Latest revision 01-11-2022

## Hypothesis by Arp

### Variable Mass Theory: Intrinsic Red-Shift (videos)The (rest) mass of atomic particles is increasing with (proper) time.

Key reference is the monograph by Barry Setterfield: Cosmology and the Zero Point Energy (Natural Philosophy Alliance Monograph series, No.1, 2013, ISBN 978-1-304-19508-1).
One of the statements in this monograph is that the rest mass of an electron has been increasing with time, as shown in e.g. Figure 4 on page 17 and figure 8 on page 395 (linked here):

Arp's Hypothesis, as the name says, is not my own invention. It seems that I've picked up the whole idea while reading the book by Donald E. Scott, The Electric Sky, especially chapter 17 about Redshift and the Big Bang. On the webpage we read (near the bottom of this page) that Halton Arp is correct in his contention that redshift is caused mainly by an object's being young, and only secondarily because of its velocity. And from the article Research With Fred: In my opinion, of the kind of explanations that the current observations require, one of the simplest is one along the lines of Hoyle's suggestion that electrons and other atomic constituents can be created with initially smaller mass. Then smaller $h\nu$ emissions result from a given atomic transition, and radiation from all objects in the new galaxy is shifted to the red. As the galaxy ages, its atomic parameters asymptotically approach that of older matter. Martin Schwarzschild's comment: You are both crazy! Arp's thinking surely represents A Different View of the Universe. Barry Setterfield meets Halton Arp here:

I had a discussion with him by letter early in the formulation of his theory. He showed
some interest in our graph of the increase in subatomic rest-masses with time and other
data from the 1987 Report. However, there were several sets of observational data which
I pointed out to him that were not in agreement with his theory. This included slowing
of atomic clocks and the maintenance of standard energy conservation. His response was
simply "Too bad". He seemed to feel that his theory was more important than the data.

So what follows now is a highly speculative theory. It's entirely against my principles, actually, because I find that: In die Beschränkung zeigt sich erst der Meister (Goethe). Indeed, most of my lifetime I've been proceeding with small and certain steps, for the purpose of solving some little problem that I find nevertheless significant. But things in cosmology are different from things in common science, it seems. Barry Setterfield meets Han de Bruijn here:
The author of the website article, Han de Bruijn, has stated that accepting an increasing
rest-mass for sub-atomic particles will alone explain many phenomena that feature in the
Monograph. In doing this, Han has adopted an approach that is commonly taken by others
in the scientific community, namely a minimalist position. This approach leaves intact
as much as possible and changes a minimum number of variables in any formula.

Indeed! There exist many different masses in physics, but there is only one speed of light and there is only one Planck constant. So it is much less risky to suppose that a particle mass is changing with time than to suppose that $c$ and $h$ are subject to change. And, what's more, it's better to have a minimalist theory that is at least (mathematically) correct than to try a framework so overly complicated that it has become impossible to tell the difference between right and wrong.

There is a link to an interesting text fragment in the Dutch version of the Wikipedia webpage about the Nobel Prize winner Jim Peebles: Cosmic Black-Body Radiation. Quote: One of the basic problems of cosmology is the singularity characteristic of the familiar cosmological solutions of Einstein's field equations. Also puzzling is the presence of matter in excess over antimatter in the universe, for baryons and leptons are thought to be conserved. Thus, in the framework of conventional theory we cannot understand the origin of matter or of the universe. We can distinguish three main attempts to deal with these problems.
1. The assumption of continuous creation
(Bondi and Gold 1948; Hoyle 1948), which avoids the singularity by postulating a universe expanding for all time and a continuous but slow creation of new matter in the universe. I have always been thinking that it is the Hypothesis by Arp.
2. The assumption (Wheeler 1964) that the creation of new matter is intimately related to the existence of the singularity, and that the resolution of both paradoxes may be found in a proper quantum mechanical treatment of Einstein's field equations. Sure, a proper quantum mechanical treatment as a panacea for all problems with Einstein's General Relativity Theory.
3. The assumption that the singularity results from a mathematical over-idealization, the requirement of strict isotropy or uniformity, and that it would not occur in the real world (Wheeler 1958; Lifshitz and Khalatnikov 1963). We don't need great names to see that any singularity has no meaning in physics and always results from a mathematical over-idealization. Take a look at our Special Theory of Continuity.

According to QED: The Strange Theory of Light and Matter by Richard P. Feynman, more than 400 "elementary particles" were known in 1985, each of them with different rest mass. Among these particles are the muons, which behave like heavy electrons. The mere existence of "heavy electrons" is another reason to suppose that increasing particle mass may be not such a risky hypothesis as it seems at first sight. Still another argument is that particle mass varying with speed is a common phenomenon in Special Relativity.
With increasing rest mass and the speed of light being constant, there is no conservation of energy. This is not much of a problem, because conservation of energy is linked to laws of nature that do not change in time. If "constants" like the rest mass of the electron actually do vary in time, then conservation of energy doesn't have to hold per se. A Wikipedia reference for this is "Example 1: Conservation of energy" in Noether's theorem. In a nutshell it says that conservation of energy is guaranteed if and only if the same physical experiment can be repeated at different times. Which is clearly not the case if a variable (rest) mass comes into play. How reasonable is it to assume that a physical experiment conducted thousands of years ago on a far away planet will give exactly the same outcome as when conducted nowadays on earth?

There are more questions than answers, though. If the particle rest mass has been increasing all the time, how small has it been in the "beginning" then? Only photons have rest mass zero. So did the cosmos begin with photons only? And did the particle mass increase continuously? Or did it increase in discrete steps?
Whatever. Let's come to business. Our purpose is to show that even a single absurd looking hypothesis, like increasing particle mass, is powerful enough to explain several phenomena as are mentioned in Setterfield's book. The mathematics employed has been kept as simple as possible (but not simpler :-). And the physics employed is no more complicated than needed: by using good Old quantum theory.

Upon further reflection, would it be wise to implement two more flavors of the Basic Hypothesis?

1. Only leptonic (electron) rest mass is increasing with (proper) time
2. Only hadronic (proton/neutron) rest mass is increasing with (proper) time
That depends. Current knowledge about the Proton-to-electron mass ratio (Wikipedia) reveals that: $$\mu = m_p/m_e = 1836.15267343(11)$$ which is an absolute constant to about 0.1 parts per billion.
On the other hand we have Indication of a Cosmological Variation of the Proton-Electron Mass Ratio Based on Laboratory Measurement and Reanalysis of $H_2$ Spectra.

We have decided to invariably opt for the first possibility, so $\mu$ is assumed to be an absolute constant: all elementary particle rest mass is increasing with proper time.

Question is: does there exist empirical evidence that is in favor of varying elementary particle rest mass?
From
Wikipedia we quote: Classical Cepheids (or Delta Cephei variables) are population I (young, massive, and luminous) yellow supergiants [ .. ]