By using some simple logic it is not so difficult to prove that all kind of universes (for example ours) should exist. It is also easy to show which laws of nature exist, why they exist and why everything in our universe all the time obeys these laws.

The explanation is checked by dozens of professors physics and scientists (from Belgium), so I will disappoint people that hope to find any logical mistakes. Except in my spelling, grammar and choice of certain specific terms, you won’t find any. But you are always free to try. All constructive feedback is welcome. Good luck!

Part 1: Why does our universe exist?

In order that a whole universe can exist, we should of course first explain how something can exist.

To work easy we will set up a reasoning for the existence of physical quantities that can be represented as vector (force, position, speed, acceleration, electric field, … but not temperature, mass, volume)

In the further text only this kind of physical quantities are considered.

Consider a force: Fx = 1 Newton with a given direction (X-axis) and magnitude.

We will start our reasoning with following statement:

0 fx exists.

Because forces are vectors, this is literal defined in the axiom’s of vector spaces.

There exists an element 0 ∈ vector space V, called the zero vector, such that v + 0 = v for all v ∈ V.

http://en.wikipedia.org/wiki/Vector_space

As we all know this zero vector equals 0 multiplied with a vector.

Although unnecessary we can also proof that 0 Fx exists.

At least one of both expressions (1 and 2) is true, and both lead to the same conclusion that 0 Fx exists.

Expression 1: n Fx exists (with n ≠ 0)

n Fx = (n + 0) Fx = n Fx + 0 Fx

=> (n Fx + 0 Fx) exists => 0 Fx exists

Expression 2: n Fx does not exist (with n ≠ 0)

Because force is a physical quantity(!), it is obvious that the “not existence of n Fx” correspond with “0 Fx exist”.

(Comparable with “dragons does not exist” is the same as “0 dragons exist” )

=> 0 Fx exists

So, like stated in the axioms of vector spaces 0 Fx exists, and this is therefore a good basis to build up the further reasoning.

We will call “0 multiplied with the unit of a physical quantity” from now on the “zero-quantity” (from a physical quantity).

Because 0 Fx exists, there also exist an infinite number of other representations (ex. 5 Fx – 5 Fx, 5 Fx – 3 Fx – 2 Fx, …) that are completely equivalent with 0 Fx. (It is always the same 0 Fx, just represented in different ways.)

From now on we will talk about collections (of elements) that are equivalent with the zero-quantity.

ex. {5 Fx, –5 Fx} or {5 Fx, –3 Fx, –2 Fx}

The reasoning that is made for forces can be made for all other physical (vector) quantities in our universe (electric field, position in space, …)

To make the picture complete of all that exist (also what is not part of our universe) we can write the following:

In order that a collection of values of a physical quantity exist, two conditions must be met.

1. All values (in the considered collection) should be possible.

And “something is possible”, is exactly the same as saying “something is not impossible” (= double negation)

So, if there is no reason that exclude a value of a physical quantity then the value is possible.

The big importance of this condition will become clear in the further text (Part 2).

2. The sum of the values (in the considered collection) should equal the zero-quantity.

As shown before, the zero-quantity exists, so other representations that are equivalent with the zero-quantity of course also exist.

Part 2: Why does nature’s laws exist?

The simple rule that the sum of the (possible) values of physical quantities should equal the zero-quantity, in order that the collection exists, is of course not sufficient to explain the complex laws of nature in our universe. Although …

As long as one physical quantity is considered, or multiple physical quantities are considered that exist on itself, completely unconnected from each other (ex. time and position on an X-axis), then there are no physical laws possible as in our universe.

The situation changes completely when multiple physical quantities are considered that are somehow connected with each other. We will call physical quantities that are connected with a relation to each other from now on “bound physical quantities”.

Example 1:

Consider following bound physical quantities:

. x: Position on an X-axis. (m)

. t: Time (s)

. v = dx/dt: Speed (m/s)

What does this really mean?

. The physical quantity “speed” implies, because of its definition (dx/dt) that the rule dx = v . dt should always be respected. This can be compared with a law of nature in physics.

. The physical quantity “speed” implies, because of its definition (dx/dt) that dx and dt should also exist.

. dx and dt implies, because of their definitions that also position and time should exist.

Conclusion: a speed implies that also space and time exist, and that those 3 physical quantities are connected with each other by following rule (law of nature): dx = v . dt

We could as well choose more complex examples of bound physical quantities, but that leads obviously to more complex laws of nature. (see example 2)

For each of the three physical quantities of example 1 we can define unit quantities.

. Ex: unit on the x-axis (1 m)

. Et: unit of time (1 s)

. Ev: unit of speed (1 m/s)

We will call a set of linear independent unit quantities from now on a “basis”.

Elements that can be expressed as a linear combination of the 3 unit quantities will be noted as follows: (x, t, v)

This element corresponds with respectively the 3 following values for the 3 physical quantities:

x . Ex , t . Et , v . Ev

We call “the unit quantities of the basis multiplied with 0” the “zero-element”.

In this example the zero-element is (0, 0, 0).

Universe

Consider a basis, consisting of unit quantities for a collection of bound physical quantities.

We will call a “universe”, a collection of elements, where each of these elements can be expressed as a linear combination of the unit quantities from the considered basis. Thereby each element of the collection should be possible, and the sum of the elements must equal the zero-element.

Thereby the following is already shown:

. That the zero-element is an element that effectively exists.

. That complex nature’s laws exist because the physical quantities are bound.

. That elements that are possible (no reason that exclude the existence of these elements), effectively exist on the condition that the sum of these elements equals the (existing) zero-element.

Some examples:

Consider the basis from example 1, and choose for x0, t0, v0 values different from 0.

1. {(x0, t0, v0), (x0 +3, t0, v0)}

This is of course no universe, because the sum of the elements does not equal (0,0,0).

2. {(x0, t0, v0), (-x0, -t0, -v0)}

The sum of the elements equal (0, 0, 0), but still it is no universe.

The speeds (corresponding with the expression “dx/dt”) in this example are discontinuous elements in space and time. But as we all know from mathematics: dx and dt do not exist for discontinuous elements, en therefore can also not be calculated.

So the two elements in the collection are both not possible.

3. {…, (x0, t0, v0= dx/dt), (x0+dx, t0+dt, dx/dt), …}

This might be a universe. All elements of the collection should of course be known, to be able to check the conditions of a universe.

(For a concrete development of a mini universe, see example 2)

Remarks:

1. Our universe, of course, also obeys the definition of a universe given above.

2. In our universe we see that everything is connected with everything through nature’s laws. This is precisely what we expect when the elements of a universe are a linear combination of a set of bound unit quantities.

3. The explanation in this text is completely conform with current physics. Every physical concept or formula can be translated to the concept of bound physical quantities.

4. The here proposed universe explains well the singularity (big bang theory) from which our universe originates. This is the zero-element (of course t = 0 s) in the given explanation.

5. Scientists agree that space itself expands, starting from the big bang. This is also what we expect, based on the explanation in this text. The zero-element corresponds of course with t = 0 s. When we assume that on that moment there are no other elements with t = 0 s part of our universe (= collection of elements), then there also doesn’t exist any space at that time. Space starts existing after (and maybe before) t = 0 s.

6. The given explanation allows the existence of all kind of particles with similar characteristics (ex. wave character) as the particles in our universe. The stability of particles can be explained by the presence of (values of) different physical quantities (= fields), where the (bound) physical quantities are so defined, that because of purely mathematical reasons they induce each other. Comparable with electric and magnetic fields that induce each other and lead to the phenomenon of electromagnetic radiations. For particles this could be standing waves.

Each of the remarks above can be worked out further, but it is not the purpose of this text to write a whole book with a lot of mathematics. When someone is interested, then each of the statements above can be discussed in further detail.

To make everything a bit more concrete, an example of a mini universe is given.

Example 2

Here we will consider a mini universe where some elements behave as if they are particles (charged or not) that move (purely because of logical and mathematical reasons, that have nothing to do with physics) in an electrical field, precisely like this would be in our universe.

=> we will show that what we call physics, is in fact just a logical and mathematical necessity.

. To reduce the writing only one spatial dimension is considered.

. To make the example recognizable we will of course choose physical quantities and corresponding relations that also exist in our universe.

. For the same reason we use the name conventions and unit quantities generally used in physics.

Consider following mathematical rules that exists between bound physical quantities:

. E = F/q ; with F = m . a

= m . a/q

= (m/q) . a

= k . a (with k = m/q)

. a = dv/dt

. v = dx/dt

With:

. E: electric field (N/C)

. F: force (N)

. a: acceleration (m/s²)

. v: speed (m/s)

. x: position on an x-axis (m)

. q: charge (C) ; (C: Coulomb)

. m: mass (kg)

. k = m/q (kg/C)

It is perfectly possible to work out the example without using the k physical quantity. In that case we have to work with a mass m and a charge q (that cannot be represented immediately as vectors), what leads to a little longer reasoning.

Consider now a basis B with following set of bound unit quantities (EE, Ea, Ev, Ex, Et, Ek)

These are the unit quantities for respectively the following physical quantities E, a, v, x, t, k.

We make the example universe so that for a part of the elements the E physical quantity differs from 0 N/C, for the other part of the elements E = 0 N/C. This can be compared with the presence of an electrical field in a part of the example universe.

Initially, we define the elements of our example universe as follows:

. E = “elements in electric field” and “elements outside electric field”

E = (15 - x) /(10^6) N/C when x ∊ [10,20]

and

E = 0 N/C when x ∊ {[-xmax,10[ U ]20,xmax]}

. a = 0 m/s²

. v = 0 m/s

. x ∊ [-xmax, xmax]

. t ∊ [-tmax, tmax]

. k = 0 kg/C

Notice that this collection of elements is a possible (= not impossible) way to represent the (existing) zero-element (the sum of all elements is (0,0,0,0,0,0)). As explained before, this collection therefore also exists.

Now we will change the k value and the speed of an element (we call it e0) and see what happens.

To get a result that is identical to the movement of an electron in an electric field in our universe we choose for k following value:

k = mass electron / charge electron

= 9,109534×(10^-31)kg / 1,6022×(10^-19)C

= 5,69×(10^-12)kg/C

e0 has now following data:

. t0 = 0 s

. v0 = 1258 m/s

. x0 = 15 m

. k0 = 5,69×(10^-12)kg/C ; see calculations electron

. E0 = (15 – 15) / (10^6) = 0 N/C ; see definition of electric field in this example universe

. a0 = E/k = 0 / 5,69×(10^-12) = 0 m/s²

We will explain that e0 cannot exist as discontinuous element on its own.

A speed (≠ 0m/s) without changing of position (dx) and changing of time (dt) is a contradiction with the definition of speed (v = dx/dt) and can therefore not exist.

=> at least following elements should also exist in the basis (EE, Ea, Ev, Ex, Et, Ek)

e1(…, …, …, x0 - v0 . dt, t0 - dt, k0) and e2(…, …, …, x0 + v0 . dt, t0 + dt, k0)

Notice that acceleration and speed should be defined as applicable on a k physical quantity. Therefore we can also fill in k0 for the elements e1 and e2.

But for element e0 we had already: E0 = 0 N/C => a0 = 0 m/s²

Because the acceleration a0 is 0 m/s², the speed of elements e1 and e2 is the same as for element e0, otherwise this is a contradiction with the definition of acceleration. So we have:

e1(…, …, v0, x0 - v0 . dt, t0 - dt, k0) and e2(…, …, v0, x0 + v0 . dt, t0 + dt, k0)

But when e1 and e2 exist, then there should also exist e3 and e4 for the same reason as described above. => we become a whole path of elements in space and time.

Now, what about the other physical quantities: E, a?

. E: in a more complex basis that allows the existence of stable particles, there will be electric fields as a result of those particles. So, not just a given electric field like in this example.

. a: is by definition E/k.

Conclusion: an element like e0 cannot exist as discontinuous element on its own. In the given basis can only a complete path (collection of elements) in space and time exist.

For this example the complete path can be found by solving following equation:

d²x/dt² = a = E/k

= (15-x)/( (10^6) . 5,69×(10^-12) )

= 175747 (15-x)

This is a differential equation for which we give immediately the solution:

. x = 15 + 3 sin(419,22 t) m

. v = dx/dt = 1258 cos(419,22 t) m/s

. a = dv/dt = -527378 sin(419,22 t) m/s²

The values of the other physical quantities for describing the “state” of the “particle” completely are:

. E = (15 - x) / (10^6) N/C

. t ∊ [-tmax, tmax]

. k = 5,69×(10^-12)kg/C

These are exactly the same results we have for an electron in a similar electric field in our universe.

In order that the universe with this “moving” element (= collection of elements) can exist, the sum of all elements of this universe should equal the zero-element. We will check this for each physical quantity.

. E: was initially OK (sum = 0 N/C), and the “particle” changes nothing to this.

. a: as long as multiples of full periods (tmax = n . pi/419,22 s with n an integer) are considered is this OK (sum = 0 m/s²), and is there nothing that should be compensated. It doesn’t matter where the period starts.

. v: as long as multiples of full periods are considered is this OK (sum = 0 m/s), and is there nothing that should be compensated. It doesn’t matter where the period starts.

. x: was initially OK (sum = 0 m), and the “particle” changes nothing to this.

. t: was initially OK (sum = 0 s), and the “particle” changes nothing to this.

. k: here is a problem. This should be compensated in one way or another, so that the universe can exist. One of the many solutions to compensate this, is that a second “particle” is introduced (just changing some values of physical quantities of elements in the example universe) that exists as long as the first “particle”, and wherefore the charge is opposite (k = -5,69×(10^-12)kg/C). The introduction of multiple particles, with different k values, that exist longer or shorter is of course also possible. The place of the particles doesn’t matter, as long as they are within the space and time of the universe from this example.

We will work out the example by choosing a second compensating “particle” that exists as long as the first “particle”, and wherefore the charge is opposite (k = -5,69×(10^-12)kg/C).

To make an interesting example, we also consider an extra electric field:

. E = (x - 100) / (10^6) N/C ; x ∊ [80, 120]

The position and the size of the field doesn’t matter, as long as the sum = 0 N/C.

Notice that this electric field is opposite to the field where the first “particle” moved in. (here is written +x instead of –x in the equation of E) This is necessary, to get an acceleration in the right direction. The k value of the “particle” will be opposite compared with the first “particle”, therefore the field must also be opposite.

A possible valid solution for the second “particle” can be following collection of elements:

. E = (x - 100) / (10^6) N/C

. a = 527378 sin(419,22 t) m/s²

. v = -1258 cos(419,22 t) m/s

. x = 100 - 3 sin(419,22 t) m

. t ∊ [t3, t4] s ; t4 – t3 = t2 – t1

. k = -5,69× (10^-12)kg/C

In general there are lots of compensation mechanisms possible, so that the sum of the elements of a universe equals the zero-element.

Here are some possible compensation mechanisms:

. Particles with opposite charge. Ex. Electron <-> proton.

. In general people consider a particle, as a core and a separate field around. It is also possible to see both as one field (values of a physical quantity ≠ zero-quantity), so that the elements in the core compensate (completely or partly) for the elements around. A particle can of course be built up out of multiple fields (values of different physical quantities ≠ zero-quantity), comparable with an electro-magnetic wave, that is built up of an electric and magnetic field.

. Wave motion, like an electric field that becomes alternating positive and negative.

. Particles that turn around each other. => In case there are multiples of complete periods considered, the resultant of the speed and the acceleration of the particles both equal the zero-quantity.

. The existence of a dual universe. With this principle, an apparent imbalance in one part of the universe can be compensated by the opposite imbalance in the other part of the universe. Example: Matter in one part of the universe, and antimatter in the other part.

A dual universe means that the two parts doesn’t exist in the same space. The most obvious is that the separation happens by the physical quantity time. In one part is t > 0 s, while in the other part t < 0 s. The singularity or zero-element (t = 0 s) is the only connection between the two parts of the universe.

. …

Conclusion of example 2

Operate in a basis of bound unit quantities gives precisely the same result as the classic formulas from physics. However, classic physics does not explain why these formulas (nature’s laws) exist, while here is shown that there is no other way than that they exist in the here considered basis.

General conclusion

When we just write down which things inevitable exists, then this leads quickly to the conclusion that all kind of universes should exist. This is precisely what we expect when using some common sense: our universe exists, and it is obvious that there should be a good reason for this.