This has been a busy week, but the GM=tc^3 thread
at Counterparts continues! This forum is run by fans of the band Rush, who have more varied interests than most scientists. Rush has a new album and tour this year! My post from Sunday:
Hello All: Your interest is most appreciated. In this exciting year of a new Rush album and tour (in Houston September 25), it is very nice to see you take time for this thread. I've been quite busy with experiments involving the Moon, but I will answer your curiosity as much as possible. Special thanks to Nunavuter, who obviously knows a lot about science:
"The biggest revolution in cosmology since Einstein may be quietly brewing.
"The speed of light may not be as rock-steady as it has been deemed to be. Rather, the value of this fundamental constant may be changing -- slowing down -- as time passes.
"A number of observations made in recent years have pointed in this direction. If verified, we can bid goodbye to both the Inflationary Model of the early universe, and dispense with the idea of Dark Energy."
Thank you, Nuna, for your thoughtful words. To explain this Universe in a nutshell: Relativity states that Space and Time are one phenomenon, related by c. Applied to the Universe as a whole. its characteristic radius R would be our timelike distance from the Big Bang. R = ct, where t is about 13.7 billion years. As time t increases, the Universe expands.
We can imagine the Universe as a sphere of 4 dimensions, where the 3 dimensions we inhabit are confined to the surface. There is no centre in Space, but there is a centre in Time which we call a Big Bang. The fourth dimension, Time, measures our increasing distance from that centre. A spherical Universe was promoted by Einstein, Pascal, and even Edgar Allen Poe.
The Universe can't expand at the same rate forever, for mass and gravity slow it down. Speed of light c is further related to t by GM=tc^3. There are a number of ways to derive this, which Space does not allow me to describe. We can equate a particle's rest energy to its potential. We can also calculate the orbital velocity of photons orbiting a mass M. GM=tc^3 may also be derived from General Relativity. In Planck units, the two expressions combine in the even simpler form M = R = t.
To Quote Valium: "Another revolution that won't be televised." To quote Bastille: "You just KNOW that something is right, but it's going to take 100 years of 'proper data collection' to prove you right. And then you still have to fight the media and the politics."
Perhaps it would be nice to have more press, but the current media narrative focuses on "dark energy" and the failure of scientists to explain it. Most people, even its proponents, doubt that DE really exists. The hypoithetical reoulsive energy is considered a placeholder until something better comes along. Publishing papers about changing c is still quite difficult, so I appreciate your finding this. However there are ample reasons for optimism:
The inflationary paradigm is 30 years old with no compelling idea for its cause. Faster-than-light inflation violates both the First Law of Thermodynamics (energy conservation) and Relativity's stipulation that nothing travels faster than light. Inflation can never be proven--we can not time travel to the first 10^(-33) seconds to observe inflation, or even approach the titanic energies near the Big Bang.
It is impossible to prove the speed of light constant, because a better measurement can always prove that foolish. Scientists must construct elaborate hypotheses, complete with dark fudge factors, based on fixed c. There are many ways to measure c changing, some of which are being investigated.
As you may have seen in http://riofriospacetime.blogspot.com, NASA has allowed a scientist access to priceless Apollo samples from the Moon. The lunar surface is over 4 billion years old, and may offer a record of the Sun's variability. Additional data from the Lunar Laser Ranging Experiment, some of which is still unpublished, offers compelling evidence that c has changed.
Finally, Roger Rigid should be encouraged for trying to calculate M. However in the MKS (meter-kilogram-seconds) system, age of the Universe t is 4.34 x 10^17 seconds. Corrections are added below:
Roger: "Of the 4 variables in Louise's formula, only one is currently a guesstimate - M (the mass of the universe). The others are pretty firmly fixed.
c = 299,792,458 m/s
t = 13,750,000,000 (13,750,000,000 yrs = 4.34 x 10^17 sec)
G = 6.67428 x 10^-11
"Rearranging Louise's formula:
M = (tc^3)/G
With corrections, we get M = 1.75 x 10^53 kg. This is very close to Roger's observational estimate:
"From observation (according to wiki), we can predict that the number of stars in the universe is about 9 x 10^21.
The mass of our Sun is 2 x 10^30 kg. If our Sun is of average size for a star, the total star mass in the universe is about 1.8 x 10^52 kg."
So, Roger's estimate of star masses is very roughly 10% of M. As readers of the 2004 paper know, the baryons that stars are made of are predicted to total 4.507034%, as also observed by WMAP. From quantities measured in a lab (speed of light, graviational constant) and visible through a telescope (age of Universe, calculated from Hubble recession) one can calculate the mass of the Universe!
In conclusion, though science may appear to be gripped by dark energies, there is a light of hope. It may be possible to find the size, shape and mass of the Universe. These can be calculated from quantities found in the lab. As Aritotle suggested long ago, we may predict our Universe from pure math. It could be simple as M = R = t.
Again I appreciate the intelligence of Rush fans and your interest in diverse subjects like science.