20041210, 09:10  #45  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×5,477 Posts 
Quote:
Paul 

20041210, 15:06  #46 
Aug 2003
Snicker, AL
7·137 Posts 
Measurements of light emitted shortly after the big bang show that some of the constants we consider to be absolutes maybe weren't so absolute at some point in time. I prefer to think of PI as a Newtonian absolute just waiting for an Einstein to show that its maybe not so fixed as we think. For instance, in the vicinity of a black hole would pi retain its value? I suspect not since that sliding scale for the speed of light would be moved up the range toward the time axis. I have absolutely no proof of this however, just speculation that constants aren't and variables don't.
Fusion 
20041210, 15:35  #47  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2·5,477 Posts 
Quote:
When asking about the value of pi "in vicinity of a black hole": which pi do you mean? If by pi you mean four times the value of the sum of the series 11/3+1/51/7+1/9 ... then it most certainly does have the same value near a black hole as it does here. If by pi, you mean the result of measuring the circumference of a circle embedded in a particular spacetime, measuring the diameter of that same circle and dividing one measurement by the other, you have no need to go anywhere near a black hole. Your dining room table will do. If you measure carefully enough (and you have to be very careful) you will find that the ratio is not the same as the value of the aforementioned series. Massenergy bends spacetime, according to GR, though spacetime is very, very rigid. The entire massenergy of the earth is enough to produce a radius of curvature of around one lightyear at the earth's surface. If you'd like to experiment with a more highly curved surface, consider the surface of a sphere. An infinitesimally small circle drawn on the sphere will have the ratio c/d (circumference / diameter) infinitesimally different from the pi which is the sum of that series. (What this says is that all surfaces are locally flat, and the GR equivalent is that as long as distances and durations are small enough, SR is valid.) Make the circle bigger, and the ratio will change. Eventually, when the circle is infinitesimally smaller than the equator of the sphere, the diameter passes infinitesimally close to a pole and the ratio c/d approaches the value 2. On a surface of negative curvature, and a saddlesurface is the classical example, c/d is always strictly greater than the sum of the series. On a surface of zero curvature (flat spacetime, or Euclidean space) the two values for "pi" are strictly equal. This is a long way from random numbers and even further away from Mersenne numbers, but fun nonetheless  IMO, but if the consensus is otherwise I'll drop this discussion. Paul 

20041210, 16:32  #48 
Aug 2003
Snicker, AL
1110111111_{2} Posts 
The measurements re constants that varied was in the news about a year ago. I don't remember the full context but the gist of it was that some of the physical constants as derived by measuring quasar light from the very early universe showed small but measurable variances from the expected values. It threw certain cosmological theories into a dither trying to explain the differences. There were implications for Planck's constant as well as a couple of others.
Re the value of pi, my intent was to say that pi near an area of highly curved space such as near a black hole would have a different value than pi in normal space. Essentially the same thing you posted above though the geometry would neither be sphere nor saddle. I read a well thought out discussion that the universe is approximately 150 billion light years across. This is based on observed oldest light of @13 billion years and taking into account the effect of expansion. It implies that there are parts of the universe that we can't see because light would not have had time to reach us yet. Our universe. The ultimate random event. Humanity? Probably only one of many billions. Fusion Last fiddled with by Fusion_power on 20041210 at 16:38 
20041210, 23:18  #49  
13×281 Posts 
Quote:
Ok where do I start, maybe I am dim on this... Dim Shane As variant (lol) Type 1a supernova proves a static universe(IMHO), without disproving an expansive one. I had already thought this before the finding, as I published on a website. The speed of light is fixed to the wavelength(meters), and yet we find this absurd opposite behaviour with 1a waves. It had been thought that the universe was slowing down in it's expansion, but now we also know that it speeding up. Am I on the same page? Shane.Brain = "Overload" 

20041211, 00:17  #50  
Dec 2003
Hopefully Near M48
2×3×293 Posts 
Quote:
Unfortunately, as with most science news headlines, the title somewhat distorts the actual scientific findings. The title implies that the Universe is about 156 billion light years in "diameter", but if you read into the body of the article, you'll see that this was not the finding. The actual result was that the Universe is at least 156 billion light years across, possibly more. However, if you read the actual scientific paper itself, written by Cornish et al. you'll see that even that is not wholly accurate. Actually, what the researchers did was examine different possible topologies (shapes) the Universe might take and compare them with observations. They were able to rule out the possibility that the Universe is less than 156 billion light years (they use the figure 24 Gpc, which is just a different unit) across for some topologies. Thus, in fact, it may still be possible for the Universe to be less than 156 billion light years across. You can read their findings at http://arxiv.org/abs/astroph/0310233 Last fiddled with by jinydu on 20041211 at 00:18 

20041211, 01:50  #51 
Aug 2002
500_{8} Posts 
Pi is a mathematical constant, not a physical constant.
The value of C is determined by physical measurement, the value of Pi is determined by first principles. 
20041211, 02:55  #52  
Nov 2004
14_{10} Posts 
Quote:
Quote:
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20041211, 04:40  #53 
Dec 2003
Hopefully Near M48
2·3·293 Posts 
Maybe I should try to restate my point then:
If I tell my computer to calculate pi to 2 decimal places, the outcome will be: 3.1 If I tell my computer to calculate pi to 3 decimal places, the outcome will be: 3.14 Furthermore, it can be proven mathematically that those are the only possible outcomes for 2 decimal places and 3 decimal places, respectively. It is impossible for the computer to output say, 3.2 in the first case. Last fiddled with by jinydu on 20041211 at 04:40 
20041212, 13:09  #54  
Nov 2004
2·7 Posts 
Quote:


20041212, 15:29  #55  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
25312_{8} Posts 
Quote:
There is no dispute, as far as I am aware, that your quantity pi is not a constant but depends on the curvature of the space. The mathematician's pi is indeed a constant and independent of the precise geometry in question. Paul 

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