1. What (not) is the theory of relativity

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root(La relatività non dice che  tutto è relativo)
    
    La relatività non è una teoria filosofica
            La relatività non è solo una teoria
        
    La relatività non è paradossale e contraria al senso comune.
        La relatività ha impatto anche sulla vita pratica.
    
    La relatività non è un capitolo a parte nella fisica
        La relatività ristretta si applica ad elettromagnetismo e velocità vicine a quella della luce
            La relatività generale si applica a gravitazione, astrofisica e cosmologia        
        
    La relatività non dice che massa ed energia sono esattamente la stessa cosa       
        La relatività non c'entra granchè con la bomba atomica
        
    La relatività non è unica ma sono tre teorie distinte
       La relatività generale non è una teoria alternativa ma estende la relatività ristetta 

       
    La relatività non si può spiegare solo con parole semplici senza matematica
        La matematica della relatività ristretta non è complicata
            La relatività generale invece richiede matematica avanzata
                        
        La relatività ristretta non è difficile da capire
            La relatività generale invece non è facile da capire
    
    La relatività ristretta non è stata un fulmine a ciel sereno
        La relatività generale invece non era nell'aria
            La relatività non è una scoperta a cui ha collaborato anche la prima moglie
    

Note¹

Relativity does not say that “everything is relative”

The name relativity was a rather unfortunate choice, as Sommerfeld noted (²): “The name relativity theory was not a lucky choice: relativity of space and time is not the essential property, as is the independence of the laws of Nature from the observer’s point of view.” the main concept is the invariance of the laws of physics, the physical laws are the same for all observers in all places and all times, they are not relative.

Exactly the opposite of “everything is relative”, a completely meaningless phrase beloved of philosophers, poets and laymen who have no understanding of it.

Unfortunately, philosophy, literature, poetry, and common sense often transport words that make sense in a certain context (scientific disciplines, human activities,…) to other contexts where they no longer do, and they like to misunderstand their meaning by mistaking their confusion for critical thinking.

Relativity of motion (Galileo) and relativity of motion, space and time (Einstein) are secondary consequences of the main postulate of invariance of physical laws. If the measurement of a quantity is relative to the observer it means that it is being used incorrectly, and there is some other quantity with greater physical significance that is the same for all observers.

Summing up in three words: *relativity means “same law for all “ (John Archibald Wheeler)³

Relativity is not a philosophical theory.

It has nothing to do with more or less campy reflections and lucubrations about the nature of space, time, mass, energy and reality.

But it deals with concrete predictions about natural phenomena, confirmed by experiments, according to the scientific method, with practical applications.

Relativity is not just a theory

To some clueless people, theory means mental speculation or abstruse hypothesis, far removed from practice and real life. But a theory such as relativity has been confirmed by countless experiments, is bread and butter in many fields of physics, and has practical applications (e.g., satellite tracking with GPS).

In spite of this every day wafflers and pikers (crackpots, in English) think to disprove it, with absurd ravings that start from faulty assumptions and proceed from one error to another.

Narrow relativity is not paradoxical and contrary to common sense.

People often make the mistake of giving examples from common experience to explain the concepts of a theory such as relativity to laymen in simple words.

This is not a good idea, because using a theory outside its scope leads to fake paradoxes, seemingly absurd results, and can confuse logical consequences with the theory’s postulates.

Relativity is not a separate chapter in physics.

Special relativity is closely related to electricity, magnetism and optics, indeed they are coherent parts of the same theory (classical electromagnetic field theory), and it is a tool in daily use in high-energy physics: particles, cosmic rays, plasma, nuclear reactions.

General relativity is the basis of cosmology and an indispensable tool for astrophysics, dealing with very intense gravitational fields over great distances.

Historically there are three theories of relativity

One theory of Galileo and two theories of Einstein, with differences between them, but a common main postulate, laws of nature are the same for different observers, otherwise it would be impossible to do science:

• galileo’s relativity applies to the laws of motion, for velocities small compared to those of light, and observers in uniform rectilinear motion, i.e., with constant relative velocity, without sudden shocks or acceleration.
• einstein’s special (or special) relativity applies, to electromagnetism and motion for speeds close to that of light, and observers in uniform motion as per Galileo.
• einstein’s general relativity applies in the presence of intense gravitational fields, large scales (planets, stars, galaxies, cosmos) and velocities close to those of light, even to observers in nonlinear, accelerated motion.
• The last is the most general, as the name also reminds us, and includes as special cases the previous theories

Narrow relativity is not difficult to understand

So many people think that the theory of special relativity is the work of a genius that is hostile to ordinary mortals–abstruse, paradoxical, and difficult to understand for those who are not gifted in mathematics and physics. A big hogwash because its basic concepts are simple, and the mathematics to understand them quite elementary.

The mathematics of special relativity is very simple. Secondary school algebra and analytic geometry are enough to study it. Knowing what a derivative or integral is is very useful but not essential; in fact, much can be explained using only the four operations of compulsory school, powers and orders of magnitude. And for the rest, vectors, derivatives and integrals are enough.

General relativity on the other hand is not for easy to understand

In contrast, general relativity is difficult. The basic concepts are simple, profound and elegant, in fact as the great Russian scientist Lev Landau said, it is “the most beautiful of theories.” But to express them correctly and accurately is not enough common language, and neither is the expertise of a short degree in mathematics, or physics or engineering.

General relativity requires advanced mathematics.

The necessary language includes advanced mathematical knowledge in multilinear algebra, differential geometry, tensor calculus in curved n-dimensional spaces, and nonlinear partial derivative differential equations. Once these mathematical tools are acquired, general relativity is not that difficult; there are much more complicated physical theories that are far from common sense, such as quantum field theories (quantum electrodynamics, quantum chromodynamics), which require much more advanced mathematical tools.

Relativity cannot be explained only in simple words without using mathematics at all

One cannot fully understand the theory of special relativity, like no other theory, by completely forgoing mathematics, the most powerful and universal language. It takes the open-mindedness of those who are not frightened by a few formulas and can reason with numbers, order of magnitudes, data, graphs and tables.

Some arithmetic, algebra and analytic geometry are needed. Some differential calculus and linear algebra are useful but not essential.

Narrow relativity was not a bolt out of the blue

Restricted relativity was up in the air in Einstein’s day, as a logical consequence of the discoveries about electricity, magnetism, light and radio waves in the nineteenth century, and perhaps would be discovered by someone else years later. Several papers by physicists such as Lorentz, Poincaré, Larmor, Fitzgerald anticipated parts of Einstein’s theory. But no one had drawn the sums for a logical and coherent construction. Useful to the development of the theory were discussions with his friends, such as the engineer Besso and the mathematician Grossmann. And above all, the freedom to be a fanatically paid employee of the state patent office.

General relativity, on the other hand, was not in the air

In contrast, in the early twentieth century, no one thought to lay a hand on Newton’s theory of gravitation. Einstein’s work on general relativity was a stroke of genius, totally unforeseen in history, and the geometric interpretation of gravity as the curvature of spacetime a real revolution for which we might have had to wait decades before someone else got there.

General relativity is an extension of special relativity

General relativity is a logical and consistent consequence of certain concepts of special relativity: the impossibility of instantaneous actions at a distance, the generalization to observers in accelerated, nonrectilinear motion of the principle of equivalence between observers in uniform rectilinear motion, and the equivalence between the effect of gravity and an acceleration of motion in a reference system. The more general theory includes the other as a limiting case in the absence of gravitational fields, and they are consistent with each other. The two relativities thus logically form a single theory, the most beautiful of all (Landau).** **

Relativity does not say that mass and energy are exactly the same thing

These are two closely related physical quantities, and are equivalent under certain conditions, depending on what is meant by mass. A stationary particle has an energy at rest proportional to its mass.

But they are not exactly the same physical quantity:

- The rest mass of a body m is a scalar number, invariant between reference systems, the same for every observer. But it does not satisfy a conservation principle; there are phenomena at the subatomic level, of interaction between multiple particles, in which it is not conserved.

- Total energy is not invariant, because it depends on the velocity of the observer, however, it satisfies a conservation principle.

The most famous formula in physics is almost never written in the right way

Writing the famous equivalence formula between mass and energy as E=mc^(2) , where m is the so-called relativistic mass, is not accurate. Relativistic velocity-dependent mass is a misleading and incorrect concept, even according to Einstein, and to all modern specialists in matter. In order not to risk confusion, the formula should be written differently, using the value of the rest mass m, i.e., measured in a reference system in which the body is not in motion, a value that is the same for all observers, and a numerical correction factor, γ or Lorentz gamma factor , which depends on the relative velocity v. Thus as E = γmc^(2) where γ is a function of the ratio (v/c). See ⁴,⁵

Relativity has little to do with the atomic bomb

The formulas of special relativity that link mass, energy and momentum also give the correct energy balance for phenomena in which matter is transformed into energy and vice versa, such as in nuclear reactions, annihilation between matter and antimatter, and the creation of particles from vacuum.

But these microscopic phenomena, discovered a decade later, are not explained by the theory of relativity; instead, they are the subject of nuclear and elementary particle physics.

Relativity also has an impact on practical life.

It is not true that relativity has nothing to do with everyday life**.** Many technologies impacting everyday life are based on the theory of relativity, which so many people use without having any idea of what is inside the box. For example, in GPS satellite tracking, the synchronization of clocks between the four satellites and the device on the ground needs both special relativity and general relativity, as well as, of course, quantum physics for the design of ultra-high-precision atomic clocks.

Relativity is not a discovery in which the first wife also collaborated

It is absolutely not true that Einstein would have been helped in his studies by his first wife Mileva Maric.

An examination by historians of science in the archives of Maric’s manuscripts and letters ( even by the more partisan feminist researchers, who were naturally disappointed) showed that in the years 1901 to 1905 she was occupied with other things. Maric followed her future spouse’s studies at most until 1901, when Einstein still believed in the old ether theory and absolute time. In that year she became pregnant, then lost the baby, but after that date she never passed any more mathematics or physics examinations, never graduated, and was never an expert in these subjects, despite her good will to follow a career then reserved for men. From 1901 she no longer followed the research that would lead about four years later to Einstein’s publication of four seminal papers.⁶,⁷,⁸,⁹

The wives’ contribution is a ‘highly improbable idea, with no concrete evidence in its favor, hatched by charlatan parapsychologists, disaffected feminist fanatics, and drug-addled pikers. Unfortunately, this fake news has generated a deluge of urban legends on the Internet and social media, which so many gullible people have taken the bait for out of ideological bias.