Migration votes calculation

When political polls take place, usually the results are greatly publicized. A certain party won a tot number of votes, another one lost tot other votes, and so on. On the political and mathematical point of view, it is interesting to get the statistical knowledge not only of the simple final results, the percentages obtained by the various parties, but also of the flows of votes from one party to another. By example, if party A got x_A votes in the last poll and in the current poll gained δx_A, it might be useful to know from which parties it got those votes, while, if it lost them, towards which parties they got transferred. Purpose of this article is to determine the formulae that permit to calculate in a poll the flows of votes between parties.

Let N be the number of polling stations where polls take place, n the number of eligible parties, and let p_ij, with 1 <= i,j <= n, the migration probabilities, i.e. the probabilities according to which the voter that in the preceding poll had voted in favour of the i-th party, subsequently votes for the j-th. Finally, let u_k/i be the percentages of votes the i-th party obtained in the k-th polling station in the last poll, and v_k/i those obtained in the current poll. With these definitions we can say that in the k-th polling station of the current poll the i-th party lost in the average a u_k/i ∙ p_ij percentage of votes in favour of the j-th party. Summation over all the parties produces the most probable percentage of votes obtained in the current poll by the j-th party in the k-th polling station:

Σ_l=1ⁿ u_k/l ∙ p_lj = v_k/j.

Here we underlined the symbol v_k/j in order to express the fact that it doesn’t represent the true percentage value, but the one obtained through the use of probabilities. As for the entire poll, which includes all the polling stations, the following relations hold:

u_i = Σ_k=1^N u_k/i, v_i = Σ_k=1^N v_k/i.

It is to be noted that the summations also include the contributions from the voters that remained faithful to their previous party. Now the problem consists in determining the migration probabilities p_ij, which, when multiplied by the percentages of voters of the preceding poll and summed over all polling stations, produce the percentage evaluations of the migratory flows.

Σ_k=1^N u_k/i ∙ p_ij = v_i → j .

For this purpose, let’s consider for each party the half sum  A_i ( p_ji ), made over all the polling stations, of the squares of the differences between the percentages calculated in the current vote by means of the migration probabilities, v_k/i, and those effectively obtained, v_k/i:

A_i ( p_ji ) = Σ_k=1^N ( v_k/i – v_k/i )² / 2 = Σ_k=1^N ( Σ_j=1ⁿ  u_k/j ∙ p_ji – v_k/i )² / 2.

The statistically most probable migration probabilities are then obtained by imposing the condition that the A_i ( p_ji ) be minimal, i.e. that ∂A_i / ∂p_ji = 0 for each i,j:

1)     ∂A_i / ∂p_ji = Σ_k=1^N ( Σ_l=1ⁿ u_k/l ∙ p_li – v_k/i ) ∙ u_k/j = 0.

Condition (1) determines a system of n² non-homogeneous linear equations in the n² unknowns p_ij. Now we must impose the condition that the p_ij really represent probabilities. That corresponds to require that for each i the following relations hold:

2)     Σ_j=1ⁿ p_ij = 1.

Summation is made over the second index, since it must express the totality of votes getting out of the i-th party. Condition (2) requires the addition of n further linear equations in the unknowns p_ij to system (1). Thus the total number of equations to be satisfied becomes n ∙ (n + 1). By assuming that all the equations are linearly independent, the system solvability requires the introduction of n further unknowns. Which ones to introduce? The meaning of the system itself gives us the answer. Since the results we want to determine represent estimates of values subjected to statistical fluctuations, we expect that the migration probabilities p_ij do not necessarily satisfy the n² equations (1). Hence it makes sense to introduce new unknowns δ_i, in order to account for such discrepancies. With these additions, equations (1) get the following expression:

3)     Σ_k=1^N ( Σ_l=1ⁿ u_k/l ∙ p_li – v_k/i ) ∙ u_k/j = δ_i.

Now the system of equations (2) and (3), in the unknowns p_li and δ_j, is made up of n ∙ (n + 1) linear equations with n ∙ (n + 1) unknowns, and is therefore solvable. 

On the origin and evolution of the universe

The past century has seen the theory of the structure of the universe change in order to comply with its observed expansion and the theory of general relativity. However, new observations put under strain that picture, for at least two reasons: it requires the introduction of unknown forces that tend to increase with time the rate of expansion; it does not explain the existence of quasars. In the following we are going to introduce a new, rather sketchy description of how things might instead work.

Let’s try to derive the picture by starting from the concept of a three dimensional spherical universe. Let it be expanding and, where concentrations of matter are sufficiently high, let black holes form, which suck away matter and energy.

Therefore we imagine this cosmos as a space-like three-dimensional hyper-surface immersed in a four-dimensional ether. In two dimensions we represent it as a circle.

In this picture, black holes tend to bring matter toward the center. This does not necessarily mean that matter is attracted toward the center, but that it simply tends to bend space-time in one preferred direction, which must be a property of the ether.

As the tips of the black holes come in contact with each other, we imagine that they unite, and that, since there is little matter, the merging region expands, creating a new universe.

The new universe keeps on expanding and, as near the holes the concentration of matter increases, with time it will give rise to stars, galaxies and black holes.

Because of the high energy involved in passing through the holes, the squeezing tends to break the nuclei bonds, and we can imagine that the matter that gets out of the holes be mostly constituted of hydrogen atoms.

So, in this picture we have an undefined number of concentric universes that keep on expanding and pouring matter into younger ones. Every now and then, a new universe is created, and the oldest one vanishes when all its matter is transferred to the one immediately younger. Here is a very rough sketch of how the universes might look like:

Once created, we imagine that the universes tend to expand, but are affected by the holes in a way or another. Black holes tend to oppose expansion, while white holes favor it. So, as more white holes merge with younger universes, their rate of expansion increases.

Since the rate of expansion of the universe we live in keeps on increasing, we argue that it must be rather young.

At this point the following two obvious questions arise: Do white holes that bring particles and energy in our universe exist, and what properties should the particles and radiation that pours out from them have?

Regarding particles, as for me, it is unclear right now. I shall eventually write a post about them later on. What about radiation?

If we consider that radiation is mainly emitted in regions where space-time is strongly bent, and that afterwards it spreads in regions that are almost flat, in passing from a bended to a flat region its frequencies must diminish. This fact is independent of the direction in which space-time is bent. So the exiting radiation must be highly redshifted.

Do in the sky exist very small objects that spew up highly redshifted radiation? Yes. Quasars emit that type of radiation. According to this picture, quasars are not very far objects, as the strong redshift suggests, and the energy they emit is not tremendously high, but more reasonable.

This description provides an explanation of the origin of matter in our universe, and shows that there is no beginning, nor end for the system of universes, but single universes are born and die. The system of universes keeps on rejuvenating itself; it has always existed and will always exist.

The description also shows that there seems to be no means that permit anything with a structure to pass from one universe to another, because the only communications between universes occur through black-white holes, which crush everything to its most elementary constituents.

 

(If you want to know more on the subject, please contact trevisan.diego@alice.it)

 Other posts from Diego Trevisan:

Arguments related to ether and inertia: 

— Relativity and the duration of time

— Space-time and ether

— Ether and inertia

— Earth’s velocity with respect to the ether

— The origin of the Minkowski metric 

 

The leading time theory and the Compton effect:

— Space-time and destiny

— The direction of time

— The leading time and the Compton effect

— Compton effect and uncertainty

— The dual aspect of the elementary particles

— The Compton effect – Part 2

 

Astrophysics: 

— The puzzle of the solar corona

— Sunspots and solar flares

 

Lightnings: 

— The origin of lightnings

 

The following post provides a brief description of each argument:

— Physical topics – Main

  

The origin of the Minkowski metric

 In the following we’ll examine 1) the reason why the physical space-time manifests the behavior expressed by the Lorentz transformations and how the Minkowski metric originates, 2) the difference between the physical space-time and the ether with regard to the measure of distances, and 3) the relationship that exists between the physical and the ether coordinates, with its implication regarding the earth’s velocity with respect to the ether.

In previous blogs we already took into account some of the aspects we consider here, but with minimal use of mathematical formulas. Here we’ll consider those aspects in more detail by using the appropriate mathematical tools.

1) Origin of the Minkowski metric

The investigation of the reason why time dilates in passing from an inertial system of reference to one moving with constant velocity with respect to the former one showed that it looks reasonable to think that what changes is not the time length (in fact a purely hypothetical transformation cannot change the time lengths), but its measuring unit, which is proportional to the periods associated to the elementary particles.

 In fact, if we consider a time t and a period T associated to an elementary particle, if subject to a Lorentz transformation they change according to the following laws: t’ = t ∙ γ, T’ = T / γ, where γ = 1 / √(1 – v² / c²). Consequently, T’ ∙ t’ = T ∙ t. By choosing T as time unit, we see that t is nothing but the number of oscillations along its own time-like direction, while τ = t ∙ T represents the corresponding invariant time interval.

 As for the spatial part, consider a rod (or a wavelength) of length L placed parallel to the direction of motion. As its velocity increases, its length appears to shorten according to L’ = L / γ. If one extreme lies at the origin of the system of reference and the other one has coordinate x¹, under a change of reference the new coordinate is related to the old one by x¹‘ = x¹ ∙ γ. Although in terms of coordinates its length increases, the product λ = L ∙ x¹ remains the same in any system of reference. Hence, L represents the unit in the space-like direction.

These reasonings suggest that the physical space-time manifests its odd (Minkowskian) behavior for the fact that times and distances are measured in terms of periods and wavelengths, which act as measuring units and whose lengths depend on the direction in space-time along which they are measured, that is, on the velocity of the observing system.

By taking into account a period T and a wavelength L, one can draw the following picture, which represents all trhe values T and L assume as the velocity changes from -c to c (in the drawing, the units of space and time are chosen such that c = 1):

The above picture, which is understood to be drawn in a system of physical coordinates, is invariant under Lorentz transformations. In fact, in deriving it we didn’t mention any particular frame (it is to be noted, though, that there correspond no waves moving along the spatial part of the picture, since no known particles move faster than the speed of light).

Any other transformation doesn’t leave the above shape invariant, but bends, or squeezes it in some way. Consequently, only the Lorentz transformations preserve the form of the physical equations under change of reference. For this reason, they are the only transformations fitted for changing system of reference.

On its part, the only metric that is invariant under Lorentz transformations is the Minkowski one. One can check this by considering any bilinear combination of coordinates and subject it to a Lorentz transformation. The requirement that the metric remain invariant has only one solution: the Minkowski metric!

Therefore, since it expresses the physics that underlies the transformations that involve motion, the above shape determines both the type of the transformations that preserve the form of the physical equations, as well as the space-time metric. If waves behaved differently, neither the Lorentz transformations nor the Minkowski metric would be meaningful in the physical context.

Besides this, we can also say that all vectors of space-time behave as they do because of that shape, i.e. all vectors that are related to ether waves must obey the Lorentz law of transformation. On the other hand, we expect that vectors that aren’t originated by ether waves shouldn’t be subject to the Lorentz law but, if related to the ether, should follow the rules of ordinary rotations.

This is an aspect that is to be proven by experiments, like the one for measuring the earth’s velocity with respect to the ether proposed in a previous blog. This aspect is considered in more detail in the third part of this blog.

2) Ether and physical distances

 

The above reasonings are the base for accepting the ether, characterized by the ordinary Euclidean metric, whose waves provide the measuring units in the physical world. In other words, in an orthonormal system of reference, the square of the distance between two points P and Q having coordinates x_P and x_Q, is given by the well known Pythagoras formula:

d ²  = (x_Q⁰ – x_P⁰)² + (x_Q¹ – x_P¹)²  + (x_Q² – x_P²)²  + (x_Q³ – x_P³)² ,

or, using the shorter tensor notation,

d ²  = e_μν (x_Q^μ – x_P^μ) (x_Q^ν – x_P^ν),

where e_αβ is the ordinary Euclidean metric tensor.

In terms of the physical coordinates y_P and y_Q, the square of the same distance is given by

d ²  = (y_Q⁰ - y_P⁰)² - (y_Q¹ - y_P¹)²  - (y_Q² - y_P²)²  - (y_Q³ - y_P³)² ,

and, in tensor notation,

d ²  = η_μν (y_Q^μ - y_P^μ) (y_Q^ν - y_P^ν),

where η_αβ is the Minkowskian metric tensor.

3) Relationship between the ether and the physical coordinates

What relation exists between the ether coordinates x^μ and the physical ones y^μ? Consider the case in which the physical coordinates are at rest with respect to the ether (we call such a system fundamental). If the coordinates are both orthonormal, then they can be made to coincide, and in that case y^μ = x^μ.

Suppose that the physical coordinates are subjected to a Lorentz transformation: y^μ‘ = L^μ_ν x^ν, where L^μ_ν is the matrix that expresses the transformation. In particular, if the motion occurs along the x¹ direction with velocity v, then:

y⁰‘ = ( x⁰ + v ∙ x¹ / c ) ∙ γ ,

y¹‘ = ( x¹ + v ∙ x⁰ / c ) ∙ γ ,

where γ = 1 / √( 1 - v² / c² ), while the other coordinates remain unchanged.

Now consider the axes of the new x^μ‘, and require that they be parallel to those of the y^μ‘. Of course, they are no longer orthogonal. However, we require that the referencing units be preserved. The corresponding ether transformations then are the following:

x⁰‘ = x⁰ ∙ cos( θ ) + x¹ ∙ sin( θ ),

x¹‘ = x¹ ∙ cos( θ ) + x⁰ ∙ sin( θ ),

where θ = arctg( v / c ), cos( θ ) = 1 / √( 1 + v² / c² ), sin( θ ) = ( v / c ) / √( 1 + v² / c² ). Each axis is subject to an ordinary rotation, but on opposite directions, so that both terms with the sin( θ ) have the same sign, either positive or negative, depending on the direction of rotation.

In terms of the velocity v, the above rotations have the following expression:

x⁰‘ = ( x⁰ + v ∙ x¹ / c ) / √( 1 + v² / c² ),

x¹‘ = ( x¹ + v ∙ x⁰ / c ) / √( 1 + v² / c² ),

with inverses:

x⁰ = ( x⁰‘ - x¹‘ ∙ v / c ) ∙ √( 1 + v² / c² ) / ( 1 - v² / c² ),

x¹ = ( x¹‘ - x⁰‘ ∙ v / c ) ∙ √( 1 + v² / c² ) / ( 1 - v² / c² ).

Substitution of this into the y^μ produces the following result:

y⁰‘ = x⁰‘ ∙ γ ∙ √( 1 + v² / c² ),

y¹‘ = x¹‘ ∙ γ ∙ √( 1 + v² / c² ),

In conclusion, with appropriately chosen axes and measuring units, the following general relationship exists between the physical and the ether coordinates:

y⁰ = x⁰ ∙ Γ,

y¹ = x¹ ∙ Γ,

y² = x²,

y³ = x³,

where Γ = √[( 1 + v² / c² ) / ( 1 - v² / c² )], and v is the velocity of the physical system with respect to the fundamental one (ether at rest).

Along the direction of motion with respect to the ether, the lengths are dilated. A precise monitoring of some orbital motions should permit to determine the velocity of the earth with respect to the ether

.

 

 

(If you want to know more on the subject, please contact trevisan.diego@alice.it)

 

Other posts from Diego Trevisan:

Arguments related to ether and inertia: 

— Relativity and the duration of time

— Space-time and ether

— Ether and inertia

— Earth’s velocity with respect to the ether

 

The leading time theory and the Compton effect:

— Space-time and destiny

— The direction of time

— The leading time and the Compton effect

— Compton effect and uncertainty

— The dual aspect of the elementary particles

— The Compton effect – Part 2

 

Astrophysics: 

— The puzzle of the solar corona

— Sunspots and solar flares

 

Cosmology: 

— On the origin and evolution of the universe

Lightnings: 

— The origin of lightnings

 

Physical topics – Main

Physical topics

by Diego Trevisan (email: trevisan.diego@alice.it)

The author in 1974, after a conference on relativity in Israel

Several years have passed since that conference. Not long after that, because of a traumatic experience, he abandoned research. Only in the past few years he got interested in physics again, made some discoveries, and published them in the net. Generally, blogs aren’t meant to be the means of choice for publishing scientific work. So, in the description he avoided (perhaps wrongly) the use of sophisticated maths, in order to make the material comprehensible to people that don’t possess a university degree, since the new discoveries regard matters that excite the fantasy and may be appreciated even by people that aren’t dedicated to the physical science. In this he’s been helped by the fact that the arguments he dealt with could also be explained with the use of simple maths, if not just by words. Even if in some cases tensors would have been the most appropriate mathematical tools, he treated the arguments by means of simple algebra.

The discoveries presented here are very important, because they give an answer to questions that have puzzled scientists for several decades. They also open the way for new research and new ways of looking at the universe we live in.

Contents:

1. Relativity and the duration of time. According to relativity, the duration of time varies with the system of reference. Here it’s shown why that happens, what lies behind the time dilation (and the space contraction as well).

2. Space-time and destiny. At each point of space-time either there’s something or nothing. This means that past, present and future can’t be changed, unless…

3. The direction of time. Can signals propagate backward in time? This post may be considered as an introduction to The leading time and the Compton effect that follows.

4. The leading time and the Compton effect. The Compton effect is explained in a novel way, by means of electron waves moving both forward and backward in time, in accordance with the leading time theory.

5. Compton effect and uncertainty. It’s shown with reference to the Compton effect described in post n. 4 what lies behind the uncertainty principle. An experiment is proposed.

6. The dual aspect of the elementary particles. By referring to the preceding posts, this one shows the reason why the wavefunction collapse occurs, and also an interesting conclusion concerning the elementary particles.

7. Space-time and ether. The concept of distance is investigated both in the physical space-time and in the ether, together with the relationship that links the two spaces.

8. Ether and inertia. It’s shown why inertia can be thought as a local property of space-time.

9. Earth’s velocity with respect to the ether. By considering the relationship existing between the ether and the physical universe, and their properties under Lorentz transformations, a possible way for detecting the velocity of the earth with respect to the ether is described. An experiment is proposed.

10. The puzzle of the solar corona. The post offers a possible explanation of the reason why the solar corona is characterized by very high temperatures.

11. Sunspots and solar flares. By exploiting the same effect that produces high temperatures in the solar corona, an explanation of the workings that lie behind sunspots and solar flares is given.

12. The origin of lightnings. The post offers a description of how storms give rise to huge potential differences between clouds and earth.

13. The Compton effect, part 2. Further aspects of the Compton effect according to the leading time theory are considered, in particular those related to the energy-momentum balance and the shape of the electron waves.

14. The origin of the Minkowski metric. The following topics are investigated: 1) The reason why the physical space-time manifests a Minkowski metric; 2) Measurements of distances in the ether and in the physical space-time; 3) Relationship between the physical and the ether coordinates.

15. On the origin and evolution of the universe. This post provides a description of how our universe was born, in which black holes and quasars play a fundamental role. It also shows that our universe may be part of a system of universes that keeps on rejuvenatinbg itself.

The Compton effect, part 2

In a previous post we considered the Compton effect from the point of view of the leading time (LT) theory. In that description, a photon interaction with an electron produces two electron waves along both time directions. Subsequently, an electron wave coming from the future interacts with the discontinuity remnant of the previous interaction and gives rise to two new electron waves, which erase the old ones, and a photon that completes the Compton effect (see The Compton effect).

Now we want to consider the description in more detail, in particular with regard to energy-momentum and the shape of the electron waves. The analysis will show that in this theory the electron waves don’t satisfy the Dirac equation, and the reason is simple: the solutions to the Dirac equation are meant to provide some tools apt to calculate probabilities, while those considered here should represent the true waves associated to the elementary particles.

Le’s consider the energies and momenta involved in the process. For simplicity we work in the frame in which the momenta of the electron and the incoming photon have equal but opposite values. If we call (E_e, p_e) and (E_p, p_p) their energies and momenta, then p_e = -p_p, and the total energy-momentum is (E_T, p_T) = (E_e + E_p, 0).

Although at rest, the resulting (total) energy after the first interaction is obviously greater than the electron energy, i.e. greater than the electron mass times c². (Note: E_e isn’t equal to the electron rest mass times c², because its momentum p_e is different from zero).

This shouldn’t surprise, since what we have considered thus far constitutes only part of the observable Compton effect. Up to this point a photon has been absorbed, but nothing has been emitted; consequently the resulting total energy is greater than that of an electron at rest. The extra energy will be needed in order to emit a photon at the end of the process.

An important result comes out of this simple calculation: The fact that the merging of the photon and electron waves at the point of interaction produces an increase of the rest energy, with the abrupt stop of the photon wave and the emission of two electron waves, shows that the ether cannot accept (rest) energies different from those of an admissible set.

In other words, since in terms of waves energy means frequency, the ether can’t accept any frequency along time-like directions, but only those associated to particles existing in nature. This explains why particles have well specified rest energies. Along null directions (along light rays), instead, there’s no such limitation.

Hence, it’s the merging of the waves, with its consequent production of inadmissible frequencies what produces the abrupt stopping of the photon wave and emission of two new electron waves.

In The Compton effect we saw that the incoming photon had two fronts, one pointing backward and another one forward. After the interaction the photon doesn’t exist anymore, but two new wave fronts are moving, those associated to the two new electron waves, one moving backward, the other one forward. Consequently the process conserves the number of wave fronts (the wave front associated to the incoming electron isn’t altered).

Another consequence of the fact that the ether admits only specific frequencies is that the amplitude of the waves produced by the interaction remains constant. In fact, a Fourier series of the waves along any direction of motion requires that the wave amplitudes remain unchanged for them to be composed of a single frequency.

This looks quite odd, because as waves expand in the macroscopic world their amplitudes decrease; it’s a matter of conservation of energy. Such law doesn’t apply here, because energy is a concept attached to the number of waves per unit of time. Evidently ordinary laws have no meaning in this realm, and don’t apply. The stringent law here is that along any time-like direction issuing from the point of origin only specific frequencies are permitted.

This explains why in classical mechanics the amplitudes of the electron waves don’t affect physics, which is expressed by the fact that they don’t appear in any physical equation, while in quantum mechanics they require normalization. Therefore, in this scenario where we don’t talk about probabilities, the wave amplitudes are unchangeable physical quantities.

What is the form of the wave issuing from the point of interaction? In the system of reference in which (E, p) = (E_e + E_p, 0), the directions along which the electron may move must be such that at the end of the process the laws of conservation of energy and momentum (and spin) are to be satisfied.

To get this and in order that the energy and momentum of the issuing photon be related by E = | p | ∙ c, the issuing photon must have the same energy as that of the incoming photon. In other words, the set of all possible momenta of both photon and electron (remember that p = p_e = -p_p) describes a sphere in momentum space, with the projections of the momenta along any spatial direction varying from -| p | to | p |.

Correspondingly, along any spatial direction the electron velocity varies from -v to v, with v = | p | / ( m_o ∙ γ ), where m_o is the electron rest mass and γ = 1 / √( 1 - v² ). Consequently, as seen from this system of reference, the electron wave front propagates like the surface of an inflating sphere.

 

(If you want to know more on the subject, please contact trevisan.diego@alice.it)

 

Other posts from Diego Trevisan:

 

The leading time theory and the Compton effect:

— Space-time and destiny

— The direction of time

— The leading time and the Compton effect

— Compton effect and uncertainty

— The dual aspect of the elementary particles

 

Arguments related to ether and inertia: 

 

— Relativity and the duration of time

— Space-time and ether

— Ether and inertia

— Earth’s velocity with respect to the ether

— The origin of the Minkowski metric

 

Astrophysics: 

— The puzzle of the solar corona

— Sunspots and solar flares

 

Cosmology: 

— On the origin and evolution of the universe

Lightnings: 

— The origin of lightnings

 

The following post provides a brief description of each argument:

— Physical topics – Main

The origin of lightnings

Lightnings are phenomena of electrical discharge that happen whenever a great potential difference occurs between clouds, parts of a cloud, or between a cloud and the earth. If the discharge occurs between a cloud and the earth’s surface, the cloud possesses a negative charge, the soil underneath positive.

What mechanism gives rise to such big potential difference, and what other phenomenon is produced by it besides lightnings?

During storms, strong currents of warm and humid air ascend with velocities that can reach one hundred kilometers per hour (a few months ago in Australia a paraglider was unwillingly pulled about 10,000 meters above sea level by such a current).

In these currents of warm air a great power is involved. Evidently, it’s this phenomenon that in some way electrically charges the clouds. How?

It’s the same phenomenon that charges isolated materials when they get rubbed. It’s the one that sometimes makes us feel an electric shock in getting out of a car. The car is electrically isolated from the soil; as it moves, the air friction charges it. Another manifestation of this phenomenon occurs when we strongly rub a plastic bag against a wool dress. If we put afterward the bag above our head, the accumulated electric charge pulls our hair up. How does this phenomenon electrically charge the clouds?

The distribution of velocity, humidity, and temperature of the ascending air current is variable, and we can imagine it as a bunch of thin threads having different velocities, humidities and temperatures.

The rubbing that takes place between nearby threads with different speeds produces a transfer of electrons from the warmer threads to the colder ones. The overall effect is a transfer of negative electrons from the flow of ascending air to the surrounding regions, which gain a negative charge, while the rising air gets positively charged.

Because of this, huge potential differences get created between parts of a single cloud, or between nearby clouds, something of the order of several tens of millions volts. When these huge potential differences discharge, lightnings take place.

Not all the positive ions that are brought upward produce lightnings, though. What happens of the others? Since at high altitudes the atmosphere is a good electrical conductor, this upward draft of electric charges gets transferred over all the upper atmosphere, contributing to maintain it positively charged, while the lightnings transfer negative charges on the earth.

Therefore, the lightnings that hit the earth combined with the constant upward draft of positive charges act in such a way that a high potential difference is maintained between the entire earth’s surface and the upper atmosphere, which is of the order of a few hundreds of thousands volts, a potential difference, however, much lower than the one that produce lightnings.

Since in the average there are about three hundred active storms over the entire earth at any time of day and night, consequently through the terrestrial atmosphere constantly flows a tiny electric current.

In summary, the upward currents of moist and warm air electrically charge the clouds and the upper atmosphere. The discharge between clouds, or between clouds and soil occurs by means of lightnings, the one between the upper atmosphere and the earth’s surface through a tiny electric current that flows day and night.

From the same author:

 

Arguments related to ether and inertia: 

— Relativity and the duration of time

— Space-time and ether

— Ether and inertia

— Earth’s velocity with respect to the ether

— The origin of the Minkowski metric 

 

The leading time theory and the Compton effect:

— Space-time and destiny

— The direction of time

— The leading time and the Compton effect

— Compton effect and uncertainty

— The dual aspect of the elementary particles

— The Compton effect – Part 2

 

Astrophysics: 

— The puzzle of the solar corona

— Sunspots and solar flares

 

Cosmology: 

— On the origin and evolution of the universe

 

The following post provides a brief description of each argument:

— Physical topics – Main

 

 

 

 

Sunspots and flares

In the preceding post we saw how at equal temperatures an extremely rarefied gas acquires through radiation more energy than it loses, with the consequence that its equilibrium temperature is considerably higher than normal. Now we’ll see how this effect produces sunspots.

Under the solar surface lies another surface, where sometimes intense magnetic fields suddenly release huge amounts of energy, producing bubbles as big as the earth of hot and rarefied gas.

The thermodynamical conditions of such gas bubbles are similar to those that are found on the solar corona, even if not so extreme: high temperatures and low densities, the ideal conditions for the Trevisan effect to become operational (see the preceding post The puzzle of the solar corona).

This effect acts in such a way that the bubbles continue to heat up by subtracting heat from the denser and cooler gases around them, and the heating continues until a temperature is reached that maintains the bubbles in radiative equilibrium with their surrounding gases.

Since the gas bubbles possess a very low density, they slowly rise toward the sun’s surface. On the other hand, because of the cooling of the surrounding gases caused by the heating of the bubbles, the layers of gas lying over them lack the normal heat, the one that permits the sun to shine. Consequently the temperature of the region of the solar surface above the gas bubbles cools down, and a sunspot arises.

In other words, the sudden release of energy below the sun’s surface by the intense magnetic fields gives rise to a cooler region on the solar surface. This may look paradoxical. In reality there’s no contradiction. At the end, the gaseous bubbles reach the solar surface and radiate in space all the energy accumulated, producing the so-called solar flares.

At that point, due to the flares, the energetic balance gets adjusted. Indeed, flares and sunspot combined emit from the sun’s surface more energy than normal, the excess corresponding to the energy released by the magnetic fields under the surface of the sun.

A further application of the Trevisan’s effect occurs in the cosmos. The matter density there is very low, and the particles of this very rarefied gas travel in the average very long distances without interacting, certainly the longest non-interacting paths in the universe.

These solitary particles are subject to a faint radiation, because they lie very far from any star or galaxy. However, due to the long paths the particles travel without interacting, their equilibrium temperatures must be very high. How much? It’s hard to tell, but because of the rarefaction, this gas is probably characterized by the highest temperatures in the universe.

The extraordinary velocities and energies of these gas particles are probably the same that are found in the cosmic rays. If that’s the case, the cosmic rays are nothing but particles of the intergalactic space that have been overheated by the cosmic radiation.

Where should the highest temperatures, or the most energetic particles, be found in the cosmos? Of course, in the (almost) empty space in the vicinity of galaxies. If one could see the cosmic rays as one sees ordinary light, one should see the galaxies surrounded by a halo. Does such a halo exist? Yes. It has recently been discovered that the cosmic rays come mainly from the regions near the galaxies. This experimental fact strongly supports the above conclusion, that cosmic rays originate in the cosmic space through stellar radiation .

 

(If you want to know more on the subject, please contact trevisan.diego@alice.it)

 

Other posts from Diego Trevisan:

 

Astrophysics: 

— The puzzle of the solar corona

 

Cosmology: 

— On the origin and evolution of the universe

 

Arguments related to ether and inertia: 

 

— Relativity and the duration of time

— Space-time and ether

— Ether and inertia

— Earth’s velocity with respect to the ether

— The origin of the Minkowski metric 

 

The leading time theory and the Compton effect:

— Space-time and destiny

— The direction of time

— The leading time and the Compton effect

— Compton effect and uncertainty

— The dual aspect of the elementary particles

— The Compton effect – Part 2

 

Lightnings: 

— The origin of lightnings

 

The following post provides a brief description of each argument:

— Physical topics – Main

 

The puzzle of the solar corona

The solar corona is the part of the sun, ordinarily not visible, that extends for over a million kilometers beyond its surface. The density of its plasma is very low, about one thousandth of a billionth of the sun’s surface. Another characteristic that makes the solar corona extraordinary is its temperature, which is of the order of a few million degrees Celsius.

A well known fact, expressed by a thermodynamic law, is that heat proceeds from hotter to cooler regions. The solar corona, instead, while having at its interior a much cooler surface, the sun’s surface, and being surrounded by the very cold cosmos, possesses and maintains very high temperatures. Why is it so hot and doesn’t cool down?

In order to keep such high temperatures there has to be a mechanism that operates in an unusual way, in the sense that in this extreme environment the law according to which heat flows from hotter to cooler regions must not work. Does such mechanism exist? If yes, how does it work?

The clue for it to work must be another peculiar characteristic of the coronal gas, its density, which is so low that if it occurred on earth, one would talk about vacuum. What happens when a gas is so rarefied?

The corona is heated from the sun and loses heat by emitting radiation. For the corona to remain in radiative equilibrium and maintain its high temperatures, there has to be balance between absorption and emission of radiation.

A peculiar fact happens here. The energy each gas particle receives from the sun doesn’t depend of the presence of other particles in its vicinity. In other words, it doesn’t depend on the gas density. A photon may hit a particle independently from the fact that other particles are near it.

On the contrary, the energy a single particle radiates does depend on the presence of other particles in its vicinity. For what reason? The fact is that the energy possessed by the coronal plasma particles is kinetic. The greater the gas temperature, the greater the average kinetic energy of the gas particles.

Under these circumstances, the only way a plasma particle can lose energy and emit radiation is by hitting another particle. In fact, from its point of view each particle is at rest and can’t radiate as long as it doesn’t interact with other particles, because without moving it doesn’t possess any kinetic energy, and it can’t evidently lose what it doesn’t have.

The case is different when two particles interact. As a result of the collision, the two particles change their state of motion, their average kinetic energy relative to the common center of mass decreases, and the excess energy is emitted through radiation.

Due to the very low gas density, the probability for two gas particles to interact is very low. The lower the density, the lower the probability that two particles collide. For this reason, the more the gas is rarefied, the less it radiates.

Hence, in order to attain radiative equilibrium, the gas temperature must increase. In fact, as the temperature – and the average velocity of the particles – increases, also the collision probability and the average energy radiated during a collision increase, because higher energies are involved.

One question one might ask is: For what reason doesn’t this mechanism work on the rarefied gas that surrounds the earth, being that the air density decreases with the altitude, and reaches the very low levels of the cosmos?

In reality, the very rarefied gas that lies a few hundred kilometers above the earth’s surface possesses temperatures of the order of some hundreds degrees Celsius. Similarly, the external atmospheres of the other planets of the solar system have temperatures considerably higher than those of their atmospheres below.

This doesn’t mean, however, that a satellite passing through this hot gas gets cooked, since the gas extreme rarefaction almost nullifies the transfer of heat by contact.

The above described phenomenon occurs whenever a gas becomes extremely rarefied and occupies a very large volume, so that no heat exchange takes place by contact. Lacking a better name, in the future references I’ll call it the Trevisan effect.

 

(If you want to know more on the subject, please contact trevisan.diego@alice.it)

 

Other posts from Diego Trevisan:

 

Astrophysics: 

— Sunspots and solar flares

 

— Relativity and the duration of time

— Space-time and ether

— Ether and inertia

— Earth’s velocity with respect to the ether

— The origin of the Minkowski metric 

 

The leading time theory and the Compton effect:

— Space-time and destiny

— The direction of time

— The leading time and the Compton effect

— Compton effect and uncertainty

— The dual aspect of the elementary particles

— The Compton effect – Part 2

 

Lightnings: 

— The origin of lightnings

The following post provides a brief description of each argument:

— Physical topics – Main

 

 

 

Earth’s velocity with respect to the ether

In a preceding post (Space-time and ether) we saw that the ether is an ordinary Euclidean space, while the physical space is Minkowskian. What does this difference imply?

Let’s consider first the physical universe. In this space, given an orthonormal coordinate system, the distance from the origin of a point P of coordinates (t_ph, x_ph) is given by (for simplicity of notation, only the spatial coordinate in the direction of motion is taken into account):

(1): d = √| c² ∙ t_ph² - x_ph² |.

This expression is invariant in form with respect to the Lorentz transformations, i.e., expression (1) is the same in any inertial coordinate system.

As a consequence, the speed of light is independent of the system of reference. Hence, any effort to determine the velocity of the earth by means of measurements of the speed of light is destined to fail, as Michelson and Morley proved with their famous experiment.

Now, regarding the ether, given an orthonormal system of coordinates, the distance of a point P = (t_e, x_e) expressed in terms of them has the following expression (see Space-time and ether):

(2): d = √( c² ∙ t_e² + x_e² ).

Therefore, the ether metric is ordinary Euclidean, and equation (2) represents nothing but Pythagoras theorem, where c ∙ t_e and x_e are the sides, and d the hypotenuse. Differently from (1), this expression isn’t invariant with respect to the Lorentz transformations that involve a change of motion, and the metric coefficients depend on the velocity of the observer with respect to the ether.

In other words, equation (2) defines a unique temporal direction and, up to translations, a unique system of reference. We say that a reference system is fundamental if it’s characterized by this temporal direction. Therefore expression (2) isn’t valid if the system of reference is in motion with respect to a fundamental system, because the metric coefficients depend on the velocity, and the knowledge of the metric coefficients allows to calculate the velocity of an observer with respect to the ether. How?

Observations involving laws of physics that are subject to the Minkowski metric – which are invariant with respect to the transformations that involve a change of velocity – are out of question. The only way to obtain the metric coefficients of the ether is by means of laws that depend on the metric itself, laws that aren’t invariant with respect to the Lorentz transformations. Do such laws exist?

Probably the only candidate is the gravitational law. In fact, gravitation doesn’t transmit through ether waves, as it occurs for example with electromagnetism. Therefore the gravitational law is the most promising candidate for determining the velocity of the earth with respect to the ether. How?

Consider a planet orbiting the sun. It’s subject to forces that depend on the curvature of the ether, not on its oscillations, because no periods, nor wavelengths are implied in the space-time curvature that gives rise to the gravitational force.

Consequently, the planets orbits should differ slightly from those that would occur if the gravitational law were invariant with respect to the Lorentz transformations. The measurements of such tiny discrepancies of the trajectories should permit to calculate the coefficients of the ether metric, and from these also the velocity of the solar system and of the earth with respect to the ether.

 One point is to be noted. If the direction of motion of the solar system with respect to the ether is orthogonal to the ecliptic plane, the planets orbits may not show much discrepancy, since the effect due to the fact that the planes of their orbits don’t coincide with the ecliptic plane shouldn’t produce appreciable results.

In any case, the best way to measure the ether drift is to send two probes in space moving along orbits whose planes be mutually orthogonal.

 

(If you want to know more on the subject, please contact trevisan.diego@alice.it)

 

Other posts from Diego Trevisan:

 

Arguments related to ether and inertia: 

— Relativity and the duration of time

— Space-time and ether

— Ether and inertia

— The origin of the Minkowski metric 

 

The leading time theory and the Compton effect:

— Space-time and destiny

— The direction of time

— The leading time and the Compton effect

— Compton effect and uncertainty

— The dual aspect of the elementary particles

— The Compton effect – Part 2

 

Astrophysics: 

— The puzzle of the solar corona

— Sunspots and solar flares

 

Cosmology: 

— On the origin and evolution of the universe

Lightnings: 

— The origin of lightnings

 

The following post provides a brief description of each argument:

— Physical topics – Main

 

Ether and inertia

The existence of the ether is fundamental to understand the phenomenon of inertia. In fact, a basic requirement in order that a body possess inertia is that its position in space be referable to something physical.

The denial of the existence of the ether had brought Einstein to imagine that inertia be due to the action on matter by the so-called fixed stars. He did this in 1918 by citing the work of a physicist that had died two years earlier, Ernst Mach, and enunciating a principle that in his honor he called Mach’s principle.

The comprehension of inertia by means of the ether is based on the fact that the ether provides a reference for the positions of the masses, contrary to the fact that if there’s no reference it’s meaningless to talk about motion, as well as inertia.

On the other hand, how and in which way does the ether influences the motion, so that the greater the body’s mass, the smaller its acceleration, as one understands from the second Newton’s law (f = m ∙ a)?

One can understand this by remembering that to any particle is associated a wave, whose frequency is proportional to its mass. In the absence of interaction the wave moves along the temporal direction orthogonal to its front. The direction of motion doesn’t change unless there occurs an interaction with another wave, as is described for example in the Compton effect (see The leading time and the Compton effect).

The modification to the direction of motion generated by the interaction is inversely proportional to the frequency of the hit particle, i.e., it produces exactly the effect one expects from a body with inertia.

Hence, inertia is a manifestation of the fact that in order that a wave associated to an elementary particle change its direction of motion in the ether it’s necessary an interaction, and the average acceleration produced by several interactions is inversely proportional to the particle frequency, i.e. to its mass, in agreement with the second Newton’s law.

 

(If you want to know more on the subject, please contact trevisan.diego@alice.it)

 

Other posts from Diego Trevisan:

 

Arguments related to ether and inertia: 

— Relativity and the duration of time

— Space-time and ether

— Earth’s velocity with respect to the ether

— The origin of the Minkowski metric 

 

The leading time theory and the Compton effect:

— Space-time and destiny

— The direction of time

— The leading time and the Compton effect

— Compton effect and uncertainty

— The dual aspect of the elementary particles

— The Compton effect – Part 2

 

Astrophysics: 

— The puzzle of the solar corona

— Sunspots and solar flares

 

Cosmology: 

— On the origin and evolution of the universe

Lightnings: 

— The origin of lightnings

 

The following post provides a brief description of each argument:

— Physical topics – Main