Latest revision 29-11-2023

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VPM debunked?

VPM = Varying elementary Particle rest Mass. From an email correspondence we quote. My own writings are in black, those of my opponent are in red.
Unfortunately for UAC theory, it is known experimentally that the mass of particles does not change enough to satisfy a change of $m/m_0$. Measurements of atomic frequencies to 18 significant digits (see attached) always give the same value, even if different atoms (created at different times) are used. Since the Rydberg constant depends on the mass of the electron, we know that their masses does not change with time.

This rules out models by Arp, Narlikar, Van Flandern, etc. that require the mass of electrons to change with time.


Concerning the variable mass hypothesis, I think your conclusions are too hasty.
The article mainly talks about extremely accurate atomic clocks. Which is OK. Upon searching "mass" it says:

Page 564. In addition to providing a critical advance for redefining the SI
second, we use these measurements to test a model of ultralight dark
matter, tightening constraints on its coupling parameter to standard
model fields by as much as a factor of ten over five orders of magnitude
in particle mass.

I am not talking anywhere about "dark" matter. All of UAC's mass is just common mass.

Page 567. In addition to their use in metrology, frequency ratios of optical
clocks are sensitive probes of physics beyond the standard model.
Some models postulate dark matter composed of ultralight bosonic
particles [ .. ]

I don't postulate anything of the kind, therefore I find the article not applicable to my work.

Page 567. The overall constraints are improved
by as much as an order of magnitude across five orders of magnitude
in particle mass compared to previous constraints.

That's nice, but it says nothing. The crux of the matter is that the frequency of an atomic clock
itself is dependent on (electron) mass via the Rydberg constant, according to $f/f_0 = m/m_0$.
We are running in a vicious circle when trying to measure varying particle mass with atomic clocks,
because they consist of the same particle mass and shall be varying accordingly (if theory is right).


[ .. ] the 'atomic clock' paper I sent you was only to show that atomic clocks today reach an absolute accuracy in the $10^{-18}$ range; you won't find anything serious that is cosmology related in the paper. The aluminium-ion clock described in the paper relies on the mass of a single electron. Of course, two atomic clocks built with electrons will drift together, even if the Arp/Narlikar hypothesis is correct, so no signal can be detected.

Orbital time is no longer used in metrology, time is always based on atomic clocks. And orbital times are not accurate enough to test the Arp/Narlikar cosmological hypotheses, so it is irrelevant.

My argument: In Narlikar's model, an electron is created with a null mass which increases with its age. That's how Arp explains the redshift of distant objects and the discordant redshifts of QSOs.

Single-ion atomic clocks are now so accurate, they can measure the difference in mass between two electrons that were created less than four seconds apart in time. It has been measured that Al+ clocks tick at the same rate for any electron taken from aluminium originating from different places on Earth. So all electrons have been born within 4 seconds of each other. However, over 750000 quasars have been observed in the universe; these would have produced electrons with a wide spread of ages and even electrons born within a quasat would have been created at different times differing by a lot more than 4 seconds (that's what I meant in my last email by "different atoms (created at different times)". Yet, an Al+ clock doesn't detect a difference larger than 4 seconds in the age of any electron used to make it tick. The Arp/Narlikar hypothesis does not stand against these tests.

I will sign you up to the ACG forum, you should receive confirmation and instructions within minutes. Most members have a weaker grasp of physics than you do, so don't be surprised if the discussions are not rigorous. [ .. ]


Orbital time is no longer used in metrology, time is always based on atomic clocks. And orbital times are not accurate enough to test the Arp/Narlikar cosmological hypotheses, so it is irrelevant.
It took a while, but understanding is underway now :-)

First your aluminium clock.
[ Use has been made of the formula $\,\Delta m/m \approx H_i\Delta t\,$ according to Hubble Parameter ]
A few calculations with my theory indicate that you may be right:

# 1 megaParsec
Mpc := 3.08567758*10^22;
# Hubble constant (2022-02-08)
hubble := 73.4*1000/Mpc;
# Electrons that were created
# less than four seconds apart in time
# resulting in atomic clock drift
difference := hubble*4;
                                             23
                       Mpc := 0.3085677580 10
                                              -17
                     hubble := 0.2378732000 10
                                                -17      -18
                   difference := 0.9514928000 10     > 10

# Age of the earth
earth := 4.543*10^9;
# Seconds in a year
year := 31556926;
# Hubble parameter
hubble := 2/(earth*year);
# Same as above
difference := hubble*4;
                                              10
                      earth := 0.4543000000 10

                           year := 31556926
                                              -16
                     hubble := 0.1395058975 10
                                                -16     -18
                   difference := 0.5580235900 10    > 10
So there is something to think about indeed.
In retrospect, it seems to me that your argument concerning the detectable variable particle mass (VPM) is not a very strong one.
Your aluminium ion quantum clock of course cannot tell what is causing the VPM. Now suppose that the effect is purely relativistic.
Then we have: $\mbox{VPM} = 1/\sqrt{1-(v/c)^2}-1\,$ with $v=$ velocity electron and $c=$ speed of light. Approximately: $v = c\,\sqrt{2\,\mbox{VPM}}$ .
With $\mbox{VPM} = 10^{-18}$ resulting in $v = 0.423970 \; m/s = 1.5 \; km/hr$ .
This would mean that your clock can distinguish an electron at rest from an electron moving with $1.5 \; km/hr$ .
I still have to see such slow electrons in common applications (or inside the Al+ ions themselves).
[..] the relativistic effect you describe is included in the uncertainty evaluation of a clock. Time dilation from velocity (often called 'second order Doppler effect' because of the $(v/c)^2$ term) will be below $10^{-18}$ in a clock that is claimed to be accurate to $10^{-18}$.

I'll find a better paper, but for now consider the clock I was working on 17 years ago (paper [ not ] attached). The Strontium ion is maintained at a temperature of $16\;mK$ (p. 2) which corresponds to a velocity of $2\;m/s$ and a relative time dilation $4.5\times 10^{-17}$. It would take a difference $\gt 3$ minutes in the time origin of electrons for a mass difference to be detectable with that clock.

Considering that the sun sends us electrons (solar wind) and these are absorbed in the atmosphere (auroras), mixed by the winds and mixed into metals such as aluminium, it is hard to imagine that random electrons from distant pasts would not end up in these clocks.

Even in 2005, I could not accept that the individual electrons we were using for the clocks originated within three minutes of the same moment. I discussed this with Halton Arp over a tele-conference but the connection was too lousy (and Arp's hearing was quite bad), he didn't get the implications of the argument). Jayant Narlikar never answered my emails.

I'll look for a more recent paper with an explicit value on the error on the relativistic fractional shift.


Here is a more recent paper (attached): the uncertainty on the relativistic frequency shift is 1.2E-18 ("Secular motion second-order Doppler" highlighted on Table IV at the bottom of p. 53204-9). Multiplied by the Hubble constant this gives 0.55s. (That's for a portable clock design. I'm sure other laboratory clocks are better, but I am not in the field anymore and I haven't followed up on the latest developments.)

Clocks can distinguish between the mass of an electron created 13 billion years ago and another electron created half a second later. How could they all have all appeared within such a small time interval? Also, over billions of years, some electrons would have travelled faster than 0.23 m/s relative to others and would have aged differently in their proper time. None of that is seen, different Al-ions in a clock give the same frequency relative to lattice clocks.

Therefore: the change of mass of electron, if linear with time, is insufficient to explain the cosmological redshift. If the mass changes quadratically with time (as in Narlikar's law) then the conclusions from clock measurements are even more restrictive.


UAC theory is sometimes difficult to comprehend (read "unacceptable"), because of the following ideas.
  1. General Relativity is abandoned altogether. And of course "the Big Bang never happened".
    Jayant Narlikar actually has proved that GR is redundant by adopting Varying Particle (rest) Mass (VPM)
  2. The universe, as something that contains everything, does not exist. Way of speaking: it's infinite.
  3. There does not exist another geometry in nature than common Euclidean geometry and no space-time.
  4. There are two separate clocks in nature, defining Atomic time XOR Orbital / Gravitational time.
    This is the additional element in UAC which makes our theory robust against your argumentation so far.
  5. Atomic time can only be measured with gravitational time / gravitational time only with atomic time.
  6. As a consequence, Grand Unified Theories will never be found: gravity is separate from the rest.
  7. Length Contraction is universal and observationally equivalent with the Expansion of Empty Space.
  8. According to Narlikar's law, elementary particle mass increases quadratically with orbital time.
  9. Arthur Milne has proposed a formula, connecting the two times scales, which can be derived by us.
  10. Tom van Flandern has proposed a formula connecting distance with redshift, also derived by us.
  11. The outcomes of UAC theory are - mathematically (only) - consistent with those of Tired Light.
  12. The age of the universe - there may be one in orbital time - is anyway two times a Hubble time.
If one of the above issues is dismissed, such as the existence of orbital time, then UAC shall not work.
[ .. ] on
the video you can see the name of Ekkehard Peik, whom I have known personally when I was a Humboldt fellow in Munich. He was researching an atomic clock based on a nuclear transition, but I believe he has not found one that works (after 30 years of measurements...) Clocks based on ion pairs have exceeded what could be done with a clock based on a nuclear transition. I have left this very interesting field of research to concentrate on cosmology, but these people are making tremendous progress.

Concerning your past emails: time is always based on atomic clocks and only based on atomic clocks. You disagreed by writing that "this not true", but you don't know the time scales and their definition. The atomic scale called TAI (Temps Atomique International) is the reference time scale from which every other is derived. (You don't mention TAI anywhere on your webpages!) The other time scale called UTC (Universal Time Coordinated) is a legal time used by countries around the world. The leap seconds are inserted to keep up with the irregular rotation of the Earth (you have seen the graph, e.g. this one) so that solar noon happens at UTC noon. Please read-up on the topic.

The difference between TAI and the average of UTC has a historical explanation: when the timing of the Earth's orbit was measured 60 years ago astronomers did not have a precise value. The value of "One Second" = "9192631770 oscillation of the hyperfine transition of Cs" was chosen based on an inaccurate measurement. You claim that "the difference between the two time scales can be calculated with your theory", but this is impossible since the difference originates in a measurement inaccuracy and a human construct, not a physical process.

So your point 04. in the email dated 2022-10-08 has no meaning. Instead the Earth's rotation is influenced by weather patterns and earthquakes that are unpredictable, it is not an accurate time scale. For example, between 1999 and 2005 no leap second was inserted because the Earth was spinning faster! If the Earth's rotation is so unreliable over five years, it cannot be used over thousands of years as you do in your calculations. The eight points following point 04. are not valid.


[ .. ] time is always based on atomic clocks and only based on atomic clocks.

I didn't say that varying particle mass is the truth. It's a ("wild") hypothesis, no more, no less.
If you decide to reject that hypothesis, then you are right: orbital time is identical to atomic time.
But if you accept the hypothesis, then you are wrong: then orbital time is not atomic time.

You have to accept eventually that Newton's laws and some simple laws of quantum mechanics are true.

If you accept all of the above, then it's a straightforward exercise to show that there are two time scales.
And if varying particle mass bears truth, then Newton's laws for orbital motion do not work with atomic time.

Fortunately there is force (mass times acceleration) that does work with both orbital and atomic time scales.
Details are found in the sections
Time Dilation and Support by Hoyle at the Unified Alternative Cosmology site.

It all means that: orbital time = atomic time   if and only if   elementary particle mass is not varying.

UAC theory may be true or false, it is consistent and you cannot dismiss anything without destroying everything.
I could make an axiom system of it, like mathematicians do, but I am too much of a physicist to do it.
Is there a flaw in my maths? Please tell me! Honestly, I'm never sure :-(

This rules out models by Arp, Narlikar, Van Flandern, etc. that require the mass of electrons to change with time.

That's only true for Arp, Narlikar and Hoyle. Van Flandern and Milne did their discoveries independent of Arp's VPM.
More than just independent. For example Arthur Milne's Formula has exactly the opposite physical meaning of mine:
our atomic time is his orbital time, and his atomic time is our orbital time. MOND theory is independent of UAC too.
Yet many elements in common as well as in alternative cosmologies are in agreement with my theory. Coincidence?

About the experimental verification / falsification. Of course, I have searched for examples with a certain bias in mind.
Yes, physical effects are extremely small (as is also the case with the three tests of General Relativity dismissed by me).
So it's easy to find alternative explanations as a reason why there are three UAC numbers in agreement with experience:
the shrinking kilogram, the leap second ("due to the slowing rotation of the Earth") and the widening orbit of the moon.
But I dare to make a prediction: your atomic clocks shall be running too fast forever, in comparison with orbital time.

However, the most significant evidence of all is found in the ("new") section MOND = UAC. That is not a small effect!

Continuing story at The Refutation.