Abstact: Scientists are amazed by the fact that in quantum mechanics the space-

time seems to know instantly what’s going on (in spite of the theory of relativity,

which states that information cannot travel faster than light). This phenomenon is

variously called “entanglement”, “non-locality”, “ spooky action at distance “, etc. ..

The equations of Brahmagupta and the sphere of Rieman can explain

mathematically the paradoxes of quantum mechanics. The infinite space-time is a

continuum, an ether made of infinite atoms ( logons ) of space-time of zero

dimensions and zero mass, whose total sum is 1 and whose total probability is 1.

Space-time represents the Substance of God. ( The Talmud of Scicli: Google,

massimo melli blog ). The physical reality, the visible world that we can see and

measure floats inside this Substance that fills all the gaps without leaving voids.

Subatomic particles create waves of probability within this Substance obeying to the

uncertainty principle of Heisenberg because they “ exist”. Events that have a

probability to occur within space-time describe cones of certainty within whose

limits the events can happen. Because the atoms of space-time are dimensionless,

also a cone of certainty and a spherical wave of probability, in spite of being limited

in size, contain infinite atoms of space-time and their total probability is also 1. This

fact is the key to understand quantum mechanics and its laws.

Cone of Certainty

"The diameter of the Aleph, will have been two or three centimeters, but it contained all

the cosmic space, without its vastness suffering from it. Everything ... was infinite,

because I could see it clearly from all points of the Universe. "

Jorge Luis Borges

What is the cone of certainty defined by me in the Talmud of Scicli?

Let us define the field of action in space of “probability” (i.e. for example the

probability of the "clash of two balls or two particles") .In the case of the two balls

(or two particles), we can define around them a physical field of the event "clash of

the two balls" shaped like a cone, with apex on A and base on the meridian of B. The

clash, if it happens, occurs inside this cone, which, in the Talmud of Scicli, I called the

cone of certainty. Before the clash occurs, each of the two balls is limited in its

potential movement in space by the presence of the other ball, and therefore each

ball "feels the presence" of the other as a limit to its freedom to move in space. This

is the field of probability which I called cone of certainty, because it is certain that in

the future the event will occur inside this cone. ( Note: this field depends only on the

position in space of the two balls and is independent of time. It exists even if a ball is

on the moon and the other is on Mars.)

But can an inanimate object "feel something"?

To explain this phenomenon we have to assume that space-time is a continuum, an

ether made of infinite atoms ( logons ) of space-time of zero dimensions and zero

mass, whose total sum is 1 and whose total probability is 1. It represents the

Substance of God ( in Hebrew: En Sof ) which consists of infinite dimensionless

atoms of a substance that we call “ether “. The “ether” is a continuous substance, a

continuum that fills all the infinite space without leaving voids. Only if these infinite

atoms were of zero size and zero mass, would they be linked together without

leaving any voids. Their sum is therefore 1, the Infinite Unity of all things.

The ether which fills all space-time without leaving any gaps, must necessarily be

able to transmit the information immediately. While the probability of an event

depends on the time available for it to occur, the probability field in which the action

takes place, depends only on the existence of an ether within a given space. The

figure below describes the cone of certainty.

The concept could be applied to any event that has a non zero probability of occurring in space-time in the future. The field of probability is the key to understand also the phenomenon of entanglement. The field of probability is a

typical "non-local" phenomenon. In the case shown above time is not involved in the action until the event "clash" occurs. That's why the ball (or particle) A will immediately forward the information of its cone of certainty to the ball B, and vice versa. It seems that the ball A knows what will happen. Let's see why.

Before it gets going, the ball A has a probability field restricted to the cone of certainty of the event "clash of the two balls."

Space is a continuum and in the absence of time, the information is transmitted at infinite speed because the distance AB divided by a time zero is crossed by information with infinite speed, even if a ball is on the Moon and the other on Mars. But before the event occurs, AB is a real distance?

To understand this phenomenon when applied to subatomic particles of infinitesimal dimensions we must first understand two fundamental concepts: the probability wave that defines the spatial position of the particle and the concept of future.

To understand what happens let’s analyze the double slit experiment, illustrated below.

If some subatomic particles are shot against a screen that is located behind a double slit, they form an interference pattern, consisting of alternating black and white stripes. On the dark stripes are the footprints of the particles on the screen, on the white there are no footprints. How do we explain this phenomenon?

A particle located in front of the double slit, if it’s free to act and nothing limits its cone of certainty, faces a probability field that includes the two slits, and may therefore choose either the right or the left slit, being free to choose each of the two slits. Since each particle ( because of the uncertainty principle ) is located within

a probability wave, moving through the two slits the waves are diffracted and alternating interference patterns are formed along the x direction on the screen behind the two slits.

A macroscopic cone of certainty which includes multiple choices is also formed when a bullet is fired against a rotating wind mill. If the trajectory is not calculated to perfection, the bullet will strike any one of the blades or pass over without touching them.

The cone of certainty in the case of the bullet, will include a more complex probability than the clash of the two balls shown in the first example, where the probability is very simple. If the ball A moves forward in the cone of certainty, it will eventually hit the ball B, otherwise, if it moves outside, it will pass over without touching it. In this case the ball has only one choice.

In the experiment of the two slits, if with special devices one narrows the choice of the particles to only one slit, their cone of certainty narrows and the interference patterns are not formed. When the cone of certainty is as simple as in the case of the two balls, the choice of the route becomes limited to only one possibility, and the result is that for a single slit passes a single probability wave at a time, without forming interference patterns. After studying the examples discussed above we can derive the fundamental law of the cone of certainty: "The sum of all possible probabilities within a cone of certainty is always equal to 1, that is equal to certainty."

Wave of Probability

To understand what is a probability wave we must refer to the uncertainty principle of Heisenberg which says that a particle can never stand still in space-time, because otherwise one would know its position delta x and its momentum p = mv, which are always indeterminate magnitudes. For this reason, the particle must always be in motion inside a very small probability field, forming a probability wave within which the particle is located.

Here is the famous Heisenberg formula:

Passing through the two slits the probability waves of the particles (in this case, the photons of light) are diffracted, forming black and white stripes:

If with special devices the trajectory of the photons passes through only one predetermined slit, the photons don’t form the interference figures, because their cone of certainty is restricted to a single slit, as shown in the lower part of the drawing where the light coming from the source has only one choice. It must necessarily pass through a single slit.

We can then define the product "delta x delta p" of Heisenberg’s equation as a physical quantity equivalent to a probability, because on the basis of this product is defined the probability field of the particles that can never be 0. We obtain then the second law based on the principle of Uncertainty: "The field of probability of a particle that exists in space-time can never be 0."

But can this product be 1, that is a certainty? This happens in the cone of certainty before the event occurs. Here is "my possible" explanation.

Future

What is the future? To understand what is the future we must study the diagram of Minkowski, which describes not only the event Big Bang, but it can also be applied to every event that occurs in space-time. In reality the future is nothing but the representation of the probability that a given event can occur after a certain time interval within a cone of certainty. In the case of the Universe, before Big Bang, its likelihood to develop into the cone of light was 1, that is a certainty, because no part of it could exceed the speed of light. The future is virtual, and at any given moment, it doesn’t exist, but what exists is only the present and the history, i.e. the past.

The time of the future is still, until it becomes present. Everybody knows that. So if we apply the Heisenberg formula to the cone of certainty described in the example of the clash of two particles, we have the following result.

The particle A is located on the point of the observer, the red dot, inside its small wave of probability, but since the time is still the particle must be motionless. (Using

a quantum mechanics terminology we can say that its wave function is collapsed) The particle B is located on the arrow of time of the virtual universe, on the future of A, also in its small wave of probability, and it too will be still. (Wave collapsed)

The distance between A and B is a virtual distance equal to zero, because before the event occurs B is in the future of A, which has not yet come true since the time is stopped. Then A and B are the same particle and are joined together: they are entangled. The momentum of the AB system formed by the two particles is 0/0, since the two particles coincide and are motionless. Since the distance AB of the entangled particles is 0 and the time is 0, the velocity of the system will be: v = 0/0 and we will have that p = m 0/0 = 0/0

It follows that for the formula of Heisenberg, the product delta x delta p becomes:

0 multiplied by 0/0 = 0/0 = 1 (for the proof that a zero divided by zero is equal to 1, see the Appendix of the Talmud Scicli)

This way the result is not in conflict with the uncertainty principle that says that the product delta x delta p can never be zero, if a particle exists.

In other words, before the event takes place at the beginning of its cone of certainty, when the time is stopped, the probability is 1, i.e. it is certain that the event will occur in accordance with the limitations imposed by its cone of certainty. This fact applies not only to quantum mechanics in order to explain entanglement and the "spooky action at distance" of non-locality hated by Einstein. It also applies to the Big Bang and to the probability that all that is possible will occur during the first instants of the Universe.

In conclusion, the particles "know" what will happen in the cone of certainty of any event that involves them, because, before the event occurs, the time is zero, and the distance between the apex of the cone of certainty and the event is zero.

I realize that in this explanation there are too many zeros. I am a specialist of zero, one of the three holy numbers that describe God in the Talmud of Scicli, and for me of course it is easy to visualize the "cone of certainty" explained to myself. Sometimes I write things that even I can’t understand, but this time, miraculously, I have a clear idea, at least from a geometrical point of view, so I try to give further explanations of the geometry of the cone of certainty.

Collapse of probability field in one point

So far I have tried to explain the concept of "probability field" of a future event that I called cone of certainty, because it is certain that in the future the planned event, if it occurs, will occur inside the cone. We must try to explain the concept of the

collapse of the probability field, which is a fundamental concept of quantum mechanics.

The sphere of Rieman

Let’s start from the usual equation of Brahmagupta:

that, in addition to explaining the infinite unity of the substance of God, is also used by the great mathematician Rieman to describe the accumulation of infinite geometric points of space in one single point.

Let's analyze the sphere of Rieman.

You can see the sphere of Rieman from different perspectives complementary to

each other. At the algebraic level we consider the point at infinity as a result of

the equation:

In other words it is possible, using the sphere of Rieman, to accumulate infinite

dimensionless geometric points of space (points of zero dimension) only in one

point, because the sum of infinite zero is equal to 1.

Studying the geometric design shown above we see that it is possible to project

all the infinite dimensionless points of a space enclosed by a cone into a single

point, the apex of the cone.

Let's take a concrete example to explain the concept, showing the cone of

certainty of a bullet fired against a rotating wind mill, the instant immediately

prior to the shot. To facilitate our understanding we repeat the drawing already

shown to explain the cone of certainty.

Before the shot occurs, from the point of view of the bullet, there exists in its future

a cone of probability that encloses all future trajectories that the bullet can take to

hit the target. The bullet has, as the case may be, the possibility of hitting any one of

the blades, or to pass over without hitting them. The bullet sees in front of it the

accumulation of all its possible trajectories, as in the cone of the sphere of Rieman

shown above. All possible trajectories are therefore enclosed in a point that

coincides with the bullet, but the trajectories are indeterminate until the event

"firing" occurs.

If, by some calculations, we can accurately hit only one of the blades, the bullet will

see, before being fired, in front of it a cone of certainty restricted to the blade that it

will strike according to the calculations. Its field of probability will be much smaller

than in the previous example, where the bullet had the chance to hit each one of

the blades, or to pass over without hitting them. Before moving, it seems that the

bullet "knows" which cone of certainty it will face. This is a characteristic of all

subatomic particles used in the experiments of quantum mechanics. It seems that

the particles know in advance if in front of them there will be an indeterminate cone

of certainty, in which they will be free to choose different trajectories to reach the

target or if their choice will be restricted to a single predetermined path. In the

experiment of the two slits, in the case that the result is indeterminate from the

start, the particles will create interference patterns on the screen that describes the

result of the experiment. If instead the result is already known at the start, the

interference patterns will not form and the particles will not behave as waves, but

as corpuscles, well defined from the point of view of their spatial dimension.

It seems that for the particle the cone of certainty of its future collapses

instantaneously at a point that coincides with the particle itself, before the

experiment starts. You can’t even "cheat" it while it is on its way to the goal,

because the particle "notices" the trick and adapts its cone of certainty to the new

rules of the game immediately. If the particle starts with an indeterminate cone of

certainty with two possible choices (two slits) and while is traveling one of the slits is

closed, the particle behaves as a corpuscle and the interference patterns disappear.

Only after the event has occurred, we can no longer change the rules of the game.

This is called "non-locality", which means that the space in front of the particle

disappears, becomes zero. Let's see why.

The particle does not have a brain, and even if it vibrates all the time like a wave it

does not have a conscience, but it "knows itself" within the small sphere of

probability defined by the Heisenberg uncertainty principle.

Collapse of the probability wave

The evolution of the quantum state of a physical system, such as a photon or an

electron, after a measurement is made on it, can be explained by what happens to a

soap bubble. In response to a measurement of a property of the system, such as the

position, the spin or the speed of a subatomic particle, its cone of certainty narrows

to a single point, because the collapse of its probability wave takes place .

If in a double slit experiment is observed the trajectory of a particle, the interference

patterns are destroyed because the uncertainty of its spatial position, which can be

represented by a sphere of probability, disappears. The mechanism responsible for

this phenomenon is called the collapse of the wave function and can be understood

by studying what happens to a soap bubble.

. A

If the sphere of this design represents a

soap bubble, when the bubble comes into

collision with an object, (for example the

dot A, top right), the bubble bursts and the

radius r becomes zero almost instantly.

The bubble collapses at the point where

the collision took place and disappears.

Imagine that the bubble illustrated above is

the wave of the probability of a photon

that expands in the space-time at the

speed of light.

Here's what says about this phenomenon Anton Zeilinger, famous quantum

physicist, in his book The veil of Einstein: "... in the case of quantum physics we

speak of probability waves. If a photon is emitted from a very small point source, it

corresponds to a spherical probability wave, the intensity of which in a certain

position indicates the probability of finding the particle in that point. With the

increase of the distance from the source, this sphere becomes larger and larger, and

thus its intensity decreases in each point. The probability calculated over the whole

sphere must be equal to 1, because the particle must be somewhere in the ball

itself: it can’t disappear. What happens when we detect the particle at a given point,

that is, when the detector is triggered by the presence of the photon? If the particle

is detected in a certain point (for example in point A in the drawing, this comment is

mine) it can’t certainly be in another point. So, by the time the detector is triggered

the probability must immediately become zero in the rest of the sphere. "

Zeilinger then writes that Einstein was irritated by the fact that, contrary to his

theory of relativity, this phenomenon occurred instantaneously at infinite speed, yet

nothing in the universe was supposed to exceed the speed of light.

All of these concepts are tested and retested by many experiments and are part of

the baggage of the paradoxes of quantum physics, so they are very solid physical

realities that we must try to understand.

The infinite speed can be achieved in two ways:

1- Assuming a spatial dimension "zero"

2- Assuming a movement that takes place with time "zero"

So, in order to explain the phenomenon of infinite speed, we must invoke one or the

other of these two conditions.

Note: if time and space are both "zero" for one dimensionless point of space-time,

its probability is 1, and the point is either a singularity or a logon. (In the Talmud

Scicli I discussed this, in connection with my explanation of the Big Bang and the

logon).

Spatial dimension zero

If a particle has zero chance to exist in a point of space-time, it means that it doesn’t

exist in that point. In the case of the photon discussed by Zeilinger, when this

photon is materialized in point A, its probability of being in that point becomes 1,

that is, certainty, and automatically its probability to exist in other points B, C, of its

spherical wave of probability vanishes instantly. If the radius of the sphere

disappeared at the speed of light, the effect would be the paradox that for a

moment there would be a non-zero probability of finding the photon in some point

B, C, of the sphere, while contemporaneously the probability would be 1 of finding it

with certainty in point A. The total probability of finding it in points A + B + C would

then become greater than 1, that is, greater than certainty, and this would be

impossible. So when the spherical probability wave collapses, the collapse will be

instantaneous and will happen at infinite speed. “When the sphere of probability

collapses in one point, the sphere passes from any spatial dimension to a zero size

instantaneously.” Its space becomes zero.

Time zero

According to the definition of the ancient Greek philosophers, which has never been

questioned by anyone, time is the measure of movement. Einstein has made an

important clarification to this definition by adding that if the movement is rapid,

time flows slowly, until it stops for an object that, relative to us, travels at the speed

of light. If the movement is slow, time passes more quickly. And if one is moving

progressively slower, time continues to run faster and faster? And in the absence of

movement, it makes sense to talk about time? To these questions there is no

answer.

Time stands definitely still in a black hole or for a photon traveling at the speed of

light. Outsides of the cone of light of the Universe, relative to those who are in the

Universe, time must be stopped, because if an object belonging to the universe

would be moving in that place, that is, in an inverted cone of darkness, it would

travel faster than light. In that place an object that is part of our universe, if it exists,

must be still. In our universe the time never stops, except in black holes, or on the

surface of the cone of light of the Minkowski diagram. All these places are

inaccessible to us and therefore are useless for our purpose to demonstrate an

infinite velocity. But there is another place where time is definitely still: the plane of

the present of this same diagram. Let's see how this plane can serve to explain some

of the paradoxes of quantum physics. In the Talmud Scicli Jacob ( Aharon Nathan )

gave this brilliant definition of the present: "Time is made of past and future. The

present does not exist because as soon as it exists it becomes past. The present is

virtual. It’s obviously invented to understand the past and the future. It's like your

zero. It is there to understand the plus sign that is tomorrow and the minus sign that

is yesterday. "

The brilliant definition of Jacob, that explains very well to us human beings what is

the present, is also valid for an elementary particle such as a photon or an electron?

How does a particle see the reality? I think that for the particle exists only the

present and the arrow of time pointing to the future, but for it is the future that is

virtual, it’s the future that does not exist because it has not yet occurred and

therefore it doesn’t count.

How does its cone of certainty look like in the perception of the particle, since it is

located in the future, but has its origin in the present? Obviously, as a motionless

point on the still plane of the present which concentrates all its future probabilities,

whose sum is 1. The diagram of Minkowski explains this concept very well. When

the time is set in motion, the particle begins its journey to the future knowing that

its goal should be, in all circumstances, to respect the law of the cone of certainty,

that the sum of all its probabilities should always be 1 .

Entanglement

The Minkowski diagram is used in physics to describe the physical events and it’s

applicable very well to quantum mechanics. Using this diagram, we can try to

understand another strange phenomenon of quantum physics: entanglement.

Let’s study a wave representing the motion of a particle that vibrates up and down

in the space-time. The particle, moving within a sinusoidal wave, passes from the

position zero, which represents the present, to the positions of maximum and

minimum amplitude and returns to zero. Each cycle the particle repeats the same

path. The zero is located on the plane of the present of the cone of certainty of the

probability of the particle.

Suppose that two entangled particles are created together in the point O of the

plane of the present, in such a way that one moves on a plane to the West and one

moves simultaneously towards the East. The characteristic, that binds them

together in the same cone of certainty are the following: they have equal waves, but

one wave is out of phase relative to the other by 180 °. Therefore the cone of

certainty linking them contains the information that the total probability of the two

particles must be a flat wave, that is, the sum of their waves. The diagram below

illustrates the concept: at the top there is a wave that propagates in space-time

while remaining true to itself. In the central drawing there is the superposition of

two equal waves, out of phase by 180 °, which cancel each other resulting in a flat

wave. In the drawing below, the two waves are out of phase by 120 °, and their sum

produces a hybrid wave of intermediate value between the two waves.

Suppose that the two entangled particles behave in the manner described in the

drawing in the middle, i.e. that they are out of phase by 180 ° and their sum is

represented by the drawing shown below, a flat wave.

What happens when one of the two particles is detected by an instrument? Let us

assume that the instrument detects that the particle vibrate as wave 1 in this latter

design. The other must necessarily vibrate as wave 2, so that inside the cone of

certainty that links them is preserved the certainty that their sum is always equal to

0, namely, that the two waves will cancel each other. It has been shown by many

experiments that "The identification of the properties of one of the two entangled

particles, leads to the immediate identification of the properties of the

“correlated” particle, regardless of the distance that separates them." This

phenomenon is explained by the transmission of information at infinite speed on

the plane of the present with time stopped. The same phenomenon occurs if the

two entangled particles have opposed properties of another type, such as the spin,

polarization, etc ...

Conclusions

The concept of the "cone of certainty" together with the concept of the spherical

probability wave helps to understand the paradoxes of quantum mechanics. The

probability seems to be a property of space-time, such as gravity, inertia, energy and

other basic properties. Here are the laws that describe the cone of certainty and the

probability field:

1- “The sum of all possible probabilities within a cone of certainty is always

equal to 1, that is equal to certainty.”

2- “The field of probability of a particle that exists in space-time can never be 0.”

3- “When the sphere of probability collapses in one point, the sphere passes

from any spatial dimension to a zero size instantaneously.”

4- “The identification of the properties of one of the two entangled particles,

leads to the immediate identification of the properties of the “correlated”

particle, regardless of the distance that separates them."

Now that I understand the geometry I have no problem accepting the above

Laws of quantum mechanics, because I believe in the infinite unity of all things

that exist within space-time, which for me represents the Substance of God, the

great One, the infinite Mind that includes everything.

Here is what I believe:

“If a scientist designs an experiment with a result that is planned in advance

and he knows the result, the infinite Mind knows even before him because his

thoughts are registered in the space-time. If the scientist does not know, the

infinite Mind applies to the experiment the rules of the cone of certainty: the

sum of all the probabilities must be 1.”