A matter wave clock is a type of

clock A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and t ...

whose principle of operation makes use of the apparent wavelike properties of matter.

Matter wave Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wav ...

s were first proposed by

Louis de Broglie Louis Victor Pierre Raymond, 7th Duc de Broglie (, also , or ; 15 August 1892 – 19 March 1987) was a French physicist and aristocrat who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis, he postulated the wave n ...

and are sometimes called de Broglie waves. They form a key aspect of

wave–particle duality Wave–particle duality is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. It expresses the inability of the classical concepts "particle" or "wave" to fully describe th ...

and experiments have since supported the idea. The wave associated with a particle of a given mass, such as an

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...

, has a defined

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is ...

, and a change in the duration of one cycle from peak to peak that is sometimes called its ''Compton periodicity''. Such a matter wave has the characteristics of a simple clock, in that it marks out fixed and equal intervals of time. The twins paradox arising from

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...

's theory of

relativity Relativity may refer to: Physics * Galilean relativity, Galileo's conception of relativity * Numerical relativity, a subfield of computational physics that aims to establish numerical solutions to Einstein's field equations in general relativit ...

means that a moving particle will have a slightly different period from a stationary particle. Comparing two such particles allows the construction of a practical "Compton clock".Lan, S-Y et al.; "A Clock Directly Linking Time to a Particle's Mass", ''Science'' 1 February 2013: Vol. 339 no. 6119 pp. 554–557

Matter waves as clocks

De Broglie proposed that the frequency ''f'' of a matter wave equals ''E''/''h'', where ''E'' is the total energy of the particle and ''h'' is Planck's constant. For a particle at rest, the relativistic equation ''E''=''mc''² allows the derivation of the ''Compton frequency'' ''f'' for a stationary massive particle, equal to ''mc''²/''h''. De Broglie also proposed that the wavelength ''λ'' for a moving particle was equal to ''h''/''p'' where ''p'' is the particle's momentum. The period (one cycle of the wave) is equal to 1/''f''. This precise ''Compton periodicity'' of a matter wave is said to be the necessary condition for a clock, with the implication that any such matter particle may be regarded as a fundamental clock. This proposal has been referred to as "A rock is a clock."Sanders, R.; "A rock is a clock: physicist uses matter to tell time", ''UC Berkeley News Center''

(retrieved 4 July 2014)

Applications

In his paper, "Quantum mechanics, matter waves and moving clocks", Müller has suggested that "The description of matter waves as matter-wave clocks ... has recently been applied to tests of general relativity, matter-wave experiments, the foundations of quantum mechanics, quantum space-time decoherence, the matter wave clock/mass standard, and led to a discussion on the role of the proper time in quantum mechanics. It is generally covariant and thus well-suited for use in curved space-time, e.g., gravitational waves."Müller, H.; "Quantum mechanics, matter waves, and moving clocks", "To be published in the proceedings of the International School of Physics "Enrico Fermi" 2013"
arXiv:1312.6449v1
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Implications

In his paper, "Quantum mechanics, matter waves and moving clocks", Müller has suggested that "

he model He or HE may refer to: Language * He (pronoun), an English pronoun * He (kana), the romanization of the Japanese kana へ * He (letter), the fifth letter of many Semitic alphabets * He (Cyrillic), a letter of the Cyrillic script called ''He'' i ...

has also given rise to a fair amount of controversy. Within the broader context of quantum mechanics ... this description has been abandoned, in part because it could not be used to derive a relativistic quantum theory, or explain spin. The descriptions that replaced the clock picture achieve these goals, but do not motivate the concepts used. ... We shall construct a ... description of matter waves as clocks. We will thus arrive at a space-time path integral that is equivalent to the Dirac equation. This derivation shows that De Broglie's matter wave theory naturally leads to particles with spin-1/2. It relates to Feynman's search for a formula for the amplitude of a path in 3+1 space and time dimensions which is equivalent to the Dirac equation. It yields a new intuitive interpretation of the propagation of a Dirac particle and reproduces all results of standard quantum mechanics, including those supposedly at odds with it. Thus, it illuminates the role of the gravitational redshift and the proper time in quantum mechanics."

Controversy

The theoretical idea of matter waves as clocks has caused some controversy, and has attracted strong criticism.

Atom interferometry

atom interferometer An atom interferometer is an interferometer which uses the wave character of atoms. Similar to optical interferometers, atom interferometers measure the difference in phase between atomic matter waves along different paths. Atom interferometers h ...

uses a small difference in waves associated with two atoms to create an observable interference pattern. Conventionally these waves are associated with the electrons orbiting the atom, but the matter wave theory suggests that the wave associated with the wave–particle duality of the atom itself may alternatively be used. An experimental device comprises two clouds of atoms, one of which is given a small "kick" from a precisely-tuned laser. This gives it a finite velocity which, according to the matter wave theory lowers its observed frequency. The two clouds are then recombined so that their differing waves interfere, and the maximum output signal is obtained when the frequency difference is an integer number of cycles. Experiments designed around the idea of interference between matter waves (as clocks) are claimed to have provided the most accurate validation yet of the

gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy ...

predicted by

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. ...

. A similar atom interferometer forms the heart of the Compton clock. However, this claimed interpretation of the interferometry function has been criticised. One criticism is that a real Compton oscillator or matter wave does not appear in the design of any actual experiment.Pease, R.; "The time? About a quarter past a kilogram", ''Nature.com news'', 201

/ref> The matter wave interpretation is also said to be flawed.Wolf, P. et al.; "Testing the Gravitational Redshift with Atomic Gravimeters?" (2011) Wolf, P. et al.; "Reply to the comment on: 'Does an atom interferometer test the gravitational redshift at the Compton frequency?'" (2012)

Compton clocks

A functional timepiece designed on the basis of matter wave interferometry is called a Compton clock.

Principles of operation

The frequency of the wave associated with a massive particle, such as an atom, is too high to be used directly in a practical clock and its period and wavelength are too short. A practical device makes use of the

twin paradox In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. Thi ...

arising from the theory of

, where a moving particle ages more slowly than a stationary one. The moving particle-wave therefore has a slightly lower frequency. Using

interferometry Interferometry is a technique which uses the '' interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber o ...

, the difference or "beat frequency" between the two frequencies can be accurately measured and this beat frequency can be used as a basis for keeping time.

Measurement of mass

The technique used in the devices can theoretically be reversed to use time to measure mass. This has been proposed as an opportunity for replacing the platinum-iridium cylinder currently used as the 1 kg reference standard.

References

{{reflist Quantum mechanics Clocks Theory of relativity Fringe physics