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The windows of time for our space
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- THE UNIVERSAL TIME
- THE RELATIVISTIC TIME
- THE EIGEN-TIME
- THE COSMIC (EIGEN-)TIME
- THE ATOMIC TIME
- THE IMAGINARY TIME
- THE ENTITY OF SPACE AND TIME
- THE ENTITY OF MASS AND ENERGY
- TABLE OF CONTENTS
With universal time we mean the time, which we use normally. We speak also of dynamic time instead of universal time to indicate that this is the time, which is used in the dynamics of Newton.
In general we assign time to a certain object at a certain position in the space. We fix this position in a system of coordinates with ourselves as an observer in the origin.
The space in which the objects are located, to which we donate the universal time, is the ordinary Euclidean space. This is a space where Euclidean geometry is valid. The objects in the universe can be determined by 3 mutually perpendicular coordinates x, y and z (length, width and altitude). To the distance r of an object to the origin (earth) applies the law of pythagoras: r²=x²+y²+z².
We call the teamwork, of space and time coordinates (x, y, z, t) of an object, an event. Events in the space-time are described by four dimensional vectors (4-vectors).Our space-time is the Euclidean space with the universal time. To the same event all observers assign the same time. In this case we talk of a real universal time. Also can we talk of an absolute time in contrary to the relavistic time of Einsten.
If this window of time describes the real space-time well, depends on which connections we want to describe between events. Anyway this window of time satisfies excellent for events, which take place with velocities, which are small with regard to the speed of light.
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The relativistic time is the time, which is used in the special theory of relativity of Einstein. This time is liable to the Lorentz transformations. These transformations describe the connections between coordinate systems (with observers in the origin), which move with constant velocities with regard to each other. These constant velocities v can be even large with regard to the speed of light c, provided v<c.
For observers in O, respectively O', which move with velocity v with regard to each other, does not apply r=r', where r²=x²+y²+z², but s=s' with s²=c²t²-x²-y²-z². Under the transformation does not remain the spatial distance r constant, but the space-time distance s, defined by s²=c²t²-r².
When distance r does not continue to be conserved but s, this implies that also time t does not continue to be conserved. The two observers do not donate the same time to the same event.
We call the space, in which the events take place, the Minkovsky space. Our space-time is now the Minkovsky space with the relativistic time.
With this window of time we can describe reasonable well connections between events, which take place with large velocities.
An important condition however is connected to the applicability of the Lorentz transformations for two observers, viz. that these observers can set their clocks at the same time, e.g. time zero at the same place, e.g. the origin. We say also that the observers must have a common origin in the space-time. Of course also the condition remains, that the relative velocities of the different observers may not change in the course of the time.
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The eigen-time is defined as the time, which a clock, comoving with the observer, indicates.
Designate our laboratory time t and the eigen-time t' for a (coordinate) system, which moves from us with constant velocity v.
Because of s²=c²t²-r²=c²t'² (r'=0) and r=vt we have
t'=t.(1-v²/c²)1/2. The eigen-time will be then always smaller than the laboratory time.
To a system, which has a variable velocity v, no longer applies s=constant, but ds=constant (ds is infinitesimal small). Then: ds²=c²dt²-dr²=c²dt'² and dr=vdt => dt'=dt.(1-v²/c²)1/2. The eigen-time is to find by using the integral sign for both sides of the last equality, what is only possible if v is known as function of the time.
The eigen-time is therefore also defined for systems, which experience accelerations. However, there must exist a common origin in the space-time. This is the case for all universe models with a big bang as the very first event.
The time window of the eigen-time exists also for other then Minkovsky spaces, e.g. Riemann or Lobatjevsky spaces.
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With cosmic time we mean the expansion time of an expanding universe with a big bang.
The best thing to do is to indicate the cosmic time in eigen-time. Then each galaxy has its own cosmic time, which is a measure for the natural (physical) age of that galaxy.
Each galaxy in the Hubble field has then an age, which is smaller, then we would expect by the factor (1-v²/c²)1/2.
For an universe model without big bang we should have problems by the lacking of a common origin in the space-time, as a result of which the theoretical observers are unable to set their clocks at the same time.
Also we can work with the relative cosmic time x. This is defined as the relative expansion time in x=t/T, in which T is the current age of the universe and t the elapsed time since the time zero of the big bang.
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Except observers placed in a certain space, who determine their time according to certain rules, also the clocks are important and physical processes, on which these clocks are based.
Thus we speak of atomic time if we work with a clock, which is based on atomic processes, e.g. vibrating atoms. Nuclear time for a clock, which is based on the radioactive decay of atomic nuclei or mass losses by nuclear fusion in the core of stars.
Dynamic time for a clock, which is based on the movements of a pendulum or the rotation of the earth or planet movements.
It could be that the above mentioned clocks over very long periods no longer would indicate the same time. This would mean, that the constants of nature, such as speed of light, gravitational constant, etc. are not real constant, but do change in the course of the time.
For the time being we will adopt, that to the laws of nature the perfect cosmological principle applies: that they do not change in the course of the time.
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f. The imaginary time in open and closed worlds.
Prof. Stephen Hawking got the idea to take the time (lifetime of the universe) imaginary and to give the time the same role as the spatial coordinates. In the two dimensional analogon for a closed world, the North Pole of the earth is now the beginning of the time and the distance from the North Pole to a parallel-circle is the lifetime of the universe. The radius of a parallel-circle remains again a measure for the spatial dimension of the universe. This universe remains finite and unlimited in the space. The South Pole represents then the final contraction or collapse of the universe. In the real time we have a beginning and an ending (two singularities), whereas there happens nothing in the imaginary time in particular. If we walk from the North Pole to the South Pole on the real sphere, we can simply keep walking arriving on the South Pole and return eventually to the North pole. The poles have on our globe no meaning as singular points are to be considered as normal points. In a simultaneous manner the poles are no singular world points on our two dimensional analogon for this imaginary time-space.
If the imaginary time is the real time, we can state that the universe is also unlimited in the time and nevertheless has a finite (or cyclic) existence. The laws of nature were and remain always valid also during the beginning and ending phases of the universe.
In the same way we can consider the narrow opening of a trumpet for the analogon for the open world as the beginning of the time and the radial distance along the trumpet in the direction of the end as the age of the universe.The radius of the parallel-circle (in a cross-section of the trumpet) remains also here a measure for the spatial dimension of the universe. This universe remains unlimited and infinite in the space. If we close the opening of the beginning of the trumpet with a spherical surface with a positive curvature, this world is also unlimited in the time. The laws of nature remain valid for the beginning of the universe. Because this universe continues to expand eternally, there is no end phase. Also the open universe is infinite in the time.
More about this: see the lecture of prof. Hawking about The Beginning of Time.
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See also the Mathematical appendix.
g. The entity of space and time.
In the general field equations of Einstein the geometry of the space-time (determined in the geometrical tensor) is expressed in the energy contents, including all masses, of a space-time volume (in the energy tensor). Under the assumption of isotropy and homogeneity in our system of coordinates these field equations are to solve even without too much effort.
There exist three possible solutions, which correspond to a closed spherical, open flat or open pseudo-spherical universe with corresponding geometry such as Riemann, Minkovsky or Lobatsjevki space-time.
At local level, such as the area of our solar system, we can consider the space-time as almost flat, whereas at more precise calculations, in the neighborhood of our sun, the space-time is deformed to a Riemann space-time. The same applies to our galaxy core, because the presence of a giant black hole in the center.
For larger distances up to approximately three billion light years the space-time is also almost flat, except in the neighborhood of black holes in the cores of galaxies. For larger distances our knowledge is at present time such that this space-time area seems flat, except in the neighborhood of large concentrations of galaxies. The properties of these Riemann space-time areas are determined by the masses of our sun, black holes or large concentrations of galaxies with each their own specific solutions.
The solution of the general field equations of Einstein for our solar system exists for a long time and is known as the so-called Schwartzschild solution. Also for black holes there exist similar solutions. The solutions for the space-time as a whole like above outlined, exist already almost a century.
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h. The entity of mass and energy.
Such as space and time are aspects of the same entity in the space-time tensor, also mass and energy are aspects of the same entity, in the mass-energy tensor, such as is expressed in the general field equations. To our large surprise these tensors however are also equal to each other. The three simple solutions of the field equations can be set into a form, which has irrefutable agreements with three possible quantum situations.
This we can see also in the form of the formula for the scalar curvature R of the space-time, expressed in the energy contents T of a space-time volume: R = - k.T, where the constant k is dependent on the gravitation constant in the law of Newton for the universal gravitation and R respectively. T can be a zero, positive or negative quantity.
In which situation our current universe finds itself as a whole, is still an unsolved riddle for our scientists. Some recent discoveries plead for a flat universe (R is zero) and other for a hyperbolic or a pseudo-spherical universe (R is negative), whereas also a spherical universe (R is positive) seems not yet excluded.
According to the modern quantum mechanics, a certain probability is granted to each possible quantum situation, where also a combination of all possible situations with several probability factors is allowed. According to my conviction our current universe exists from such a combination of these quantum situations. It will last probably still a while, before our scientists can give more information about this.
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<< 1 TEXTS ABOUT OUR SPACE-TIME
== 8 THE WINDOWS OF TIME FOR OUR SPACE
<< 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
>> 9 TERMINOLOGY FOR COSMOLOGY
>> 10 MATHEMATICAL APPENDIX PART 1 | PART 2
>> 11 SUMMARY OF THE CHAPTERS
>> 12 REFERENCES AND LITERATURE
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