Exhibit 3: Supernovae
The "accelerating universe" is considered the most profound question in science. The only direct evidence is from Type Ia supernovae. Low redshifts increase linearly, according to Hubble expansion. High redshifts mysteriously curve upward, showing that ratio of an object's recession velocity over the speed of light v/c has been increasing. A child could see what was overlooked: What if redshifts appear to accelerate not because velocity v increases, but because c slows down?
We have M = R = t in Planck units. In MKS units that is R = ct:
GM = tc^3
c(t) ~ t^{-1/3}
R(t) ~ t^{2/3}
In the distant past of high-redshift supernovae, speed of light ci was greater than co today.
We then have a ratio of scale factor Ro today compared to the past:
Ro/Ri = (to/ti)^{2/3} = 1 + Z
ci/co = (to/ti)^{1/3} = sqrt(1 + Z)
When light of redshift Z was emitted, c was faster by sqrt(1 + Z). Apparent redshift is therefore decreased. This factor is negligible for low redshifts, where Z increases linearly. An object of redshift 1.0 recedes at 60% of our present speed of light. That is only 42% of c at the time its light was emitted. Apparent redshift of this object is just 0.57. Supernovae produce that light according to E=mc^2. Energy output is here doubled, for a magnitude shift of -0.75. Connect the dots, and the curve of Type Ia redshifts is precisely predicted without ethereal energies.
As many know, it is possible to believe that c is constant and the Universe is accelerating due to some repulsive "dark energy." One can believe that this energy inexplicably evolves to fit the redshift curve. It is also possible to believe you are the centre of everything and planets revolve around Earth in epicycles. No such repulsive energy has ever been observed in nature. DE does allow physicists to keep themselves employed filling journals with speculative ideas while calliing the problem unsolved.
One plane striking a building can be blamed on a fantastic accident. If two aircraft strike the same target, even the dullest know that there is a connection. Three completely independent lines of evidence indicate not just that c is changing, but that it slows at the rate GM = tc^3 predicts. Perhaps there is something to the Theory. A THIRD PLANE HAS STRUCK.
Labels: physics, speed of light
posted by L. Riofrio at 9:10 AM
6 Comments:
Imagine a lot of masses distributed in space. If they undergo gravitational collapse, the energy release would be the gravitational potential energy,
E = (M^2)G/R,
where R is a measure of the effective mean distance the masses would have to fall in the collapse.
If we apply this to the universe, the upper limit for R is
R = ct
where t is the age of the universe.
Hence
E = (M^2)G/(ct),
and remembering Einstein's mass-energy equivalence E=Mc^2 (you need that much energy to cause the big bang, because it was initially all energy and mass was produced from that energy in the early stages from radiation by the process of pair-production), we get
Mc^2 = (M^2)G/(ct)
Which cancels and rearranges to give:
MG = tc^3
which is your basic equation, which can also be checked dimensionally.
What fascinates me is that when I pointed this out, I think on Clifford's blog last year, someone (Jacques Distler?) said it was all nonsense because I wasn't using tensor calculus. I did tensor calculus while doing general relativity in a cosmology course years ago; it is irrelevant for this particular derivation.
I can't see why other people don't immediately grasp the point I'm making. Is it the presentation? Don't people understand gravitational potential energy? Don't they understand that initially the big bang consisted of energy E=Mc^2 which was partly converted into mass by pair-production at high energy (within a second)? What part of this is it that they don't understand?
R = ct is not a completely accurate assumption here because R is just the effective average fall distance for all the masses as seen in our reference frame, which will be somewhat less than ct. So R = fct, where f is a fraction (less than 1), but is is easy to show f must be a constant if the geometry is fixed (because the equation is scalable).
Hence MG = ftc^3 is correct (f ~ 1 as a first approximation, since in our reference frame most of the mass of the universe is at great distances approaching ct) and since f is constant, the equation implies that some constant must be varying (e.g., c or G or both). Hence these investigations into varying constants are vitally important.
I think the problem is that people look at such calculations and it looks "too simple", and they can't believe that straightforward reasoning is any use in physics. "If this is right, then why didn't Einstein, Dirac, or Feynman spot it half a century ago?" (The answer here is that Dirac and Teller investigated it but got it wrong, as I showed before.)
Another argument is that there are lots of people with "pet" ideas, and it is best to ignore them all and only to read peer-reviewed papers that have been checked by expert string "theorists".
What those people don't grasp is that there aren't really any "pet" ideas: there are just right, wrong, and not even wrong ideas. Science doesn't belong to an owner, like a pet dog.
String theory is still "not even wrong", so those guys must listen.
In my comment above for gravitational potential energy, I used
E = (M^2)G/R
which is of course only approximate. Strictly speaking the total gravitational potential energy of the universe (in our frame of reference of course) should be calculated by an integral to take account of the actual distribution (you then find that because of the variation of density with the age of the universe, the distant universe goes toward infinite density, but in practice this is offset by the way that the redshift of exchanged gravitons which cause the gravitational field will also tend toward infinity, cancelling out infinite density contributions from the early time universe; obviously this redshift effect is also why we don't see a bright glow from the early fireball of the universe at great distances - that radiation has simply been redshifted from infrared down to microwave background). I've been checking some of these integrals.
One very simple way to think of a collapsing sphere of mass of radius R = ct, is to consider the two hemispheres separately, each one being of mass m.
This means that M = 2m, so the gravitational potential energy equation becomes
E = (M/2)*(M/2)G/R
= (1/4)*(M^2)G/R
However, R = ct is an exaggeration since for distributed mass the average radius is less than ct.
As a result, we might have R equal to some fraction of ct, for example:
R = (1/4)ct,
which implies:
E = (1/4)*(M^2)G/R
= (1/4)*(M^2)G/[(1/4)ct]
= (M^2)G/(ct)
so inserting E=Mc^2 gives us
Mc^2 = (M^2)G/(ct)
Hence:
MG = tc^3.
I didn't mention the reason why the inertial energy equivalent of mass M in E = Mc^2 for the universe should be equal to its gravitational potential energy: it is because, from general relativity, inertial mass is equivalent to gravitational mass (which, being the charge of quantum gravity, has it's own quantum gravity force field around it, containing energy).
Because both types of mass are equivalent, the inertial energy equivalent of the mass M of the universe, E = Mc^2, should be equal to the gravitational potential energy equivalent of the mass of the universe M, E ~ (M^2)G/(ct)
This simple equivalence,
E = Mc^2 ~ (M^2)G/(ct)
implies
GM = tc^3.
So your formula not at all anti-general relativity, but is a statement equivalent to its most fundamental principle according to Einstein.
It is possible to put varying "constants" into Einstein's field equation of general relativity, but the analytical solutions for cosmology then become much harder if not impossible without computer calculations.
However, the continuously variable differential equations of tensors in general relativity are just a classical (continuum field) approximation anyway. You can't have continuous differential equations correctly representing discrete particles of mass/energy. It might work as a statistical approximation in some limits, but it will fall on small scales (where individual graviton interactions impart discrete kicks not smooth curvature) and on big scales (where redshift of gravitons will weaken gravitational interactions between masses receding from one another at relativistic velocities in an expanding universe). Any real quantum field theory should ultimately be capable of Monte Carlo evaluation; computer random simulation of quantum interactions which produce the forces, etc.
This is one of the things I want to investigate in detail.
Just to make the above comment crystal clear:
Einstein's equivalence principle of inertial and gravitational mass:
M(inertial) = M(gravitational).
Hence by E = Mc^2,
E = M(inertial)*c^2
= M(gravitational)*c^2
Here, the energy equivalent of the gravitational mass of the universe is equal to the gravitational potential energy of the universe.
This is because gravitational mass is quantum gravity charge, and quantum gravity relies on the potential energy of the gravitational field.
If the gravitational potential energy of the universe were different in value to Mc^2 where M is inertial mass, then Einstein's equivalence principle between gravitational and inertial mass would be violated.
It isn't. Hence, based on experimental findings, the gravitational potential energy of the universe should be equal to its Mc^2 energy.
Hence the reason why the geometry of the universe is flat. If gravitational potential energy is equal to the E=Mc^2 of the big bang, it is flat. If gravitational potential energy was the bigger, then the universe would collapse.
The physical mechanism for why the gravitational potential energy of the universe equals its inertial mass energy equivalent seems to be the mechanism for gravity itself. If gravity is powered by the expansion of the universe via Newton's 3rd law, both will have the same value, explaining Einstein's equivalent principle between inertial and gravitational mass:
As the mass of the universe accelerates outward, carrying an outward force F=ma according to Newton's 2nd law, then by Newton's 3rd law you get a reaction force which is equal and inward-directed. This inward force is carried by quanta, "gravitons", and causes gravitation and related curvature-like effects. Hence it is readily possible to not only use Einstein's equivalence principle to derive GM = tc^3, but it is also possibly to go further and to show why the equivalence principle exists in the first place. It exists because of Newton's 3rd law, which ensures that the outward force of big bang, of energy E = Mc^2, is exactly equal to the inward force which produces quantum gravity (my detailed calculations for this quantum gravity mechanism are at http://nige.wordpress.com/about/ ).
Could I add that I agree that the mainstream belief about the "acceleration" of the universe due to a small positive cosmological (dark energy) is wrong, although my perspective is different.
In October 1996, years before Perlmutter's software automated observations of supernovae at very large redshifts, the then editor of Electronics World kindly made available a paper I wrote via that issue's letters pages.
My starting point was that the normal Hubble expansion law
v = dR/dt = HR
is equivalent to acceleration
a = dv/dt = d(HR)/dt = H*dR/dt = Hv = (H^2)R.
Hence, Hubble's law is equivalent to an acceleration a = (H^2)R, which is significant at very large distances.
This leads to outward force F = ma and by the 3rd law, equal inward reaction force (delivered by gravitons, causing "curvature" and its effects such as gravity).
Smolin states in "The Trouble with Physics" that the acceleration observed by Permutter is actually very similar in magnitude to this Hubble acceleration (on the order 10^(-10) metres per second^2 or so).
However, the quantum gravity physics here is pretty complicated. You have force causing gauge boson radiation, gravitons, being exchanged between receding masses in an expanding universe. Over long distances, the recession of masses is relativistic, so the exchanged radiation will be received by each mass in a severely redshifted form (with little energy). This will severely decrease the effective value of the gravitational coupling constant, G, for the interaction.
The mainstream ignores this entirely by not correcting general relativity solutions for such obvious quantum gravity effects.
So the mainstream cosmological model, the Friedmann-Robertson-Walker metric, is found to underestimate the expansion velocity at extreme redshifts.
This underestimate of expansion velocity is because it assumes that redshifted gravitons exchanged over such extreme distances don't lose energy (they obviously do lose energy, because of Planck's law E = hf, which applies to quanta).
When you allow for this graviton redshift and other associated quantum gravity mechanism effects (which I've calculated), you find that gravitational retardation on the big bang is being seriously exaggerated by the Friedmann-Robertson-Walker metric.
The error of injecting a small positive cosmological constant (powered by "dark energy") into that metric to make it fit Perlmutter's data is that you are not correcting the error in the original Friedmann-Robertson-Walker metric: you are adding an ad hoc, false epicycle to cancel out the quantitative unwanted effect of the error, without actually removing the error.
These people don't understand physics. What they are doing is just what Ptolemy did. Ptolemy was a mathematician who didn't understand physics, but thought his model was beautiful and true, while ignoring the solar system proposed earlier by Aristarchus of Samos. Those who told Ptolemy he was wrong were ridiculed and insulted, and told to understand the math of epicycles ... things don't change much on a social level in physics!
Another nice and thoughtful comment. The mainstream string and "dark energy" pafaadigms are indeed frustrating in that they hold back real advances in physics. Nige's work in the 1990's explains the Universe much better than the Perlmutter group's ad hoc ideas. The similiarities to Ptolemy and Aristarchus should be compelling.
Post a Comment
<< Home