Einstein postulated that the speed of light c is constant in a vacuum (presumably far from gravitational sources and independent of motion). Can the speed of light vary locally, as a perfect vacuum does not exist near Earth? - by Viktor T. Toth and Arif Saifee - Quora Question review

This document contains a review of the answer by Viktor T. Toth and by Arif Saifee on the question in Quora: "Einstein postulated that the speed of light c is constant in a vacuum (presumably far from gravitational sources and independent of motion). Can the speed of light vary locally, as a perfect vacuum does not exist near Earth?"
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Contents

• 1. Answer Review by Viktor T. Toth
• 2. Answer Review by Arif Saifee

Reflection

• Reflection 1 - Question Review

1. Answer Review by Viktor T. Toth

Indeed, the speed of light can vary.

Why did Einstein not mention this?

First, in a medium the speed of light changes in accordance with the medium’s index of refraction. In air, the difference is rather small; in water, it gets rather dramatic, as light travels roughly 25% slower underwater than in a vacuum.

That is not the behaviour Einstein studied. I expect he assuemed extra galactic space.

In gravitational fields, things get more interesting. When you make a local measurement, e.g., you measure the speed of light here in the gravitational field of the Earth in a laboratory, it will be what it always is, the vacuum speed of light. But to someone watching you from space, you would appear to move a little slower because of gravitational time dilation; and your ray of light in that lab will also appear slower. So to a distant observer, light in a gravitational field will indeed appear to slow down. This is an important contribution to what is known as the Shapiro delay, the delay that a ray of light or radio wave suffers as it travels through the gravitational field of a massive object.

You need much more information to understand this information.

This is something that is known, measured, and must be kept in mind for instance when radio signals are used to navigate spacecraft in the solar system. When the spacecraft is on the other side of the Sun, and the radio signal passes near the Sun, the delay can be substantial and if it is not calculated properly, it could lead to significant errors in the calculated position of the spacecraft.

2. Answer Review by Arif Saifee

No, it can never vary. A short answer to your question is, light, whenever it travels, is always travelling in empty space. When travelling through a denser medium (like glass), it either travels in the empty space between atoms of the medium, or hits, say an electron, and gets absorbed by it (so it doesn’t exist anymore). I’ll explain this later in this post. But because light travels only in empty space and because its speed in empty space is invariant ( ≈ 300 000 k m / s ), the speed of light cannot change. Also note that Einstein did not postulate that light speed is a constant. The constancy of the speed of light (& all EM waves for that matter) was a consequence of Maxwell’s laws of electromagnetism. Maxwell calculated the speed at which an electromagnetic wave travels to be:

c = sqrt(1/ε0 µ0) ≈ 3 × 10^8 ms ^−1

In the above equation, ε0 and µ0 are the electrical permittivity & magnetic permeability of empty space. When you plug in their values, you get approximately 300000 km/s . An interesting thing in the above equation is that 1 , µ0 and ε0 are invariants (constants). Their values, by definition, will remain unchanged in every frame of reference. Since the speed of light is derived from constants only, it is invariant as well. It cannot change, ever. This is completely counter-intuitive as nothing else in nature behaves like this. Isn’t motion always relative to something? That’s what Galilean relativity is based on. That’s what Newton assumed in his theory. An absolute light speed would mean that people travelling towards and away from a light source at 0.5c will still measure light speed as c . This was one reason why Maxwell’s theory did not generate sufficient interest upon publication.

In 1905, Einstein, using the prior work done by Lorentz and Henri Poincare, managed to successfully argue that the reason c remains invariant is because space & time are not invariant as was previously thought.
Speed = distance(space)/time . If light speed is constant, then space & time must shrink/stretch in lockstep so that light speed remains constant.

Time flows at different rates depending on several factors and space shrinks/stretches accordingly. An observer in one reference frame will have a local version of space & time, different from an observer in a different reference frame. When they both compute the speed of light, their local space/time equation will always return c .

Doesn’t gravity slow down light?

As per Einstein’s General Relativity, the presence of mass causes spacetime to curve - which we call as “gravity”. Hence, light, which is moving in spacetime, takes a curved (longer path) in a gravitational field, as compared to a shorter straight line if the mass wasn’t there. In the diagram below the green lines shows “geodesics” of space itself curving due to the presence of the Sun. Light always follows the geodesics and if space itself is curved, so will the path taken by light.

Hence gravity appears to slow down light, when in fact light is always travelling at c . Its just that the longer distance it is travelling due to curved spacetime might not be apparent to an observer, and so the observer might feel that light is slowing down when it travelling near, say, the Sun or any other sizeable mass.

If light speed is a constant, why does light travel slower in glass than in vacuum?

Light takes more time to travel through denser media like glass than in vacuum, not because it slows down, but because it gets absorbed and re-emitted by the electrons in the glass as well as gets scattered by glass atoms. The absorption/re-emission takes time. The scattering increases the path length. The net result is, the path light takes in glass is never the shortest path. It zig-zags all over the glass, and by the time it comes out, a lot of time has passed. To an observer timing it, it would appear that it slowed down. But whenever it was travelling in glass, it was always moving at c . Note that light can travel only in the empty space between glass atoms and as we know, its speed in empty space is c.

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