1 Theory vs. Reality
1.1 Incongruence Between Observations and Theory
Theoretical physics is an unscientific mess. This fact cannot be sugar coated. Theoretical physics is a mess because the standard models, of cosmological and quantum scale physics, do not resemble observed reality. They are mathematically self-consistent models that only resemble themselves. Both models make absurd claims about the nature of physical reality. Nonetheless both models are touted by the scientific community as a great success.
1.1.1 The Cosmological Realm
The Standard Model of Cosmology is commonly referred to as the Big Bang Theory but scientists currently prefer to call it the Lambda-CDM Concordance Model. Sticking with that preference it will henceforth be referred to as ΛCDM. This name provides a nice introduction to the model’s difficulties with physical reality.
The Λ portion of the name refers to a so-called dark energy. According to the model, dark energy is needed to account for a claimed accelerating expansion of the Universe. The accelerating expansion claim is in turn based on an ΛCDM model-dependent interpretation of an observed discrepancy between the redshift and luminosity distance estimates for some distant SN Ia type supernovae.
CDM stands for cold dark matter which is a substance required by the model to account for an alleged discrepancy between predictions made by gravitational theory (either Newtonian or General Relativity) and observations regarding the rotational velocity of outlying stars and gases, and the observed velocity of galaxy cluster members.
The dark in both dark energy and dark matter simply means that neither required entity can be directly observed or detected; both exist only within the context of the model that requires them. They are both, in layman’s terms, invisible.
So scientists have named their latest version of the standard cosmological model after two glaring weaknesses. The model requires things to exist for which nature provides no observational evidence. Much of the problem with modern science stems from this propensity to insist that otherwise undetectable things must exist in reality if a theoretical model includes or requires them.
And so it is that the modern cosmological model contains, besides dark matter and dark energy, several additional entities and events that are likewise impervious to direct detection. These would be, to begin at the beginning,
- the big bang event and its inexplicable original condition
- the subsequent epoch of inflation
- physical space and time or physical spacetime
- black holes
- singularities
None of these features of the ΛCDM model make an appearance in observed reality.
Accepting ΛCDM as an accurate representation of the observed cosmos also requires acceptance of the model’s two foundational propositions, one implicit and one explicit; these are also unsupported by any empirical evidence. The first, the unitary assumption, underlies Alexander Friedmann’s 1921 solutions to the field equations of General Relativity which are the foundation of ΛCDM.
By creating a singular model of the cosmos it is necessary to assume that the cosmos is a singular, unified, coherent, and simultaneous entity. Friedmann assumed, in other words, that the cosmos was in fact a Universe.
At the time, the known scale of the cosmos was that of our galaxy and so the unitary assumption was not totally unreasonable. However, since the known scale is now many orders of magnitude larger and the full extent of the cosmos is currently unknown and likely unknowable, the idea that the cosmos is a unified entity seems, shall we say, scientifically naive, if not downright preposterous.
It should also be noted that the unitary assumption contradicts a fundamental tenet of Relativity Theory – the absence of a universal reference frame. A unitary model of the cosmos inherently imposes a universal reference frame on the cosmos. It is in effect antithetical to Relativity Theory to use the equations of General Relativity to create a unitary model.
If a cosmological model were to be designed from scratch on the basis of current knowledge, it is unlikely that it would include the unitary assumption. Unfortunately there is, in the scientific academy an innate conservatism that clings to dubious concepts long after their inadequacies have become glaringly apparent.
The second foundational assumption of ΛCDM is that the cosmological redshift-distance relationship first established by Edwin Hubble in 1929 is, in fact, the result of a cosmological recessional velocity. That is, redshifts correlated with distance are interpreted as arising from an overall expansion of the (previously assumed) Universe. Although Hubble never completely reconciled himself to this particular view, it nonetheless became widely accepted.
This recessional velocity interpretation is of a peculiar nature. In order for the theory to work, meaning for it to produce, from an alleged singular origin and universal expansion, a current Universe that resembles the cosmos we observe, the expansion cannot be driven by a thermodynamic explosion. Instead, we are told that the metric of spacetime itself is expanding and so carrying distant galaxies apart.
So we have arrived at the previously noted invisible physical spacetime of ΛCDM. No human being, scientist or not, has ever demonstrated or made a direct observation of a physical spacetime. Space and time as they are commonly understood are relational concepts, like temperature. They are not real things in themselves, they only describe relationships between objects and events.
Spacetime, on the other hand, is a mathematical concept associated with Relativity Theory in which space and time have been reified into physical entities and unified as the 4 dimensional continuum which acts upon, and is acted upon by, the matter and energy content of the Universe.
It is interesting to note that while spacetime is integral to the modern conception of both Special and General Relativity, it is only the relational concept that is actually necessary to either. An explication of this point will be part of a later section. For now there is this late in life opinion of Einstein’s to ponder.
There is no such thing as an empty space, i.e. a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field.
– Albert Einstein, Relativity, The Special and General Theory, 15th ed. 1952
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The ΛCDM model may bear scant resemblance to the observed cosmos, but the unitary assumption persists because it provides the framework within which it can be said that ΛCDM is the best model we have for the cosmos. However, if the unitary assumption is false and it almost certainly is, then ΛCDM has, just as it appears, nothing to do with the observed cosmos.
When all is said and done, ΛCDM might prove to be a crude starting point for a model of galactic systems in a physically rational cosmological model, but first the cosmological enterprise will have to be pried from the stranglehold of the mathematical over-extrapolators who currently control the scientific endeavor.
As it now stands, ΛCDM tells a most peculiar story:
According to the model, the vast cosmos we observe began 13.8 billion years ago in a unique event that originated from an incredibly dense and inexplicable original condition that may or may not have been a singularity (a physically meaningless, mathematical concept).
This inexplicable original condition then transitioned, for an inexplicable reason, to a fully explicable state that began expanding rapidly, allegedly driven by something called an inflaton field, that no longer exists, until the universe arrived at its current state.
We are then informed that in its current state 5% of the universe consists of those things that we actually observe in the cosmos while the remaining 95% is comprised of the invisible dark matter and dark energy whose only purpose is to reconcile this absurd model with the cosmos we observe. Modern cosmology is an unscientific mess.
1.1.2 The Quantum Realm
If the standard model of cosmology is absurd, the situation on the quantum scale incoherent. It is possible, at least, to understand what ΛCDM says about the cosmos, even if it appears physically nonsensical. In Quantum Field Theory it is almost impossible to understand what QFT says about the nature of physical reality at all, as most of it consists of a long self-referential chain of mathematical logic which has only an occasional, almost incidental, relationship to empirical reality.
It is worthwhile to read through the Wikipedia article on QFT here, to get an overview of just how mathematically abstract the theory is. Of course, given the fundamentally unobservable nature of quantum processes, a certain amount of abstraction is to be expected.
However, what has transpired in the scientific community is a runaway usurpation of the scientific endeavor by mathematics. This has resulted in a model wherein, even the marginally observable aspects of say, the atomic realm where quantum events are first encountered, are supplemented by an array of invisible “entities” derived solely for the purpose of supporting and extending the mathematics of the model.
The Wikipedia article includes the following chart of elementary particles. This would seem to be a convergence point between theory and observation but, in fact it is not. Most of these supposedly elementary particles have never been observed directly. Of the 17 particles, only four, the electron, muon, tau, and photon can be directly observed, and of those four, the muon and tau have mean lifetimes on the scale of 10^-6 and 10^-13 seconds respectively. That is, when produced in high speed collision events, muons and taus decay in minute fractions of a second.
On the atomic scale, the known fundamental, component particles are the electron, the proton and the neutron, all three of which are directly detected. The electron and proton are completely stable – they have never been observed to decay while a free neutron decays (into an observable proton and electron, and a theoretical antineutrino) in just under 15 minutes. Nonetheless, only the electron shows up in the chart above. The proton and neutron aren’t considered elementary because they are theorized to be composed of undetectable quarks.
This theory of elementary particles is only a small part of QFT which makes other claims about the nature of physical reality that have no apparent relationship to observations. Quantum Field Theory does not lend itself to ready explication as even a cursory glance at this Wikipedia entry will make clear.
2 Math is not Science
2.1 Science Defined
Science is the open-ended investigation into the nature of physical reality employing the complimentary probes of logic and empiricism. Neither logic nor empiricism, by themselves, constitute science.
2.2 Mathematics Defined
Mathematics is an abstract logical discipline based on counting.
2.3 A Peculiar Belief System and Its Pernicious Effects
Mathematicism is the belief that mathematics underlies and is determinant of physical reality. Although this belief has no scientific basis it is widely held in the scientific academy and is, in fact, the default operational mode in both cosmology and quantum physics. As a consequence, mathematical models now take precedence over observed reality when there is a discrepancy between the two.
Mathematicism is the root cause of the so-called crisis in modern physics. It has enabled theoretical physicists to rummage about in their mathematical imaginations in search of models they find aesthetically satisfying while completely ignoring the vast amount of empirical data that has accumulated over that last century. The resulting incoherent and absurd standard models of theoretical physics, documented in the first section, are the misbegotten off-spring of mathematicism running amok in the halls of science.
3 Qualitative Analysis in Modern Science
Qualitative analysis is neither taught nor employed in the scientific academy.
3.1 Consequent Analytical Failures
3.1.1 Dark Matter and the Keplerian Method
The widely held belief in the existence of undetectable (hence dark) matter in the cosmos is directly attributable to an inability of the modern theoretical physics community to construct reasonable qualitative models as a necessary precursor to their quantitative calculations. The dark matter claim stems mainly from the inability of theorists to accurately calculate the rotation curves of galaxies using a mathematical framework designed for the solar system.
The Keplerian method for calculating the rotational velocity of planets in the solar system consists of treating the case of each individual planet as a separate two-body problem involving the planet and the sun. This works to a reasonable degree of accuracy because 98% of the mass of the solar system is concentrated at the center of the solar system, in the sun, allowing the masses of other non-solar bodies to be ignored.
However, the morphological structure of a typical disk galaxy is nothing like the solar system. A significant portion of the overall mass of the system is dispersed non-uniformly throughout the disk. There is no rational basis for equating the two systems via either the Keplerian method, or the equally inappropriate Newtonian method (the shell theorem).
It should be noted that a Keplerian decline is usually invoked as an expectation, with respect to galactic systems, not as an actual calculation. For example in this seminal paper by Rubin, et al, there is this:
Thus, the small Sc’s exhibit in their rotational properties the same lack of Keplerian decreasing velocities as do the high-luminosity galaxies…
None of the rotation curves have the “classical” shape, adopted so frequently in the past, of a long nearly Keplerian drop in velocity after the initial rapid rise.
There are available mathematical solutions capable of properly calculating the rotation curves – see here for instance. Unfortunately, dark matter has a constituency in the careerist-oriented world of modern theoretical physics. Books and papers have been written. In the immortal words of Upton Sinclair, “It is difficult to get a man to understand something, when his salary depends on his not understanding it.”