Weekly Papers on Quantum Foundations (50)

Gao, Shan (2018) Why we cannot see the tails of Schrödinger’s cat. [Preprint]

Authors: Blake C. Stacey

In 1996, N. David Mermin proposed a set of desiderata for an understanding of quantum mechanics, the “Ithaca Interpretation”. In 2012, Mermin became a public advocate of QBism, an interpretation due to Christopher Fuchs and Ruediger Schack. Here, we evaluate QBism with respect to the Ithaca Interpretation’s six desiderata, in the process also evaluating those desiderata themselves. This analysis reveals a genuine distinction between QBism and the IIQM, but also a natural progression from one to the other.

Authors: Philip K. SchwartzDomenico Giulini

In this paper we extend the WKB-like `non-relativistic’ expansion of the minimally coupled Klein–Gordon equation after Kiefer and Singh [1], L\”ammerzahl [2] and Giulini and Gro{\ss}ardt [3] to arbitrary order in $c^{-1}$, leading to Schr\”odinger equations describing a quantum particle in a general gravitational field, and compare the results with canonical quantisation of a free particle in curved spacetime, following Wajima et al. [4]. Furthermore, using a more operator-algebraic approach, the Klein–Gordon equation and the canonical quantisation method are shown to lead to the same results for some special terms in the Hamiltonian describing a single particle in a general stationary spacetime, without any `non-relativistic’ expansion.

Authors: Yang WuWenqiang LiuJianpei GengXingrui SongXiangyu YeChang-Kui DuanXing RongJiangfeng Du

A fundamental axiom of quantum mechanics requires the Hamiltonians to be Hermitian which guarantees real eigen-energies and probability conservation. However, a class of non-Hermitian Hamiltonians with Parity-Time ($\mathcal{PT}$) symmetry can still display entirely real spectra. The Hermiticity requirement may be replaced by $\mathcal{PT}$ symmetry to develop an alternative formulation of quantum mechanics. A series of experiments have been carried out with classical systems including optics, electronics, microwaves, mechanics and acoustics. However, there are few experiments to investigate $\mathcal{PT}$ symmetric physics in quantum systems.Here we report the first observation of the $\mathcal{PT}$ symmetry breaking in a single spin system. We have developed a novel method to dilate a general $\mathcal{PT}$ symmetric Hamiltonian into a Hermitian one, which can be realized in a practical quantum system.Then the state evolutions under $\mathcal{PT}$ symmetric Hamiltonians, which range from $\mathcal{PT}$ symmetric unbroken to broken regions, have been experimentally observed with a single nitrogen-vacancy (NV) center in diamond. Due to the universality of the dilation method, our result opens a door for further exploiting and understanding the physical properties of $\mathcal{PT}$ symmetric Hamiltonian in quantum systems.

Authors: Pasquale BossoSaurya Das

We show that the standard Lorentz transformations admit an invariant mass (length) scale, such as the Planck scale. In other words, the frame independence of such scale is built-in within those transformations, and one does not need to invoke the principle of relativity for their invariance. This automatically ensures the frame-independence of the spectrum of geometrical operators in quantum gravity. Furthermore, we show that the above predicts a small but measurable difference between the inertial and gravitational mass of any object, regardless of its size or whether it is elementary or composite.

Authors: Eugenio BianchiAnuradha GuptaHal M. HaggardB. S. Sathyaprakash

Black hole entropy is a robust prediction of quantum gravity with no observational test to date. We use the Bekenstein-Hawking entropy formula to determine the probability distribution of the spin of black holes at equilibrium in the microcanonical ensemble. We argue that this ensemble is relevant for black holes formed in the early universe and predicts the existence of a population of black holes with zero spin. Observations of such a population at LIGO, Virgo, and future gravitational wave observatories would provide the first experimental test of the statistical nature of black hole entropy.

Authors: Marios H. MichaelJoerg SchmiedmayerEugene Demler

Recent experimental realizations of uniform confining potentials for ultracold atoms make it possible to create quantum acoustic resonators and explore nonequilibrium dynamics of quantum field theories. These systems offer a promising new platform for studying the dynamical Casimir effect, since they allow to achieve relativistic, i.e. near sonic, velocities of the boundaries. In comparison to previously studied optical and classical hydrodynamic systems ultracold atoms allow to realize a broader class of dynamical experiments combining both classical driving and vacuum squeezing. In this paper we discuss theoretically two types of experiments with interacting one dimensional condensates with moving boundaries. Our analysis is based on the Luttinger liquid model which utilizes the emergent conformal symmetry of the low energy sector of the Lieb-Liniger model. The first system we consider is a variable length interferometer with two Y-junctions connected back to back. We demonstrate that dynamics of the relative phase between the two arms of the interferometer can be analyzed using the formalism developed by Moore in the problem of electromagnetic vacuum squeezing in a cavity with moving mirrors. The second system we discuss is a single condensate in a box potential with periodically moving walls. This system exhibits classical excitation of the mode resonant with the drive as well as nonlinear generation of off-resonant modes. In addition we find strong parametric multimode squeezing between modes whose energy difference matches integer multiples of the drive frequency.

Callender, Craig (2018) Can We Quarantine the Quantum Blight? [Preprint]
Pruss, Alexander R. (2018) Underdetermination of infinitesimal probabilities. [Preprint]
Bacelar Valente, Mario (2018) What do light clocks say to us regarding the so-called clock hypothesis? THEORIA. An International Journal for Theory, History and Foundations of Science, 33 (3). pp. 435-446. ISSN 2171-679X
Huggett, Nick (2018) Spacetime ‘Emergence’. [Preprint]
Huggett, Nick (2014) Reading the Past in the Present. [Preprint]

Theory has established the importance of geometric phase (GP) effects in the adiabatic dynamics of molecular systems with a conical intersection connecting the ground- and excited-state potential energy surfaces, but direct observation of their manifestation in chemical reactions remains a major challenge. Here, we report a high-resolution crossed molecular beams study of the H + HD -> H2 + D reaction at a collision energy slightly above the conical intersection. Velocity map ion imaging revealed fast angular oscillations in product quantum state–resolved differential cross sections in the forward scattering direction for H2 products at specific rovibrational levels. The experimental results agree with adiabatic quantum dynamical calculations only when the GP effect is included.

After the historic announcement in February 2016 hailing the discovery of gravitational waves, it didn’t take long for skeptics to emerge.

The detection of these feeble undulations in the fabric of space and time by the Laser Interferometer Gravitational-Wave Observatory (LIGO) was said to have opened a new ear on the cosmos. But the following year, a group of physicists at the Niels Bohr Institute in Copenhagen published a paper casting doubt on LIGO’s analysis. They focused their criticism on the experiment’s famous first signal, a squiggly line — representing the collision of giant black holes more than a billion light-years away — that was printed in newspapers worldwide and tattooed on bodies.

Even as LIGO sensed more gravitational-wave signals and its founders received Nobel Prizes, the Copenhagen researchers, led by professor emeritus Andrew Jackson, claimed to have found unexplained correlations in the “noise” picked up by LIGO’s twin detectors. The detectors — L-shaped instruments whose arms alternately stretch and squeeze when a gravitational wave passes — are located far apart in Livingston, Louisiana, and Hanford, Washington, to ensure that only gravitational ripples from space could wiggle both instruments in just the right way to produce the telltale signal. But according to Jackson and his team, the correlations in the noise data suggested that LIGO might have detected not gravitational waves but some terrestrial disturbance, perhaps an earthquake. They claimed that, at the very least, something was not right with the instruments or with the LIGO scientists’ analysis.

The findings were worrisome. LIGO scientists checked their work again, and a party of experts visited the Niels Bohr Institute last year to dig into the details of Jackson and colleagues’ algorithms. Two groups of researchers set out to independently analyze LIGO’s data and the Copenhagen group’s code.

Now both groups have completed their studies. The new papers explain different aspects of the problem that led Jackson and his coauthors to make their claim. Both analyses definitively conclude that the claim is wrong: There are no unexplained correlations in LIGO’s noise.

“We see no justification for lingering doubts about the discovery of gravitational waves,” the authors of one of the papers, the physicists Martin Green and John Moffat of the Perimeter Institute for Theoretical Physics, said in an email.

The pair has no direct ties to LIGO. “It’s important for science for people to do analysis of data and results independently of the group,” Moffat said, “especially for such a historic event in the history of physics.”

Frans Pretorius, a gravitational-wave expert at Princeton University who was not involved in any of the recent studies, said that for more than a year, he and most of the physics community have been satisfied that LIGO’s analysis, and its discovery, are sound. Nevertheless, he said, “it’s important that finally there is a thorough analysis in the form of a paper,” rather than “media back and forth.”

The spokesperson of the 1,200-person LIGO Scientific Collaboration, David Shoemaker of the Massachusetts Institute of Technology, said by email that the new findings corroborate internal discussions among the team. “Seeing those two non-Collaboration re-analyses does reaffirm my certainty that the detections are genuine,” Shoemaker said, “and also is a reinforcement of our earlier perception of where the Jackson et al. paper has problems.”

In an email, Jackson called Green and Moffat’s paper, which was published in Physics Letters B in September, “absolute rubbish.” When asked to elaborate, he appeared to wrongly characterize their argument and didn’t address the most important issues they raised about his team’s work. Jackson also dismissed the second set of findings by Alex Nielsen of the Max Planck Institute for Gravitational Physics in Hannover, Germany, and three coauthors, whose paper appeared on the physics preprint site arxiv.org in November and is under review by the Journal of Cosmology and Astroparticle Physics. “We are in the process of writing a response to this latest paper,” Jackson wrote, so “I will not explain where they (once again) made their mistakes.”

“The Copenhagen group refuse to accept that they may be wrong,” Moffat said. “In fact, they are wrong.”

Experts say the problem came down to a combination of blunders: several by the Copenhagen physicists, and one by LIGO.

To help tease out the puny wiggle of a passing gravitational wave from a noisy background, LIGO’s algorithms constantly compare the lengths of the twin detectors’ arms, which oscillate when agitated by a passing gravitational wave or background noise, to “template waveforms” — possible gravitational-wave signals calculated from Einstein’s general theory of relativity. When there’s a close match between a signal detected in Hanford and one sensed shortly before or after in Livingston that also fits a template waveform, email alerts fly around the world.

The scientists then carefully determine the “best-fit” gravitational waveform that most closely matches the signal in the two detectors. When this waveform is subtracted from each of the signals, this leaves behind “noise residuals” — the remaining little wiggles in the detectors that should be uncorrelated, since the instruments are about 2,000 miles apart.

In their 2017 paper, the Copenhagen group claimed to have discovered that the noise in Livingston matched the noise in Hanford seven milliseconds later, just as the putative gravitational-wave signal arrived at both detectors. They interpreted this to mean that LIGO either hadn’t cleanly separated their signal from the noise, or correlations in the noise at exactly the right moment were responsible for the entire signal.

However, Green and Moffat identified a series of errors in the Copenhagen team’s data-handling that they say conspired to create a correlation that wasn’t really there.

To look for correlations in the residuals, Jackson and his colleagues picked a 20-millisecond segment of Livingston data and slid 20-millisecond segments of Hanford data across it, registering correlations whenever peaks overlapped with peaks and troughs with troughs. They found that strong correlations happened when the data was offset by seven milliseconds. But Green and Moffat noticed that when they took Jackson and colleagues’ code and reversed the procedure, fixing the Hanford noise data and sliding Livingston data segments across it, the correlation at seven-milliseconds offset went away. “This was a big red flag because it says, OK, you don’t have a calculational method that’s robust,” said Green, an expert in digital signal processing. Rather, the lengths of the data segments and their asymmetric treatment were “tuned to obtain a correlation signal at just about any desired time offset,” he said.

In a separate calculation, Jackson and his team seemed to find non-random, correlated patterns of peaks and troughs throughout the noise records in the two detectors. But Green and Moffat inferred that the Copenhagen physicists had not “windowed” the two sets of noise data. Windowing is a standard technique of smoothly dialing a signal to zero at the beginning and end of a segment of data before doing a mathematical operation called a “Fourier transform” that facilitates comparisons to other data. The Fourier transform treats a data segment as if it is cyclical, looping together the beginning and end. If the segment isn’t windowed, abrupt changes at the endpoints called “border distortions” can wind up looking like correlations when the data is compared with a second data set.

When Green and Moffat windowed the two sets of noise data, the claimed correlations went away. “Our concern is that the calculation that was done by the Copenhagen group was contrived to get the result they wanted to get,” Green said.

Nielsen and his coauthors — Alexander Nitz, Collin Capano and Duncan Brown — also concluded that the claimed correlation in the noise isn’t real, but they say the error can be attributed at least in part to LIGO’s mistake in providing the wrong data in the first figure of their 2016 discovery paper in Physical Review Letters.

Figure 1 is “the thing people have tattooed on their arms,” said Brown, a gravitational-wave astronomer at Syracuse University and a former LIGO member, who left the collaboration this year to pursue independent analyses of the data.

The figure’s top panel shows side-by-side squiggly lines representing the gravitational-wave signal detected in Livingston and Hanford. Below that are template waveforms closely matching the signals and, in the bottom panel, jagged lines representing the “noise residuals” in the two detectors, after the template waveform has been subtracted from each data set.

Brown explained that Jackson’s code, which he examined in detail during a visit to Copenhagen last year, detects an overlap in the residuals at seven milliseconds offset for a mundane reason: The template waveform shown in Figure 1 is not the “best-fit” waveform that LIGO actually used in its rigorous analysis. The figure was created for illustrative purposes, Brown and others explained. The figure-maker had matched a template waveform to the twin signals by eye, rather than using the best-fit signal as determined by careful calculations. Small imperfections in the subtracted waveform meant that there was some gravitational-wave signal left in both data sets that didn’t get subtracted off, and which ended up mixed in with the noise shown at the bottom of Figure 1 — producing correlations that could be teased out by Jackson and colleagues’ algorithms. “What they discovered was an imperfect subtraction” of the signal waveform, Brown said. “When we subtract a better waveform than the one used in the PRL paper, we find no statistically significant residuals.”

“If LIGO did anything wrong,” he added, “it was not making it crystal-clear that pieces of that figure were illustrative and the detection claim is not based on that plot.” Jackson, however, accused LIGO scientists in an email of “misconduct” and making “the conscious decision not to inform the reader that they were violating one of the central canons of good scientific practice.”

Which is to blame, LIGO’s sloppy figure or the Copenhagen group’s faulty calculations? “In reality, I think it’s both,” Brown said. If Jackson and his colleagues were able to tune their parameters to create correlations at seven milliseconds offset, as Green and Moffat’s findings suggest, this would have essentially biased their calculations. Then, at the same offset, their biased algorithm picked out the imperfectly subtracted bits of signal in the noise, reinforcing the false impression.

Jackson, however, maintains that the unexplained correlations are present and says he and his colleagues are preparing a rebuttal to the recent work. He still thinks LIGO’s first, most powerful gravitational-wave signal (and all others by extension) might have been something else altogether — perhaps, he said, “a lightning strike in Burkina Faso, seismic, or even one of the mysterious ‘glitches’ that LIGO detectors see about once an hour.”

But both new papers reviewed and reanalyzed LIGO’s raw data and rediscovered the gravitational-wave signals within it, using different algorithms than LIGO’s. Other researchers have done the same.

“I think the pursuit of independent analyses of gravitational-wave data is a very important and valuable thing to do, and we are delighted that more people are getting involved,” said Shoemaker, LIGO’s spokesperson. “That the Jackson et al. work has stimulated some additional independent investigations can be seen as a positive outcome, but I personally think it comes with a fully unnecessary cost of ‘drama.’”

Meanwhile, LIGO’s twin detectors, along with a third instrument in Europe called Virgo that switched on in 2017, have recorded 10 black hole collisions to date and one space-time wiggle from colliding neutron stars. Scientists announced the four latest black hole detections this month and released dazzling graphics showing the universe’s growing population of these mysterious, invisible, super-dense spheres. When the neutron-star collision was detected last year, 70 telescopes swiveled toward the fireworks; their observations indicated the cosmic origin of gold, the expansion rate of the universe and more.

Brown said it isn’t surprising that LIGO’s revolutionary discovery invited skepticism. A powerful event was detected “basically the day we turned it on,” he said, and the rate of black hole collisions in the cosmos has turned out to be at the high end of expectations.

“The universe loves gravitational-wave astronomers,” he said.

show enclosure

White holes are black ones in reverse, spewing out matter– and they could give us our first glimpse of the quantum source of space-time, says physicist Carlo Rovelli
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 474, Issue 2220, December 21, 2018.
Huggett, Nick (2018) What Can We Learn from Stringy Black Holes? [Preprint]
Huggett, Nick (2018) A Philosopher Looks at Non-Commutative Geometry. [Preprint]
Jaimes Arriaga, Jesús Alberto and Fortin, Sebastian and Lombardi, Olimpia (2018) A new chapter in the problem of the reduction of chemistry to physics: The Quantum Theory of Atoms in Molecules. [Preprint]
Fortin, Sebastian and Labarca, Martín and Lombardi, Olimpia (2018) On the ontological status of molecular structure: is it possible to reconcile molecular chemistry with quantum mechanics? [Preprint]
Abstract

Recently, there has been some discussion of how Dutch book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory (Feintzeig [2015]; Feintzeig and Fletcher [2017]; Wroski and Godziszewski [2017]). In this paper, we argue that the form of inconsistency underlying this alleged irrationality is deeply and comprehensively related to the more familiar inconsistency phenomenon of contextuality. Our main result is that the hierarchy of contextuality due to Abramsky and Brandenburger [2011] corresponds to a hierarchy of additivity/convexity-violations that yields formal Dutch books of different strengths. We then use this result to provide a partial assessment of whether these formal Dutch books can be given a convincing normative interpretation.

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