Thoughts on a Slowing Speed of Light
Are the spinning spheres that compose the universe always decelerating?
The more distant a galaxy is, the longer the wavelength of light it emits. The most popular explanation for the observed redshift is that galaxies are receding due to an inflationary dark energy, and the further away they are the faster they are moving away from us. Like a train blowing its whistle as it speeds by, the whistle’s pitch is lower when it moves away from us, and the faster it’s moving the lower its pitch (and thus the longer its wavelength). It’s intuitive to apply this same reasoning to the observation of galactic redshift and think that galaxies must be speeding away from us, but it’s wrong. The effect is caused by the gradual diminishment in the speed of light in accordance with the above equation.
To unravel its meaning we first have to establish the theoretical basis of our approach: the Planck Spherical Unit (PSU). In the previous article, The Oscillating Planck Spherical Unit, I outlined Nassim Haramein’s proposed granular, space-filling unit and showed how its proportional oscillations manifest the atomic particles. To maintain continuity with Haramein’s model, I adopted his formulation that the PSU diameter is equal to the Planck length (ℓP) and its mass is equal to the Planck mass (mP), both of which are derived by combining 3 fundamental physical constants:
Now, to eliminate unnecessary coefficients present in Haramein’s approach, we’ll have to be more precise and attribute the Planck length to the PSU radius rather than its diameter. And we may also drop the assumption that each individual PSU has a mass equal to the Planck mass and think of it instead as an emergent property of PSUs bound into stable states, i.e. protons and electrons. Let’s begin with the holographic mass solution for the proton:
There are 3 ratios at work in this formula, each expressing a physical property of the proton in terms of Planck units:
- S - the spherical surface area of the proton as defined by its charge radius (4π rp²) to the equatorial disk of the PSU (π ℓP²).
- V - the spherical volume of the proton (4π/3 rp³) to the spherical volume of the PSU (4π/3 ℓP³).
- mp/mP - the proton mass (mp) to the Planck mass (mP).
The ratio of S to V yields mp/mP. Or more specifically, there is equivalence between the proton mass distributed evenly among the PSUs tiled on its surface (mp/S) and the Planck mass distributed evenly among the PSUs within the proton’s volume (mP/V). With PSUs filling its volume and covering its surface, rp is the radius that balances out the proton’s internal Planck mass energy with its rest mass energy projected on the surface horizon. Because the charge radius is the least well-defined parameter here, we can reasonably infer that this relation establishes the size of the proton based on the inputs of mp, G, h, and c. And unlike the value predicted by the Standard Model which is 4% larger than observations, the value obtained for rp through this relation (0.8412 fm) is in perfect agreement with the most precise measurements.
Next let’s examine the holographic mass solution for the electron. The expected distance between a single proton and a single electron in the lowest energy state of the simplest atom is the Bohr radius (a0). While the proton’s charge radius is an essentially permanent boundary for protons under normal conditions, electrons are not permanently bound to the Bohr radius. An electron moving along the Bohr radius also has a velocity less than c. For these reasons we’ll need a different formula to compute the electron’s holographic mass with respect to the Bohr radius than the one we used for the proton and its charge radius:
Here we have 4 ratios, each expressing a physical property of the electron in relation to the corresponding PSU parameter:
- R - the Bohr radius (ao) to PSU radius (ℓP).
- A - the circular area within the Bohr radius (π ao²) to the PSU equatorial disk (π ℓP²).
- α - the velocity of the electron (cα) to the surface velocity of the rotating PSU (c).
- me/mP - the electron mass (me) to the Planck mass (mP).
The value of α is equal to the fine-structure constant which is approximately 1/137.036. The ratio of R to the multiple of A and α thus yields me/mP. As a PSU completes 1 rotation of 2π ℓP at a velocity of c, the electron located at its most stable distance from the proton travels a distance of 2π a0*α at a velocity of cα, sweeping an area equal to απ a0² in its partial orbit around the proton. So there is equivalence between the electron mass distributed evenly among the PSUs lined up 1 ℓP apart between the proton and electron (me/R), and the Planck mass distributed evenly among the PSUs in the area swept by the electron (mP/αA) during 1 PSU rotation (2π ℓP/c).
To posit the existence of Planck Spherical Units requires 2 main assumptions: that the Planck length is a fundamental unit of space with spherical geometry, and the Planck mass relates the fundamental energy of these units when bound in stable states. By applying 2 different but related formulas to the 2 different but related phenomena associated with protons and electrons we can compute the size of a proton and the size of the simplest atom, respectively, in terms of PSUs. Unlike Haramein’s original approach which requires 2 unexplained coefficients, we attain simpler relations by attributing the Planck length to the PSU radius rather than its diameter. And it’s logical: just as the proton and electron masses each have a direct relationship with the Planck mass, the proton radius and Bohr radius each have a direct relationship with the Planck length which is the PSU radius, not its diameter.
With PSUs providing a physical structure to the universe, we can now extend the analysis from the atomic domain to the cosmological. The Hubble constant (H0) measures the apparent recessional velocity of a light source at a given distance. So at a distance of 1 megaparsec (~3x10¹⁹ km) the apparent recessional velocity is 73.8 ± 1.1 km/s/Mpc according to the latest direct measurement (combining the H0LiCOW and standard-candle measurements). Because H0 has units of velocity per distance, we can cancel out the spatial units and define its inverse 1/H0 as the apparent age of the universe. That is, if we assume the speed of light is constant then 1/H0 is the time it takes for light from the farthest point in the observable universe to reach us. This means that the ratio of c to H0 yields the radius of the observable universe (Ru). We previously measured the number of PSU radii in the Bohr radius, so let’s now compare the universe’s largest measurable radius (Ru) with the smallest radius (ℓP):
It is quite the coincidence that the PSU radii contained within this cosmological horizon, an extremely large number, is similar to the PSUs contained within the volume of a single proton, which we applied in the holographic mass solution of the proton: V= (rp/ℓP)³ = 1.41x10⁵⁹. But it bears more than just a passing resemblance. In fact, the ratio of the PSU radii in the radius of the observable universe to the PSUs in the volume of the proton is equal to the 4th power of the mathematical constant e.
Just as the proton’s holographic mass solution predicts a value for the proton radius that is more accurate than the value predicted by the Standard Model, this equation predicts a value for the Hubble constant (74.35 km/s/Mpc) that is in better agreement with the recent measurement of 73.8 ± 1.1 km/s/Mpc than the value predicted by the standard ΛCDM model, which differs by over 5 standard deviations. And we know this relation is part and parcel with the holographic mass solutions for the proton and electron due to the use of similar ratios with respect to the PSU: the proton mass accords with a ratio of 2-dimensional surface area to 3-dimensional volume; the electron mass accords with a ratio of 1-dimensional distance to 2-dimensional area; and the e⁴ term arises from the ratio of 1-dimensional distance (as with the electron but between the largest and smallest radii in the universe) to 3-dimensional volume (same as the proton).
But how do we interpret this result? With spinning PSUs filling space there is one simple solution: e⁴ refers to the decay in velocity that occurs as PSUs rotate. That is, if we accept that PSUs form the granular unit of space, and to transmit photons in accordance with observations PSUs must rotate at the speed of light, then the speed at which they rotate may be eternally constant or it may continually decrease. The available evidence seems to indicate it’s the latter. Thus, if each diminished velocity maintains a constant proportion with the previous velocity, as suggested by the presence of the natural exponential term e⁴, then the rotational rate will never reach zero. And if the deceleration is small enough then its effects will only manifest at large scales, such as in the measurement of light from distant galaxies.
Every proton has a spherical horizon defined by its charge radius which contains a quantity of PSUs equal to V, and another spherical horizon that extends radially a distance of V*ℓP, beyond which photons cannot be observed. V PSUs can be arranged linearly along this radius and overlap so that the distance between each one is ℓP. A photon traveling through this series of PSUs will experience a decay in velocity each time step of t in which the photon advances to the next PSU after completing a rotation of 2π ℓP. Then, beginning with a velocity of co*e⁴ at t=-V and winding up with a velocity equal to the observed speed of light co at t=0, we would find the speed of light decreasing as follows:
Like π, the mathematical constant e is given to us by nature. Of relevance here is that f(x) = e^x is the only exponential function equal to its own derivative, meaning the “instantaneous rate of change” or gradient (d/dx) of e^x is always equal to e^x. So, as a photon advances and t increases, the constant change in e^(4t/V) always produces the same proportional change to the photon’s speed (ct), which is a unique attribute of the exponential function e^x.
Looking out into the night sky, a series of rotating PSUs connects your eye and a light-emitting atom at the very edge of the observable universe. It is undetectable by the naked eye, of course, but a photon following this path arrives nonetheless. At time t=-V (~13 billion years ago) the photon moved through the first PSU with a velocity equal to co*e⁴. It continued to move through every PSU in the series, diminishing in velocity every turn so by the time it was halfway to its destination (t=-V/2) its velocity was equal to co*e², and by the time it enters your eye (t=0) its velocity is equal to co. The gradual diminishment in its velocity over the course of its journey has elongated the original wavelength of light, so it appears to be stretched out compared to more local light sources. If you could wait another 13 billion years (t=V) and observe another light-emitting atom at the edge of the observable universe, you would observe the same elongation but know that its velocity at arrival would now be co/e⁴. Empirical measurements of c would be unchanged from 13 billion years ago, but that’s because the clocks are all moving slower by a factor of 1/e⁴ as well. Everything is moving slower as a result of this universal deceleration.
Dark energy acts upon the 1 dimension of time rather than the 3 of space. It is the perpetual decrease in the rotational rate of the PSUs that transmit light that leads to the elongated wavelengths of light (and the associated decrease in frequency) observed from distant galaxies. The more PSUs a photon passes through, the greater its redshift. Every observer in the universe perceives the same redshift in photons that pass through the same number of PSUs, and thus the illusion of an expanding universe appears to all observers no matter when or where they are. So this new understanding of light implies that the universe is not 13.8 billion years old and the Big Bang is a 20th century creation myth.
Galaxies rotate faster than what Newton’s laws predict based on the amount of visible matter they contain. The most popular explanation for the rotational anomaly is that an unobservable dark matter provides mass to galaxies without any other significant interaction. Galaxies appear to be missing mass so it’s intuitive to suppose they must be bound together by a form of matter that is impossible to detect directly, but it’s wrong. Mordehai Milgrom has proposed an alternative solution called Modified Newtonian Dynamics (MOND) that describes the rotation of galaxies based only on the distribution of visible matter. The key postulate is that of a low limit acceleration that has the effect of modifying inertial mass. Mike McCulloch, in a version of this called Quantized Inertia (QI), describes the modification as follows:
The inertial mass of an object (mi) is equal to the difference between its standard mass (m) and this mass reduced by the ratio of a minimum acceleration (a′) to the acceleration of the object relative to surrounding matter (|a|). At terrestrial accelerations like the 9.8 m/s² we experience, the subtracted term is minuscule so our inertial mass relative to Earth is essentially equivalent to our standard mass and thus Newton’s laws prevail. But the typical distances present at the galactic scale lead to accelerations of an order small enough to substantially increase the subtracted term, and thereby reduce an object’s inertial mass in a significant way.
Both MOND and QI predict stellar motion across a diverse range of galaxies, galaxy clusters, as well as wide binary star systems within reasonable margins of error. They agree on the existence of a minimum acceleration such that, beginning from rest, an object accelerating at this rate would approach the speed of light in the apparent age of the universe. However the theories differ in their precise definition and interpretation of this acceleration. Milgrom determined MOND’s acceleration constant (denoted aM here) empirically by fitting it to observed galaxy rotation curves. It is known to be similar in magnitude to the Hubble constant multiplied by the ratio of c to 2π. McCulloch, on the other hand, attributes the acceleration limit in QI (denoted aQ here) to “Unruh radiation which is subject to a Hubble-scale Casimir effect.” Given a constant speed of light c, aQ depends on the co-moving cosmic diameter (Θ = 8.8 x 10²⁶ m), a theoretical horizon that extends beyond the visible universe.
With our new understanding of light, however, we can now identify the acceleration constant in MOND as the deceleration in velocity that occurs each PSU rotation. The time it takes for a PSU to initially complete 1 rotation is 2π ℓP/co, where co is the observed speed of light. After completing V rotations the rotational rate becomes co/e⁴. The ratio of the reduced velocity co/e⁴ to the total rotational time V*2π ℓP/co yields the deceleration per rotation (aU, denoting universal). Given the uncertainty in determining the quantity of matter in a galaxy, the ~4% difference between aU and aM make them virtually indistinguishable.
Every galaxy has a radius, dependent on the quantity of matter contained within it, beyond which the observed acceleration toward the galactic center approaches this quantum of deceleration. The velocities of stars orbiting in this region exceed what Newton’s laws predict because the small standard acceleration they experience toward the galactic center is substantially compounded by the universal deceleration. The small but continuous reduction in the speed of light effectively reduces the inertial mass of an orbiting star at the galactic perimeter to keep it bound to the galaxy. Its escape is thus impeded at every point along its trajectory by the gradual slowing down of the field of rotating spheres that transmits it.
To what physical process might we attribute this perpetual deceleration? PSUs must continuously change the orientation of their spins to accommodate the state of the electromagnetic field. This process must come at some expense so it seems logical that they would spin slower with every adjustment. A dynamic electromagnetic field is thus possible only if there is universal deceleration, and the evidence for this shows up in the rotation of galaxies and their apparent recession from us.
In a universe without a diminishing speed of light, we encounter perplexing anomalies at large scales. Galaxies seem to be simultaneously accelerating away from us and rotating too fast. To make sense of this while maintaining a perfectly constant speed of light, we must adjust our understanding of space and matter, making the former expand and the latter mostly invisible. But perhaps in retrospect it will seem obvious that we need only reconsider our concept of time. The ever-rotating Planck Spherical Unit provides us with a natural framework to accommodate the diminishing speed of light. We then see there is no expansion of space but of time. And if we know that there is a deceleration happening at every moment and every point in space, then galaxies need not be held together by an invisible matter but can be bound in its low-acceleration regions by the compounding effect of universal deceleration.
Watching the Sun and Moon move across the sky, it’s intuitive to think that they move in the same manner around us. Indeed, it appears as if all the objects in the celestial sphere move in circles with the Earth at the center, but that’s wrong. Despite its initial strangeness, there is a clear simplifying logic to Copernicus’s idea that the Earth and planets revolve around the Sun. It’s certainly a bizarre and unsettling thought that everything is moving slower all of the time, but it’s also a simple and logical solution to the strange phenomena associated with galaxies. Dark energy and dark matter are the epicycles of the modern era. It’s time we recognize universal deceleration as the correct solution and see the world in a new light.
