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Comment by cryptonector | Hacker News Reader

The speed of light will always be seen to be the same no matter what, no matter where you are, no matter when you are. That's because we measure the speed of light with light, and we measure distances using light or light-by-proxy (because the electronic interactions that make normal forces what they are... electronic and subject to the speed of light, as is everything else).

Other constants might change, but it would be very surprising if the speed of light (as observed locally) could possibly vary.

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c is no longer measured, it is defined, and unless some contradiction to special relativity is discovered, c cannot change. If the speed of causality changes, then our measure of distance would change. For example, if c halves in some sense, then this means light travels half as far during N ticks of a clock, and the meter will halve (and all internet latencies will approx double!). If we keep the old meter, then we might say c has changed; it's truly a matter of definition (and practicality) at that point.

Same goes for their new thorium “clock”. They define it as their unit to measure everything else. They assume that all constants may be changing but not their thorium clock. I think this is an unjustified assumption.

If they detect that the change there would be a strong incentive replicating the setup as well as to put into scrutinity. Academia even with its faults is a very good institution for that.

Wouldn't a different speed of light impact the Schwarzschild radius of black holes of a given mass?

Assuming that you can create a standard clock, and given a black hole of standard mass, you can then measure speed of light in black hole radii per unit of time, which will differ with different speeds of light.

> Wouldn't a different speed of light impact the Schwarzschild radius of black holes of a given mass?

No it wouldn't. Our fundamental unit of distance (the meter) is defined in terms of the speed of light, so the radius will stay exactly the same, in meters.

> Our fundamental unit of distance (the meter) is defined in terms of the speed of light, so the radius will stay exactly the same, in meters.

Why so?

The Schwarzschild radius formula (r(s) = 2 * G * M / c²) uses c² as dividing constant. So when the speed of light is reduced by half, the radius of a black hole of the same mass will be larger by a factor 4.

Add to that the reduced distance light travels in the same time, and you'll get that the time light takes to travel the distance equivalent to the schwarzschild radius of a black hole with iso-mass is 8x larger in a universe with a speed of light 1/2 that of ours, assuming no other constants have been modified.

You're ignoring the units of G. The gravitational constant has units N * m^2 / kg^2 = m^3 / (kg * s^2). That contains a length unit raised to the third power, which exactly balances the factor of 8 that you identified.

extraordinary. you’ve demolished his argument with purely dimensional analysis. bravo!

Black holes also frequently send ambassadors to the White House so they can comply with US law. Human leadership in physical law is well respected universally.

If you take a piece of string to measure the radius, and then later c changes and you measure it again, the two pieces of string will have a different length when put next to each other. Saying it doesn't change because the length of the meter changed in the meantime is playing with words. The reason humans came up with a definition based on light is the assumption that c is constant and thus would be a more reliable choice as a standard than some physical bar of metal kept in Paris. But if the constant is not constant after all then something else will be needed as reference.

The point was that we wouldn't be able to tell that there was a change, not that a change couldn't happen.

We're inside the system (I don't mean this in the 'we're in a simulation' sense) - changes fundamental to how the system works are not necessarily measurable to us. It's one thing if the speed of light is localized and the changes are visible at different scales/distances. It's another if it's universal and changes - you have to understand that the speed of light is fundamental to how things works. It influences things like electromagnetic forces, which define atomic structure.

The speed of light changing would mean that even a physical object like a meter long ruler would also change.

Which is why, to my layperson understanding, this is such an exciting field of study - the different fundamental forces in play with these nuclear clocks might enable us to catch relative changes to the fine structure constant, which includes the speed of light as a component.

We can try to use gravitational waves (speed of gravitation propagation) to measure length.

Gravitational waves travel at the speed of light as well. So if the speed of light changes, so would the speed of gravity waves, presumably - otherwise, they would probably not be equal today (though of course it could always be a coincidence).

Gravitational waves and light travel at the same speed in a vacuum.

What if you took a very very very long piece of glass and sent both gravity waves and light waves through it?

The light will be slowed down. Google tells me that there is something analogous to the refractive index for gravity waves, so there should also be some slowing of the gravity waves, but would the optical refractive index and the gravitational refractive index be the same?

I'd expect that it would not be the same. The optical refractive index if I recall correctly doesn't depend on the masses of the particles that make up the medium it is traveling through. Just charge and arrangement.

Gravity waves should only depend on mass and arrangement.

The speed of light in a medium is always some constant specific to that medium times c. If c changes, the constant will not be affected. So I don't see how you could use the speed of light in a medium to deduce anything about c. The same logic applies to gravitational waves. And as long as the speed of gravitational waves is always equal to the speed of light, the relative values of the two will still not change.

Say old light speed in glass is k*c1, new speed is k*c2. Old gravity wave speed if n*c1, new is n*c2. How do you you use these numbers to find out if c1 == c2 or not?

Speed of light can also be derived from the speed of a signal through a length of wire.

I think the point is that if the speed of light changes, so does the length of the wire.

Basically. I suppose that ε0 and μ0 could change in different ways such that c remains the same, or in different ways such that c does change but the change might be noticeable.

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