Rate of Time/Mass: Is There a Constant?

[CuriAus]

Is there a constant for the rate at which time slows relative to the amount of mass? If so would there be a base measure eg time being present with 0 mass

 

[Ibix]

Is there a constant for the rate at which time slows relative to the amount of mass? If so would there be a base measure eg time being present with 0 mass

Time does not slow, although you will often find it stated in popsci sources that it does. A better way of phrasing it is that clocks at a lower gravitational potential tick slowly compared to clocks at a higher potential. The tick rate for a stationary clock hovering at radius $r$ is $\sqrt{1-2GM/c^2r}$ ticks per tick of a clock at infinity. Note that this goes wrong at $r=2GM/c^2$ and lower - the event horizon of a black hole. This is one manifestation of why it's wrong to say "time is slow near mass".

I don't really know what you mean by "a base measure". We usually measure time in seconds, and there's no reason to think that a second measured in one place is more of a "base measure" than any other. I am perfectly entitled to think that a clock at infinity ticks fast, just as the owner of that clock could look at mine and say mine ticks slowly. Neither viewpoint is wronger or righter than the other.

 

[CuriAus]

Time does not slow, although you will often find it stated in popsci sources that it does. A better way of phrasing it is that clocks at a lower gravitational potential tick slowly compared to clocks at a higher potential. The tick rate for a stationary clock hovering at radius $r$ is $\sqrt{1-2GM/c^2r}$ ticks per tick of a clock at infinity. Note that this goes wrong at $r=2GM/c^2$ and lower - the event horizon of a black hole. This is one manifestation of why it's wrong to say "time is slow near mass".

I don't really know what you mean by "a base measure". We usually measure time in seconds, and there's no reason to think that a second measured in one place is more of a "base measure" than any other. I am perfectly entitled to think that a clock at infinity ticks fast, just as the owner of that clock could look at mine and say mine ticks slowly. Neither viewpoint is wronger or righter than the other.

Thanks for the reply Ibix, I do understand that time is relative to the observer. When talking about mass distorting space time would then time be equally distorted to distance ie they both actually don’t change? Thanks

 

[Ibix]

Thanks for the reply Ibix, I do understand that time is relative to the observer. When talking about mass distorting space time would then time be equally distorted to distance ie they both actually don’t change? Thanks

I'm afraid that this doesn't really make sense.

Any observer anywhere can use their own rulers and clocks and (as long as they stay in a windowless box) they cannot tell if they are in a region of curved spacetime or not. This isn't because "time and space are equally distorted", though. It's for much the same reason that you can treat your kitchen floor as a flat plane even though it's on the curved Earth - over small regions, the effects of its non-flatness are negligible.

However, if they look outside their windowless box they can see other clocks and compare tick rates. When they do that, they will see clocks higher up ticking faster compared to those ticking lower down. The point I was making is that neither the higher nor the lower clock is "right". It isn't that "time and distance change", it's that there are complexities in comparing times and distances measured in one place to those compared in others.

Another analogy to the surface of the Earth: stand near the south pole (in deference to your user name) and lay a meter rule due east-west. Extend a line due north through one end of the ruler and another due north through the other end. Those lines will cross the equator far more than a meter apart. This doesn't mean that a meter at the equator is somehow different to a meter near the pole. It just means that drawing "straight" lines on the surface of the Earth is not the same as doing it on a flat surface. Spacetime is not spherical but it is curved, and comparing times at a distance means drawing lines of "now" through each end of a timelike distance in spacetime. Just like the lines through the ends of the meter rule don't stay one meter apart, these lines don't stay one second apart. Just like one meter at the equator isn't different to one meter at the pole, one second close to a mass isn't different to one second far from the mass. But directly comparing them is tricky.

 

[Dale]

Extend a line due north through one end of the ruler and another due north through the other end. Those lines will cross the equator far more than a meter apart.

Nice example!