Theory of Relativity
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In physics, the term relativity is refer generically to the mathematical transformations to be applied to descriptions of phenomena in the transition between two frames of reference in relative motion. The expression theory of relativity is used to refer to one of the particular theories, such as the theory of special relativity or general Einstein, who as a fundamental element in a particular principle of relativity.
Evolution of the theory of relativity
The ancient Greeks began to wonder about nature, its order (cosmos) and the possibility of the existence of principles and laws of nature. Almost all the ancient philosophers, including Heraclitus, Parmenides, Zeno, Leucippus, Democritus, Plato and Aristotle, dealing with issues that are at least partly related to what is now called physics, the word has Greek origins and which represents "the things of nature." In Aristotle's physics are those that could be regarded as the first theory, in the modern sense, on the motion, although he is not a precursor of the principle of inertia, one can already recognize in his writings, some thematic still present. Some scholars have found there relativistic intuitions.
Modern science begins with the fundamental assumption, due to Galileo Galilei, the laws of physics have the same form with respect to any reference system is adopted which is worth the principle of inertia. This assumption was established in 1609, is now called the principle of Galilean relativity, which is still valid. It is based on Galileo's great insight in the composition of motions, and then the law of the sum of velocities: if two observers are in relative motion between them and each of them moves with consistency, so that the relative velocity is constant, will measure spaces different compared to the same event, but the "form" of their comments is the same as algebra. Still, nothing is said about the timing.
The concept that time is linked to the reference system is the proper and original contribution of Albert Einstein. In fact, when Newton, reading and studying carefully is the Dialogue on the Chief World Systems, is the Discourses on a New Science, interpreted the original insights in these geometrically in the writings of Galileo, the assimilated and made his own, thus giving rise to the mathematical form of mechanics and physics, he faced the principle of relativity and it became manifest that its adoption would involve so need a reference in which the first law of motion (Galileo's law of inertia) were in full force. The real problem however was and still is where to place the reference system: solved the dilemma by asserting that all the spaces for were references to an absolute space, the only existing unchanged and unchangeable, and the immutability of absolute space was nothing but the expression of the existence of an absolute time, which flows uniformly, pervading all space overall.
Newton's solution was brilliant and it became a paradigm that will last for centuries. Even Galileo, however, with his attempts to measure the speed of light terrestrial, expressed doubts unresolved at the time about how we should understand the principle of relativity and the principle of inertia so closely related to it. These doubts remained dormant, overshadowed by the splendor of the great success of Newtonian mechanics, until 1905.
With the advent of Maxwell's equations, the Lorentz transformations, and finally the theory of relativity Einstein is not the concept, which had been taken for granted, of absolute time. The restricted theory assumes that if the speed of light is constant then the time and space are variables. Time and space are linked together to form what is called space-time. When you are moving relative to a reference system time slows down and the mass increases increasingly as one approaches the speed of light. From here we deduce the reason why the theory of relativity says that you can not exceed or even reach the speed of light, time would stop and the mass would become infinite. General relativity postulates equality instead of gravitational mass and inertial mass, and derive from the "shape" of spacetime, ie its general metric.
It says "theory" of relativity theory, not because it is a simple yet to be confirmed, but simply because that is the name given at birth and since then has never been changed. Although it has limitations, since it considers the matter and still leave out the spacetime and quantum mechanics, remains one of the most precise theory ever tested experimentally.
Galilean theory with classical physics was born from the mathematical point of view, is represented by a system of equations linking the coordinates of a reference system with those of a second reference system that moves with constant velocity v with respect to it. The classical transformations are: Galilean relativity, the relativity of Galileo and Newton-Galilean transformation.
Two observers, who must communicate with each other, producing two different positions for the same object that is moving at a given location. Both OI and OII observers who study the motion of a single point P simultaneously determine the position of observer and the other P, PI (OI distance between the observer and the point P) and PI-II (distance between OI and OII) for OI and PII (OII and distance between the point P) and PII-I (distance between the two observers) for OII. Since the Euclidean space is considered, they know that
PI - II = - PII - The
The relationship between the two measures is:
PI = PII + PI - II
or
PII = PI + PII - The
and then both, using the its measures, are able to calculate what the other was measured. It can also do one of two observers make measurements and send another to the calculations. If the observers determine the position of P at different times of the time sequence are then able to determine the position vector of P as a function of time based on the following report
PI (t) = PII (t) + PI - II (t )
The same remarks carried out on the floor you can reproduce in space.
order to relate the two determinations, they must be performed at the same instant. The two observers must then exchange a sign to agree on when to take the measurement and the signal must propagate instantaneously (ie with infinite speed). On the contrary, if the signal should be transmitted with finite speed and note the two observers before walking away from each other, to go and perform their measures, they can synchronize their watches, but you can assume that the movement watch does not alter the timing or pace of the clocks themselves (assuming that the clocks are of the same bill), which can be exchanging test signals, but it still gets a measure "not correct", that is in contradiction with the concept of absolute time.
Galileo was clear the problem, said the attempt to measure the speed of light, only it was based on a terrestrial distance of about 30 km, the distance between two hills in Tuscany, one of which he, with an assistant on the other Hill would have to measure time of propagation of light of a lantern, first covered with a cloth and then explore briefly, the beating of your wrist in this condition could not even hear two beats of his wrist that had already come to light from Galileo deduced that the speed was extremely high, but in his heart was ready to swear it was over. You could then ignore the propagation delay of the signal.
This allows the performance of synchronous measures. This is the nearest of the relativity of Galileo, very valuable in common situations in which the speeds involved are well below the speed of light.
Galilean theories of everything good in the field of mechanics, dynamics and kinematics, have however not valid in the fields of physics such as electromagnetism, in which phenomena and processes involved with speeds comparable to the speed of light in these situations it becomes necessary to measure physical quantities in other inertial systems other than their own, apply the Lorentz transformations, discovered by Albert Einstein in 1905. They are also valid only for speeds small compared to the speed of light, when Einstein's relativistic effects are small compared to the amount at stake. According to the physical
Leonardo Ricci, Galilean relativity was known before its formulation, at least in general principles, related to the relativity of space. In support of his hypothesis, Ricci cites Dante Alighieri. Hell in Canto XVII, namely in verses 115-117, the poet writes:
"He goes very slowly noticing;
Wheels and descends, but not me n'accorgo
except that al viso e di sotto mi venta»
In un articolo pubblicato su Nature nel 2005, Ricci fa notare come Dante fosse ben consapevole della visione scientifica del mondo suo contemporaneo; senza di essa non avrebbe potuto scrivere la sua opera. Di passaggio, Ricci rileva che fu proprio Galileo, profondo conoscitore della Divina Commedia, a fornire una prima stima del diametro del girone, in circa 60 chilometri. Galilei si basò su due indicazioni precise (verso 9 del canto XXIX e ai versi 86-87 del canto XXX). Aggiunge Ricci: «Un fisico contemporaneo può dimostrare che, date queste dimensioni e qualunque sia la velocità, la forza fittizia centrifuga avvertita dal passeggero risulterebbe molto più piccola della forza superficiale dovuta the apparent wind: no force of this kind is mentioned in the narrative. Although such reasoning goes beyond those individuals who had knowledge of the Middle Ages, Dante, however, had sensed that his motion was in fact straight: he indicates the direction, by splitting the vector that describes the apparent wind in the two horizontal components ("the face ") and vertical (below).
Critique of Galilean relativity
In late 1800, Ernst Mach, and several others, including Hendrik Lorentz, clashed with the limitations of the Galilean relativity, can not be used for electromagnetic phenomena. Einstein is thus faced with two different transformations: those of Galileo, mechanism is valid in Lorentz, valid for electromagnetism but without a convincing theoretical support. The situation was very unsatisfactory.
PARADOX: A paradox
, paratroopers from the greek (against) and doxa (opinion), it is something that defies conventional wisdom: it is, in fact (according to the definition given by Mark Sainsbury) of
"a conclusion apparently unacceptable, which is derived from apparently acceptable premises via apparently acceptable reasoning. "
In philosophy and economics the term paradox is used as a synonym of antinomy. In mathematics, we tend to distinguish the concept of paradox, which consists of a proposition perfectly demonstrated, but far from the intuition, the concept of antinomy, which consists of a real logical contradiction.
History
main supporters of the matter was Herbert Dingle, English philosopher. Despite having received numerous logical refutations of Einstein and Bohr, he continued to write to newspapers, and when the latter began to refuse publication, spoke of a plot against him. Statement of the paradox
Consider a spaceship from the Earth in the year 3000; that maintaining a constant speed v reaches the star Wolf 359, 8 kilometers away light years from our planet, and that just arrived, reversed course and returns to the Earth, speed always v. Di una coppia di fratelli gemelli, l'uno salga sull'astronave, mentre l'altro rimanga a Terra.
Volutamente, nei calcoli trascuriamo per semplicità l'accelerazione e la decelerazione della navetta, anche se, per portarsi a velocità relativistiche in tempi brevi, occorrerebbero accelerazioni insostenibili per l'uomo e per la nave.
Supponiamo che v sia di 240.000 km/sec, cioè v = 0.8 c. Per questa velocità si ha:
per cui, secondo la teoria della relatività ristretta, nel sistema in movimento il tempo scorre al 60% del tempo nel sistema in quiete. Quindi:
Nel sistema di riferimento della Terra, l'astronave percorre 8 anni luce in 10 anni nel viaggio forward, and it employs many in the return trip: it then returns to Earth in 3020. On the ship, however, time flows at 60% of the time on Earth, according to the clock of the astronaut and then the trip takes 6 years for the outward and the same for the return: on arrival, therefore, the timing of ' ship is the year 3012. The brother left on Earth is therefore, after the journey, eight years older than his twin.
In the frame of the ship, due to the relativistic contraction of lengths, the distance between Earth and Wolf 359 is shortened to 60%, ie, at 4.8 light years at a rate of 0.8 c, are used then, according to ' watch of the ship, 6 anni per l'andata e 6 per il ritorno, coerentemente con quanto calcolato nel sistema di riferimento della Terra. Ma, poiché in questo sistema di riferimento è la Terra a muoversi, è il suo orologio che va al 60% del tempo dell'astronave: quando l'astronave fa ritorno, sulla Terra sono trascorsi solo 7.2 anni, perciò non è l'anno 3020, ma il 3007, ed è il fratello a bordo dell'astronave ad essere di 4.8 anni più vecchio.
Paradossi di Zenone
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I paradossi di Zenone ci sono stati tramandati attraverso la citazione che ne fa Aristotele nella sua Fisica. Zenone di Elea, discepolo ed amico di Parmenide, per sostenere l'idea del maestro, che la realtà è consists of a unique and immutable, proposed a number of paradoxes that show, strictly speaking, the impossibility of multiplicity and motion, despite the appearances of everyday life.
Zeno's arguments are perhaps the first examples of the method of proof known as reductio ad absurdum or indirect proof. Are also considered a prime example of the dialectical method, later used by the sophists and Socrates.
today is no longer given physical value to the arguments of Zeno, but their influence was very important in the history of philosophy and mathematics.
Zeno's paradoxes are also a useful exercise in logic, to reflect on how Construction of human reasoning. Remember two paradoxes against pluralism and four against the motion.
Paradoxes against pluralism
first paradox
The first paradox, against the plurality of things, says that if things are a lot of them are both a finite and an infinite number: they are finite in that they are neither more nor less how many are endless and as between the first and second there is a third and so on.
Second paradox
The second paradox instead argues that if these units do not have size, the things they have not made up in size, while if the units have a certain size, things made of endless drive will have an infinite magnitude.
Gemini and curved space
The famous twin paradox is based on the fact that the two twin on the ship and that part of the twin who stays still appear symmetrical but in reality they are not, why go back to the astronaut twin should accelerate, thereby losing the quality of the inertial system. If the universe were bent on itself, that would be hypothetically possible from a point and going forward we would find, after going through all the Universe, the very point, what would happen if the astronaut twin compiesse this long journey in motion constant speed and found himself at the same point without having accelerated? Returning to the Earth who would be older? (Of course both would die before the journey can be completed but we admit that human life is very long ...)
according to Einstein relativity with Albert Einstein's theory of relativity was a further development and now we are inclined to associate to this theory the name of German physicist. His theory is composed of two different mathematical models, which go under the name:
Special relativity General relativity Special relativity
relativity, also called special relativity, was the first to be made by Einstein, with the ' article "Zur Elektrodynamik bewegter Körper (Electrodynamics of Moving Bodies), 1905, to reconcile the principle of Galilean relativity with the equations of electromagnetic waves.
Prior to that end, several theories were proposed which were based on the existence of a means of propagation electromagnetic waves, called ether, but no experiment was able to measure the speed of an object relative to the ether. In particular, with the Michelson-Morley experiment had shown that the speed of light is constant in all directions, regardless of the motion of the Earth, thus reflecting the so-called "ether wind".
Einstein's theory then discards the concept of ether, which today is no longer used by physicists, even if informally, there is talk of light to indicate the space in which electromagnetic waves propagate.
relativity examines what happens when observers move relative to each other but does not take into account the effects of the gravitational field that will instead be introduced in the theory of general relativity. It accepts the principle of Galileo under which it is not possible to discern whether an observer is in motion with respect to another if the target system will take two observers, given that space is homogeneous and isotropic. The theory is based on two assumptions:
The laws of physics are the same for all observers in inertial motion.
The speed of light in vacuum is constant in any frame of reference
general relativity theory of general relativity was presented as a series of readings at the Prussian Academy of Sciences, from November 25, 1915, after a long period of preparation . There is controversy regarding the publication of a vintage field equations between the German mathematician David Hilbert and Einstein, but some documents with some confidence ascribe primacy to Einstein.
The foundation of general relativity is the assumption, known as the principle of equivalence, that acceleration is indistinguishable from the effects of a field gravity, and therefore that the inertial mass is equal to the gravitational mass. Using the tensor calculus, Einstein was able to determine the structure of spacetime, starting from three simple assumptions of special and general relativity.
While proving extremely accurate over time, general relativity is a classical theory, a theory of the continuum, as developed independently by quantum mechanics and have never been reconciled with it, as well as quantum physics, but may include special relativity, does not take account of general relativity.
It may be assumed that if Einstein had been less skeptical about the mechanics Quantum, which had also contributed to the history of physics would have been different. In general relativity limits are due mainly to the treatment of singularities and states of matter in which the gravitational interactions and quantum come to have the same order of magnitude. Among the changes proposed by this theory, the most famous and investigated are string theory and loop quantum gravity.
relativity in an absolute sense is a difficulty, since it refers to the absolute void, which in reality does not exist, since even the single attraction that changes the speed of the bodies through the mass, in fact, actually a ray of light that falls perpendicular to a liquid at low light resistance deviates, understand that doing so decreases its kinetic rate.
E = mc ²
The formula E = mc ², his theory of relativity is one of the most famous mathematical formulas and probably the most famous of all, this is thanks to its extreme elegance and simplicity. In essence, the formula takes into account:
E = energy m = mass
c = speed of light
also becomes easy to understand how mass and energy are equivalent and how they are two sides of same coin, is essentially the mass highly concentrated energy. It is this equivalence between mass and energy explains how, by concentrating a large amount of energy can create mass, and so on, as well as you can get a huge amount of energy from a small mass.
A practical application of this concept, you can see the takeoff of the Space Shuttle. When off, all the fuel used only about a gram becomes energy, everything else is converted into smoke and combustion products. Using nuclear energy yield increases, but in an ordinary atom bomb, for example, is converted into energy only about 0.5% of the total mass of fissile material. If it were possible to convert the entire mass into energy, the need energy of Earth's inhabitants would undoubtedly solved: one kilogram of matter corresponds to 25 billion kWh (25,000 GWh). This enormous amount of energy equivalent to the monthly consumption of electricity in Italy (which in 2004 was an average of 25,374 GWh). The mass-energy equivalence has demonstrated its awesome power with atomic bombs. The Hiroshima bomb was 13 kilotons, equivalent to 54.6 trillion joules (13 x 4.2 x 10 ¹ ² J), but this energy is only 60% of what was released from the conversion of one gram of matter, which amounted to 90,000 billion joules.
The formula expressed in any reference system energy total stop of a particle.
If the body is in motion, the correct formula (and complete) is:
with.
For a body starting from rest is that v = 0 and γ = 0, and find that particular case.
The mass is here understood as a relativistic mass of the body, to distinguish from the inertial mass m The inertial mass can be considered a property of the body, as in an inertial motion, it remains unchanged. In an inertial motion, do not be a difference of gravity, speed, direction and orientation of motion are unaffected. In contrast a change in the gravitational coimplica a variation of the velocity vector: If you change the speed the body is its mass anmodificare the external field, by contrast, a significant variation in the gravitational environment can clearly modify the intensity and path of motion.
The concept of relativistic mass can be understood by imagining a grave of one kg of weight, which falls to the ground at a speed of 100 km / h does the same damage of a grave of a ton of weight falling from a few inches height. The power of the damage depends on the momentum, mass and velocity factors. The concept of mass reativistica, extends the concept of gravitational mass, as Einstein's theory generalizes the gravity of Newton.
With this in mind it makes sense to define a mass that depends on the speed (and it would be the product of its mass, inertia, for the term γ):
m = m (v), and in particular that:
, and that:
.
In other words, the relativistic mass is not a property independent of the speed v, but grows with it. When speed is approximate to that of light, the mass of the body tends to infinity.
To accelerate a body and a mass different from zero, aside from the speed of light would require infinite energy. This would be necessary not only to overcome the speed of light, but to get at least a small amount of what you want, an infinitesimal.
A second reason for the qule can not be overcome by the speed of light, derived from the equation explaining the contraction / expansion of space-time in special relativity.
assumptions about the origins and authorship
The genesis of the theory of relativity, as it was developed by Albert Einstein, is surrounded by a sort of mystery that comes back to surface periodically, generating discussion in the scientific world. In the eighties a group of scholars brought forward in an Italian newspaper, Il Giornale di Vicenza, a long fight to support an argument that Einstein's famous equation, E = mc ², was made to derive directly the study hypothesis of ether in the life of the universe, presented in 1903 at the Royal Institute of Sciences, Letters and Arts in Schio (VI) by Olinto De Pretto (1867-1921). De Pretto, a graduate in agricultural, industrial occupation but passionate about physics and geology, but never did not claim authorship - even in a nutshell - the famous formula. In 1999, the "De Pretto Case" has found new life, however, by Umberto Bartocci, professor of mathematics at the University of Perugia, who narrated his vision of the facts in the pamphlet - also received with skepticism by 'academic environment - Albert Einstein and Olinto De Pretto, the true history of the world's most famous formula. But Einstein, based on the assumptions made in the time around his work, may have been assisted in its analysis on general relativity by another Italian: the mathematician Gregorio Ricci Curbastro (1853-1925) who devised their own special tensor calculations. The curvature of spacetime
A layman's famous illustration of the curvature of spacetime caused by mass, represented here by the Earth.
The theory states that spacetime is more or less curved by the presence of a mass and another smaller mass moves then the effect of this curvature.
Often, it portrays the situation as a ball that deforms the floor of the pool with his weight, while another ball is accelerated by this deformation of the plan and in fact drawn from the first.
This is just a simplification to the size shown here, as is to be warped space-time and not only the spatial dimensions, which is impossible to depict and difficult to design.
The only situation that we can correctly portray is that of a universe in a spatial and a temporal dimension. Any material point is represented by a line (world line), not a point, which provides its position all the time: that is stationary or in motion will only change the slope of this line. Now we turn to this universe using the third dimension: what was once the line describing a point, it is now a surface.
on a curved surface that is non-Euclidean geometry, in particular, can draw a triangle whose angles do not provide added 180 and is also possible to proceed in the same direction, returning after a certain time to the starting point.
description of gravitation
Every particle of matter moves at constant speed along a curve, called geodesic that at any time (ie locally) can be considered straight. Its speed is the ratio between the spatial distance traveled and the proper time, where time is right that measured in the reference of the particle, while the spatial distance depends on the metric that defines the structure of space-time. The curvature determines the actual shape of geodesics, and then the body follows a path over time.
In other words, a free body moves in space-time along a geodesic always in the same way as in classical mechanics a body is not subjected to forces moving along a straight line. If the structure of space-time at that point is flat, the geodesic will be just a straight line, otherwise it will take different forms, but the body will follow anyway. In this way, the gravity is to be incorporated into the structure of space-time.
Once again, it should be Note that this curvature is applied not only to the spatial coordinates, but also to that time, this leads to significant practical difficulties in groped to imagine such a surface in 4 dimensions.
Fundamentals of the theory
Even electromagnetic pulses are deflected by the gravitational force on the theory of relativity. In the image a graphical representation of a signal from a probe that is deflected by the gravity of the Sun reaches Earth
In the presence of accelerated systems (or, which is the same systems under the influence of gravity), we can defined as areas with local inertial reference and for short periods. This corresponds to approximated with a flat surface that would be a curved surface on a large scale. In such situations still apply Newton's laws.
Now the principle of equivalence states that there is no local experiment to distinguish between a free fall in a gravitational field and uniform motion in the absence of field (Einstein's lift)
Mathematically, Einstein described space-time as a pseudo Riemann-space to 4 dimensions, and its field equation linking the curvature at a point in the energy tensor at that point, as such a tensor dependent on the density of matter and energy.
The field equation given by Einstein is not the only possible, but is distinguished by the simplicity of the coupling between matter and energy and curvature.
This equation contains a term Λ, called the cosmological constant, introduced by Einstein to allow a static universe. In ten years later, Hubble observations showed that the universe is (or appears) in the expansion and the cosmological term was omitted (Einstein himself thought it his introduction the biggest mistake he had committed in life). But it seems that Einstein was sentenced to be right even when wrong: as it happened to quantum theory, which helped to establish certain principles and then feel bad (like the Heisenberg uncertainty principle), even the cosmological constant has been rehabilitated. In 1998, observation of red shift of distant supernovae, has forced astronomers to use a cosmological constant to explain the accelerating expansion of the Universe.
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