While William Rowan Hamilton isn’t a household name like, say, Einstein or Hawking, he might have been. It turns out the Irish mathematician almost stumbled on quantum theory in the or around 1827. [Robyn Arianrhod] has the story in a post on The Conversation.
Famously, Newton worked out the rules for the motion of ordinary objects back in 1687. People like Euler and Lagrange kept improving on the ideas of what we call Newtonian physics. Hamilton produced an especially useful improvement by treating light rays and moving particles the same.
Sure, he was using it as an analogy. But fast forward a bit, and we find out that while light is like a wave, it is also like a particle. In 1924, de Broglie proposed that perhaps, then, matter could also be a particle or a wave. He was right, and this was the birth — or at least the conception — of what we now call quantum mechanics. This led to work from Schrödinger, Dirac, and others. Schrödinger, in particular, was intrigued with Hamilton’s analogies and joined them to de Broglie’s ideas. This led to his famous wave equation.
Hamilton did many other things, too. He was an amateur poet and developed the algebra of quaternions, although another mathematician, Benjamin Rodrigues, had written about an early version of them a few years earlier. He was also famous, or perhaps infamous, for being struck by inspiration while on a walk and carving an equation into a nearby bridge.
“I want to emphasize that light comes in this form — particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves. I’m telling you the way it does behave — like particles.”
…and…
“EVERY instrument that has been designed to be sensitive enough to detect weak light has always ended up discovering the same thing: light is made of particles.”
—Richard P Feynman
Except of course, the common understanding of “particle” as a sharply defined nugget of some solid substance doesn’t apply here and the particle he’s talking about has the characteristic of a wave in a medium of space.
“characteristic” eh. Perhaps explain what you mean with that compared to jawhenry’s post.
As for you ‘nugget’, when light is absorbed by an atom for instance it seems to do so in quanta does it not? Isn’t that why science speaks of photons? Because you can treat is as packets when detected, or what? And detection always comes down to interacting directly.
Not that I have the final truth, in fact I think we are yet to get a final complete grip on the subject. And obviously the word particle makes us think of something with volume and mass, which is a bit confusing when talking about things like light and perhaps we should avoid the word altogether.
The emphasis is on “sharply defined”.
See Feynman’s solution where a photon takes all possible paths simultaneously, and the outcome depends on which paths sum up constructively and which ones cancel each other out, which would be impossible if the photon was one sharply defined thing.
That can be demonstrated by pointing a laser on a mirror, and then blocking the direct shortest path of the reflection. The laser dot still appears in reflection, but from the wrong portion of the mirror, where it’s not supposed to go.
The real explanation of course is: if we don’t measure the particle, the particle isn’t described as being in any position, or taking any path. That could not be if the photon was a particle of a definite size, shape, etc. because those properties beg the important question: where is it?
Note here: if we say “the photon is 1 nanometers wide”, then we also have to ask, “okay, then where is the left edge? Where is the right edge?” – because if you can’t define those then how can you say the photon is 1 nanometers wide? If the boundaries of the shape are not defined, then the photon has no size, and what is a particle of no size?
If it had zero size, it wouldn’t be anywhere. Having no definite size, it’s “everywhere” which is the same as nowhere in particular.
That is the whole point now isn’t it? Light is both a particle and a wave in its properties, and the logic of showing one property to argue the other property isn’t there is silly since you could reverse it and do the same starting with the particle property.
It’s weird though because light is the same as radio albeit a higher frequency and we don’t argue that radio is particles. But maybe we should, stir up the pot a bit, see what’s cooking :)
It’s all about definitions though, as you argue “okay, then where is the left edge? Where is the right edge?” You can say the same of all particles we learn from quantum mechanics do we not? And what do you consider ‘the edge’? You are projection a structure on it that is imaginary and not applicable in the first place.
More importantly, definition implies information – to say that something is precisely this big, or exactly here, requires you to define it with infinite precision. Information, being related to energy, is limited. We can only pack so much in so little space without causing another big bang.
As for the particle being quantized, that is in no contradiction. The only point is that energy is absorbed in discrete units.
Because energy can only be absorbed in discrete quanta and not split between two locations, once we absorb the energy here, it cannot also happen over there, and so it appears that the particle was “here”.
Once we measure the particle to be “here” and not “over there”, it’s just as good as if it was never over there in the first place – but if we didn’t measure it here, then we might have measured it over there since the energy has to go somewhere.
““I can explain it to you, but I can’t comprehend it for you.”
― Edward I. Koch
https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality
“If I say they behave like particles I give the wrong impression; also if I say they behave like waves. They behave in their own inimitable way, which technically could be called a quantum mechanical way. They behave in a way that is like nothing that you have seen before. Your experience with things that you have seen before is incomplete. The behavior of things on a very tiny scale is simply different. An atom does not behave like a weight hanging on a spring and oscillating. Nor does it behave like a miniature representation of the solar system with little planets going around in orbits. Nor does it appear to be somewhat like a cloud or fog of some sort surrounding the nucleus. It behaves like nothing you have seen before.”
Also Richard P Feynamn
There’s really two things going on: the particle, and the position.
Position at the quantum level isn’t a fixed (or moving) coordinate, it’s a probability wave. A probability wave implies the probability of finding the particle at any one coordinate, and as a wave it can be split into components.
For example, you can split the wave into the sin() and cos() components and send these down different paths, which is exactly what happens in a Mach–Zehnder interferometer. If you could slow down the photon and attach a little indicator LED to it, you would see the LED get bright down one path, then dim while getting bright down the other path, back and forth among the two paths, each time moving a little further down each path.
The position of the photon oscillates between the paths, indicating that the position isn’t really specified yet and could be found in either path. When you insert a barrier in one path and catch the photon you get all the energy of the photon delivered to the barrier.
Curiously, if you insert the barrier and don’t catch the photon, you’ve specified the position of the photon as being in the other path. This gives rise to the Elitzur–Vaidman bomb tester, a thought problem where you can detect whether there is a barrier in the path (that would catch the photon) without actually catching the photon.
The idea that determining where the photon isn’t changes the state of where the photon is is the weird part. We’re used to expecting that the photon has one and only position determined by a specific coordinate. In reality, the photon has a probability of being in multiple positions, and those positions can be made arbitrarily far apart.
Two entangled photons share the same two positions and swap back and forth – if one is found here, then the other one is found over there. Measuring at my position finds one photon, and at the same time determines where the other photon isn’t, both wave functions are reset, and the distant photon continues with a new probability wave.
If you can understand probability waves, knowing that measuring where a photon isn’t affects it’s actual state is the key concept.
One way of saying it is, when the photon comes to existence, information about it starts spreading out at the speed of light into the universe, and when the photon interacts with something, the universe decides where it should appear so it would be consistent with whatever else is there.
And, when we say “the photon isn’t here”, it isn’t “there” either – because “there” doesn’t exist to us here until enough time has passed that the information can reach us. By that time, the information about the photon has gone back and forth between both locations and everything in the universe can agree on where it was.
Sorry folks, but I have to top all the speculative comments here with the ultimate nonsense bomb.
Nobody has yet “hacked” light–matter correlations to 100 % – not even with Hamiltonians, quantum field theory, or however fancy your equations are.
There’s only one figure in near human history consistently associated with light: Jesus.
He literally called himself “the light of the world” — and what happened? He got killed.
A whole religion was built on that death, a god-human concept that makes most scientists roll their eyes (fair enough).
But think of it this way: reality itself might be a hack of light, where information was rerouted away from Jesus —
as if some cosmic controller switched the channel just before he could upload the technical documentation for existence.
He might have been on the verge of delivering the ultimate Grand Unified Theory — answering all our questions —
but history ended his experiment prematurely.
And since we’re already down the rabbit hole: maybe it wasn’t Romans at all.
Maybe 👁️ Illuminati-grade aliens did it —
beings who already knew from other Earth-like planets
that this guy could crack the code of light and start a technical revolution.
So they “pulled the plug” to keep the rest of the universe on a stable firmware version.
The 🔺 was sealed, the knowledge locked, and the rest of us left in closed-source reality.
If that’s not a light–matter conspiracy, I don’t know what is.
But then who was Paul Simon talking with, when he said, “Hello darkness my old friend.”
There’s a Hamilton Walk every year to celebrate the writing on the bridge incident. 16th of October, I’m considering going but I don’t understand quaternions
You can go as a connoisseur of vandalism :)
It would expand your travel opportunities immensely in general if you took that role.
And you could get some dosh writing articles on vandalism for newspapers once you established this discipline.