Big gains for physics as Obama signs stimulus bill

Science fared well in the $787bn package to stimulate the US economy that President Barack Obama signed into law today. The “recovery and reinvestment bill” includes $21.5bn for research and development (R&D), the bulk of which — some $18bn — will go directly to researchers. The remaining $3.5bn is allocated for facilities and equipment.

Politicians have been bickering over the bill since it was fist unveiled on 15 January. American legislation takes a circuitous course on its way to the President. Typically, the House of Representatives and the Senate approve different versions of a bill, and then appoint negotiators to agree on compromise legislation that both houses must approve again before sending to the President.

"These prudent investments lay the necessary foundation for long-term economic growth and prosperity for our country"
Cherry Murray, American Physical Society

The $838bn Senate bill on 10 February included significantly less funding for physical science than the $825bn House bill on 29 January. Even though the Senate bill may have higher priority, most of the cuts to the physical sciences were reversed in the final $787bn bill agreed on 14 February. Indeed, physicists have welcomed the $21.5bn for science, with more than $10 bn of it going to government agencies responsible for funding the physical sciences.


NSF is a winner

The National Science Foundation (NSF) will receive $3.0 bn in stimulus funding on top of its $6.0bn budget for 2009. This will include $1bn for research infrastructure and construction and $2 bn for “other research and related activities.”

The DOE’s Office of Science, meanwhile, will get $1.6 bn in funding beyond its 2009 budget of $4.0 bn. Two other DOE programmes: energy efficiency and renewables, and fossil energy will receive $2.5 bn and $1.0 bn respectively, which is almost twice as much as their 2009 budget allocations of $1.2 bn and $576 m.

With a budget of $737 m for this year, the National Institute of Standards and Technology will receive an extra $580 m, of which $360 m will go on building research facilities. NASA will receive an extra $1.1 bn beyond its current budget of $17.2 bn with $400 m going towards its science and exploration programme.

"The good news is that there is a lot of money for infrastructure. The big challenge is how to spend it"
Kei Koizumi, American Association for the Advancement of Science

“The surprise is how much money there is for science in the final bill,” says Kei Koizumi, budget analyst at the American Association for the Advancement of Science. “The good news is that there is a lot of money for infrastructure. The big challenge is how to spend it.”


“These critical investments will not only benefit American science and innovation, but they will put thousands of Americans back to work through construction and manufacturing projects,” American Physical Society president Cherry Murray said in a statement. “Furthermore, these prudent investments lay the necessary foundation for long-term economic growth and prosperity for our country.”

The fresh funding has implications for US science beyond the current financial year. It puts back on track the goal of doubling federal government support for physical science — an ambition of the America COMPETES Act of 2007 that had fallen behind schedule.

Further evidence of the Obama administration’s ambitions for science will become clear later this month, with the release of its revised budget for the 2009 financial year, which started on the 1st of October last year.

FONTE: Peter Gwynne is North America correspondent for Physics World

Esticando o tempo e voltando ao passado

Por Roberto Belisário

Boa notícia para os atrasados e os apressados: é possível “dilatar” o tempo, de forma a transformar um dia em dez dias, e também viajar ao passado e depois voltar ao presente para contar a história!

Não é ficção: trata-se de possibilidades teóricas previstas pela física moderna. A dilatação do tempo acontece corriqueiramente na física subatômica; viagens para o futuro acontecem de forma natural e automática em viagens aéreas, ainda que através de intervalos de tempo minúsculos. Viagens para o passado são ainda apenas previsões teóricas, mas há quem aposte que aparecerão espontaneamente casos microscópicos e raros de “máquinas do tempo” naturais dentro do LCH, um acelerador de partículas que entrará em operação em maio de 2008.

É possível ousar mais e imaginar se, no futuro, não será possível implementar esses fenômenos em uma tecnologia cotidiana que ajude a diminuir um efeito nocivo que o próprio avanço tecnológico, indiretamente, produz: a falta de tempo, a cultura da pressa, o acúmulo de tarefas. Na verdade, a tecnologia está o tempo todo sendo usada para esse fim: máquinas para fazer serviços domésticos, computadores, automóveis e aviões, todas essas inovações têm a função principal de permitir concentrar mais tarefas em menos tempo e com menos esforço. Mas o que se pergunta aqui é se é possível usar os efeitos descritos anteriormente para manipular diretamente o tempo de modo a, ao invés de diminuir a demora das atividades humanas, “esticar” o próprio tempo, ou mesmo “andar para trás no tempo”, de modo a termos mais horas disponíveis para nossos caprichos.

A resposta não é animadora: o uso prático de tais fenômenos na vida cotidiana requer quantidades tão grandes de energia e aglomerados de matéria tão densos – trilhões de vezes maior do que a das rochas mais duras – que é virtualmente impossível com a atual tecnologia à disposição. Mas nada impede que alguma idéia brilhante e nova possa eliminar algumas limitações, como tantas vezes já aconteceu. Algumas já foram imaginadas e aumentaram um pouco as possibilidades.

Como transformar um dia em duas semanas

A dilatação do tempo chega a ser banal: acontece naturalmente e de forma automática quando se compara o ritmo do “passar do tempo” para duas pessoas deslocando-se uma em relação à outra. Trata-se de um efeito previsto pela teoria da relatividade especial, em 1905, produzida por Albert Einstein, Henri Poincaré, Hendrik Lorentz e outros, e que substituiu a mecânica de Newton, inconteste pelos 300 anos anteriores. Até então, imaginava-se o tempo como uma entidade absoluta, cujo “fluir” seria o mesmo para todos os observadores. Algo bem diferente de outros conceitos que sabemos que dependem de um referencial, como a velocidade. A rigor, a especificação da velocidade só é completa quando se diz em relação a quê. Um carro pode estar a 100 km/h em relação à estrada; mas, em relação ao Sol, estará a 180 mil km/h, acompanhando o movimento de translação da Terra ao redor dele.

O que a teoria da relatividade mostrou sobre o tempo foi que ele é tão dependente de um referencial quanto a velocidade. Se eu olho para o relógio de alguém deslocando-se em relação à mim, vejo-o andar mais lentamente que o meu; os seus batimentos cardíacos parecem (e estão) mais vagarosos; suas palavras chegam até mim mais espaçadas e sua voz mais grave, vejo-a envelhecer mais devagar e assim por diante.

Neste ponto, para os atrasados e apressados, há uma boa notícia e uma má. A má é que seria necessário que dois observadores se afastassem a 42% da velocidade da luz para produzir um atraso de apenas 10% no correr do tempo entre um e outro. Portanto, é muito difícil e caro produzir uma dilatação do tempo útil, que transforme horas em mais horas, de forma que eu não precisasse mais escrever este texto para amanhã, mas só para daqui a duas semanas. Além disso, trata-se de um efeito que acontece entre observadores. Se eu permaneço parado em relação ao editor desta revista, meu tempo flui necessariamente da mesma forma que o dele. A não ser que alguém tenha alguma idéia brilhante...

Na verdade, alguém teve uma idéia brilhante: Einstein e o matemático francês Pierre Langevin. E esta é a “notícia boa” prometida acima. Trata-se de um efeito chamado “paradoxo dos gêmeos”; Einstein previu-o em 1905 e, em 1911, Langevin colocou-o nos termos dramáticos seguintes. Imaginemos dois irmãos gêmeos, Ulisses e Penélope, sendo que Ulisses realiza uma viagem espacial em alta velocidade e volta anos depois. Segundo a previsão da relatividade, durante a viagem, Penélope observaria daqui da Terra todos os fenômenos relacionados a Ulisses mais lentos que o normal, desde as batidas do seu coração até a velocidade do seu caminhar. E isso inclui o ritmo do seu envelhecimento. De forma que, quando Ulisses retornar à Terra, estará alguns dias mais novo que Penélope.

Esse efeito já foi demonstrado substituindo-se os gêmeos por relógios atômicos, que são relógios de altíssima precisão. Em 1971, os físicos J. C. Hafele e R. E. Keating sincronizaram dois desses relógios e embarcou-se um deles em um vôo comercial ao redor do mundo, enquanto o outro permaneceu no Observatório Naval dos Estados Unidos, em Washington. O experimento foi feito duas vezes, uma num vôo de oeste para leste e outra de leste para oeste. Na primeira, o relógio atrasou-se 59 bilionésimos de segundo (59 nanossegundos) e, na segunda, adiantou 273 nanossegundos. Os resultados foram compatíveis com as previsões das equações da relatividade.

Viagens ao futuro e ao passado

A idéia de Einstein e Langevin foi boa o suficiente para se poder observar a dilatação do tempo sem grande dificuldade com velocidades perfeitamente acessíveis e vencer completamente a limitação do referencial entre eu e meu editor. Mas ela não é boa o suficiente para resolver as urgências do dia-a-dia – a velocidade envolvida teria que ser colossal. Há, porém, projetos de naves espaciais que talvez possam alcançar tais velocidades acelerando constantemente durante um longo tempo – para isso, usam como fonte de energia os raios cósmicos, que existem em qualquer lugar do espaço.

Mas, se o problema é a velocidade, a teoria da relatividade geral, feita também por Einstein e por David Hilbert entre 1905 e 1916, sugere uma forma de dilatar o tempo com os dois observadores parados: com o auxílio de campos gravitacionais intensos. Pela teoria, um observador no espaço interestelar (praticamente sem gravidade) vê tudo o que acontece quando outro observador na superfície da Terra correr mais devagar, da mesma forma que no caso de observadores em movimento. O campo gravitacional tem um efeito sobre o tempo. Mas é necessário um campo muito intenso para produzir uma diferença sensível e, para produzi-lo, seria necessário dispor de um acúmulo de matéria muito grande. Em 1976, foi medida a dilatação do tempo gravitacional entre um relógio atômico na Terra e um outro em um foguete lançado a 10 mil quilômetros de altura pelo Observatório Astrofísico Smithsonian, em Cambridge, nos EUA. O resultado foi de 4,5 partes em 10 bilhões (um desvio de apenas 0,01% em relação à previsão da teoria). Para produzir uma diferença de 10%, um objeto do tamanho da Terra teria que ter 10 elevado à 26ª potência (“1” seguido de 26 zeros) vezes o peso do nosso planeta, o que significa uma densidade só superada por um buraco negro.

E com relação à viagem no tempo? A coisa interessante com a idéia brilhante de Einstein e Langevin é que o paradoxo dos gêmeos não é apenas uma dilatação no tempo: é um deslocamento através do tempo. Podemos dizer que Ulisses, em seu périplo, viajou em direção ao futuro. Na verdade, sempre que alguém se desloca pelo espaço, desloca-se também no tempo, em relação a observadores que permanecem parados. Isso significa que estamos viajando para o futuro o tempo todo. O efeito é evidentemente diminuto demais em situações cotidianas – mas existe.

Já a volta ao passado, que seria útil para as urgências da modernidade (se não cair em mãos erradas!), é de implementação muito mais difícil. Muitas vezes, tem-se a idéia popular de que uma viagem ao passado implicaria em uma velocidade superior à da luz. Não é verdade: pode-se fazer tais viagens sem ultrapassá-la. O que se precisa nesse caso, segundo a relatividade geral, é de um campo gravitacional de formato muito exótico – o que implica em uma porção de matéria com formato igualmente exótico e extremamente densa. Esse campo produziria uma espécie de “túnel” no espaço-tempo chamado “buraco de verme” ou “buraco de minhoca”. Ele permitiria deslocamentos em grandes distâncias e/ou através do tempo. Seriam necessárias também enormes quantidades de energia para impedir que esse túnel colapsasse e se fechasse quase instantaneamente. Foi esse efeito que inspirou a “velocidade warp” da série Jornada nas Estrelas e tantos outros saltos espaciais e temporais em filmes de ficção científica.

Se assim aconteceu, assim acontecerá

Além disso, a teoria aparentemente não prevê a possibilidade de mudar o passado. Não seria possível, por exemplo, um homem voltar algumas décadas e matar a própria mãe antes de ele próprio nascer, pois esse filho não só estaria alterando um evento que já aconteceu (seu nascimento), como também impossibilitando a própria alteração. Mas as equações não impedem que essa pessoa volte no tempo e ajude sua mãe a conhecer seu pai, de modo que o nascimento ocorra. Tem-se aqui uma típica situação circular no tempo (tecnicamente, chamada “curva tipo tempo fechada” ou CTC), mas que quase não apresenta contradições lógicas (“quase” porque em algumas situações parece ser possível produzir informação a partir do nada). A ficção científica também explorou casos semelhantes, como no filme O Exterminador do Futuro, de 1984, e na sua continuação, de 1991, dirigidos por James Cameron.

De qualquer forma, “buracos de minhoca” podem ser, teoricamente, produzidos em condições extremamente energéticas, como as que acontecem nas colisões subatômicas em aceleradores de partículas. Há cientistas que acreditam que eles poderão aparecer, ainda que raramente e microscópicos, no acelerador LHC, que está sendo construído no Centro Europeu de Pesquisas (CERN), perto Genebra, na fronteira entre França e Suíça. Tais buracos de minhoca, porém, seriam demasiadamente pequenos, da ordem de um “comprimento de Planck” (ou seja, de um centésimo de quintilionésimo do diâmetro de um próton). Além disso para transformar um deles em uma máquina do tempo boa para seres humanos, seria preciso colocar uma de suas pontas em um campo gravitacional extremamente intenso, como o de uma estrela de nêutrons – e aí volta o problema de se arrumar uma porção de matéria extremamente densa.

Nada impede, porém, que alguma outra idéia brilhante e nova possa contornar algumas dessas limitações e permitir a produção de algum aparelho capaz de distorcer o tempo de forma a transformar 50 minutos em 60 minutos. Mas não terá essa possibilidade o mesmo destino dos outros “sucessos” da tecnologia no aumento do tempo livre das pessoas? Afinal, mesmo com todas essas máquinas, continuamos com falta de tempo! As pessoas continuam correndo, executivos trabalham com laptops em viagens à noite, empresários bem-sucedidos ficam em atividade 14 horas por dia. Se tivéssemos um dia de 48 horas, provavelmente a jornada de trabalho pularia para 32 horas diárias... O que pode melhorar o problema de gerenciamento do tempo não são novas inovações tecnológicas, mas uma mudança de atitude para com o trabalho e a vida.

Ao leitor interessado, o livro A evolução da física, escrito pelo próprio Einstein e por Leopold Infeld, explica as teorias da relatividade especial e geral de forma bastante compreensível para não-físicos. Uma quantidade de experimentos possíveis sobre relatividade especial utilizando material caseiro aparece no site da Feira de Ciências, de Luiz Ferraz Netto. Um especial sobre o tempo, incluindo artigos sobre física – e um de Paul Davies sobre como construir uma máquina do tempo –, apareceu na Scientific American Brasil de outubro de 2002, que foi republicada neste mês de outubro de 2007. Uma abordagem sobre viagens no tempo mais extensa e acessível a não-fisicos está no livro Máquina do tempo – um olhar científico, do físico brasileiro Mário Novello.


Fonte: Roberto Belisário é doutor em física, professor de eletrônica digital e física nas Faculdades Integradas Pedro Leopoldo (MG).

Tuning up for teleportation

H-bars

A new technique for controlling the speed of “teleportation” in quantum systems has been created by physicists in the US and the UK. The researchers have demonstrated a way of “tuning” beams of light to distribute quantum information to specific points in space and time. Manipulating and storing data in this way is an important step towards developing new communication devices and eventually a quantum computer, say the researchers.

In quantum teleportation, the sender (Alice) instantaneously transfers the quantum state of a particle to a receiver (Bob). In 1997 physicists captured public attention by teleporting quantum states between “entangled” photons for the first time. Entanglement is a feature of quantum mechanics that allows particles with two distinct quantum states to share a much closer relationship than classical physics allows.

Over the intervening 12 years teleportation has been demonstrated over increasing distances and between larger particles.

Now, Alberto Marino and colleagues have addressed a different challenge of quantum computing – the need to control the flow of quantum information. In the experiment, two beams of light were “entangled” then slowed down in a controlled manner as they passed through a cloud of hot rubidium vapour (Nature:2009.10.1038).

“In classic computing, information needs to arrive at the processor just at the right time. In quantum computing, exactly the same is true,” says Marino, a quantum-information researcher at the University of Maryland.

Harnessing the random

Until now researchers have sought to develop quantum memory for long-term data storage. Unfortunately, these systems have been highly inefficient, losing at least 80 % of the data. By slowing the speed of quantum data flow, Marino and colleagues have created a short-term memory device that is, according to the researchers, significantly more reliable.

Firstly the team split a laser beam into two before firing the it at a cloud of hot rubidium gas. Rubidium atoms have just one loosely bound electron in the outer shell, leading to a gas that is highly nonlinear in the way it interacts with light. Within the gas the incoming laser beams become entangled in a process known as “four-wave mixing”.

Quantum information is then carried in the form of fluctuations in the phase and intensity of the beams. Initially, the information travels at the speed of light but is then slowed in a controlled way in the atomic vapour.

“This type of delay will be essential for the realization of quantum networks,” says Hans-Albert Bachor, a quantum-computing researcher at the Australian National University.

Applications?

Using this mechanism, detection of quantum information was delayed for up to 27 nanoseconds. “Our quantum ‘images’ are the equivalent of the data buses in digital computers,” says Marino. The reason this delay could not be even longer is that the longer data are stored, the more noise is introduced. “Our next challenge is to preserve the quantum correlations while maintaining their quality,” said Vincent Boyer, also at the University of Maryland.

In Bachor's opinion, it is too early to consider applications for this system, but this is "limited only by our imagination”.

“Short term applications might include quantum sensors; these could work with only short fractional delays,” said Boris Blinov, a quantum systems researcher at the University of Washington.

Fonte: James Dacey is a reporter for physicsworld.com

Electricity unplugged

In the near future, wireless electricity could replace the ubiquitous power cable. Aristeidis Karalis looks at a revolutionary new way of transmitting power without wires

The judge was driving back late one cold winter night. Entering the garage, the battery-charging indicator in his wirelessly powered electric car came on. “Home at last,” crossed his mind. He swiped his personal smartcard on the front-door detector to be let in. He heard a “charging” beep from his mobile phone. The blinking cursor on the half-finished e-mail on the laptop had been waiting all day on the side table. He picked the computer up and walked towards his desk. “Good evening, your honour. Your wirelessly heated robe,” said the butler-robot as it approached from the kitchen. Putting on the electric garment, he sat on the medical desk chair. His artificial heart was now beating faster.


Science fiction usually expresses society’s impeding desires and sense of anticipation for certain technological miracles to happen. A society without power cables is pretty much a given in most science fiction. Indeed, today we do live in the “wireless age”, in which the air that we breathe probably contains more information than oxygen. However, this is also an age where mobile phones, MP3 players, laptop computers and domestic robots exist alongside old-fashioned power wires and bulky batteries. Unlike information, electrical energy is still physically confined to these borderline anachronistic appliances. Overcoming these last obstacles would finally make this a truly wireless world. Science? Yes. Fiction? Not anymore.

It all started a few years ago when Marin Soljačić, a physicist at the Massachusetts Institute of Technology (MIT) in the US, was driving back home one cold winter night and he heard an unfriendly beep from his mobile phone. It was the annoying reminder that the battery was running out, once again. It then suddenly occurred to Soljačić how great it would be if the mobile phone could take care of its own charging. The next morning, he returned to his office at the MIT determined to find a solution to the problem.

An exhaustive literature search soon revealed that wireless transmission of power was not an original idea. Back in the 1890s Nikola Tesla, one of great pioneers of electromagnetism, was the first to envisage that electricity, then a newly found form of energy, should be delivered to every house, in every city, in every country on the planet. However, Tesla did not foresee that people would be willing to drag wires around the entire globe to use electricity. Instead, he dreamed of a way of transferring electrical energy wirelessly over long distances. This would be achieved using big, coupled electromagnetic resonators able to generate very large electric fields, which were meant to propagate most likely either via conduction through the ionosphere (presumably including gigantic sparks) or through the Earth (possibly via intermediate coupling to the Earth’s charge resonances, so-called Schumann resonances). The epitome of Tesla’s efforts to achieve his goal was Wardenclyffe Tower, a 57 m high structure in Long Island that was meant to deliver electricity to the entire planet. The construction was interrupted in about 1905, not because the method was considered impractical or dangerous, but because the funder, the famed financier and banker J P Morgan, was concerned that there would be no way to bill remote electricity users. Nowadays, more than a century after Tesla, electricity reaches nearly every home through a global electrical grid. Nevertheless, J P Morgan’s objections meant a premature end to the first attempt at wireless electricity.
No wires attached

Today, we know of a variety of methods to transmit power without wires. The simplest example is electromagnetic radiation, such as radio waves. Omni-directional radiative antennas are one of the most widely used technologies, which are utilized in the provision of wireless Internet services, mobile telecoms, and radio and TV broadcasting. These antennas typically operate in the high-MHz/low-GHz frequency regimes. Even though such antennas are highly robust and suitable for use with mobile receivers, since they can operate in all directions and do not require a line of sight to the receiver, they are highly inefficient. Only a tiny portion of the radiated power in the direction of the receiver is actually picked up, since the vast majority of the radiation is lost in all the other directions. The use of a highly directional antenna, such as a microwave-beam antenna, in principle solves this problem and achieves a high efficiency in power transmission even over long distances (i.e. kilometres). On the other hand, this type of antenna does require an uninterrupted line of sight, which in itself requires a complicated device-tracking and beam-steering mechanism. Also, high-power focused beams may constitute a safety hazard.

An alternative approach to antennas is the use of an inductive transformer, a device commonly used in power circuits and electromechanical motors (for example electrical toothbrushes and chargers). A transformer typically operates up to mid-kHz frequencies. It essentially transfers electrical energy from one circuit to another via induction: the time-varying magnetic flux produced by a primary coil crosses a secondary coil and induces in it a voltage. The primary and the secondary coils are not physically connected, hence the method is wireless. Transformers can be very efficient but the distance between the coils must be very small (typically a few millimetres). For distances a few times the size of the coils, the efficiency drops significantly.

Part of the underlying physics for most of the existing methods for the wireless transfer of electricity is the fundamental principle of resonance: the property of certain physical systems to oscillate with maximum amplitudes at certain frequencies. It follows that, for any type of excitation (mechanical, acoustic, electromagnetic, nuclear) with a given frequency, a receiver will pick up the transmitted energy efficiently only when designed to resonate at the excitation frequency. Only then do successive excitations after each oscillation period add coherently in phase and lead to a build up of energy within the receiver.

To illustrate, consider 100 glasses filled with wine at different levels so that they support acoustic resonances at different frequencies. Now let an electric-guitar player produce and sustain a very well-defined note. Only one of the glasses, the one resonant with the frequency of this note, will respond to the excitation, to the extent that it may even break, while the rest will remain unaffected. Similarly, we tune the electromagnetic antenna of a radio to be resonant with the frequency of the station we want to listen to. Many transformers used in power circuitry and elsewhere are also designed to employ resonance to enhance the power transmission.
Cutting the cord at MIT

Since these days electricity is delivered to pretty much every single house in the world, it is not necessary anymore to transmit electricity over large distances à la Wardenclyffe Tower. Transmitting electricity within a room, namely over distances a few times greater than the size of the receiving devices themselves (what engineers define as mid-range distances), is sufficient for most modern applications. Achieving this goal with satisfactory efficiency, safety and low cost remains an unsolved problem. That was the challenge for Soljačić and his collaborators at the MIT labs: John Joannopoulos, Peter Fisher, Andre Kurs, Robert Moffatt and me.

Power up

The “quality factor”, Q, of a coil (see main text for details) that can be used for wireless power transmission at frequencies of about 10⁷ Hz when Q is at its peak, which is when the combined losses due to resistive absorption (green) and radiation (blue) are slowest.

Revisiting the fundamental principle of resonance, we posed the question of which physical conditions maximize the efficiency of energy transfer between two resonant objects. The energy of any resonator naturally decays due to intrinsic energy-loss mechanisms (friction for mechanical resonances, radiation and resistive absorption for electromagnetic resonances, collisions with phonons and spontaneous emission for atomic resonances). Losses are typically quantified by the number of oscillation periods that it takes for the energy to decay by a factor of 2.72. This number, represented by the “quality factor” Q, is an intrinsic property of resonators and depends on the strength of the loss mechanisms. (As a simple analogue, water inside a bucket with a hole will leak out at a rate that depends on the size of the hole.)

If two equal resonators exchange energy, it also takes a characteristic number of oscillation periods to transfer the energy from resonator A to resonator B, which is proportional to a constant that quantifies the strength of the coupling between the resonators, Qk. (If water is pumped from one bucket to another via a hose, then the transfer time depends on the strength of the pump.) Clearly, for energy transfer to be efficient, Q needs to be much larger than Qk, i.e. the rate at which energy is being transferred needs to far exceed the rate at which energy is being lost. (Water will be efficiently transferred between two leaking buckets if the pump is faster then the leaks from the holes.) The efficiency of the system can then be characterized by Q/Qk. The transfer of energy is efficient only when this ratio is larger than one, the so-called strong-coupling regime.

For our wireless method, we used one of the most basic electric circuits as a resonator: the LC circuit. This circuit is an electromagnetic resonant circuit that consists of an inductor (L), made by a wire coil, and a capacitor (C). Two such wire coils transfer energy via induction, like a transformer device, and the Qk clearly depends on the distance between the coils. For mid-range distances and long enough wavelengths, the spatial-decay rate of the magnetic field means that Qk is roughly proportional to the cube of the ratio of the distance between the coils, D, and the size of each coil, d, while showing little dependency on the frequency and the geometry of the coils. This means that, for mid-range distances, Qk will be large and the coupling very weak.

As a result, the best way to maximize the efficiency is to engineer the resonators to have the highest possible value of Q (try to seal the holes in the buckets). The resonance frequency of each coil (which has to be the same for both coils) can be tuned by varying the capacitance (and tuning a circuit element is exactly what the knob is tuning in a radio antenna). Q varies with the tuneable frequency, and this variation is shown in the figure above for a coil with a diameter of 60 cm made of copper pipe with a radius of 2 cm. It can be seen that, for high-MHz frequencies, the resonator loses energy fast (low Q, often even less than 10) due to radiation. This is exactly how an antenna is designed to work. Similarly, for mid-kHz frequencies, it loses energy fast (Q less than 100) via resistive absorption, which is typical of transformers. This explains why both omni-directional antennas and transformers fail to be efficient power transmitters at mid-range distances: the transfer-time measure Qk is large because of D, and Q is small. On the other hand, in the intermediate, low-MHz regime, much longer loss-times are observed, with Q often larger than 1000. That was our chosen regime.

Based on our theory, we started experiments in late 2006. The main challenges consisted of designing a driving circuit that would operate in our desired low-MHz regime and constructing coils that would resonate with a high enough value of Q. After a trial-and-error phase, we realized that a simple coil design without a separate capacitor, but using the coil’s self-capacitance to achieve resonance, was the best option in terms of Q.

We made two copper-pipe coils with 60 cm diameters and with five turns, such that they resonate at 10 MHz and have Q = 1000. A 60 W light bulb was our chosen device, since it operates at the tested frequencies (and what can be a clearer sign of the functionality of a system than the switch on of a light bulb?). We suspended the coils from the ceiling with fishing wire, at a distance of 2 m from each other, tuned them up, turned them on and…there was light. At an efficiency of 45%, this was, to our knowledge, the first-ever demonstration of midrange efficient wireless energy transfer.
On the safe side

The selective property of resonance means that almost all of the source power will be transmitted to the destined device and not to anywhere else. This is because any random object, including a biological organism, is almost always a non-resonant structure. Even if an object happens to be resonant, say a mobile-phone antenna, its resonance will be very different from the precise source-resonator frequency (just like those 99 wine glasses). Furthermore, even in the extremely unlikely case of it having the same resonance frequency, its Q value would be so low that no significant amount of power would be transmitted to it.

Wireless innovators

Martin Soljačić (left), the current author (middle) and John Joannopoulos from the Massachusetts Institute of Technology, along with a lab demonstration of their technology — used here to light a 60 W bulb. (Credit: Donna Coveney/MIT)

In our long-wavelength regime of operation (30 m wavelength at 10 MHz compared with 60 cm coils), power is transmitted from one object to another by spreading away from the source resonator and then “focusing” back into the device resonator. In contrast to higher frequencies, where power would be radiated across as a focused beam with a much smaller cross-sectional area, the former mechanism implies that, in our system, the power density locally and thus the fields will be considerably smaller at all points, except perhaps those too close to the coils. Smaller fields obviously imply safer performance.

Furthermore, our wireless-electricity method uses magnetic, rather than electric, fields to transfer energy. From the point of view of magnetic fields, most poor conductors, like wood, bricks, plastics and people, look a lot like air. On the other hand, electric fields do pose health hazards, because they can interact with biological organisms. With our method, these electric fields are confined to the capacitor inside our resonator. This method is quite similar to induction hobs on cookers, whereby a hob may transmit kilowatts of power to a metallic pot via induction, but it is safe to touch with our non-conducting hands. Note also that even the “large” magnetic fields in our system actually have tiny strength, approximately 10–4 T near the coils for 60 W of transmitted power, about the order of the time-invariant magnetic field of the Earth. It is the high-Q resonance that magically converts this tiny field into considerable usable power.
Wireless mobility

Long-wavelength fields naturally wrap and redistribute themselves around random objects in their vicinity or those standing between the source and mobile receiver. Therefore, while a radiated beam would immediately be interrupted by obstacles, our method stays robust and does not require an uninterrupted line of sight to the source. Sources can be hidden under floors, behind walls or inside furniture, and the receiving devices do not find shade while roaming freely behind random objects or when integrated inside other systems.

The near field produced by a resonant source coil spreads out quite uniformly in all directions, in contrast to a directed radiation beam. Thus, appropriate placement of one or more device coils can guarantee omni-directional coverage with low system complexity and thus cost.

The response of the system to dynamic variations of its parameters due to variable interaction with its environment during motion can be as fast as within 0.1 ms, based on the available frequency bandwidth of the sharp MHz resonances. This is good enough for the changes associated with daily motion.

Ray Bradbury, the prolific science-fiction writer, once said that “Anything you dream is fiction, and anything you accomplish is science.” If our innovation is successfully commercialized, then the concept of a completely wireless world could soon leap from dream to widespread accomplishment. We will forget charging our mobile phones, laptops and other personal digital devices. The maze of cables behind every home or office apparatus will disappear. Cars will drive on electricity for much longer and more cheaply. Robots will completely forget about returning to their charging stations. Micro-robots will forever hide inside electronic chips. Battery-powered sensors buried underground will never die. And the story of the judge will soon belong to history.

“Dad, I found a lamp in the basement, but it doesn’t work, see?” said the 10 year old, while ascending the stairs. “It does my son,” replied the judge, “but it connects to a wall plug and our new house does not have any of those.”
About the author

Aristeidis Karalis is at the Massachusetts Institute of Technology in the US

Fonte: PhysicsWorld

The greatest equations ever

Maxwell's equations of electromagnetism and the Euler equation top a poll to find the greatest equations of all time. Robert P Crease discusses the results of his reader survey

Earlier this year I asked readers to send me their shortlists of great equations. I also asked them to explain why their nominations belonged on the list and why, if at all, the topic matters (Physics World May p19).

James Clerk Maxwell

I received about 120 responses -- including single candidates as well as lists -- proposing about 50 different equations. They ranged from obvious classics to "overlooked" candidates, personal favourites and equations invented by the respondents themselves.

Several people inquired about the difference between formulae, theorems and equations -- and which I meant. Generally, I think of a formula as something that obeys the rules of a syntax. In this sense, E = mc² is a formula, but so is E = mc³. A theorem, in contrast, is a conclusion derived from more basic principles -- Pythagoras's theorem being a good example. An equation proper is generally a formula that states observed facts and is thus empirically true. The equation that describes the Balmer series of lines in the visible spectrum is a good example, as are chemical equations that embody observations about reactions seen in a laboratory.

However, these distinctions are not really so neat. Many classic physics equations -- including E = mc² and Schrödinger's equation -- were not conclusions drawn from statements about observations. Rather, they were conclusions based on reasoning from other equations and information; they are therefore more like theorems. And theorems can be equation-like for their strong empirical content and value.

It thus makes sense to classify both kinds as equations, which is exactly what respondent David Walton from the University of Manchester did. He distinguished between equations (such as F = ma) that comprise axiomatic models that "define the interrelationships between various observables for all circumstances" and equations that are approximate models (such as Hooke's law), which define "the interrelationships between the various observables over a defined range and within a defined accuracy". I therefore interpreted the term "equation" loosely.

Simplicity

Respondents had many different criteria for greatness in equations. Half a dozen people were so impressed with simplicity that they proposed 1 + 1 = 2.

"I know that other equations have done more, express greater power [and have a] broader understanding of the universe," wrote Richard Harrison from Calgary in Canada, "but there's something to be said for the beauty of the simplest things of their kind." He then recalled how 1 + 1 = 2 was the first equation he taught his son. "I remember [him] holding up the index finger of each hand as he learned the expression, and the moment of wonder when he saw that the two fingers, separated by his whole body, could be joined in a single concept in his mind."

Neil Blackie also voted for 1 + 1 = 2. "For this equation to come into being there had to be the invention of a method for representing a physical reality, quantities had to be given names and symbols," he argued. "There had to be a system to show how these quantities could be grouped together or taken apart. The writing down of this equation gave us the ability to present ideas, to discuss concepts, which led to an ever-expanding sphere of knowledge."

Other simple equations that were proposed included v = H₀d, which Edwin Hubble composed in 1929 to describe the fact that the galaxies are moving away from us at a speed, v, that is proportional to their distance, d, where H₀ is the Hubble constant. Balagoj Petrusev, an undergraduate student at the Institute of Physics in Skopje, Macedonia, suggested the Hamiltonian variational principle in the form δS = 0. A proper selection of the form of SPhysics World last month (September p64). articulates "a universal principle that stands true in classical mechanics, classical electrodynamics, relativistic mechanics, non-relativistic quantum mechanics and so on". In fact, Andy Hone from the University of Kent wrote a eulogy to this equation in

The unifying power of a great equation is not as simple a criterion as it sounds. A great equation does more than set out a fundamental property of the universe, delivering information like a signpost, but works hard to wrest something from nature. As Michael Berry from Bristol University once said of the Dirac equation for the electron: "Any great physical theory gives back more than is put into it, in the sense that as well as solving the problem that inspired its construction, it explains more and predicts new things" (Physics World February 1998 p38).

Great equations change the way we perceive the world. They reorchestrate the world -- transforming and reintegrating our perception by redefining what belongs together with what. Light and waves. Energy and mass. Probability and position. And they do so in a way that often seems unexpected and even strange.

For this reason, several respondents proposed equations that linked two or more disparate concepts, concrete and abstract things, the visible and the invisible. They included Boltzmann's equation S = k InW.

It relates entropy, S, which emerged as a concept during the development of thermodynamics early in the 19th century, and a purely abstract quantity, W, that emerged from the statistical treatment of systems with many degrees of freedom. Bragg's equation (nλ = 2dsinϑ)wrote another respondent, "links diffraction spots (visible reality) with the underlying crystal structure (invisible reality) and can be easily visualized with a standard textbook picture."

One of the most frequently mentioned equations was Euler's equation, e^iπ + 1 = 0. Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty"; and "mind-blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing?" The equation contains nine basic concepts of mathematics -- once and only once -- in a single expression. These are: e (the base of natural logarithms); the exponent operation;π; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero.

Practicality

Many respondents were impressed by equations that have a practical influence on human life. These included: the compound-interest equation, the implications of which from the Renaissance to the present are "obvious, staggering and unwelcome"; income-tax formulae; the simple ratio a/b = c/d, which is basic to construction, surveying and so forth; simple electrical equations, such as V = IR; basic mechanical equations, such as work done = force x distance; Shannon's capacity equation, which relates to the modern world through the Internet and digital communication; and, last but not least, Pythagoras's theorem.

Roger Bailey nominated the "sunrise equation" cos(time) = -tan(lat) x tan(dec), which identifies the time of sunrise or sunset as a function of latitude and solar declination. This, he pointed out, is "fundamental to our sense of time" and it "fits on a T-shirt". Engineer John Wilcher suggested the ideal-gas law, PV = nRT, pointing out that "the relation of pressure, volume and temperature is relevant to almost everything we do", including common but often overlooked uses such as car tyres, angioplasty procedures and oil drilling.

Meanwhile, Iain Christison, an emeritus professor of animal agriculture at the University of Saskatchewan, Canada, suggested E_M = H + P -- metabolized energy equals heat plus product. It describes the fact that "all of the useful energy consumed by animals, including people, is released as heat or stored as product". The equation, he added, "carries within it an intricate balance of cause and effect that influences all of us with every mouthful and with every step".

Historical relevance

Some respondents proposed equations that played key roles in the history of science. For example, Alan Denham proposed the Balmer series 1/λ = R (1/n₁² + 1/n₂²). The long history of this equation stretches from Fraunhofer's studies of the spectrum of sunlight in 1814, to Kirchhoff's suggestion in 1859 that each atomic species has a unique spectrum, to Angstrom's publication of the wavelengths of a thousand Fraunhofer lines in 1868, to schoolteacher Johann Balmer, who in 1885 noticed that the frequencies of light emitted by hydrogen atoms were mathematically related. The equation's history was continued by Lyman's observations in the ultraviolet region and by others in the infrared, by Rydberg (who gave his name to the constant R in the equation), and by Bohr, whose work in 1913 explained the equation. "As soon as I saw Balmer's formula the whole thing was immediately clear to me," Bohr once said.

These equations are listed in order of the number of people who proposed them. The first two received about 20 mentions each out of a total of about 120; the rest received between two and 10 each. Equations are given, where appropriate, in their most common form.

"Thus this century-long story," Denham wrote, "involving the theoretical and practical investigation of science by some of its most distinguished practitioners, would be incomplete without giving due honour to the contribution of a secondary-schoolmaster who spotted that the published scientific data conformed to a pattern that none of the scientists of his day were aware of."

Maxwell's equations

The responses suggested that there is no single criterion for greatness, and that a truly great equation ranks high in each of the above criteria. However, most votes were given to Euler's equation and to Maxwell's equations, which describe how an electromagnetic field varies in space and time. Although Maxwell's equations are relatively simple, they daringly reorganize our perception of nature, unifying electricity and magnetism and linking geometry, topology and physics. They are essential to understanding the surrounding world. And as the first field equations, they not only showed scientists a new way of approaching physics but also took them on the first step towards a unification of the fundamental forces of nature. A firm called Ocean Optics in Florida even sells T-shirts with Maxwell's equations on.

Tony Watkins recalled how he learned the equations during his second year as an undergraduate at Southampton University almost 20 years ago. "I still vividly remember the day I was introduced to Maxwell's equations in vector notation," he wrote. "That these four equations should describe so much was extraordinary...For the first time I understood what people meant when they talked about elegance and beauty in mathematics or physics. It was spine-tingling and a turning point in my undergraduate career. After a year of rapidly dwindling interest in physics (and rapidly decreasing results!), my passion was reignited by four lines of symbols." He even renamed his next bicycle Maxwell in honour of the great man, having previously ridden on his Carnot Cycle. Sadly for him, he never got round to learning tensors to see Maxwell's equations expressed even more simply.

The critical point

Nobody accepted my invitation to discuss why greatness in equations matters, which leaves me free to address the topic myself. Debating the issue has drawbacks, for it can foster the idea that equations are independent tools rather than embedded in networks of other equations, practices and information. Nevertheless, it helps us to recollect, among other things, what Richard Harrison called that "moment of wonder" that was apparent in his son's contemplation of 1 + 1 = 2.

As adults, we lose that wonder. We come to think of equations as just another set of tools that lie about ready-at-hand in the world. We lose our appreciation for their origin, thinking that they are not really of human origin: on the eighth day, God created equations as the blueprint for His recent work. As Galileo wrote -- disingenuously, polemically -- the Book of Nature is written in mathematical symbols. That's untrue, of course. We write, and continually rewrite, the book of nature.

As the philosopher Immanuel Kant once wrote: "When we discover that two or more heterogeneous empirical laws of nature can be unified under one principle that comprises them both, the discovery does give rise to a noticeable pleasure...even an admiration that does not cease when we have become fairly familiar with its object". This delight is more than having our expectations fulfilled or surprised, more than about the domination and control of nature, more than a biological product. The pleasure, Kant continued, is a feature of the exercise of the human intellect. "Even the commonest experience would be impossible without it," he wrote, which is why we "gradually come to mix it with mere cognition and no longer take any special notice of it."

In reawakening that sense of wonder, debating what makes equations great therefore re-educates us about the fundamental nature of science, and knowledge, itself.

About the author

Robert P Crease is in the Department of Philosophy, State University of New York at Stony Brook, and historian at the Brookhaven National Laboratory.

Fonte: PhysicsWorld

Journeys to greatness

To practising physicists, the great equations of physics might seem obvious, logical and trivial. But to their discoverers, Robert P Crease argues, that was far from true

Readers, I hope, will forgive me for a shameless bit of self-publicity about my latest book, The Great Equations: Breakthroughs in Science from Pythagoras to Heisenberg (Norton). But then the book is partly yours too, inspired as it was by the responses of Physics World readers to my request for suggestions of great equations (see “Critical Point: The greatest equations ever”). In the book, I chose to discuss not the most frequently mentioned equations, but those that seem to have engaged their discoverers in the most remarkable journeys.

The journey metaphor may seem misleading if taken to suggest smooth and steady progress to an already known destination. The scientific journeys I recount — which include those culminating in F=ma, and the equations of Maxwell and Schrödinger — were unpredicted, often protracted and erratic. The journey metaphor should also not imply that the travellers passively observed the changing scenery; in fact, the scientists interacted with their environment while altering it.

But the journey metaphor does capture one important aspect of the birth of these equations, which is how their originators’ ideas about what was important changed during the course of their research. Newton, Maxwell, Schrödinger and others each inherited a “landscape” or view of how knowledge about nature was organized. But during their research, new concepts — such as mass and force, entropy and displacement current, quanta and wave equations — appeared on the horizon, grew in importance and displaced others to assume positions as indispensable landmarks in the conceptual landscape.

For the ultimate destination of such scientists was not a particular location that they saw beforehand, but clarity. They were dissatisfied with what they had, perceived a vision of what might take its place, and were able to carry out the inquiry needed to realize it. At each step, they found the world to be somewhat discordant — not fully grasped — with hints of another, deeper order just over the horizon. This discordance is what makes newly realized equations seem, strangely, to be both discovered and invented.

Oliver Heaviside, who transformed Maxwell’s then-convoluted equations into their now-familiar versions, once remarked that “it was only by changing its form of presentation that I was able to see it [electromagnetism] clearly”. The sense of that remark — you transform to clarify — could have been said by any of the scientists mentioned in The Great Equations.

No royal road

Most of the time we are less interested in journeys than in where they take us. But we can learn much from them. One is just how varied such journeys are. Sometimes they are taken by scientists who talk and argue constantly with one another, as with the equations of thermodynamics and the uncertainty principle. Other journeys were undertaken by individuals working essentially by themselves, such as Einstein in his path to general relativity and Schrödinger to his wave equation, though such individuals in effect carried on conversations with colleagues even when working alone. There is no royal road to discovery.

Another thing we learn is that equations are not simply inert tools that work only in the hands of scientists and engineers. They can also exert an educational and even cultural force that shapes our view of the world. The Pythagorean theorem teaches us what proof means, the second law of thermodynamics keeps in check our dreams of free energy, Einstein’s equations changed our understanding of space and time, and the work of Schrödinger and Heisenberg forces us to rethink what being a “thing” means.

We also learn to appreciate how deeply affecting the scientific life can be. The scientists who took those journeys were never blasé, never disinterested. They were infused with curiosity, consternation, bafflement, frustration and wonder. And each scientist had what might be called a particular style. Some succeeded because they were only satisfied when they found what they were looking for, while others succeeded only because they were prepared to see something more than they expected.

Most of all, the journeys allow us to glimpse the mutability of nature and our role in it. The journeys teach us that nature could be otherwise — that it was otherwise for us until a moment ago, and for all we know it could change in the future. In such instances, we experience a transcendent moment in which a higher thought emerges in the middle of an existing one.

The critical point

The Great Equations ends by relating a conversation I had while writing the book, with an elderly physicist who expressed little comprehension and sympathy. To his workmanlike mind, the equations I mentioned seemed so obvious and logical that he could not picture not having known them, and he saw no value in making them more enigmatic. “Such equations”, he told me, “would not be wonderful if people realized how trivial they are. You should help them do so.”

I could have hugged him. At that moment, I finally realized exactly what I was trying to do. It was exactly the opposite — to undo that sense of obviousness and triviality, and to take readers back to the moment just before the equations were discovered, to appreciate how untrivial they are. Readers could, I hoped, thereby relive the wonder of the moment when the equations were first grasped — when they seemed simultaneously discovered and invented.

Scientists such as my physicist acquaintance tend to focus on the formal, discovered — what he meant by “trivial” — aspect of the birth of equations, whereas philosophers and historians tend to focus on the other aspect, having to do with their invention. It ought to be possible, I felt, to capture both aspects at once — which would, I thought, finally provide a more complete picture of the discovery process itself.

About the author

Robert P Crease is chairman of the Department of Philosophy, Stony Brook University, and historian at the Brookhaven National Laboratory, US

Fonte: PhysicsWorld