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Theory of relativity, NEW APPROACHES, NEW IDEAS
On the 100th anniversary of the theory of relativity
Article Author: VM Myasnikov
- introduction
- Frame. Inertial frame of reference. The actual (physical) and virtual ISO
- Ether
- The postulate of relativity (Galileo, Poincaré, Einstein)
- The principle of relativity. The postulate of relativity, covariant coordinate system +
- Quater - New mathematical objects in physics
- SRT * - new edition
- Adding effects * in the SRT. Addition rates. Tachyons
- The speed of light in air. luminiferous ether
- The speed of light in the medium. Cerenkov effect
- Instead of a conclusion
Quater - New mathematical physics objects
Then, before moving on to the theory of relativity, tell briefly about the mathematical apparatus, through which all the results obtained.
As one of the general principles of the philosophy of physics, I formulated the principle of adequacy of mathematics and physics. Its essence is that mathematical objects used in certain physical theory, should have physical counterparts in this theory. If well chosen mathematical apparatus (adequate), the formal mathematical theory can be seen as a physical and sometimes even "point Nature" as it to be in one or another physical situation. I argue that the so-called 4-vectors of the traditional theory of relativity is not adequate, the physics of space-time, this does not mean that they can not use, but it means that they might have "surprises" (contradictions, singularities, and the like), not peculiar to physics itself . I propose a new mathematical objects - quater adequate to all theories, which I consider (classical physics, the theory of relativity, in whole or in any part thereof). The following are considerations in favor of the quater.
The numbers in mathematics are called objects (so-called linear algebra), to which the operations of addition and multiplication, satisfying the three laws of arithmetic:
Ia - commutative addition,
Ib - commutativity of multiplication,
II - associativity of addition and multiplication,
III - distributivity of addition / multiplication.
The best known are the so-called real and complex numbers. It is proved mathematically rigorous (G.Frobenius) that no other mathematical objects, which could be called the number does not exist. Quaternions are mathematical objects "closest" to the numbers, for they performed all the laws of arithmetic, but one - the multiplication is commutative. All other objects (linear algebra) are "farther" from the concept of number.
Therefore, quaternions, on the one hand, permit handling formally as a number (only about remembering noncommutativity multiplication) on the other hand, can be interpreted as "amount of a scalar and a vector." That is what opens up the possibility for their use in physics. My books and articles - this illustration.
Quater - a special form of the quaternion scalar part of the imaginary and the real vector (or vice versa - the real and imaginary scalar vector). Such mathematical objects (quaternium calculus), when used in physics, can not only with remarkable grace and vividly describe the known physical phenomena, but also to predict a completely new, unknown phenomenon (think "heuristic potential" quater very big. My job - this is only the beginning of the use of quaternium calculation capabilities, "lying on the mind"). For example, in the quaternion space-time Lorentz transformations are defined as hyperbolic rotation, Maxwell's equations - as a "reaction" to the introduction of space-time quaternium electric charge density or mass density. In the first case we obtain Maxwell's electromagnetic equations, the second - gravity. Actually conclusion takes a few lines of text (and a few pages of comments), and Lorentz covariance equations immediately obvious. Furthermore, a completely new physics, but it is natural to quaternium-on-year, the concept of space-weight naturally leads to the concept of the gravitational field, the new law of gravitation, is equally well described and Newtonian gravity, and gravity of the universe as a whole, etc. etc. ( "Etc etc" includes both this article).
print version
Author: VM Myasnikov
PS material is protected.
Publication date 09.02.2005gg
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