Spinors visualized

Here is a Youtube video on the complex version of basic geometric shapes.  It's entertaining, enlightening, and beautiful.

Here is one of the final images from the video.  It's source is a simple function.  But if you look at it, you'll realize it is a graphical representation of spinors.  Spinors are a quantum effect that requires 720 degrees of rotation to return to their starting condition.  They're supposed to be really weird and without precedent in the "Real" world.  Right.  They're simple functions in the complex (4-D) plane.

Happy Thanksgiving!

 Wishes for a happy Thanksgiving to one and all!

"We gather together to ask the Lord's blessing."

More novel goodness!

  Alma Boykin has released into the wild her latest Familiars book, "Hunter and Horseman".  This one is following the adventures of Jude, the lone and lonely defender of his rural county.  The Batman of the back country, and his nearly night-blind raptor Familiar.

  Cedar Sanderson also published a new novella, "Running Into Time".  This one is a stand-alone time travel story, inspired by some of the "weekly writing prompts" a group of authors challenge each other with.  

  Chris Nuttall has edited the seventh anthology in the series: "Fantastic Schools - Staff".  He works with quite a few good authors on these as part of the "superversive" literary movement.

The nature of time

Time is change.  Perceived time is relative to the total energy of a particle and its environment.  Spacetime is a field of potential energy governing motion.  I've gone over all this before, but now I have something even simpler.

Proper (perceived) time is potential energy.  Period.  What kind of potential energy?  All of it.  The less energy is used by a particle, the faster time runs for it.  Proper time is properly (hah!) measured in imaginary units, but we see its effects in our real-valued universe, and its measure is almost always squared.  (The square of i is -1, by definition.)  So we mostly ignore its imaginary nature, except that comes back to bite us in general relativity, which is why the (squared) time element of the spacetime metric is negated.  (Or all three space axes are negated instead.  Same difference.)

For those not familiar with the math/geometry, the imaginary axis is 90 degrees to the real axis, satisfying the need for dimensions to be perpendicular to each other.  The imaginary direction can also represent a rate of change, satisfying the nature of time itself.

This explains spinors, by the way.  What we perceive as 360 degrees of rotation is really 180 degrees in a complex field, of which we can only measure the real valued portion.  We have no means of experiencing or measuring the imaginary valued portion, except to note that after a single passage from like to like values, the direction is opposite what we would expect.  That's exactly what happens when you rotate a point along a circle in a complex plane - the real value goes from +1, through 0, to -1.  It then passes back through 0 to +1 again.  What we perceive as two rotations is really a single one, but in a complex plane which we cannot directly perceive.  Especially when you square the function, eliminating the negative portion entirely (but leaving the problem of opposite directions to every other wave).

This is most likely the root cause of neutrino oscillation.  We simply can't directly perceive things outside of our real-valued, three dimensional space.

Yes, I realize this may sound a bit incoherent.  It's all a beautifully simple whole in my head which I have a hard time explaining.  Yes, I do realize what I just wrote.  Go ahead and laugh, but when you're done laughing, please think.  Many of these ideas are not original to me.  Minkowski himself wrote time as an imaginary component when he created the math behind 4-D spacetime and general relativity.  It was later simplified to a negative squared term, leaving out the explanatory "i".  That "i" is the whole reason for the negative term in the spacetime metric, and the cause of hyperbolic spacetime.  Euclidean space + imaginary time = hyperbolic spacetime.  The geometry is simple.  The math is horrific.

Oh, and to reiterate - there is a maximum and minimum energy density, resulting in (or from) a maximum and minimum flow of time.  Time cannot run backwards, because there can't be negative potential energy.  Time cannot exceed a certain rate, because there cannot be negative energy.  (Energy in a different direction is not negative, it's merely opposite.)

Whither redshift? And other musings on the nature of photons.

I have never seen any attempt to explain any physical process by which the expansion of space would cause redshift, or by what means the expansion of space would accelerate or decelerate.  Now, this doesn't mean there is no explanation, just that I, in looking, have never found one.  I don't claim to be a professional (or even well trained) physicist, so there are real limits to my knowledge.

That being said, this lack raises my hackles.  Results must have causes.

After a great deal of thought, I have come up with this.  If space is expanding, and if that expansion somehow causes photons to lose energy (redshift), then lower energy, longer wavelength photons would necessarily lose proportionately more energy than higher frequency, shorter wavelength photons.  This would appear as acceleration.

This thought experiment should be testable, as different frequencies of light from the same source would show ever so slightly different redshifts.  If this is true, then the expansion of space need not be accelerating.  If this s not true, the how is space expansion affecting photons, if it doesn't stretch longer waves more?  Unless the wavelength of a photon is an artifact of a point-like spin frequency, and not an inherent property.

And where does the lost energy go?  Is energy simply not conserved?  That is what the theory implies.  Remember, if energy is lost, it must be lost as some particular time and place.  For that to happen, it must go somewhere, or be transferred into some other form.  Unless all energy is slowly being reduced over the entire history of the universe, of course.  Then it would be time causing redshift, not distance.  A distinction without a difference, really, since it's all spacetime, but intellectually more satisfying.

Come to think of it, what is the wavelength of a photon newly emitted by an electron?  If the frequency is in the AM radio band, the wavelength is measured in many meters.  How would it work for a photon with a wavelength of, say, ten meters, to be emitted and then absorbed by two atoms a mere centimeter apart?  Where is the energy held in a photon?  The leading edge of a wave, with the wavelength being an artifact of its passing?  It cannot be a pointlike center of a full wave, or even the entire wave.  No, it has to be the leading edge, for something has to cause the leading edge, and nothing can travel faster than the photon itself.  It makes the most sense if the photon has a spin, and the wavelength is an artifact of the frequency of spin interacting with the EM field, trailing along behind.  But that makes the double slit experiment results rely on the passage of previous photons, negating all the "woo-hoo" effects.  That would also mean the wave function wouldn't have to exceed to speed of light (in some directions but not others) to achieve the necessary addition and subtraction effects.  (Yes, the standard explanation of the double slit diffraction grating requires a variable speed of light - for the same photon.  Measure the paths.)

I knew I liked where that thought was heading.  Has anybody ever done a double slit experiment while also shining a strong light of the same wavelength longitudinally between the grating and the detector?  I honestly don't know.  I do know that I have seen no evidence of the experiment ever actually being performed with single photons, mostly because I don't think anybody has ever found a way to create a reliable means of emitting single photons of the same wavelength from a source.  No, applying filters doesn't count, especially when the wavelength is longer than the average separation.

The last victory

 9 November 1989

The 11th hour, of the 11th day, of the 11th month

In Flanders Fields
by John McCrae


In Flanders fields the poppies blow
Between the crosses, row on row,
That mark our place; and in the sky
The larks, still bravely singing, fly
Scarce heard amid the guns below.


We are the Dead. Short days ago
We lived, felt dawn, saw sunset glow,
Loved and were loved, and now we lie,
In Flanders fields.


Take up our quarrel with the foe:
To you from failing hands we throw
The torch; be yours to hold it high.
If ye break faith with us who die
We shall not sleep, though poppies grow
In Flanders fields.

Support hungry authors!

Support your favorite independent authors!  They're, if not starving, probably hungry.  A bit peckish, at least.

Cedar Sanderson - The Groundskeeper 3 - My Ghoul

Toward a theory of motion (and everything)

Motion is distance over time. Notice that this fundamental concept is actually quite complex. It involves both distance and time, unified and separated by division.

I have never seen a theory of motion. That's what I've been working on since I started grasping the fundamentals of relativity. (Quantum theory is intimately related, of course.) Newton's Laws explain how things move, but not why. An object in motion remains in motion. Why?  To answer that, we must discuss spacetime.

3D space is flat (Euclidean). The Pythagorean theorem (a^2 + b^2 = c^2) works perfectly well. The complications come in when you add time. Why? Because time is imaginary. (Every dimension is at 90 degrees to all others.) The Pythagorean theorem still holds, but when you square i, you get -1, so the result is hyperbolic (a^2 - b^2 = c^2). 

Add in the principles that the total energy everywhere is a constant and spacetime is a field governing motion, and you have a fairly complete theory. Simple principles. Complicated mathematics.

Motion is, effectively, a vector (velocity).  Time (as perceived by the object) is, effectively, a spin.  These are the legs of a triangle connected by a hypotenuse whose length is c, the speed of light.  Speed and perceived time are thus intimately connected.  When one gets longer, the other must get shorter.

Why does something move?  Because it exists inside a curved bit of spacetime.  It's motion is defined by the curvature (with the direction of motion towards the lowest energy), and the curvature is defined by the momentum.  It can't speed up, because the speed vector would require more energy.  It can't slow down, because the time spin would require more energy.  So, lacking outside energy to change these, it continues on without change.  (Photons, lacking mass, don't have perceived time.  They only have motion.  They're still weird.)

Note that the curved bit of spacetime adequately explains redshift all by itself.  Photons gain energy in the forward direction, and lose energy in the opposite.  This applies to both the emitting and receiving particles.  So if they move in concert, no redshift is detected, because the gain and loss cancel.

Related - the most fundamental principles of the universe are:

• The total energy at every point is a constant.
• The total, over a large enough scale, of most properties other than energy, is zero.  (Charges cancel out.  Spins cancel out.  Everything except energy cancels out.)

This all implies that time is a spin.  This implies that antiparticles have an opposite time spin.  Thus, their description as "moving backwards in time" is essentially correct, but only for perceived time.  (Actual time always moves forward, regardless of everything else.  This is how photons move.  If perceived time were all there was, photons could not move, and the universe would be an unchanging, tiny ball of energy.)

This implies that the weak force, being only perceived by left-handed particles (and right handed antiparticles), is related to the spin of time.  This also implies that the negative and positive charges are opposite spins.  Electrons and positrons would, for example, maintain the same charge spin, but since the time spin would be backwards, the charge effect would also be backwards.

Side note - magnetism is caused by the tension of a moving charge.  A stationary charge causes no new deformation (tension) of the EM field.  A moving charge, since everything is limited by the speed of light, creates a build up of tension in the direction of motion, a lack of tension in the opposite direction, and sideways motion between the two - just like the waves created by a ship moving through the water.  (No, these are probably not the proper terms.  But they get the point across, don't they?)  By the way - gravity works in a remarkably similar manner, piling up in front of a moving object, and stretching out behind.  This is part of why the orbit of Mercury doesn't match Newton's predictions - the sun is in motion around the Milky Way.

More intuitive spacetime interval

Space is Euclidean.  Spacetime is hyperbolic.  Why?  Because time is imaginary.

From the Wikipedia article on the spacetime interval:

There are two sign conventions in use in the relativity literature:

${\displaystyle {�}^2=(��{)}^2-{�}^2-{�}^2-{�}^2}$

and

${\displaystyle {�}^2=-(��{)}^2+{�}^2+{�}^2+{�}^2}$

Let us take the second convention and rewrite it to a more standard hyperbolic form:

    s2 = x2 + y2 + z2 – (ct)2

But, since time is imaginary, we can rewrite this to the Euclidean (Pythagorean theorem) form:  
    s2 = x2 + y2 + z2 + (cti)2

The result is the same.  The addition of i (the imaginary number, square root of -1), when squared, reverses the sign of the time component.  But this formulation shows exactly what is going on in this distance equation.  The Pythagorean theorem holds in space as well as spacetime, but spacetime is hyperbolic because time is imaginary.

There are no inconsistencies, there are no contradictions.  Every concept is simple, even if the math is complex.  It even helps show that time is at 90 degrees to every space dimension, because the imaginary number line lies at 90 degrees to the real number line.

QED