Tutorial 1

As an introduction, The basics of Quirk Theory are as follows:

There exists a set of fundamental identical particles from which all others are constructed. Each fundamental particle has no property except location, and a logical connection rule to each and every other particle. Location is defined as our rulers measure in flat orthogonal Euclidean complex co-ordinates (normal vector rules apply!) The particles are zero dimensional objects with no other properties (such as mass or charge) (i.e. they are mathematical points)

There exists a set of coordinate shape "states" for these particles. This set is restricted only by the requirement that the relevant coordinate difference between every pair of particles obeys the rule called the "Equation of Natural State" which states that the sum of squares of the complex relative coordinates for each pair of particles equals zero.

There exists a mechanism by which the Universe changes from one state to another. The details of what changes in state can occur is defined by the ordinary differentials of the Equation of Natural State with respect to a parametric variable called "system phase" common to all particles. This is a mathematical parameter only, of convenient use to track state change in the manifold. The first differential can be called a "phase velocity" not to be confused with the common definition of velocity in physics.

Each shape state therefore in the differential limit has a subset of states permitted to follow or precede the "present" one and this subset is given by the solutions to the differential equations integrated forward and backward in phase.

One of these solution states is chosen at random with equal probability of following the last. The available paths that a particle might follow with system phase may in general be interpreted by a probability distribution.

Each particle solution path with phase has a time-line associated with it, defining the elapsed time (t) of a local clock attached to that point. This time-line is a general non-linear function of system phase whose shape is determined by the need to absolutely conserve the physical definitions of momentum and energy at all times and all places.

The reasons for this model form and axiomatic underpinnings, and its possible relationship to physical law and empirical evidence will be discussed separately.

Charles,

Agreed it is a brave attempt!. But the mathematical formulation of Quirk theory is complete. It is the relevance to physics which is the "work in progress" As an engineer, I am of course well outside the theoretical physics community. So if not "brave", then how else to gain access to the expert knowledge and advice I require to progress it to "rigorous" , or alternatively to dismiss it if shown to give a result that contradicts existing theory. It is a fact of life that I will always be off the radar of the appropriate departments where I could myself progress this work to a rigorous outcome (and believe me I have tried for several years to advance this as a PhD thesis topic in physics, but have to date never been given the opportunity to present my case let alone be rejected for it!) I am a mature student, and running out of options and time, so what would YOU suggest.

Charles,

I counter by saying every probability distribution has an underlying "sampled variable" The location in this case is the sampled variable underpinning QM statistics.. Calling location a hidden variable in this theory is like calling "spin" a hidden variable in QM.

I also point out that the uncertainty principle allows measurement of position to arbitrary accuracy, but at the expense of uncertainty in velocity. So no, I do not agree with your assertion that this is incompatible with QM for the reasons given above.

Charles,

Thank you for the reference. I will examine it for examples suitable for equivalence testing, but most such QED textbook studies are not suitable for immediate testing with Quirk theory for reasons as follows:

Before a comparison with full QED is attempted, both the electron and proton solution in quirk space must be found, in which case it is the proton/electron mass ratio which would be found first before equivalence to QED is demonstrated. This is because there is no a priori potential field that can be assumed in Quirk space to approximate the proton, as is the case of worked examples in QED. Work to date would indicate an electron is most likely a configuration of three points (the neutrino likely being two) with several more complicated possibilities for the proton. However the photon solution Is known in Quirk theory, and corresponds to the GR solution. Indeed several interesting interpretations relevant to physics also arise as part of this solution. Numerical simulations of the Dirac relativistic photon solution also indicate valid solutions of this, are also valid solutions in Quirk space.

It is proven there can be no analytic transform between particle/interaction rule models and field theories based in differential Cartesian geometry. There are only approximate transforms whereby equivalent frameworks in the two might be shown to approach the same result to arbitrary precision. This is a fact of life even at low energy densities, and of course it is only in the high energy density limit that a reasonable divergence in outcome might be expected. Such densities do not usually occur in QED, but can occur with gravity also involved. I guess comparison of a Bose-Einstein condensate might be relevant.

Charles,

Hang on, I never said that I was modelling QM as a classical probability theory. Where did you get that idea from? All I said was that a probability distribution can always be interpreted as a sampling of a "sampled" variable. To clarify I will give a quick explanation of how Quirk theory samples these position states by explicitly using the uncertainty principle.

The sampling of the position state in Quirk theory is determined entirely by the solutions to the first and second differential of the equation of natural state (ENS). This first differential exposes the conjugation of position and velocity relationship of the fundamental particle, and explicitly requires that (delta x)(*(delta v) >= constant. Now the v here is the phase velocity, but each phase velocity has a related function of local time associated with it, so the same conjugation occurs in the time domain as in the phase domain. The second differential of the ENS explicitly exposes the energy time conjugation in a similar manner.

Quirk theory says that the uncertainty principle applies to the most fundamental particle in nature, from which all else is built. therefore all observations will exhibit the uncertainty principle regardless if it is an electron or a proton or a double decker bus.

So in summary, Integrating these position states forward or back in phase in Quirk space requires the action of the uncertainty principle in the mathematics of Quirk Space. I cannot see why you would conclude from this that Quirk theory is a classical probability theory.

By the way, there is also an explicitly non-classical explanation for quantum spin in Quirk space (and an explicit cause of the angular momentum of the electron) that agrees with QM, and not with classical mechanics, but that is a story for another day.

Charles,

Thank you for the additional references. For the record, I am not entirely ignorant of the foundations of Quantum Mechanics and its relationship to QED as many people in RG seem to tend to assume (Is it because they think engineers are not capable by definition of understanding such stuff? I sometimes wonder). Quirk theory is NOT something I have just plucked out of thin air. It is the result of several years of study around the specific issues facing the unification of physical law, which includes as it happens all the on going arguments around QM and QED.

Charles,

All the non classical parts of QM are done in Quirk space before the sampling is done. It is built into Quirk space by the spatial correlations in the Equation of Natural State. It is only after this that the sampling is done as I have allready explained. I presume you would let me do sampling of a measurement during an experiment? This is exactly the same process in quirk theory of translating QM results back into real empirical measurements.

I do not understand what it is you don't get about that. The position sampling is not the only thing going on in quirk space. All the interesting stuff happens prior to the sampling.

Yes I agree we have reached an impass. You say I dont understand QM and I say you don't understand Quirk space, so the onus is on me is to explain it better, since QM is the status quo. I will get back to you when I can do so.

About the only thing I can add to my explanation right now is that you say QM does not have location between experiments. That is correct. But neither does quirk space have a known location between experiments. It has a contuinuum of configuration states representing a continuum of locations between measurements.

Charles,

OK I have figured out where our misunderstanding is. I probably gave you the wrong impression that a particular moment in time (like the present) has a single configuration state associated with it, with a convoluted but known trajectory over time that is then sampled. No, this is not the case. As you correctly say repeatedly, and I agree with you repeatedly, It cannot be that way.

In quirk space each "present" has a continuum of configuration states associated with it.. So yes you are correct that it is the wave-function by another name. For example one would expect a snapshot in quirk space of a stationary hydrogen atom in ground state to show a "picture" of the 1S orbital by plotting all the valid configuration states associated with that moment in time.

By the way it should (if the discovery works as I think it does) also show the complete wave function of the proton in this atom as well, and it will do all this without a-priori knowledge of the rest mass of these particles. An ambitious project indeed, but necessary for a unification attempt, and this is where my simulations of these systems seem to be heading right now as I develop understanding in how to solve them.

So why not use the standard QM language? Because quirk space is intended to be much more than just QM. It is an attempt at a unified theory of physics.

The formulation in Quirk space also has some very special and useful properties. A very good example is that the total system energy is not dependent on the reference frame chosen in Quirk space (unlike in Cartesian geometry where it most definitely is dependent.).

Every reference frame in Quirk space has an exact equivalence to the center of momentum reference frame in Cartesian geometry. Strange but true, and a VERY useful outcome, because you can travel around in Quirk space without having to worry about reference frame transforms, and then just translate back as required.

In Quirk space the co-ordinate is a function of the particle, whereas in QM the particle is a function of the co-ordinate. It is a very different way of looking at the same thing. It takes quite some time to understand properly. So I ask you not to dismiss it so quickly. I accept such a change of focus will be very contentious but I have been working with this structure for several years now and it really does seem to have useful depths to it.

Here is a list of some of the additional benefits this formulation should provide:

a) Special relativity is implicit in the ENS.

b) Combinations of different numbers of these fundamental particles in Quirk space should express the full and varied quantum numbers of the entire standard particle model, including those of QED and QCD. For example the combined wave-functions of three of these fundamental particles should express the quantum numbers of the electron, combined wave-functions of two particles, the neutrinos, and so on.

c) The congregation of large numbers of these particles should produce a local time dilation effect due to gravity (i.e. GR)

d) The Quirk Space formulation explicitly allows continuum tracking through singularity states without the consequent calculation of infinite properties. Infinities never happen in the mathematics of quirk space and re-normalization is never required.

e) The equation of natural state is supposed to precondition the configuration states so that only valid QM solutions are present. This should significantly reduce the computational burden of solutions. In principle all you have to do is specify the known empirical setup, and the system can be iterated quite quickly to the required QM answer.

These are the sort of consequences that the discovery of this equation should lead to, given my current understanding of the background work that led to the discovery of it. Whether in fact does or not is the rigorous part of proof you refer to.

@Charles Francis

I believe i have a found a paper that might break our current impasse on this topic one way or the other.

Quantum Theory from Five reasonable Axioms - Lucien Hardy

http://arxiv.org/pdf/quant-ph/0101012.pdf

Can you find time to give it a brief look to see if this paper a correct derivation of Quantum Mechanics?

While Quirk theory diverges from this derivation by including an equation intended to combine QM with Special Relativity, This change should not have broken the 5 axiomatic underpinnings referred to by Lucien.

Tutorial 2:

Solving for a valid state configuration in Quirk Space.(4C example)

Take four complex numbers. Square each of them. Add them together. If the result is zero you have solved the Equation of Natural State. Repeat for every pair of qits (points) in quirk space. The four complex numbers required for each pair are the arithmetic difference in each complex co-ordinate between one particle and t'other.

The solution is a valid Quirk Space Configuration State.

Charles F,

This is just classical probability unitarity - you can always transform a measurement scale to 0-1 to define a probability scale, so a measurement is also a probability no worries at all.

Charles F,

Except that four of the five axioms only require classical probability to do their thing so this is not a problem. It is the only the 5th axiom that is unique to quantum mechanics probability and the equation of natural state is demonstrably continuous and reversible, thus meeting this 5th criterion.

I have been discussing this with others, and apparently this approach of Lucien's is already known and quite well understood and accepted within the discipline of quantum computation. It is quite OK to do large parts of the solution in classical probability, just not ALL of it - you must at some point also make sure the 5th is met. I plead the 5th!

In quirk space because the equation ensures axiom 5, it puts the onus on the method of solution, not to the equation itself.......In solving the quirk space you must provably connect the configuration states up by a continuous reversible function - that is by one that meets the first and second differential criteria of the Equation of Natural State (ENS), and if you do, the results must reflect the answer that quantum mechanics would give as well.

The ENS is an harmonic function - Schrodinger also had to chose such a function in his derivation - that choice of his had to meet two criteria, classical unitarity, AND continuous reversibility. That is why what he did worked, and that is why the ENS in the context of Quirk space is also an explicitly quantum mechanical system.

By the way I really do appreciate the time you have put into this, which is why i am attempting to use arguments other than my own to counter your criticism.

Charles F,

Maybe we should seek some independent arbitration on this point by inviting a third party to look through the threads and comment on our impasse. You have anyone to suggest?. I would put forward Matthew Brown as a possible candidate

Charles,

My only motivation has been seeking help on process of how to do those rigorous deductive arguments, or a falsification counter argument (which presumably on your part would also require your own rigorous deduction) I only seek this not for arguments sake but because I have a day job, many dependent people around me to support, and very limited time to progress this on my own.

I was under the hopeful impression that someone out there might already possess the knowledge to actually suggest how I might go about those arguments, or alternatively a compelling argument why it must be false.

Instead of this, we reached an immediate impasse because any mention of the word classic probability caused you a problem. When I pointed out that a very respected person in Quantum computation (Lucien Hardy) has no problem at all using classical probability as part of the quantum computation process, and I pointed out the exact part of my theory that went to establishing axiom 5 of his work (that presumably does constitute a rigorous proof) you instead reverted back to the classical probability argument.

From my perspective it is you having the argument for its own sake, or you would have refuted my case by saying why you thought the ENS was not reversible and continuous thus ensuring axiom 5 of his work was not satisfied. instead you reverted to your original complaint - any mention of classical probability is a big no.

I am not making any great claims - those are entirely your words not mine - All I am making is an hypothesis which i wrongly assumed people might be interested in tossing around the merits/flaws/deductive possibilities of, given that it is trying to replicate Dirac's work in a different mathematical framework, but without the rest mass term at all appearing anywhere.

If you were not taking it in that spirit, why did you start except to have an argument?