John,
You wrote: "How nature chooses the laws of physics may be unknowable". In my article I provided metaphysical arguments for the necessity of many paradoxical features of quantum physics. So I think there are knowable reasons for the choice, as I found such reasons (not for all details of course but for some main features), as opposed to other classes of universes such as deterministic ones like those described by classical mechanics, which I consider excluded from the possibility of physical existence able to carry conscious life.
"Quantum field theory suggests there are infinite combinations". From a mathematical point of view it is indeed naturally analyzed as involving potential infinities of underlying full descriptions (shapes of fields or trajectories), however the global result of these combinations is that they only leave a locally finite number of possible effective states (in a quantum sense) for each given limited amount of available energy, as I also explained in my essay. (See also my web page of introduction to quantum theory, starting from principles coherent with quantum field theory even if the mathematical correspondence between the formal infinity of combinations of quantum fields and this effective local finiteness of available states is a rather subtle one).
To roughly explain this articulation : these mathematical details of the continuous description (the shape of a field or trajectory) are not physically real but can only become real when created by an act of physical measurement of these details at a given scale of resolution (and the thinner details we want to measure, the more energy we need to measure them).
"the statistics of QM is really a measure of measurement error as the Bohm Interpretation suggests. The Bohm Interpretation argues against ideas of infinitely many paths of particles until a collapse happens".
How amazing to see you simply claim how things would "really" be, as if it was obvious or simply acceptable without problem, this kind of view that of course very many physicists were very persistently trying to imagine, but which scientific evidence also persistently dismissed for any try to keep things reasonable. See my page on the Bohm interpretation, where I show it has so many troubles that I cannot consider it seriously plausible. Even in this interpretation that is the closest we can find to the idea of "measurement error", randomness is still not any effect of a measurement error but the result of the absolute impossibility to measure something even in principle. Ironically as opposed to your remark, one of the main troubles I see with the Bohm interpretation is that it reintroduces an actual infinity in physics which the fundamental features of quantum theory remarkably avoided (standard quantum theory considers randomness as a pure fact created by observation that does not hide any real detail, while the Bohm interpretation claims that observation only reveals some data from a hidden actual infinity of real details, those of continuous variables that would really exist with infinite accuracy ; my essay explains how quantum physics makes the continuity of variables only behave as a potential infinity, not an actual one).
"Mathematics characteristics may eliminate many of the possible interpretations of QM as being unphysical." What do you mean ? Well, we can say that mathematics practically eliminates the Bohm interpretation as being too mathematically inelegant as explained in my web page. But I cannot see what else you may mean here, as you did not even define what means "unphysical" as if there was such a thing as physicality that had to be satisfied (the paradoxes of quantum theory rather argue against the idea of physical reality, as not having a natural fit with what we observe).
"Newtonian mechanics has a calculation problem as r в†' 0" : only if we assume the presence of point masses, which is not a claim of Newtonian mechanics.
"GR suggest the universe is homogenous to avoid the r в†' 0 issue." Well no, what GR does instead near r=0 is that a high concentration of mass gives a black hole with a smooth horizon (that is a locally non-special region of space-time) from which no information can go out.
The difference you assumed that is a difference between point masses and smooth densities, is not an effective difference at all, but only a difference of the mathematical tools which are used for formulating theories or their consequences, but are not really associated to the theory. For example, Newtonian gravitation can be equivalently expressed between formulations using singular masses and formulations using smooth densities, in this way : a smooth density can be understood as a dense regular accumulation of point masses ; a point mass can be understood as the limit of a high density in a small region. According to distribution theory, each concept can be understood as the limit of the other in the dual space of the space of continuous fields g on the physical space:
A distribution of point masses (mi at point Pi) defines the linear map (from the set of continuous fields g into в„ќ)
g ↦ sumi (mi g(Pi))
that is the finite linear combination of Dirac masses at each Pi (that is, g ↦ g(Pi) ), with coefficients mi.
A smooth distribution with density П† defines the linear map
g ↦ integralx φ(x) g(x) dx
These 2 spaces (the space of distributions of point masses, and the space of smooth densities) both duals of the same vector space of continuous fields, are parts of the more general dual of this space where they are the limits of each other and where the law of gravitation is naturally extended as long as we are not considering physical cases where it leads to divergences in its consequences.
"Mathematics shows only two mutually exclusive characteristics in reality - discrete (counting) and continuous (geometry)"
No : in the dual space mentioned above, the discrete and continuous distributions are not the only possibilities which are the limits of each other. Another kind of possible distribution, intermediate between the discrete and the continuous distributions, and also corresponding with them as being the limits of each other, is the case of a Cantor set distribution, with any choice of fractal dimension between 0 and the dimension of the containing space.
However this does not say which kind of distribution is actually involved in physics. When analyzing whether some equations initially written in differential form finally lead to convergent or divergent results, different things can happen.
What really happens at sub-atomic scales has to be given by quantum field theory, however what this gives is not any definite distribution of anything, since it is a quantum reality, not a classical one: we do not have any definite distribution of anything but states of regions that can be analyzed as differently made of superpositions of possibilities depending on how you analyze it (with which scale of resolution of the analysis).
Quantum field theory is full of mathematical expressions written in a formalism which seems to require some class of regularity of fields, until it turns out that the fields actually involved are not in this regularity class, so then we need to develop techniques to make these ill-defined equations provide results despite their lack of definiteness. In quantum field theory, this is the question of whether a field (or interaction) is renormalizable or not. Sometimes we exclude some interactions as they are not renormalizable (they diverge), other times we still accept them, admitting that we do not know what happens at very small scales (high energies).
General relativity admits distributions of mass down to space dimension 1 where the resulting geometry becomes singular (may it be a line or a Cantor set distribution with fractal dimension 1), below which we get black holes.
You mention "scale relativity". This "theory" by French "physicist" Laurent Nottale is not even a theory but pure senseless bullshit, as I explained in details many years ago. I wrote the detailed explanations in French but you can see here my short report in English on this issue (see also my related notes on science and pseudo-science).
"Perhaps the "space" of GR, the wave medium of QM, and the plenum are the same physical constituent. If the frequency of the wave is related to the particle, resonance produces quantum entanglement."
Perhaps, perhaps... of course, as long as you do not make the work of seriously learning the mathematical structures of the world that were discovered and so well verified in modern physics, any fantasy will seem equally plausible to your eyes.
"The fractal principle suggests that observed geometric relationships apply in all levels of systems. Because pi = circumference / diameter in two dimensions, pi must be the same number in three dimensions."
Well, pi is the same number no matter anything such as the dimension of anything, because it is absolutely well-defined as a fixed real number independently of anything. However if you ask about generalizations in other dimensions, of the ratio circumference / diameter, then I'm sorry but it takes different values. These values can be expressed using pi, but these are different expressions. By the way, what is the circumference of a sphere ? A sphere has a surface, that you can compare to... the square of the diameter. Then the ratio still happens to be pi in the 3-dimension space but this is a coincidence that no more works in higher dimensions. And it does not have anything to do with the fractal principle (which is not a physical principle but a property of abstract geometrical objects which only happens to approximately fit some natural objects inside some limited range of scales), where things are similar at different scales but with the same fractal dimension (please, please, don't play with the ambiguity of the word "dimension" in the English vocabulary, which may mean 2 completely different mathematical concepts ! this is so ridiculous).
"The relatively easy developments of Euclidean geometry compared to curved space geometries suggest the universe is flat."
The universe is not flat. Only the global geography of the universe, that is the map that can be abstractly rebuilt in terms of the relative positions of all galaxies considered at a common age of the universe, has been observed to be quite close to flatness from, for example, the data of the cosmological background radiation. This should not be confused with any cancellation of space-time curvature. For more details, see my text of cosmology.
"Life on Earth can increase although entropy increases because Earth is an open system with energy supplied by the Sun. That fractal mathematics works suggests the universe must also be an open system. This suggests the universe is not adiabatic."
Ridiculous. The universe is adiabatic. Its cooling down results from its expansion, giving a wider and wider intergalactic space able to absorb (accumulate) all the entropy created by so many material processes, mainly in the form of visible and infrared radiations.
I skip parts of your article as I am getting bored, I stumble on "The temperature of the universe appears to be a fine tuned parameter and it is very close to the natural logarithm base e K". Sorry, it is not fine tuned. The universe cools down during expansion. Thus its temperature depends on its age, but anyway it is now cool enough for this heat to be insignificant for the issue of habitability. You are making ridiculous numerology here, because the Kelvin is not a natural unit, but the 1/100 fraction (according to our human decimal conventions) of the interval between the temperature of ice fusion (which is almost independent of pressure) and water boiling which is highly dependent of pressure : we take here as reference the average atmosphere pressure at sea level on Earth, which has no reason to be the same on other habitable planets. Other habitable planets may have different sea level atmospheric pressures, such as half or twice ours, leading to very different values of water boiling temperature, and thus other conventions of temperature units, still assuming by chance these aliens to have the same numerical conventions.
"Mathematics is deterministic. Given an equation and the initial data, a definite result is calculated. This implies that the universe is deterministic. If there is free-will, then the mathematics humans have developed needs a new function like fractal development or a model of the mechanism of apparent free-will."
Your sentence seems to express a confident belief in determinism, though it is not clear as you seem to beg for an articulation with a possibility of free will. Why expect something new ? As I explained in my essay, we already have the needed "math of free will" under hand : determinism was spectacularly dismissed by quantum physics, and all the so popular tries to reinterpret it in deterministic manners remain so desperate (mainly with the Bohm interpretation, even though I do not see it genuinely deterministic, while other interpretations are even less deterministic). Determinism is only sociologically normal in the sense that it is a very popular sport to keep bumping one's head on the wall of the physical evidence of indeterminism, baselessly dismissing (by metaphysical prejudice) this evidence from quantum physics as a mere irrelevant temporary accident hiding a deterministic reality that we must work to discover...
"There may be no standard capable of fulfilling the physics definition of a standard that reflects the mathematics characteristic of different mutually exclusive discrete and continuous".
In this article and also the other article you wrote ("Photon diffraction and interference") you express your general assumption that there would be a problem in physics about the compatibility between the discrete and the continuous, between the concepts of waves and particles. The real fact is that there is no such problem : the coherent mathematical formulation of quantum fields and how it articulates the aspects of fields and particles, is now well-understood by professional physicists since a long time. Of course this idea looks very unintuitive for people not familiar with these mathematical concepts, which cannot be simply explained without high mathematics, so that many people keep the illusion that a problem subsists. You seem to have this illusion. If that is the case, it would be a pity, meaning that you did not study physics at a high level enough to understand the known solution of this paradox yet.
Now from your comments:
"But then general relativity also mathematically suggests gravitational ether. A gravitational ether (called ``space'' today) is influenced by matter and influences matter through a gravitational field that exerts a force by contact through its divergence. "
This seems to show that you are not familiar with General Relativity either. General relativity explains gravitation by concepts that do not include such a thing as "a gravitational field that exerts a force" in this naive (Newtonian) way you are describing.
"Therefore, the ``consciousness'' is part of our world and physics and math should be able to study it. But there is no math to describe consciousness, yet. As I said a new form of math is required." I consider that the fundamental character of consciousness is that it escapes mathematical description. However as I explained in my essay, some special mathematical features of physical laws are needed and provided by quantum physics to allow for the interaction between mind and matter. There cannot be a math to describe consciousness. There is a clear concept of what is math and what is not math. A "new form of math" is nonsense : if it is still math then it is math as we know it in its generality (see the foundations of mathematics describing this generality); if it is radically different then it is not math anymore.