Coiling Trajectories of Particles & Charge

[metacogitans]

1. Since the waves of all fundamental forces are sinusoidal, then acceleration of a particle by a fundamental force can only produce sinusoidal curvature in the particle's trajectory.

 

2. Since the direction a particle is traveling in can only change from being accelerated by a force, and forces only curve a particle's path sinusoidally, then particles' trajectories can only ever curve, without there ever being sharp angles; when there seems to be a sharp angle in trajectory, viewed at a small enough scale there would only be sinusoidal curvature.

 

3. Since trajectories of particles only consist of sinusoidal curves, and a particle is affected by forces from every direction constantly with their intensity diminishing over distance as a ratio of a sphere's radius to its surface area, the distribution of the intensity of surrounding waves of force in a section of spacetime would also fall off as a sinusoidal curve. Thus, the path of any particle when plotted out would be coiling in shape.

 

4. Due to the intrinsic geometry of a coil, the clockwise or counterclockwise orientation of a coil is unchanging, and is preserved no matter how the coil is flipped or rotated. As long as the coil only consists of curves, the clockwise/counterclockwise orientation stays the same, and can only change from sharp angles in the coil - at which point it technically ceases to be a coil.

 

5. Since waves of force are produced by a particle whenever it is accelerated, and since a coiling trajectory is constant acceleration, waves of force constantly propagate out from a particle as the trajectory of the particle curves.

 

6. The waves of force produced from the coiling trajectory of a particle would also maintain a coiling shape while propagating out from the particle, with the clockwise/counterclockwise orientation of the coiling preserved as well.

 

7. Particles affected by waves of force with opposite clockwise/counterclockwise orientations in the coiling of their trajectories, would, for geometrical reasons, be highly inclined to be 'stalled' in the oppositely-coiling waves of force produced by the other particle, the latter particle would also be inclined to become 'stalled' in the force waves coming from the former particle. The resulting effect would be predicted to appear similar to attractive 'pairing' between opposite charges.

 

Is any part of all that definitely not correct or most probably wrong?

If you have graphing software, you could put the 'sinusoidal coiling' preserving its clockwise/counterclockwise orientation to the test: try to curve the trajectory of a point particle with only sinusoidal curves, and the forces accelerating can't cheat the inverse square law. I think you'll find that the more you try to implement sharp curves, the more you will displace the particle, and that to have higher intensity waves of force requires more mass/energy considered over a larger volume, which will be lost to entropy of the system, or would affect all nearby particles to a similar extent, and the particle would still have a coiling trajectory relative to those particles. You'd probably need to consider extreme scenarios like supernovae, quasars, particle colliders, or black holes.

If you tried using powerful equipment to knock a particle back and forth between alternating electromagnets to get a non-sinusoidal curve in the particle's trajectory, you could still only decrease the diameter of the coil to smaller and smaller scales so its hard to observe, or drown it out with other signals, but the frequency of the coiling would still be present no matter how tiny. Coiling trajectory is also true at the largest of scales; celestial bodies orbiting each other are moving through space in pseudo-unison while in orbit with each other, making their trajectory through space-time coiled.

 

Another possible way to view the concept geometrically I was thinking of (it could be false though, I don't know); consider the distance between two particles with the distance between them growing/shrinking due to forces affecting the particles trajectory - the change in distance graphed on an XY coordinate grid would be indistinguishable from two points moving along the circumferences of two separate ellipses, with the dimensions of the ellipses changing randomly to match their real movements in spacetime, and graphing the change instead as the changing curvature proportional to the rate they're traveling the circumference. The graphed increase/decrease in both cases would also consist of sinusoidal curves. Relative to each other, the two particles could be thought of as coiling orthogonal to the plane of the two ellipses.

Edited May 9, 2016 by metacogitans

[swansont]

1. Since the waves of all fundamental forces are sinusoidal, then acceleration of a particle by a fundamental force can only produce sinusoidal curvature in the particle's trajectory.

 

2. Since the direction a particle is traveling in can only change from being accelerated by a force, and forces only curve a particle's path sinusoidally, then particles' trajectories can only ever curve, without there ever being sharp angles; when there seems to be a sharp angle in trajectory, viewed at a small enough scale there would only be sinusoidal curvature.

 

 

 

Waves are not all sinusoidal, depending on what you mean. Any periodic function can be expressed as a sum of sine waves, but wave functions can be other functions.

 

Curved paths can be circular, e.g. a charge in a uniform magnetic field.

[metacogitans]

Zitterbewegung Con

 

 

 

Waves are not all sinusoidal, depending on what you mean. Any periodic function can be expressed as a sum of sine waves, but wave functions can be other functions.

 

Curved paths can be circular, e.g. a charge in a uniform magnetic field.

What are a few examples in particular of wave functions that are fully non-sinusoidal? Also, would they apply if I'm looking strictly at the waves of fundamental forces (where energy is being directly transferred through the wave) and the paths of particles as they are accelerated by those forces?

 

As for circular paths, aren't circular curves technically sinusoidal from any fluctuating imperfections in the cosmic background making the circle slightly elliptical and sinusoidal? Also, even if circular relative to itself as a point of referece, won't it technically be coiled from other points of reference, as its source object is likely moving through the macroscopic cosmos, as most matter in the universe does, at a varying velocity?

Edited May 9, 2016 by metacogitans

[swansont]

Zitterbewegung Con

 

What are a few examples in particular of wave functions that are fully non-sinusoidal? Also, would they apply if I'm looking strictly at the waves of fundamental forces (where energy is being directly transferred through the wave) and the paths of particles as they are accelerated by those forces?

 

As for circular paths, aren't circular curves technically sinusoidal from any fluctuating imperfections in the cosmic background making the circle slightly elliptical and sinusoidal? Also, even if circular relative to itself as a point of referece, won't it technically be coiled from other points of reference, as its source object is likely moving through the macroscopic cosmos, as most matter in the universe does, at a varying velocity?

 

 

As I said, it depends on what you mean by sinusoidal, since any periodic function can be expressed as a sum of sine waves. It's Fourier analysis. (It's why epicycles work for orbits). Is a square wave a sinusoid? I would say no; to me a sinusoid means you can vary the period and phase (i.e. a cosine is a sinusoid)

Is a line drawing of Homer Simpson a sinusoid (since it's made up of circles)? (If you say yes, then OK, all closed curves are sinusoids, and the terms sorta loses meaning. You travel a sinusoid path to and from work, or any errand, where you have a closed path.)

 

If your position or momentum is well-known, then its wave function is a delta function, while the other one will be a constant. For a particle in a box, the wave function in the potential barrier is an exponentially decaying function.

[metacogitans]

Okay. The total force affecting a particle at a given instant is the derivative of velocity. Since the particle is affected by force in every direction constantly, and the closer it moves to the source of those forces the stronger they affect the particle, the greater the intensity of that force affecting the particle, with intensity increasing/decreasing as a curve (never instantaneously.

Because the derivative of total force is a vector (a single tangent line), the multiple frequencies of a particle across the spectrum, when plotted as the particles trajectory, would have to be coiling.

Because it is coiling, it has an intrinsic clockwise/counter-clockwise orientation. If we conceptualize these waves of force as all being intrinsically repulsive, it would be predicted that oppositely-coiling waves of force would result in the phenomenon of attraction, out of geometric inclination.

 

To translate this from classical to quantum, we could conceptualize particle's position in spacetime only existing as relations to each other; thus, the 'waves of force', at the smallest of scales, break down from a wave function into discrete 'locations' based on relative position. For example, something along the lines of 'particle A is closer to particle B than to particle C or D' transitioning to 'particle A is closer to particle C than particle B or D' would constitute 'wave-function collapse' when particle A is put through a bottleneck where it must be one or the other. Due to space-time being the sum of relations, it would then be expected to follow a manifold - perhaps the tensors described in the General Relativity field equations. Since spacetime does indeed follow a manifold due to the fact that it only exists as the sum of its contents, it seems plausible.

 

Is there any part of that though that is definitely incorrect?

Edited May 16, 2016 by metacogitans

[swansont]

Force is not derivative of velocity, it's derivative of momentum.

 

A particle is not affected by a force in every direction.

 

Trajectories do not have to coil, whatever that means. Not sure what "multiple frequencies of a particle across the spectrum" is supposed to mean.

 

 

Conclusions and extrapolations drawn from the above are thus dubious.

[metacogitans]

 

 

A particle is not affected by a force in every direction.

 

Trajectories do not have to coil, whatever that means. Not sure what "multiple frequencies of a particle across the spectrum" is supposed to mean.

I'll agree with your post but are you sure about those two points you've made?

 

How are particles not affected by forces in every direction, if the electromagnetic field of a particle is constantly present in 3 dimensions (at least 3 dimensions, 4 or possibly more if we're getting technical).

 

Electromagnetic waves have a 'clockwise' or 'counter-clockwise' orientation, and this would seem to explain electric charge:

[swansont]

I'll agree with your post but are you sure about those two points you've made?

 

How are particles not affected by forces in every direction, if the electromagnetic field of a particle is constantly present in 3 dimensions (at least 3 dimensions, 4 or possibly more if we're getting technical).

 

Electromagnetic waves have a 'clockwise' or 'counter-clockwise' orientation, and this would seem to explain electric charge:

 

 

You might note that the propagation direction is a straight line in your diagram. The sine curves are field amplitudes, not trajectories.

 

Photons have no charge. It is possible to polarize EM waves so that the direction of the electric and magnetic fields rotates.

 

Your very first premise is flawed. All that follow from it is invalid. Instead of throwing good ideas after bad, you need to show that "acceleration of a particle by a fundamental force can only produce sinusoidal curvature in the particle's trajectory." (and good luck with that)

 

Here's a picture of an electron beam going in a straight line.

http://www.clemson.edu/ces/phoenix/labs/cupol/eoverm/beam.jpg

 

I recognize that apparatus. It looks like a lab where you add a magnetic field to bend the path (since the force is perpendicular to the velocity, you get a circular path. Circles are not sinusoids)

 

Then you get something like this

https://upload.wikimedia.org/wikipedia/commons/d/d4/Electron_beam_in_a_magnetic_field.jpg

[metacogitans]

 

 

You might note that the propagation direction is a straight line in your diagram. The sine curves are field amplitudes, not trajectories.

 

Photons have no charge. It is possible to polarize EM waves so that the direction of the electric and magnetic fields rotates.

 

Your very first premise is flawed. All that follow from it is invalid. Instead of throwing good ideas after bad, you need to show that "acceleration of a particle by a fundamental force can only produce sinusoidal curvature in the particle's trajectory." (and good luck with that)

 

Here's a picture of an electron beam going in a straight line.

http://www.clemson.edu/ces/phoenix/labs/cupol/eoverm/beam.jpg

 

I recognize that apparatus. It looks like a lab where you add a magnetic field to bend the path (since the force is perpendicular to the velocity, you get a circular path. Circles are not sinusoids)

 

Then you get something like this

https://upload.wikimedia.org/wikipedia/commons/d/d4/Electron_beam_in_a_magnetic_field.jpg

When I used the term 'trajectory' applied to waves of force, I didn't mean to imply a straight line.

I've been of the impression for quite some time that 'photons' are not discrete particles, rather a convenient placeholder variable in equations.

 

As for 'the charge of photons', I'm of the impression that the geometry of electromagnetic waves is what produces the effect of 'charge' in the first place; I do not think that EM waves themselves have an intrinsic charge, but over time, the geometry of the waves produces the phenomenon of 'charge'.

Edited July 10, 2016 by metacogitans

[swansont]

When I used the term 'trajectory' applied to waves of force, I didn't mean to imply a straight line.

 

I thought you meant to imply a sinusoid.

[metacogitans]

I thought you meant to imply a sinusoid.

 

Well, sinusoidal in 3+ dimensions

Edited July 10, 2016 by metacogitans

[swansont]

Well, sinusoidal in 3+ dimensions

You can only move in one direction at a time. And if you change velocity, you need a force. How would a constant force give you a sinusoidal trajectory?

[metacogitans]

You can only move in one direction at a time. And if you change velocity, you need a force. How would a constant force give you a sinusoidal trajectory?

I was referring to the electromagnetic field of a particle, emitted from the particle in all directions at the speed of light.

I agree that the particle can only move in one direction at a time.

 

Actually, that's why I think the particle's trajectory would have to be coiling; considering the change in velocity of the particle over an increment of time. A particle's velocity can only change through acceleration, and since waves of force emitted from other particles have a travel time c, a change in velocity can never be abrupt.

Edited July 11, 2016 by metacogitans

[swansont]

I was referring to the electromagnetic field of a particle, emitted from the particle in all directions at the speed of light.

That doesn't seem to be reasonable translation of "acceleration of a particle by a fundamental force can only produce sinusoidal curvature in the particle's trajectory."

 

As far as direction goes, the field of a charge is not a sinusoid. The field of a photon is not a sinusoid. As I said, the sinusoid you see is an amplitude, varying in time.

 

I agree that the particle can only move in one direction at a time.

 

Actually, that's why I think the particle's trajectory would have to be coiling; considering the change in velocity of the particle over an increment of time. A particle's velocity can only change through acceleration, and since waves of force emitted from other particles have a travel time c, a change in velocity can never be abrupt.

Not being abrupt is a far cry from being a sinusoid, and that refers to a rate rather than a direction. "Trajectory" implies direction.

[metacogitans]

Oh yeah, well this guy seems to agree with me:

 

 

Born2bwire Re: Not HW: Why are light waves in the form of the sine wave, instead of some other w

They are and they aren't. We simply think of them as being sinusoidal because it is an easy mathematical basis to work with. When you work out the wave equations from Maxwell's equations, assuming a time-harmonic wave (sinusoidal) greatly simplifies the mathematics. Most materials are linear in regards to light, this means that frequency in == frequency out, and so if we can describe a signal, any signal, as a superposition of frequencies, then the analysis of the system can be greatly simplified. And so it is with light since classical electrodynamics follows the principle of linear superposition. So, can I have an electromagnetic signal that is not a pure sine wave? Sure, to an extent. We can send approximations of square waves and saw-tooth waves. I say approximation because the necessary bandwidth for these signals is infinite and thus our ability to reproduce them is restricted by the bandwidth of our own signals. But when you get down to it, even a square wave is nothing but a superposition of sine waves. Fourier series is a good means of showing that you can pretty much decompose any real world signal into a summation of sine waves. The limit to his theorem, being that you cannot correctly reproduce discontinuous signals (like the square wave) is generally reflected in the real world too.

 

https://www.physicsforums.com/threads/not-hw-why-are-light-waves-in-the-form-of-the-sine-wave-instead-of-some-other-wave.347805/

Edited August 10, 2016 by metacogitans

[swansont]

Oh yeah, well this guy seems to agree with me:

 

Not if you understand what he's talking about. Field amplitude, not trajectory.

[studiot]

Rather than following a flippant treatment such as presented in your post#15 quote, I suggest you look up the following

 

An angle modulated radio/light wave may not be sinusoidal, or expressible as a linear combination of them.

What is the waveshape of light received from a body which is continually accelerating away?

Solitons (solitary waves) as applied to (modern) optics.

The difference between dispersion and dissipation as applied to waves.

Gibbs phenomena in periodic functions.

Edited August 10, 2016 by studiot