How information helps to banish quantum weirdness - the fivefold way.

One of the strands in the current excitement about information is that it can provide a narrative for explaining our experiences of the world* that does away with the mental contortions that other scientific narratives demand. An easy example - or rather the one I find most useful - is that you can stop worrying about 'spooky action at a distance' if no information is communicated faster than the speed of light (see my past posts on the EPR paradox).

* The New Scientist would spin it by saying 'explaining reality' but I think I am a reality-agnostic. Anyway, I don't like word.

More generally, a number of narratives are developing that are more of less 'grand'.

Quantum purity: How the big picture banishes weirdness

Anil Ananthaswamy

We have become accustomed to the universe blowing our minds – perhaps too accustomed. Quantum weirdness – things like particles being in two places at once, or appearing to share a telepathic link – has been baffling us for more than a century now. The physicist Richard Feynman once said that nobody really understands the quantum world. Or as others have put it: if you think you understand it, then you definitely don't. So it is tempting to throw up our hands and say human brains can never grasp it.

But maybe we shouldn't be so defeatist. Isn't it just possible that we simply haven't yet got to the bottom of how quantum mechanics really works? That's what Giacomo Mauro D'Ariano of the University of Pavia in Italy, and his colleagues Giulio Chiribella and Paolo Perinotti think – and they have been doing something about it. They have come up with a non-weird foundation from which all quantum weirdness can arise.

Ananthaswamy goes on to draw parallels from scientific history, of how we had descriptions of the world that worked but seemed arbitrary until we later found an underlying principle that help it all together.

Kepler's laws of planetary motion worked but were arbitrary until underwritten by Newton's universal law of gravity. Lorentz's equations were ad-hoc solutions to accommodate contradictory experimental observations about the speed of light until Einstein proposed some physical principles – that the speed of light in a vacuum is constant and independent of the motion of the source of light – from which he was able to derive Lorentz's transformations

"When I look at quantum theory, I see something that's akin to the ad hoc nature of Kepler's laws of planetary motion and of Lorentz transformations," says Hardy [Lucien Hardy of the Perimeter Institute in Waterloo, Canada]. "What we need is some deeper set of principles."

In the early 2000s, Hardy made his own attempt at coming up with some. It wasn't a full solution, he admits, but it inspired D'Ariano, Perinotti and Chiribella to dig deeper. "The idea was to somehow reprogram the genetic code of quantum mechanics, choose some physical properties and say, 'this is the fundamental thing', and re-derive the rest from it," says Chiribella, who is now at Tsinghua University in Beijing, China.

For both Hardy and D'Ariano's team, the "fundamental thing" has to do with information.

[...]

Eventually, they came up with five fairly common-sense ideas that worked: things like ensuring the future can't influence the past

Here are those five ideas:

Causality
Stuff in the future cannot affect a measurement you're making right now.

Distinguishability
If a state is not too noisy, then there exists another state that can be distinguished from it.

Composition
If you know everything it is possible to know about all the stages of a process, then you know everything you can about the whole process.

Compression
There are ways to efficiently transmit all the information relevant to a measurement of a physical system without having to transmit the system itself.

Tomography
When you have a system with several parts, the statistics of measurements carried out on the parts is enough to identify the state of the whole system.

Communicating information faster than light

The New Scientist has been agonising about reality again. The cover of the issue of 3 August 2013 advertises the article thus:

Reality

Relativity

Causality

Free Will

One of them is wrong. But which?

Michael Brooks, "Reality Checked" New Scientist Volume 219 No 2928.
Online version: Quantum weirdness: The battle for the basis of reality accessed 1/9/13

It comes down to entanglement in quantum mechanics requiring the violation of causality because it requires the communication of information faster than the speed of light. I've discussed this before (see my posts labelled causality) and my speculation was that whatever it is that is sent faster than the speed of light is not really information, and therefore there wasn't a problem.

Well this latest article argues quite explicitly that that get-out has been proved to be wrong.

Relativity only forbids an influence propagating above light speed when it carries information. So what if some weird phenomenon unknown to physicists could break relativity, connect two entangled particles, while being information-free?

We have even less idea what that sort of influence might look like. Chances are it doesn't matter: since last year, this escape route back to normality has also been blocked off. Together with Gisin and others, Jean-Daniel Bancal at the University of Geneva worked through what would happen within a network of four senders and receivers that could synchronise their measurements of entangled photons. In this theoretical set-up, influences could travel through space-time at whatever speed they liked, just as long as they contained no information.

And it failed to reproduce reality. There was no way any physical mechanism of any stamp could produce the quantum correlations seen in experiments unless hidden influences within the network could also send information at above light speed (Nature Physics, vol 8, p 867). 

I remember the moment at school when I first got really excited by physics. It was during an A-level physics lesson when I was introduced to relativity and the idea that time itself was relative, that time in a moving object passed at a different 'rate' than time in a stationary object (so to speak). It was the discovery that our every day common-sense interpretation of reality could be wrong - and that physics knew better. Of course that aspect of relativity is no big deal any more. That's to say, I've got used to it and realised that the world still makes perfect sense with the speed of light rather than time as the universal reference.

I'm back there now, though, losing my footing in reality. Now that physicists are closing off the escape routes.  Can I comprehend a universe that doesn't respect causality? Or one without free-will?

Information Theory "proves" the uncertainty principle

Or rather, it helps with an intuitive justification of the uncertainty principle, which is what the authors were seeking, and, maybe, suggests the search for 'hidden variables' explanations of the uncertainty principle are unlikely to succeed.

From the New Scientist 23rd June 2012:

Stephanie Wehner and Esther Hänggi at the National University of Singapore's Centre for Quantum Technology have taken a new tack, recasting the uncertainty principle in the language of information theory.

First, they suggest that the two properties of a single object that cannot be known simultaneously can be thought of as two streams of information encoded in the same particle. In the same way that you can't know a particle's momentum and location to an arbitrarily high level of accuracy, you also can't completely decode both of these messages. If you figure out how to read message 1 more accurately, then your ability to decrypt message 2 becomes more limited.

Next the pair calculate what happens if they loosen the limits of the uncertainty principle in this scenario, allowing the messages to be better decoded and letting you access information that you wouldn't have had when the uncertainty principle was in force.

Wehner and Hänggi conclude that this is the same as getting more useful energy, or work, out of a system than is put in, which is forbidden by the second law of thermodynamics. That is because both energy and information are needed to extract work from a system.

To understand why, imagine trying to drive a piston using a container full of heated gas. If you don't know in which direction the gas particles are moving, you may angle the piston wrongly and get no useful work out of the system. But if you do know which way they are moving, you will be able to angle the piston so that the moving particles drive it. You will have converted the heat into useful work in the second scenario, even though the same amount of energy is available as in the first scenario.

Being able to decode both of the messages in Wehner and Hänggi's imaginary particle suddenly gives you more information. As demonstrated by the piston, this means you have the potential to do more work. But this extra work comes for free so is the same as creating a perpetual motion machine, which is forbidden by thermodynamics (arxiv.org/abs/1205.6894v1).

"The second law of thermodynamics is something which we see everywhere and basically no one is questioning," says Mario Berta, a theoretical physicist from the Swiss Federal Institute of Technology in Zurich, who was not involved in the work. "Now we know that without an uncertainty principle we could break the second law."

Jessica Giggs "To be quantum is to be uncertain", New Scientist v214 n2870 (online here)

Those neutrinos travelling faster than light

Amplify’d from www.scientificamerican.com

An Italian experiment has unveiled evidence that fundamental particles known as neutrinos can travel faster than light. Other researchers are cautious about the result, but if it stands further scrutiny, the finding would overturn the most fundamental rule of modern physics—that nothing travels faster than 299,792,458 meters per second. [...]

The idea that nothing can travel faster than light in a vacuum is the cornerstone of Albert Einstein's special theory of relativity, which itself forms the foundation of modern physics. Read more at www.scientificamerican.com

See this Amp at http://bit.ly/ozVWVZ

This claim that 'nothing can travel faster than light' is sloppy, because you have to interpret what counts as a 'thing' in the word 'nothing'.

There's no problem at all with a phase velocity being faster than the speed of light. For example, an interference pattern can easily 'travel' faster than light, and the pattern might look like a 'thing'. Just think of two plane waves propagating at v and crossing at a shallow angle (say theta), then the intersection of the wavefronts 'travels' at a speed vp where vp = v/sin(theta/2). (I need for find an image of this). By making theta small vp can be as big as you like.

In a waveguide (such as an optical fibre) this is the phase velocity, but the more meaningful speed is the group velocity vg.  The group velocity is the speed at which information can be transmitted, and is always less than v. In fact vg x vp = v^2.

My point is that the 'thing' that can't travel faster than light is information, which is the point I made before about the EPR paradox.

Of course all this probably irrelevant as far as the neutrino story is concerned. If particles are travelling faster than light and being detected, then presumably information could be transmitted using them.  Still, it seemed like that at first sight with the EPR paradox yet when you analyse it carefully (which is way beyond my understanding but has been done by people who know) it turns out that you can't actually use it to send information faster than the speed of light.

My bet is that whatever the resolution of this latest neutrino story, it'll turn out that you can't send information faster than light. 

Information, causality and the EPR paradox

Some thoughts linked to my earlier post about the EPR paradox, arising from Dretske: Knowledge and the flow of information.

I was arguing earlier that the issue with faster-than-light travel is to do with the communication of information. Ie, that the 'thing' you can't allow to go faster than light is information. But implicit in my reason for that was a direct link between causality and information: for A to cause B it is necessary to convey information from A to B. But Dretske argues that there is no such link between causality and information and, furthermore, argues that there can even be information flow backwards in time. If this were to be so, then clearly by argument about information flow in EPR would be incorrect.

Dretske says that A can cause B without information from from A to B, and that information can flow from A to B without A causing B. His arguments for these conclusions are illustrated by the following diagram (from Dretske, 1991, page 28).


The arrows show causal connections: s2 causes r2 etc. Dretske argues that the causal link does not tell us anything about the information flow, because the fact that other events at s can also cause r2 means that the information r2 gives about s is reduced. So knowing that s2 causes r2 tells us nothing about the information about s learned from r2: causal link does not imply information flow.

Similarly, s4 can cause any one of r1, r3, r4. Now r1 tells us s4, so r1 gives good information about s, even though we can't say 's4 causes r1'. Hence information flow does not imply causal connection.

As to information flowing backwards in time, see Figure 1.8 from Dretske (page 38).


There is no physical connection between B & C, yet knowledge of C can be gained from observation of B. Dretske argues that there is an informational link between B & C. (Figure 1.8 looks very like the EPR experiment.) Dretske comments

Nothing at B causes anything at C or vice versa; yet C contains information about B and B about C. If C is further from the transmitter than B, the events occurring at C may occur later in time than those at B. [...] This sounds strange only if the receipt of information is confused with causality. For, of course, no physical signal can travel backwards in time carrying information from C to B.

EPR paradox

Here's my understanding of the paradox (the story I tell myself about it), and why in terms of information there's no problem.

(I'm writing this from memory, so it could be rubbish, but I think I have some of the essence in here. And it's not the original EPR - Einstein, Podolsky and Rosen - formulation, which I think was based on beta decay.) Imagine launching two entangled particles, say photons, heading off to two different locations. You take a measurement on one of them, say you test for spin up or down. The result of the measurement on one immediately tells you the result you'll get on taking the same measurement on the other. Eg, you measure photon A and find spin up, so you know measuring photon B will give you spin down. OK, no big deal so far. But, quantum mechanics tells you that photon A didn't decide it was going to be spin up until you measured it. So photon B has to be told, instantaneously, what photon A had decided to give as its result. Hence the need for instant communication (faster-than-light = violates causality, 'non-localisation')

But, as explained so far, it is pretty unconvicing to say that photon A didn't decide on what result it was going to give until it was measured. There's more to it. Instead of measuring for spin up or down, you could instead measure another parameter, say for spin rotation, clockwise or anticlockwise.* If you measure for spin rotation, then if A is clockwise B will measure anticlockwise and vice versa. But, if you measure for rotation then you lose coherence (is that how to express it?) for spin up or down. So, if you measure A for rotation, B can now be spin up or down with equal probablity. Likewise if you measure A for up or down, B can be closkwise or anticlockwise with equal probability. So now what is happening is that A 'tells' B whether you measured for rotation or up/down (as well as the result). Again, it has to happen instantaneously, hence the contradiction with relativity.

Experiments have been done, apparently, which test for this - the effect that measuring A influences the outcome of measurements on B. Now, I have not yet got an understanding of how these experiments are done. I'd love to know. But, my understanding of the conclusions of the experiments is:

- they have proved that there is an influence at a distance that happens faster than the speed of light
- but, you can not communicate information faster than the speed of light in this way

Now, here's my punchline: that final point somehow ruins it all! If you are not communicating information, then what's the big issue? Surely it is just like phase velocity in, say, waveguides? There's no problem at all with phase velocity exceeding c, because you can't carry information on the phase. It is the group velocity that matters.