Shoe-edge space.

Classical Mechanics was an attempt to keep us away from asking what is there beneath the shoe-edge. There is nothing important would be the basic reaction if anybody asked. But its not so.

Physics has been, in essence, an effort to refine our present knowledge of geometry.

We have always been successful at it.

And particle physics is a study of the behavior of particles where these particles represent angles in something called a phase space.

So when we find new particles, say a Higgs Boson, or a “B’s of S of resonance” we find new angles that we did not know existed or we hypothesized these angles and found to be true; that they did exist, and they changed our knowledge of geometry, because these angles gave us more and more precision-centric methods to see if each time what Euclid knew; are going to be confirmed or not.

This way, we can know more than Euclid, but we can never know less than Euclid, that’s when we say Euclid is scientifically correct. Science once done correctly transcends its performers.

In science, we always add knowledge, because its now, refined. But we can’t subtract.

The fact that particle physics is true, means, the Euclid’s trigonometry has to be correct, in addition to something more refined.

So literally, the edge of our compass that the geometry box maker didn’t produce properly hides all the mystery of particle physics and Heisenberg uncertainties.

They were not directly knowable from telescopes either.

But the fact that telescope is ray optics, might have given a way to study geometry in better precision, only if something didn’t work out as Euclid predicted.

It turns out that that was in-fact the case. So we gradually figured out how it is that Euclid is not correct.

First he was not correct in an Einsteinian way and then in a Schrodingerian way.

There were discord or discrete discrepancies in the constituency of our physical world which showed up as peculiar characteristics in the physical attributes like black-body spectrum.

The fact that the lower-energy-strata existed, meant that, there is particle behavior and the fact that there is higher-energy-strata meant, there is wave or many-particle behavior.

Altogether there is wave-particle behavior. So all these were hidden into the lack of precision of something as astounding as our shoe.

By refusing to honor the shoemaker’s hypothesis as sacrosanct, the physicists did not become denigrated little douche-bags, but they brought new knowledge.

And we can safely say; the whole quantum mechanical and general & special relativistic world was hidden in the edge of the shoe.

Phase Space.

When we deal with what we call particle physics, we always have to bring into discussion; whats a phase space. Its the most basic thing to do, in that involvement. Its like each time we make pizza we have to think of whats the dough and whats the topping. At-least the theoretical and experimental particle physicists would think so.

Whats phase space? How is it that the special relativity was hidden into a small angle?

Lets first talk phase space.

Phase space literally means a space of angles. A phase is an angle. But what is the angle? The angle that gives us the direction of momentum. And the magnitude of the momentum is directly connected to the energy.

So we know what the momentum and energy are.

For each particle that is present there, there is; {Energy, Momentum}, which are 4 quantities. Do not be shocked, momentum is really 3 different values, if we formulate the physics in terms of 3-dimensional frame work of coordinate system.

So if we draw these 4 quantities for each particle, then we have what is called a phase space. That’s the most precise definition that I know, that we can give without any inconsistency with actual physics formalism.

Its because most of the Physics is right when we can predict or fit the right amount of energy. Right energy will often lead to right Physics, in most cases. Because energy is quite high-up in the definition of things in physical systems, only one step below the most powerful “action”.

Due to conservation of energy and momentum; we have the knowledge of what produced what and what not.

So we know the topography or a branching of various particles into each other.

eg A >> B+C is a topography.Its the most basic topography though, things become messier when we include more and more.

Particle Topography. Particle A goes to particles B and C. Their motion makes angle wrt each other and provide information regarding what comes from what and what comes not from what, in accordance with Laws of Physics, such as conservation of momentum and energy.
Particle Topography. Particle A goes to particles B and C. Their motion makes angle wrt each other and provide information regarding what comes from what and what comes not from what, in accordance with Laws of Physics, such as conservation of momentum and energy.

Because when we have more, B can go to D and E and so on, therefore to get knowledge of E we have to get the knowledge of A, B, C and D.

Then the phase space is the total {energy, momentum, angle, …} information of each of the particle, individually or together.

That means the motion of A will extend some angle, with the motion of say E.

Therefore the particles A, B, C, D and E are said to be angles in phase space.

Particles are angles in phase space, as well as they are; solutions to differential equations.

That means the angles are predicted from the differential equation, by the more appropriate (physics wise) name; equations of motion.

Since angles are ratio of sides, they are differentials or ratio of little deflection which is what speed and momentum etc are.

If one knows a phenomenon called aberration one realizes that this phenomenon is a special relativistic effect.

In the first order of speed v = tan (theta) where, theta is the angle, or deflection or aberration. Aberration is simply a shift in energy, due to a shift in the angular position, due to a relative speed v.

A very slow object will produce a very small deflection but can be detected by a Radar or frequency-device.

The angular deflection is occurring, because we are moving with respect to the star light. So if we think the star is present somewhere its actually present at a slightly different angle, depending on how fast we are moving wrt it, while we are observing or detecting it.

Now we did not realize, that there are small deviations in angular position of objects until we had fast moving particles or photons, whose frequency or energy shifts told us that story.

The high speed of photons meant large deflection over due time, and that’s inbuilt into Relativistic Laws of nature. Aberration is therefore directly related to Relativity in general and Doppler shift of light in particular. Doppler effect of light explains the aberration phenomena or in other words Special Relativity was hidden into small angles.

This is also true about General Relativity which is merely Special Relativity + Potential Energy implications of Special Relativistic new Laws.  

That means the speed that decided how imminent relativistic effects are, can also be due to the gravitational mass or field in the location, where things are observed. That’s because, as it is from Einstein’s understanding, there is no difference between the kinematic (due to motion) energy or Gravitational (due to mass) energy.

Mass and Motion, both produce equivalent deflections in energy.

That means sitting in an accelerated car always increases our mass and therefore weight. Acceleration and Gravity are equivalents. This comes from a general principle that, kinetic energy and potential energy have the same physical effect even if they might look different mathematically.

This principle (known also as Equivalence Principle, which has both weaker and strong forms like Newton’s laws does) I have described in much detail in many related articles and in-fact derived in one instance independently, from first principles of Physics.

All the discussions above, literally mean, all these “new” laws were only hidden into the shoe-edge angles or less. In-fact, I have found myself very proud in the past, to speak how Gravity is a millimeter range effect (in the least and on Earth’s weak field approximations of 10^-9) therefore shoe-edge being mm range, there is much gravity effects that were hidden there too.

If one wondered why Einstein bent a slight bit more, what was he thinking when he was fixing the lace, this is what he was thinking. Pun Intended. He was certainly not trying to discover a Graviton, but thinking how this Gravity force evolved into such a weak strength and yet prevails every where. Am I impersonating Einstein here, a little beat.

Of course tying the shoe lace story is akin to the story of apple falling, why can anyone make up a story and me not :).

The fact that Gravity must be hidden into dimensions in the mm range which is what shoe-edges must be, led to understanding General Relativity, because Einstein had to study Non-Euclidean laws of geometry which essentially deals with the little edges of Euclid that don’t fit into Reality.

And Einstein was successful at that. His discovered laws, his application of geometry into physical phenomena, bore fruit and physical phenomena such as Perihelion of Mercury were found to be explained by his new laws.

Moral: One can look into smaller than the small, as is understood in an age, and if one  is good one will find something. If one is nuts with it one may even win a prize. There are tons of prizes. No offense. But that’s the whole idea behind applying geometry to Physics. New laws of Physics will be discovered just from trigonometry

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