Refining the Zwicky Constant:
A new more soundly-based constant for inter-galactic distances
replacing the Hubble Constant

David Noel
Ben Franklin Centre for Theoretical Research
PO Box 27, Subiaco, WA 6008, Australia.

Hubble and Red Shifts
Back in the 1920s, the famous astronomer Edwin Hubble first observed that the light from very distant objects, such as galaxies outside our own Milky Way, were "red-shifted".

The range or spectrum of light from such objects is not continuous, but has "lines" across it, due to absorption or addition to the light from precise processes (such as energy changes in hydrogen atoms) at the emitting source.

Figure RZC1. Red shifts in light from distant galaxies. From [6].

The illustration, from Wikipedia [6], shows "Absorption lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to absorption lines in the optical spectrum of the Sun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases)".

When light is shifted towards the red (longer wavelength), it represents a loss in energy. If a sample of light starts at wavelength L and is affected by processes which double its wavelength to 2L, it has lost half its energy. Visible light has wavelengths from 380 to 740 nm (nm means nanometres, billionths of a metre). Red light has about twice the wavelength of blue light.

What Red Shifts mean
When Hubble released the news about redshifts to the community (interestingly enough, through the New York Times newspaper, as an older astronomer tried to bar inclusion in professional journals), it naturally enough demanded explanations be found.

In 1929 the brilliant Swiss-American astrophysicist Fritz Zwicky, born in Bulgaria, published a paper "On the red shift of spectral lines through interstellar space" in the Proceedings of the National Academy of Sciences [3]. In this he examined four possible explanations for redshifts.

Figure RZC2. Fritz Zwicky. From [2].

The mechanism which Zwicky thought best explained the redshifts was what he called "The Gravitational Drag of Light". He said that according to relativity theory, a light quantum has an inertial and gravitational mass. A quantum passing a mass M would be expected to transfer momentum and energy to M, and during this process the light quantum will change its energy and therefore its frequency [3].

Zwicky was a giant of his time and his influence and findings have echoed down to the present, even if widely unrecognized. In an article about gravitational lensing [2], Adam Rogers brings out some idea of Zwicky's place in modern science. He says:

"I need to sidetrack a little bit and introduce one of the most prolific, colourful and criminally under-appreciated astrophysicists of all time: Fritz Zwicky. The list of Zwicky's contributions is monumental and reads like an introduction to modern astrophysics.

Zwicky is a unique figure because he stands at the crossroads of several branches of study considered separate today. Despite being largely unrecognized and unknown by the general public at large, Zwicky is responsible for a significant number of essential contributions to modern cosmology and astrophysics.

He coined the term 'supernova', and suggested the huge complexes of glowing gas and dust known as nebulae are actually the radioactive ashes of these titanic explosions that signal the deaths of massive stars. In fact, Zwicky went one step beyond and also predicted that a neutron star should be left behind after particularly massive stars meet their violent ends in supernova explosions. This startling prediction came only two years after the discovery of the neutron by James Chadwick in 1932!

Zwicky reasoned (correctly) that the monumental densities found at the centers of these explosions should collapse down the cores of giant stars to combine even the protons and electrons in their atoms into dense neutron material. This prediction was eventually verified by Jocelyn Bell Burnell with her observation of the pulsating radio source PSR B1919+21, the first pulsar, which was later determined to be a neutron star, just as Zwicky proposed forty years prior.

Zwicky also made use of supernovae as 'standard candles' to measure cosmic distances in 1938. A particular kind of supernova explosion, known as a Type Ia supernova, is found to always reach the same peak brightness. This means that the observed intensity of these explosions tells us their distance, just like a 100-watt light bulb held close to you looks brighter than the same bulb far away from you. This method for estimating distances is now a cornerstone of modern cosmology."

Zwicky also did pioneering work on gravitational lensing, and on the relationship between masses and rotation speeds of galaxies [2], which threw up a big disagreement with classical mechanics. Investigating the Coma cluster, a vast complex of over a thousand galaxies, he found that in order for the cluster to be stable, there must be ten times more mass present than could be directly observed.

This "missing" mass was crucial for keeping the cluster together. If it were not there in some form, the member galaxies would not be bound to one another and would go flying off into space. So in order for the cluster to exist at all, there must be much more mass within the cluster and the individual galaxies than we can directly detect in the form of stars, gas and dust.

When faced with this apparent contradiction, Zwicky shrugged and concluded that the missing mass must just be some cold, dark stuff that doesn't give off much light, so we can't see it directly. He called this non-luminous stuff Dark Matter. He began to investigate other clusters, and found similar results for each of them.

Adam Rogers says [2] "The unobservable dark mass, whatever it is, must be extremely important in holding large structures together. There must be a lot of it out there, too -- the Coma cluster alone is almost 90% unobservable by mass. This means that when you look at an image of a galaxy cluster, you are seeing only a small fraction of what's really out there. In fact, Zwicky was the first investigator to uncover a profound cosmic mystery that remains unexplained to this day."

(A simple explanation of the nature and position of Dark Matter has only very recently become available, and has not yet penetrated very far into the astrophysics world. It can be found at The Cosmic Smog model for solar system formation, and the nature of 'Dark Matter'.)

The Other Explanation for red shifts
Very unfortunately, Zwicky's lucid explanation of red shifts came to be ignored in the face of an apparently simpler model. Red shifts (and their converse, blue shifts) are genuinely observed in the case of astronomical and local phenomena due to what's called the Doppler effect.

When you observe waves coming from a body moving away from you, these waves are stretched out by the movement away, meaning their wavelength appears longer. There is an extended explanation of this in [5].

Figure RZC3. Wave frequency change in the Doppler effect. From [7].

At the time of Hubble's discoveries, red and blue shifts were already known in astronomy, from relative movements of stars away from or towards the Earth within our own galaxy, the Milky Way. So perhaps it was understandable that Hubble's rather bigger red shifts came to be ascribed to Doppler movement of distant galaxies away from our own.

This simple confusion, at the time of galactic red-shift's early discovery, was the cause of perhaps the biggest fallacy of modern astronomy -- that our Universe is expanding. That is, that shifts in spectral lines of very distant galaxies, compared to the positions of those lines in close objects such as our Sun, are caused by the distant galaxies moving away from us.

This idea was never accepted by the original discoverer of galactic red-shifts, Edwin Hubble himself. In the Wikipedia article on Hubble, quoted in [5], it says "Hubble believed that his count data gave a more reasonable result concerning spatial curvature if the redshift correction was made assuming no recession. To the very end of his writings he maintained this position, favouring (or at the very least keeping open) the model where no true expansion exists, and therefore that the redshift 'represents a hitherto unrecognized principle of nature.' "

Ignoring Zwicky and Hubble
In the event, both Zwicky and Hubble were ignored by the astronomical community. In those earlier times, it made little practical difference. Galactic red-shifts could still be used for their main purpose, of estimating how far particular galaxies lay from Earth -- the bigger the red-shift, the further away the galaxies were -- to a fair approximation at least.

But this straying from the Zwicky path was to lead into increasingly dense thickets of confusion, increasingly twisted and unsound explanations of logical deductions from the Doppler assumption. The first of these was obvious. If the Universe was expanding, and the rate of expansion was known, it was a simple thing to calculate backwards to the time when expansion began. The usual answer is around 13.7 billion years.

So, the world was told that the Universe "began" 13.7 billion years ago, and light from this beginning had now reached the edge of the "observable Universe", a sphere 13.7 billion light-years in radius. This is with the assumption that the light travelled at 'c', the 'speed of light in a vacuum', a genuine natural constant equal to about 300,000 km/sec. This speed is accepted to be the maximum possible for light or any type of electromagnetic radiation or matter.

Nasty Difficulty No. 1. If the Universe began at a single "expansion point" and has since spread out to fill the Universe, where did all the matter and energy come from? Cosmologists' answer to this lay in "The Big Bang Theory", first put forward in 1931.

According to the Big Bang Theory, at some point in the past, the whole Universe burst into being from a single infinitesimally small point, and expanded (initially at much more than the speed of light) to give us the current Universe. All the matter in our Universe was somehow created from nothing.

It might be thought that scientists of the time would object to the breaking of fundamental concepts such as the conservation of mass-energy and the limitation of the speed of light. These concepts are insisted on in all other branches of science, why should cosmology be exempt?

What is "Science's" answer to this point? It has no answer!

Wikipedia has a long listing of 99 different creation myths [11], including 9 for 'ex nihilo' (out of nothing). Really, there is nothing scientific about Big Bang, it just adds on to the list nicely, to make a round 100 myths, of which a dozen are 'ex nihilo'.

Figure RZC4. Australian Dreamtime creation myth. From [12].

More problems
Nasty Difficulty No. 2. If galaxies at the far outside limits of the "observable Universe" are each close to 13.7 billion light-years away, then today it must be about 27.4 light-years across this Universe. Has it taken 27.4 billion years for two points now at opposite ends of the Universe to become separated, twice the age of the Universe? Or does this mean that Earth is at the centre of the Universe?

The Big Bangers say No, everywhere the Universe is expanding, and 'space-time' expands with the Universe, so nowhere is at the "centre". Maybe you can handle this paradox.

Nasty Difficulty No. 3. According to Big Bangers, very distant galaxies are receding at very high speeds. A 2011 reference [13] says that "pushing the Hubble Space Telescope to the limit of its technical ability, an international collaboration of astronomers have found what is likely to be the most distant and ancient galaxy ever seen, whose light has taken 13.2 billion years to reach us.

Figure RZC5. Hubble Telescope image showing part of the deepest infrared image ever taken of the universe. From [13].

This image of the Hubble Ultra-Deep Field is part of the deepest infrared image ever taken of the universe. The small blue box outlines the area where astronomers found what may be the most distant galaxy ever seen, 13.2 billion light-years away, "meaning its light was emitted just 480 million years after the Big Bang".

Remember that the further away a galaxy is, the faster it is supposed to be moving away. Reference [14] has a little calculator which says that if the galaxy is 13.2 billion light-years away, it is moving at 98.36% of c, the speed of light.

There are two problems here. If galaxy G at one point in the Universe is moving away at 98% of the speed of light, and galaxy H on the opposite side is moving away at 98% of c, then G is moving away from H at 1.96 times c -- not permitted in the real Universe. Explanation? All to do with relativity...

Then there is the energy involved. Where is all the energy coming from to move these galaxies? And in this case, relativity is no help, because it says the closer a body gets to the speed of light, the more energy is needed. Infinite energy is needed to reach c, for a material body.

Nasty Difficulty No. 4. If the Universe has greatly expanded, then if we look at an image of a region as it was in the "early days" of the Universe, as in Figure RZC5, then the galaxies should be packed much more closely together.

In fact, the image in RZC5 is typical of images taken at any scale -- images of very distant ("older") sections of the Universe have the same general appearance as close regions. The expected early close packing does not exist.

Nasty Difficulty No. 5. For very large red-shifts, the Big-Bang calculations become very complex. This is because when bodies such as galaxies are travelling very fast, say over half the speed of light, the effects of Einstein's Theory of Relativity must be taken into account. Moreover, when distant galaxies are considered, if you assume that they are receding, a whole new factor called Cosmological Red Shift [15] comes into play.

It's a laugh, really. You use red-shifts to deduce that the Universe is expanding, then you have to factor in the idea that it is expanding to explain high red-shifts -- you get these because the Universe is expanding. It's mathematicians' heaven.

Nasty Difficulty No. 6. If you look at red shifts for lines of different wavelengths coming from the same object, it can be seen that the red-shifts are different for different wavelengths. In fact, the red-shifts are proportional to the individual wavelengths -- this was noted by Fritz Zwicky in his 1929 article [3]. If you look at the formulas for red-shift [5], the actual magnitude of a Doppler red-shift is independent of wavelength -- this physically equates to different parts of the same body necessarily moving at the same speed -- so red-shifts which vary with wavelength cannot be due to Doppler, if they come from the same object.

In fact, the graphic at the start of this article, RZC1, must be inaccurate. As the wavelength of red light is about twice that of blue light (at the other end of the visible spectrum), the shift for the red end should be about twice that for the blue. In this case, the arrows marking the shifts would not be parallel.

Measuring the Universe
We go now to look at the bases of factors used in expressing distances in the Universe. These include H (or H0), the Hubble Constant, z (small z), the Redshift Ratio, and Z (big Z), the Zwicky Constant.

The Hubble Constant, "H", has been in use since the early red-shift days. It is named after Edwin Hubble (although he did not invent it, and in fact rejected it as a constant). The Hubble Constant purports to represent the speed at which the Universe is expanding.

Figure RZC6. A typical plot of Red-shift (interpreted as "Recessional Velocity") against distance of a galactic source. From [1].

In this figure, the slope of the purple line defines Hubble's Constant (H), the speed at which galaxies are moving away from us, as worked out from the conventional formulas from their red-shift. H is around 20 km/sec/Mly [9], that is, for every million light-years you go out into the Universe, the "rate of expansion" of the galaxies there appears to increase by another 20 kilometres per second.

But Hubble's "Constant" is not a true natural constant, just the average slope of numbers plotted on a graph. The figure shows how the data points each lie in a region of uncertainty (the horizontal lines drawn through them). Typically, a quoted figure for the Hubble Constant will include an uncertainty of over 5%, and depending on the basic assumptions used, can be over 30% [5].

It is understandable that "H" cannot be measured very accurately. It is based on the implicit assumption that distant galaxies are all receding, and at a rate proportional to their distance. This assumption is challenged (disproved?) here.

The Redshift Ratio "z" is a measure used to indicate distances of more remote objects. It is the ratio of shift in wavelength of an observed line from a distant object (that is, the observed wavelength minus the original, unshifted wavelength) over the original wavelength. So if an original wavelength of L was weakened to stretch it out to 2L, the value of z would be (2*L-L)/L, or 1. More on the formulas involved may be found at [5].

So "z" values are pure numbers, without units of dimension. For very distant objects, such as the galaxy pictured in RZC5, "z" is quite high, equal to about 10. According to [10], a value of z=1 is found for a an object around 7.7 billion light-years away.

Conventional calculations from "z" on such things as distances are subject to the "relativity" consideration as above, for "speeds" over half the speed of light, "c". This speed corresponds to a "z" value of 0.73, so deductions from higher values may be suspect.

The Zwicky Constant, "Z" is a distance, the distance at which Gravitational Drag on a beam of light causes its wavelength to double (or its frequency to halve). So as above ([10]), a current value for "Z" is around 7.7 billion light-years.

The Zwicky Constant "Z" equals about 7.7 billion light-years

This is an initial figure for "Z", and needs refinement. As with "H", "Z" is not a natural true constant, but will depend on the actual gravitational fields encountered in a 7.7 billion-year journey. But this distance is so great, compared to distances usually used in measuring the Universe, that local variations will have evened out. It is likely that the uncertainty in "Z" can be brought down to well under 1%.

Recalibrating the Universe
Although "Z" and "z" have a meeting-point at around 7.7 billion (light)-years, they are quite different quantities, and the differences have massive implications on our view of the Universe.

We saw above that the most distant object so far detected had a "z" value of about 10, we'll assume that it is exactly 10. That is, its redshift is 11 times its original emission wavelength (z = (11*L-L)/L). The galaxy's distance from us is, according to Big Bang calculations, about 13.2 billion light-years.

In the Zwicky "Gravitational Drag" model, wavelengths from distant objects are stretched to twice their original value for every 7.7 billion light years travelled.

We saw above that wavelengths are doubled for light which has travelled 1 "Z" in distance, at which point "z"=1. For light which has travelled 2 "Z", its wavelength will have doubled again, to four times the original. At this distance, small "z" equals 3 (z = (4*L-L)/L).

Now a distance of 2 "Z" is equal to about 15.4 billion light-years, much more than the "Big Bang" radius of the Universe, at 13.7 billion light-years. According to [18], z=3 corresponds to an object that is about 11.5 billion light-years away.

This is a very significantly different result from the two approaches. The Zwicky result is not only about 34% higher than the Big Bang result, it is above the maximum allowed by Big Bang.

Now consider a further doubling in wavelength, to 3 "Z". At this point, small "z" equals 7 (z = (8*L-L)/L). According to [19], z=7 galaxies are about 13 billion light-years away, while the Zwicky formula gives 23.1 billion light-years, a 77% bigger result.

It will be apparent that for bigger "z", for yet more distant objects, the difference will be greater again. For another doubling, with "z" = 15, we would be at 4 "big Z", 30.8 billion light-years. We are still a long way short of z = 15, but even so, the Zwicky formula says that we are currently observing objects as far away as 25 billion light-years.

The main reason for the disagreement is, of course, the use in Big Bang of formulas assuming distant objects are receding at significant fractions of the speed of light, and so relativity considerations must be included.

The Zwicky formula is free of all relativity worries. It just assumes that light gains in wavelength in direct proportion to distance travelled in the cosmic gravitational field. In this it is like isotope half-lives; if half of a radioactive isotope substance decays in 100 days, after 200 days there will be a quarter left, after 300 days, one-eighth.

The Cuckoo in the Nest
Everyone will know about cuckoos, that they lay their eggs in the nests of other birds and avoid the bother of raising their own young. But not everyone will know how vicious and destructive the process may be.

According to Broodfellas: Nest parasitism and Mafia involvement among cuckoos [8], a cuckoo egg in the nest of another bird will hatch first, before the host-mother bird's own eggs. It does this because the cuckoo mother carries the egg within its body for longer. As soon as it hatches, the cuckoo baby sets to work to dispose of its nestmates, by pushing their unhatched eggs out of the nest. In this way, it gains the undivided attention of its host-parents.

Figure RZC5. Using a shallow depression in its back, the newly-hatched cuckoo disposes of its nestmates. From [8].

The illustration is of the nest of a reed warbler (Acrocephalus arundinaceus). The newly-hatched, naked cuckoo dumps the other eggs over the side of the nest, so the host parents lose all their own offspring. For the rest of the season, they devote all their attention to the interloper child.

Figure RZC6. Baby cuckoo (on left) being fed by reed-warbler host mother. From [8].

Left with the task of raising the monster child, the host parents labour on to feed a baby which is quite unlike their own. A cuckoo chick can grow to five times the weight of a reed-warbler chick, and take even longer to bring to the fledgeling stage.

A bad situation for the host parents, which exhaust themselves to raise the alien child, and are left at season's end with none of their own offspring.

Why do the host-parents do this, why don't they just toss the cuckoo egg out of their nest themselves? If they recognize an alien egg in the nest, they may do just this.

But the cuckoos are one step ahead. Female cuckoos of the same species fall into 'clans', with each female in the clan evolved to produce an egg very similar to the natural egg of the particular host species. Often, this is a much smaller egg than most cuckoo eggs, just the size of eggs of the parasitized species.

Well, as the cuckoo chick is fed and grows into a bird looking quite different to the host-parents' natural chicks, why don't they cease feeding it and kick it out?

By then it is too late. The mother-child instinct is such, that if your child turns out quite different to what you expect, it is still your child, and it is your duty and nature to raise it as best you can.

"Big Bang" the Cuckoo in the Astronomy nest
And so we have the reasons why, in spite of apparently irrefutable proof, the "Big Bang" cuckoo has not been easily ejected from the Astronomy nest.

When it started off, it seemed to fit in OK, no reason not to accept it. As time went on, well there were some problems, but fixes could be found, logic and testing compromises made. True enough, it was looking more and more of a monster, but in the eyes of the establishment, it was "their" monster.

And at the end of the day, there was too much labour, thought, and money invested, too many career positions involved, to think of jettisoning the whole ugly caboodle. Better to just coast on quietly, and leave the mess to be sorted out by the next generation. Or the next. Or the next.

Theory behind Zwicky's "Gravitational Drag"
Currently the Zwicky Constant is an empirical constant, with little underlying theoretical analysis. Because it is based on passage of light through gravitational fields in the larger Universe, there must be some underlying variation in measurements because of random variations in the gravitational patterns of areas passed through.

On the other hand, for measurements based on very distant objects such as the galaxy in the Hubble image RZC5, these must necessarily have low effects from intervening matter, because they are situated in 'empty' areas of the sky. If these objects were not in 'empty' areas (visible from Earth without screening by intermediate objects) they would not be likely to be picked up.

Mathematical analysis of Zwicky Drag should be possible, perhaps using data on the average density of matter in the Universe (about 10-30 g/cm3, according to [16]). There might also be a clue in work on refractive index -- a glass prism spreads a beam of white light into colours because its internal structure has a slightly different effect on light of different wavelengths [17].

Listen to Ockham
In the final wash-up, it is always better to Listen to Ockham, to apply Ockham's Razor to the intellectual framework you have before you. William of Ockham's tenet was to say, in brief, if you have to decide between a number of explanations of a matter, you should always choose the simplest.

Certainly the explanation given here of red-shifting in light from distant galactic objects is far, far, simpler than the massive and clumsy traditional alternative.

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References and Links
1. Redshifted Galaxies. .
2. Adam Rogers. General relativity and gravitational lensing: Part 2, Dark Matter.
3. F. Zwicky. On the Red Shift of Spectral Lines through Interstellar Space. Proceedings of the National Academy of Sciences of the United States of America, Vol. 15, No. 10 (Oct. 15, 1929), pp. 773-779. Online at:
4. Edwin Hubble.
5. David Noel. R.I.P. Expanding Universe (b. 1930, d. 2012): (The Big Bang never happened). .
6. Redshift. .
7. Illustration of the Doppler Effect. .
8. Broodfellas: Nest parasitism and Mafia involvement among cuckoos. .
9. Hubble's Law. .
10. How Far Away is this Galaxy?
11. List of creation myths. .
12. Australian Aboriginal Creation Myths. .
13. UCSC astronomers find most distant galaxy candidate yet seen. .
14. Red Shift. .
15. Cosmological Redshift. .
16. Density of the Universe. .
17. David Noel. The Photon Hoop Model for light: A new model to aid analysis and computation of light reflection and refraction phenomena, and towards a resolution of the dichotomy between wave models and particle models for light. .
18. Lyman-break galaxies. .
19. Recap. .

Stablemate articles:

About the newer model of the Universe, superseding the Big Bang: The Placid Universe Model -- Why the Universe is NOT Expanding, or, The real origin of CMBR, Cosmic Microwave Background Radiation.

About proving the Big Bang Theory is wrong: R.I.P. Expanding Universe (b. 1930, d. 2012): (The Big Bang never happened).

About the nature and position of Dark Matter: The Cosmic Smog model for solar system formation, and the nature of 'Dark Matter'.

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Draft Version 1.0, 2014 Nov 4-17.
First version 1.1 on Web, 2014 Nov 21. Version 1.2, minor correction, 2021 Mar 25.