What is Time? What is Space?
Introduction.
The material world is made up of particles (electrons, protons, etc.) and fields (electromagnetic, gravitational, etc.) Both particles and fields have energy, and Physics is the fundamental science of the material world. Experimentation is the ultimate method of progress in Physics. The role of a theory is to systematically create a vision of known experimental results and to attempt to predict any future discoveries as well as to indicate possible directions for progress.
The path to any discovery usually includes the development of the appropriate instruments. Whether the instrument used is a meter, timer or balance – all experiments need their instrumentation.
Before any special physical instruments, the most simple type of experiment involved using one’s observation. A simple experiment of observing lightning would consist of counting the time from observing the lightning until the sound of the thunder would reach you. This would provide you with the knowledge of the distance to the place where the lightning strike occurred. If you knew that it took 3 seconds from the moment you saw the lightning bolt to the moment, when the sound of the thunder reached you, it becomes possible to estimate the distance (~990 m), from your position to the place where the lightning struck by multiplying the speed of sound (~330m/sec) by time (~3 sec).
This is an example of a simple experiment in which only one instrument was used – a timer. Whether you use your watch, your heartbeat, or if you just count seconds in your mind, these are all examples of using a timer. The accuracy of your observation could be different, but no conclusion is possible in the absence of time measurement in such an experiment.
The fast development of science brought forward more complicated instruments. However, the most important instrument in physics is Mathematics. Every rule and every law of Mathematics is based on physical experiments. In essence, Mathematics is the ideal representation of an absolute and perfect physical experiment. The word “ideal” in that sentence has a special meaning.
Mathematics operates only with ideal instrumentation.
It is one of the fundamental principles of science. Any deviation from that principle means conflict and contradiction. If such a contradiction is not resolved, then the whole science must be rebuilt from the very beginning.
1. Space.
When we measure size, we compare big and small objects. Historically, the measurements of large objects were made by utilizing smaller objects as a ruler and utilizing them several times until the ratio of the sizes, or of the distances were found. If the distance is a foot, then we measure the distance in the units of feet. If the distance is the size of a whole step, then the units could be yards or meters.
Over the centuries, scientists worked hard to make an accurate standard. Instrumentation such as a wood ruler would change size with differences in humidity, and a metal ruler would change length with temperature. As a result of these efforts, a ruler made with a special alloy became the international meter standard, and is has been kept in France for hundreds of years.
The twenty first century demands a much higher accuracy of the standards of length and time. As a result, modern technology widely use lasers as a standard and a ruler. In spite of the fact that such a standard is a huge improvement over a wooden ruler, an optical ruler also has its own problems and limitations, such as for example refraction index changes.
This idea brings us back to Mathematics. As an ideal instrument, Mathematics abstracts itself from any specific physical bodies and their specific problems. In Mathematics the unit of length is not associated with any specific physical ruler, but is instead an abstract ideal unit. That unit has the length, which is orthogonal to any physical parameter, such as temperature or humidity, and as such mathematical length is independent of any changes of the world around it.
Such a measurement unit does not exist in our material world. It is a product of our human brain. That is why it is ideal and abstract.
Length definition:
Mathematical (ideal) length is an infinitely accurate standard, which is approximated, but can never be achieved in the material world.
2. Time.
The idea of time has existed forever. Or at least for as long as human civilization has existed. Time was introduced as a way to measure the rate of change of the material objects in the world. The material world never stops changing. The world is in a state of constant movement.
(The specific reason for the constant movement of electrons and other particles will be further analyzed in another project titled “Atomic and molecular orbitals and quantum electrodynamics”).
(The specific reason for the constant movement of electrons and other particles will be further analyzed in another project titled “Atomic and molecular orbitals and quantum electrodynamics”).
Such movements result in a change of state, whether it is a change in an object’s position or gas-liquid-solid state, or any other state. Some changes happen fast, others slow. Time is used in order to characterize the speed of any changes in the world. The value of change divided by time is called the rate of change.
Similar to a ruler, which is used for length measurements, fast periodic processes can be used to measure the speed of changes. Nobody knows for sure, but it is quite possible that physiological time (such as the time to eat and the time to sleep) were among the first time measurements, used by humans.
Time to eat is a physiological time, based on the processes in a stomach, the time for plants to drop leaves is a biological time, the solar calendar is an example of an astronomical time, atomic time is based on the processes in an atom (such as radioactivity) and optical time is based on the period of electromagnetic waves. But these variations of time are not an ideal scientific time.
Time to eat is a physiological time, based on the processes in a stomach, the time for plants to drop leaves is a biological time, the solar calendar is an example of an astronomical time, atomic time is based on the processes in an atom (such as radioactivity) and optical time is based on the period of electromagnetic waves. But these variations of time are not an ideal scientific time.
A lifetime is a sequence of events in our lives. A healthy heart beat rate is close to 1 beat per second, the Earth’s rotation around its axis is a day-night cycle or 24 hours, the time of Earth’s travel around the Sun is 1 year. People have used astronomical time for centuries and have recognized the advantages of a more accurate way of measuring time.
Time definition:
Scientific mathematical time is ideal and an infinitely accurate periodic process, the accuracy of which can be approximated, but can never be achieved by any real physical process in our material universe. Ideal time is independent of any material object or any experimental parameter.
Time is a mankind invention and exists only in human minds. Projection and realization of the idea of time in a material world is just an approximation of time and it should not be called time, but should instead be called clock, watch, timer, etc.
It means that physiological, psychological, astronomical or optical time are not actually time, but are instead different types of time measuring apparatus (timers, clocks, etc) and scientists should recognize the difference between time and instruments that measure it.
| Material World of Physics | Ideal World of Mathematics |
| Timers, Clocks, Watches (Seconds) | Ideal Time (Seconds) |
| Metal, Plastic or Wood Rulers, Laser Meters (Meters) | Ideal Length (Meters) |
| Inertial, Gravitational, Longitudinal, Orthogonal Mass (Kilograms) | Ideal Mass (Kilograms) |
Time must be orthogonal to any material object. Time is independent from any material process. That is why time is not a material object and it exists only in our human mind. A clock is a material object, which emulates the function of time. In order to work properly, a clock must be independent from the process, whose rate of change it measures. For example, a clock with a pendulum cannot be used to measure the speed of elevation of an air balloon, because the period of a pendulum changes with gravitational constant as the balloon rises into the sky.
The accuracy of any real periodic process used for time measurements is limited. Solar clocks were substituted first with mechanical clocks, then with electronic and atomic, but all of them have accuracy limitations. Ideal scientific time is always infinitely accurate and never stops.
Mathematics operates with ideal units of length, time, mass, etc. This logic brings us to the only conclusion – there is only one ideal time, length, mass, etc. And all these basic ideal measurement units cannot depend on any material object or property.
Conclusion:
Einstein’s Relativistic Time and Space should be completely identical to the Classic Galileo Time and Space. The difference must be found in the material clock and ruler, used in appropriate experiments.
3. Optical system of coordinates. (Special Relativity).
Einstein’s description of his imaginary experiment creates an illusion of dealing with ideal scientific length and time. That impression is enhanced by using such expressions as instant measurements and ideal clock. However, in reality Einstein simply described Michelson’s experiment, where Einstein’s solid rod is a shoulder of the interferometer with the mirrors fixed and tuned at the end of each shoulder.
In their experiments, Einstein and Michelson used light as both a ruler and a clock. The length is measured in the units of wavelength and the time is measured in the units of wave phase, because they both registered an interferometer pattern shift.
This is an obvious contradiction to the principle of choosing the clock, which must be independent from the process, which rate of change it measures. An optical clock is dependent on the speed difference of the inertial systems according to the Doppler Effect.
That is why Relativistic Time is not the ideal Scientific Time, but is instead, an Optical Clock. And Relativistic Space Length is not the ideal Scientific Length, but a simple Optical Ruler or Meter.
In order to prove our point and underline the differences between an ideal time and an optical clock as well as the differences between the ideal space length and an optical ruler, we introduce optical coordinates.
In optical coordinates the length is measured in units of the number of wavelengths and the time is measured in the units of wave periods.
In optical coordinates the length is measured in units of the number of wavelengths and the time is measured in the units of wave periods.
4. Relativistic experiment.
The first equation of Einstein’s relativistic imaginary experiment (page 6, above) calculated the time, which is necessary for the light to travel along the solid rod to the mirror (tforward) and the time to travel back (tback). The rod is positioned along the vector of Earth’s movement. Einstein compares that time with the reference time (t0), which is necessary for the light to travel the length of solid rod L in the absence of Earth’s movement, when the speed v = 0.
Using Michelson’s experimental data, Einstein states that these time intervals are equal:
$t_{forward} + t_{back} -2 t_0 =0$ (1).
Without any reason Einstein decided to neglect the value of x’=vt and substituted it with differential dx. It is a mistake. The value of x’ shows the shift between two inertial systems in the time, which is needed for light to travel from one mirror to another mirror. Differential dx has an infinitely small value. Both speeds v and c are constant. There is no (and cannot be any) justification for using a differential in inertial systems. There is also no need to do so. We shall solve this problem without any approximation.
In the above equation:
$c t_{forward} =L + v t_{forward}$ (2)
Einstein’s equation is based on the results of Michelson’s experiments. Still it goes against common sense and has an obvious contradiction for anyone, who has ever tried to swim in a river in the direction opposite to the waters current. Swimming against the current takes more time and effort than swimming in a pool in the absence of a current. That is why the results of Michelson’s experiment, as well as the Lorentz transformations and whole Theory of Relativity are so contradictive.
But for now we shall stick to the specific conditions of Einstein’s imaginary experiment.
Time tforward can be expressed as:
Time tforward can be expressed as:
$t_{forward} = {L \over{c – v}}$ (3).
The length of the path forward for the light is equal to $c t_{forward}$:
$L_{forward} = {L \over{1 – {c \over v}}}$ (4).
Accordingly, the time needed for the light to travel back can be calculated as:
$t_{back} = {L \over{c + v}}$ (5).
The length of the path back for the light is equal to $c t_{back}$:
$L_{back} = {L \over{1 + {c \over v}}}$ (6).
Michelson wanted to measure the time difference:
$ \Delta t = t_{forward} + t_{back} -2 t_0$ (7).
between his moving and reference (not moving) shoulder of interferometer.
In the absence of movement, the time t0 is needed for the light to travel along the length L of the stationary rod. Einstein stated that the difference between these times in his ideal experiment must be equal to zero.
In order to solve this contradiction between Michelson and Einstein let us remember that both Einstein’s imaginary and Michelson’s real experiments were made in an Optical Coordinate System. The both never measured Time and Length. They instead measured the shift of the interference pattern. Even now there is no other timer or ruler, which are capable to make measurements with the required accuracy.
The Time in Optical Coordinates is measured in the Units of Frequency (or Wave Periods) and the Length is measured in the Units of Wavelength:
The Time in Optical Coordinates is measured in the Units of Frequency (or Wave Periods) and the Length is measured in the Units of Wavelength:
$ \lambda = {c \over f}$ (8).
Since Einstein’s solid rod moves with the speed v, we should take into account the change of the wavelength and frequency because of the Doppler Effect:
$f = f_0 {(1 \pm {v \over c})}$ (9).
Taking into account that the wavelength is equal to:
$ \lambda_{forward} = {c \over{f_0(1 – {v \over c})}}={ \lambda_0 \over{1 – {v \over c}}}$ (10).
on the first half of its trip, when it travels to the far right mirror.
On the way back the wavelength is equal to:
$ \lambda_{back} = {c \over{f_0(1 + {v \over c})}}={ \lambda_0 \over{1 + {v \over c}}}$ (11).
In these expressions $\lambda_0$ – is the wavelength of the light, when the system is not moving, i.e. v =0.
Since the direct measurements of time were impossible in both Michelson’s and Einstein’s experiments, the time and the length changes were measured by the shift of the interferometer pattern. The value of the observed interferometer pattern shift should be equal to:
Since the direct measurements of time were impossible in both Michelson’s and Einstein’s experiments, the time and the length changes were measured by the shift of the interferometer pattern. The value of the observed interferometer pattern shift should be equal to:
$ \Delta_{forward} = {L \over \lambda_0} – {L_{forward} \over \lambda_{forward}}$ (12),
when the light travels to the mirror.
On the way back the shift will be equal to:
$ \Delta_{back} = {L \over \lambda_0} – {L_{back} \over \lambda_{back}}$ (13).
Interference pattern shift in forward direction is equal to zero:
$ \Delta_{forward} = {L \over \lambda_0} – {L_{forward} \over \lambda_{forward}}={L \over \lambda_0}-{L \over{1 – {v \over c}}}{{1-{v \over c}} \over \lambda_0} =0 $ (14).
Interference pattern shift in back direction is also equal to zero:
$ \Delta_{back} = {L \over \lambda_0} – {L_{back} \over \lambda_{back}}={L \over \lambda_0}-{L \over{1 + {v \over c}}}{{1 + {v \over c}} \over \lambda_0} =0 $ (15).
1. The result shows that the Lorentz transformations and the Doppler Effect have an identical dependence along the x-axis and both have no dependence in the orthogonal direction.
It means that the result along any other direction, which is a combination of x- and y- directions, also must be identical for both the Lorentz transformations and the Doppler Effect.
2. This result also proves that Einstein’s Theory of Relativity and Doppler Effect describe the same physical phenomenon.
3. Both the Doppler Effect and Lorentz transformations must be described with the same identical formulas.
Since the formulas were not identical, it also means that either the Doppler Effect formula, the Lorentz transformations, or both of them need corrections in order to bring their formulas to be equivalent.
Summary.
1. The result, obtained here proves that it is NOT TIME or SPACE being transformed. It is OPTICAL TIMER (CLOCK) and OPTICAL METER that are not constant.
Optical timer slows down together with decreasing wave frequency, according to the Doppler Effect. Optical length meter changes its length together with the change of wavelength.
It is the same as an attempt to measure the size of two different boxes with a meter made of soft rubber. You will not get correct results by stretching the rubber meter.
2. Although Einstein neglected accurate calculations, he did not make a mistake in the resulting formulas for the relativistic $\beta$.
Michelson’s experiment could not produce a positive result. There is none and could never be a shift of interference pattern.
In his analysis of the reference shoulder of the interferometer, Einstein introduced a coefficient, which is known as the relativistic beta. Einstein stated that “obviously” it is necessary to introduce this coefficient for a reference channel. Besides the word “obviously” there is no other explanation.
Even so, that expression for the relativistic $\beta$ was accepted as correct.
The reason can be found in the name of these transformations. They are called the “Lorentz transformations”. It was Poincare, who produced these transformations and who named them after Lorentz, because it was Lorentz, who put forward the idea of two coordinate systems for two inertial systems in Michelson’s experiment. Poincare explained that a coefficient is needed in order to keep the Maxwell equations spherically symmetric in both coordinates.
No explanation from Einstein was required.
3. Poincare specifically underlined that the Lorentz transformations are correct only for the special geometry of Michelson’s experiment.
Einstein’s Theory of Relativity is not correct for moving planes or space objects. Einstein’s Theory of Relativity is incorrect, when origin points of two inertial systems do not coincide at the start time. It is incorrect, when the distance between two inertial systems decrease with time.
Imagine a spaceship travels from Earth to Mars and you use Einstein’s Relativity in your calculations. When the same ship comes back from Mars to Earth, the Theory of Relativity would produce incorrect result.
In order to use the Lorentz transformations in non-Michelson’s geometry it is necessary to find the GENERAL SOLUTION for the problem of two inertial systems, moving in arbitrary directions.
This is the end of the first part of our “Time and Space” project.
In the next two parts we shall find the general solution of the Maxwell equations for two relativistic inertial systems and present the correct general formulas for Einstein’s relativistic $\beta$ (Part 2), and for the Doppler Effect (Part 3).
In the next two parts we shall find the general solution of the Maxwell equations for two relativistic inertial systems and present the correct general formulas for Einstein’s relativistic $\beta$ (Part 2), and for the Doppler Effect (Part 3).