{"id":167937,"date":"2025-09-25T07:49:16","date_gmt":"2025-09-25T07:49:16","guid":{"rendered":"https:\/\/www.newsbeep.com\/ca\/167937\/"},"modified":"2025-09-25T07:49:16","modified_gmt":"2025-09-25T07:49:16","slug":"100-years-before-quantum-mechanics-one-scientist-glimpsed-a-link-between-light-and-matter","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/ca\/167937\/","title":{"rendered":"100 years before quantum mechanics, one scientist glimpsed a link between light and matter"},"content":{"rendered":"

The Irish mathematician and physicist William Rowan Hamilton, who was born 220 years ago last month, is famous for carving some mathematical graffiti<\/a> into Dublin\u2019s Broome Bridge in 1843.<\/p>\n

But in his lifetime, Hamilton\u2019s reputation rested on work done in the 1820s and early 1830s, when he was still in his twenties. He developed new mathematical tools for studying light rays (or \u201cgeometric optics\u201d) and the motion of objects (\u201cmechanics\u201d).<\/p>\n

Intriguingly, Hamilton developed his mechanics using an analogy between the path of a light ray and that of a material particle. This is not so surprising if light is a material particle, as Isaac Newton had believed, but what if it were a wave? What would it mean for the equations of waves and particles to be analogous in some way?<\/p>\n

The answer would come a century later, when the pioneers of quantum mechanics realised Hamilton\u2019s approach offered more than just an analogy: it was a glimpse of the true nature of the physical world.<\/p>\n

The puzzle of light<\/p>\n

To understand Hamilton\u2019s place in this story, we need to go back a little further. For ordinary objects or particles, the basic laws (or equations) of motion had been published by Newton in 1687. Over the next 150 years, researchers such as Leonard Euler, Joseph-Louis Lagrange and then Hamilton made more flexible and sophisticated versions of Newton\u2019s ideas.<\/p>\n

\u201cHamiltonian mechanics\u201d proved so useful that it wasn\u2019t until 1925 \u2013 almost 100 years later \u2013 that anybody stopped to revisit how Hamilton had derived it.<\/p>\n<\/p>\n

His analogy with light paths worked regardless of light\u2019s true nature, but at the time, there was good evidence that light was a wave. In 1801, British scientist Thomas Young had performed his famous double-slit experiment, in which two light beams produced an \u201cinterference\u201d pattern like the overlapping ripples on a pond when two stones are dropped in. Six decades later, James Clerk Maxwell realised light behaved like a rippling wave in the electromagnetic field.<\/p>\n

But then, in 1905, Albert Einstein showed some of light\u2019s properties could only be explained if light could also behave as a stream of particle-like \u201cphotons\u201d (as they were later dubbed). He linked this idea to a suggestion made by Max Planck in 1900, that atoms could only emit or absorb energy in discrete lumps. <\/p>\n

Energy, frequency and mass<\/p>\n

In his 1905 paper on the photoelectric effect, where light dislodges electrons from certain metals, Einstein used Planck\u2019s formula for these energy lumps (or quanta): E = h\u03bd. E is the amount of energy, \u03bd (the Greek letter nu) is the photon\u2019s frequency, and h is a number called Planck\u2019s constant.<\/p>\n

But in another paper the same year, Einstein introduced a different formula for the energy of a particle: a version of the now-famous E = mc\u200a\u00b2. E is again the energy, m is the mass of the particle, and c is the speed of light.<\/p>\n

So here were two ways of calculating energy: one, associated with light, depended on the light\u2019s frequency (a quantity connected with oscillations or waves); the other, associated with material particles, depended on mass. <\/p>\n

\"Photo<\/a><\/p>\n

In 1905, Albert Einstein published two ways of calculating the energy of a particle: one linked to the frequency of wave, the other to the mass of the particle itself.
\n Hulton Archive \/ Getty Images<\/p>\n

Did this suggest a deeper connection between matter and light?<\/p>\n

This thread was picked up in 1924 by Louis de Broglie, who proposed that matter, like light, could behave as both a wave and a particle. Subsequent experiments would prove him right, but it was already clear that quantum particles, such as electrons and protons, played by very different rules from everyday objects.<\/p>\n

A new kind of mechanics was needed: a \u201cquantum mechanics\u201d.<\/p>\n

The wave equation<\/p>\n

The year 1925 ushered in not one but two new theories. First was \u201cmatrix mechanics\u201d, initiated by Werner Heisenberg and developed by Max Born, Paul Dirac and others. <\/p>\n

A few months later, Erwin Schr\u00f6dinger began work on \u201cwave mechanics\u201d. Which brings us back to Hamilton.<\/p>\n

Schr\u00f6dinger was struck by Hamilton\u2019s analogy between optics and mechanics. With a leap of imagination and much careful thought, he was able to combine de Broglie\u2019s ideas and Hamilton\u2019s equations for a material particle, to produce a \u201cwave equation\u201d for the particle.<\/p>\n

An ordinary wave equation shows how a \u201cwave function\u201d varies through time and space. For sound waves, for example, the wave equation shows the displacement of air, due to changes in pressure, in different places over time.<\/p>\n

But with Schr\u00f6dinger\u2019s wave function, it was not clear exactly what was waving. Indeed, whether it represents a physical wave or merely a mathematical convenience is still controversial.<\/p>\n

Waves and particles<\/p>\n

Nonetheless, the wave-particle duality is at the heart of quantum mechanics, which underpins so much of our modern technology \u2013 from computer chips to lasers and fibre-optic communication, from solar cells to MRI scanners, electron microscopes, the atomic clocks used in GPS, and much more.<\/p>\n

Indeed, whatever it is that is waving, Schr\u00f6dinger\u2019s equation can be used to predict accurately the chance of observing a particle \u2013 such as an electron in an atom \u2013 at a given time and place. <\/p>\n

That\u2019s another strange thing about the quantum world: it is probabilistic, so you can\u2019t pin these ever-oscillating electrons down to a definite location in advance, the way the equations of \u201cclassical\u201d physics do for everyday particles such as cricket balls and communications satellites.<\/p>\n

Schr\u00f6dinger\u2019s wave equation enabled the first correct analysis of the hydrogen atom, which only has a single electron. In particular, it explained why an atom\u2019s electrons can only occupy specific (quantised) energy levels.<\/p>\n

It was eventually shown that Schr\u00f6dinger\u2019s quantum waves and Heisenberg\u2019s quantum matrices were equivalent in almost all situations. Heisenberg, too, had used Hamiltonian mechanics as a guide. <\/p>\n

Today, quantum equations are still often written in terms of their total energy \u2013 a quantity called the \u201cHamiltonian\u201d, based on Hamilton\u2019s expression for the energy of a mechanical system.<\/p>\n

Hamilton had hoped the mechanics he developed by analogy with light rays would prove widely applicable. But he surely never imagined how prescient his analogy would be in our understanding of the quantum world.<\/p>\n","protected":false},"excerpt":{"rendered":"The Irish mathematician and physicist William Rowan Hamilton, who was born 220 years ago last month, is famous…\n","protected":false},"author":2,"featured_media":167938,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[49,48,314,66],"class_list":{"0":"post-167937","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-ca","9":"tag-canada","10":"tag-physics","11":"tag-science"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/167937","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/comments?post=167937"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/posts\/167937\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media\/167938"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/media?parent=167937"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/categories?post=167937"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ca\/wp-json\/wp\/v2\/tags?post=167937"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}