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ravisastry
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Hi, this thought came to my mind..not sure how correct this is. In extreme gravity, the space curves. Will the value of Pi change in this case, for a circle near such gravity ? pi = circumference/diameter.
In general the ratio of circumference to diameter for a circle varies with the size of the circle and the nature of the distance metric (which depends on geometry). In Euclidean space and using the Euclidean norm the ratio is constant and is equal to pi by definition. In any other space, or any other metric, the ratio of circumference to diameter may or may not be equal to pi. This does not mean that pi has a different value in that space / with that metric.ravisastry said:Will the value of Pi change in this case, for a circle near such gravity ? pi = circumference/diameter.
D H said:This does not mean that pi has a different value in that space / with that metric.
bcrowell said:Except in Indiana, where it equals 3.
ravisastry said:pi is a component of the fine structure constant and what i was thinking was...light follows curved path near high gravity. will the fine structure constant be different near such gravity because of pi ?
Yes. An angle is a local thing, and the local geometry of spacetime is always flat.Mentz114 said:Isn't the angle all the way around a circle always 2 pi ? And similarly with solid angles ?
Completely agree. I added a graph to show this. If we measure the ruler distance between R and R+1 for decreasing values of R we observe that the ruler distance increases. Also, observe the behavior of the radar distance (total roundtrip time) in an additional graph.pervect said:By definition, we know the circumference of a circle at Schwarzschild coordinate R is 2*pi*R, and the area is 4*pi*R^2 - that's how the schwarzschild radial coordinate R is defined. What we don't know is the "radial distance to the center of the black hole". The question is probably basically meaningless. Among other issues, inside the black hole, r is not a spatial coordinate - i.e. if we consider two nearby points (r,t) and (r+dr,t), there is a timelike separation between these points, not a spacelike separation.
I've no idea what you mean by this. If [itex]\theta[/itex] and [itex]\phi[/itex] are both zero, you must be talking about a radial straight line, not a circle.Passionflower said:(we assume theta and phi is 0, so the circle is drawn 'flat')
Aarg...I see my mistake.DrGreg said:I've no idea what you mean by this. If [itex]\theta[/itex] and [itex]\phi[/itex] are both zero, you must be talking about a radial straight line, not a circle.
Extreme gravity refers to extremely strong gravitational forces, such as those found near massive objects like black holes. These forces can distort the fabric of space-time, causing changes in the mathematical constant Pi. Specifically, extreme gravity can cause Pi to deviate from its expected value of 3.14159...
Scientists use various methods, such as mathematical modeling and observations of astronomical phenomena, to study the effects of extreme gravity on Pi. They also conduct experiments using specialized equipment, such as high-precision clocks and lasers, to measure the changes in Pi caused by extreme gravity.
Studying the impact of extreme gravity on Pi can help us better understand the laws of physics and the behavior of space-time. This knowledge can also be applied to various fields, such as astrophysics and engineering, to improve our understanding of celestial objects and develop better technologies for space exploration.
Yes, there have been several instances where extreme gravity has been observed to cause changes in the value of Pi. For example, the gravitational pull of a supermassive black hole at the center of a galaxy can cause the orbits of stars around it to deviate from their expected paths, resulting in changes in the value of Pi.
While extreme gravity can cause Pi to deviate from its expected value, it cannot change Pi to be a completely different value. This is because Pi is a mathematical constant and its value is determined by the ratio of a circle's circumference to its diameter, which cannot be altered by external forces.