Category Archives: Quantum Physics

In a different corner of the social media universe, someone left comments on a link to Tuesday's post about quantum randomness declaring that they weren't aware of any practical applications of quantum physics. There's a kind ofLife of Brian absurdity to posting this on the Internet, which is a giant world-spanning, life-changing practical application of quantum mechanics. But just to make things a little clearer, here's a quick look at some of the myriad everyday things that depend on quantum physics for their operation.

Computers and Smartphones

Intel Corp. CEO Paul Otellini show off chips on a wafer built on so-called 22-nanometer technology... [+] at the Intel Developers' Forum in San Francisco, Tuesday, Sept. 22, 2009. Those chips are still being developed in Intel's factories and won't go into production until 2011. Each chip on the silicon "wafer" Otellini showed off has 2.9 billion transistors. (AP Photo/Paul Sakuma)

At bottom, the entire computer industry is built on quantum mechanics. Modern semiconductor-based electronics rely on the band structure of solid objects. This is fundamentally a quantum phenomenon, depending on the wave nature of electrons, and because we understand that wave nature, we can manipulate the electrical properties of silicon. Mixing in just a tiny fraction of the right other elements changes the band structure and thus the conductivity; we know exactly what to add and how much to use thanks to our detailed understanding of the quantum nature of matter.

Stacking up layers of silicon doped with different elements allows us to make transistors on the nanometer scale. Millions of these packed together in a single block of material make the computer chips that power all the technological gadgets that are so central to modern life. Desktops, laptops, tablets, smartphones, even small household appliances and kids' toys are driven by computer chips that simply would not be possible to make without our modern understanding of quantum physics.

Lasers and Telecommunications

Green LED lights and rows of fibre optic cables are seen feeding into a computer server inside a... [+] comms room at an office in London, U.K., on Tuesday, Dec. 23, 2014. Vodafone Group Plc will ask telecommunications regulator Ofcom to guarantee that U.K. wireless carriers, which rely on BT's fiber network to transmit voice and data traffic across the country, are treated fairly when BT sets prices and connects their broadcasting towers. Photographer: Simon Dawson/Bloomberg

Unless my grumpy correspondent was posting from the exact server hosting the comment files (which would be really creepy), odds are very good that comment took a path to me that also relies on quantum physics, specifically fiber optic telecommunications. The fibers themselves are pretty classical, but the light sources used to send messages down the fiber optic cables are lasers, which are quantum devices.

The key physics of the laser is contained in a 1917 paper Einstein wrote on the statistics of photons (though the term "photon" was coined later) and their interaction with atoms. This introduces the idea of stimulated emission, where an atom in a high-energy state encountering a photon of the right wavelength is induced to emit a second photon identical to the first. This process is responsible for two of the letters in the word "laser," originally an acronym for "Light Amplification by Stimulated Emission of Radiation."

Any time you use a laser, whether indirectly by making a phone call, directly by scanning a UPC label on your groceries, or frivolously to torment a cat, you're making practical use of quantum physics.

Atomic Clocks and GPS

TO GO WITH AN AFP STORY BY ISABELLE TOUSSAINT A woman holds her smartphone next to her dog wearing a... [+] GPS system on its collar in La Celle-Saint-Cloud on July 1, 2015. The Global Positioning System (GPS) collar help owners to track their pets remotely. AFP PHOTO / MIGUEL MEDINA (Photo credit should read MIGUEL MEDINA/AFP/Getty Images)

One of the most common uses of Internet-connected smart phones is to find directions to unfamiliar places, another application that is critically dependent on quantum physics. Smartphone navigation is enabled by the Global Positioning System, a network of satellites each broadcasting the time. The GPS receiver in your phone picks up the signal from multiple clocks, and uses the different arrival times from different satellites to determine your distance from each of those satellites. The computer inside the receiver then does a bit of math to figure out the single point on the surface of the Earth that is that distance from those satellites, and locates you to within a few meters.

This trilateration relies on the constant speed of light to convert time to distance. Light moves at about a foot per nanosecond, so the timing accuracy of the satellite signals needs to be really good, so each satellite in the GPS constellation contains an ensemble of atomic clocks. These rely on quantum mechanics-- the "ticking" of the clock is the oscillation of microwaves driving a transition between two particular quantum states in a cesium atom (or rubidium, in some of the clocks).

Any time you use your phone to get you from point A to point B, the trip is made possible by quantum physics.

Magnetic Resonance Imaging

Leila Wehbe, a Ph.D. student at Carnegie Mellon University in Pittsburgh, talks about an experiment... [+] that used brain scans made in this brain-scanning MRI machine on campus, Wednesday, Nov. 26, 2014. Volunteers where scanned as each word of a chapter of "Harry Potter and the Sorcerer's Stone" was flashed for half a second onto a screen inside the machine. Images showing combinations of data and graphics were collected. (AP Photo/Keith Srakocic)

The transition used for atomic clocks is a "hyperfine" transition, which comes from a small energy shift depending on how the spin of an electron is oriented relative to the spin of the nucleus of the atom. Those spins are an intrinsically quantum phenomenon (actually, it comes in only when you include special relativity with quantum mechanics), causing the electrons, protons, and neutrons making up ordinary matter behave like tiny magnets.

This spin is responsible for the fourth and final practical application of quantum physics that I'll talk about today, namely Magnetic Resonance Imaging (MRI). The central process in an MRI machine is called Nuclear Magnetic Resonance (but "nuclear" is a scary word, so it's avoided for a consumer medical process), and works by flipping the spins in the nuclei of hydrogen atoms. A clever arrangement of magnetic fields lets doctors measure the concentration of hydrogen appearing in different parts of the body, which in turn distinguishes between a lot of softer tissues that don't show up well in traditional x-rays.

So any time you, a loved one, or your favorite professional athlete undergoes an MRI scan, you have quantum physics to thank for their diagnosis and hopefully successful recovery.

So, while it may sometimes seem like quantum physics is arcane and remote from everyday experience (a self-inflicted problem for physicists, to some degree, as we often over-emphasize the weirder aspects when talking about quantum mechanics), in fact it is absolutely essential to modern life. Semiconductor electronics, lasers, atomic clocks, and magnetic resonance scanners all fundamentally depend on our understanding of the quantum nature of light and matter.

But, you know, other than computers, smartphones, the Internet, GPS, and MRI, what has quantum physics ever done for us?

The rest is here:

What Has Quantum Mechanics Ever Done For Us? - Forbes

Quantum chemistry computer programs are used in computational chemistry to implement the methods of quantum chemistry. Most include the HartreeFock (HF) and some post-HartreeFock methods. They may also include density functional theory (DFT), molecular mechanics or semi-empirical quantum chemistry methods. The programs include both open source and commercial software. Most of them are large, often containing several separate programs, and have been developed over many years.

The following tables illustrates some of the main capabilities of notable packages:

Slater-type_orbital

"Academic": academic (no cost) license possible upon request; "Commercial": commercially distributed.

Support for periodic systems (3d-crystals, 2d-slabs, 1d-rods and isolated molecules): 3d-periodic codes always allow simulating systems with lower dimensionality within a supercell. Specified here is the ability for simulating within lower periodicity.

2 QuanPol is a full spectrum and seamless (HF, MCSCF, GVB, MP2, DFT, TDDFT, CHARMM, AMBER, OPLSAA) QM/MM package integrated in GAMESS-US.[13]

10 Through CRYSCOR Archived 2019-12-26 at the Wayback Machine program.

See the rest here:

List of quantum chemistry and solid-state physics software

Details

Posted: 10-Oct-22

Location: Albuquerque, New Mexico

Categories:

Physics: Applied

Sector:

Government and National Lab

Non-Profit

Work Function:

Postdoctoral Research

Required Education:

Doctorate

Additional Information:

Employer will assist with relocation costs.

What Your Job Will Be Like:

The Multiscale Fabrication Science & Technology Development Department, 5229, is seeking a Postdoctoral Appointee to perform experimental investigations of quantum and semiclassical devices supporting fundamental science projects in areas ranging from quantum information and sensing to radiation detection, characterization of novel superconducting materials, and neuromorphic computing.

On any given day, you may be called upon to:

Drive research in a defined area of interest as part of established, diverse teams of physicists, engineers, and material scientists.

Contribute significantly at the forefront of one of the following areas:

Applications in radiation detection. Microfabricated devices of interest include superconducting quantum bits (qubits), transition-edge-sensors, and single electron transistors. Cryogenic measurements will span a range of temperatures.

Applications in neuromorphic computing, particularly stochastic devices. Microfabricated devices of interest include tunnel diodes and single electron transistors. Room-temperature measurements will require high-speed data acquisition and statistical analysis.

Applications in novel materials, including superconductivity. Microfabricated devices of interest range from Hall bars to Josephson junctions.

We seek a self-motivated experimentalist to advance existing projects while advancing their career through peer-reviewed publications and presentations as well as internal and external interactions. While the primary technical responsibility will be device measurement, we encourage hands-on involvement with device modeling or device fabrication. A significant amount of coordination with other staff and technologists to meet the needs of the teams is required. In this highly collaborative environment excellent teaming and communications skills are a requirement for success.

Due to the nature of the work, the selected applicant must be able to work onsite 100% of the time.

Qualifications We Require:

PhD in physics, electrical engineering, or related field conferred within five (5) years prior to employment

Ability to acquire and maintain a DOE L security clearance

Qualifications We Desire:

Presentations at technical conferences or meetings

Experience performing original research, as demonstrated by a record of first-author publications in peer-reviewed journals

Experience with:

Cryogenic electrical transport measurements

High-speed device measurement

Devices used in radiation detection

Superconductivity and superconducting devices

Neuromorphic computing devices

Devices used in quantum information science or quantum sensing

Techniques used in superconducting or silicon device fabrication

Device modeling using technology computer aided design (TCAD)

About Our Team:

The Multiscale Fabrication Science & Technology Development Department leverages a diverse capability set to provide science and technology products to enhance Sandia's national security missions. The department includes a broad set of expertise including atomic physics, quantum information S&T, micro-optics, and electrochemistry. We provide solutions including atomic physics based sensors; microfabrication at the atomic scale, atomic level experimental setups, atom and ion trapping microelectronic devices, and electrochemical materials expertise. In addition to work for internal Sandia organizations, we have an established record of successful engagement, collaboration, and delivery to both internal and external customers. The department leverages strong relationships with the Microsystems Engineering Sciences and Applications (MESA) facility, the Center for Integrated Nanotechnologies (CINT), and other internal and external organizations to develop advanced solid-state electronic device technology.

About Sandia:

Sandia National Laboratories is the nations premier science and engineering lab for national security and technology innovation, with teams of specialists focused on cutting-edge work in a broad array of areas. Some of the main reasons we love our jobs:

Challenging work with amazing impact that contributes to security, peace, and freedom worldwide

Extraordinary co-workers

Some of the best tools, equipment, and research facilities in the world

Career advancement and enrichment opportunities

Flexible work arrangements for many positions include 9/80 (work 80 hours every two weeks, with every other Friday off) and 4/10 (work 4 ten-hour days each week) compressed workweeks, part-time work, and telecommuting (a mix of onsite work and working from home)

Generous vacations, strong medical and other benefits, competitive 401k, learning opportunities, relocation assistance and amenities aimed at creating a solid work/life balance*

World-changing technologies. Life-changing careers. Learn more about Sandia at: http://www.sandia.gov*These benefits vary by job classification.

Security Clearance:

Sandia is required by DOE to conduct a pre-employment drug test and background review that includes checks of personal references, credit, law enforcement records, and employment/education verifications. Applicants for employment need to be able to obtain and maintain a DOE L-level security clearance, which requires U.S. citizenship. If you hold more than one citizenship (i.e., of the U.S. and another country), your ability to obtain a security clearance may be impacted.

Applicants offered employment with Sandia are subject to a federal background investigation to meet the requirements for access to classified information or matter if the duties of the position require a DOE security clearance. Substance abuse or illegal drug use, falsification of information, criminal activity, serious misconduct or other indicators of untrustworthiness can cause a clearance to be denied or terminated by the DOE, resulting in the inability to perform the duties assigned and subsequent termination of employment.

EEO:

All qualified applicants will receive consideration for employment without regard to race, color, religion, sex, sexual orientation, gender identity, national origin, age, disability, or veteran status and any other protected class under state or federal law.

Position Information:

This postdoctoral position is a temporary position for up to one year, which may be renewed at Sandia's discretion up to five additional years. The PhD must have been conferred within five years prior to employment.

Individuals in postdoctoral positions may bid on regular Sandia positions as internal candidates, and in some cases may be converted to regular career positions during their term if warranted by ongoing operational needs, continuing availability of funds, and satisfactory job performance.

Job ID: 685453

About Sandia National Laboratories

Sandia National Laboratories is the nations premier science and engineering lab for national security and technology innovation, with teams of specialists focused on cutting-edge work in a broad array of areas.

Read the original post:

Postdoctoral Appointee - Experimental Quantum Sensing in Albuquerque ...

Juno Delivers Stunning New Views of Great Red Spot to Physics of the Multiverse (The Galaxy Report)  The Daily Galaxy --Great Discoveries Channel

Go here to read the rest:

Juno Delivers Stunning New Views of Great Red Spot to Physics of the Multiverse (The Galaxy Report) - The Daily Galaxy --Great Discoveries Channel

Intrinsic form of angular momentum as a property of quantum particles

Spin is a conserved quantity carried by elementary particles, and thus by composite particles (hadrons) and atomic nuclei.[1][2]

Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. The orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution and appears when there is periodic structure to its wavefunction as the angle varies.[3][4] For photons, spin is the quantum-mechanical counterpart of the polarization of light; for electrons, the spin has no classical counterpart.[citation needed]

The existence of electron spin angular momentum is inferred from experiments, such as the SternGerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum.[5] The existence of the electron spin can also be inferred theoretically from the spinstatistics theorem and from the Pauli exclusion principleand vice versa, given the particular spin of the electron, one may derive the Pauli exclusion principle.

Spin is described mathematically as a vector for some particles such as photons, and as spinors and bispinors for other particles such as electrons. Spinors and bispinors behave similarly to vectors: they have definite magnitudes and change under rotations; however, they use an unconventional "direction". All elementary particles of a given kind have the same magnitude of spin angular momentum, though its direction may change. These are indicated by assigning the particle a spin quantum number.[2]

The SI unit of spin is the same as classical angular momentum (i.e., Nms, Js, or kgm2s1). In practice, spin is given as a dimensionless spin quantum number by dividing the spin angular momentum by the reduced Planck constant , which has the same dimensions as angular momentum, although this is not the full computation of this value. Very often, the "spin quantum number" is simply called "spin". The fact that it is a quantum number is implicit.

Wolfgang Pauli in 1924 was the first to propose a doubling of the number of available electron states due to a two-valued non-classical "hidden rotation".[6] In 1925, George Uhlenbeck and Samuel Goudsmit at Leiden University suggested the simple physical interpretation of a particle spinning around its own axis,[7] in the spirit of the old quantum theory of Bohr and Sommerfeld.[8] Ralph Kronig anticipated the UhlenbeckGoudsmit model in discussion with Hendrik Kramers several months earlier in Copenhagen, but did not publish.[8] The mathematical theory was worked out in depth by Pauli in 1927. When Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it.

As the name suggests, spin was originally conceived as the rotation of a particle around some axis. While the question of whether elementary particles actually rotate is ambiguous (as they appear point-like), this picture is correct insofar as spin obeys the same mathematical laws as quantized angular momenta do; in particular, spin implies that the particle's phase changes with angle. On the other hand, spin has some peculiar properties that distinguish it from orbital angular momenta:

The conventional definition of the spin quantum number is s = n/2, where n can be any non-negative integer. Hence the allowed values of s are 0, 1/2, 1, 3/2, 2, etc. The value of s for an elementary particle depends only on the type of particle and cannot be altered in any known way (in contrast to the spin direction described below). The spin angular momentum S of any physical system is quantized. The allowed values of S are

Those particles with half-integer spins, such as 1/2, 3/2, 5/2, are known as fermions, while those particles with integer spins, such as 0, 1, 2, are known as bosons. The two families of particles obey different rules and broadly have different roles in the world around us. A key distinction between the two families is that fermions obey the Pauli exclusion principle: that is, there cannot be two identical fermions simultaneously having the same quantum numbers (meaning, roughly, having the same position, velocity and spin direction). Fermions obey the rules of FermiDirac statistics. In contrast, bosons obey the rules of BoseEinstein statistics and have no such restriction, so they may "bunch together" in identical states. Also, composite particles can have spins different from their component particles. For example, a helium-4 atom in the ground state has spin0 and behaves like a boson, even though the quarks and electrons which make it up are all fermions.

This has some profound consequences:

The spinstatistics theorem splits particles into two groups: bosons and fermions, where bosons obey BoseEinstein statistics, and fermions obey FermiDirac statistics (and therefore the Pauli exclusion principle). Specifically, the theory states that particles with an integer spin are bosons, while all other particles have half-integer spins and are fermions. As an example, electrons have half-integer spin and are fermions that obey the Pauli exclusion principle, while photons have integer spin and do not. The theorem relies on both quantum mechanics and the theory of special relativity, and this connection between spin and statistics has been called "one of the most important applications of the special relativity theory".[10]

Since elementary particles are point-like, self-rotation is not well-defined for them. However, spin implies that the phase of the particle depends on the angle as e i S {displaystyle e^{iStheta }} , for rotation of angle around the axis parallel to the spin S. This is equivalent to the quantum-mechanical interpretation of momentum as phase dependence in the position, and of orbital angular momentum as phase dependence in the angular position.

Photon spin is the quantum-mechanical description of light polarization, where spin+1 and spin1 represent two opposite directions of circular polarization. Thus, light of a defined circular polarization consists of photons with the same spin, either all +1 or all 1. Spin represents polarization for other vector bosons as well.

For fermions, the picture is less clear. Angular velocity is equal by Ehrenfest theorem to the derivative of the Hamiltonian to its conjugate momentum, which is the total angular momentum operator J = L + S. Therefore, if the Hamiltonian H is dependent upon the spin S, dH/dS is non-zero, and the spin causes angular velocity, and hence actual rotation, i.e. a change in the phase-angle relation over time. However, whether this holds for free electron is ambiguous, since for an electron, S2 is constant, and therefore it is a matter of interpretation whether the Hamiltonian includes such a term. Nevertheless, spin appears in the Dirac equation, and thus the relativistic Hamiltonian of the electron, treated as a Dirac field, can be interpreted as including a dependence in the spin S.[11] Under this interpretation, free electrons also self-rotate, with the Zitterbewegung effect understood as this rotation.

Particles with spin can possess a magnetic dipole moment, just like a rotating electrically charged body in classical electrodynamics. These magnetic moments can be experimentally observed in several ways, e.g. by the deflection of particles by inhomogeneous magnetic fields in a SternGerlach experiment, or by measuring the magnetic fields generated by the particles themselves.

The intrinsic magnetic moment of a spin-1/2 particle with charge q, mass m, and spin angular momentum S, is[12]

where the dimensionless quantity gs is called the spin g-factor. For exclusively orbital rotations it would be 1 (assuming that the mass and the charge occupy spheres of equal radius).

The electron, being a charged elementary particle, possesses a nonzero magnetic moment. One of the triumphs of the theory of quantum electrodynamics is its accurate prediction of the electron g-factor, which has been experimentally determined to have the value 2.00231930436256(35), with the digits in parentheses denoting measurement uncertainty in the last two digits at one standard deviation.[13] The value of 2 arises from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the correction of 0.002319304... arises from the electron's interaction with the surrounding electromagnetic field, including its own field.[14]

Composite particles also possess magnetic moments associated with their spin. In particular, the neutron possesses a non-zero magnetic moment despite being electrically neutral. This fact was an early indication that the neutron is not an elementary particle. In fact, it is made up of quarks, which are electrically charged particles. The magnetic moment of the neutron comes from the spins of the individual quarks and their orbital motions.

Neutrinos are both elementary and electrically neutral. The minimally extended Standard Model that takes into account non-zero neutrino masses predicts neutrino magnetic moments of:[15][16][17]

where the are the neutrino magnetic moments, m are the neutrino masses, and B is the Bohr magneton. New physics above the electroweak scale could, however, lead to significantly higher neutrino magnetic moments. It can be shown in a model-independent way that neutrino magnetic moments larger than about 1014B are "unnatural" because they would also lead to large radiative contributions to the neutrino mass. Since the neutrino masses are known to be at most about 1eV, the large radiative corrections would then have to be "fine-tuned" to cancel each other, to a large degree, and leave the neutrino mass small.[18] The measurement of neutrino magnetic moments is an active area of research. Experimental results have put the neutrino magnetic moment at less than 1.21010times the electron's magnetic moment.

On the other hand elementary particles with spin but without electric charge, such as a photon or a Z boson, do not have a magnetic moment.

In ordinary materials, the magnetic dipole moments of individual atoms produce magnetic fields that cancel one another, because each dipole points in a random direction, with the overall average being very near zero. Ferromagnetic materials below their Curie temperature, however, exhibit magnetic domains in which the atomic dipole moments are locally aligned, producing a macroscopic, non-zero magnetic field from the domain. These are the ordinary "magnets" with which we are all familiar.

In paramagnetic materials, the magnetic dipole moments of individual atoms spontaneously align with an externally applied magnetic field. In diamagnetic materials, on the other hand, the magnetic dipole moments of individual atoms spontaneously align oppositely to any externally applied magnetic field, even if it requires energy to do so.

The study of the behavior of such "spin models" is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction. These models have many interesting properties, which have led to interesting results in the theory of phase transitions.

In classical mechanics, the angular momentum of a particle possesses not only a magnitude (how fast the body is rotating), but also a direction (either up or down on the axis of rotation of the particle). Quantum-mechanical spin also contains information about direction, but in a more subtle form. Quantum mechanics states that the component of angular momentum for a spin-s particle measured along any direction can only take on the values[19]

where Si is the spin component along the i-th axis (either x, y, or z), si is the spin projection quantum number along the i-th axis, and s is the principal spin quantum number (discussed in the previous section). Conventionally the direction chosen is the zaxis:

where Sz is the spin component along the zaxis, sz is the spin projection quantum number along the zaxis.

One can see that there are 2s + 1 possible values of sz. The number "2s + 1" is the multiplicity of the spin system. For example, there are only two possible values for a spin-1/2 particle: sz = +1/2 and sz = 1/2. These correspond to quantum states in which the spin component is pointing in the +z or z directions respectively, and are often referred to as "spin up" and "spin down". For a spin-3/2 particle, like a delta baryon, the possible values are +3/2, +1/2, 1/2, 3/2.

For a given quantum state, one could think of a spin vector S {textstyle langle Srangle } whose components are the expectation values of the spin components along each axis, i.e., S = [ S x , S y , S z ] {textstyle langle Srangle =[langle S_{x}rangle ,langle S_{y}rangle ,langle S_{z}rangle ]} . This vector then would describe the "direction" in which the spin is pointing, corresponding to the classical concept of the axis of rotation. It turns out that the spin vector is not very useful in actual quantum-mechanical calculations, because it cannot be measured directly: sx, sy and sz cannot possess simultaneous definite values, because of a quantum uncertainty relation between them. However, for statistically large collections of particles that have been placed in the same pure quantum state, such as through the use of a SternGerlach apparatus, the spin vector does have a well-defined experimental meaning: It specifies the direction in ordinary space in which a subsequent detector must be oriented in order to achieve the maximum possible probability (100%) of detecting every particle in the collection. For spin-1/2 particles, this probability drops off smoothly as the angle between the spin vector and the detector increases, until at an angle of 180that is, for detectors oriented in the opposite direction to the spin vectorthe expectation of detecting particles from the collection reaches a minimum of 0%.

As a qualitative concept, the spin vector is often handy because it is easy to picture classically. For instance, quantum-mechanical spin can exhibit phenomena analogous to classical gyroscopic effects. For example, one can exert a kind of "torque" on an electron by putting it in a magnetic field (the field acts upon the electron's intrinsic magnetic dipole momentsee the following section). The result is that the spin vector undergoes precession, just like a classical gyroscope. This phenomenon is known as electron spin resonance (ESR). The equivalent behaviour of protons in atomic nuclei is used in nuclear magnetic resonance (NMR) spectroscopy and imaging.

Mathematically, quantum-mechanical spin states are described by vector-like objects known as spinors. There are subtle differences between the behavior of spinors and vectors under coordinate rotations. For example, rotating a spin-1/2 particle by 360 does not bring it back to the same quantum state, but to the state with the opposite quantum phase; this is detectable, in principle, with interference experiments. To return the particle to its exact original state, one needs a 720 rotation. (The Plate trick and Mbius strip give non-quantum analogies.) A spin-zero particle can only have a single quantum state, even after torque is applied. Rotating a spin-2 particle 180 can bring it back to the same quantum state, and a spin-4 particle should be rotated 90 to bring it back to the same quantum state. The spin-2 particle can be analogous to a straight stick that looks the same even after it is rotated 180, and a spin-0 particle can be imagined as sphere, which looks the same after whatever angle it is turned through.

Spin obeys commutation relations[20] analogous to those of the orbital angular momentum:

where jkl is the Levi-Civita symbol. It follows (as with angular momentum) that the eigenvectors of S ^ 2 {displaystyle {hat {S}}^{2}} and S ^ z {displaystyle {hat {S}}_{z}} (expressed as kets in the total S basis) are

The spin raising and lowering operators acting on these eigenvectors give

where S ^ = S ^ x i S ^ y {displaystyle {hat {S}}_{pm }={hat {S}}_{x}pm i{hat {S}}_{y}} .

But unlike orbital angular momentum, the eigenvectors are not spherical harmonics. They are not functions of and . There is also no reason to exclude half-integer values of s and ms.

All quantum-mechanical particles possess an intrinsic spin s {displaystyle s} (though this value may be equal to zero). The projection of the spin s {displaystyle s} on any axis is quantized in units of the reduced Planck constant, such that the state function of the particle is, say, not = ( r ) {displaystyle psi =psi ({vec {r}})} , but = ( r , s z ) {displaystyle psi =psi ({vec {r}},s_{z})} , where s z {displaystyle s_{z}} can take only the values of the following discrete set:

One distinguishes bosons (integer spin) and fermions (half-integer spin). The total angular momentum conserved in interaction processes is then the sum of the orbital angular momentum and the spin.

The quantum-mechanical operators associated with spin-1/2 observables are

where in Cartesian components

For the special case of spin-1/2 particles, x, y and z are the three Pauli matrices:

For systems of N identical particles this is related to the Pauli exclusion principle, which states that its wavefunction ( r 1 , 1 , , r N , N ) {displaystyle psi (mathbf {r} _{1},sigma _{1},dots ,mathbf {r} _{N},sigma _{N})} must change upon interchanges of any two of the N particles as

Thus, for bosons the prefactor (1)2s will reduce to +1, for fermions to 1. In quantum mechanics all particles are either bosons or fermions. In some speculative relativistic quantum field theories "supersymmetric" particles also exist, where linear combinations of bosonic and fermionic components appear. In two dimensions, the prefactor (1)2s can be replaced by any complex number of magnitude1 such as in the anyon.

The above permutation postulate for N-particle state functions has most important consequences in daily life, e.g. the periodic table of the chemical elements.

As described above, quantum mechanics states that components of angular momentum measured along any direction can only take a number of discrete values. The most convenient quantum-mechanical description of particle's spin is therefore with a set of complex numbers corresponding to amplitudes of finding a given value of projection of its intrinsic angular momentum on a given axis. For instance, for a spin-1/2 particle, we would need two numbers a1/2, giving amplitudes of finding it with projection of angular momentum equal to +/2 and /2, satisfying the requirement

For a generic particle with spin s, we would need 2s + 1 such parameters. Since these numbers depend on the choice of the axis, they transform into each other non-trivially when this axis is rotated. It is clear that the transformation law must be linear, so we can represent it by associating a matrix with each rotation, and the product of two transformation matrices corresponding to rotations A and B must be equal (up to phase) to the matrix representing rotation AB. Further, rotations preserve the quantum-mechanical inner product, and so should our transformation matrices:

Mathematically speaking, these matrices furnish a unitary projective representation of the rotation group SO(3). Each such representation corresponds to a representation of the covering group of SO(3), which is SU(2).[21] There is one n-dimensional irreducible representation of SU(2) for each dimension, though this representation is n-dimensional real for odd n and n-dimensional complex for even n (hence of real dimension 2n). For a rotation by angle in the plane with normal vector ^ {textstyle {hat {boldsymbol {theta }}}} ,

where = ^ {textstyle {boldsymbol {theta }}=theta {hat {boldsymbol {theta }}}} , and S is the vector of spin operators.

Working in the coordinate system where ^ = z ^ {textstyle {hat {theta }}={hat {z}}} , we would like to show that Sx and Sy are rotated into each other by the angle . Starting with Sx. Using units where = 1:

Using the spin operator commutation relations, we see that the commutators evaluate to i Sy for the odd terms in the series, and to Sx for all of the even terms. Thus:

as expected. Note that since we only relied on the spin operator commutation relations, this proof holds for any dimension (i.e., for any principal spin quantum number s).[22]

A generic rotation in 3-dimensional space can be built by compounding operators of this type using Euler angles:

An irreducible representation of this group of operators is furnished by the Wigner D-matrix:

where

is Wigner's small d-matrix. Note that for = 2 and = = 0; i.e., a full rotation about the zaxis, the Wigner D-matrix elements become

Recalling that a generic spin state can be written as a superposition of states with definite m, we see that if s is an integer, the values of m are all integers, and this matrix corresponds to the identity operator. However, if s is a half-integer, the values of m are also all half-integers, giving (1)2m = 1 for all m, and hence upon rotation by 2 the state picks up a minus sign. This fact is a crucial element of the proof of the spinstatistics theorem.

We could try the same approach to determine the behavior of spin under general Lorentz transformations, but we would immediately discover a major obstacle. Unlike SO(3), the group of Lorentz transformations SO(3,1) is non-compact and therefore does not have any faithful, unitary, finite-dimensional representations.

In case of spin-1/2 particles, it is possible to find a construction that includes both a finite-dimensional representation and a scalar product that is preserved by this representation. We associate a 4-component Dirac spinor with each particle. These spinors transform under Lorentz transformations according to the law

where are gamma matrices, and is an antisymmetric 44 matrix parametrizing the transformation. It can be shown that the scalar product

is preserved. It is not, however, positive-definite, so the representation is not unitary.

Each of the (Hermitian) Pauli matrices of spin-1/2 particles has two eigenvalues, +1 and 1. The corresponding normalized eigenvectors are

(Because any eigenvector multiplied by a constant is still an eigenvector, there is ambiguity about the overall sign. In this article, the convention is chosen to make the first element imaginary and negative if there is a sign ambiguity. The present convention is used by software such as SymPy; while many physics textbooks, such as Sakurai and Griffiths, prefer to make it real and positive.)

By the postulates of quantum mechanics, an experiment designed to measure the electron spin on the x, y, or zaxis can only yield an eigenvalue of the corresponding spin operator (Sx, Sy or Sz) on that axis, i.e. /2 or /2. The quantum state of a particle (with respect to spin), can be represented by a two-component spinor:

When the spin of this particle is measured with respect to a given axis (in this example, the xaxis), the probability that its spin will be measured as /2 is just | x + | | 2 {displaystyle {big |}langle psi _{x+}|psi rangle {big |}^{2}} . Correspondingly, the probability that its spin will be measured as /2 is just | x | | 2 {displaystyle {big |}langle psi _{x-}|psi rangle {big |}^{2}} . Following the measurement, the spin state of the particle collapses into the corresponding eigenstate. As a result, if the particle's spin along a given axis has been measured to have a given eigenvalue, all measurements will yield the same eigenvalue (since | x + | x + | 2 = 1 {displaystyle {big |}langle psi _{x+}|psi _{x+}rangle {big |}^{2}=1} , etc.), provided that no measurements of the spin are made along other axes.

The operator to measure spin along an arbitrary axis direction is easily obtained from the Pauli spin matrices. Let u = (ux, uy, uz) be an arbitrary unit vector. Then the operator for spin in this direction is simply

The operator Su has eigenvalues of /2, just like the usual spin matrices. This method of finding the operator for spin in an arbitrary direction generalizes to higher spin states, one takes the dot product of the direction with a vector of the three operators for the three x-, y-, z-axis directions.

A normalized spinor for spin-1/2 in the (ux, uy, uz) direction (which works for all spin states except spin down, where it will give 0/0) is

The above spinor is obtained in the usual way by diagonalizing the u matrix and finding the eigenstates corresponding to the eigenvalues. In quantum mechanics, vectors are termed "normalized" when multiplied by a normalizing factor, which results in the vector having a length of unity.

Since the Pauli matrices do not commute, measurements of spin along the different axes are incompatible. This means that if, for example, we know the spin along the xaxis, and we then measure the spin along the yaxis, we have invalidated our previous knowledge of the xaxis spin. This can be seen from the property of the eigenvectors (i.e. eigenstates) of the Pauli matrices that

So when physicists measure the spin of a particle along the xaxis as, for example, /2, the particle's spin state collapses into the eigenstate | x + {displaystyle |psi _{x+}rangle } . When we then subsequently measure the particle's spin along the yaxis, the spin state will now collapse into either | y + {displaystyle |psi _{y+}rangle } or | y {displaystyle |psi _{y-}rangle } , each with probability 1/2. Let us say, in our example, that we measure /2. When we now return to measure the particle's spin along the xaxis again, the probabilities that we will measure /2 or /2 are each 1/2 (i.e. they are | x + | y | 2 {displaystyle {big |}langle psi _{x+}|psi _{y-}rangle {big |}^{2}} and | x | y | 2 {displaystyle {big |}langle psi _{x-}|psi _{y-}rangle {big |}^{2}} respectively). This implies that the original measurement of the spin along the xaxis is no longer valid, since the spin along the xaxis will now be measured to have either eigenvalue with equal probability.

The spin-1/2 operator S = /2 forms the fundamental representation of SU(2). By taking Kronecker products of this representation with itself repeatedly, one may construct all higher irreducible representations. That is, the resulting spin operators for higher-spin systems in three spatial dimensions can be calculated for arbitrarily large s using this spin operator and ladder operators. For example, taking the Kronecker product of two spin-1/2 yields a four-dimensional representation, which is separable into a 3-dimensional spin-1 (triplet states) and a 1-dimensional spin-0 representation (singlet state).

The resulting irreducible representations yield the following spin matrices and eigenvalues in the z-basis:

Also useful in the quantum mechanics of multiparticle systems, the general Pauli group Gn is defined to consist of all n-fold tensor products of Pauli matrices.

The analog formula of Euler's formula in terms of the Pauli matrices

for higher spins is tractable, but less simple.[23]

In tables of the spin quantum number s for nuclei or particles, the spin is often followed by a "+" or "". This refers to the parity with "+" for even parity (wave function unchanged by spatial inversion) and "" for odd parity (wave function negated by spatial inversion). For example, see the isotopes of bismuth, in which the list of isotopes includes the column nuclear spin and parity. For Bi-209, the only stable isotope, the entry 9/2 means that the nuclear spin is 9/2 and the parity is odd.

Spin has important theoretical implications and practical applications. Well-established direct applications of spin include:

Electron spin plays an important role in magnetism, with applications for instance in computer memories. The manipulation of nuclear spin by radio-frequency waves (nuclear magnetic resonance) is important in chemical spectroscopy and medical imaging.

Spinorbit coupling leads to the fine structure of atomic spectra, which is used in atomic clocks and in the modern definition of the second. Precise measurements of the g-factor of the electron have played an important role in the development and verification of quantum electrodynamics. Photon spin is associated with the polarization of light (photon polarization).

An emerging application of spin is as a binary information carrier in spin transistors. The original concept, proposed in 1990, is known as DattaDas spin transistor.[24] Electronics based on spin transistors are referred to as spintronics. The manipulation of spin in dilute magnetic semiconductor materials, such as metal-doped ZnO or TiO2 imparts a further degree of freedom and has the potential to facilitate the fabrication of more efficient electronics.[25]

There are many indirect applications and manifestations of spin and the associated Pauli exclusion principle, starting with the periodic table of chemistry.

Spin was first discovered in the context of the emission spectrum of alkali metals. In 1924, Wolfgang Pauli introduced what he called a "two-valuedness not describable classically"[26] associated with the electron in the outermost shell. This allowed him to formulate the Pauli exclusion principle, stating that no two electrons can have the same quantum state in the same quantum system.

The physical interpretation of Pauli's "degree of freedom" was initially unknown. Ralph Kronig, one of Land's assistants, suggested in early 1925 that it was produced by the self-rotation of the electron. When Pauli heard about the idea, he criticized it severely, noting that the electron's hypothetical surface would have to be moving faster than the speed of light in order for it to rotate quickly enough to produce the necessary angular momentum. This would violate the theory of relativity. Largely due to Pauli's criticism, Kronig decided not to publish his idea.

In the autumn of 1925, the same thought came to Dutch physicists George Uhlenbeck and Samuel Goudsmit at Leiden University. Under the advice of Paul Ehrenfest, they published their results.[27] It met a favorable response, especially after Llewellyn Thomas managed to resolve a factor-of-two discrepancy between experimental results and Uhlenbeck and Goudsmit's calculations (and Kronig's unpublished results). This discrepancy was due to the orientation of the electron's tangent frame, in addition to its position.

Mathematically speaking, a fiber bundle description is needed. The tangent bundle effect is additive and relativistic; that is, it vanishes if c goes to infinity. It is one half of the value obtained without regard for the tangent-space orientation, but with opposite sign. Thus the combined effect differs from the latter by a factor two (Thomas precession, known to Ludwik Silberstein in 1914).

Despite his initial objections, Pauli formalized the theory of spin in 1927, using the modern theory of quantum mechanics invented by Schrdinger and Heisenberg. He pioneered the use of Pauli matrices as a representation of the spin operators and introduced a two-component spinor wave-function. Uhlenbeck and Goudsmit treated spin as arising from classical rotation, while Pauli emphasized, that spin is non-classical and intrinsic property.[28]

Pauli's theory of spin was non-relativistic. However, in 1928, Paul Dirac published the Dirac equation, which described the relativistic electron. In the Dirac equation, a four-component spinor (known as a "Dirac spinor") was used for the electron wave-function. Relativistic spin explained gyromagnetic anomaly, which was (in retrospect) first observed by Samuel Jackson Barnett in 1914 (see Einsteinde Haas effect). In 1940, Pauli proved the spinstatistics theorem, which states that fermions have half-integer spin, and bosons have integer spin.

In retrospect, the first direct experimental evidence of the electron spin was the SternGerlach experiment of 1922. However, the correct explanation of this experiment was only given in 1927.[29]

Continue reading here:

Spin (physics) - Wikipedia

POSITION SUMMARY

Applications are invited for postdoctoral research positions as Flatiron Research Fellows (FRF) at the Center for Computational Astrophysics (CCA). The CCA offers FRFs the opportunity for independent research in areas that have strong synergy with the CCA or other centers at the Flatiron Institute.

The mission of the Flatiron Institute is to advance scientific knowledge through computational methods, including data analysis, theory, modeling, and simulation. It currently houses five centers, focused on computational astrophysics (CCA), biology (CCB), mathematics (CCM), neuroscience (CCN) and quantum physics (CCQ), as well as a scientific computing core (SCC) that maintains state-of-the-art computing facilities for use by Flatiron scientists. The CCA's mission is to create, develop, and disseminate computational methods, tools, and frameworks that allow scientists to build or analyze big astronomical datasets, and to use computational and statistical techniques to understand complex, multi-scale physics in astrophysical systems ranging in scales from planets to the Universe.

Please see https://www.simonsfoundation.org/flatiron/center-for-computational-astrophysics/ for a full description of CCA research areas and scientific staff.

Flatiron Research Fellows are expected to carry out an active research program that can be independently directed and/or involve substantial collaboration with other members of the CCA or Flatiron Institute. In addition to their own research, Fellows help build the rich scientific community at the CCA and Flatiron Institute by: participating in seminars, colloquia, and group meetings; developing their software, mathematical, and computational expertise through internal educational opportunities; and sharing their knowledge through scientific publications, presentations, and/or software releases. Flatiron Research Fellows may also have the opportunity to organize workshops and to mentor graduate and undergraduate students through the CCA Pre-Doctoral Program, the CUNY Astrophysics Masters Program, the Simons-NSBP Scholars Summer Program, and the AstroCom NYC Program. FRFs are welcome to take advantage of CCA partnerships with the Simons Observatory, the Terra Hunting Experiment, Sloan Digital Sky Survey V, Gaia, and the NASA SPHEREx mission. In addition, individual CCA research scientists have significant roles in a variety of collaborations and projects, including Learning the Universe, SIMBIG, Vera Rubin, Euclid, Roman, CAMELS, MESA, AstroPy, NANOGrav, and would welcome FRF collaborators. Many CCA scientists have joint appointments with other neighboring institutions as well.

The CCA welcomes any applicant who feels that their research program would thrive at the CCA. We have also identified a number of strategic areas where we would particularly welcome applicants' participation, listed on this webpage under the Strategic Areas tab.

FRF positions are generally two-year appointments that can be renewed for a third year, contingent on performance. FRFs receive a research budget and have access to the Flatiron Institute's powerful scientific computing resources. FRFs may be eligible for subsidized housing within walking distance of the CCA. These positions will be based in our New York City offices, with anticipated start dates between late August and early October 2023.

In addition, The Center for Computational Astrophysics at the Flatiron Institute and the Astronomy Department at Columbia University invite applications for a joint postdoctoral position. The chosen applicant of this position will conduct independent research as well as contribute to the goals of the Learning the Universe collaboration (www.learning-the-universe.org). If you are interested, please review the full job ad https://bit.ly/3D9KZpy, and indicate your interest when prompted in the Simons Foundation's application questionnaire.

Education

Related Skills & Other requirements

Application Materials

Applicants should follow the detailed guidelines at https://jobregister.aas.org/postdoc-application-guidelines, except that a list of references is not required.

Deadline: All application materials (including letters) must be received by November 1, 2022.

Selection Criteria: Applicants must have a PhD in a related field or expect to receive their PhD before the start of the appointment. Applications will be evaluated based on: 1) past research accomplishments; 2) the proposed research program; 3) the synergy of applicant's expertise and research proposal topic with existing CCA staff and research programs, and potential to cross boundaries between CCA groups and/or the Flatiron Institute's centers.

Any queries about the application process or about CCA should be directed to astro@simonsfoundation.org. Queries about the CCA may also be directed to any of the scientific staff at CCA.

THE SIMONS FOUNDATION'S DIVERSITY COMMITMENT

Many of the greatest ideas and discoveries come from a diverse mix of minds, backgrounds and experiences, and we are committed to cultivating an inclusive work environment. The Simons Foundation actively seeks a diverse applicant pool and encourages candidates of all backgrounds to apply. We provide equal opportunities to all employees and applicants for employment without regard to race, religion, color, age, sex, national origin, sexual orientation, gender identity, genetic disposition, neurodiversity, disability, veteran status, or any other protected category under federal, state and local law.

Read more:

Flatiron Research Fellow, CCA in New York, NY for Simons Foundation

Subatomic particles can be linked to each other even if separated by billions of light-years of space.

But this strange and spooky phenomenon hadnt been proven until Walnut Creek-based physicist John Clauser performed a pioneering experiment at UC-Berkeley in 1972 an accomplishment that on Tuesday was honored with the Nobel Prize in Physics.

Clauser, 79, shares the $900,000 prize with two fellow physicists who followed in his footsteps: Alain Aspect of Universit Paris-Saclay and cole Polytechnique in France, and Anton Zeilinger, of the University of Vienna in Austria.

This discovery, now a core concept of quantum mechanics, could revolutionize computing, cryptography and the transfer of information via what is known as quantum teleportation, according to the Nobel committee.

Working independently, the three scientists conducted experiments that demonstrated quantum entanglement, an odd phenomenon in which one particle can instantaneously influence the behavior of other particles even if they are far away, such as at opposite sides of the universe.

Clausers work measured the behavior of pairs of tiny photons, which were entangled, or acting in concert. It showed, in essence, that nature is capable of sending signals faster than the speed of light.

This phenomenon, the foundation of todays quantum computers and other modern quantum technologies, is so weird that physicist Albert Einstein called it spooky action at a distance.

Today we honor three physicists whose pioneering experiments showed us that the strange quantum world of entanglement is not just the microworld of atoms, and certainly not a virtual world of mysticism or science fiction, but the real world we live in, said Thors Hans Hansson of the Nobel Committee for Physics during a news conference in Stockholm.

Clauser, now retired, spends his days racing his 40-foot yacht Bodacious in San Francisco Bay, the greatest place in the world for sailing.

In an interview Tuesday, he told the Bay Area News Grouphe was thrilled by the 3 a.m. news from Stockholm and the tsunami of congratulatory calls. It took me over an hour to get my pants on, he joked.

Clauser, born a year after Pearl Harbor in 1942, grew up in the suburbs of Baltimore where his father had been hired to create Johns Hopkins Universitys aeronautics department.

He credits his father with his love of electronic tinkering, an essential skill for future experimental discoveries.

After school, when he was supposed to be doing homework, mostly what I would do is just sort of wander around the lab and gawk at all of the nifty laboratory equipment, he said in an oral history recorded by the American Physics Institute.

My dad was absolutely a marvelous teacher, my whole formative years, he recalled. Every time I asked a question, he knew the answer and would answer it in gory detail so that I would understand it. I mean, he didnt force feed me, but he did it in such a way that I continuously hungered for more.

Clauser first came to California in the early 1960s to study physics at the California Institute of Technology, then earned his PhD at Columbia University.

The study of Advanced Quantum Mechanics a field he would later revolutionize initially daunted him. He didnt understand its mathematical manipulations, and repeated the class three times before earning the requisite B grade.

I just didnt really believe it all. I was convinced that there were things that were wrong, he said. My Dad had always taught me, Son, look at the data. People will have lots of fancy theories, but always go back to the original data and see if you come to the same conclusions. Whenever I do that, I come up with very different conclusions.

That skepticism paved the way for his future Nobel. While working at UC Berkeley, he stumbled upon a fascinating theory by Northern Irish physicist John Stewart Bell, which explored what entanglements spooky action said about photons behavior and the fundamental nature of reality.

But wheres the experimental evidence? Clauser wondered. He knew Bells theorem could be tested.

He told PBSs Nova how he rummaged around the hidden storage rooms of Lawrence Berkeley National Laboratory, scavenging for old equipment to design the experiments he needed.

There are two kinds of people, really. Those who kind of like to use old junk and/or build it themselves from scratch. And those who go out and buy shiny new boxes, he said. Ive gotten pretty good at dumpster diving.

He faced criticism from many fellow physicists. Everybody told me I was crazy, and I was going ruin my career by wasting his time on such a philosophical question, he recalled.

In an experiment in the sub-basement of UC Berkeleys Birge Hall, conducted alongside the late fundamental physicist Stuart Freedman, he measured quantum entanglement by firing thousands of photons in opposite directions. They showed that the photons could act in concert despite being physically separated.

The experimentwas so novel that it was completely underappreciated at the time, said Berkeley Lab Director Mike Witherell. It was 10 years before physicists started to realize how quantum entanglement could be exploited. That was when the next decisive experiments were done, leading to the new quantum era we are now experiencing.

Unable to find a job as a professor, Clauser moved to Lawrence Livermore National Laboratory to do controlled fusion plasma physics experiments but later left because he refused to do classified work.

His insights are now the scientific underpinning for todays efforts to develop quantum cryptography, a method of encryption that uses the properties of quantum mechanics to secure and transmit data in a way that cannot be hacked.

Such powerful commercial applications were inconceivable at the time, he said.

I was totally unaware of how much money and interest there was in cryptography, he said. Heck, most of my computers didnt even require passwords. The only reason I have them on now is because we have all of the ones in the house all networked, and you cant put it on a network without putting passwords on them.

Original post:

Bay Area physicist and quantum physics pioneer wins Nobel Prize

A mind-bending, jargon-free account of the popular interpretation of quantum mechanics.

...

Quantum physics is strange. At least, it is strange to us, because the rules of the quantum world, which govern the way the world works at the level of atoms and subatomic particles (the behavior of light and matter, as the renowned physicist Richard Feynman put it), are not the rules that we are familiar with the rules of what we call common sense.

The quantum rules, which were mostly established by the end of the 1920s, seem to be telling us that a cat can be both alive and dead at the same time, while a particle can be in two places at once. But to the great distress of many physicists, let alone ordinary mortals, nobody (then or since) has been able to come up with a common-sense explanation of what is going on. More thoughtful physicists have sought solace in other ways, to be sure, namely coming up with a variety of more or less desperate remedies to explain what is going on in the quantum world.

These remedies, the quanta of solace, are called interpretations. At the level of the equations, none of these interpretations is better than any other, although the interpreters and their followers will each tell you that their own favored interpretation is the one true faith, and all those who follow other faiths are heretics. On the other hand, none of the interpretations is worse than any of the others, mathematically speaking. Most probably, this means that we are missing something. One day, a glorious new description of the world may be discovered that makes all the same predictions as present-day quantum theory, but also makes sense. Well, at least we can hope.

Meanwhile, I thought I might provide an agnostic overview of one of the more colorful of the hypotheses, the many-worlds, or multiple universes, theory. For overviews of the other five leading interpretations, I point you to my book, Six Impossible Things. I think youll find that all of them are crazy, compared with common sense, and some are more crazy than others. But in this world, crazy does not necessarily mean wrong, and being more crazy does not necessarily mean more wrong.

If you have heard of the Many Worlds Interpretation (MWI), the chances are you think that it was invented by the American Hugh Everett in the mid-1950s. In a way thats true. He did come up with the idea all by himself. But he was unaware that essentially the same idea had occurred to Erwin Schrdinger half a decade earlier. Everetts version is more mathematical, Schrdingers more philosophical, but the essential point is that both of them were motivated by a wish to get rid of the idea of the collapse of the wave function, and both of them succeeded.

As Schrdinger used to point out to anyone who would listen, there is nothing in the equations (including his famous wave equation) about collapse. That was something that Bohr bolted on to the theory to explain why we only see one outcome of an experiment a dead cat or a live cat not a mixture, a superposition of states. But because we only detect one outcome one solution to the wave function that need not mean that the alternative solutions do not exist. In a paper he published in 1952, Schrdinger pointed out the ridiculousness of expecting a quantum superposition to collapse just because we look at it. It was, he wrote, patently absurd that the wave function should be controlled in two entirely different ways, at times by the wave equation, but occasionally by direct interference of the observer, not controlled by the wave equation.

Although Schrdinger himself did not apply his idea to the famous cat, it neatly resolves that puzzle. Updating his terminology, there are two parallel universes, or worlds, in one of which the cat lives, and in one of which it dies. When the box is opened in one universe, a dead cat is revealed. In the other universe, there is a live cat. But there always were two worlds that had been identical to one another until the moment when the diabolical device determined the fate of the cat(s). There is no collapse of the wave function. Schrdinger anticipated the reaction of his colleagues in a talk he gave in Dublin, where he was then based, in 1952. After stressing that when his eponymous equation seems to describe different possibilities (they are not alternatives but all really happen simultaneously), he said:

Nearly every result [the quantum theorist] pronounces is about the probability of this or that or that happening with usually a great many alternatives. The idea that they may not be alternatives but all really happen simultaneously seems lunatic to him, just impossible. He thinks that if the laws of nature took this form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of a featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jelly fish. It is strange that he should believe this. For I understand he grants that unobserved nature does behave this waynamely according to the wave equation. The aforesaid alternatives come into play only when we make an observation which need, of course, not be a scientific observation. Still it would seem that, according to the quantum theorist, nature is prevented from rapid jellification only by our perceiving or observing it it is a strange decision.

In fact, nobody responded to Schrdingers idea. It was ignored and forgotten, regarded as impossible. So Everett developed his own version of the MWI entirely independently, only for it to be almost as completely ignored. But it was Everett who introduced the idea of the Universe splitting into different versions of itself when faced with quantum choices, muddying the waters for decades.

It was Hugh Everett who introduced the idea of the Universe splitting into different versions of itself when faced with quantum choices, muddying the waters for decades.

Everett came up with the idea in 1955, when he was a PhD student at Princeton. In the original version of his idea, developed in a draft of his thesis, which was not published at the time, he compared the situation with an amoeba that splits into two daughter cells. If amoebas had brains, each daughter would remember an identical history up until the point of splitting, then have its own personal memories. In the familiar cat analogy, we have one universe, and one cat, before the diabolical device is triggered, then two universes, each with its own cat, and so on. Everetts PhD supervisor, John Wheeler, encouraged him to develop a mathematical description of his idea for his thesis, and for a paper published in the Reviews of Modern Physics in 1957, but along the way, the amoeba analogy was dropped and did not appear in print until later. But Everett did point out that since no observer would ever be aware of the existence of the other worlds, to claim that they cannot be there because we cannot see them is no more valid than claiming that the Earth cannot be orbiting around the Sun because we cannot feel the movement.

Everett himself never promoted the idea of the MWI. Even before he completed his PhD, he had accepted the offer of a job at the Pentagon working in the Weapons Systems Evaluation Group on the application of mathematical techniques (the innocently titled game theory) to secret Cold War problems (some of his work was so secret that it is still classified) and essentially disappeared from the academic radar. It wasnt until the late 1960s that the idea gained some momentum when it was taken up and enthusiastically promoted by Bryce DeWitt, of the University of North Carolina, who wrote: every quantum transition taking place in every star, in every galaxy, in every remote corner of the universe is splitting our local world on Earth into myriad copies of itself. This became too much for Wheeler, who backtracked from his original endorsement of the MWI, and in the 1970s, said: I have reluctantly had to give up my support of that point of view in the end because I am afraid it carries too great a load of metaphysical baggage. Ironically, just at that moment, the idea was being revived and transformed through applications in cosmology and quantum computing.

Every quantum transition taking place in every star, in every galaxy, in every remote corner of the universe is splitting our local world on Earth into myriad copies of itself.

The power of the interpretation began to be appreciated even by people reluctant to endorse it fully. John Bell noted that persons of course multiply with the world, and those in any particular branch would experience only what happens in that branch, and grudgingly admitted that there might be something in it:

The many worlds interpretation seems to me an extravagant, and above all an extravagantly vague, hypothesis. I could almost dismiss it as silly. And yet It may have something distinctive to say in connection with the Einstein Podolsky Rosen puzzle, and it would be worthwhile, I think, to formulate some precise version of it to see if this is really so. And the existence of all possible worlds may make us more comfortable about the existence of our own world which seems to be in some ways a highly improbable one.

The precise version of the MWI came from David Deutsch, in Oxford, and in effect put Schrdingers version of the idea on a secure footing, although when he formulated his interpretation, Deutsch was unaware of Schrdingers version. Deutsch worked with DeWitt in the 1970s, and in 1977, he met Everett at a conference organized by DeWitt the only time Everett ever presented his ideas to a large audience. Convinced that the MWI was the right way to understand the quantum world, Deutsch became a pioneer in the field of quantum computing, not through any interest in computers as such, but because of his belief that the existence of a working quantum computer would prove the reality of the MWI.

This is where we get back to a version of Schrdingers idea. In the Everett version of the cat puzzle, there is a single cat up to the point where the device is triggered. Then the entire Universe splits in two. Similarly, as DeWitt pointed out, an electron in a distant galaxy confronted with a choice of two (or more) quantum paths causes the entire Universe, including ourselves, to split. In the DeutschSchrdinger version, there is an infinite variety of universes (a Multiverse) corresponding to all possible solutions to the quantum wave function. As far as the cat experiment is concerned, there are many identical universes in which identical experimenters construct identical diabolical devices. These universes are identical up to the point where the device is triggered. Then, in some universes the cat dies, in some it lives, and the subsequent histories are correspondingly different. But the parallel worlds can never communicate with one another. Or can they?

Deutsch argues that when two or more previously identical universes are forced by quantum processes to become distinct, as in the experiment with two holes, there is a temporary interference between the universes, which becomes suppressed as they evolve. It is this interaction that causes the observed results of those experiments. His dream is to see the construction of an intelligent quantum machine a computer that would monitor some quantum phenomenon involving interference going on within its brain. Using a rather subtle argument, Deutsch claims that an intelligent quantum computer would be able to remember the experience of temporarily existing in parallel realities. This is far from being a practical experiment. But Deutsch also has a much simpler proof of the existence of the Multiverse.

What makes a quantum computer qualitatively different from a conventional computer is that the switches inside it exist in a superposition of states. A conventional computer is built up from a collection of switches (units in electrical circuits) that can be either on or off, corresponding to the digits 1 or 0. This makes it possible to carry out calculations by manipulating strings of numbers in binary code. Each switch is known as a bit, and the more bits there are, the more powerful the computer is. Eight bits make a byte, and computer memory today is measured in terms of billions of bytes gigabytes, or Gb. Strictly speaking, since we are dealing in binary, a gigabyte is 230 bytes, but that is usually taken as read. Each switch in a quantum computer, however, is an entity that can be in a superposition of states. These are usually atoms, but you can think of them as being electrons that are either spin up or spin down. The difference is that in the superposition, they are both spin up and spin down at the same time 0 and 1. Each switch is called a qbit, pronounced cubit.

Using a rather subtle argument, Deutsch claims that an intelligent quantum computer would be able to remember the experience of temporarily existing in parallel realities.

Because of this quantum property, each qbit is equivalent to two bits. This doesnt look impressive at first sight, but it is. If you have three qbits, for example, they can be arranged in eight ways: 000, 001, 010, 011, 100, 101, 110, 111. The superposition embraces all these possibilities. So three qbits are not equivalent to six bits (2 x 3), but to eight bits (2 raised to the power of 3). The equivalent number of bits is always 2 raised to the power of the number of qbits. Just 10 qbits would be equivalent to 210 bits, actually 1,024, but usually referred to as a kilobit. Exponentials like this rapidly run away with themselves. A computer with just 300 qbits would be equivalent to a conventional computer with more bits than there are atoms in the observable Universe. How could such a computer carry out calculations? The question is more pressing since simple quantum computers, incorporating a few qbits, have already been constructed and shown to work as expected. They really are more powerful than conventional computers with the same number of bits.

Deutschs answer is that the calculation is carried out simultaneously on identical computers in each of the parallel universes corresponding to the superpositions. For a three-qbit computer, that means eight superpositions of computer scientists working on the same problem using identical computers to get an answer. It is no surprise that they should collaborate in this way, since the experimenters are identical, with identical reasons for tackling the same problem. That isnt too difficult to visualize. But when we build a 300-qbit machinewhich will surely happenwe will, if Deutsch is right, be involving a collaboration between more universes than there are atoms in our visible Universe. It is a matter of choice whether you think that is too great a load of metaphysical baggage. But if you do, you will need some other way to explain why quantum computers work.

Most quantum computer scientists prefer not to think about these implications. But there is one group of scientists who are used to thinking of even more than six impossible things before breakfast the cosmologists. Some of them have espoused the Many Worlds Interpretation as the best way to explain the existence of the Universe itself.

Their jumping-off point is the fact, noted by Schrdinger, that there is nothing in the equations referring to a collapse of the wave function. And they do mean the wave function; just one, which describes the entire world as a superposition of states a Multiverse made up of a superposition of universes.

Some cosmologists have espoused the Many Worlds Interpretation as the best way to explain the existence of the Universe itself.

The first version of Everetts PhD thesis (later modified and shortened on the advice of Wheeler) was actually titled The Theory of the Universal Wave Function. And by universal he meant literally that, saying:

Since the universal validity of the state function description is asserted, one can regard the state functions themselves as the fundamental entities, and one can even consider the state function of the whole universe. In this sense this theory can be called the theory of the universal wave function, since all of physics is presumed to follow from this function alone.

where for the present purpose state function is another name for wave function. All of physics means everything, including us the observers in physics jargon. Cosmologists are excited by this, not because they are included in the wave function, but because this idea of a single, uncollapsed wave function is the only way in which the entire Universe can be described in quantum mechanical terms while still being compatible with the general theory of relativity. In the short version of his thesis published in 1957, Everett concluded that his formulation of quantum mechanics may therefore prove a fruitful framework for the quantization of general relativity. Although that dream has not yet been fulfilled, it has encouraged a great deal of work by cosmologists since the mid-1980s, when they latched on to the idea. But it does bring with it a lot of baggage.

The universal wave function describes the position of every particle in the Universe at a particular moment in time. But it also describes every possible location of those particles at that instant. And it also describes every possible location of every particle at any other instant of time, although the number of possibilities is restricted by the quantum graininess of space and time. Out of this myriad of possible universes, there will be many versions in which stable stars and planets, and people to live on those planets, cannot exist. But there will be at least some universes resembling our own, more or less accurately, in the way often portrayed in science fiction stories. Or, indeed, in other fiction. Deutsch has pointed out that according to the MWI, any world described in a work of fiction, provided it obeys the laws of physics, really does exist somewhere in the Multiverse. There really is, for example, a Wuthering Heights world (but not a Harry Potter world).

That isnt the end of it. The single wave function describes all possible universes at all possible times. But it doesnt say anything about changing from one state to another. Time does not flow. Sticking close to home, Everetts parameter, called a state vector, includes a description of a world in which we exist, and all the records of that worlds history, from our memories, to fossils, to light reaching us from distant galaxies, exist. There will also be another universe exactly the same except that the time step has been advanced by, say, one second (or one hour, or one year). But there is no suggestion that any universe moves along from one time step to another. There will be a me in this second universe, described by the universal wave function, who has all the memories I have at the first instant, plus those corresponding to a further second (or hour, or year, or whatever). But it is impossible to say that these versions of me are the same person. Different time states can be ordered in terms of the events they describe, defining the difference between past and future, but they do not change from one state to another. All the states just exist. Time, in the way we are used to thinking of it, does not flow in Everetts MWI.

John Gribbin, described by the Spectator as one of the finest and most prolific writers of popular science around, is the author of, among other books, In Search of Schrdingers Cat, The Universe: A Biography, and Six Impossible Things, from which this article is excerpted. He is a Visiting Fellow in Astronomy at the University of Sussex, UK.

Read the rest here:

The Many-Worlds Theory, Explained | The MIT Press Reader

1. What quantum physics tells us about reality  Financial Times
2. Scientists win 2022 Nobel Prize by proving that reality is not locally real  Boing Boing
3. Does God play dice? A Note on the 2022 Nobel Prize in Physics  The Week
4. Nobel Prize in Physics Boosts Quantum Encryption  Security Boulevard
5. Physics Nobel Prize Awarded to Three Pioneers of Quantum Mechanics The European Conservative  The European Conservative
6. View Full Coverage on Google News

Read the original here:

What quantum physics tells us about reality - Financial Times

Physicist Carlo Rovelli explains the strange principles of relational quantum mechanics - which says objects don't exist in their own right - and how it could unlock major progress in fundamental physics

By Michael Brooks

Carlo Rovelli at the Cornelia Parker exhibition, Tate Britain

David Stock

Carlo Rovelli stands in front of an exploding shed. Fragments of its walls and shattered contents parts of a childs tricycle, a record player, a shredded Wellington boot hang in mid-air behind him. I have come to meet the physicist and bestselling author at an exhibition at the Tate Britain art gallery in London. The scattered objects are the work of Cornelia Parker, one of the UKs most acclaimed contemporary artists, known for her large-scale installations that reconfigure everyday objects.

For Rovelli, based at Aix-Marseille University in France, Parkers work is meaningful because it mirrors his take on the nature of reality. I connect with the process: of her coming up with the idea, producing the idea, telling us about the idea and of us reacting to it, he tells me. We dont understand Cornelia Parkers work just by looking at it, and we dont understand reality just by looking at objects.

Rovelli is an advocate of an idea known as relational quantum mechanics, the upshot of which is that objects dont exist independently of each other. It is a concept that defies easy understanding, so Parkers reality-challenging exhibition seemed like it might be a helpful setting for a conversation about it and about what else Rovelli is up to. It is a happy coincidence that Parkers shed is called Cold Dark Matter, a reference to the unidentified stuff that is thought to make up most of the universe. Because Rovelli now thinks he knows how we might finally pin

The rest is here:

Carlo Rovelli on the bizarre world of relational quantum mechanics - New Scientist