Measuring pi using gravitational waves

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plodder
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Measuring pi using gravitational waves

Post by plodder » Wed May 13, 2020 12:59 pm


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Gfamily
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Re: Measuring pi using gravitational waves

Post by Gfamily » Wed May 13, 2020 1:11 pm

My question is whether pi (as in circumference/diameter) is dependent on the curvature of spacetime.
My avatar was a scientific result that was later found to be 'mistaken' - I rarely claim to be 100% correct

plodder
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Re: Measuring pi using gravitational waves

Post by plodder » Wed May 13, 2020 1:20 pm

I think that's factored into the mumble mumble

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dyqik
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Re: Measuring pi using gravitational waves

Post by dyqik » Wed May 13, 2020 7:19 pm

Gfamily wrote:
Wed May 13, 2020 1:11 pm
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.

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Gfamily
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Re: Measuring pi using gravitational waves

Post by Gfamily » Wed May 13, 2020 10:16 pm

dyqik wrote:
Wed May 13, 2020 7:19 pm
Gfamily wrote:
Wed May 13, 2020 1:11 pm
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?
My avatar was a scientific result that was later found to be 'mistaken' - I rarely claim to be 100% correct

Holylol
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Re: Measuring pi using gravitational waves

Post by Holylol » Thu May 14, 2020 7:02 am

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.

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dyqik
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Re: Measuring pi using gravitational waves

Post by dyqik » Thu May 14, 2020 1:30 pm

Gfamily wrote:
Wed May 13, 2020 10:16 pm
dyqik wrote:
Wed May 13, 2020 7:19 pm
Gfamily wrote:
Wed May 13, 2020 1:11 pm
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.

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Gfamily
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Re: Measuring pi using gravitational waves

Post by Gfamily » Thu May 14, 2020 1:43 pm

dyqik wrote:
Thu May 14, 2020 1:30 pm
Gfamily wrote:
Wed May 13, 2020 10:16 pm
dyqik wrote:
Wed May 13, 2020 7:19 pm


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.
My avatar was a scientific result that was later found to be 'mistaken' - I rarely claim to be 100% correct

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dyqik
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Re: Measuring pi using gravitational waves

Post by dyqik » Thu May 14, 2020 1:55 pm

Gfamily wrote:
Thu May 14, 2020 1:43 pm
dyqik wrote:
Thu May 14, 2020 1:30 pm
Gfamily wrote:
Wed May 13, 2020 10:16 pm


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
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Re: Measuring pi using gravitational waves

Post by MartinDurkin » Thu May 14, 2020 2:14 pm

dyqik wrote:
Thu May 14, 2020 1:55 pm
Gfamily wrote:
Thu May 14, 2020 1:43 pm
dyqik wrote:
Thu May 14, 2020 1:30 pm


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
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Re: Measuring pi using gravitational waves

Post by Holylol » Thu May 14, 2020 4:04 pm

dyqik wrote:
Thu May 14, 2020 1:55 pm
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.

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