• Quantum Magic, Quantum mystery

In the first of five ground-breaking 1905 papers, Albert Einstein proposed a new idea, which he claimed was really revolutionary (rather than his more popular: “Theory of Relativity” ). Einstein re-interpreted theory proposed by Berlin professor, Max Planck, five years earlier. He said energy, for example, light travelling from a star, reaches us as a series of packages: “Light Quanta”. If human eyes were more sensitive, we could see starlight, as sensitive electronics can, as a series of blips: quantum packets of energy which have travelled independently through space. Einstein, a lowly Swiss Patents clerk, found his “Revolution” roundly dismissed - even by Planck. Einstein had proposed an experiment to test his theory and while accurate measurements 10 years later agreed precisely with his predicted behaviour, the jury remained unconvinced. In 1921 though, Einstein was awarded the Nobel Prize in Physics for this work. Subsequently, quantum theory has proved remarkably illuminating - much of basic physics, most of chemistry and biology depend on it. Examples of useful applied Quantum Magic are legion, (even obtrusive: there are more mobile devices than humans). But Quantum Mystery remains: “I think I can safely say that nobody understands quantum mechanics” (Richard Feynman, 1965); “…. Crazy after all these years” (Jim Al-Khalili, 2014). The course will tackle both aspects - a simple person’s view which which attempts to be generally accessible. Some background reading will help: Jim Al-Khalili’s (2003) classic: “Quantum” is excellent.

What is light? A Historical summary•55 BC Lucretius: ‘Light & heat of the sun.. composed of minute atoms.’•1637 Descartes: light is a type of wave, like water waves.•Gassendi (1592-1655) proposed a particle theory of light .

•Newton (1642-1726) proposed a “corpuscular” theory of light.

•Thomas Young (1773-1829) challenged Newton’s with a wave theory.•Support from Maxwell’s (1861) “electromagnetic” waves.

•Planck (1900) suggested radiation is emitted from a hot body in small “Quanta” of energy which travel by Maxwell’s waves through the “ether”.

•Einstein (1905): “revolutionary” suggestion that light travels as Quanta (later called Photons). Also (1905): the ether is redundant.

•Young’s two-slit experiment shows fringes appear with individual photons, suggesting the wavelike character of photons.

•De Broglie (1924): electrons have wavelike character and waves can behave like moving particles.

Isaac Newton (1642 - 1726)

• Newton studied Gassendi’s work and proposed that light consists of particles (he called them “corpuscles”).

• Showed light travels in straight lines.

• Passed through a prism white light is converted to a “spectrum”.

• An individual colour - yellow, say - remains yellow after passing through another prism.

• Discovered that the shadow of light passing an object has “rainbow” colours at the edge and appears to bend slightly.

• “Diffraction”, is also seen when water waves pass an obstacle.

• Despite the similarity between light and water waves, Newton retained his belief that “...light consists of extremely subtle corpuscles and that matter is made of grosser particles”.

• Due to Newton’s immense stature (and his “persuasive personality”, the corpuscular theory of light remained unchallenged for a century.

Wave patterns passing through slits

Wave passing through a broad slit causes bending: this is diffraction.

The effect was known to Christian Huygens (1678) and later to Newton.

Waves passing through a narrow slit.

Secondary waves appear to start at the slit and radiate outwards - a principle proposed by Huygens.

Thomas Young (1773-1829)

• Born Milverton, Somerset into a Quaker family. Thomas eldest of 10 children.

• Hugely precocious. at 14 had learned Latin and Greek.

• “Acquainted with”: French, Italian, German, Hebrew, Chaldean, Syriac, Samaritan, Persian .... • 1814 Interpreted the full text of the Rosetta stone.

• Devised “Young’s Double Slit experiment” to show the nature of light:

Young’s drawing of the “Fringe” pattern

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THE SPECTRUM OF THERMAL RADIATION

1859 Gustav Kirchoff emphasised

the importance of understanding

the spectrum of light emitted from

hot bodies.

This started a 40 year programme in

Germany involving experimentalists

and theorists.

This culminated in 1900 with Max

Planck’s equation & the Quantum.

Followed in 1905 by Einstein’s

revolutionary explanation of the

nature of light.

7

Measurement of the “Black-Body” spectrum( Lummer & Pringsheim 1899)

Ene

rgy

Wavelength,

Blue Red

Max Planckat the time of his Nobel award

•Born Kiel, 1858. •Diligent - but not outstanding undergrad.•Gifted pianist

•Professor advised him against physics:“All finished apart from loose ends….”Planck thought this would suit him fine:“No wish to make new discoveries…..”

•Opposed to “atomic” models of Boltzmann; and his statistical thermodynamics – Planck needed certainty.

•1889 moved to BerlinBecame interested in heat radiation from “Black Bodies”

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Theory• In reverence to all the “Classical” investigations - particularly

Maxwell’s equations (“... was it God that wrote those lines?” (Boltzmann)), theorists stayed with the “classical” theoretical understanding of heat.

• A key feature of classical approach is to divide the available heat energy equitably between all the possible modes of motion:

• low-frequency vibrations of ”oscillators” (like atom-sized tuning forks)

• generation of E-M waves stretching over the whole of the spectrum.

• Lord Rayleigh and James Jeans in England, using this approach found that the share of energy would go to infinite values at high frequencies.

• Equipartition of energy leads to this “ultra-violet catastrophe” because of infinite number of modes of motion of waves.

• Willhelm Wien in Germany - was able to fit experimental data at

high frequencies but failed at low frequency. 34

Failure of Classical physics

On Dec 14th 1900, Max Planck proposed a new idea - energy is emitted from a hot body in little packets, quanta, of Energy,E = hν, where ν is frequency and h is Planck’s constant.

This “fortunate guess” allowed Planck to fit experimental data exactly.

Frequency

Planck made it clear that his idea was no more than a mathematical dodge, designed to fit experiment, with no reality in nature.

He thought of ‘oscillators’ in the black body which behaved in this way , without saying what these were.

He didn’t really believe in the existence of atoms at that time - although Boltzmann published theories of heat, based on atoms and molecules.

Note: Indian philosophers proposed smallest particles of matter in 6th Century BC; Greek philosophers in 5th Century BC.

Classical and Quantum pictures of motion

Planck’s reconciliation of his theory with Maxwell’s

• Planck thought that the quantum model only applied to the emission of e.m. waves from a hot body.

• He imagined atoms vibrating (with reluctance because he didn’t really accept atoms).

• It was the vibrations that caused electromagnetic

wave energy to be emitted in packets.

• After that Planck clung to the view that Electromagnetic energy moved as waves – as Maxwell had taught.

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Maxwell - Last Works

• Maxwell continued with the classical approach to light and other forms of electromagnetic radiation.

• Light from a star, say, would spread out across the universe as waves, and a part of those waves would be detected by our eyes.

• Maxwell believed that for waves to travel they must travel through some medium - the ether.

• This was thought of as an invisible, tenuous, transparent medium - the “luminiferous ether”.

• In other works he founded, with Austrian Ludwig Boltzmann, theories of gases and liquids based on probability - the statistical properties of collections of molecules.

• Major departure from the deterministic “clockwork universe” favoured by Newton in which properties of bodies could be determined exactly.

• Maxwell died in 1879 - leaving Boltzmann to fight on - as there were serious critics of his approach - and even in the existence of atoms.

• Boltzmann, succumbed to the critics and committed suicide in 1906.28

Planck’s view of Planck’s equation

Max Planck was absolutely clear that his equation was no more than a fit to experiment without a theoretical basis.

“ a fortunate guess”

Planck was a reluctant revolutionary: worked hard to prove that h in E = hν must be zero – then the quantum would disappear.

When this didn’t work, he tried to explain the value of h in terms of other constants of nature, like c, G, – again failure.

But he had discovered the basis for a “natural units” of mass, length, time etc. rather than arbitrary practical units: metres, gram, second.

Natural units are not very practical, however! The unit of time is 10-43 sec

However, Planck’s equation fitted the facts & this was enough to elevate the reluctant revolutionary to world renown.

17

But the result of Planck’s news was -- a dead squib

• Scientists - particularly on the Continent - were reluctant to believe in atoms - preferring a continuous, undivided, structure.

• So the thought of energy - in packets - was additionally disconcerting.

• Anyway, apart from Planck’s black body theory, everything else fitted the standard “classical” notions beautifully.

• And classical theory - especially Maxwell’s work - was extremely hard to understand. So, once learned, (by a few only) why learn something else, new and untried.

• And there was no independent experimental data which showed that “Quanta” were necessary.

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Albert Einstein 1879-1955

Born Ulm GermanyFather electrical salesman & engineer.At 15 father’s company failed Family moved to ItalyAlbert stayed in Munich but rebelledAlbert to school in SwitzerlandRenounced German citizenshipAt 17 enrolled at Zurich PolytechnicMet Mileva Maric – fellow studentRomance lead to illegitimate daughterMarried 1903 at 24 Son, Hans Albert born 1904.Difficulty getting a job.Eventually succeeds at Swiss Patent Office in Bern1905: Annus mirabilis: Thesis and 4 ground-breaking papers.Including Special Relativity and E=mc2.

The Rest is History

Max Planck, Albert Einstein and the Quantum Revolution - Summary

• In 1905 Einstein’s Special Relativity made news (and his reputation).

• • But the earlier Quantum paper was the one he claimed was

really revolutionary & which closed the era of Classical Physics.

• Before this, in 1900 Planck, had “stumbled” on Quantum Theory

• 1905 Einstein showed just how revolutionary Planck’s work is.

• However, Planck (whose work Einstein supported) was extremely slow to recognise the value of Einstein’s contribution.

• Einstein’s revolution was only accepted after many years of neglect, but now forms the basis for modern understanding across the sciences - in Physics, Chemistry and Biology.

Einstein’s Revolution

Einstein, familiar with the problem of black body radiation, saw Planck’s

E= hν as a truly revolutionary statement.

“It was as if the ground had been pulled under one…”

He then thought about it for 4 years.

In 1905, came the first of his series of 5 ground-breaking papers

(the last being Special Relativity: E = mc2) in which he proposed a new theory of light. ”

Contrary to Maxwell: …”the energy of a light ray is not distributed over ever-increasing volumes of space,

but as a number of energy quanta that move together

…. and can be absorbed or generated only as complete units…”.

He then corrected Planck’s paper! It was seriously in error.

FAQ “ Why do we not see light as a stream of quanta?

Answer: For visible light, the quantum has very little energy. 60watt bulb emits about 1021 per sec.

Electromagnetic spectrum

Photoelectric effect• Einstein suggested a measurement that could test his theory.• Philipp Lenard had shown u.v. light can excite certain metals

leading to emission of electrons: photoelectric effect.

• But no matter how intense the light, electrons are not emitted unless the frequency is sufficiently high – like u.v. light.

• Einstein proposed that a Quantum of light with energy E= hν, where ν is high, transfers all that energy to an electron in the metal, exciting the electron which then escapes.

• The emitted electron loses some energy, W, to escape from the metal surface and emerges with energy = (hν - W).

• Unless hν is greater than W, no electrons are emitted however bright the light.

• If hν is greater than W, electrons are emitted - more with a brighter light.

Frequency ν

Reactions to Einstein’s “light quantum” hypothesis

• In 1905 Einstein was an unknown dogsbody in the Swiss patent office.

• Very few physicists were prepared to abandon classical physics.

• And particularly abandon waves – which they could visualise: “ like waves on water”.

• Moreover, Einstein was linking energy of a quantum, via E= hν to a frequency, ν, and this didn’t make sense unless the radiation was a wave!!!

• In 1905, photoelectric data was too sketchy to support Einstein but in 1915 Robert Millikan, who spent years trying to disprove Einstein’s photoelectric formula, found his measurements agreed fully with Einstein.

• Not that he was prepared to accept Einstein’s notion: ”I spent 10 years... testing that 1905 equation.....I was compelled to assert its unambiguous experimental verification in spite of its unreasonableness, since it seemed to violate everything we knew about the interference of light.”

• Note Einstein was awarded the 1921 Nobel Prize for his discovery of the law of the photoelectric effect.

• NOT the photon OR Special Relativity (1905) OR General Relativity (1916)!!!

Faint praise for Einstein

• 1913 Planck and others propose Einstein for membership of Prussian Academy:

• “In sum, one can say that there is hardly one among the great problems in which modern physics is so rich to which Einstein has not made a remarkable contribution.”

• But what comes next?

• “That he may sometimes have missed the target in his speculations, as for example in his hypothesis of light quanta, cannot really be held too much against him, for it is not possible to introduce really new ideas even in the most exact sciences without sometimes taking a risk.”

Newton and Einstein

• Newton’s laws have been superseded.• But they are only incorrect for very high speeds or energies.• Einstein’s equations reduce to Newton’s for speeds much less

than c.

• Footnote Imagine looking at a star, say 1000 light years away.• We are seeing light that has, by our timing, been travelling at

speed of light for 1000 years.

• Suppose we could ask a photon (a particle of light) how long has it been travelling.

• What answer would we get?• The photon would be puzzled. All it ”knew” was that it was just

setting out!