I recently wrote about Eugene Tatum’s assertion that the CMB is related to the Hawking Temperature of the universe. The coauthor of that particular paper was Espen Gaarder Haug. I didn’t mention it before, but Tatum is a Doctor, of Anatomic and Clinical Pathology. Haug is also a Doctor, in the area of finance, specifically quantitative finance. He got his doctorate in something relevant to options and trading (his doctoral thesis was on that anyway) but I can’t find out what he did his undergraduate in (presumably economics, but not necessarily). He’s currently a finance professor at the Norwegian University of Life Sciences.
Haug and Tatum are coauthors on a range of papers about the flat cosmological model (which they
sometimes refer to as the Haug-Tatum cosmology [HTC] model),
while Haug has a quite a few papers of his own about the quantisation of
gravity.
During research for No Eugene Tatum, Hawking Temperature is not
Related to CMB, I stumbled upon one of Haug’s paper on the quantisation
of gravity: God Time = Planck Time: Finally Detected!
And Its Relation to Hubble Time.
Note that, like most of Haug’s papers, this one was published at scirp.org,
which is a predatory publisher. That said, being published in an odd place
does not necessarily make the content wrong.
It’s just easier to get such publishers to publish bad and low-quality
science – and even easier to publish at a blog under a pseudonym. When you find a paper published by a pay-to-play
or predatory publisher, you just need to be more careful and engage your critical
thinking more intently than you might otherwise, such as when the source is more
reputable.
The very first thing drew my attention was the title. “God time”?
I wondered if I was looking at the work of someone like Luke Barnes, a person
dabbling in physics to support a theological world view. On closer inspection, and in the context of Haug’s
other papers, including two others that mention “god”, it appears that he is
just using a hook to draw attention rather than making any serious claim about
the existence of an actual god. Haug does
refer to the “the god particle” in at least two of his papers without mentioning
that the Higgs boson was know as the “god-damned particle” due to its reticence
to reveal itself, which is unfortunate but, in the conclusion to the God Time paper,
he indicates that historical references to indivisibility at the smallest scales,
including apparent biblical references, are not important.
The basic claim of the God Time paper, and the one that I have
a problem with, is that knowledge of G, ħ, and c
is unnecessary to establish the value of tP, the Planck time. (In another paper, and another, Haug seems most intent on
removing the use of G entirely, which is odd. There are problems in those papers too, but I
will try to restrict my efforts here to addressing Haug’s efforts to eliminate fundamental
constants.)
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The standard definition of Planck time is:
Given that the defined value consists of G, ħ,
and c, and only G, ħ, and c, establishing
Planck time without the use of those fundamental constants should be quite a challenge. Haug does it by using the equation:
Which he later generalises (in a special case) to:
In his numerical example for the first equation, Haug sets object
1 to the Sun and object 2 to the Earth.
The term δ
is used to refer to the effect of gravitational lensing by object 1
(the Sun), expressed in radians. (Note
that in the link provided, the symbol θ is used.) The
term g refers to the magnitude of gravitational acceleration at object
2 (the Earth). Note that the equation at
the link has a direction that is implied by the minus sign, it’s
not intended to refer to a negative value.
The term λ is a
reference to the Compton wavelength of the mass of
the relevant object, but in this case it is the reduced variant, in the same way
that the reduced Planck constant is given by ħ=h/2π. So,
for clarity, Haug provides the numerical result for this equation (using subscripts
E for Earth and S for Sun):
where (per the
links above)
If we substitute these into Haug’s
equation, we get:
which resolves to
In his generalised version, Haug is talking about a single
mass, so no subscripts are required, and:
which also resolves to
So, yes, you can get Planck time using Haug’s equation which
does not explicitly use G, ħ and c. However, there is a problem with his assertion
that we can therefore reach a value for Planck time without using any of the fundamental
constants because, in order to use his method, we must establish the values for
at least gravitational lensing deflection and the reduced Compton wavelength.
The value for gravitational lensing deflection due to the Sun
has been measured, first by Eddington in 1919, so while
not so easy, this is entirely possible – with some caveats. The apparent radius r in the equation
(per Wikipedia), θ=4GM/c2r, is not
necessarily the radius of the body with the mass M, but rather the
distance between the centre of the mass and the radiation being deflected. The value measured by Eddington was for light
that grazed the surface of the sun, hence
the need to observe a total solar eclipse.
The related deflection is, therefore, at the photosphere, which is
considered be the surface of the sun, and r=Rs.
The Compton wavelength, on the other hand, is not something that is
measured for, and probably doesn’t even apply to, bodies at the scale of the Earth
and the Sun (because it’s a quantum mechanical property). We can calculate it, sure, but to do so we need
to use both ħ and c.
(This could explain Haug’s fixation on eliminating G in his other
papers, if he has noted that he can’t get around using ħ and c. He says it explicitly in section 6 of another paper.)
If we forgive this, then we still have some problems to
address. The accuracy of the value of tP
that can be determined using Haug’s first equation depends on the accuracy of
the measurement of:
Deflection due to gravity as light
grazes the surface of the sun – 3%
Gravitational acceleration at some
point on the Earth with a distance from the centre of RE (not the
defined standard gravity value which is nominal
and limited by caveats) – about 0.7% assuming it’s somewhere on the surface
The distance to the centre of the
Earth used above (about ±30mm
in 6378km) – 0.0000005%
The radius of the photosphere – 0.02%
The mass of the Sun (for calculating the reduced Compton wavelength)
– 0.005%
The mass of the Earth (ditto)– 0.01%
We don’t need to worry about the accuracy of h and c, because these
values are both defined. The only inaccuracy
in ħ will be due to the
approximation to π that is used, but this can be set
arbitrarily low by using π
to many significant numbers. So this
means the resultant inaccuracy in the measurement of tP would
be, approximately:
3%+(0.7%/2)+0.02%+0.005%+0.0000005%+(0.01%/2)=3.38%
Presumably, from a value of tP determined
this way, we could calculate a value for G using the standard definition
of tP and the defined values of ħ and c. This value would have an accuracy of approximately
6.76%.
Compare this with the NIST values which have accuracies of 0.0011% for tP
and 0.0022% for G.
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As indicated above, Haug seems to realise that he can’t get around
using ħ and c, and is therefore laser focussed on
eliminating the use of G, even in the process of determining the value
of tP.
This, to me, is madness.
If expressed in Planck units, all the four values listed above, ħ,
c, G and tP, resolve to unity. (In addition, mP, lP,
qP, vP, iP, TP,
EP, kB, ke, mP,
reduced μ0 and raised ε0 also resolve to
unity. Even the unitless gravitational and electromagnetic coupling
constants resolve to unity when Planck values for mass and charge are
used as the reference rather than arbitrary values like a proton or electron
mass or the elementary charge.)
---
In other papers, like Quantum Gravitational
Energy Simplifies Gravitational Physics and Gives a New Einstein Inspired
Quantum Field Equation without G and Not Relying on the Newton Gravitational Constant Gives More Accurate
Gravitational Predictions, Haug suggests that he’s hit upon some evidence
of the quantisation of gravity – all which seem to relate to the notions of “collision
length” and “collision time” (which is expanded on in Collision-space-time: Unified quantum
gravity – where he assigns photons with a mass (an extremely tiny mass,
admittedly)).
In the first two papers above, Haug mentions the “factor”:
Which he refers to as “reduced Compton frequency per Planck
time”. This is an odd way of putting it,
for more than one reason. First, as a simile,
we could say that GmP2/ħ is “Planck length per Planck time”. This not completely untrue, because GmP2/ħ=c=lP/tP,
but it’s an odd way of putting it. The second
reason may not be immediately clear, but we can look at Haug’s own words, from Quantum Gravitational
Energy Simplifies Gravitational Physics and Gives a New Einstein Inspired
Quantum Field Equation without G:
It's not anything “per Planck time”, it’s a value that is multiplied
by Planck time, not divided. If anything,
it’s equivalent to “Planck time per reduced Compton period”, noting that there’s
another error buried in there.
Haug states that the reduced Compton frequency is the speed
of light divided by the reduced Compton wavelength. Presumably, the vanilla Compton frequency (fc)
is the speed of light (c) divided by the vanilla Compton wavelength (λc):
If we implement the reduced Compton wavelength, which is the
Compton wavelength divided by 2π, we have (using the bar as an indication of some sort of modification,
not necessarily reduction):
So it’s not a reduced Compton frequency, it’s a raised
Compton frequency.
He could, however, express things somewhat less awkwardly. Using the definitions of reduced Compton wavelength
and Planck length, we see that:
And, in flat universe, we know that*:
So, Haug’s “factor” is, in fact, simply an expression for the age of the
universe (at time t) divided by Planck time (or, to put it another way,
the magnitude of the age of the universe when expressed in Planck time). Or, as I have used frequently elsewhere, ꬱ (first introduced in Avoiding a Contravention of the Extended
Consistency Principles). It’s a
useful term in that context, but not so much when mixed up with the notion of a
confused (reduced? raised?) Compton frequency.
---
I did reach out to Haug to discuss the above but have not,
yet, heard back from him.
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* There's a little oversimplification here. Keen-eyed readers will note that M has not been explained here. It's not quite the mass of the universe, because in a flat universe, the mass is mP.ꬱ/2. To understand what is going on a review of The Conservatory - Notes on the Universe might help. In brief though, if we think of a standing wave between two nodes (null points), then the minimum full wavelength is twice the minimum distance possible between nodes - because there is a node in the middle of a full wavelength. The consequence of this, if we have granularity (as in a FUGE Universe), is that when the universe expands by one Planck length, there is one additional node added, allowing for one more half wavelength, or λ(t)=c.t/2. Each half wavelength corresponds to an extra half a unit of Planck mass/energy, so the M value above (if it were the mass of the universe) would be M(t)=mP/2.t/tP.
Note that because, in the FUGE conception, increments are in half wavelengths, Haug’s “factor” would become (noting the caveats above):
