2c2L' = L \sqrt{1 - \frac{v^2}{c^2}}L′=L1?c2v2, Time dilation: t′=t1?v2c2t' = \frac{t}{\sqrt{1 - \frac{v^2}{c^2}}}t′=1?c2v2t, Relativity of simultaneity: Events occurring simultaneously in one frame are not simultaneous in another.

These effects cancel out any measurable difference in light travel times between the two arms of the interferometer, leading to the null result.

3. Can Fringe Shift Prove the Non-Existence of Ether?

The null result of the Michelson-Morley experiment is often interpreted as evidence against the ether. However, this interpretation has limitations:

1. Fringe Shift Assumption is Based on Classical Physics: The expectation of a fringe shift relied on the classical assumption that the speed of light changes relative to the motion of the apparatus through the ether. Special relativity invalidates this assumption because light’s speed is constant, independent of any medium.
2. Null Result Does Not Prove No Medium Exists: The null result only disproves the classical stationary ether hypothesis, which assumed a preferred reference frame for light propagation. It does not rule out the possibility of a medium that is: Isotropic: The same in all directions, with no detectable “ether wind.” Co-moving: A medium that moves with the Earth, making relative motion undetectable. Modern Concepts: For example, the quantum vacuum can be thought of as a medium but behaves fundamentally differently from the classical ether.
3. Special Relativity's Postulates Are Independent of Ether: Special relativity does not require the absence of a medium. It only states that: The speed of light is invariant in all inertial frames. The laws of physics are the same in all inertial frames. These postulates are consistent with a null result, regardless of whether a medium exists.

4. Is the Assumption Wrong?

Yes, the classical assumption underlying the fringe shift expectation is wrong under special relativity. The null result of the Michelson-Morley experiment:

• Does not prove that no medium (ether) exists.
• Only shows that if a medium exists, it does not produce observable effects consistent with classical ether models (e.g., anisotropic speed of light).

This limitation means the experiment alone cannot disprove all possible mediums, only the classical stationary ether.

5. Modern Interpretations

While the Michelson-Morley experiment was crucial historically, modern physics no longer relies on it to address the concept of a medium:

1. Quantum Vacuum as a “Medium”: In quantum field theory, the vacuum is not empty but filled with virtual particles and fields. This can be thought of as a kind of medium, but it does not influence the speed of light in the way the classical ether was expected to.
2. Special Relativity Replaces Ether: The invariance of the speed of light and the relativity of motion make the concept of a classical ether unnecessary.

6. Conclusion

The null result of the Michelson-Morley experiment does not definitively prove the non-existence of any medium or ether. It only disproves the classical ether hypothesis with anisotropic effects. Under special relativity:

• The speed of light remains constant regardless of the medium.
• The expected fringe shift assumption is invalid because relativistic effects cancel out the path difference.

Thus, the experiment cannot be used to prove there is no medium in space—it only rules out the classical stationary ether as a framework for understanding light propagation. This limitation is why physicists have moved to broader theories like quantum field theory to explore the nature of space and light propagation.

?