Discussion
Started 8 September 2021
What underlies the 4/3 scaling that applies to diverse phenomena?
Possibly: 4/3 scaling is a fundamental universal principle. Nothing underlies it. Why? It accounts for expanding cosmological space. Since 4/3 scaling brings 3 dimensional space, and hence everything else, into existence, it must be fundamental.
Can that be right? What favors and disfavors this notion?
Most recent answer
Another is 7/4. These may have common physical causes.
All replies (13)
Please, consider the fractal geometry approach. Maybe, it may help to better understand nature. this value appears in several fractal dimension estimates.
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Preston Guynn.
Thank you for the reply you posted yesterday (Sept 8).
Your reply included this important and relevant observation: "Schmidt et al., 1998 states in their section 6.2. The Luminosity Distance to SN 1995K, "we derive Δm15(B) = 1.15 ± 0.1 mag for SN 1995K"."
I should have addressed that expressly in
Preprint Theory of constant cosmic expansion
Please excuse my sloppiness.
The answer is:
The 4/3 theory assumes that the universe has 2 contemporaneous reference frames. One has 4 degrees of freedom consisting of 3 dim space and one DF motion (light motion proportional to time in the 4 DF reference frame).
The static space reference frame has 3 DF.
The difference in DF causes 3 DF space to expand in size by 4/3.
Why is there the discrepancy in measurement that you astutely identified in Schmidt et al 1998?
The current cosmological model assumes there is a single reference frame of cosmological space. The 4/3 law is inconsistent with the assumption of a single 3 DF reference frame.
Schmidt et al must have assumed that the inverse square law applied to the 3/4 decrease in SN brightness, hence, apparently a 4/3 higher squared distance, on the assumption the inverse square law applies. Take the square root of 4/3 (I can't believe I did not do that before your reply prompted me) and you find SQRT (4/3) = 1.15 (or acc to the MSoft calculator, about 1.15325625946). Spot on! Gosh, I wish I had done that before.
Many thanks, as always.
Best regards.
Bob Shour
Preston Guynn
I referenced your reply, and added my response, as a comment to the The Theory of Constant Cosmic expansion article.
Thank you again.
Considering phenomena in a three-dimensional volume (inside a sphere), we translate their description into a two-dimensional space (surface of a sphere). We get the ratio of the volume and surface of the sphere at a unit radius: 4/3. "We look into the volume of a sphere through its surface."
The ratio between the whole volume of the universe and the dynamical part of the same volume is about 1 : 0,74... (the quantity of the dynamical part is determined by an irrational number). In quantum field theory it means that the ratio between the volume of the Higgs field and the volume of the electric field in vacuum space is about 0,74 : 0,26 (total = 1,0).
Vector fields like the magnetic field and the field of Newtonian gravitation have no spatial dimension on their own. Einstein’s theory of general relativity describes the dynamical part of the volume of our universe – otherwise space cannot curve – thus the consequence is that the model of spacetime is restricted to 26% of the whole volume of the universe. The consequence is that gravity is an emergent force field (like Eric Verlinde proves for Newtonian gravity).
We may expect that ratios at the lowest scale size of reality that are present everywhere in the universe will “multiply” their ratio at larger scale sizes (like fractals do).
With kind regards, Sydney
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Take D=lnN/lnP,
for N=2,3,... and
P=primes 》3.
One Will find a good info theory
The first results are:
0,63;
0,68;
0,71;
0,67;
0,69;
0,68;
Preston Guyn.
You posted a reply on Sept 8, 2021 to the question:
Carroll and Ostlie in the 2d edition of their opus An Introduction to Modern Astrophysics discuss how distance is calculated for type IA SN. The inverse square law is implicit but is not express, in the R^2 on page 1042 (5th line). I today found a more explicit explanation of the inverse square law on this site:
This 3 page PDF is probably that of the physicist Francis Halzen at the U. of Wisconsin. On the first page the second equation says that the luminosity distance is (d_L)^2 etc.
From my perspective that is a disaster. On one hand, we have 1.15^2 approx 4/3, another strong support for the validity of the 4/3 law as a universal and general law of physics.. On the other, the 4/3 law asks the cognoscenti to accept not only the existence of two cosmological reference frames but also that the inverse square law cannot be applied to a redshifted luminosity distance. For a physics theory, that is a marketing disaster.
Otherwise, best wishes to you and regards
I agree with you, that this may be fundamental. This phenomenon appears because of the dual nature of the universe, where certain phenomena can sometimes be described as a particle and at other times as a wave. For a spherical particle, the dimensionless factor is 4pi/3, and for a wave or wave length, the dimensionless factor is 2pi. The ratio of these two dimensionless factors is 2/3. 4/3 is simply a multiple of this 2/3 relationship.
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Suppose instead, that dimensional capacity, a simple principle embedded but unnoticed in Galileo’s 1638 strength of materials scaling explains dark energy. The scaling principle is that scaling weight by exponent 3 requires the cross-sectional area of weight-bearing bone to get fatter by scaling by 3/2 relative to scaling of weight. Weight has 3/2 the dimension of area, area gets bigger by 3/2 disproportionately, so there is enough bone mass to support increased weight.
For dark energy, suppose the 4 dimensions of space + light motion results in 3D space getting fatter, so 3D radial distances are 4/3 of 4D distances.
As in :
Preprint Flowchart for deriving 4/3 scaling
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Apart from space-time, are there any other mathematical models of physical phenomena using a fourth dimension?
I searched yesterday and could not find any references, apart from hypercubes etc, to mathematical modeling using 4 dimensions other than my articles on arXiv and RG. That may explain why the role of 4/3 scaling has been unnoticed by physics.
I think a fourth dimension does play a role in modeling:
3/4 metabolic scaling.
Peto’s paradox
Brain weight scaling
4/3 fractal envelope of Brownian motion.
Clausius 1860 article on gas molecular mean path lengths.
Waterston on the energy to maintain a levitating elastic plane in a gravitational field (Roy Soc 1892 publication of 1845 submission).
Dark energy.
Are there any others?
Several articles on RG discuss 4/3 scaling, which involves the 4th dimension, including:
Preprint Dark energy modeled by scaling
Preprint Flow as a fourth dimension
and several other RG articles back to .
Is there a quantum gravity theory that can generate entire table of standard model particles with a single formula?
A quantum gravity theory based on the equivalence of gravitational and relativistic mass is developed from Newton's inverse square law which assumes a form of Schrodinger like wave equation. Solution of this wave equation generates the entire table of standard model particles.Is there a comparable theory that can do the same thing?
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