Daily Archives: February 1, 2022

Quantum physicists in the city have conducted experiments proving that reality as we think of it may not exist and in the process have not only conclusively disproved an Einsteinian idea of reality but have also paved the way for more secure information transfer.

That all of this should be achieved by quantum scientists should come aslittle surprise. Quantum mechanics has already been expanding our concept of what reality is. Previous experiments around the world, for example, have shown that particles can be in more than one place at a time, but a key tenet of quantum theory is that an object only assumes a definite position if it is seen by the observer.

Bothered by this, Albert Einstein famously said, I like to think that the moon is there even if I am not looking at it.

His statement reflects the every-day believed notion of realism, which suggests that a system has well-defined properties in any instant, even when not measured. But what if the quirks of quantum physics go beyond mere atoms or particles?

Testing realism

This has prompted a spate of experiments to determine, in the words of New Scientist, if there is a hard boundary between the quantum and classical worlds. Central to this is the Leggett-Garg inequality, devised in 1985 by Anthony Leggett and Anupam Garg. This inequality looks for correlations between measurements to see whether quantum or classical rules are being followed, the New Scientist states. In essence, it is a means of testing realism.

Professor Urbasi Sinha of Raman Research Institute (RRI) explained that the experimental violation of such inequality would not only falsify realism but also would confirm that quantum mechanics is not limited to the micro-world, but can be applied to bigger objects, such as the moon.

Leggett and Garg realized they could test the quantumness of big objects in theory. Their inequality could tell us whether realism holds true in the everyday world, she said.

She added that, this could also make way for harnessing non-classicality or quantumness of single photons for technological applications such as secure quantum communications and quantum sensing, which are crucial in todays requirements of secure information transfer.

In recent years, Leggett-Garg experiments carried out on various quantum systems from superconducting fluids and photons to atomic nuclei and tiny crystals have demonstrated that the microscopic world is non-real. For this they have found ways of measuring particles without disturbing it.

Testing the macroscopic limit of quantum mechanics is an important area of research because it can reveal up to what extent quantum principles dominate revealing the quantum-classical boundary.

However, these experiments have limitations. Scientists worldwide are trying to come up with better technology and appropriately designed strategies for achieving a fully conclusive experimental test.

Now, a team of scientists from RRI has successfully addressed this challenge.

In the course of a two-year experiment, she showed a significant amount of violation of Leggett Garg inequality by studying single photons.

The experiment was performed at the Quantum Information and Computing laboratory of RRI and was led by Urbasi along with her PhD student Kaushik Joarder. Theoretical contributions from Professor Dipankar Home of the Bose Institute Kolkata and Dr Debashis Saha of the S N Bose Centre for Basic Sciences Kolkata played a significant role in the work.

First experiment

The work, published in PRX Quantum, is the first ambiguity-free experiment to show violation of Leggett Garg inequalities.

The team conducted the experiment with single photons (particles of light) and proved the quantumness of the single photon comprehensively. This is the first experiment that shows the most decisive refutation of the notion of realism by the closure of what are known as loopholes plaguing all relevant experiments to date, Urbasi said.

Loopholes are elements, such as equipment limitations or study-related factors which can inadvertently alter the experiment or conspire to deviate results, she told DH.

She added that the strategies and technologies developed for the closure of all the existing loopholes will prove to be very useful for harnessing such non-classicality/quantumness of single photons for technological applications in secure quantum communications and quantum sensing.

Moreover, the experiment further shows remarkable agreement with quantum physics predictions. In our analysis, we have been able to show that not only are we violating the Leggett Garg inequality in a loophole-free manner, but that we were also showing remarkable agreement with the predictions of quantum mechanics, Urbasi said.

This work was partially funded by the Centre of Excellence in quantum technologies grant from the Ministry of Electronics and Information Technology as well as the Quantum Enabled Science and Technology grants from DST.

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An experiment that disproves Einstein's idea of reality - Deccan Herald

Kenneth Hicks| The Columbus Dispatch

If you likesuperheromovies, you may have heard about the new one starring Spiderman. I havent seenit, but I heard that it explores a topic called the multiverse.In its simplest form, theidea isthatmultiple universes exist, separate from our own but parallel in time.

Thisideamay sound like fantasy, but actuallyitsbased in science.

The multiverse is often used in cosmology as a way to justify the Big Bang.Our current theory of the Big Bang isfroma process called inflation, where space and time can expand at an exponential rate according to Einsteins general relativity,triggered bya quantum fluctuation in the empty vacuum.

To unpack that last sentence would take a book, so just focus on the last part: it all began with a small quantum fluctuation.

In quantum mechanics, fluctuations in space-time (where particle pairs can pop into existence for a fleeting moment, then disappear) are part of quantum theory. Quantum theory is one of thefoundations of modern physics, having been verified by countless experiments.For example, quantum theoryled to the invention oftransistors, which are used inallcomputers and cellphones.

The quantum fluctuation that led to the Big Bangwas averylow probability event.You might call it a once-in-a-universe likelihood.But if it happened once, then maybe it could have happened twice (or a multitude of times) somewhere in the vastness of the empty void that preceded the Big Bang. Hence, the idea of the multiverse.

The idea of the multiverse has been extended from the vastness of space to the vastness of time.Here, the idea is that whenever a choice is made, the universe splits into different branches in time, spawning two universes, one stemming from each choice.

This idea is key to understanding quantum theory, where probabilistic outcomesdetermine the fate of small particles. This interpretation of quantum theorystemsfrom the work of Nobel Laureate Richard Feynman, who developed the path-integral approach.

The problem with the multiverse theory is that it cant be proven correct ornot.Just like we cant move backward in time, we cantseebeyond the space of our universe.In other words, we cant make contact with any other universe except our own.

Popularmovies would have you think thatthere is a wayfor youtomove backward in time(or into an alternate universe)but thatsfiction.

Although Spiderman isallowedone to move around freely inthe multiverse,we must live in the real world. But if it were possibleto discover a connection to the multiverse, thebeststarting point wouldlikelybe adegreein quantum physics, just like the fictional character of Spidermans alias, Peter Parker.

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Astronomy: The multiverse might exist outside of Marvel - The Columbus Dispatch

The grandfather paradox is a self-contradictory situation that arises in some time travel scenarios that is illustrated by the impossible scenario in which a person travels back in time only to kill their grandfather (who could no longer go on to produce one's parent, and hence where does that leave you and your ancestor-killing event?). The paradox is sometimes taken as an argument against the logical possibility of traveling backward in time, according to the Stanford Encyclopedia of Philosophy. Within the framework of modern physics, however, there are ways to avoid the paradox without dispensing with time travel altogether.

Related: 5 sci-fi concepts that are possible (in theory)

Let's suppose you have a time machine that allows you to travel back into the past. While you're there, you accidentally kill one of your grandparents or any other direct ancestor before they have any offspring. That would alter a whole chain of future events, including your own birth, which would no longer happen. But if you weren't born in the future, then you couldn't kill your ancestor in the past hence the paradox. It's a scenario that became popular in the science-fiction magazines of the 1920s and 1930s, according to the Historical Dictionary of Science Fiction, and the name "grandfather paradox" was firmly established by 1950.

Actually, you don't even need to kill anyone; there are many other ways you could change history that would result in your future non-existence. Perhaps the best known example is the movie "Back to the Future," in which the time-traveling protagonist inadvertently drives a wedge between his parents before they were married and then has to work frantically to bring them together again.

Moving from science fiction to science fact, one person who was eminently qualified to talk about the realities of time travel was the late Stephen Hawking, arguably the most brilliant physicist of recent times. In 1999, he gave a lecture on "space and time warps," which showed how Einstein's theory of general relativity might make time travel possible, by bending space-time back on itself.

One theoretical possibility that would allow time travel (and thus the ability to somehow kill off a critical ancestor) is a special kind of wormhole. Among the most dramatic consequences of general relativity, wormholes are often described as shortcuts between one point in space and another. But, as Hawking explained in his lecture, a wormhole could possibly loop back to an earlier point in time a situation technically known as a "closed time-like curve" (CTC).

But if physics allows backward time travel, wouldn't the grandfather paradox still cause issues? Hawking suggested two possible ways to get around the paradox in this scenario. First, there's what he referred to as the "consistent histories" model, in which the whole of time past, present and future is rigidly predetermined; in that way, you can only travel back to an earlier point in time if you had already been there in your own history. In this "block universe" model, as it's sometimes called, one could travel to the past but doing so would not alter it, according to the Australian Broadcasting Corporation. Taking this view, the grandfather paradox could never arise. With Hawking's second option, on the other hand, the situation is more subtle.

This second approach to traveling back in time invokes quantum physics, where an event may have several possible outcomes with different likelihoods of occurring.

As described by the Stanford Encyclopedia of Philosophy, the "many worlds" interpretation of quantum theory sees all these various outcomes as occurring in different, "parallel" timelines. In this view, the grandfather paradox could be resolved if the time traveler starts out in a timeline where their grandfather lived long enough to have children, and then after going back and killing their forebear continue along a parallel time track in which they will never be born. (Stanford Encyclopedia has a more detailed look at why you cant jump back and forth between parallel timelines at will.) As Hawking pointed out in his 1999 lecture, this seems to be the implicit assumption behind sci-fi treatments such as "Back to the Future."

At the time that movie was made in 1985, the "parallel world" explanation of the grandfather paradox was merely a philosophical conjecture. In 1991, however, it was put on firmer ground by the physicist David Deutsch, as New Scientist reported at the time. Deutsch showed that, while parallel timelines are normally incapable of interacting with each other, the situation changes in the vicinity of a closed time-like curve (CTC), when a wormhole curves back on itself. Here, just as the sci-fi writers imagined, the different timelines are able to cross over so that when a CTC loops back into the past, it's the past of a different timeline. If that's proven, then you really could kill an infant grandparent without paradoxically eliminating yourself in the process. In that case, your grandfather would never have existed only in one parallel world. And you, the grandfather-killer, would only have existed in the other.

As surprising as it sounds, there's actually some experimental support for Deutsch's solution to the grandfather paradox. In 2014, a team at the University of Queensland examined a simpler time-travel scenario that entailed a similar logical paradox. The researchers described the work in their paper published that year in the journal Nature Communications. The idea was that a subatomic particle had to go back in time to flip the switch that resulted in its creation; if the switch wasn't flipped, the particle would never exist in the first place.

A key feature of Deutsch's theory is that the various probabilities have to be self-consistent. For instance, in the Queensland research example, if there's a 50:50 chance the particle travels back in time, then there must also be a 50:50 chance that the switch gets flipped to create that particle in the first place. In the absence of a time machine, the researchers set up an experiment involving a pair of photons, which they claimed was logically equivalent to a single photon traveling back in time to "create" itself. The experiment was a success, with the results validating Deutsch's self-consistency theory.

Killing your grandfather when he was a child is a sure-fire way to ensure you're never born. But there are also subtler possibilities for messing up the timeline. In a sufficiently complex system, even the tiniest change can have serious long-term consequences as in the butterfly effect, by which the flapping of a butterfly's wings can eventually trigger a tornado thousands of miles away. Sci-fi writer Ray Bradbury produced a time travel counterpart to this in his 1952 story "A Sound of Thunder," which can be read online at the Internet Archive. Bradbury's protagonist travels back to the time of the dinosaurs, where he accidentally steps on a butterfly then returns to the present to find society changed beyond recognition. It's easy to imagine that, if the societal changes were sweeping enough, the time traveler might have prevented his own birth as surely as if he'd slain a grandparent.

But would that really be the case, using the quantum approach to the grandfather paradox? Recent work at the Los Alamos National Laboratory indicates that the course of history is more resilient than the butterfly effect might suggest. The researchers used a quantum computer to simulate time travel into the past, where a piece of information was deliberately damaged the computational equivalent of stepping on a Jurassic-era butterfly. But unlike Bradbury's story, the knock-on effect in the "present" of the computer simulation turned out to be relatively small and insignificant. That, of course, is great news for would-be time travelers. As long as you refrain from blatantly silly acts like killing a direct ancestor, it may be possible to go back in time without any paradoxical consequences at all.

Historical Dictionary of Science Fiction. https://sfdictionary.com/view/2178/grandfather-paradox

"Many-Worlds Interpretation of Quantum Mechanics," Stanford Encyclopedia of Philosophy, 2021. https://plato.stanford.edu/entries/qm-manyworlds/

"Time Travel without the Paradoxes," New Scientist, 1992. https://www.newscientist.com/article/mg13318143-000-science-time-travel-without-the-paradoxes/

"The block universe theory, where time travel is possible but time passing is an illusion," Australian Broadcasting Corporation, 2018. https://www.abc.net.au/news/science/2018-09-02/block-universe-theory-time-past-present-future-travel/10178386

"Experimental simulation of closed timelike curves," Nature Communications, 2014. https://www.nature.com/articles/ncomms5145

"A Sound of Thunder," Ray Bradbury, Internet Archive. https://archive.org/details/Planet_Stories_v06n04_1954-01/page/n5/mode/2up

"Simulating quantum 'time travel' disproves butterfly effect in quantum realm," Los Alamos National Laboratory, 2020. https://www.lanl.gov/discover/news-release-archive/2020/July/0728-quantum-time-travel.php

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What is the grandfather paradox? - Livescience.com

Physicists hope to detect asymmetry in spinning black holes using NASA's LISA telescope to finally provide proof of quantum gravity.

Detecting gravitational waves using Earth-based observatories has become a powerful tool for studying the properties of black holes.

Recently, a group of theoretical physicists has analyzed the process of gravitational wave emission and showed that the proposed space-based gravitational wave detector, LISA, will have enough sensitivity not only to detect more black hole mergers, but to measure a feature of spinning black holes an asymmetry between their northern and southern hemispheres in particular that will help elucidate a longstanding mystery.

The asymmetry is imprinted in a precise waveform of the gravitational radiation and is absent in the theory of general relativity, the most accepted theory of gravity, but is predicted by its quantum extension.

Quantum mechanics has been successfully used to study and explain the behavior of atoms, nuclei, and subatomic particles, while general relativity, which describes gravity as a curvature of spacetime, explains and predicts the dynamics of stars, galaxies, and the universe as a whole.

The unification of quantum mechanics and general relativity has been a formidable task made difficult by the fact that the usual rules of quantization required to convert a classical theory into a quantum one dont appear to work for gravity.

Since the typical scale of physical systems described by these two theories differ by many orders of magnitude, there is no need to use both simultaneously to describe a given event or behavior. But sometimes this is necessary. For example, a quantum mechanical description of gravity is needed to understand what happens in the vicinity of black holes surfaces and centers, as well as describe the behavior of the universe during the first moments of its life.

So far, theoretical physicists have proposed a number of theories for quantum gravity, but experimental studies are extremely complicated. The problem being that the typical energy scale at which the quantum gravity effects become important in the elementary particles interactions which scientists usually study to understand the fundamental physics are many orders of magnitude higher than the energies that can be achieved in colliders. For this reason, researchers have been seeking another way to explore it.

The most promising systems in which these effects are possible to measure are black holes, and physicists have already begun probing quantum effects in their physics by studying their membranes, which should exist above a black holes surface according to some theories of quantum gravity.

This is done by analyzing gravitational waves emitted during black hole merger events, which physicists currently detect with the Earth-based gravitational wave observatories LIGO and Virgo. Gravitational waves, which were first theorized by Albert Einstein, are ripples in the fabric of spacetime, and black hole mergers are so important in this realm because they generate the most powerful gravitational radiation in the universe.

Recently, two scientists from the Institute for Theoretical Physics in KU Leuven have proposed that studying these waves can also be used to measure the asymmetry between the northern and southern hemispheres of spinning black holes, giving us another chance to study quantum gravity with gravitational waves.

The best way to identify this, the researchers say, is to analyze the amplitude and spectrum of gravitational waves emitted when a relatively light black hole with a mass just a few times larger than the mass of our Sun is consumed by a supermassive neighbor a process that physicists call extreme mass-ration inspirals. The gravitational radiation generated in such events should carry an imprint of the aforementioned black hole asymmetry.

After analyzing gravitational waves from said event, the research team, unfortunately, had to conclude that the change in the gravitational wave signal due to the black hole asymmetry is too small to be detectable by currently operational gravitational wave detectors on Earth.

This problem could be solved with the launch of NASAs space-based gravitational wave observatory, LISA, which will have a much greater sensitivity to tiny changes in the spacetime geometry caused by passing gravitational waves.

LISA consists of three spacecrafts arranged in an equilateral triangle with sides that are 2.5 million km long (in comparison to 4 km arm lengths of LIGO), and moves along an Earth-like orbit around the Sun. When spacetime is distorted by celestial bodies found in our Solar System, the distances between the spacecraft stay the same. But when a gravitational wave passes through the LISA orbit, it leads to small oscillations in the triangle side lengths.

In order to detect these oscillations, laser beams are set up to travel between each spacecraft. When the distances along which the light beams travel change, a pattern in the combined beam signal changes as well, signaling the detection of the wave. The amplitude of the distance change between the spacecraft is proportional to the distance itself. The giant size of the space observatory will allow it to detect very small oscillations in the spacetime geometry, making it extremely sensitive. To put into perspective, LISA is expected to be able to measure relative shifts in the position of each spacecraft at distances that are less than the diameter of a hydrogen atom.

Its launch scheduled for the mid-2030s, and hopefully, it will allow us to put our theories of quantum gravity to the test.

Reference: (preprint) Kwinten Fransen, et al., On Detecting Equatorial Symmetry Breaking with LISA, arXiv:2201.03569

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Black hole asymmetry puts quantum gravity to the test - Advanced Science News

Basics of the general CK oscillator with nonextensivity

Various physical systems subjected to a friction-like force which is a linear function of velocity can be modeled by the formal CK oscillator. The Hamiltonian of the CK oscillator is given by34,35

$$begin{aligned} {hat{H}} = e^{-gamma t} frac{{hat{p}}^2}{2m} + frac{1}{2} e^{gamma t} m omega ^2 {hat{x}}^2, end{aligned}$$

(1)

where (gamma) is a damping constant. This Hamiltonian can be generalized by replacing the ordinary exponential function with a deformed one that is defined by1,37

$$begin{aligned} exp _q {(y)} = [1+(1-q)y]^{1/(1-q)}, end{aligned}$$

(2)

with an auxiliary condition

$$begin{aligned} 1+(1-q)y ge 0, end{aligned}$$

(3)

where q is a parameter indicating the degree of nonextensivity. This generalized function is known as the q-exponential and has its own merit in describing non-idealized dynamical systems. The characteristic behavior of the q-exponential function is shown in Fig.1. In the field of thermostatistics, a generalization of the Gaussian distribution through the q-exponential is known as the Tsallis distribution that is well fitted to many physical systems of which behavior does not follow the usual BG statistical mechanics38.

q-exponential function for several different values of q.

In terms of Eq.(2), we can express the generalized CK Hamiltonian in the form1

$$begin{aligned} {hat{H}}_q = frac{{hat{p}}^2}{2m exp _q{(gamma t)}} + frac{1}{2} exp _q{(gamma t)} m omega ^2 {hat{x}}^2. end{aligned}$$

(4)

This Hamiltonian is Hermitian and, in the case of (q rightarrow 1), it recovers to the ordinary CK one that is given in Eq.(1). From the use of the Hamiltons equations in one dimension, we can derive the classical equation of motion that corresponds to Eq.(4) as

$$begin{aligned} ddot{x} + frac{gamma }{1+(1-q)gamma t}{dot{x}} + omega ^2 x = 0. end{aligned}$$

(5)

In an extreme case where (q rightarrow 0), Eq.(2) reduces to a linear function (1+y). Along with this, Eq.(5) reduces to

$$begin{aligned} ddot{x} + frac{gamma }{1+gamma t}{dot{x}} + omega ^2 x = 0. end{aligned}$$

(6)

If we think from the pure mathematical point of view, it is also possible to consider even the case that q is smaller than zero based on the condition given in Eq.(3). However, in most actual nonextensive systems along this line, the value of q may not deviate too much from unity which is its standard value. So we will restrain to treating such extreme cases throughout this research.

In general, for time-dependent Hamiltonian systems, the energy operator is not always the same as the given Hamiltonian. The role of the Hamiltonian in this case is restricted: It plays only the role of a generator for the related classical equation of motion. From fundamental Hamiltonian dynamics, we can see that the energy operator of the generalized damped harmonic oscillator is given by26,39

$$begin{aligned} {hat{E}}_{q} = {hat{H}}_q/exp _q{(gamma t)}. end{aligned}$$

(7)

Let us denote two linearly independent homogeneous real solutions of Eq.(5) as (s_1(t)) and (s_2(t)). Then, from a minor mathematical evaluation, we have40,41

$$begin{aligned} s_1(t)= & {} {s}_{0,1}sqrt{frac{pi omega }{2gamma (1-q)}} [exp _q{(gamma t)}]^{-q/2} J_nu left( frac{omega }{(1-q)gamma } + omega t right) , end{aligned}$$

(8)

$$begin{aligned} s_2(t)= & {} {s}_{0,2}sqrt{frac{pi omega }{2gamma (1-q)}} [exp _q{(gamma t)}]^{-q/2} N_nu left( frac{omega }{(1-q)gamma } + omega t right) , end{aligned}$$

(9)

where (J_nu) and (N_nu) are the Bessel functions of the first and second kind, ({s}_{0,1}) and ({s}_{0,2}) are constants which have dimension of position, and (nu = {q}/{[2(1-q)]}). From Fig.2, we see that the phases in the time evolutions of (s_1(t)) and (s_2(t)) are different depending on the value of q. Now we can represent the general solution of Eq.(5) in the form

$$begin{aligned} x(t) = c_1 s_1(t) + c_2 s_2(t), end{aligned}$$

(10)

where (c_1) and (c_2) are arbitrary real constants.

Time evolution of (s_1(t)) (A) and (s_2(t)) (B) for several different values of q. We used (omega =1), (gamma =0.1), and (s_{0,1}=s_{0,2}=0.1).

We introduce another time function s(t) that will be used later as

$$begin{aligned} s(t) = sqrt{s_1^2(t)+s_2^2(t)}. end{aligned}$$

(11)

This satisfies the differential equation42

$$begin{aligned} ddot{s}(t) + frac{gamma }{1+(1-q)gamma t}{dot{s}}(t) + omega ^2 s(t) - frac{Omega ^2}{[mexp _q{(gamma t)}]^2} frac{1}{s^3(t)} = 0, end{aligned}$$

(12)

where (Omega) is a time-constant which is of the form

$$begin{aligned} Omega = m exp _q{(gamma t)} [s_1 {dot{s}}_2 - {dot{s}}_1 s_2 ]. end{aligned}$$

(13)

By differentiating Eq.(13) with respect to time directly, we can readily confirm that (Omega) does not vary in time.

In accordance with the invariant operator theory, the invariant operator must satisfy the Liouville-von Neumann equation which is

$$begin{aligned} frac{d {hat{I}}}{d t} = frac{partial {hat{I}}}{partial t} + frac{1}{ihbar } [{hat{I}},{hat{H}}_q] = 0. end{aligned}$$

(14)

A straightforward evaluation after substituting Eq.(4) into the above equation leads to24,40

$$begin{aligned} {hat{I}} = hbar Omega left( {hat{b}}^dagger {hat{b}} + frac{1}{2}right) , end{aligned}$$

(15)

where ({hat{b}}) is a destruction operator defined as

$$begin{aligned} {hat{b}} = sqrt{frac{1}{2hbar Omega }} left[ left( frac{Omega }{s(t)} -i m exp _q{(gamma t)} {dot{s}}(t) right) {hat{x}} + i s(t) {hat{p}} right] , end{aligned}$$

(16)

whereas its hermitian adjoint ({hat{b}}^dagger) is a creation operator. If we take the limit (gamma rightarrow 0), Eq.(16) reduces to that of the simple harmonic oscillator. One can easily check that the boson commutation relation for ladder operators holds in this case: ([{hat{b}},{hat{b}}^dagger ]=1). This consequence enables us to derive the eigenstates of ({hat{I}}) in a conventional way.

The zero-point eigenstate (| 0 rangle) is obtained from ({hat{b}}| 0 rangle =0). The excited eigenstates (| n rangle) are also evaluated by acting ({hat{b}}^dagger) into (| 0 rangle) n times. The Fock state wave functions (| psi _n rangle) that satisfy the Schrdinger equation are different from the eigenstates of ({hat{I}}) by only minor phase factors which can be obtained from basic relations24. However, we are interested in the SU(1,1) coherent states rather than the Fock states in the present work.

The SU(1,1) generators are defined in terms of ladder operators, such that

$$begin{aligned} hat{{mathcal {K}}}_0= & {} frac{1}{2} left( {hat{b}}^dagger {hat{b}} + frac{1}{2}right) , end{aligned}$$

(17)

$$begin{aligned} hat{{mathcal {K}}}_+= & {} frac{1}{2} ({hat{b}}^dagger )^2, end{aligned}$$

(18)

$$begin{aligned} hat{{mathcal {K}}}_-= & {} frac{1}{2} {hat{b}}^2. end{aligned}$$

(19)

From the inverse representation of Eq.(16) together with its hermitian adjoint ({hat{b}}^dagger), we can express ({hat{x}}) and ({hat{p}}) in terms of ({hat{b}}) and ({hat{b}}^dagger). By combining the resultant expressions with Eqs.(17)(19), we can also represent the canonical variables in terms of SU(1,1) generators as

$$begin{aligned} {hat{x}}^2= & {} frac{hbar s^2}{Omega } (2hat{{mathcal {K}}}_0 + hat{{mathcal {K}}}_+ + hat{{mathcal {K}}}_-), end{aligned}$$

(20)

$$begin{aligned} {hat{p}}^2= & {} frac{hbar }{s^2} Bigg [ 2 left( Omega + frac{[mexp _q(gamma t)]^2}{ Omega } s^2{dot{s}}^2 right) hat{{mathcal {K}}}_0 -left( sqrt{Omega } - frac{imexp _q(gamma t)}{ sqrt{Omega }} s{dot{s}} right) ^2 hat{{mathcal {K}}}_+ nonumber \&-left( sqrt{Omega } + frac{imexp _q(gamma t)}{ sqrt{Omega }}s{dot{s}} right) ^2 hat{{mathcal {K}}}_- Bigg ]. end{aligned}$$

(21)

The substitution of the above equations into Eq.(4) leads to

$$begin{aligned} {hat{H}}_q = delta _0(t) hat{{mathcal {K}}}_0 + delta (t) hat{{mathcal {K}}}_+ + delta ^*(t) hat{{mathcal {K}}}_- , end{aligned}$$

(22)

where

$$begin{aligned} delta _0(t)= & {} frac{hbar }{s^2} left( frac{Omega }{mexp _q{(gamma t)}} + frac{1}{Omega } mexp _q{(gamma t)} s^2 {dot{s}}^2 right) + frac{hbar }{Omega } mexp _q{(gamma t)}omega ^2 s^2 , end{aligned}$$

(23)

$$begin{aligned} delta (t)= & {} - frac{hbar }{2 mexp _q{(gamma t)} s^2} left( sqrt{Omega } - i frac{mexp _q{(gamma t)}s{dot{s}}}{sqrt{Omega }} right) ^2 + frac{hbar }{2Omega } mexp _q{(gamma t)} omega ^2 s^2 . end{aligned}$$

(24)

In accordance with Gerrys work (see Ref. 43), Eq.(22) belongs to a class of general Hamiltonian that preserves an arbitrary initial coherent state. In the next section, we will analyze the properties of nonextensivity associated with the SU(1,1) coherent states using the Hamiltonian in Eq.(22).

The SU(1,1) coherent states for the quantum harmonic oscillator belong to a dynamical group whose description is based on SU(1,1) Lie algebraic formulation. The analytical representation of the SU(1,1) coherent states provides a natural description of quantum and classical correspondence which has an important meaning in theoretical physics. On the experimental side, optical interferometers like radio interferometers that use four-wave mixers as a protocol for improving measurement accuracy are characterized through the SU(1,1) Lie algebra44,45.

According to the development of Perelomov46, the SU(1,1) coherent states are defined by

$$begin{aligned} | {tilde{xi }};k rangle = hat{{mathcal {D}}}(beta )|{{{tilde{0}}}} rangle _k , end{aligned}$$

(25)

where (hat{{mathcal {D}}}(beta )) is the displacement operator, (|{{{tilde{0}}}} rangle _k) is the vacuum state in the damped harmonic oscillator, and k is the Bargmann index of which allowed values are 1/4 and 3/4. The basis for the unitary space is a set of even boson number for (k=1/4), whereas it is a set of odd boson number for (k=3/4). Here, the displacement operator is given by

$$begin{aligned} {hat{D}}(beta )= & {} exp left[ frac{1}{2} (beta ^2 hat{{mathcal {K}}}_+ - beta ^{*2} hat{{mathcal {K}}}_-) right] nonumber \= & {} e^{{tilde{xi }} hat{{mathcal {K}}}_+} exp {-2ln [cosh (|beta |^2/2)] hat{{mathcal {K}}}_0} e^{-{tilde{xi }}^* hat{{mathcal {K}}}_-}, end{aligned}$$

(26)

where (beta) is the eigenvalue of ({hat{b}}) and ({tilde{xi }}) is an SU(1,1) coherent state parameter of the form

$$begin{aligned} {tilde{xi }} = frac{beta ^2}{|beta |^2} tanh (|beta |^2/2). end{aligned}$$

(27)

The above equation means that (|{tilde{xi }}| <1). For (k=3/4) among the two allowed values, the resolution of the identity in Hilbert space is given by47

$$begin{aligned} int dmu ({tilde{xi }};k) | {tilde{xi }} ; k rangle langle {tilde{xi }} ; k| = mathbf{1}, end{aligned}$$

(28)

where (dmu ({tilde{xi }};k)=[(2k-1)/pi ] d^2 {tilde{xi }} /(1-|{tilde{xi }}|^2)^2). More generally speaking, this resolution is valid for (k>1/2). For a general case where k is an arbitrary value, the exact resolution is unknown. Brif et al., on one hand, proposed a resolution of the identity with a weak concept in this context, which can be applicable to both cases of (k>1/2) and (k<1/2)47. In what follows, various characteristics of the damped harmonic oscillator with and without deformation in quantum physics, such as quantum correlation, phase coherence, and squeezing effect, can be explained by means of the SU(1,1) Lie algebra and the coherent states associated with this algebra48,49.

The expectation values of SU(1,1) generators in the states (| {tilde{xi }};k rangle) are50

$$begin{aligned} langle {tilde{xi }} ;k | hat{{mathcal {K}}}_0|{tilde{xi }};krangle= & {} k frac{1+|{tilde{xi }}|^2}{1-|{tilde{xi }}|^2 } , end{aligned}$$

(29)

$$begin{aligned} langle {tilde{xi }} ;k | hat{{mathcal {K}}}_+|{tilde{xi }};krangle= & {} frac{2k{tilde{xi }}^*}{1-|{tilde{xi }}|^2 } , end{aligned}$$

(30)

$$begin{aligned} langle {tilde{xi }} ;k | hat{{mathcal {K}}}_-|{tilde{xi }};krangle= & {} frac{2k{tilde{xi }}}{1-|{tilde{xi }}|^2 }. end{aligned}$$

(31)

Using the above equations, the expectation values of the Hamiltonian given in Eq.(22) are easily identified as50,51

$$begin{aligned} {{mathcal {H}}}_{q,k}= & {} langle {tilde{xi }} ;k | {hat{H}}_q |{tilde{xi }};k rangle nonumber \= & {} frac{k}{1-|{tilde{xi }}|^2} { delta _0(t)(1+|{tilde{xi }}|^2) +2 [delta (t){tilde{xi }}^*+delta ^*(t){tilde{xi }}] } . end{aligned}$$

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Analysis of the effects of nonextensivity for a generalized dissipative system in the SU(1,1) coherent states | Scientific Reports - Nature.com

January 26, 2022

Two University of Rochester faculty members have been elected fellows of the American Association for the Advancement of Science (AAAS). Nicholas Bigelow, the Lee A. DuBridge Professor of Physics and a professor of optics, and Michael Scott, the Arthur Gould Yates Professor of Engineering and also a professor in and chair of the computer science department, are among 564 members of the association recognized this year for their scientifically or socially distinguished efforts on behalf of the advancement of science or its applications.

Bigelow has helped advance the understanding of quantum physics and quantum optics through his pioneering research on the interactions between light and matter. His lab uses laser light to cool atoms to nearly absolute zero temperatures to better manipulate and study them.

Bigelows current projects include creating and manipulating Bose-Einstein condensatesa quantum state of matter made from an atomic gas cooled to temperatures close to absolute zeroand investigating the quantum nature of atom-photon interactions. This research has important applications in areas of quantum mechanics such as quantum computing and sensing. He is also director of the NASA-funded Consortium for Ultracold Atoms in Space and the principal investigator of cold atom experiments running aboard the International Space Station.

Bigelow joined the faculty of the University of Rochester in 1992 and served as chair of the Department of Physics and Astronomy from 2008 to 2014.

He has twice received the Universitys Society of Physics Students Award for Excellence in Undergraduate Teaching (in 1998 and 2006) and has held various positions in University governance and leadership, including serving as chair of the Board on Academic Honesty for the College from 1998 to 2004, chair of the University of Rochester Presidential Search Committee in 2004, cochair of the Universitys Middle States Accreditation Committee, and chair of the Faculty Senate.

Bigelow is a fellow of the American Physical Society and of Optica (formerly OSA, or the Optical Society of America).

Scotts widely cited research focuses primarily on systems software for parallel and distributed computing, including developing new ways to share data among concurrent activities, to automate its movement and placement, and to protect it from accidental loss or corruption.

He is best known as a cocreator of the MCS mutual exclusion lock and as the author of Programming Language Pragmatics, one of the definitive and most widely used textbooks on programming language design and implementation. Several algorithms from Scotts research group have been incorporated into the standard library of the Java programming language.

He is a fellow of the Association for Computing Machinery (ACM) and the Institute of Electrical and Electronics Engineers (IEEE). In 2006, he shared the Edsger W. Dijkstra Prize in Distributed Computing.

Scott, who joined the faculty in 1985, also chaired the Department of Computer Science from 1996 to 1999, and was interim chair for six months in 2007, and again in 2017. He received the Universitys Robert and Pamela Goergen Award for Distinguished Achievement and Artistry in Undergraduate Teaching in 2001, the William H. Riker Award for Graduate Teaching in 2020, and the Lifetime Achievement Award from the Hajim School of Engineering & Applied Sciences in 2018.

He has played an active role in University governance, including serving as cochair of the Faculty Advisory Committee for the presidential search in 2018.

Ultimate vacuum chamber creates nothing

Nicholas Bigelows lab conducts experiments using a box of nothing, an ultimate vacuum chamber that allows researchers to interact with and manipulate atoms. But is nothing ever possible? How have scientists, philosophers, and mathematicians thought about the concept of nothing throughout history and up to the present?

Tags: Arts and Sciences, award, Department of Computer Science, Department of Physics and Astronomy, Hajim School of Engineering and Applied Sciences, Institute of Optics, Michael Scott, Nicholas Bigelow

Category: Science & Technology

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Two Rochester researchers named AAAS fellows : NewsCenter - University of Rochester

Despite bold philosophical and scientific claims, theres still no good reason to doubt the existence of free will.

In the last several years, a number of prominent scientists have claimed that we have good scientific reason to believe that theres no such thing as free will that free will is an illusion. If this were true, it would be less than splendid. And it would be surprising, too, because it really seems like we have free will. It seems that what we do from moment to moment is determined by conscious decisions that we freely make.

We need to look very closely at the arguments that these scientists are putting forward to determine whether they really give us good reason to abandon our belief in free will. But before we do that, it would behoove us to have a look at a much older argument against free will an argument thats been around for centuries.

The older argument against free will is based on the assumption that determinism is true. Determinism is the view that every physical event is completely caused by prior events together with the laws of nature. Or, to put the point differently, its the view that every event has a cause that makes it happen in the one and only way that it could have happened.

If determinism is true, then as soon as the Big Bang took place 13 billion years ago, the entire history of the universe was already settled. Every event thats ever occurred was already predetermined before it occurred. And this includes human decisions. If determinism is true, then everything youve ever done every choice youve ever made was already predetermined before our solar system even existed. And if this is true, then it has obvious implications for free will.

Suppose that youre in an ice cream parlor, waiting in line, trying to decide whether to order chocolate or vanilla ice cream. And suppose that when you get to the front of the line, you decide to order chocolate. Was this choice a product of your free will? Well, if determinism is true, then your choice was completely caused by prior events. The immediate causes of the decision were neural events that occurred in your brain just prior to your choice. But, of course, if determinism is true, then those neural events that caused your decision had physical causes as well; they were caused by even earlier events events that occurred just before they did. And so on, stretching back into the past. We can follow this back to when you were a baby, to the very first events of your life. In fact, we can keep going back before that, because if determinism is true, then those first events were also caused by prior events. We can keep going back to events that occurred before you were even conceived, to events involving your mother and father and a bottle of Chianti.

If determinism is true, then as soon as the Big Bang took place 13 billion years ago, the entire history of the universe was already settled.

So if determinism is true, then it was already settled before you were born that you were going to order chocolate ice cream when you got to the front of the line. And, of course, the same can be said about all of our decisions, and it seems to follow from this that human beings do not have free will.

Lets call this the classical argument against free will. It proceeds by assuming that determinism is true and arguing from there that we dont have free will.

Theres a big problem with the classical argument against free will. It just assumes that determinism is true. The idea behind the argument seems to be that determinism is just a commonsense truism. But its actually not a commonsense truism. One of the main lessons of 20th-century physics is that we cant know by common sense, or by intuition, that determinism is true. Determinism is a controversial hypothesis about the workings of the physical world. We could only know that its true by doing some high-level physics. Moreover and this is another lesson of 20th-century physics as of right now, we dont have any good evidence for determinism. In other words, our best physical theories dont answer the question of whether determinism is true.

During the reign of classical physics (or Newtonian physics), it was widely believed that determinism was true. But in the late 19th and early 20th centuries, physicists started to discover some problems with Newtons theory, and it was eventually replaced with a new theory quantum mechanics. (Actually, it was replaced by two new theories, namely, quantum mechanics and relativity theory. But relativity theory isnt relevant to the topic of free will.) Quantum mechanics has several strange and interesting features, but the one thats relevant to free will is that this new theory contains laws that are probabilistic rather than deterministic. We can understand what this means very easily. Roughly speaking, deterministic laws of nature look like this:

If you have a physical system in state S, and if you perform experiment E on that system, then you will get outcome O.

But quantum physics contains probabilistic laws that look like this:

If you have a physical system in state S, and if you perform experiment E on that system, then there are two different possible outcomes, namely, O1 and O2; moreover, theres a 50 percent chance that youll get outcome O1 and a 50 percent chance that youll get outcome O2.

Its important to notice what follows from this. Suppose that we take a physical system, put it into state S, and perform experiment E on it. Now suppose that when we perform this experiment, we get outcome O1. Finally, suppose we ask the following question: Why did we get outcome O1 instead of O2? The important point to notice is that quantum mechanics doesnt answer this question. It doesnt give us any explanation at all for why we got outcome O1 instead of O2. In other words, as far as quantum mechanics is concerned, it could be that nothing caused us to get result O1; it could be that this just happened.

Now, Einstein famously thought that this couldnt be the whole story. Youve probably heard that he once said that God doesnt play dice with the universe. What he meant when he said this was that the fundamental laws of nature cant be probabilistic. The fundamental laws, Einstein thought, have to tell us what will happen next, not what will probably happen, or what might happen. So Einstein thought that there had to be a hidden layer of reality, below the quantum level, and that if we could find this hidden layer, we could get rid of the probabilistic laws of quantum mechanics and replace them with deterministic laws, laws that tell us what will happen next, not just what will probably happen next. And, of course, if we could do this if we could find this hidden layer of reality and these deterministic laws of nature then we would be able to explain why we got outcome O1 instead of O2.

But a lot of other physicists most notably, Werner Heisenberg and Niels Bohr disagreed with Einstein. They thought that the quantum layer of reality was the bottom layer. And they thought that the fundamental laws of nature or at any rate, some of these laws were probabilistic laws. But if this is right, then it means that at least some physical events arent deterministically caused by prior events. It means that some physical events just happen. For instance, if Heisenberg and Bohr are right, then nothing caused us to get outcome O1 instead of O2; there was no reason why this happened; it just did.

The debate between determinists like Einstein and indeterminists like Heisenberg and Bohr has never been settled.

The debate between Einstein on the one hand and Heisenberg and Bohr on the other is crucially important to our discussion. Einstein is a determinist. If hes right, then every physical event is predetermined or in other words, completely caused by prior events. But if Heisenberg and Bohr are right, then determinism is false. On their view, not every event is predetermined by the past and the laws of nature; some things just happen, for no reason at all. In other words, if Heisenberg and Bohr are right, then indeterminism is true.

And heres the really important point for us. The debate between determinists like Einstein and indeterminists like Heisenberg and Bohr has never been settled. We dont have any good evidence for either view. Quantum mechanics is still our best theory of the subatomic world, but we just dont know whether theres another layer of reality, beneath the quantum layer. And so we dont know whether all physical events are completely caused by prior events. In other words, we dont know whether determinism or indeterminism is true. Future physicists might be able to settle this question, but as of right now, we dont know the answer.

But now notice that if we dont know whether determinism is true or false, then this completely undermines the classical argument against free will. That argument just assumed that determinism is true. But we now know that there is no good reason to believe this. The question of whether determinism is true is an open question for physicists. So the classical argument against free will is a failure it doesnt give us any good reason to conclude that we dont have free will.

Despite the failure of the classical argument, the enemies of free will are undeterred. They still think theres a powerful argument to be made against free will. In fact, they think there are two such arguments. Both of these arguments can be thought of as attempts to fix the classical argument, but they do this in completely different ways.

The first new-and-improved argument against free will which is a scientific argument starts with the observation that it doesnt matter whether the full-blown hypothesis of determinism is true because it doesnt matter whether all events are predetermined by prior events. All that matters is whether our decisions are predetermined by prior events. And the central claim of the first new-and-improved argument against free will is that we have good evidence (from studies performed by psychologists and neuroscientists) for thinking that, in fact, our decisions are predetermined by prior events.

The second new-and-improved argument against free will which is a philosophical argument, not a scientific argument relies on the claim that it doesnt matter whether determinism is true because indeterminism is just as incompatible with free will as determinism is. The argument for this is based on the claim that if our decisions arent determined, then they arent caused by anything, which means that they occur randomly. And the central claim of the second new-and-improved argument against free will is that if our decisions occur randomly, then they just happen to us, and so theyre not the products of our free will.

My own view is that neither of these new-and-improved arguments succeeds in showing that we dont have free will. But it takes a lot of work to undermine these two arguments. In order to undermine the scientific argument, we need to explain why the relevant psychological and neuroscientific studies dont in fact show that we dont have free will. And in order to undermine the philosophical argument, we need to explain how a decision could be the product of someones free will how the outcome of the decision could be under the given persons control even if the decision wasnt caused by anything.

So, yes, this would all take a lot of work. Maybe I should write a book about it.

Mark Balaguer is Professor in the Department of Philosophy at California State University, Los Angeles. He is the author of several books, including Free Will, from which this article is adapted.

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Why the Classical Argument Against Free Will Is a Failure - The MIT Press Reader

About the Centre for Quantum Technologies

The Centre for Quantum Technologies (CQT) is a research centre of excellence in Singapore. It brings together physicists, computer scientists and engineers to do basic research on quantum physics and to build devices based on quantum phenomena. Experts in this new discipline of quantum technologies are applying their discoveries in computing, communications, and sensing.

CQT is hosted by the National University of Singapore and also has staff at Nanyang Technological University. With some 180 researchers and students, it offers a friendly and international work environment.

Learn more about CQT atwww.quantumlah.org.

Job Description

The candidate will help the research team working on quantum technologies with experiment preparation and support for the current research efforts. This includes data analysis, programming as well as CAD design. The candidate will be embedded in the research group and help with the day to day experimental work.

Job Requirements

Additional Information

At NUS, the health and safety of our staff and students is one of our utmost priorities and COVID-vaccination supports our commitment to ensure the safety of our community and to make NUS as safe and welcoming as possible. Many of our roles require significant amount of physical interactions with student / staff / public members. Even for job roles that can be performed remotely, there will be instances where on-campus presence is required.

With effect from 15 January 2022, based on Singapores legal requirements, unvaccinated workers will not be able work at the NUS premises. As such, we regret to inform that job applicants need to be fully COVID-19 vaccinated for successful employment with NUS.

MOM Updated advisory on COVID-vaccination at the Workplace, subject to changes in accordance with the national COVID-19 measures

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Research Assistant, Experimentation, Centre for Quantum Technologies job with NATIONAL UNIVERSITY OF SINGAPORE | 279321 - Times Higher Education (THE)