Archive for quantum theory

Can single-world interpretations of quantum theory be self-consistent?

Posted in The Universe and Stuff with tags , on May 4, 2016 by telescoper

I saw a provocative-looking paper on the arXiv the other day (by Daniela Frauchiger and Renato Renner)  with the title Single-world interpretations of quantum theory cannot be self-consistent. No doubting what the authors think!

Here’s the abstract:

 According to quantum theory, a measurement may have multiple possible outcomes. Single-world interpretations assert that, nevertheless, only one of them “really” occurs. Here we propose a gedankenexperiment where quantum theory is applied to model an experimenter who herself uses quantum theory. We find that, in such a scenario, no single-world interpretation can be logically consistent. This conclusion extends to deterministic hidden-variable theories, such as Bohmian mechanics, for they impose a single-world interpretation.

Since this is a subject we’ve had interesting debates about on this blog I thought I’d post a link to it here and see if anyone would like to respond through the comments. I haven’t had time to read it thoroughly yet, but I do have a bit of train travel to do tomorrow…

 

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Do Primordial Fluctuations have a Quantum Origin?

Posted in The Universe and Stuff with tags , , , , , , on October 21, 2015 by telescoper

A quick lunchtime post containing a confession and a question, both inspired by an interesting paper I found recently on the arXiv with the abstract:

We investigate the quantumness of primordial cosmological fluctuations and its detectability. The quantum discord of inflationary perturbations is calculated for an arbitrary splitting of the system, and shown to be very large on super-Hubble scales. This entails the presence of large quantum correlations, due to the entangled production of particles with opposite momentums during inflation. To determine how this is reflected at the observational level, we study whether quantum correlators can be reproduced by a non-discordant state, i.e. a state with vanishing discord that contains classical correlations only. We demonstrate that this can be done for the power spectrum, the price to pay being twofold: first, large errors in other two-point correlation functions, that cannot however be detected since hidden in the decaying mode; second, the presence of intrinsic non-Gaussianity the detectability of which remains to be determined but which could possibly rule out a non-discordant description of the Cosmic Microwave Background. If one abandons the idea that perturbations should be modeled by Quantum Mechanics and wants to use a classical stochastic formalism instead, we show that any two-point correlators on super-Hubble scales can exactly be reproduced regardless of the squeezing of the system. The later becomes important only for higher order correlation functions, that can be accurately reproduced only in the strong squeezing regime.

I won’t comment on the use of the word “quantumness” nor the plural “momentums”….

My confession is that I’ve never really followed the logic that connects the appearance of classical fluctuations to the quantum description of fields in models of the early Universe. People have pointed me to papers that claim to spell this out, but they all seem to miss the important business of what it means to “become classical” in the cosmological setting. My question, therefore, is can anyone please point me to a book or a paper that addresses this issue rigorously?

Please let me know through the comments box, which you can also use to comment on the paper itself…

A Very Clever Experimental Test of a Bell Inequality

Posted in The Universe and Stuff with tags , , on August 26, 2015 by telescoper

Travelling and very busy most of today so not much time to post. I did, however, however get time to peruse a very nice paper I saw on the arXiv with the following abstract:

For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. In his seminal work, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. Bell showed that in any local realist theory the correlations between distant measurements satisfy an inequality and, moreover, that this inequality can be violated according to quantum theory. This provided a recipe for experimental tests of the fundamental principles underlying the laws of nature. In the past decades, numerous ingenious Bell inequality tests have been reported. However, because of experimental limitations, all experiments to date required additional assumptions to obtain a contradiction with local realism, resulting in loopholes. Here we report on a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell’s inequality. We employ an event-ready scheme that enables the generation of high-fidelity entanglement between distant electron spins. Efficient spin readout avoids the fair sampling assumption (detection loophole), while the use of fast random basis selection and readout combined with a spatial separation of 1.3 km ensure the required locality conditions. We perform 245 trials testing the CHSH-Bell inequality S≤2 and find S=2.42±0.20. A null hypothesis test yields a probability of p=0.039 that a local-realist model for space-like separated sites produces data with a violation at least as large as observed, even when allowing for memory in the devices. This result rules out large classes of local realist theories, and paves the way for implementing device-independent quantum-secure communication and randomness certification.

While there’s nothing particularly surprising about the result – the nonlocality of quantum physics is pretty well established – this is a particularly neat experiment so I encourage you to read the paper!

Perhaps some day someone will carry out this, even neater, experiment!

PS Anyone know where I can apply to for a randomness certificate?

The Joy of Natural Units

Posted in The Universe and Stuff with tags , , , on March 5, 2010 by telescoper

I’m glad it’s the end of the week. It’s been ridiculously busy. It didn’t help that I was already exhausted before it started, after a hectic three days in Geneva. Part of the reason for being so heavily occupied is that my teaching duties have just doubled. I teach the second half of a module called Nuclear and Particle Physics, and I’ve just taken over  for the second half of the semester to cover the part about particle physics. I started my set of 11 lectures with one about natural units, which is a lot of fun because it usually divides the class into two opposing camps.

About half the students think natural units are crazy, and the other half think they’re great. I’m in the second camp. The motivation is straightforward: particle physics combines quantum theory, which involves Planck’s constant

\hbar \simeq 1.05 \times 10^{-34}\,\,\,{\rm Js}

with special relativity, which involves the speed of light

c\simeq 3 \times 10^{8}\,\,\,{\rm m s}^{-1} .

Using everyday SI units (metres, seconds and kilograms) to deal with quantities that are either ridiculously small or ridiculously large doesn’t make any sense but, more importantly, the SI units don’t really reflect the physics very clearly.

In natural units we take these two constants to be equal to unity, so they don’t appear in any formulae:

\hbar = c =1

For example, the energy invariant in special relativity is usually written

E^2=p^2c^2 + m^2c^4

This is where the most famous equation in physics

E=mc^2

comes from. However, the equivalence between mass and energy (and also momentum) is much more clearly expressed in the natural units system:

E^2=p^2 + m^2

None of those tiresome factors of c^2 to remember! Mass, energy and momentum are all expressed in terms of the same natural unit of energy (usually, in particle physics, the GeV).  You can keep track of which is which by the simple expedient of using different names.

Velocities are, of course, always expressed as a fraction of c in this system so have no units.

In quantum theory we find energy E=\hbar \omega becomes E=\omega so energy is expressed in the same units as frequency. Energy is thus a measure of inverse time.  Momentum p =\hbar k becomes just p= k so momentum is an inverse length.  This is in accord with the various forms of Heisenberg’s Uncertainty Principle too:  \Delta p \Delta x \sim \hbar is \Delta p \Delta x \sim 1 and \Delta E \Delta t \sim \hbar becomes \Delta E \Delta t \sim 1. A particle with a finite lifetime thus has a finite energy width which is inversely proportional to the lifetime. It makes sense to use energy units for both of these things.

As an extra bonus we can dispense with the clumsy way that electromagnetism is handled in the SI system by noting that

\frac{e^2}{4\pi \epsilon_0 \hbar c} \equiv \alpha\simeq \frac{1}{137}

is dimensionless. In the SI system the coulomb force between two electrons is \frac{e^2}{4\pi \epsilon_0 r^2} whereas in natural units it is just \frac{\alpha}{r^2}, which is much nicer. Incidentally, the strange quantity \epsilon_0 that appears in the SI version is called the permittivity of free space. Nice name, but I wonder what it means?

The dimensionless quantity \alpha on the other hand, has a very clear  physical meaning: it is the fine structure constant,  a coupling constant that measures the strength of the electromagnetic interaction.

Some people – including emeritus professors of observational astronomy – object to natural units because they hide the units that things are expressed in. They don’t actually. What they do is express things in units that are better geared to the physics. In any case, if you want to convert back to SI units you can always do so straightforwardly with a little bit of dimensional analysis. This is necessary if you have to talk to engineers and the like, perhaps so they can build you a particle accelerator, but in the more elevated company of particle physicists you should definitely follow proper etiquette and keep your units natural.