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The space-time in the microcosm
- DISTANCE AND TIME IN OUR MICROCOSM
- MASS AND ENERGY IN OUR MICROCOSM
- THE FOUR SORTS OF FORCES OF NATURE
- THE LAWS OF CONSERVATION
- THE VALIDITY OF THE LAWS OF CONSERVATION
- THE LAW OF CONSERVATION OF MASS AND ENERGY
- THE LAW OF CONSERVATION OF MOMENTUM
- THE LAW OF CONSERVATION OF SPIN
- THE LAW OF CONSERVATION OF CHARGE
- THE LAW OF CONSERVATION OF FAMILY NUMBER
- THE TIME REVERSAL
- THE SPACE REVERSAL
- THE CHARGE REVERSAL
- DE THE LAW OF CONSERVATION OF STRANGENESS
- THE LAW OF CONSERVATION OF ISOSPIN
- THE THREE SORTS OF QUARKS AND THE CONSERVATION LAWS
- TABLE OF CONTENTS
Distance and time in our microcosm.
The microcosm is the realm of the atomic and subatomic particles. As we know the atom consists of a positive nucleus with spinning negative electrons around it. We call the phenomena which appear between electrons and atomic nucleus and electrons mutually atomic. The atomic nucleus for its part consists of two types subatomic particles, also called nucleons.
These nuclear particles are the neutrons and protons. The protons have a positive charge and the neutrons have no charge. The phenomena, which take place in the atomic nucleus, are of a nuclear nature. Atomic distances, such as the diameters of atoms, lie in the order of 10-9 meter, whereas nuclear distances, such as the diameters of nucleons, lie in the order of 10-15 meter.
The distances, which are important for us for the closer study of the space-time, lie in the order of the size of the nucleons. The intervals of time, which belong to these distances, are those intervals of time, which the light needs to travel these distances.
Also for elementary particles apply the Lorentz-transformations to distance and time, whereby the space-time interval remains invariant.
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Mass and energy in our microcosm.
In the microcosm we have to deal with the masses of electrons, neutrons and protons, included the masses of their anti-particles. The energy exchanges which appear at these particles lies in the order of size of the energy equivalents of their masses according to the Einstein formula E=mc2. The form in which we find this energy is in general in the form of photons. The photons of the electromagnetic radiation can have a energy quantity from practically immeasurably small to the size of energy equivalents of a lot of nucleons together. Recently one has met even photons in the cosmic radiation, which have converted himself in contact with our atmosphere, as individual photon into millions protons and anti-protons, whereas thereby the arisen rain of nucleons itself changed in a rain of electrons and anti-electrons.
The anti-electrons have got the name positrons after their discovery in 1932. Also shortly after that discovery the scientists supposed that there must exist another massless subatomic particle to maintain the laws of conservation of momentum, spin and mass-energy. This is the in the meanwhile found neutrino and anti-neutrino, a particle which moves with the velocity of light and has no energy equivalent for his restmass, but surely has a spin. Also a neutrino has no charge, such as we could presume from his name. There is a supposition that we must see the neutrino as a neutral electron. This because the other known nucleons appear mostly in the form of charged common particle, neutral particle or opposite charged anti-particle.
The Lorentz transformations for energy E and momentum p apply for all these particles, whereby the total energy remains invariant, inclusive the energies of masses, according to the relation of Einstein E=mc˛. As we know, the momentum p is defined as the product of mass m and velocity v, according the relation p=mv.
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The four sorts of forces of nature.
The forces of nature which appear in the atomic area, are the forces between electrons mutual and between electrons and atomic nucleus. These are the electromagnetic forces, which are caused by the interaction between photons and charged particles.
In the nuclear area we know two sorts of forces. On the one hand the strong nuclear force, which keeps together the particles in the atomic nucleus. This force finds its cause in the interaction between protons and neutrons in the atomic nucleus, the nucleons mutual. On the other hand the weak nuclear force, which appears at the conversion of neutrons in protons and the other way round and where neutrinos appear at the stage. This force takes care for the interaction between nucleons and neutrinos.
Finally we know also the gravitational force, which relies on a still unknown interaction between all particles which have mass. On the atomic and nuclear scale, as far as that is for us accessible, we can entirely neglect the gravitational force, compared to the other three types of forces of nature. Just on planetary and cosmic scale the gravitational force becomes interesting, whereas there the other three sorts of forces play no more a role.
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All called forces have been bound to certain laws of nature. These are the conservation laws. A certain physical quantity remains unchanged at a physical process. These processes are for example nuclear fusion and nuclear fission or collisions between nuclear particles with each other or with photons and neutrinos. The processes, as nuclear reactions, can be described by an equation, where the physical quantity, which must remain conserved, is just as large at the left-hand side, as this quantity is at the right-hand side of the equation.
The strong interaction knows twelve quantities, which must be conserved:
1 - mass and energy,
2 - momentum,
3 - spin,
4 - charge,
5 - electron number,
6 - muon number,
7 - baryon number,
8 - time reversal,
9 - space reversal and charge reversal together,
10 - space reversal and charge reversal individually,
11 - strangeness,
12 - isospin.Look at a conservation law as a prohibition for changing a certain quantity. There applies that all is allowed, what not is forbidden. The quantities, which must be conserved, we call also the invariant quantities.
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The validity of the laws of conservation.
The strong interactions are absolutely bound to all twelve conservation laws.
For the electromagnetic interactions expires the conservation of isospin.
The weak interactions are subject absolutely to the first nine of above said conservation laws, whereas the last called three are not binding.
Because we know that the gravitational force does depend exclusively on the mass and not on the charge and nature of the particles, there remain the law of conservation of mass and energy, momentum, spin, time inversion and space inversion.
In the following sections (under translation and coming soon) we will try to examine, what the conservation laws imply and how these laws are connected with the structure of our space-time.
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The law of conservation of mass and energy.
Mass and energy can be converted into each other according to E=mc2 and can be considered as aspects of and the same entity, what we could call mass-energy. If we take the sum of the energy equivalents of the masses and the kinetic energy of the particles, including the energy of photons, involved in a process of change, then this sum remains unchanged. We can consider this as the generalized law of conservation of energy. Energy can be converted from one to another form, but can not be lost and can also not appear out off nothing. This way formulated, mass is to be considered as a form of high concentrated energy.
The conservation of the total energy of a closed system, this is a system on which no forces acts from outside, has do with the uniformity of the time. On which time one takes the sum of all energy, is independent of this time. The sum is invariant in the time. This is a symmetry of the space-time.
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The law of conservation of momentum.
The momentum of a particle is the product of mass and velocity and a vector quantity, with the same direction as the orientation of movement of the particle. Also a photon has a momentum vector with the size of the product of the mass equivalent of the photon energy and the velocity of light and with the direction of the movement of the photon. When we take the sum of all momentum vectors of particles and photons with each other in interaction in a closed system, then this sum is constant in size and direction. We take this sum in the point of gravity of the system. When we suppose that we are in the same situation of movement as this point of gravity, then we cannot imagine, that this point of gravity can sets itself in movement in one or another direction, no matter where this point of gravity is situated. This should contradictory, as it happens, to the homogeneity of the space. We see here a symmetry of the space-time.
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The law of conservation of spin.
When we place a compass needle in a closed system, on which no forces act from outside, then we cannot imagine, that this needle could set itself in a turning movement, no matter in which direction the needle is placed. This would mean a violation of the isotropy of the space.
The compass needle exists of atoms and the spins of all these atoms together determine the turning of the compass needle. The sum of all spins produces no turning movement in this case. This is only to explain by adopting that this sum remains invariant.
The turning movement of a particle around its own axis, we call the spin. Here too the conservation of spin applies. When we take the sum of the spins of all particles in a closed system, this sum will remain invariant.
When we obtain a sum that is not zero, we can not set us in a situation of movement, in which we can transform this sum to zero, such as that was the case for the momentum vector. What this concerns, we always keep a turning movement, which is determined by the turning around an axis through the point of gravity.
As direction of turning movement (spin) we take this axis. This axis for the spin points to the direction, where the stretched thumb of the right hand points, if the spin direction is in same direction as the bent fingers of the same hand point. Both the amount of spinning and the direction of spinning remain invariant as a result of the isotropy of the space, as special case of a space-time symmetry.
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The law of conservation of charge.
As elementary charge one takes the negative charge of the electron, since its discovery in 1897 by Thomson. Afterwards was proven, that this is also the smallest charge and that each charge exists of whole multiples of this electron charge. The proton has a charge just as large as the electron charge, but then with positive sign.
The atom is in its whole neutral, because it has as many electrons around the nucleus, as protons in the nucleus. Masses existing of a lot of atoms, with each other in interaction, try to make each component atom neutral, by exchange of electrons. This because, if this is not the case, there appear automatically electric forces, which will do that.
It is adopted generally, that the universe contains as much positive as negative charge and that large masses are neutral, because the very old age of the universe.
By the study of anti particles one has reached the conclusion, that we can describe an anti particle as an ordinary particle, that walks back in the time. Thereby the reversing of the arrow direction, for the time in the space-time diagrams, will be coupled with inversion of charge. Here we talk of a space-time symmetry.
Since the arrival of the quarks in science one has discovered, that there exist smaller charges, then the charge of the electron. In the subatomic particles the quarks action however exclusively in such combinations, that always the sum of the charges of the quarks in a combination is a positive or negative multiple of the elementary charge. The interactions between these quarks are showed using space-time diagrams. Here we see emerging symmetries of the space-time, such as we shall see for the time inversion, space inversion and charge inversion.
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The law of conservation of family number.
The elementary particles are classified in a number of families. Thus we know the electron, muon and baryon family. To each family applies that the number of family members does not change in the course of the time. The total number of particles of the family is invariant. The ordinary particle get assigned as family number +1 and the anti particle family number -1. If we add up charges then match the positive and negative contributions against each other. In the same way this applies to the particles with positive and negative family numbers.
The electron family exists of electron (+1) and anti electron or positron (-1). Moreover the electron neutrino (+1) and anti electron neutrino (-1) also belong to the family.
The muon family exists of muon (+1), anti muon (-1), muon neutrino (+1) and anti muon neutrino (-1).
The baryon family has the nucleons and hyperons (+1) as members, together with their anti particles, the anti nucleon and anti hyperon (-1). Hyperons are particles, which are heavier than the nucleons, the proton and neutron.
On the basis of above mentioned numbers, it is not too risky to assume, that the electron neutrino is a neutral electron and the muon neutrino is a neutral muon. However, if we look at the masses of the particles, then this assumption is surely risky, because both neutrinos have no rest mass. In this last case it is more difficult to understand, why they belong to the same families.
As we know, an anti particles is to consider as an ordinary particle, where the time walks back, a symmetry of the space-time. On the basis of the connection of this symmetry for charge and mass for elementary particles, these things also must apply to the universe as a whole.
We would expect, that there is in the universe as much ordinary matter as anti matter present. The total mass of the universe then would be zero, as well as is the case for the total charge of the universe. As the conservation laws for the family numbers apply absolutely, then in this case for each family the total number of particles would match against each other, concerning particles and anti-particles.
The law of conservation of family numbers coincides directly with the other conservation laws, such as conservation of mass and energy, momentum, spin, charge, etc. and reflect with that the symmetries of the space time.
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In the mathematical formulas, which apply to elementary particles, we can reverse everywhere and always the sign for the time. It speaks for itself, that the inversion of future and past, a reflection in the time, is a clear example are of a space-time symmetry.
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As an example of a space inversion, we take the spin of an elementary particle, described by the right hand rule. Suppose that the particle spins in the direction of the bent fingers of the right hand, if the particle moves in the direction of the stretched right thumb. When we look at the right hand in a mirror then we see the left hand. The spin direction turns, whereas the movement of the particle keeps the same direction. This is as if a right propeller changes in a left propeller. The space inversion, also called parity transformation, is a reflection in space.
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The law of conservation for the inversion of a physical quantity means, that when a physical interaction between particles appears, also the same interaction exists at inversion of the sign of these quantity.
The inversion of the charge has to do with the arrow direction of the time in the space-time diagrams of charged particles and here also we can talk of space-time symmetries.
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The law of conservation of strangeness.
There exist a number of particles in nature, with interactions mutually and with other particles, which we can explain only by giving a number for strangeness to these particles, just as the family number. Why these particles belong to the same family, one found that strange and the family connection is still being under examination.
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The law of conservation of isospin.
Not so long ago, one discovered a property of particles, that one gave the denomination isospin, because it resembled the properties of the spin. One could not explain the isospin however in the well-known dimensions of our space-time, such as the ordinary spin.
Possibly the isospin proves to be soon nothing else then a space-time symmetry in realm of the quarks.
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The three sorts of quarks and the consevation laws.
Gel-Mann and Ne'eman composed recently a satisfactory diagram, based on the theory of groups, in which the hyperons were classified, according to isospin and charge. From this followed the theoretical forecast of the existence of three types of quarks.
The hyperons can be thought, to be built from quark trio's, as well as the nucleons. There also exist three anti quarks. From duo's of quark and anti quark also particles can be formed. Thus one speaks of the d-quark (d) with isospin -1/2 (down) and a charge -1/3 (of the electron charge). The u-quark (u) with isospin +1/2 (up) have a charge of +2/3 and the s-quark (s = strange) with isospin zero has a charge of -1/3. The proton exists from the combination uud and the neutron from the combination udd. We give the quarks baryon number 1/3 and the anti quarks -1/3. Valid combinations can be only formed, with complete numbers for the sum of baryon and charge numbers in the combination. See the Table for quarks and hadrons.
The number for strangeness of a particle, existing of quarks, appeared afterwards to correspond exactly with the number of strange quarks (s) in the composition. Also it has been later discovered, that there are six quark types, instead of three (such as was described in the original model). Likewise, there are also six types of leptons. The later discovered types however do not appear in nature this way frequently. See the Table for quarks and leptons.
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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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