3. Relativity in a nutshell


flowchart TD
    A0(<strong> Principio di relatività</strong>: <br /> Le leggi fisiche sono le stesse  per tutti gli osservatori )
   A0 --> A1([le leggi fisiche sono invarianti per trasformazioni di Lorentz tra sistemi di riferimento inerziali ])
   A1 --> A2([La velocità della luce nel vuoto è una costante indipendente dal moto degli osservatori o della sorgente ])
   A1 --> A3([Diminuisce l'accelerazione in risposta alla stessa forza  applicata])
   A2 --> C1([le particelle di massa nulla si muovono sempre nel vuoto alla stessa velocità della luce])
   A2 --> C2([La velocità della luce non può essere raggiunta da corpi dotati di massa diversa da zero])
   A3 --> C2

Some words from physics

  • Reference System: a point of view from which the motion of an object is observed; it can be stationary or integral to another moving object.
  • Inertial Reference Systems: move uniformly with respect to each other.
  • Uniform Motion: the motion of an object moving at a constant speed in a straight line, without acceleration, jerkiness or change of direction.
  • Galileo’s transformations: the formulas for the change of coordinates between two inertial reference systems in Galileo’s relativity
  • Lorentz transformations: the formulas for the change of coordinates between two inertial reference systems in Einstein’s relativity
  • Covariance: invariance of equations expressing physical laws by Lorentz transformations

The speed c of light in vacuum is not only a constant but a limiting speed

We specify in a vacuum, because there are many dense media with high refractive index, such as water or diamonds, in which light is slower, and particles such as electrons can go faster, with spectacular effects, such as the blue flashes of Cerenkov radiation in a water-cooled nuclear reactor. It is not as important that there is the speed of visible light as that it is a limiting speed In fact, in the vacuum all electromagnetic waves (radio waves, microwaves, infrared and ultraviolet, X-rays, gamma rays), gravitational waves, every other interaction at a distance, even of a different nature, have the same speed as light. The key point is that this is an insurmountable limit.

Particles of zero mass always move at the speed of light

Photons, the particles that carry light and electromagnetic interaction in general, have zero mass. The speed of light c cannot be reached by bodies with mass other than zero. This is a very high speed, over a billion kilometers per hour, but not infinite; in fact, for example, light from the Sun takes about eight and a half minutes to cover the approximately 150 million kilometers between it and Earth. Light from distant galaxies also takes billions of years to reach us.

Classical mechanics cannot explain a limiting speed

If that of light is a limiting speed, one has to change the laws of classical mechanics, which do not predict a limiting speed, a body endowed with mass can theoretically reach any speed.


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title: IL MONDO A VELOCITA' VICINE A QUELLA DELLA LUCE 
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flowchart TD
    C1([ il tempo si dilata e rallenta per un osservatore fermo rispetto ad un osservatore in movimento ad alta velocità  ])
    C2([ la lunghezza si contrae per un osservatore fermo rispetto ad un osservatore in movimento ad alta velocità ])
    C3([ spazio e tempo non devono essere trattati separatamente ma ha senso solo una unione dei due concetti ])
     C1 --> B2([spazio&nbsp;e&nbsp;tempo&nbsp;sono&nbsp;le&nbsp;coordinate di un evento nello spaziotempo a quattro dimensioni])
     C2 --> B2
     C3 --> B2
     B2 --> A3([la&nbsp;separazione,&nbsp;o&nbsp;distanza, tra&nbsp;due&nbsp;eventi&nbsp;nello&nbsp;spazio&nbsp;tempo è la stessa per tutti gli osservatori])

The consequences of the principle of relativity

Einstein’s relativity postulate of equality of physical laws for all observers seems very reasonable at first glance, and not particularly bold or revolutionary, before deriving its logical implications, which at first glance are paradoxical. They are not paradoxes only after understanding the new theory and the consideration that near-light speeds are so far away from direct daily experience: light travels at about a billion kilometers per hour, an airplane at about 900 kilometers per hour, a spaceship or satellite orbiting at about 30,000 kilometers per hour. So common language and concepts derived from experience at low speeds are not suitable for understanding phenomena at such high speeds.

At speeds close to the unreachable speed of light, time expands, and space contracts, in the same direction of uniform rectilinear motion (remains the same in the directions transverse to the motion)

If by chasing a ray of light one can never reach it, in a sense the distances must shorten and the time intervals dilate, time is as if slowing down. In this way the speed of the body, the ratio of distance traveled to time interval, always remains smaller than that of light.

And the ratio of force to acceleration, the inertia in Newton’s second law, must increase, to make it more costly to increase of the speed that brings it closer to the light beam.

Space, time and simultaneity are no longer absolute The concept of absolute time is lost; a simultaneous event for one observer is not simultaneous for another.

At speeds close to that of light space and time are not independent and separate

In fact, in the formulas of coordinate transformation between inertial (Lorentz) reference systems are related to each other and the relative velocity between the observers