**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.

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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