## Wormholes and quantum entanglement

 Embed from Getty Images 

Been a while…

There is a fascinating article in this week’s New Scientist about the idea that quantum mechanics and general relatively could be linked via the idea of the “wormhole” – a fold in spacetime that links what appears to be two very distant parts of the universe.

The article – as is generally the case in a popular science magazine – is more hand wavy than scientific, but the concepts involved don’t seem to be difficult to grasp and they might answer some of the more mysterious aspects of quantum mechanics – especially the problem “spooky action at a distance“: quantum entanglement.

Quantum entanglement is the seeming evidence that two particles separated by distance appear to exchange information instantaneously: for when one particle changes state (or rather when its state is observed), the other does too. The suggestion is that, actually, these two particles are not separated by distance by are linked by a wormhole.

Sounds like a piece of Hollywood science, for sure, but it is an idea based on our understanding of black holes – a prediction of Einstein’s general relativity that we have lots of (indirect) evidence for: these would seem to be surrounded by entangled particles – the so-called quantum firewall.

## Interstellar

I watched Interstellar last night. It’s rare that I don’t like any half-decent science fiction movie, so it gets a thumbs up, though it had its high- and low-points.

It would be difficult to get away with describing Interstellar as truly a “hard science” movie – but it makes quite a few nods in that direction, my favourite being its insistence that a worm hole, as an anomaly in three-dimensional space, should actually be a “worm sphere”.

The fundamental conceit of the film – that a hick farmer from the western US (or somewhere meant to look like the western US) was really a top quality pilot – was difficult to buy into while Michael Caine’s performance was universally dismal.

And, of course, the overall plot feels like an attempt to reimagine 2001: A Space Odyssey – which, despite being nearly 50 years old now, remains unsurpassed as filmic musing on humanity’s destiny in space.

## The gravitational perpetual motion machine?

Perhaps I should have thought about this years ago – when I was surrounded by physicists and cosmologists and the like, and so could have got an answer: but I didn’t – until I started reading Lee Smolin‘s Time Reborn: From the Crisis in Physics to the Future of the Universe.

Here’s the issue: as Smolin states, nothing stops gravity. You cannot muffle it or block it.

Then let us think of an object with mass – it sends out “gravitons” (we assume – these have never been detected of course) and these exert a force on every object they meet. If we go one step further and suggest that the universe is infinite, do we not end up with our massive body being the source of an infinite amount of force and hence an infinite amount of energy?

Getting into murky waters here – but as I understand it, physics gets round this with something of an accounting trick: bodies with gravitational potential energy are deemed to have negative energy and so all that happens is that our massive body converts this negative energy into a positive energy and the total amount of energy in the universe is unchanged.

Is that really it?

## Copernicus was wrong (maybe)

No, I haven’t taken leave of my senses and decided the Sun moves around the Earth (but here is a pop quiz for all of you laughing at that idea – can you think of a simple experiment that would prove to a 10-year-old that the Earth moves around the Sun?).

In fact the issue here – the so-called Copernican Principle, or in its grander form the Cosmological Principle – was almost certainly not Copernicus’s view at all. But his paper – De Revolutionibus – opened the door to it, and indeed to the positivist idea of science in general.

The Copernican Principle states that there is nothing special about the position of Earth, the grander Cosmological Principle states that, at a sufficiently large scale, the universe looks the same in all directions – including (and this is important for what is coming) from where we are. In other words not just Earth is nothing special, but nowhere is anywhere special.

But what is that is all wrong? A fascinating article in this week’s New Scientist looks at just this.

That there are limits to the Cosmological Principle is obvious – the world is not smooth, even at some very large scales (look at the night sky – most of it is dark).

The standard scientific response to this is to state that at a sufficiently large scale – around 400 million light years – the matter density between galaxies and the inter galactic void evens out. But that assumption is based on our observations of our locality: yet what if, actually, we were in an atypical part of the universe? The atypicality could even be meta-typical (in other words we could have a super-Cosmological Principle but accepted that the universe was lumpy.)

This matters because our cosmological models are based on the assumption that the Cosmological Principle is correct and that therefore we are typical observers of the universe: hence the phenomena we see are ones that would be seen by any observer and are therefore artefacts of the universe’s physical nature and not our observational position.

So, for instance, we have data that appear to show that the expansion of the Universe is speeding up. We do not know why this is, so we call it “Dark Energy“. But what if the apparent speed up was because, actually, the universe was not isotropic (did not look the same in all directions) and the additional mass in one direction was impacting on the perceived rate of expansion of the universe?

The beauty of this question is that asking it does not mean challenging Einstein’s General Relativity – it’s not an exercise in metaphysical speculation but an argument firmly within the positivist realm bequeathed to us by Copernicus in the first place.

And finally…It is actually quite tough to devise a simple experiment to show that the Earth revolves round the Sun – but the orbits of Venus and Mercury are probably the best examples: these planets are never in opposition to the Sun. Though binoculars to observe the planets’ phases are probably needed to fully escape any Ptolemaic theories’ grasp.

Finally, finally… this book – Can You Speak Venusian? A Trip Through the Mysteries of the Cosmos – was very funny when I read it about 35 years ago, whether it has stood the test of time I am not sure.

## Integration by parts

Saw this referred to in A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity and it made me shudder – as I always seemed to struggle with it at ‘A’ level maths – so here, for my own benefit, is a quick proof/explanation of the method.

The general rule is:

$\int v(x) \frac{du}{dx} dx = u(x)v(x) - \int u(x) \frac{dv}{dx} dx$

And why is this so?

From the product rule we know:

$\frac{d}{dx} (u(x)v(x)) = \frac{du}{dx} v(x) + \frac{dv}{dx}u(x)$

So $\frac{du}{dx} v(x) = \frac{d}{dx}(u(x)v(x)) - \frac{dv}{dx}u(x)$

And, integrate both sides and we have:

$\int v(x) \frac{du}{dx} dx = u(x)v(x) - \int u(x) \frac{dv}{dx} dx$

Of course, we still have to apply this sensibly to make our problem easier to integrate!

## In what sense do photons exist?

This is a genuine question on my part – and I would be grateful for any answers!

The inspiration for asking the question comes from Genius: Richard Feynman and Modern Physics – my current “listen while running” book – along with Feynman’s own description of radiation in QED – The Strange Theory of Light and Matter.

Feynman argues that there is no radiation without absorption: in other words a tree that falls in an empty forest does indeed make no sound (if we imagine the sound is transmitted by photons, that is).

This sounds like a gross violation of all common sense – how could a photon know when it leaves a radiating body that it is to be absorbed?

But then, general relativity comes to our rescue – because in the photon’s inertial frame the journey from radiator to absorber is instantaneous.

But how can a body that exists for no time at all, exist at all?

Then again my assumption in asking this question is that time is in some sense privileged as a dimension of spacetime. This is a pretty deep controversy in theoretical physics these days and I am not qualified to shed much light on it – but let us assume that a body can exist with a zero dimension in time but real dimensions in space, can we then have bodies which have zero dimensions in space but a real dimension in time? If so, what are they?

## “Crowd sourcing” to play a key role in fundamental physics experiment

Ordinary people are to be asked to make a contribution to an experiment which aims to determine key facts about the nature of the physical universe – reports the New Scientist.

Particle physicists at CERN – the join European experiment famous for the Large Hadron Collider – are conducting an experiment – AEgIS – into whether anti-matter interacts with the gravitational field in the same way as matter.

Most of our universe seems to be made of matter – a mystery in itself because there is no simple explanation why ‘matter’ should outnumber ‘anti-matter’ – and the two forms annihilate one another in a burst of energy when they meet – so it can be difficult to conduct experiments with anti-matter.

Anti-matter particles pair up with matter – so for the electron, the negatively charged particle in our everyday atoms, there is an anti-matter positron, which is a positively charged particle which looks like an electron except it appears to ‘go backwards’ in quantum physics experiments (i.e. if we show an electron carrying negative charge in one direction, we can show a positron going in the opposite direction – and backwards in time! – with out violating physics’ fundamental laws). Richard Feynman’s brilliant QED – The Strange Theory of Light and Matter is strongly recommended if you want to know more about that.

Conventionally it is assumed gravity interacts with matter and ant-matter in the same way, but in reality our deep physical understanding of gravity is poor. For while Einstein’s general relativity theory – which describes gravity’s impact and has stood up to every test thrown at it – is widely seen as one of the great triumphs of 20th century physics, it is also fundamentally incompatible with how other “field” theories (like that for electricity) work and as a force is much. much weaker than the other fundamental forces – all of which suggest there is a deeper explanation waiting to be found for gravity’s behaviour.

Showing that anti-matter interacted with the gravitational field in a different way from matter could open up huge new theoretical possibilities. Similarly, showing anti-matter and matter were gravitationally equivalent would help narrow down the holes in our theoretical understanding of gravity.

How can the public help? Well, on 16 August (just after the New Scientist article was printed) CERN asked for the public’s help in tracing the tracks made by particles in experiments: these tracks are then analysed to judge how gravity impacted on the particles (some of which will be anti-matter).

The public can help CERN analyse many more tracks and – crucially – help calibrate CERN’s computer analysis software.

It is expected that there will be further requests for help – so it might be worth keeping your eyes on the AEgIS site if you are interested in helping. (The tutorials are still up. but all the current tasks have been completed).

## Schrödinger’s cat: for real

Quantum Mechanics is, along with General Relativity, the foundation stone of modern physics and few explanations of its importance are more famous than the “Schrödinger’s cat” thought experiment.

This seeks to explain the way “uncertainty” operates at the heart of the theory. Imagine a cat in a box with a poison gas capsule. The capsule is set off if a radioactive decay takes place. But radioactivity is governed by quantum mechanics – we can posit statistical theories about how likely the radioactive decay is to take place but we cannot be certain – unless we observe. Therefore the best way we can state of the physical state of the cat – so long as it remains unobserved – is to say it is both alive and dead.

Now physicists still argue about what happens next – the act of observing the cat. In the classical, or Copenhagen, view of quantum mechanics the “wave equation collapses” and observing forces the cat into a dead or alive state. In increasingly influential “many worlds” interpretations anything that can happen does and an infinite number of yous sees an infinite number of dead or alive cats. But that particular mind bender is not what we are about here. (NB we should also note that in the real world the cat is “observed” almost instantaneously by the molecules in the box – this is a mind experiment not a real one, except… well read on for that).

The idea of the cat being alive and dead at once is what is known as “quantum superposition” – in other words both states exist at once, with the prevalence of one state over another being determined by statistics and nothing else.

Quantum superposition is very real and detectible. You may have heard of the famous interferometer experiments where a single particle is sent through some sort of diffraction grating and yet the pattern detected is one of interference – as though the particle interfered with itself – in fact this indicates that superposed states exist.

In fact the quantum theories suggest that superposition should apply not just to single particles but to everything and every collection of things in the universe. In other words cats could and should be alive and dead at the same time. If we can find a sufficiently large object where superimposition does not work then we would actually have to rethink the quantum theories and equations which have stood us in such good stead (for instance making the computer you are reading this on possible).

And Stefan Nimmrichter of the Vienna Centre for Quantum Science Technology and Klaus Hornberger of the University of Duisberg-Essen have proposed we use this measurement – how far up the scale of superposition we have got as a way of determining just how successful quantum mechanics’s laws are (you can read their paper here).

They propose a logarithmic scale (see graph) based on the size of the object showing superposition – so the advance from the early 60s score of about 5 to today’s of about 12 might mean we can be one million times more confident in quantum theory’s universal application. (A SQUID is a very sensitive magnetometer which relies on superconductivity.)

And they say that having a 4kg ‘house cat’ be superposed in two states 10cm apart (which might be taken for a good example of lying dead versus prowling around) would require a score of about 57 – in other words about $10^{45}$ more experimental power than currently available.

That probably means no one reading this is ever likely to see a successful demonstration that Schrödinger’s cat is rather more than a thought experiment, but it does give us a target to aim at!

## Time’s arrow

The forward march of time is possibly the most basic and shared human experience. Whatever else may happen in our lives none of us can make time run backwards  (the title of this post recalls Martin Amis‘s brilliant novel premised on this idea – time running backwards – if you’ve read it you will understand why we are never likely to see it filmed, as 90 minutes of backwards time would be just too much to take.)

Yet, as Lee Smolin points out in this week’s New Scientist, our most fundamental theories of physicsquantum mechanics and general relativity – are time free: they work just as well if time runs the other way round. Physicists square this circle by insisting on only time-forward solutions and by imposing special conditions on our universe. We have even invented a physical category – which has no material existence per se – called entropy and demanded that it always increase.

The accepted physics leaves us in the difficult position of believing that “the future” is not the future at all – it exists and has always existed but we are barred from getting there “ahead of time”. It’s a deep contradiction, though whether this is a flaw in the theories or in human comprehension is what the debate (such as it exists, those who challenge QM and GR are very much in the minority) is all about.

In Smolin’s view (or perhaps my interpretation of it) all of this violates the “Copernican principle” – that we observers are nothing special – that has guided much of physics’s advances of the last five centuries. So what if it is actually telling us that our theories are wrong and like Newtonian gravity is to general relativity, they are merely approximations?

Smolin’s argument is just this. He says we should base our theories on the fundamental observation that time flows in only one direction and so find deeper, truer theories based on unidirectional time.

## Patenting reality

(I was about to post something about this when I noticed the Stephen Fry nomination of Turing’s Universal Machine as a great British “innovation” and decided to write about that first … but the two dovetail as I hope you can see.)

I was alerted to this by an article in the latest edition of the New Scientist (subscription link) -on whether scientific discoveries should be patentable. The New Scientist piece by Stephen Ornes argues strongly and persuasively that the maths at the heart of software should be protected from patents. But having now read the original article Ornes is replying to, I think he has missed the full and horrific scale of what is being proposed by David Edwards, a retired associate professor of maths for the University of Georgia at Athens.

Of course I am not suggesting that Edwards himself is evil, but his proposal certainly is: because he writes, in the current issue of the  Notices of the American Mathematical Society (“Platonism is the Law of the Land”) that not just mathematical discoveries should be patentable but, in fact, all scientific discoveries should be: indeed he explicitly cites general relativity as an idea that could have been covered by a patent.

Edwards is direct in stating his aim:

Up until recently, the economic consequences of these restrictions in intellectual property rights have probably been quite slight. Similarly, the economic consequences of allowing patents for new inventions were also probably quite slight up to about 1800. Until then, patents were mainly import franchises. After 1800 the economic consequences of allowing patents for new inventions became immense as our society moved from a predominately agricultural stage into a predominately industrial stage. Since the end of World War II,our society has been moving into an information stage, and it is becoming more and more important to have property rights appropriate to this stage. We believe that this would best be accomplished by Congress amending the patent laws to allow anything not previously known to man to be patented.

Part of me almost wants this idea to be enacted, because like the failure of prohibition of alcohol it would teach an unforgettable lesson. But as someone who cares about science and the good that science could do for humanity it is deeply chilling.
For instance, it is generally accepted that there is some flaw in our theories of gravity (general relativity) and quantum mechanics in that they do not sit happily beside one another. Making them work together is a great task for physicists. And if we do it – if we find some new theory that links these two children of the 20th century – perhaps it will be as technologically important as it will be scientifically significant (after all, quantum mechanics gave us the transistor and general relativity the global positioning system). But if that theory was locked inside some sort of corporate prison for twenty or twenty-five years it could be that the technological breakthroughs would be delayed just as long.