Quantum Physics — A Beginning

Using Logic to tackle the Illogical

“If you think you understand quantum mechanics, then you don’t understand quantum mechanics” — Richard Feynman in a University lecture

Wow, that was encouraging, wasn’t it?

Professor Richard Feynman is at the forefront of quantum research, and he’s telling me that no one can understand it? I’d better give up then.

Let’s not hastily jump to conclusions.

I think what Prof Feynman meant by the statement is that the idea of quantum mechanics is so alien to us, so counter-intuitive that we cannot hope to “understand it” in the sense that we understand, say, Newton’s Laws of Motion, since they apply to us daily.

However, we can try to understand some of the concepts behind quantum mechanics, what they mean, and just WHY exactly quantum theories are so foreign to daily life.

In this series of articles, I will explain the proverbial double slit experiment and its variations. I believe that this experiment is the core of quantum physics, and one should understand how it works in order to grasp principles of quantum.

I have decided to order this series into “chapters” (this being chapter 1), each addressing a particular variation of the experiment that will shed light on certain fundamentals of quantum, and subsequently, its apparent weirdness.

They are also ordered in increasing complexity, since it is crucial that one builds the correct foundations before jumping to the advance stages.

Let me also proclaim right from the start that I did not study physics as an academic subject for very long. I am no expert. I am, however, interested in such areas of physics and have (hopefully) done ample research on it. I may not be right in certain nuances or distinctions that only experienced physicists can make, but I do wish that this article can cover some fundamental tenets of quantum physics simply such that it won’t remain in the realms of the “unknowable” for the layman.


Chapter 1: The Single Particle Double Slit Experiment

The simplest form of this famed experiment was performed by Thomas Young in 1801, well before the birth of quantum. Through this experiment, he demonstrated the wave-like property of light, but it was subsequently adopted by physicists to demonstrate the wave-like property of all fundamental particles — in order words, quantum properties.

Principles

  • A source fires a particle or a wave at a sheet containing two slits and reaches the detector screen on the opposite end.
  • The particle or wave (in principle) only passes through either slit.
  • The expected outcome for when a particle is fired is 2 bands of “energy” being detected on the detector screen since the particle is either allowed to pass through slit 1 or slit 2.
  • The expected outcome for a physical wave (eg water), however, is many bands of “energy”, the most prominent one being in the centre, and intensity fading when going towards either side. This is known as the interference pattern. The interference pattern is caused because firing a wave at the slits causes the wave to split into 2 waves after the split, which then interacts with itself. Where the peak and peak/trough and trough coincide, they strengthen each other and form a band. Where the peak and trough meets, they cancel each other, leaving gaps between the bands. The highest intensity band is directly behind the middle of the two slits.

The mechanics of causing an interference pattern is not crucial to understanding the experiment.

What’s most important is that one understands: if I fire a particle at the slits, 2 bands are produced. If I fire a wave at the slits, an interference pattern is produced.

Simple so far?

The Experiment

I fire one photon at a time at the double slit.

I expect 2 bands to form, since I am only firing one photon at a time.

The bands consist of discrete spots — ziyaadd.com

I instead observe an interference pattern that is:

  1. is slowly built up after firing a large number of photons
  2. made up of individual discrete spots rather than continuous band (which is what I would observe when firing a water wave)
  3. Which means to say, afer I fire one photon, it appears as one spot. I fire another, it takes up another spot. I fire enough, and a semblance of an interference pattern begins to form

Think about the implications of the second point.

The photons are being fired individually thus, they do not interact with each other. However, collectively, after fired, they form a collage of individual spots that looks like an interference pattern.

When the photon reached the detector screen, it was detected as a localised pocket of energy. This would lend credence to the proclamation that it were a particle.

However, it must have had some relation to a wave because, collectively, individual photons were able to form the interference pattern, which is the result you’d expect when you fire a wave.

How on earth do we reconcile such a fundamentally weird observation with reality?


Bottom Up — Deriving the Explanation from Observation.

Well, the truth is, we can’t. At least, we can’t use the principles of our reality such as classical physics because well, it simply doesn’t make sense that way.

Instead, what physicists did was to create an entirely separate field of physics — known as quantum physics, that was used to account these weird findings.

I could imagine the physicist saying: “Oh no…these findings completely go against all notions of established physics…how on earth would I explain it…ooh, I know! Let’s just create a separate branch of physics called “quantum” that can only be used at the realities in which I define it at so no one can prove it wrong!”

Sounds a bit like a fudge? A sham? It does, but practically we have already used these principles of quantum to build things like quantum computers, or develop un-crackable encryptions. Quantum is even touted as the most “precisely tested theory in physics”. So, even if it is a fudge, it is one very accurate fudge. Our quantum principles work.

Anyway…

Let me be clear that there are many weird explanations to explain this weird physical phenomenon. This includes theories like the multi-worlds interpretation, in which a multiverse is proposed.

I, however, am a huge subscriber to Occam’s Razor, which states that the simplest explanation of something is probably true.

In this article, I will use the Copenhagen Interpretation pioneered by Ernest Schrodinger (I’m sure you’ve must’ve heard of his incomprehensible cat — yup the one that’s dead and alive). To me, this is the theory which most makes sense.

Let’s go back to the experiment.

The individual photons could not have interacted with each other (save quantum entanglement), right? I mean, it’s not like they have walkie talkies that they use to sync their movements.

Thus, for an interference pattern to be produced, each photon must have traveled through the slit as though it was a wave for it to interact with itself.

However, the photons were detected on the screen as localised packets of energy. Which means to say, they displayed particle-like properties when detected.

Thus, the photons could not exist as a physical wave (like a water wave), since water waves don’t produce interference patterns with spots of energy, rather they produce a continuous one that represents flow.

So, what kind of wave can the photon be?

Top Down — Obtaining Observation from Explanation

Now that we have got some sort of idea of how the experiment works and some questions about the experiment begging to be answered, I think understanding would be made easier if from this point on, we assume that Schrodinger’s interpretation is correct.

So instead of trying to develop a theory based on observations (bottom up), let us assume the hypothesis that Schrodinger is correct then work our way down (top down).

Some conditionals first:

  1. If the hypothesis fails to commensurate with physical observations, it is plainly wrong.
  2. If it does explain all that we have observe, and can accurately predict phenomenon before observing it, then this hypothesis can qualify as a contender for the “objective, correct” understanding of quantum.
  3. However, it might not necessarily be the correct explanation, but based on current scientific understanding, it cannot be ruled out.
  4. If it is the simplest amongst theories that cannot be ruled out, then based on Occam’s Razor, we should accept it as the being accurate, for now.

Correct?

Okay, let’s also list down the physical observations from the double slit experiment that needs a good explanation.

  1. An interference pattern was observed even though we only fired individual photons in large quantities (which seems to allude to photons being physical waves)
  2. But when we take a closer look, these photons appear on the screen as individual pockets of energy. (thus ruling out photons being real physical waves)

Now we’re ready.

Remember that imaginary wave that the photon takes the form of?

Schrodinger thinks it called the probability wave function.

By his theory, after the photon has been fired,

  1. it magically becomes this wave-like phenomenon
  2. that represents the probability of where the photon will be at a given time
  3. This wave can interacts with itself after the split like a normal physical wave would and
  4. when it is detected, the photon’s position is localised. (Observer’s Effect)

Let’s now conduct our own hypothetical double slit experiment while assuming that his theory is true to see whether it fits the observations attained in real life.

  1. When I fire the photon, it becomes a wave, that is the same as a physical wave, the only difference being its “imaginary” status.
  2. This wave represents the probability of where a photon could be.
  3. After the wave passes through the slits, it interacts with the ‘mini waves’ like any normal wave would.
  4. When it reaches the detector screen, it is being “observed”.
  5. This causes the wave function to collapse into a single pocket of energy — a localised point.
  6. The determination where the photon lands (ie. where the localised packet of energy occurs) happens within the constraints of the probability function that defines the particle — for example, if there was a 1/4 chance that my photon would end up at spot A, if I fire 160 photons, approximately 40 of would land in spot A.

Eureka! yet?

This theory neatly explains how the photons end up in an individual spots yet collectively form an interference pattern.

The most concentrated band of spots— the one in the centre, is such because photons have the highest probability of reaching there. Thus, in reality, most number of photons do reach there. The least concentrated ones at the edges on the screen is such because the photons have the smallest probability of reaching there.

Therefore, the interference pattern represents the probability function itself. And the intensity of the bands represent how probable it is for the photon to end up there. If we fire sufficient number of photons, overall the pattern created will conform to the probabilities that define it, producing an interference pattern.

Its like, if the probability that it will rain on a given day is 1/5 (as I live in Singapore, it is sadly much higher), in five days it might not rain at all. But if we expand our sampling size to say, 2000, a pattern will start to emerge. Approximately 400 of those days will be filled with gloomy storm clouds. It might be 403, 397, but as we increase the sample size, the probability that defines our observation will emerge.

Bloody hell, this weird theory really can explain our spooky observations.

Questions

Alright, now that we’ve got the Copenhagen Interpretation sorted out, I’m sure many of you thoughtful observers would have a load of questions at the tip of your tongue.

“So why does the photon turn into a wave?”

“Why does it then reduce itself into a localised spot when detected?”

This will take us into explaining 2 key concepts of quantum physics in my next Chapter, the Uncertainty Principle and the Observer’s Effect.

For now, rest easy.

The Ghostbusters have arrived as per your call, to deal with somethin’ strange in your neighbourhood and somethin’ weird that don’ look good.

Hope that got you going!

Stay tuned for more bits of knowledge
I hope this piece has made you thoroughly question everything you thought you believed in. The next time you are struggling to find something to talk about with your other halves, don’t just revert to your phones, try this! I’m sure it will turn out to be a very meaningful discussion indeed.
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