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Experimental Confirmation of Lattice-Free Spacetime

September 1, 2012

In my previous post, I posited that spacetime cannot be a lattice at Planck scale distances, and by sheer coincidence, this completely different experimental report also confirms the likelihood that spacetime is smooth at this scale:

http://www.space.com/17399-gamma-ray-photons-quantum-spacetime.html

A smooth spacetime means that Planck scale lumpiness (a lattice of one of the types I describe in the previous post) will not explain quantization. I suspected that anyway, because quantization is scale independent. Low energy photons are quantized over distances that are enormously vast (hundreds of orders of magnitude) compared to Planck scale distances, so I did not see how a lattice could induce that quantization.

The field twist is also scale independent, so is another nice arrow in the quiver for unitary twist field theory. But I’m grappling with a big problem as I develop the specular simulator for the unitary field twist theory. The probability of electron motion is affected by its ability to self absorb a virtual photon, and this probability is directly proportionate to the fine structure constant. I believe that this number is the square of the probability to emit and the probability to absorb, making each have about an 8 percent chance of occurring. Physicists have absolutely no clue why this probability is what it is. QFT gives no guidance but uses the experimentally determined value of interaction probability as a foundation for every quantum interaction of particles and fields.

As usual, I am trying to find a geometrical reason that the unitary field twist theory might give that probability–some ideas, but nothing obvious. I have to figure something out before I can even start constructing the specular sim.

Agemoz

Tags:lattice, qft, quantization, smooth, twist theory, vector field
Posted in philosophy, Physics | Leave a Comment »

About Me

I'm an amateur physicist. I've studied physics and philosophy for a very long time, and have investigated some of the unanswered questions in physics with an intent of finding some possible explanations or theories on how they might work. Two of the most interesting questions for me are whether there is a geometrical basis for quantization and special relativity, and why there is a particle zoo (that is, is there an underlying structure that results in the particle zoo). I'm well aware of the danger of crackpot theories (usually characterized by just enough knowledge to get things wrong or silly), but allow myself to pursue ideas anyway as long as I'm clear about their speculative nature. I don't pretend that I have any significant discoveries to report, but thoroughly enjoy pursuing various ideas about how the universe works. To faciliate this study, I've created a lattice simulator that allows me to test a variety of ideas.

Unitary Twist Field Theory

A long description and justification for the thinking that has led to the Unitary Twist Field Theory. Note, IANAP (I am not a Physicist). This is long and describes the historical evolution of the Unitary Rotation Vector Field. The latest work has changed several parts, I am in the process of updating this.

Summary: A unitary rotation vector field is investigated as an underlying field that gives rise to the particles and fields of the Standard Model. The underlying field is single-valued, waves cannot pass through other waves. This is the means by which quantum interference redirects particle paths. The simulation work has revealed a new principle:

Quantum interference is responsible for redirecting particles along wave interference peaks–and also for creating those particles.

Long description: This effort to work out the details of this unitary twist field is based on the underlying assumption that our existence can emerge from nothing, and posits a reductionist approach to explaining the particle zoo. The theory basically says that there is a continuous rotation field in R3 + I that can produce stable solitons. Here is a list of the steps I have taken to arrive at this theory:

a: If existence does not require an intellect to form, the existence must arise from nothing, both space and time.

b: If existence does require an intellect (e.g, God) then further investigation isn’t really necessary because the rules for existence are set in a place we do not have access to.

c: One way to determine if the creating intellect exists would be to determine if the existence could not come into being without at least two rules, and such rules would have to come into existence from a creator. Saying that existence formed with one and only one rule is equivalent to saying that existence could arise from nothing and God is not required.

d: Finding God seems to be pretty much unanswerable without clear direct communication from God, whereas coming up with a way that existence could form from nothing seems to be an alternative possible approach for a human mind to answer the question about the existence of God.

e: Such an approach could start with the limits of current human knowledge, the known existence of the particle zoo. If a reductionist approach could be taken as to why the particles exist, we may be a step closer to saying that an intellect is not needed to create this existence. Conversely, if we can show with reasonable probability that it’s impossible to form particles from some continuous field, that’s an argument in favor of the necessity of an intellect in creating our existence.

f: I am assuming that a continuous field that can create stable particles is a reductionary step–that is, a step in the direction of finding a single rule defining this existence.

g: Now I start applying known physics to this field to determine what it must look like. I am assuming that this field is opaque, that is, there aren’t any parallel overlapping fields. This is clear because multiple rules are necessary to form two fields.

h: I assume that this field has elements that can only rotate. No displacement or magnitude can be applied to any field element. This assumption comes from the E = hv relation for particles, which basically says that particles are described only by frequency, there is no field degree of freedom equivalent to field magnitude.

i: when objects move, the field elements pass rotations via three types of momentum to adjacent elements. In this theory, no field element ever “moves”, instead particles move because field rotations pass as momentum from one field element to the next.

j: In order for E = hv to work, there has to be a means of ensuring that no partial or multiple count of rotations can exist. This is a form of field quantization, and I have proposed a background lowest energy state. In such a system, field rotations called twists start and stop at the background state rotation angle.

k: To ensure that R3 does not have an observable resonance (which would be experimentally discernable) that would undermine gauge theory symmetries, this background states points to an imaginary dimension. It is not possible to have the background state point to a basis vector in R3.

l: If the field has a crossproduct momentum transfer as well as the more standard linear translation of angular momentum of field rotation elements, this becomes a necessary and sufficient condition for forming stable linear particles of arbitrary frequency. UPDATE: simulation work shows that quantum interference is responsible for particle formation.

m: the crossproduct rule for momentum displacement allow a particle to start a single twist, and allows the particle to end the twist after one full rotation.

n: The crossproduct rule also allows the formation of twists that move along a curve. This is possible due to the vector combination of the crossproduct that is normal to the current element rotation orientation and speed. UPDATE: simulation work shows that quantum interference is responsible for path curvature.

o: If twists can curve, there are some twists that will form stable closed loops. There are many possible stable curve solutions, which I am proposing is the basis for the particle zoo.

p: A single free linear twist models a photon of some energy and length defined by the frequency of twist rotation.

q: Since the twist moves from +I background state to an R3 direction and continuing to rotate through to the +I direction, polarization of this twist arises as a linear combination of the two R3 vectors normal to the direction of twist travel. UPDATE: new simulation data suggests that quantum interference and momentum provide a basis for polarization, this will be revised.

r: The crossproduct momentum translation is necessary to allow a twist to start and to stop, otherwise field symmetry would propagate in both directions simultaneously at every point in the twist, and stable particles could not form (they would dissipate). In other words, the quantization of the field is ensured with the background state, and the ability to start and stop a twist arises from the crossproduct momentum translation. Thus it can be stated that to form stable particles from a field, it is necessary that a field capable of forming stable particles must have a handedness that can only come from a crossproduct momentum property. UPDATE: simulation results show this and following sections needs to be revised.

s: This handedness thus must be ingrained in any field solution that produces stable particles. This handedness of the field will show up in some cases as a chirality violation.

t: In order for the twist propagation to be stable, the only possible momentum transfer via crossproduct relation is at the speed of light, where the leading and trailing edge of the twist cannot be affected or connected to neighboring element rotations.

u: Any closed loop rotation sequence thus will be limited to the speed of light. If one were to unravel the cylindrical spiral path this loop takes in Minkowski space, a single quantized twist will form a right triangle where the hypotenuse is the speed of light times the time of one rotation of the twist, one side is the particle travel distance, and the other side of the triangle is the radius of the loop. This right triangle enforces a relation between the loop travel speed and the speed of light. This relation computes to the beta factor of special relativity and is the means by which special relativity geometrically arises from the twist theory.

v: A corollary to u: above is that time dilation for every particle results from the constrained stretching of the spiral helix in Minkowski space as the particle increases speed proportionate to the speed of light. In other words, each particle’s relativistic clock is implied by the time to complete a single twist. Observing from different frames of reference will alter the apparent time to complete a twist and thus affect the relative passage of time between particle and observer.

w: A single closed loop models the electron of one type of spin. The twist direction relative to direction of travel defines a spin-up or spin-down electron, whereas the loop curvature relative to the handedness of the field defines the particle vs the antiparticle version of the electron. Note that a linear twist does not have these degrees of freedom, so there is no antiparticle to the linear twist photon.

x: Quarks are posited to be linked twist loops, the up quarks have a single link going through its center and the down quark has two. The strong force results when linked twist loops are pulled apart such that twist momentums approach each other with an asymptotic direction conflict. The passage of a twist through the center of a loop affects the rotation of the loop by increasing the crossproduct momentum of the loop. Note that since electrons are modeled by a loop with no central twist going through it, electrons (and positrons) cannot combine with quarks.

z: This modeling of quarks seems to correlate to the masses of the up and down quarks–the twist going through the center of a up quark loop acts with a central force that causes the loop radius to reduce by half. The doubling of the resultant normal (to direction of twist travel) acceleration results in a loop that is 1/4 the size of the electron loop model. Similarly, a down quark has two twists going through its center, doubling again the normal acceleration of twist travel and causing that loop to be 1/8 in size. The rest masses of the electron, up quark and down quark correlate to this geometric analysis of particle loops. Electrons have a .511MeV mass, up quarks are 2.3MeV, and down quarks are 4.8MeV. Admittedly this may all be numerology, but I was surprised to find this mass correlation to loop length.

y: A possible model for the weak force results because there is a small chance for linked twist loops to tunnel through each other. If the rotation of one twist loop matches the rotation of a linked loop right at the point where linked loops are being pulled apart, the loops can separate. This is proposed as particle decay and would model the randomizing effect of the weak force.

Glossary

3D + T: the three spatial and 1 time-wise dimensions of our existence. Equations usually are set up for solutions in this space.

Causal: Causality: The property where a particle or field changes according to special relativity, that is, changes cannot propagate faster than the speed of light.

Dirac Equation: Relativistic equations using operators that effectively describes electron behavior in an atom and relativistic interactions of particles

Electron, Positron: charged fundamental quantum particles with spin (no known substructure with a fixed rest mass)

EM: EM Field: Electromagnetic Field.

Entangled Particles: A property of a system of particles where resolving a state of one of the particles instantly (non-causally) affects the remaining particles

Frame of Reference: Used in Special Relativity, refers to the observer's position relative to a system being observed. Special Relativity describes how a system (for example, a set of particles) will appear to the observer that is dependent on how fast and in what direction the observer is moving in relation to the system.

General Relativity: Einstein's theory describing the stress-energy tensor, which details the equivalence of acceleration and gravity and describes how dimensions distort and forces apply when objects are accelerated, especially as speeds approach the speed of light. For example, it describes how a particle's mass increases as it is accelerated.

Interference: Quantum interference: The property at small (quantum) scale where the probability of a particle state or location varies according to wave superposition, the trait of waves interfering with each other

Lorentz Transform: equations that describe how dimensions of time and space distort in different frames of reference (special relativity)

QFT: Quantum Field Theory: theory of how fields, such as the electromagnetic field, are quantized.

Quantum, Quanta: property where fields or particles have a property that can only have a particular value from a set (the set of real or complex numbers, for example)

Quantum Mechanics: the equations that describe the wave-like behavior of particles in various systems, such as a particle in a box.

Photon: quantum of light. Only one possible value of energy, depending on frequency.

Planck's Constant: The lower bound for simultaneous measurement of two orthogonal properties such as a particle's position and momentum.

Relativistic: Usually refers to particles or interactions of particles with velocities that approach the speed of light

Rest mass: Since any particle with mass will have that mass increase as it is accelerated, rest mass is defined as an intrinsic property of a particle that is not moving

Schroedinger Equation: Wave Equation: second order differential equation that describes the probability distribution of (for example) an electron around an atom

Special Relativity: Einstein's theory that describes how dimensions (space and time) interconnect and vary according to an observer's frame of reference. It specifies causality of all particles or field components, and that the speed of light is the same constant in every frame of reference.

Twist: Field Twist: Author's idea of how photons and electrons (twist rings) substructure could be described

Uncertainty relation: Heisenberg uncertainty principle: the lower bound (planck's constant) for resolving two orthogonal properties of a system.

Unitary: in transforms, the property that preserves magnitude (such transforms can cause rotation or displacement, but cannot change the size or shape of objects). In vector spaces (such as fields), unitarity implies that all vectors have a constant magnitude, only direction varies.

Agemoz's Physics Blog