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Space-time diagrams for particles and photons
THE CHAOS OF THE PHYSICAL VACUUM
- THE PCT THEOREM
- THE SPACE-TIME DIAGRAM OR FEYNMANN DIAGRAM
- THE ELECTROMAGNETIC INTERACTION
- THE WEAK INTERACTION
- THE STRONG INTERACTION
- THE GRAVITATIONAL INTERACTON
- THE UNCERTAINTY RELATION OF HEISENBERG
- VIRTUAL PARTICLES AND PROBABILITIES
- SELF INTERACTION AND THE CHAOS OF THE FYSICAL VACUUM
- MODERN COSMOLOGISTS - NIBBRMEU
- NIBBRMEU - INFLATIONARY UNIVERSE
- TABLE OF CONTENTS
As an example for the time inversion (T) we take the emission of a photon v by an electron e-, presented e- => v + e-. We apply the time inversion v + e- => e-. This is the absorption of a photon by an electron.
As an example for the space inversion or parity transformation (P) we take a photon emitting clockwise spinning (Right-handed) electron e-R, presented by e-R => v + e-R. This becomes under parity transformation an counter-clockwise spinning (Left-handed) electron e-L => v + e-L, whereby the photon remains unchanged.
The charge inversion or charge conjugation (C) applied to a photon emitting electron e- => v + e-, provides a photon emitting positron e+ => v + e+. The photon remains unchanged.
The time inversion (T) is general valid. The combination of parity inversion (P) and charge conjugation (C) together is also general valid; we call this the PC theorem. Then naturally also follows the PCT theorem; this is the combination of space, time and charge inversion.
Always parting from e-L => v + e-L we get respectively:
e-L <= v + e-L (T alone)
e-R => v + e-R (P alone)
e+L => v + e+L (C alone)
e+R => v + e+R (PC duo)
e+R <= v + e+R (PCT trio).
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b. The space-time diagram or Feynmann diagram.
In a space-time diagram, also called Feynmann-diagram, we use a space coordinate for the horizontal direction and a time coordinate for the vertical direction. In this diagram points represent events and lines movements of particles in the space-time. We call these points and lines also the world points and world lines of the particles. During transformations in these diagrams we leave the space coordinate and time coordinate always unaltered, while the world points and world lines are transformed.
In the diagrams the time runs always from bottom to top and our perception at a certain time, called world view, is a fictitious horizontal line, which cuts the world lines on the positions where the particle are at the time of perception. These fictitious line moves always from bottom to top in the course of the time and the intersection with the time coordinate represents then the time of perception.
World lines which go vertically, correspond to stationary particles and sloping lines with moving particles. A larger slope of world lines with the space coordinate corresponds to a smaller velocity of the concerning particle. The world lines of ordinary particles, which follow the stream of time, we represent by providing the world line with an arrow up. Anti-particles, that go against the time stream, get an arrow down.
The spin of a particle follows the right hand rule, if the stretched thumb indicates the observed orientation of movement and the bent fingers indicate the turn direction of the spin. The observed orientation of movement of the particles points always from bottom to top in conformity with our perception of the time. We represent this with an half circle around the world line with arrow point to the right for particles, which are right-handed. We represent left-handed particles with an half circle with an arrow point to the left.
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c. The electromagnetic interaction
We start with the most elementary Feynmann diagrams for the emission and absorption of photons by an electron. See picture 1. In pic.1a we see the process of emission by a counter-clockwise spinning electron. By application of the time inversion (T) follows from this the process of absorption in picture.1b.
In fig.1c we see the emission by a positron under the charge conjugation (C) applied to picture1a. Also follows this way picture1d from pic.1c under parity transformation (P) or from pic.1a under the PC transformation.
We can also reflect diagrams as in a mirror. See picture 2. If we place a mirror right of pic.2a, we get pic.2b via the P operation.
When we place a mirror under pic.2a, we get pic.2c via the CT-operation.
A mirror next to pic.2c gives pic.2d via PCT-operation. Also follows pic.2d from pic.2b via reflection.
For the creation and annihilation of particles see picture 3.
In pic.3a we see the annihilation of the electron positron pair under emission of two photons. Via time inversion follows in pic.3b the creation of this pair out off two photons. Two photons are needed to guarantee the law of conservation of momentum.
Within the boundaries of the uncertainty principle of Heisenberg, conservation of energy and conservation of momentum may be violated. For this reason we do the process of annihilation and creation no damage by taking in the future one photon in stead of two photons. Also it is permitted to take a velocity of light larger or smaller than the official invariable velocity c, provided that this situation lasts very briefly. For this reason we represent in picture 4 all world lines with angles under 45 degrees, both for photons and particles.
From pic.4a follows by rotation over 90 degrees pic.4b, by rotation over 180 degrees follows pic.4c and by rotation over 270 degrees follows pic.4d. We see appearing a large symmetry in this space-time diagrams, permitted by the uncertainty principle.
We must, however, not forget that in our perception the time flows always from bottom to top. The area below the fictitious horizontal line through a junction point or vertex of world lines, represents events preceding the events in the vertex. Likewise the area above this horizontal line represents events succeeding the events in the vertex.
The action of force between electrons and positrons relies on exchanging photons. Similar charged particles repel each other and opposite charged particles attract each other. This is understand only by assuming that an electron distinguishes between a photon emitted by a another electron and a photon emitted by a positron. This could coincide with a really existing distinction between for example ordinary photons transmitted by electrons and (anti-)photons transmitted by positrons.
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That at weak interactions the transformations P alone and C alone are not permitted, coincides with the exclusively appearance in nature of counter-clockwise spinning neutrinos and clockwise spinning anti neutrinos. The PC combination gives to truth recipe for the transformation of neutrinos in anti-neutrinos. The PCT trio gives a recipe for the change of entering neutrinos for out going anti neutrinos in the space-time diagrams. See picture 5.
The beta decay, where a neutron changes in a proton under simultaneous emission of an electron and it's anti neutrino, is characterizing for the weak interaction. Also the reversed process (T operation) and analogous processes for the anti particles (PC operation) are possible. Also interactions between light particles mutually are possible. Under light particles, also called leptons, we understand electrons and their neutrinos, muons and their neutrinos, together with the several anti particles.
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The nuclear particles (nucleons) are kept together by exchanging virtual mesons, to know pions and kaons. These particles we call we virtual, because they cannot leave the nucleus, because their short range and because they know only a very temporary existence, within the framework of the uncertainty relation of Heisenberg. They are continuously created and destroyed in the atomic core (nucleus). Mesons are particles which are built from quark and anti quark pair. The exchanged mesons can be positive, negative or neutral and the nuclear forces between nucleons result from this continuing exchange of virtual mesons.
All particles, which are liable to strong interaction, these are the mesons, nucleons and hyperons, are indicated with the denomination hadrons. The hadrons all consist of quarks. This in contrast to the leptons. These are the electrons, muons, both types neutrinos and the diverse anti particles. The leptons are single elementary particles and only liable to the weak and / or electromagnetic interaction.
As is known now, the strong interaction between quarks followsfrom the emission and absorption of gluons. The space-time diagrams for particles with strong interaction are analogous to those for the weak interaction and electromagnetic interaction, understanding that the gluons carry so-called colours and anti colors, which coincide with the particular properties of quarks.
Recently was found, that there are six quark duo's instead of three (such as has been described in the original model). Likewise also six types of lepton duo's have been found. See the table for quarks and leptons.
Transitions from one to another lepton or quark type are possible, according to certain unified field theories. Fotons create lepton-antilepton pairs or quark-antiquark pairs (mesons). Mesons combine to nucleons, etc. The reversed processes are of course talso possible.
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f. The gravitational interaction.
Concerning the gravitational interaction is not much more to tell than that this depend on the emission and absorption of gravitons by mass carrying particles or energy carrying photons.
The reversed proportionality of the gravitation between two particles with the square of the distance is simply to explain by the spatial distribution of the number of gravitons, emitted by one particle and received by another particle.
Likewise the proportionality of the gravitation with the product of the masses of both particles is in accordance with the numbers emitted and received gravitons.
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g. The uncertainty relation of Heisenberg.
The law of conservation of momentum and energy may be violated within the boundaries of the uncertainty principle, provided that dr.dp=h/(2.pi) and dE.dT=h/(2.pi) apply. In these formulas h is the constant of Planck and pi=3.14. Hereby dr and dp are the allowed uncertainties in distance and momentum, while dE and dT are the allowed uncertainties in the energy and (life)time of the particles. The virtual particles can exist only according to these relations.
Yukawa predicted the existence of mesons as particles which carry the nuclear force. The range dr of the nuclear force has a magnitude of the dimension of a nucleon. The lifetime dT, connected which that range, is the time in which the meson travels the distance dr with the speed of light c, according to dr=c.dT. The corresponding energy of this meson then is dE=h/(2.pi.dT)=hc/(2.pi.dr). When we take for de range dr the diameter of the nucleon, then we find for dE indeed the energy equivalent of the restmass of the pion.
Also leptons and other hadrons can originate out of nothing as virtual particles, provided they disappear within their allowed time. Leptons and barions must obey to the laws for conservation of family number and appear and disappear therefore always as couple, consisting of particle and anti-particle.
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h. Virtual particles and probabilities.
The vertex or knot node of world lines in a space-time diagram present an event in the space-time. Generally this event is take also as a composed event, where virtual particles on the stage appear. An apparently simple event in a vertex can just as well consist out off a multiple event, where some or several virtual particles are involved.
In fact all events are possible in a vertex, which yield the same in- and outgoing particles, as begin and end situation, provided these are not prohibited in the framework of the uncertainty principle and the conservation laws.
However, not all events are even probable. Nature has a preference for simple above more complex situations, donating these larger probabilities. What really happens, is only to predict as a sum of all these probabilities.
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i. Self interaction and the chaos of the physical vacuum.
A mass particle can step with itself in interaction by the absorption of virtual particles, which have been emitted by itself, within the framework of the uncertainty principle. The virtual particles are assumed to hang around the mass particle, as a cloud. The mass particle itself can be conceived as a concentration of these virtual particles.
Virtual particles of all kinds can exist also briefly in apparently empty vacuum and step there with each other in interaction, whereby no in- and outgoing world lines appear. This apparent chaos of the physical vacuum is however always subjected to the framework of the twelve conservation laws of the microcosm. Only to the laws of conservation of energy and momentum is any play area permitted, within the framework of the quantum conditions, included in the uncertainty principle of Heisenberg.
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Modern cosmologists - NIBBRMEU.
Many modern cosmologists (also professor Dr. Stephen Hawking) are followers of the 'NIBBRMEU'. This means 'New Inflationary Big Bang Relativistic Model of the Expanding Universe'. This is a model for an universe, that expands, obeys the laws of general relativity and came to existence as a big bang, that started with an inflation of huge magnitude. This inflation was caused by a particular temporary situation with repellent in place of attracting gravity. If we read 'NIBBRMEU' the other way round, these cosmologists accord less and less with each other, concerning the meaning of the characters.
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NIBBRMEU - Creation and inflation of the Expanding Universe.
The maximum lifetime and initial energy content of the universe could be connected by means of the uncertainty relation of Heisenberg, if the singularity in the big bang has arisen as a quantum fluctuation in the chaos of the physical vacuum. An infinite lifetime of the universe corresponds in this case with an energy content right to zero, like in a flat universe, pleased by the partisans of the NIBBRMEU. A mass energy content zero not only means in this case that the universe is flat, but also that as much matter as anti-matter will be present in the universe during the earliest stage of the big bang.
The creation of matter and anti-matter from this fore-quantum came about by means of a phase-jump, where an exponential inflation blew up the universe to enormous dimensions, during the earliest stage of the big bang. The phase of exponential expansion is to rhyme with solutions for the general field equations of Einstein, where imaginary values are permitted.
This corresponds then simply said to a situation of repulsing instead of attracting gravitation. In fact originate during this stage the four known forces of nature, among which the gravitation, from a single fore-force. The fore-quantum with energy zero transforms itself by means of the creation of particle and anti-particle pairs in an universe with positive kinetic energy and negative gravitation energy, of which the total sum of mechanical energy is still zero.
That in our current universe anti-matter is hardly are to find, coincides with the arrow direction of the cosmic time. Because the cosmic time has only one direction, a disturbance in the CPT symmetries has happened during the earliest stage of our universe. This symmetry disturbance went at the cost of anti-matter, which disappeared from the stage.
The arrow of the cosmic time results from the second law of thermodynamics, which plays a just as important role as the first law. The first law formulates the conservation of energy during a physical process in a closed system. The second law says that during this physical process the degree of order can only decrease. The disorder (entropy) grows in the course of time. This is the reason why the cosmic time knows only one direction.
After the inflationary era the universe follows the rules of the relativistic evolutionary model. Because of the possibility of the reoccurrence of the NIBBRMEU events at each time and each place in the universe is the 'steady state universe' again entirely present with an infinite number of possible universes in the infinity of the cosmic fabric of space and time. Meanwhile there are several alternatives for the original inflation theory of Alan Guth valid in our world.
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<< 1 TEXTS ABOUT OUR SPACE-TIME
<< 2 THE SPACE-TIME CONTINUUM
<< 3 THE SPACE-TIME IN THE MACROCOSM
<< 4 THE SPACE-TIME IN THE MICROCOSM
== 5 SPACE-TIME DIAGRAMS FOR PARTICLES AND PHOTONS
>> 6 TABLE FOR QUARKS AND HADRONS
>> 7 TABLE FOR QUARKS AND LEPTONS
>> 8 THE WINDOWS OF TIME FOR OUR SPACE
>> 9 TERMINOLOGY FOR COSMOLOGY
>> 10 MATHEMATICAL APPENDIX PART 1 | PART 2
>> 11 SUMMARY OF THE CHAPTERS
>> 12 REFERENCES AND LITERATURE
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