Begin n.12.1
Forbidden states are manifestation of classical collisions or rather, quantum force manifests in form of classical repulsion?
Cease to exist at focal point, amplitude would have symmetrical amplitudes. Either point would have a circular momentum and zero position, or normal position amplitude and infinite position
3rd variable to keep from collision?
super-fluid helium torus/doughnut
1) super-fluid helium ball in figure 8
2) Smooth state over figure 8
3) Vertex has antiparallel direction
4) Goes in, but has two outs, like a beam splitter (can it reverse?)
5) make a 3rd out, and a 4th, ... torus with a vertex as tangent point, no torus hole. vertex exists
iff torus is open. Taking the closure would cause a problem.
6) Make many other vertices, and you get bubbles
5) cont.
a) Like an electron
b) Capsule in vertex, if contained, it might lose position in time
c) Open doughnut skin
1) You start out with a pellet of super-fluid helium going in a figure 8
2) given enough time of being left alone, you get quantum blurring. there are a few key concepts/physics theories that result in this.
z) by the uncertainty principle, if there are no interactions with the pellet for a long time, it could be a little bit ahead of where you expected, or a little bit behind.
a) fundamental equations that have been proved/shown to work very well (goes to all physics theories, no matter how simplistic, beatufial mathematically, and experimentally accrurate have been proven to be wrong (except the current ones of course)) have the nature of position being proportional to -1*it's second derivative. there is one type of function that behaves this way: sins and cosines.
b) the sum of two periodic functions is also a periodic function.
c) a particle is not really a particle in any sense of being a point. all particles are really functions from space-time (for the most part, this can be thought of as a function from space onto the complex plane; however, unfortunately, the time variation is fundamental to this thought experiment :( ) onto the complex plane (and there some other dimensions/algebraic groups, but that can left til later).
d) it may be periodic, but not in the sense that it is a flat out sine wave. it is more like a sine wave that is very high at one point (say x=0), and then tapers off to near zero until the next... well next time around for the pellet. something like that. kinda like there are two levels of perodicity. there is a really fine one that goes up and down every 10^-83745928474 (a small number) and one that hits its max every .1 meters (if that is the total length of the preztel. this is a pretty in accurate description, but it is something like that (i hope so at least (but it doesn't really matter in the long run)).
d) the sum of two periodic functions that satisfy the key equations also satisfy the key equations (ignoring some of the find points). this is due to the linear nature of the derivative operator:
d(f+g)/d(x) = df/dx + dg/dx, and if df*dg/dx^2, = 0, then d^2(f+g)/dx^2 = (d^2f/dx^2)+(dg/dx^2).
(d^2f/dx^2) = -1*alpha*sin(f(x))
(d^2g/dx^2) = -1*alpha*sin(g(x))
(the underlying relationship doesn't change if you make f ~ a*sin + b*cos, it just makes it look more complicated.
therefore,
(d^2f/dx^2)+(dg/dx^2) = -1*alpha*sin(f(x)) + -1*beta*sin(g(x))
and if sin(x) = sin(2pi+x) then things would out nice, regardless of alpha and beta. things are a *bit* more complicated, but that's the general idea.
e) if the pellet isn't really a pellet, but a periodic function, or sorts, that happens to be very localized, but it get's more blurred and blurred, like you check it every hundred years, and it could either look like a sine wave type thing localized at the intersection point of the figure-8, or it could be localized a little ahead or behind. left alone for a long time, if you look at it, the localized are/peak of the function, could be anywhere. it is evenly distributed. this then means that it is just as likely to be at the center point/intersection/vertex going in one direction as it would be to be at the same point in the opposite direction.
f) if you can make a figure-8, you can make a clover (3 leaf or 4). By induction, you can make it so that an infinitely many "injection paths" exists, in 3 dimensions if you like.
g) if instead of being a "distant observer" you, or some complex physical object were right at the center, yet still not interacting with the preztel, things get interesting. I will refer to such an object as a 'Quantum Egg'
the quantum egg has not interacted with the pretzel at all for limit as time goes to infinity. the bath it is in has absolute uncertainty with respect to direction. it's position is defined (not in the sense that the pellet can be ONLY one place, but if the egg was to interact with it, and the egg has a definite position, then the pellet does too). in the limit as time til interaction goes to infinity, and velocity (magnitude) of the pellet goes to infinity, then the egg is in a bath of superfluid helium that has a magnitude of infinite momentum, but ZERO direction (because it has been blurred). if it were to interact, it would get a jolt, of infinite magnitude, in some direction, but it is COMPLETELY unknown, in the quantum mechanics sense. Now, if there is a particle/you were a distant observer who not only has not interacted with neither the pellet, nor the egg, then the egg has been blurred into a omni-directional explosion, except with no concept of definite time. that is the key point, ZERO concept of time. in the world quantum mechanics, not only do particles have uncertainy with respect to space, but also with time. and this uncertainty grows as the particle's energy grows. the egg now has infinite energy... thus in a sense, the quantum egg is now lost in time. it can not exist before the pretzel was created, but after that, who knows.
what if the egg somehow enters the vertex AFTER the pellet's quantum focal point?
tangent: the Super-Saturated Light Bath. this is a case where instead of a pellet having a quantum focal point, a laster does. laser's operate on the principle that bosons (like photons, and superfluid helium (kind of a defining requirement of a super-fluid (including current in a super-conductor))) have a probability of making a discrete 'jump' from one 'state' to another. in the super-fluid helium pretzel, the 'state', after a million years, is a completely uniform quantum blur. it's a lot easier for photons to achieve this state. in the case of photons, they don't tend to explode when they collide (as they don't really collide). thus, if 10^2395834589725892 photons are in the state where they are evenly distributed between two mirrors, a photon doing the same things, but just 10^-457889789934943 meters below the laser, could 'jump' up to the same state of being a quantum blur in a well-defined state, with respect to space. I am proposing that if there where two such photons in a given neiborhood (and I mean that in the mathematically vernacular, like "for every eplison there exists a delta"), if one jumps in, the other one becomes more likely to jump in. now, if you extend the uncertainty principle to time, the 2nd may actually jump in before the first. quantum mechanics is wacky (I really hope I am right on this one). I should say that all of these "tricks" of quantum mechanics are insanely small, really. but, non-the-less, if it can work for two photons, by induction, it can work for infinitely many, and thus if you were to "release" a photon 20 years after the SSLB is created, it would have an effect on the past.
to this end, dropping a quantum egg into the focal point of the super-fluid helium knot, and it "would" interact instantisly would the fluid/blur of a pellet (of infinite momentum, AND energy, at that point), it would affect the probability of THE PELLET interacting with the egg a little bit before it was dropped in. this "jump" of quantum state could be thought of as purely on the pellet's side. like one "version" of the pellet jumps the gun, then it increases the chance that ALL "versions" of the pellet do. since the pellet has some neutrons in it, and radio active decay is like a quantum clock: to an extent, it defines they age of a particle. Not specifically of course, that would be discrete and simple. but at any given moment, there is an equal change of the neutron breaking apart. thus, in a sense, it gives a VERY vague INDICATION of the age of the neutron. but it gives information, and that can not be taken away. thus the egg enters the focal point at one time, gets smacked by a pellet from ten years ago, and gets ejected with infinite velocity. the egg was from time b, and the pellet was from time a (b>a), who prevails? a specific answer would break symmetry. it would be equivalent to saying helium is real and the egg is not. however, there has been no specification on what material the egg is. I doubt that the universe is defined by "helium is real and everything else illusion", even and egg made of super-fluid helium :) and so the situation exists that regardless of when a quantum egg enters a point of infinite but directionless momentum, it is completely lost in time. this goes both ways: it can exit at any time, as definied by the pellet, or any time from the point of view of the egg (i think that this time must be greater than or equal to zero from the egg's standpoint, but i didn't really put much thought into this).
on a side note, if you think about the pellet (as non-zero in size) at the focal point, it's helium atoms are all moving around at the speed of light, in all directions, including time. it is like a subset of the ocean, with currents taken to the extreme of turbulence, beyond the initiating point of a tsunami. in addition to swirls/vortices in 3-dimensions, there are now vortices in time. helium atoms all at the same point in space, but rotationing in time.
the final step involves the nature of position being the fourier transform of momentum. this invovles adding on the notion of "spin". which is that EVERYTHING has angular momentum. now, you can take a bicycle wheel, and see it spinning, REALLY, REALLY, fast; and you can instantly know that is either going one direction or another. it's the same thing, with pretty much anything. the direction of rotation is something that gets quantum blurred pretty quickly. But, you can apply a small magnetic field and get things that have very little magnetic magnitude to line up in one direction pretty quickly. this is how an MRI works. further, it is very predictable that once things line up, they will become blurred at a certain rate. and this is specific for each type of particle/atom/whatever. an MRI is specifically designed to sniper out hydrogen, or something else. like, you know that you can get the electrons oribiting a single proton to exit their quantum blur and point in the same direction as the magnetic field. and further, you know that 20% are going to be going the other direction in some specific time. other molecules/atoms are not. and then if you put another pulse of the same strength magnetic field at time t, the machine can feel the feedback, and figure out where the hyrdogen is.
i digress, so, bottom line, if you have a figure-8, you can figure out a way to send the pellet (now there are only two directions in and out of the focal point) as being the same spin direction, or the opposite. ignoring how you could possible do this for the situation where the pellet in going in and out of the focal point in every possible direction in a 3-d point of view...
an interesting side note is that the notion of position is completely misleading, position sounds like a location, a point. but that is equivalent to talking about the "position" of a parabola. but even more misleading. talking about the position of a parabola on the x-y plane can be interpreted as shifting the drawing left or right. but in the common every-day sense, the "position" of a particle (which is a function from space-time to a point on the complex plane) is just a point on that parabola (granted that a particle looks more like a never ending pin than a parabola). since position has become like a delta-function, in the limit, the momentum looks like an even distribution across the universe. in this sense, momentum can be thought of as dx/dt. so it's kind of like it's here now, but everywhere later. i am hoping to make an analogy between this and the case of an unbound electron of the hydrogen atom.
Same spin:
Space is a delta function
Momentum is positive
No net momentum direction
Momentum magnitude >0 ~infinite
Angular momentum infinite => energy => mass
(this sounds like a heavy neutrino)
zero net spin:
this gets fun. it will get talked about, in an indirect sense, in another section of THE NOTES.
other things mentioned in the original notes that I haven't made up a good description of, or touched on, but could expand on:
delta func position => cant interact with other particles?
Construction:
Figure 8: plop successive objects on each other. 2+-D structure with 3-D overlapping
Use RF lasers to push the 8 near the 2 vertex points in opposite direction/define spin as anti parallel/coax/force
MRI
notion of having to rotate a spin 1/2 particle by 720 to get a "full" rotation is just simply the result of angular momentum inertia.
Manifolds closed or open
Magnetic properties
Spin behavior
Specifity (featuring punkmasterfresh)
v.1.3
