Hubble Distance Red-shift and the Action Quantum of Light

This is best understood in sidereal time, that is, celestial coordinates in the four-year leap year cycle.
Time and energy are conjugate variables in the action, and we think with energy.

Not chaos at all, distance red-shift slowly changes light waves in a simple and orderly process.
The discovery fits both perceived reality and quantum mechanics, yet remains to be proven.

Light's evolution is exquisitely conservative at it travels through the fundamental dimensions of space-time.

By Michael G. Lewis
ml39612 @ gmail.com

new A Universal Dual Space for Mathematics

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A Hubble Red Shift general equation
Coordinating velocity redshift and distance redshift: Galaxy Distances, Brightness and Redshift

All the pdf files in one:
Redshift is Longshift With early handwritten notes.

CONTENTS and separate PDF's
Includes 17 kilometer, 57 microsecond ds relativistic path unit

For professional red shift data in light from distant galaxies see GOODS: The Great Observatories Origins Deep Survey

An evolving wave equation, with the action quantum h as a constant of infinitesimal change in its conjugate variables, may resolve Hubble Red Shift. The slowly changing wave equation presented here is a candidate for the hitherto unrecognized principle of which Hubble has written. A single scaling constant should strongly reconcile existing spectra.

Lambda is the wavelength of light, not the proton.

Regardless of distance, light's action quanta retain their magnitude and topological integrity throughout their path. Momentum and energy slowly diffuse into the wave's quantum conjugate dimensions of wavelength and wave time. The photon is non-commutative: ( qp-pq > 0 ) , and it is an exceedingly slow diffusion as well as a wave. Here, q and p are the general quantum variables and symbolize momentum, wavelength, energy and wave time.

By Isaac Newton

-- Isaac Newton, The Principia, ref 27 p 398.

Erwin Schrodinger

It must be remembered, however, that if the co-ordinates are not Cartesian, or if the forces are momentum-dependent, this expression is ambiguous, owing to the non-commutability of q(r) and d/d(q(r)).
-- Yourgraw, quoting Schrodinger in Variational Principles in Dynamics and Quantum Theory, Ref 41 p 125.

and Edwin Hubble

The displacements, called red-shifts, increase, on the average, with the apparent faintness of the nebula observed. Since apparent faintness measures distance, it follows that red-shifts increase with distance. Detailed investigation shows that the relation is linear.
-- Edwin Hubble, The Realm of the Nebulae, Ref 19, p 33

Careful examination of possible sources of uncertainties suggests that the observations can probably be accounted for if red-shifts are not velocity-shifts. If redshifts are velocity-shifts then some vital factor must have been neglected in the investigation. -- ibid, p 197

It will be recalled that it was just possible to explain the nebular counts on the assumption that red-shifts were not velocity-shifts. If red-shifts were velocity-shifts, additional corrections, called number-effects were required, and these appeared as discrepancies. -- ibid, p 200

On the other hand, if the interpretation (of red shift from distant galaxies) as velocity-shifts is abandoned, we find in the red-shifts a hitherto unrecognized principle whose implications are unknown. The expanding redshifts of general relativity would still persist in theory , but the rate of expansion would not be indicated by the observations. ibid, p 201

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Ancient concepts of light were rooted long ago - before the pyramids were constructed - by pre-Cambrian Cephalopoda in the oceanic abyss, in subducted coal forests, and myriad other ways in life itself.

Many stars nearby and within the Milky Way are bright enough to be visible to the eye. Yet light from exterior galaxies (except Andromeda) is visible to few ununaided eyes because of its faintness.

Spectral shifts from astronomical objects are also invisible to the unaided eye but for a different reason: they are changes in color hue which are almost always slight, and the eye cannot perceive slight color change easily. Both Doppler and Hubble shift can be observed only with large, expensive telescopes to gather the faint light, sensitive and fragile spectroscopes to detect minute wavelength shifts, and cold film or low noise digital cameras to permit long-period accumulation of the light quanta.

Doppler velocity shift, discovered around 1850, is not discussed here much. In light from stars such as Doppler observed-within the Milky Way-the Doppler Shift can be either toward long wavelength OR short wavelength depending on whether the source is receding or approaching.

Two different terms exist in the diffusing wave equation which are mathematically distinct and orthogonal. They are separate integral powers. The first power term describes distance shift, and it is the second power term which describes Doppler shift. This is consistent with the observation that Doppler shift can be either to longer or shorter wavelengths, while distance shift is always to longer wavelengths.

It was not Doppler's fault that he never saw the extremely distant exterior galaxies in Edwin Hubble's realm of the nebulae. Doppler was born ahead of his time, never looked through a large modern telescope, and died long before exterior galaxies were discovered. Doppler shift itself, though not easily visible to the unaided eye, is in widespread use in airport radar for air traffic control, on streets and highways in vehicle traffic speed regulation, and other purposes. Honored for his discovery, he is remembered well because the velocity shift named after him saves many lives and much property every day.

Hubble distance shift, discovered around 1920, is the primary subject of this document. It is always invisible to the unaided eye, and is only toward long wavelength and low energy, never toward short wavelength or high energy. Even so, it has affected our understanding of light because fast as it is, its direction carries powerful implications for very long-term activity in and on the Earth, and events in human activities as well.

The idea presented here is that Hubble distance shift is not Doppler velocity shift. Conversely, Doppler velocity shift is not Hubble distance shift. Mathematically the two arise from different term orders in the differential equations describing light. The principles herein appear more satisfactory than conventional assumptions. The distinction has implications on the forms in which civilization is so far built-at present, massive structures without a basis in relativity, topology or quantum fields.

The speed of light c and action quantum h are the two primary constants in light-like waves. Few other constants exist, a vast surprise considering the immense size and duration of the Universe. Only one variable suffices to describe six different appearances of light-like waves. These six are the wavelength, energy, frequency, momentum, wave time, and wavenumber. Each is proportional to the other variables and from zero to two of the constants. When one variable changes, all others change together. Is any most absolute? What does quantum mechanics look like if a selected wavelength such as the Hydrogen 21-centimeter line is used as the primary standard for both distance and time?

A dual probability of the quantum's action may be sufficient to describe, in terms of the modern Standard Model topology of SU(2) X U(1), the second order phenomenon of Hubble distance shift although the author is not going to attempt it here, at least not yet. Perhaps the reader would enjoy that venture.

Do consider existing spectroscopic red-shift data from distant galaxies in terms of these distance-red-shift principles, which involve momentum*wavelength and energy*time conjugates. A table such as H. J. Rood's A Catalog of Galaxy Redshifts from the Uppsala General Catalog of Galaxies, sorted as you choose, snaps into order and soon registers with the terrestrial environment in the light of this equation. You will then find modern light's relation to ancient concepts of light, down in the antipodes where rabbits and electrons dwell. This theory has taken the light of the solar system.

Exterior galaxies present their spectral envelopes and the emission lines of specific elements in similar patterns. However, the spectral data of galaxies at different distances persistently appear at different wavelengths. Left: a visible light spectrum of the Sun. Right: that of a distant galaxy. 4000 is blue; 8000 is red. The shift toward longer wavelength in light from the exterior galaxy is about 450 Angstroms.

for more.

Two spectra from the Two Degree Field survey data. By permission of Anglo-Australian Observatory. Described in
Galaxy groups in the2dFGRS: the group-finding algorithm and the 2PIGG catalogue by V. R. Eke, et al, (the 2dFGRSTeam) Mon.Not.R.Astron.Soc. 348,866,878(2004)

The spectrographic plate spectra above are NOT the coherent light diffraction pattern below.

The action quantum of which light is composed is a topologically dimensioned probability which flows between conjugate dimensions. These dimensions are time, distance, momentum, energy, wavenumber, wavelength, etc. and they come in pairs. There are also two constants, c and h. This probability can be demonstrated with an inexpensive laser and a narrow slit. The wave is diffracted at the slit where the momentum-wavelength relationship is disrupted by interaction with the edges. The wave is re-radiated as in the Huygens wave front Reconstruction model, and the lateral or sideways dimension of distance becomes entangled with the wavelength of the light. The result is fringes or bands on each side. Spacing of the bands can be predicted from the wavelength and slit width.

The classical wave's action has dimensions of mass, area and time.

In light-like radiation quanta, energy E = h * nu is equivalent to mass through the Einstein mass-energy relation E = m * c^2.

Then h * nu = m * c^2. The energy within stars is in an equitable relationship with the energy in space.

TWO constants exist in the wave. They are the speed of light c, and the magnitude of the action quantum h.

Only one variable exists in the wave, yet it is observable from six different views as, variously, momentum, energy, wavelength, wavenumber, frequency and wave time.

The product of momentum and wavelength is the action quantum's constant-value h.

Wavelength is the domain (within the wave's quantum of action) to which momentum probability slowly and irreversibly flows during the megaparsecs of the photon's flight.

That flight path shows up as ds in the path's distance-time, usually in light-years or parsecs, of general relativity.

The 21-cm 1420 MHz hydrogen wave is a candidate for a ds -unit of space-time in general relativity.

Energy E is the product of momentum p and the constant speed c.

The product of energy and wave time is the action quantum's constant-value h.

wave time is the domain (within the wave's quantum of action) to which energy's probability slowly and irreversibly flows during the aeons of the photon's flight.

Wavelength has an inverse, wavenumber, which is the number of waves in each meter of length.

Frequency has an inverse, wave time, which is the time between two successive points of equal phase passing a fixed point in space.

All measurements are assumed to be with reference to the observer.

Phase becomes important when defining the point on the wave which moves at exactly! the speed of light c.

Relativistic considerations, of course, hold but won't be discussed here yet. They appear in the Schwarzschild equation, Einstein crosses, gravitational lensing and other phenomena.

The quantum of action can appear in different distributions as conjugate pairs such as momentum*wavelength, energy*time, etc. Analogous to many other real world situations, specific quantities of fluids are marketed in differently shaped containers of the same volume measure. Liter volumes of liquid are marketed in many differently shaped volumes. A hectare of land can be purchased in rectangles, squares, circles, triangles, or any simple closed loop. Labor is accounted in varying numbers of persons and an inversely proportional number of hours worked. The quantum of action is a natural constant with the dimensions of action, and we see it as a shape-shifter.

The 1899 discovery of the action quantum by Max Planck allowed the 1982 development by the author of a Hubble Distance Red-Shift wave equation of this form:

The equation above shows the action quantum h explicitly. h must be the decay constant, for the action quantum h and the speed of light c are the only two constants in the intergalactic wave.

The following two variations on that equation employ only two of many different forms of the action.

Some point in the wave always moves at exactly the speed of light. As the wave slowly lengthens and diminishes in frequency, the speed of its trailing end is infinitesimally slower than the speed of its front end.

Waves at Various Distances in Flight

Quantization of energy had been conjectured by Max Planck in 1900. The solutions proposed here were not possible before 1926 when quantization was found to exist in light as an action quantum h, describable variously as a product of momentum and wavelength, or a ratio of energy to frequency. . . . . . . . . . . . . . . Steal this

h gives each light-like wave a constant quantity of action. By 1926 however, conjecture that exponential wave decay might be the cause of Hubble Red Shift had been subsumed under wartime developments including the use of Doppler shift in both sonar and radar to determine target speeds. Interest in a changing wave function was precluded by further war and atomic energy until the Soviet launch of the orbital Sputnik Earth satellite in 1957. By then, the 1926 discovery that it is action - closely related to energy but not by itself exactly energy - that is quantized was well established and had led to many new discoveries. It was not until the Apollo manned expeditions to the Moon that the field really became clear for reconsideration. Primary points are:

1. the action in each wave remains constant at h
2. energy E evolves into wave time.
3. momentum p evolves into wavelength.
4. the wave's only two constants are the speed of light c and the action quantum h.
5. the wave has one and only variable, which appears diversely as wavelength, energy, frequency, wavenumber or wave time.
Any one of these specifies all the others.

Existing mathematics is sufficient to describe a photon evolution process that is related statistically and analogically to the equivalent decay process of very long half-life radioisotopes. The physical process of exponential decay in nature, described mathematically, is the well known first order partial time derivative term d/dt which appears in the general form of the wave equation. A zero force concept allows us to see that a diffusion term is present in the photon wave equation. The conjugate variables in the photon, momentum and wavelength, do not commute.

While the action flows rapidly in each cycle back and forth between wavelength and momentum, the actual distinction between time and space has a limit - the Planck action constant. To that extent, the wave gradually loses track of the difference between the two domains and the action slowly diffuses from the domain in which it is densest to the other domain where the action density is lower. A difference exists between each wave and the preceding and following waves. Time ordering is strong, and time reversal theorems are inapplicable to the interstellar photon.

The evolution process is also equivalent to an internal redistribution of variables due to concentration of the action in the various domains such as energy, momentum, wave time and wavelength. This means distant objects are hotter than they appear, a conclusion already known. Distant galaxies probably include many stars of the same temperature as our own sun, though they appear much cooler by the time their light reaches Earth. It will take time to estimate actual temperatures correctly; the distant universe is more energetic than it was assumed to be. Fortunately the correction should be linear, the true distances and temperatures of distant objects being estimable from the total shift and the shapes of spectra envelopes containing familiar elemental lines.

Doppler shift, which was discovered in the 1860's by the eminent Austrian astronomer Charles Doppler, is not the correct explanation for the cosmological red shift although Doppler shift certainly is very important in measuring relative radial velocities of objects at the same or nearly the same distance. Doppler shift, for instance, can measure the relative velocities of stars in a distant edge-on galaxy cluster, or the relative velocity of members of a cluster of galaxies but it cannot measure distance. Conversely the Hubble red shift can measure the radial distance from Earth to the distant galaxy cluster or the relative velocity distribution in an edge-on galaxy, but cannot not the relative radial velocity toward or away from Earth.

The fundamental points are that diffusion in the photon does not commute ( qp-pq > 0 ), and that it a diffusion as well as a wave.

Thus (A) Doppler's Velocity-shift is not Hubble's Distance Red-shift; (B) the Hubble Distance Red-shift is not the Doppler Velocity-shift; and (C) neither is false. In the case of a red shifted object with internal relative motion such as an edge-on galaxy or small group of galaxies, a limit to the possible certainty, or conversely to the necessary uncertainty, could be obtained from the product of distance determined by Hubble Red Shift and relative velocity determined by Doppler Shift.

Quantization is a natural phenomenon, and its magnitude is named the Planck Action Quantum h. Just as a fixed or standard volume of liquid can fit into containers of many shapes, the quantum appears in several proportional relations between the canonical variables E, energy, and p, momentum. These two require other dimensions to balance the naturally fixed quantity. The dimension accompanying energy is time. This appears in at least one popular consumer good in Xenon flash lamps which are rated in Joule-seconds. The dimension accompanying momentum is distance. These and other forms of the action are almost inevitably discernable in natural and artificial objects, systems and processes.

The fundamental one-dimensional variables lambda (wavelength); nu (wavenumber; tau (wave time), and f or Hz (frequency) are widely used in quantum mechanics.. Except for phase and spin these completely describe the interstellar photon at all times. Two of these, length or distance and time, were the first fundamental dimensions to be sought, and eventually resolved into measures, by human civilization.

The decay or evolution constant introduced here, [ 1 / ( h*c*c ) ], describes the stable way diffusion affects the photon as it travels through the vast distances between galaxies and stars. The resulting equation appears to be necessary and sufficient for an exponential evolution rate similar in magnitude in time and distance to that of the cosmological distance or Hubble red shift. Several radioactive isotopes, which have half-lives commensurate with photon momentum half-life, suggest that the same statistical nature of the universe is at work in both atomic nuclei and light-like waves. The problem of a medium is avoided: light-like waves are assumed to exist in the topology of space and time.


The wave equation is a member of a class of first order partial differential equations which have been extensively used in describing wave phenomena for many decades.

Adapting it to include a decay or evolution rate term would almost certainly have been achieved by astronomers before 1920 had wars at that time not interrupted almost all work except that which contributed to the allied war effort. A tentative abstract form would include the two constants h and c, and perhaps something which is related to the current values of the variables of wavelength, frequency, momentum, wavenumber, wave time and energy. These are fortunately all simply related and interdependent so that it will be necessary to specify only one of the six.

The product of wavelength and momentum is well described by the action quantum h so it is not necessary to specify the two variables p and lambda in order to obtain an evolution constant. Yet the multidimensional h itself is not so obviously definable far away from Earth. Wavelength is readily observed in the laboratory and certainly exists in distant space, and the momentum p is at least only one step removed from a knowledge of the speed of light, c, and the energy E. Secular mathematics thus tends to avoid h in favor of the more directly observable wavelength and momentum.

Constants: c (speed of light) and h (action quantum)
Canonical external variables: E (energy), p (momentum)
Canonical internal variables: lambda (wavelength), nu (wavenumber), tau (wave time), f (frequency)
Measure: t (time), x (distance)









speed of light





action quantum

























wave time








Time and distance are based on measures originating on Earth and based on the size and orbit of the Earth. The time unit of the second is based on the rotation of the Earth and coordinated with its year, while the distance unit of the meter is based on the pole-to-equator surface distance. Both distance and time, however, can be based in principle on one or a few selected spectral terms, such as the Hydrogen 21.11 centimeter line, the Hydrogen Alpha line, or the Cesium-133 line already in use for time. Any can be used for both distance and time standards, with the speed of light being the conversion constant.

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