published on 8 January 2014 in space

The crisis of classical physics

From classical physics to modern physics
“Between the late 19th century and early 20th century some experimental observations challenge the classical conception of the physical world: on one hand the behaviour of light respect to the different reference frames moving relative to one another, on the other the first insights regarding the particle structure of the energy released or absorbed in the form of radiation by various bodies. It is in the 20th century that these queries, and many others that derived from them, find their answers, in either the Theory of Relativity or in Quantum Mechanics…”. These words were spoken by the Italian physicist Edoardo Amaldi in 1955 to summarise the extraordinary events that revolutionised scientific thought in the 20th century, and that marked the transition from classical to modern physics.

Classical physics
Up until the year 1900, classical physics was able to explain all the phenomena on the basis of principles that were simple but fundamental. The most important of these, on which all the theories of classical physics are based, assumes that space and time are absolute physical quantities, in other words they are the same for all observers.
Considering time as an absolute physical quantity allows us to define a causal relation, in other words, to understand with absolute precision how what happens initially affects what happens subsequently. Moreover, time is totally independent of space.
Before Galileo’s formulation of mechanics in the 17th century, absolute space allowed the distinction between a stationary object and a moving one and moreover every object had a definite velocity.
In his Dialogue Concerning the Two Chief World Systems (1632) Galileo introduced a new concept of space (Galilean relativity or invariance) according to which it is not possible to distinguish whether an object is stationary or moving in uniform linear motion (motion along a straight line at constant velocity). As a consequence, there is no absolute velocity, but there are frames of reference, called inertial frames, in which the laws of mechanics are observed.

The crisis of classical physics: Einstein’s Theory of Relativity
In the 19th century, Maxwell’s four equations, formulated by the Scottish physicist and mathematician James Clerk Maxwell, contradicted Galilean relativity. The equations proved clearly how electricity, magnetism and light, which until then had been treated as unrelated phenomena, were actually demonstrations of the same entity: the electromagnetic field. By analysing the equations, Maxwell was able to deduce a fundamental result: light travels at a constant speed which is represented by the letter c. The result was very important and, above all, it was not consistent with Galilean relativity. It claimed that the speed of light is absolute.
For a long time scientists attempted to preserve the concept of Galilean relativity, trying to prove that there was a particular inertial frame of reference for which Maxwell’s equations held true. In other words, they attempted to show that it was possible to accept both theories.
Einstein put an end to the debate with his Special Relativity Theory formulated in 1905, in which he claimed that time and space are not absolute quantities and are intrinsically bound to form a four-dimensional space-time fabric. Einstein replaced Galilean transformations, the equations that allowed the calculation of space, time and speed depending on the observer, with Lorentz’ transformations. Einstein postulated that the speed of light in a vacuum is the same for all observers regardless of the fact that they are stationary or in movement respect to the light source.

GPS and Relativity
The Global Positioning System, more commonly known by the acronym GPS, is an essential tool for orientation today. Its great precision could not have been achieved using Galilean relativity. In fact, the GPS is based upon Einstein’s Special and General Theories of Relativity.
The GPS allows us to determine with high precision the distance between two points by means of various satellites in orbit around the Earth that transmit signals which are detected by receivers on the surface of the Earth. The GPS consists of a constellation of 27 satellites orbiting at an altitude of about 20,000 kilometres from the ground and four monitor stations on Earth that check the state of the satellites and correct their clocks and orbital positions.

A representation of the GPS constellation of satellites. Source: http://www.gps.gov

A representation of the GPS constellation of satellites. Source: http://www.gps.gov

The GPS works on a simple principle. Signals from at least 4 satellites are sent a to a receiver; they contain information regarding the satellites’ position at the exact time of transmission (with an accuracy measured in nanoseconds, 10-9 seconds). The GPS receiver calculates the distance from each satellite by using triangulation and determines its own location.
The GPS system is based upon the fundamental postulate of the Theory of Relativity, i.e. the fact that the speed of light is constant regardless of the motion of the satellite and of the receiver. However, some relativistic corrections must be taken into account. In fact, according to the Special Relativity Theory, since the satellites are in motion with respect to the receiver, their clocks will tick more slowly; however, according to the General Theory of Relativity, a gravitational field modifies both the rate at which the clocks tick and the propagation of radio signals. Taking these corrections into account, it is possible to determine the receiver’s position accurate to 10 m for a distance of 20,000,000 m; if uncorrected, errors of the order of thousands of metres could be made, which would render the GPS system useless.

Quantum mechanics
Quantum mechanics was born around 1900 when the German physicist, Max Planck solved the problem of black body radiation postulating that energy comes in discrete units. Electromagnetic radiation is emitted or absorbed by atoms only in discrete amounts, called quanta. Quantum mechanics rapidly replaced the classical laws of mechanics at a microscopic scale, introducing a viewpoint in contrast to the classical one, according to which physics is able to accurately predict the evolution of the Universe once the speeds and positions of all the particles contained in it have been determined. Quantum mechanics replaces this deterministic character of classical physics with predictions governed by the uncertainty principle.
In 1927, when he was only 26 years old, the German physicist Werner Karl Heisenberg, Nobel prize winner in Physics in 1932, formulated the well-known Uncertainty Principle according to which the position of a particle and its momentum cannot be simultaneously known with precision. In other words, the more precisely one property is measured, the less precisely the other can be measured.
As a result, it is always possible to formulate general statistical laws capable of predicting phenomena, but the physical properties related to single particles present an ineradicable uncertainty. According to Heisenberg, quantum mechanics establishes the final failure of causality; in fact, it is not possible to extrapolate what will happen in the future based on knowledge of the present because of the simple fact that “we cannot know all determining elements of the present”.

God does not play dice
Many well-known physicists disagreed with quantum mechanics, the most important of which was Albert Einstein. In short, Einstein asserted that quantum mechanics was an incomplete theory of the world and that there were some “hidden variables” which, once discovered, would have enabled a deterministic description, even of phenomena at microscopic scales.
In a letter dated 4/12/1926, addressed to the physicist Max Born, Einstein expressed his disagreement with quantum mechanics: “Quantum mechanics is certainly imposing, but an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ‘old one’. I, at any rate, am convinced the He does not play dice”.
Einstein never modified his opinion, and stated that he believed in the “possibility of a model of reality – that is to say, of a theory which represents things themselves and not merely the probability of their occurrence”. It must be said that, though he was a staunch critic of this theory, Einstein utilised and, to a certain point, contributed to the quantum theory proposing the correct physical explanation of the photoelectric effect.

The photoelectric effect
The photoelectric effect is a phenomenon which can be completely explained with quantum mechanics. It consists in the ejection of electrically charged particles from an object upon exposure to electromagnetic radiation. In practice, the energy transported by light incident on a metal surface brings about to the ejection of electrons (called photoelectrons).

Image that depicts the ejection of an electron from a metal surface due to the interaction with an incoming photon.  Source: http://www.matefilia.it

Image that depicts the ejection of an electron from a metal surface due to the interaction with an incoming photon. Source: http://www.matefilia.it

The discovery of the photoelectric effect had a fundamental role in the crisis of classical physics because it demonstrated that electromagnetic radiation had both a wave-like nature and, in some experiments, also particle-like properties. This behaviour came to be known as the wave-particle duality.
The photoelectric effect had been noticed as far back as 1880. However, the classical wave theory predicted that the energy of the ejected electrons would rise with an increase in the intensity of the incident light beam. In 1905 Albert Einstein explained the photoelectric effect by postulating that light travels in packets of light-quanta, now called photons, whose energy is directly proportional to the frequency of the radiation. When the light-quanta hit a metallic surface, they transfer a part of their energy to the free electrons of the conductor, causing their emission. The photon behaves just like a particle and the energy of the emitted electron depends only on the incoming photon’s energy.

Photoelectric cells
The functioning of photoelectric cells that are used everywhere nowadays, from the automatic opening and closing of gates to the sliding doors of elevators, can be explained by the photoelectric effect. The cells are a safety device that prevents people from being crushed in doors. How do they work? When a person moves in front of the beam of light produced by one of the cells, the beam does not reach the light-sensitive surface it was aimed on. The consequence is an interruption of the flow of electrons emitted. Specific circuits detect this change and respond by immediately opening the doors.

Wave or particle?
While experimental observations such as those regarding the photoelectric effect serve to clearly demonstrate the corpuscular nature of light, those regarding diffraction demonstrate its undulatory nature. In the 20th century this curious behaviour of light seemed contradictory and highlighted the dual nature of electromagnetic waves. This behaviour was defined wave-particle duality, which states that electromagnetic radiation can behave like a wave in phenomena such as interference and diffraction, but can exhibit particle-like behaviour, though massless, exchanging energy and momentum with other bodies which have mass. Moreover, quantum mechanics demonstrated that this duality could also be observed in particles which have mass.
Neils Bohr summarised this behaviour in 1927 in his principle of complementarity according to which the undulatory and corpuscular behaviour are never exhibited simultaneously in one experiment. If an experiment is carried out to highlight one aspect, it will be impossible to observe the other. The act of observing a phenomenon perturbs the phenomenon itself; in fact, it is impossible to talk about the behaviour of a physical object without taking into account the measuring instrument. However, the two aspects, wave-like and particle-like, are complementary because in order to obtain a complete descripton of a phenomenon, both are essential.

Agreement between classical and modern physics
For many centuries classical physics was able to explain nature perfectly. However, it is not to be considered totally outdated and useless today. In fact, as long as sub-atomic particles are excluded from the field of study, classical mechanics yields results that are in agreement with quantum mechanics, while for low speeds, it is in agreement with the Theory of Relativity.

Edited by Simona Romaniello. Astrophysicist and science populariser, Ms Romaniello is responsible for formation and development and the installation of museum exhibits for the Turin Planetarium.

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