The most basic properties of reality, are – so to say – much, much more factual than comprehensible. They are the “That’s the way it fundamentally is”–things.

The consequence of that is that, if they are not obvious, they are almost unexplainable.

Lengths are comprehensible because they are an obvious part of our everyday experience.

Energy is also something that we experience each day (i.e. the Sun makes us warm, it hurts our eyes when we look at it, etc.), but people needed much more time to find the way to properly measure, and to understand energy. With lengths it was incomparably easier.

On the other hand, the fact that the light is electromagnetic phenomenon, we cannot experience with our senses. Nor we can sense that it consists of photons. Nor we can sense the electromagnetic properties of space:  and . 

And the basic property which is hardest to grasp is the one which we denote with the word electromagnetic, that essential, dual property of both elementary energy, and of space.

The good thing is that these basic things which are not obvious, can be reasonably justified. That justification has to be double:

1) justification through experimental detection – as direct as possible, as concrete as possible detection of these things

2) and their logical, mathematical, rational, reasonable justification within the context of the things which are caused by those basic things. More precisely said: that these basic things are the unambiguous cause for the higher-level physical phenomena, and that these basic things are unambiguous result of deduction (analysis) of the higher-level physical phenomena.

So, to those basic things a man may come in two (usually interlaced) ways:

-       empirically
For example,

discovery of ,

initiated (meaning: not extracted, not explicitly presented in his equation, not yet properly discovered) by Coulomb, and

discovery of ,

initiated by Ampere,

 

and then, later,  and  were finally extracted, explicitly presented and treated as the fundamental properties of vacuum (empty space).

-       or, through logical deduction, through rational analysis of the higher-level physical phenomena.

For example, that is how the most basic equations of existence 

and

were obtained.

 We cannot explain the cause of the fact that . Nor we can explain why  has the value which it has. Nor why is it the universal constant. The only explanation which is possible, is:

-       if these basic facts would be different, our world would be different,

In other words:

-       if these basic facts are as they are, our world is as it is (if we logically/reasonably develop/derive the consequences of these basic facts, we get the results which perfectly describe the higher-complexity-level phenomena, and if we analyze the higher-complexity-level phenomena, we inevitably come to these basic facts).

 

The goal is to recognize the minimal set of basic things and their basic relations, which is sufficient to derive and explain everything else in this world. Also, the goal is that each of these basic things is detectable as directly as possible, as separately as possible, as explicitly as possible.

Meaning: to have only and exclusively real basic facts – and nothing “deeper”, undetectable, speculative (i.e. “virtual” particles (“spontaneously” “emerging”/”vanishing” in particle-antiparticle pairs), strings, branes, “spontaneous” symmetry breaks, … ).

(The recognition/selection of these basic things started in The gem (5)).

 

The goal is to make physically, logically and mathematically consistent TOE. TOE which is in explicit accordance with that what we call sapience – TOE which is comprehensible (TOE which would be like, i.e., Euclid’s geometry).

The sapience requires causality. The sapience cannot understand things if the causality does not exist. After all, the sapience – that highest, most sophisticated phenomenon in universe – would not exist without causality.

Practically, the causality and continuity are synonyms. (In this post, the basic natural cause of continuity will be deduced).

The sapience will be pleased only if there is a finite number of well defined basic things (basic physical phenomena, their basic properties, and relations among them), and if these basic things are such that all other physical phenomena, all higher-level physical phenomena, are unambiguous and causal consequence of unambiguous and causal interplay of the basic things.

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The essential way of manifestation of change is motion.

Motion is the change

-       of spatial position, and/or,

-       of spatial distribution (shape, form)

of energy in time.

Two simplest, canonical motion types are translation (straight line motion), and rotation (circular motion).

 

The straight line motion is the most essential type of motion. The simplest mode of motion.

Curvy motion is the higher mode of motion than the straight line motion. The simplest closed-path-curvy-motion is the circular motion.

 

Physical manifestation of elementary energy is photon. Photon moves. That is the way it exists. There are no such photons which do not move.

We know that the photon’s energy is electromagnetic by its nature. But, we should notice that it is also its kinetic energy.

So, in the case of a photon, in the case of that embryo-entity,

-       motion and existence are indistinguishable. Namely, the motion is the essential manifestation, inevitable manifestation of photon’s existence. In other words, on that level of existence, on the photon-level, to exist means to move.

-       also, to exist means to have energy (generally), and in the case of a photon, energy is at the same time electromagnetic and mechanical (kinetic) energy, and total energy.

-       mass is not – so to say – ripe. Precisely: it does not have inertia.

The motion of a photon is the interaction among elementary EM-energy and elementary EM-properties of spacetime.

I know that the energy is the most essential property of photon, and that the nature of that energy is electromagnetic, and I know that the velocity of photon’s motion is determined by the essential electromagnetic properties of spacetime  and :

I also know why were   and  excluded from the fundamental phenomena, and why nobody still did not notice that that exclusion was cardinal mistake – I will write about that soon, in psychology section. Right after I finish “The gem” post-series.

From everyday experience, I know that any motion requires interaction of that what moves and its environment. On elementary level, that what moves is the photon, and its basic environment is the space, and I know that the velocity of EM energy propagation is determined with electromagnetic phenomena which we call the lengthwise capacitance , and the lengthwise inductance  . Hence, the first conclusion would be that the motion of a photon is the result (the consequence) of interaction among elementary EM-energy and elementary EM-properties of spacetime. That interaction has to exist. That interaction has nothing to do with any kind of friction. So, the final conclusion is that that interaction is motion. Which is enabled by  and .

The measure of that interaction is 

So, the (proto, embyo)-mass (non-inertial mass) is electromagnetic phenomenon, which is the result of elementary convolution of photon’s EM-energy, and of fundamental EM-properties of space: the lengthwise capacitance and the lengthwise inductance of space.
Inertia is the phenomenon which requires the following precondition: stability of mass. The mass of a photon do change in interactions with other particles – before and after interaction (collision) with i.e. an electron (i.e. Compton’s experiment),

o    the velocity of a photon is the same, and the velocity of electron is different

o    the energy (that is, non-inertial mass) of photon is different, and the mass of electron is the same,

o    the change of electron’s kinetic energy is equal to the change of photon’s energy

The mass of electron is very stable, and that stability is the basic cause of the phenomenon known as inertia. If the mass of electron would not be so stable, then the interaction (collision) of electron and some other entity would affect both the velocity and the mass of electron. If electron’s mass could change without any resistance, then electron would not experience the change of velocity. (This was just a short, the simplest-case survey – we will get back to this in the next post).

 

Inseparable, inevitable, and on elementary level (on fundamental level) equally essential element (of the basic-existence-set whose elements are motion and energy) is the force.

A photon is the moving force. Namely, as it moves along its path, the change of energy occurs along that path: immediately behind the photon, the energy decreases as the photon moves forward, and also, immediately in front of the photon, the energy increases as the photon moves forward. Change (increase, decrease) of energy along length is the force.

 

The main property of motion is the velocity. Velocity has the finite upper limit:

 

The force also has the finite upper limit: 

Why does such constraint exist? Well, the general answer is: because without it, universe could not exist. Maximal possible force is one of the primary principles of existence. One of the preconditions which enables universe to exist. 

, , , and  are the most fundamental qualities&quantities of existence. Unambiguous qualities, which have finite quantities. All that what is most essential (energy, space, time, electromagnetism) is related to/by , , , and :

 

 

including the electric charge:

Let us start from the definitions of capacitance: , and of voltage 

Hence:  

Hence, on elementary level, we'd have

The quantity   , we could consider as the theoretically maximal fundamental charge (as the theoretically maximal possible charge of some individual elementary physical particle, or, as the total potential for charge of a photon [please read carefully and think – I did not say that a photon has charge, but that is has the potential for charge. And we will see in the next post why and how that potential may express/manifest itself.]).

 

 The time in gravitational field is

 is not the consequence of the universal gravitational constant  and of maximal possible velocity , but actually, the  is the consequence of the fundamental constraints  and  and . The  and the  are of utter significance. The  is even more important, it is more essential than both  and . In other words, the  is not just some constant which just appears in equations, but it is the fundamental real constraint.

Looking at the gravitational-time equation, we see that if  would be infinite, then there would not exist gravitational influence on time.

Nor on the photon’s length:

Nor on the energy of a photon:

Nor on the photon’s velocity:

Generally speaking, if the constraint “maximal possible force in universe” would not exist, any kind of interaction would be impossible.

Also, the continuity principle would not exist, that is, the causality would not exist.

Completely generally speaking, the world would/could not exist.

 

The Schwarzschild’s solution for gravitational time

will be proven to be wrong, soon. In fact, it is already definitely but implicitly (without mentioning it at all) proved wrong with that what was written in The gem 1, 2, 3, and 4).

As it was already said in The gem (1):

The GR experts would claim that it is the new equation which is wrong, because it was derived from Newton’s law of gravitation, and – according to GR – the Newton’s law of gravitation is just an approximation. But, during the course of these posts, it will become completely clear  that the situation is exactly opposite, namely, that the GR equations are approximations of reality, which are good in the area which is far away from the Schwarzschild radius

which is the GR-version (the integration constant in Schwarzschild’s solution, enabled by the Ricci’s simplification) of our characteristic radius , which was introduced in “The gem(1)”,  (in later posts, we used to denote it as ))

and become more and more wrong as we approach the Schwarzschild radius, and, finally, become totally wrong at the Schwarzschild radius.

That will be demonstrated in the best way possible: by explicit unification of physics, that is, by deriving the new equations, the equations which were already derived, in the post The gem (1), but this time (in “The gem (9)”) that derivation will be from the quantum level up. That derivation will show that the new equations are not only  the reasonable consequence of the superposition of elementary influences of elementary things, but that the new equations are the only reasonable consequence.

 

The new equations, as it was already mentioned, could had been derived in the year 1900.

Also the following derivation – another proof of their validity – could had been done then, too.

 

We have a body with a mass . We observe some point which is at a distance  from that body. The time at that point is

If another body with a mass  comes (from very far away) at some distance  from the observed point, the time equation at that point becomes

In the case of  bodies, we will have

 

Follows that the time behavior at some point which is equally distant, , from two or more objects (, , …) will be the same as the time behavior at the same distance, , from only one object whose mass  is equal to the mass-sum of those two or more objects:

So, the new equation is in accordance with the continuity principle (there are no discontinuities/singularities in energy flow/transformation/conservation, so, the causality is in effect, energy(mass) conservation is in effect. Simply, obviously, exactly.

If we use the Schwarzschild equation, the continuity principle is approximately valid (almost valid, but, ultimately, invalid):

…

Since

is very small value, and if the mass is small, then the following approximation may be applied

However and whatever, the energy conservation law is violated, and the door is open either for searching of the “scientific” patches for that problem (through introducing visionary ideas, new, unprecedented principles, …), or for “scientific” discussion about creating energy out of nothing, about turning energy into nothing, …, or for transferring it from/to “new dimensions”, “new (parallel) worlds”, multiverses, … . 

Such a small discrepancy from the energy conservation law, and such huge “possibilities” for “deeper/broader insights” into “true” reality/realities, for “upgrades” and “developments”. Kind of butterfly effect.

If the derivations presented so far (derivations in The gem 1, 2, 3, 4, and this derivation, about the energy conservation) would had been done in 1900 (and they could had been done then), the GR theory would never be accepted.

 

 

In the previous post, the fundamental continuity law was derived, from the fundamental state:

Since there exists the fundamental physical constraint , the following relations are valid always, under any real  circumstances:

(1)      

(2)    

The relation (2) means that something (meaning: that what exists in spacetime, that what has energy) cannot have 0-diameter. Nor its diameter could be infinitesimal. Nor that something could have infinite energy.

The relation (1) means that there is no change in universe which could be non-continual. No singularities can occur. The world is the perfect continuum.

Further:

on the quantum level (i.e. for a photon), we have:

Also, the minimal quantum length  cannot contain arbitrarily high energy (mass):

Generally, the following condition is always valid:

 

The minimal possible time-period of a photon’s oscillation (the minimal possible time-period of interaction of a photon with  and  properties of spacetime) would be

Or

 

In order to determine the minimal possible size of bodies which have inertial mass, we will use the exponent of the gravitational length equation

The part

of that exponent has the dimension of length.

As it was already said in “The gem (1)”, if we’d want to interpret it physically, we could consider it as „the characteristic-size-parameter of the gravitation-source whose inertial mass is “. Calculating that value for some physical object, we’d get very small value comparing to the actual size of the physical object. Having that the characteristic size is very small comparing to the real dimensions of the object of a given mass, the characteristic size should be considered as the minimal possible radius for a given mass.

And why such constraint exists? Because there exist the constraint maximal possible force:

So, due to the constraint , a body which has some inertial mass , cannot have an arbitrarily small radius, but the radius which is

 

There are no circumstances in reality in which the  could be surpassed. 

This statement will be thoroughly elaborated and justified in the post “The gem (9)”, after we explain (in the next post, “The gem (8)”) what exactly is that what we call matter. Only then it will be possible to completely explain why cannot be surpassed.

For now, we can preliminary show (mathematically illustrate) the inscrutability of , using the Coulomb's law. (And the Newton's law of gravitation will be elaborated in the post "The gem (9)").

So, the Coulomb's law is:

If we put the previously derived charge   and the minimal possible size , we have

Essentially, the existence of the constraint  enables both the perfect continuity (strict causality) of changes/processes, and finitely quantified existence, meaning:

elementary entities

-       can have neither 0, nor infinitesimal size,

-       can have neither 0, nor infinitesimal energy, and they cannot have infinite energy, neither.

Essential parameters/properties of existence

-       cannot be less than some small finite value (i.e. the size of physical entities; the values ,, 

-       cannot be greater than some big finite value (i.e., , ).

 

The perfect continuity and quantization are not things which exclude each other, but which require each other, which impose each other.

 

The discretization is the form of quantization. But the discretizations like, i.e.,

-       “up to this point, the energy is , and immediately after, it is ”,
or, i.e.,

-       refraction (fracture) of photon’s path as it enters/leaves some optical prism,

are not possible in reality.

The transitions/changes can be sharp, but cannot be fractures. The transitions/changes can be only and exclusively smoothly continual.

 

In reality, in our real world, the singularities are not possible. But they are not left unhandled – the most sophisticated and complicated thing in the real world is the human brain. There is a process in it, which we call imagination. There, in our imagination, everything is possible. And such ideas (which are impossible in reality) may be modeled mathematically, too.

 

“A man may imagine things that are false, but he can only understand things that are true, for if the things be false, the apprehension of them is not understanding.” (Isaac Newton)

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Physical manifestation of elementary energy is photon. Photon moves. That is the way it exists. There are no such photons which do not move.

Through spacetime whose  and  do not vary, photon’s path is the straight line.

Through spacetime whose  and  do vary, photon’s path is not the straight line.

Why does a photon’s path bends?

 

Photon’s (wave)length is finite.

The cross-section of a laser beam is finite. That beam consists of photons. Photons are particles (the greater the photon’s energy, the more particle-like it behaves). Hence, we can assume (by logical deduction) that a single-photon has some cross-section, which is finite. In contemporary science, the term “effective cross section” is used. Whatever it is called, it is undeniable that a photon has cross-section, meaning, the cross section which is finite, not infinitesimal.

That cross-section of a photon, and the photon’s length, define some volume. On the following 2D-picture, that volume is just conceptually (for visualization purpose) represented as it is represented:

Pic

Along the left-to-right direction on the picture, the values of  and  increase.

Therefore, according to the Maxwell’s equation, along the left-to-right direction on the picture, the allowed EM-propagation velocity decreases.

A photon is non-inertial entity, that is, a photon follows the propagation conditions without resistance.

And the propagation conditions are such that the allowed velocity on the photon’s left side is higher than the allowed velocity on its right side. So, the only thing that a photon can do in such conditions, is to turn to the right.

 

This is both essential and universal explanation. This is the explanation of:

-       why photon’s path bends in the gravitational field,

-       why photon’s path bends when it enters/exits an optical prism,

-       why photon’s path bends as it passes very near some material object (i.e., many of the short-sighted people (people who have myopia) know that when they want to see sharper some distant object, they should look at it through a tiny hole)

-       why photon’s path bends when it interacts with some particle, i.e. with an electron in Compton’s experiment

This is the core explanation of the photon’s path bending, in each and every case in which the photon’s path banding occurs.

A photon is elementary mode of existence, whose motion is the simplest mode of motion: the straight-line-motion. The higher modes of existence are formed by the photons whose motion is the higher mode of motion: circular motion. How can that be?

Well, for that, we need two photons, which have sufficiently high energies, and which approach to each other along two parallel paths which are sufficiently and appropriately near to each other.

And, we need that, when such two photons come sufficiently near to each other, they cause the increase of   and  properties of space among these two photons.

In the next post, we will explore the validity (justifiability, reasonability) and consequences of this simple assumption.