lagrangian | Agemoz's Physics Blog

Posts Tagged ‘lagrangian’

The Arrow of Time and Misuse of Statistics

June 5, 2016

As an amateur physicist I try to avoid disputing established science, but one place I believe science has it wrong is the dimensionality of time. If you read this blog at all, you’ll see I am trying to create a self-consistent world-view that conforms with peer-reviewed science. My world-view attempts to add analysis and conclusions on some of the unanswered questions about our universe such as why are there so many elementary particles or how can quantum entanglement work. I try never to dispute established science and to accept that my world-view is a belief system, not fact that must be forced on others–that is the mark of a crackpot that has just enough knowledge to waste other peoples’ time.

However, one place I break my rules of good behavior is this concept that time is one-dimensional. For a long time, I’ve recoiled at the notion that the observer’s timeline could physically intersect a particular local spacetime neighborhood of an object event multiple times. I discussed this in a previous post, but now I want to discuss this disagreement from another angle–the claim for an existence of an Arrow of Time.

The Arrow of Time is a concept that describes the apparent one way nature of the evolution of a system of objects. We see a dropped wine glass shatter on the floor, but we never see a shattered wine glass re-assemble itself and rise up back onto a table. We record a memory of events in the past, but never see an imprint of the future on our brain memory cells. This directional evolution of systems is a question mark given that the math unambiguously allows evolution in either direction. To put it in LaGrange equation of motion terms, the minimum energy path of an object such as a particle or a field element is one dimensional and there are two possible ways to traverse it. The fundamental question is–why is one way chosen and not the other?

The standard answer is to invoke statistics in the form of the Laws of Thermodynamics, and I have always felt that was not the right answer. Here is why I have trouble with that–statistics are mathematical derivations for the probability something will happen, and cannot provide a force that makes a particle go one way or the other on a *particular* LaGrangian minimum energy path. It’s a misuse of statistics to use the thermodynamics laws to define what happens here. In the case of the shattered wine glass, there are vastly more combinations of paths (and thus far higher probability) for the glass pieces to stay on the floor than there are for the glass shards to reassemble themselves–but that is not why they stay there!

The problem with the Arrow of Time interpretation comes from thinking the math gives us an extra degree of freedom that isn’t really there. The minimum energy path can truly be traversed in either the time-forward or time-backward path, but it is an illusion to think both are possible. Any system where information cannot be lost will be mathematically symmetric in time, creating the illusion of an actual path in time if only the observer were in the right place to observe the entirety of that path. Einstein developed the equations of special relativity that were the epitomy of the path illusion by creating the concept of spacetime. Does that mean the equations are wrong? Of course not–but it exemplifies the danger of using the math to create an interpretation. Just because the math allows it does not mean that the Arrow of Time exists–any relativistic system where information cannot be destroyed will allow the illusion of a directionality of time.

So what really is going on? I’ll save that for a later post, but in my world-view, time is a property of the objects in the system. There is only ONE copy of our existence, it is the one we are in right now, and visits to previous existences is simply not possible. Our system evolves over time and previous existences no longer exist to visit. Relativity does mean that time between events has to be carefully analyzed, but it does not imply its dimensionality.

Agemoz

Tags:arrow of time, lagrangian, physics, relativity, special relativity, statistics, thermodynamics, time dimension
Posted in philosophy, Physics | Leave a Comment »

Noncausal solution, Lorentz Geometry, and trying a LaGrangian solution to deriving inertia

December 31, 2012

Happy New Year with wishes for peace and prosperity to all!

I had worked out the group wave concept for explaining non-causal quantum interactions, and realized how logical it seems–we are so used to thinking about the speed of light limit causing causal behavior that it makes the non-causal quantum interactions seem mysterious. But when thinking of a universe that spontaneously developed from nothing, non-causal (infinite speed) interactions should be the default, what is weird is why particles and fields are restricted to the speed of light. That’s why I came up with the group wave construct for entities–a Fourier composition of infinite speed waves explains instant quantum interference, but to get an entity such as a particle to move, there is a restriction on how fast the wave can change phase. Where does that limitation come from? Don’t know at this point, but with that limitation, the non-causal paradox is resolved.

Another unrelated realization occurred to me when I saw some derivation work that made the common unit setting of c to 1. This is legal, and simplifies viewing derivations since relativistic interactions now do not have c carried around everywhere. For example, beta in the Lorentz transforms now becomes Sqrt(1 – v^2) rather than Sqrt(1 – (v^2/c^2)). As long as the units match, there’s no harm in doing this from a derivation standpoint, you’ll still get right answers–but I realized that doing so will hide the geometry of Lorentz transforms. Any loop undergoing a relativistic transform to another frame of reference will transform by Sqrt(1 – (v^2/c^2)) by geometry, but a researcher would maybe miss this if they saw the transform as Sqrt(1 – v^2). You can see the geometry if you assume an electron is a ring with orientation of the ring axis in the direction of travel. The ring becomes a cylindrical spiral–unroll one cycle of the spiral and the pythagorean relation Sqrt(1 – v^2/c^2)) will appear. I was able to show this is true for any orientation, and hand-waved my way to generalizing to any closed loop other than a ring. The Lorentz transforms have a geometrical basis if (and that’s a big if that forms the basis of my unitary twist field theory) particles have a loop structure.

Then I started in on trying to derive general relativity. Ha Ha, you are all laughing–hey, The Impossible Dream is my theme song! But anyway, here’s what I am doing–if particles can be represented by loops, then there should be an explanation for the inertial behavior of such loops (totally ignoring the Higgs particle and the Standard Model for right now). I see a way to derive the inertial behavior of a particle where a potential field has been applied. A loop will have a path through the potential field that will get distorted. The energy of the distortion will induce a corrective effect that is likely to be proportional to the momentum of the particle. If I can show this to be true, then I will have derived the inertial behavior of the particle from the main principle of the unitary twist field theory.

My first approach was to attempt a Lagrangian mechanics solution. Lagrange’s equation takes the difference of the kinetic energy from the potential energy and creates a time and space dependent differential equation that can be solved for the time dependent motion of the particle. It works for single body problems quickly and easily, but this is a multiple body problem with electrostatic and magnetic forces. My limited computation skills rapidly showed an unworkable equation for solution. Now I’m chewing on what simplifications could be done that would allow determining the acceleration of the particle from the applied potential.

Agemoz

Tags:causal, general relativity, lagrangian, noncausal, quantum, special relativity, speed of light, twist ring
Posted in 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.

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