Derivation of Planck’s radiation law – part 2

Another masterpiece of clarity from Rhodri


In the first part of this blog (here), I described how experimenters at the Physikalisch-Technische Reichsanstalt (PTR) determined the true spectrum of blackbody radiation during the 1890s, By the year 1900, primarily by the work of Heinrich Rubens, Ferdinand Kurlkbaum, Ernst Pringsheim and Otto Lummer, the complete spectrum, from the ultraviolet through the visible and into the infrared, was known for the very first time. As the true shape of the blackbody spectrum started to emerge from this experimental work, theoreticians tried to find a theory to explain it.

The first to meet with any success was Wilhem Wien. As I mentioned in the first part of this blog, in 1893 he came up with his displacement law, which gave a very simple relationship between the wavelength of the peak of the spectrum and its temperature.

$latex lambda_{peak} = frac{ 0.0029 }{ T }$

where $latex lambda_{peak}$ is…

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The Teleportation Tango

Quantum Teleportation has been in the news recently, so here is some background, from my book Computing With Quantum Cats.

Quantum teleportation is based on the spooky action at a distance that so disgusted Einstein but is demonstrated to be real in tests of the EPR “paradox” and measurements of the Bell inequality.  It rests on the fact — confirmed in those experiments — that if two quantum entities, let’s say two photons, are entangled, then no matter how far apart they are what happens to one of those two photons instantly affects the state of the other photon.  But the refinement is that by tweaking the first photon in the appropriate way (called a “Bell-State Measurement”) its quantum state can be transferred to the second photon, while the state of the first photon is, of course, changed by being tweaked.  In effect, the first photon has been destroyed and the second photon has become what is termed in common parlance a clone of the first photon.  Since the original has been destroyed, however, for all practical purposes the first photon has been teleported to the location of the second photon, instantly.  It is not a duplication process (and it has also been done with trapped ions!).

There’s one small catch.  In order to complete the transformation, information about the way the first photon was tweaked has to be transmitted to the location of the second photon by conventional means, no faster than the speed of light.  This information is then used to tweak the second photon in just the right way (not the same way that the first photon was tweaked, but in a kind of reverse process) to complete the transformation.  In effect, the conventional signal tells the system what tweak has been applied to photon number one, and the system then does the opposite to photon number two.  Quantum teleportation requires both a quantum “channel” and a classical “channel”; it takes two signals to dance the teleportation tango.

A large and successful research effort has gone into making this reality, not least because quantum information offers a way of transmitting information utterly securely using systems that cannot be cracked.  I have explained the details in my book Schrödinger’s Kittens, but the essential point is that information travelling by the quantum “channel” cannot be read by a third party; in addition, any attempt to eavesdrop will alter the quantum state of the photons, making it obvious that they have been interfered with.  This is not the reason why teleportation helps in the design of quantum computers; indeed, in recent times headline-making developments in quantum teleportation have concentrated on much larger scales than those appropriate for computation.  But their success emphasises the reality of the process, and how good scientists now are at working with quanta.

In 2012, two record-breaking experiments made those  headlines — by the time you read this, they will probably both have been superceded.  First, a large group of Chinese researchers succeeded in teleporting a quantum state through 97 kilometres of open air across Qinghai Lake, using a telescope to focus the photons.  Almost as an aside, the experiments confirmed the by-now-expected violation of the Bell inequalities, offering insight for the theorists into the foundations of quantum physics.  A few weeks later, a team from Austria, Canada, Germany and Norway teleported the properties of a photon across a distance of 143 km, from the astronomical observatory on La Palma, in the Canary Islands, to a European Space Agency ground station on the neighbouring island of Tenerife.  Both the transmitting station and the receiving station were located roughly 2,400 metres above sea level, where the air is thin and atmospheric interference is reduced.

But the air is even thinner at higher altitudes, so that in some ways it should be easier to carry out quantum teleportation, and achieve secure communication, by pointing the beams upward to a satellite.  The distances involved are very similar to those already achieved on the ground, and although there are, of course, many other problems involved in establishing this kind of satellite communication, the Chinese are already planning a satellite experiment, provisionally scheduled for launch in 2016 or 2017, to test the possibilities, using ground stations in Europe and in China to communicate with the satellite simultaneously for a few minutes in each orbit.  This is particularly important because this kind of quantum information is soon lost if the photons are sent through fibre optic cables.  The leader of the Chinese team, Pan Jianwei, of the University of Science and Technology of China in Hefei, envisages an eventual network of satellites acting as repeater stations for global coverage of a quantum communications network.  This could be the basis of an utterly secure quantum internet; and in all probability many of the computers plugged in to that internet will by then themselves be running on quantum principles, including teleportation.

In connection with this work, Chinese researchers have devised ever better techniques for entangling photons.  In 2004, they could produce a few four-photon entanglement events every second; by 2012, they could produce entangled groups of four photons at a rate of a few thousand per second.

Derivation of Planck’s radiation law – part 1


One of my most popular blogposts is the series I did on the derivation of the Rayleigh-Jeans law, which I posted in three parts (part 1 here, part 2 here and part 3 here). I have had many thousands of hits on this series, but several people have asked me if I can do a similar derivation of the Planck radiation law, which after all is the correct formula/law for blackbody radiation. And so, never one to turn down a reasonable request, here is my go at doing that. I am going to split this up into 2 or 3 parts (we shall see how it goes!), but today in part 1 I am going to give a little bit of historical background to the whole question of deriving a formula/law to explain the shape of the blackbody radiation curve.

‘Blackbody’ does not mean black!

When I first…

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Quantum Biology

This is the unedited version of a review of mine from the Wall Street Journal

Life on the Edge:

The coming of age of quantum biology

Johnjoe McFadden & Jim Al-Khalili

There is a sense in which all of biology is quantum biology. The entangled strands of DNA, the famous double helix of the molecule of life, are held together by a quantum phenomenon known as hydrogen bonding. The way in which those strands untwist and build new double helices during the process of reproduction is at heart a quantum phenomenon, closely related to the way in which quantum entities such as electrons can be both wave and particle at the same time.

But in this remarkable book Johnjoe McFadden, an expert in molecular genetics, and Jim Al-Khalili, a quantum physicist, join forces to explain many everyday aspects of life in terms of what is often referred to as quantum weirdness. They do so, moreover, in an easily accessible style, free from jargon, which makes complex issues clear even to the non-scientist.

After teasing the reader with an introduction presenting the puzzle of how birds can detect the Earth’s magnetic field and use it for navigation, the authors lead us gently by the hand through discussions of the nature of life itself, right down to the molecular level, and the mysteries of quantum physics. This is material which has been covered in many books, but nowhere more succinctly and clearly than here.

Thus prepared, we are ready for an explanation of what they call “the quantum robin” – the workings of the magnetic sense organ in birds and other animals. It turns out that this ability is linked to a phenomenon known as “entanglement” occurring in certain molecules in the appropriate sense organ. Entanglement involves two or more quantum entities, such as electrons, being in some sense in tune with each other, so that when one of them is prodded the other one twitches. And in certain circumstances, as McFadden and Al-Khalili explain, this makes the molecules involved sensitive to the direction of a magnetic field.

This is a profound realisation, because entanglement is such a bizarre concept, to the human mind, that for decades even many physicists doubted that it could be real. Albert Einstein famously referred to it as “spooky action at a distance”. The equations tell us that once two particles have interacted, then forever afterwards, no matter how far apart they are, a measurement of one particle will instantaneously affect the properties of the other particle. As Einstein wrote to his friend Leon Rosenfeld, “is it not paradoxical? How can the final state of the second particle be influenced by a measurement performed on the first, after all physical connection has ceased between them?” He believed that this highlighted a flaw in quantum theory, and went to his grave still looking for a better description of the Universe. But he was wrong. In the 1980s (and repeatedly since), experiments involving photons, the particles if light, have proved that the spooky action at a distance is real.

In that case, it should be expected that natural processes make use of it, just as living things make use of sunlight for photosynthesis. Why should they? Because it is there. Life uses whatever is available, whether that thing is food, energy, or the laws of physics. So it should be no surprise that the phenomenon of entanglement is not used solely by European robins. Monarch butterflies and fruit flies are among the other species which make use of quantum effects in navigation. Nor are quantum processes confined to the animal world. Photosynthesis is the basic mechanism in plants which provides the energy that is used to manufacture plant material, and ultimately the food we eat, out of basic chemicals such as water and carbon dioxide. This, too, depends on quantum processes which “push” the absorbed energy of sunlight in the right direction.

Pre-quantum physics, the laws discovered by Isaac Newton, is often referred to as classical physics. “Most biologists’” the authors point out, “still believe that the classical laws are sufficient. With Newtonian forces acting [to explain photosynthesis] in strictly classical terms . . . with light acting like some golf club able to whack the oxygen golf ball out of the carbon dioxide molecule.” But, as with Einstein and spooky action at a distance, they are wrong. The key step in the process involves electrons “hopping” from one molecule to another in an orderly fashion. Some extraordinary experiments described in this book (in what is admittedly a slightly more technical passage) have revealed that energy is flowing through such a system by, in effect, following several routes simultaneously, thanks to a phenomenon known as coherence. This is a purely quantum effect.

The discovery is particularly exciting because quantum physicists working on the development of computers that operate on quantum principles incorporate quantum coherence into their designs. Not for the first time, nature got there before the scientists, and so far does a better job of “computing” the most efficient way to get energy from A to B. Not that the quantum computer scientists were quick to embrace the idea. Al-Khalili and McFadden quote one of those researchers describing his colleagues’ immediate reaction, when they saw a New York Times article suggesting that plants might operate as quantum computers: “it’s like, ‘Oh my God, that’s the most crackpot thing I’ve heard in my life’”. But they have since changed their tune.

All this is dramatic enough, and well worth the price of admission. But the authors have saved the best – if admittedly the most speculative – idea for (nearly) last. These speculations involve consciousness and the mechanics of thought, but also the processes that go on inside quantum computers and, we now know, during photosynthesis. By tracing back the process of painting a picture (they imagine an artist in Palaeolithic times painting a picture of a bison on a cave wall) from the fingertips of the artist through the muscles and neurons in the arm to the brain, they focus in on the chemistry involved. At one level, this is an entirely causal, mechanistic chain of processes, like that of a machine. But who, or what, is in charge of the machine? Who is pulling the levers?

It is an old question, going back to philosophers such as Descartes. How does mind make matter move? The new answer presented here draws from the physics behind the workings of those quantum computers. Where an “ordinary” computer can be thought of as operating through a series of switches that can be set to 0 or 1, the power of a quantum computer depends on the ability of quantum entities to be in two states at the same time, known as a superposition. So the switches in a quantum computer are both on and off (set at 0 and set at 1) at the same time. Building on ideas proposed by the Oxford physicist Roger Penrose, McFadden and Al-Khalili look at the quantum chemistry that just might be involved in conscious thought. “The scheme”, they say, “is certainly speculative, but it does at least provide a plausible link between the quantum and classical realms in the brain.” After all, if a plant can operate like a quantum computer in carrying out the process of photosynthesis, why couldn’t the human brain act as a quantum computer in carrying out the processes of thought? Given nature’s ability to make use of whatever is available, it would be surprising if it did not.

After that, almost anything would be an anticlimax – even a chapter discussing the puzzle of how life began. It would seem more natural to have this before the discussion of consciousness, since, after all, life began before it became conscious. But still, it is an important topic that could not be left out of a book such as this. For my (hopefully conscious) mind, though, this is the weakest section of the book, necessarily highly speculative, and not entirely convincing. There are clearly more questions than answers, but at least this means that there is plenty of work for the next generation of quantum biologists to do.

It may not be necessary, though to understand how life began to use an understanding of how life operates today at the quantum level to build completely artificial living organisms from the bottom up. Such a process would involve what the authors call “living technology” to manufacture from scratch organisms such as microbes which could produce antibiotics tailored to human requirements. This would be quite different from recent experiments with “artificial” life, which involve tinkering with DNA molecules, introducing them into already living cells, and persuading those cells to function in accordance with the instructions coded in the new DNA. This is inefficient because even after being “adapted” in this way, such modified cells continue to make lots of stuff that is of no use to us. The bottom up approach would result in what the authors describe as “a brave new world of quantum synthetic living organisms that could free their natural-born relatives from the drudgery of providing humanity with most of its needs.” A fine sentiment – unless, of course, those synthetic organisms turn out to be conscious.

Lifge on the Edge is a fascinating and thought-provoking book which manages to combine solid science, respectable extrapolation from the known into the unknown, and plausible speculation to give an accessible overview of a revolutionary transformation in our understanding of the living world. I will certainly look at robins with more respect in future.

John Gribbin is a Visiting Fellow in Astronomy

At the University of Sussex

And author of Computing with Quantum Cats: From Alan Turing to Teleportation