Measuring pi using gravitational waves

[plodder]

obvs

https://mobile.twitter.com/CJHaster/sta ... 6128757761

[Gfamily]

My question is whether pi (as in circumference/diameter) is dependent on the curvature of spacetime.

[plodder]

I think that's factored into the mumble mumble

[dyqik]

My question is whether pi (as in circumference/diameter) is dependent on the curvature of spacetime.

It is. The proper distance in GR is path dependent, so the proper distance along a circular path about a mass is not π times the proper distance along a diameter (if a diameter is even uniquely defined).

See the Black Hole Image - measuring the distance travelled by a photon across the last stable circular orbit can mean taking a path that starts off moving away from the center depending on your choice of direction.

[Gfamily]

My question is whether pi (as in circumference/diameter) is dependent on the curvature of spacetime.

It is. The proper distance in GR is path dependent, so the proper distance along a circular path about a mass is not π times the proper distance along a diameter (if a diameter is even uniquely defined).

See the Black Hole Image - measuring the distance travelled by a photon across the last stable circular orbit can mean taking a path that starts off moving away from the center depending on your choice of direction.

That's interesting, does that mean that Euler's Identity (e^iπ + 1 = 0) is also dependent on the curvature of the universe?

[Holylol]

I think we should differentiate between the mathematical definition of pi, and its measurement in real life.

If you want to define pi using a circle as a mathematical concept, gravity doesn't play a role. But then if you want to apply it in the real world, your circle may not really be a circle anymore.

[dyqik]

My question is whether pi (as in circumference/diameter) is dependent on the curvature of spacetime.

It is. The proper distance in GR is path dependent, so the proper distance along a circular path about a mass is not π times the proper distance along a diameter (if a diameter is even uniquely defined).

See the Black Hole Image - measuring the distance travelled by a photon across the last stable circular orbit can mean taking a path that starts off moving away from the center depending on your choice of direction.

That's interesting, does that mean that Euler's Identity (e^iπ + 1 = 0) is also dependent on the curvature of the universe?

No, because that doesn't involve a ratio between a circumference and a diameter in 2 or 3 spacelike dimensions.

[Gfamily]

It is. The proper distance in GR is path dependent, so the proper distance along a circular path about a mass is not π times the proper distance along a diameter (if a diameter is even uniquely defined).

See the Black Hole Image - measuring the distance travelled by a photon across the last stable circular orbit can mean taking a path that starts off moving away from the center depending on your choice of direction.

That's interesting, does that mean that Euler's Identity (e^iπ + 1 = 0) is also dependent on the curvature of the universe?

No, because that doesn't involve a ratio between a circumference and a diameter in 2 or 3 spacelike dimensions.

Hmm, the reason I asked is that the derivation of Euler's Identity (AFAIK) does involve the McLaurin expansion of the trigonometric functions sin and cos, which means they map to a flat geometry. So in a sense it does.

[dyqik]

That's interesting, does that mean that Euler's Identity (e^iπ + 1 = 0) is also dependent on the curvature of the universe?

No, because that doesn't involve a ratio between a circumference and a diameter in 2 or 3 spacelike dimensions.

Hmm, the reason I asked is that the derivation of Euler's Identity (AFAIK) does involve the McLaurin expansion of the trigonometric functions sin and cos, which means they map to a flat geometry. So in a sense it does.

Only coincidentally. The Argand plane is a Euclidean 2-space, but it isn't a physical space or spacetime.

[MartinDurkin]

No, because that doesn't involve a ratio between a circumference and a diameter in 2 or 3 spacelike dimensions.

Hmm, the reason I asked is that the derivation of Euler's Identity (AFAIK) does involve the McLaurin expansion of the trigonometric functions sin and cos, which means they map to a flat geometry. So in a sense it does.

Only coincidentally. The Argand plane is a Euclidean 2-space, but it isn't a physical space or spacetime.

See this kind of stuff is why I come here, even if I only partially understand it.

[Holylol]

Only coincidentally. The Argand plane is a Euclidean 2-space, but it isn't a physical space or spacetime.

That's a much better way of saying it than what I tried to do.