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  • Аннотация:
    most general natural science about our Universe

http://budclub.ru/k/kuznecow_d_j/physicsr.shtml Русская версия этой статьи

Physics is the general natural science about our Universe, that is based on observability, measurement, space, time, field, interaction, causality, and entropy, using apparatus of mathematics to formulate the basic laws of the nature.
The most of physics of IXX-XX centuries assumes the homogeneity of space and time, that leads to the conservation of several physical quantities. At the consideration of quantum phenomena the unitarity appears as the basic postulate; and at the consideration of statistical phenomena, this postulate is replaced to the law of raise of the entropy. In both cases, the causality is assumed. The following basic concepts are used to formulate the specific laws: isolated system, coordinate, velocity, vector of state, observable, evolution, energy, temperature.

Physics and mathematics are widely used in other sciences and technologies. Some branches of physics, as, for example, chemistry and astronomy, may be considered as independent science, due the lack of ability to calculate some basic things (such as coupling energy and reaction rates) in chemistry, or the lack of ability to make relatively basic experiments (such as creation of stars and planets) in the astronomy.
Observability, reproducibility and measurement

The objects considered in Physics are supposed to allow the observation and meausrement. This means the physical phenomenon can be observed (and measured) again and again; at least in principle, such observation should be possible. This refers to some measurements of frequency, mass, distance, volume, area, speed, momentum, angular momentum, force, and quantities related to the electromagnetic phenomena and fundamental constants.

The cases with doubtful reproducibility usually cause serious discussions: for example, the phenomenon of creation of the Universes, or falling of the observer together with his/her laboratory into the black hole, or creation of living objects and subjects from the non-lining matter.
Similar, or even worse, problems are caused by the lack of measurement. The meausrement means, that the result of observation is characterized with number(s). For example, even the repeated (id est, in some sense reproducible) appearance of the Hamlet's father or Canterville Ghost, or even the hound of the Baskervilles, described in literature are difficult to measure and treat by methods of physics or mathematics; the descriptions of such phenomena belong to other kinds of the human knowledge, perhaps, mysticism, but neither physics, nor even science.

Proportionality and the precision

Often, the physical laws are expressed as linear equations between the physical quantities. The size, length of a physical object are supposed to be proportional to the number of times it can be covered with the etalon, id eat, the special object, used as unit of length. The volume of a liquid or a dust can be measured in a similar way.
For example, the mass or a volume occupied by the heap of some "identical" grains is supposed to be proportional to the number of grains; one can uses some vessel as unit of measure. At the moving of the heap from one place to another with the same vessel, filling it again and again, the number of times the vessel can be filled characterizes the volume of the heap, id eat, the amount of grains.

Often, the physical quantities are expressed with real numbers; the physical measurements return an approximate value. In the example with grains, it is possible to count the grains one by one and get the exact (integer) value. The number of molecules of water in a cup also would be measurable in a similar way; but the vaporing at the normal conditions anyway makes the measurement approximated. One has to freeze the water into the ice; preferably to the absolute zero temperature, in order to prevent the escape of some occasional successive molecule. However, the measurement should be performed in a vacuum, in order to avoid some molecule of water from the air to join the piece of ice. Up to the beginning of XXI century, there is no way to count the number of molecules in a cup exactly, getting the definite (and reproducible) integer number. This is typical case. Usually, there is no way to measure the physical quantities exactly; the measurements are approximations.

Roughly, the precision of a measurement is characterized with the number of significant figures, id est, decimal digits, that reproduce at the repetition of the measurement. The physical quantity is supposed to reproduce being measured with different ways. Various methods of the measuring and applying various laws of physics can be used in the measurement.

There is important question about the about the maximal precision that can be achieved. In the case of counting of grains, the maximal number of significant decimal digits is determined by the amount of grains. However, we heed to assume that no one grain brakes to parts during the counting. In the case of molecules of water, this becomes more difficult, because of dissociation. Such a dissociation may be caused not only by a thermal fluctuation, but also by a cosmic particle that comes from the space and is almost impossible to avoid. As one improves the precision, the more and more mechanisms should be taken into account in order to exclude various physical effects that can affect the measurement. This refers not only to the counting of grains or molecules, but to measurement of any physical wuantity. In principle, all the physical effects, laws, phenomena apply to a measurement, if it is performed at high precision. The special branch of physics, namely, metrology deals with ways to make the measurements more precise.

The measurement is based on some kind of proportionality. Many physical laws have lineal form and deal with proportionality. These laws are based on the approximation of our Universe with the Euclidean space, neglecting the effects of the general theory of relativity and treating the physical quantities as real numbers, not as a linear operators, as it is supposed in quantum mechanics. In order to have good approximations for the measuring of length, or distance, the reference particles should be enough heavy. However, the mass of the measuring device is not supposed to bee too large; the device should not collapse into a black hole, and it cannot be too big: the speed of light is finite, and the precise measurement is supposed to be finished during a time, small compared to the age of the Universe and, preferably, during a time, small compared to the lifetime of the physicist who is interested in the result of the measurement.

In principle, it is impossible to get exact values for even for such basic physical quantities as length, time, mass. But the Creator of our Universe is generous to physicists: the smallness of some physical constants, for example, the quantum of time compared to the age of the Universe, in principle, this give a way to measure of order of a hundred of decimal digits of various quantities; and it is pretty far from the best precision of measurement, achieved for the beginning of XXI century. The most precise measurements deal with the standards of frequency and give of order of 20 decimal digits; such precision covers the needs of technology with good reserve. Measurement of other physical quantities uses the measuring of the frequency; the linearity of the physical laws allows to derive the corresponding standards.

Kinematics. First Law by Newton

The measuring of time is based on the periodic processes. They allows to make a clock. The homogeneity of space and existence of relatively solid materials allows to make s ruler. Then, the ability to watch the movement of a relatively small object allows to register its position with respect to some reference frame and treat it as a smooth function of time. This allows to describe the movement of a body in terms of kinematics, the coordinate x appears as function X of time t:

x = X(t)

If the movement is unidimentional, then x can be treated as scalar.
In physics, the coordinates of physical objects are supposed to be smooth functions of time. The derivative of function X is called velocity; often, velocity is denoted with letter v:


The time derivative of velocity is called acceleration:


In physics, the accelerations of bodies is attributed to the mutual interactions. Bodies that are far enough from each other are supposed not to interact; this is the main idea of the principle of locality of the interaction.

Observation of kinematics allows to formulate the First Law by Newton:

There exist reference frames such that the coordinate of any object that is far from other objects is linear function of time.

Formulation of such a law can be attributed to Isaac Newton, as well as to Galileo Galilei. In the earlier formulation of this principle, the object was is qualified as "non-interacting", "no one force act on it". However, while this law is First, the concept of force should not be used for the definition.

Forces. Statics. Law of Hook.
The force as physical quantity characterizes the interaction between physical bodies. In classical and non-relativistic physics, the force appears as 3-vector, allowing the summation and multiplication. The stressed dynamometer, at fixed deformation, could be considered as etalon of force. Forces allow the addition, according the the rules of vectorial algebra. Forces were investigated by Robert Hooke and used by Isaac Newton to formulate his Second, Third and Fourth laws of mechanics. In certain approximation, the force is holomorphic function of deformation of a solid (elastic) body. At the small deformation, the force F is proportional to deformation z:
F = f(z) = k z + ...
where elasticity k is first coefficient of the Taylor expansion of the function f at the zero deformation, and symbol "..." means the highest terms of the Taylor expansion; in many cases these terms can be neglected. The resulting aproximaiton is called the Hooke's law; the force is proportional to the deformation.

Second law of Newton

For the Second law of Newton, the concept of time, and that of coordinate as function of time by Halileo Halilei, is required; the kinematics should be established. Also, the Second law of Newton, needs the concept of force, elaborated by Robert Hooke. Let F be sum (vectorial) of all forces acting on some physical object, and x = X (t) be its coordinate as function of time t, and a = X''(t) be the acceleration. Then, the Second law of Newton can be formulated with expression

F = m a

where the coefficient proportionality m is called mass. In many cases, this parameter can be considered as a constant, specific for each body. However, such an assumption is only approximation: it somebody eats too much and becomes fat, his/her mass cannot be treated as a constant; but in this case, it is also difficult to characterize the position of such a body with single or few coordinates. However, there exist more physical examples of movement of a body of variable mass, like a missile that spends its fuel.

Newtonian physics

The Newtonian physics is based on the concept that the bodies are made of particles, and each particle can be treated as an object without internal structure.

The Third Law of Newton allows the interactions only among the pairs of particles: While particle A acts to particle B with force F, then particle particle B acts to particle A with force -F. Interaction of particles with any "universal ester" are prohibited.

The Third Law of Newton specifies the gravitational interaction between bodies; the force F from particle A to particle B is expressed with equation

F = G MA MB (XA-XB) / |XA-XB|3

where MA and MB are masses of the particles, and XA and XB are their coordinates, the vertical bars indicate the length of the vector, and G is universal gravitational constant, which is assumed to be real number. The masses of all the material particles are supposed to be positive; the gravitational interaction is always attraction.

In the similar way, the interaction between electric charges can be written; the constant should be replaced, and the masses of the particles shoulcd be substituted to their electric charges, forming the law of Columb. In principle, other kinds of interactions and forces between particles are allowed in the Newtonian physics to describe the mutual interaction of material bodies.

The distributed systems strings, membranes, liquids and elastic bodies can be considered in the similar way. The general formalisms by Euler, Lagrange and Hamilton and were developed to simplify consideration of the mechanical systems, making the classical mechanics just a part of mathematics, where the initial statements are postulated as axioms, and all the results can be deduced as theorems.

The Newtonian physics seems to be sufficient for the description of the most of mechanical constructions in XVIII - XXI centuries.

Modern physics

During a century, the laws of Newton were believed to make the core of physics, determining the evolution of any physical system with known interactions. Basing on the law of Columb and the law of Newton, the knowldge of forces between bodies was supposed to give the detailed description of the physical world.
In the post-Newtonian era, the so-called modern physics was developed, that includes:
statistical physics, describing the thermal phenomena,
theory of electromagnetism (that led to the Maxwell equations and the Theory of relativity),
quantum mechanics that is necessary to include chemistry into physics as its part,
quantum field theory necessary for understanding of the processes of emission and absorption of light and nuclear physics, that become important part of energetics since XX century.
The consideration of interaction between particles and deformation of the metric of space due to the gravitational interaction leads to the need to consider quantum mechanics in curved space, where the components of the metric tensor cannot be treated as real numbers, and even topology of the space at small scale is not trivial. With the last topics, the physical picture of the world becomes more and more complicated; the simplification and generalization of the scientific knowledge is necessary.


Writing this text, all the time I have to remember that I write the dictionary, not a textbook on the theoretical physics. The aim of this text is to specify the terms and concepts, in order to avoid the terminological confusions.
Related topics:
Science, kind of scientific knowledge that include Physics
mathematics, kind of science, widely used in physics
Optics, kind of physics, that deal with emission, absorption and propagation of waves
Lasers, kind of optics that deal with the specific range of the elecromagnetic waves and ways of their generation.
http://budclub.ru/k/kuznecow_d_j/blackhole.shtml Blackhole, introduction to the astrophysics
http://budclub.ru/k/kuznecow_d_j/physicsr.shtml Русская версия этой статьи

External links
http://www.ipod.org.uk/reality/reality_wigner.pdf Eugene Wigner. The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Communications in Pure and Applied Mathematics, vol. 13, No. I (February 1960).

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