Every Tom, Dick, and Harry

(trying to shed some more light on quantum)

Newton was the first (that I know about) to have speculated that light arrives in little ‘packets’ - little blobs of light. Today we call those blobs photons and most people have heard the term, if only through Sci-Fi programs like Star Trek, where the heroes regularly break out the photon torpedoes. I’ve no idea what one of those is, either, but it sounds good.

Newton was a bit of an odd egg. When he wasn’t writing guilt-ridden ramblings about how he was visited by sexual demons at night, or reading the Jewish scriptures in their original Hebrew, or writing reams of theological speculation, or doing a spot of alchemy, or hanging people for debasing the coinage of the realm (he was Master of the Mint later on in his career), he slipped in the odd bit of science here and there.

Scholars have estimated that only 1/6th of his output was actually scientific. I wonder what he could have achieved if he’d just stuck to what he was good at?

The story of light, and our attempts to understand it, are intimately connected with the story of science itself. What exactly IS this stuff?

I’m not going to tell you, because I don’t know what it is either, but it’s fascinating stuff. All I can do is to describe some of the mystery. Why was Einstein so puzzled?

You’ll probably be pleased to know I’m not going to need any maths for this. I’ll save that for later articles when I will try to go a bit deeper into how we actually use maths to describe the quantum world.

I’m going to describe experiments, and their results, and then leave us with the question : how, in the name of Newton’s crusty socks, do we explain these results?

I can certainly use the maths of quantum mechanics to “explain” the results, but ultimately this rests on a position of this is what the maths says - take it or leave it. I can’t explain why the maths is what it is, or give you any ‘picture’ that can aid in understanding what’s going on, because any such attempt to do so leads to contradictions and inconsistencies.

Most of us are probably aware that light is a form of electromagnetic (EM) radiation. Radio waves, microwaves, UV radiation, X-rays and gamma rays are also forms of electromagnetic radiation. The stuff that (allegedly) turned Bruce Banner into the Hulk, those mysterious-sounding ‘gamma rays’, is just the same stuff as light. Light is just the name we give to the portion of the electromagnetic spectrum that we can ‘see’, or perhaps more accurately, is used for vision in humans.

Gamma rays are just EM waves that wiggle ‘faster’ than light.

OK, you may have noticed, just hang on there a moment you dullard Mr Rigger. You started talking about blobs of light, about photons, and now you’re talking about waves? Which is it? Is light a particle (a blob), a wave, or both?

Yes. And no. Is the best answer I can give to that.

Forming an Image in Our Minds

A lot of (classical) physics is understood by building a kind of mental ‘picture’ of what’s going on. We form pictures of particles and can imagine them colliding, like mini golf balls, off one another. Or we form pictures of waves, like ripples on a pond, and we can imagine them to interfere to create some nice patterns. You get the idea.

The problem with light is that it sometimes behaves like particles and sometimes behaves like waves.

We’re going to start off by adopting the photon picture. We’re going to make the bold assumption that, yes, light really does consist of little blobs, but when we have a lot of these blobs (like we do with a lightbulb, or the sun) it’s their collective behaviour that looks like a ‘wave’.

So with this ‘intuition’ we perhaps think that if we take one of these light sources (eg a laser) and crank the ‘volume’ down, we’ll be able to see the individual blobs, these particles, these photons.

Sure enough - this does seem to be the case. In the famous “two slit” experiment you can actually see one of these interference patterns of light (associated with ‘wave’ behaviour), being built up one dot at a time as these photons individually strike a light-sensitive screen.

I want to look at another version of this famous experiment which (perhaps) is a bit cleaner and brings out the mysteries involved in a different way.

I’m going to be talking about ideal devices and experimental situations, but experimental physicists have been perfecting these lab techniques for some 3 decades, at least, now and they’ve gone from difficult-to-do research lab experiments to routine demonstrations at undergraduate level.

“Proving” that Photons Exist

We need 3 pieces of ‘kit’ for our first experiment (we’ll see we need a bit more, but let’s not run away with ourselves, just yet).

• A source of single photons (think perhaps of laser light with the ‘volume’ (the intensity) turned waaaaaay down.

• A single photon detector. This is a device that can go ‘ping’ when a single photon hits it.

• A beamsplitter. This is a device that splits a light beam into 2 (or more) parts. They’re easy to make (a half silvered mirror will do the trick) and we’re just going to focus on what’s known as a 50:50 beamsplitter which just splits the incoming light beam equally into two beams.

What we’re going to do is to start with our laser operating normally and fire it at the beamsplitter. We can check that half of the beam (half the intensity) goes one way and half goes the other.

Then we’re going to crank that intensity waaaaay down so that we get little chunks of light, these alleged photons, arriving at the beamsplitter and see what happens.

We have two output ‘arms’ (or ports), A and B, and we stick a single photon detector in each output arm.

[Edit : as WW pointed out, this way of drawing the experimental design can lead to confusion when the second beamsplitter is added. What I haven’t mentioned here is that the beamsplitters here have two input arms. Only one of the input arms is ‘used’ in this picture. See the more accurate diagram below]

I’ve included the mirrors here (extra pieces of ‘kit’), although not necessary at this point. They’re not doing anything except re-directing the light (the photons) to where we want it to go.

What do we find when we do this experiment?

Let’s add in another feature (together with the associated ‘kit’ to control and measure this); that of time. We’re going to suppose that our light source produces photons at a rate of 1 per minute.

We might see results like the following:

Minute 1 : Detector A pings, Detector B stays silent
Minute 2 : Detector A pings, Detector B stays silent
Minute 3 : Detector A stays silent, Detector B pings
Minute 4 : Detector A pings, Detector B stays silent
Minute 5 : Detector A stays silent, Detector B pings
.
.
.

We could write this as a set of binary tuples where 1 means ‘ping’ and 0 means ‘silent’ - with the first entry being for detector A and the second being for detector B. The table of results above could then be written as

Minute 1 : (1,0)
Minute 2 : (1,0)
Minute 3 : (0,1)
Minute 4 : (1,0)
Minute 5 : (0,1)
(and so on)

What we find is that whenever detector A pings, detector B stays silent (and vice versa).

We never¹ see the results (1,1) - both detectors ping, or the result (0,0) - neither detector pings.

We can repeat this simple experiment with many, many, thousands of single photons. In practice, of course, the timeslot is not a minute long, but could be milli or micro (or even nano) seconds.

The fact that we never see the detectors ping together in any timeslot indicates that ‘something’ is going one way or t’other. The beamsplitter is not able to split it any further. There is, as far as the beamsplitter is concerned, an individual ‘unit’ that gets sent along A or B.

The technical way of saying this would be to say that the coincidence count of the detectors is zero.

It certainly looks like we have some indivisible ‘unit’ of light stuff - and we’re going to think of this indivisible unit as the photon.

But that’s not all.

When we look at the data a bit more closely, what do we find?

We look at the data for just A, the list of ones and zeroes, and find it’s a random binary string². It passes every test for randomness that we throw at it. There’s no way to predict which output arm the photon will enter.

We could try to argue that if we knew all the details of the beamsplitter we could predict this sequence of ones and zeroes, the randomness is only arising because of ignorance of the full set of properties, but we’re going to hit the brick wall of QM at some point because we know that if we assume things have these definite properties (that allow us to predict the results) then there are things in QM that cannot be explained by any theory that makes such an assumption.

So, to summarize.

• The photon (the energy) goes one way or another. Never both

• Which way this energy goes is entirely random

Interfering With Our Minds

So, it seems our initial picture, that we have these discrete units of light (photons), is really true. There’s some fundamental ‘unit’ of light that doesn’t get split up at the beamsplitter - and all the energy in this unit goes one way or the other.

We’ve now got this picture of light arriving at the beamsplitter in little discrete blobs and, although we can’t predict which way any particular blob is going to go, we know (or think we know) that the blob will go one way or the other.

Right. Let’s see what happens if we add another beamsplitter into the mix.

Here’s what we do next. We channel the outputs from the first beamsplitter (beamsplitter 1) into the inputs to a second beamsplitter (beamsplitter 2) and put our single-photon detectors in the output arms of beamsplitter 2. It looks something like this

(see the picture at the end for a better, and more typical, diagram of this experimental arrangement. The first beamsplitter also has two inputs - one being the single photon source and the other being ‘nothing’)

We’re pretty confident about these single photons and so we can imagine a situation like the one pictured. A photon has emerged from the upper arm of beamsplitter 1 and is now on its way to one of the input arms of beamsplitter 2.

What happens at beamsplitter 2?

It’s just the same as what we had in the first picture isn’t it? We have a single photon source putting a photon into the input of a beamsplitter. OK, we’ve mucked about a bit with the original source, but fundamentally our ‘picture’ is telling us we have a single photon heading towards a beamsplitter (beamsplitter 2, in this instance).

We know what happens don’t we? We’re just going to see a random firing of either detector A or detector B. That’s what we got with our first set-up.

Wrong.

We can arrange it (by adjusting the path lengths in the upper and/or lower arms) so that ONLY detector A (or detector B) fires.

But we really have a single photon heading towards a beamsplitter. We know it’s going to be in the upper OR lower arms (of beamplitter 1), so why don’t we get a random output in our 2nd experiment?

There must be some ‘influence’, an influence that carries no energy, that goes into the output arm of beamsplitter 1 that doesn’t contain a photon. Or maybe this influence goes into both arms whilst the photon only goes into one?

Whatever this influence is, it changes the output behaviour at beamsplitter 2. We were expecting a random output at the 2nd beamsplitter, but we got certainty.

Some aspect of a ‘photon’ must be being transmitted into both arms at the first beamsplitter. But if we try to measure this ‘aspect’ we can’t find it; it only makes itself known if we don’t try to measure it before the 2nd beamsplitter.

Where have we heard this kind of thing before? If you were brave enough, you might have read my previous article on Bell’s inequality. In that article I outlined why QM isn’t the kind of theory where you can assume things have definite properties; if you do approach your analysis this way, you’re going to predict the wrong things.

In our first experiment above we set things up to measure ‘particle’ properties. In the 2nd experiment we set things up to measure an interference effect of both outputs - and interference like this is a characteristic of waves.

So is light a ‘particle’ or is it a ‘wave’? Well, yes it is. It’s both, and neither, of those things.

Is Nature Non-Binary?

It all sounds a bit like the claims made by the Enbies. I’m just sooooooo special. Far richer than just being a man or woman, I’m neither, and both, all at the same time. Glory in my rainbow richness.

Perhaps photons are just narcissistic entities?

The difference is really that photons don’t have definite properties, whereas an Enby will, or will not, have a cock - which is a fairly definite property. Strictly speaking, the external genitalia are not really the defining characteristic - it’s whether someone has, from conception, the ‘instructions’ to send the developing being along one of two distinct developmental pathways. It’s like a beamsplitter for sex.

But enough of this entertaining modern frippery - let’s get back to something real.

There seems to be this ‘vagueness’ at the heart of nature. You may have heard it expressed in terms of “wave-particle” duality which is really just one special case of a whole set of things that happen because the world is quantum (or at least because the world cannot fully be described by any theory that ascribes definite properties).

Einstein was the first to discover this weirdness at the heart of things, the first to realize this strange wave-particle thing. I think it was in 1907, but it could have been 1909, he wrote a paper analysing the fluctuations in something called black body radiation. Basically, you take a metal box and heat it up and look at the radiation inside the box.

He found that some of the fluctuations of this radiation behaved like ‘particle’ fluctuations, and some of them behaved like ‘wave’ fluctuations. Einstein was a very smart cookie, and this is another of his ‘firsts’ that isn’t well-known. Those people who (for some utterly inexplicable reason) think Einstein just “copied” his stuff from others are somewhat deranged. It’s usually his work on relativity that gets bashed by these strange people, but even if you took Einstein’s work on relativity out of the picture, he’s still one of the most important physicists of the 20th century.

Feynman famously³ once said that the two-slit experiment contains all of the mysteries of quantum mechanics. I’ve discussed a version of this experiment here, and have only really scratched the surface of the kind of weird things that happen.

I’m certainly not going to disagree with Feynman here. It is weird and can’t be explained by any kind of mental picture involving ‘waves’ or ‘particles’.

That we can’t construct any mental picture in this fashion is, itself, interesting. We can ‘understand’ what’s going on through the maths - but that, in my view, is only a partial understanding. I can’t give any good reason for you to accept the various quantum postulates - other than that they ‘work’.

And that’s it for now. More quantum stuff will follow in the fullness of time. The problem is that we haven’t really been able to shed much light on light. It’s weird stuff - and when you add in some of the effects of relativity it really does mess with your head.

We’re left with a conundrum that, perhaps, only another Newton will be able to resolve - but let’s hope the next one isn’t quite such a tortured being.

Appendix

WW made an important point. The beamsplitters here have 2 inputs and 2 outputs. I tried to be “smart” and just include the single photon input at the first beamsplitter. I was trying to strip everything back to bare bones - and overlooked this rather crucial element that there are two input ports. It’s unforgiveable, really, because when you analyse this system using QM, the 2nd input (‘nothing’) is actually critical - because what you get after the 1st beamsplitter is an entanglement of the two output modes. The ‘nothing’ that is ‘input’ into the first beamsplitter is the quantum vacuum state - which is a bit different than simply ‘nothing’.

1. We’re talking about ideal experiments here. In practice, we might get these results. The detector may not register (it’s not 100% efficient), or a detector may record a spurious ping (the detectors are not perfectly noise-free). A lot of work has gone into addressing these limitations, but it’s a bit too technical (and distracting) to discuss it here.

2. And this must be the case for B also - since the data for B is just the logical complement of the data for A. And it must also be true (for the same reason) when looking at the tuples (0,1) and (1,0) as individual data points.

3. Famous amongst physicists, that is