
#1
Nov2903, 08:21 AM

P: 38

Is the value of Pi related to the curvature of spacetime?
Is it the value that it is because spacetime is more or less flat? If the universe were of a greater open or closed curve, would Pi be a different value? Thanks, Glenn 



#2
Nov2903, 09:17 AM

Sci Advisor
PF Gold
P: 2,226

Pi is a constant, so it's value is absolute. but if you take it as the ratio between the area of a circle and the square of it's radius then you are perfectly correct, it's value is dependent on the curvature of space time. If we imagine the universe (ignoring all other curvature) as negatively or postively curved then the ratio of a circle's area to it's radius squared would not by pi, but it would tend to pi the smaller the radius of the circle.




#3
Nov2903, 11:31 AM

P: 271

I fundamentally believe that it's related to the curvature of spacetime itself. If spacetime had a different curvature, I believe that would have a different value. For our 3dimensional space/time pairing, I suspect that 3.00000000000. . . would be the value if the cosmological constant were exactly one.
Some current workers in this field suggest that the graviton must be a supermassive particle. I doubt this, however. Even if they find a supermassive particle that they believe to be the mediator of the gravitational force, I think that eventually a very much less massive particle will turn up. This is, of course, rather muddied by the fact that their is a relationship between mass, momentum and energy that makes mass a variable for any given object or moment. The fact that no quantizable unit of mass has been found subatomically, even more fundamental than quarks, may be due to this relationship. 



#4
Nov2903, 12:01 PM

Sci Advisor
PF Gold
P: 2,226

Pi and Spacetime
What's the cosmological constant got to do with this? I think you mean the density parameter [itex]\Omega[/itex] which is equal to 1 when the curvature of the universe [itex]\kappa[/tex] is equal to zero.
Pi is not just a geometric property it is a number in it's own right and can only have 1 value and whatever the curvature of the universe this is not 3. Even in a nonflat space, the ratio of a circels area to it's radius squared can only equal three for certain sized circles in spaces with a certain curvature. In a truly flat space a circle will always have the ratio pi which is equal to 3.14..... I've never herad of the graviton evre being proposed as a massive particle as such a thing would go against what is known about gravity and what quantum field theory says. 



#5
Nov2903, 05:57 PM

Sci Advisor
P: 5,935

Pi is the ratio of the circumference to the diameter of a circle in Euclidean (plane) geometry. It is a mathematical constant and has nothing to with the physical geometry of the universe.




#6
Mar1508, 10:08 AM

P: 2

phi = 2 cos(pi/5). 



#7
Mar1508, 10:48 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879

Yes, "phi is related to pi by phi = 2 cos(pi/5)", but phi is not "characteristic of growth in the natural world" except in a few special situations where we can find a number approximately equal to phi. 



#8
Mar1508, 11:21 AM

Mentor
P: 16,470





#9
Mar1508, 11:38 AM

Mentor
P: 8,287

This thread is extremely old (4 and a half years old, in fact!). I suspect that when the post was made, PF had a different level strictness than it does now. I think this thread should be closed or, at best, moved to the mathematics forum, since this has nothing to do with relativity!




#10
Mar1508, 02:34 PM

P: 2





#11
Mar1508, 03:11 PM

Mentor
P: 14,433





#12
Mar1608, 04:45 PM

P: 15

Pi is totally mathematical constant and has no relation with experiment; it can be computed in many ways.
Check this link for more information (http://en.wikipedia.org/wiki/Computing_%CF%80). So if there is a curvature of space then the circle will have different ratio (circumference/radius) than (2π), and that is one way to know that the space is curved, so the flat circle is from our (Mind Inventions and Creation) and have nothing to do with Physics, and Math is not an experimental science it is an absolutely (A Mind Creation). 



#13
Mar1608, 11:19 PM

P: 213

pi is a mathematical constant...if you introduce curvature of spacetime into calculating the value of pi then you are introducing curvature of spacetime into circle...so upon introducing this curvature,circle cant be a circle becasue the distance from the center to its boundary would be different in some places if you introduce curvature of spacetime into circle and hence circle(curved spacetime) is not a circle and so the pi(curved spacetime) is not the pi...




#14
Mar1708, 02:04 AM

P: 19

I kinda support Jeebus's comments. Here is why i do believe so. If you look at the way relativity was discovered, it goes like this
1. Newton said  spacetime and fundamental observables like mass are absolute. 2. SR said  these are all relative 3. GR said  spacetime bends, they are not even straight. in all these, one thing is either assumed or taken as axiom  "Laws or nature are absolute, they will not vary". Laws of nature are essentially mathematics expressions. If you take realtivity to the next level you may get "Mathematics is not absolute either"  I know this goes against the current school of thought which was indeed started by Plato. What of Maths was relative. say  under heavy curvature of space time 1 electron + 1 more may not give 2 electorns. in other words let the number line be bent  this will distort PI, Exp and all other magical numbers. A straight numberline = euceldain geometry. wht if the number line was bent  bent against the imaginary axis ? 



#15
Mar1708, 11:22 AM

P: 869





#16
Mar1708, 12:18 PM

P: 28





#17
Mar1708, 01:06 PM

Mentor
P: 14,433

This is getting ridiculous. [itex[\pi[/itex] is an abstract mathematical concept. We will not need to change the value for [itex]\pi[/itex] if we find the universe is curved. We already know that the circumference of a circle of radius [itex]r[/itex] on the surface of the Earth is (assuming a spherical Earth), [itex]c=2\pi R_e \sin\frac r {R_e}[/itex] rather than [itex]c=2\pi r[/itex]. This fact does not alter either the value of [itex]\pi[/itex] or the equation of the radius of a circle on a Euclidean plane.




#18
Mar1708, 02:22 PM

P: 15

It is so Silly !!! Pi is totally mathematical constant, it will not be changed with any change in the space or time or atoms or electrons .............. If physics would try to change mathematics then all physics theories will be a trash, since that special relativity and the general relativity are based on (strong mathematical background + experiments) or else it will not be anymore an acceptable theory. So if you say that a physical theory will change mathematics, then you are saying that a theory will change itself.
This issue is a philosophically problem, it belong to the (Philosophy of Mathematics). 


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