3 ms·

> 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 met

by orlp 2y ago

> 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.

Zamicol 2y ago
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.
mattashii 2y ago
> 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.
- Thorondor 2y ago
  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.
  - dxbydt 2y ago
    extraordinary. you’ve demolished his argument with purely dimensional analysis. bravo!
ajnin 2y ago
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.
- cryptonector 2y ago
  The point was that we wouldn't be able to tell that there was a change, not that a change couldn't happen.
- cthalupa 2y ago
  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.

by orlp 2y ago

Zamicol 2y ago

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.

mattashii 2y ago

> 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.

Thorondor 2y ago
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.
- dxbydt 2y ago
  extraordinary. you’ve demolished his argument with purely dimensional analysis. bravo!

ajnin 2y ago

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.

cryptonector 2y ago
The point was that we wouldn't be able to tell that there was a change, not that a change couldn't happen.
cthalupa 2y ago
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.