Physics is like...

Physicists like analogies. It is a way to bridge the gap in knowledge, not only between those with ample background and those without, but it also helps to enforce understanding between peers and offers a different viewpoint to a problem.

A well known physicist (guess the person) once said:

If you can’t explain it to a six year old, you don’t understand it yourself.

Well if you said Einstein then give yourself a biscuit. Yes, apparently the legendary physicist did say this, or was it something about a bar maid?

Similarly Feynman once said:

If you can’t explain something in simple terms, you don’t understand it.

But how do you explain quantum field theory (QFT) and path integrals to a six year old, someone who has no formal mathematical training or appropriate language to share and express the fundamental ideas of such a theory? How do you explain it in simple terms? We will of course ignore the famous other quote from Feynman:

I think I can safely say that nobody understands quantum mechanics.

We can use analogies to help explain complicated concepts and (maybe) even quantum mechanics in simple terms. That is fundamentally what an analogy is - providing a correspondence between two distinct things. In the case of physics we create a correspondence between the mathematical formulation of a theory to a real life, relatable human experience. A particular favourite of mine is one from Feynmans lecture series involving Dennis the menace and conservation of energy. I won’t spoil it for you here but I thoroughly suggest reading the Feynman lecture series for a very good grounding in physics.

I’d like to illustrate a very simple, but hopefully powerful analogy between indirect measurement of a quantity via experiment to fuel consumption. In physics we typically cannot directly measure the “thing” of interest in an experiment, for example let’s say we want to measure the momentum of an incoming neutrino inside a detector. We cannot simply stop and ask the neutrino what it’s momentum was before it interacted, we have to measure it indirectly, that is, to infer its value by other measurements. We would do this by examining the properties of outgoing secondaries (other particles) produced at the interaction, which are mainly charged particles and gammas, since these are easier to detect. One way the neutrino interacts (at around a couple GeV) is via a Charged Current Quasi Elastic (CCQE) interaction, producing an outgoing muon and proton from an interaction with a neutron in an atom in the detector material. This is considered one of the “easiest” ways to measure a neutrino - neutrino physicists like this interaction due to the muon and proton being charged and therefore easier to reconstruct their paths. Plus you don’t get all the hadronic mess coming out! This reconstruction is a complicated affair that I will not go into, for which my analogy hopes to explain sufficiently, but involves good knowledge of our experimental setup and apparatus and the associated uncertainties and backgrounds. Essentially we measure the muon and proton energy and momentum, apply our conservation laws and voila we have our neutrino momentum (to some level of uncertainty).

Now imagine you are a driver who is not very concerned about fuel economy nor do they ever record the miles per gallon (MPG) of the car. Additionally, the odometer does not work (this person is a poor PhD student). All of a sudden the insurance company calls you for a renewal and asks how many miles you drive per year, but they don’t know because they never record it. Oh dear! However, all is not lost, backtracking through bank statements show you how frequently they fill up the car and how much each visit cost. Now we can apply some conservation laws, approximations, and some simple algebra to figure this out.

Firstly, we need to estimate our MPG for the car. The driver takes good care of the vehicle and regularly checks oil, tyre pressures, and gets the car serviced each year, therefore we can roughly estimate the MPG from the manual and apply some approximations to that value. For instance we know that the daily commute is quite busy and therefore they rarely get out of third gear for most of the journey. The driver determines a function based on seasonal and traffic effects and applies this to the MPG (with some uncertainty). We could go further and do some experiments by measuring the actual MPG in different scenarios but let’s assume this doesn’t happen. Secondly the driver goes back and correlates previous fuel prices to dates in bank statements at the petrol station and estimates the number of gallons used between filling times. Then, quite simply, the product of these two produce our annual mileage, with some uncertainty associated with it arising from both the MPG measurement and fuel consumption. The driver can then happily provide their annual milage estimate (based on a conservative value including the uncertainty) and safely drive on for another year.

It is apparent that this analogy breaks down at some point but works to relate the two disparate ideas and hopefully motivates my point.

One final point relates to the other part of the quote, which states something about our learning and understanding. QFT, or even quantum mechanics, is so far fetched from reality it is unimaginable. It is simply nothing like what we experience in our high level world, where people do not suddenly jump through walls or become fuzzy when they are standing still. Fundamentally it makes it hard to understand as humans. It is only through the formalism of mathematics that we can begin to understand it, but this is not enough, physics is more than maths, it adds meaning and through meaning we must relate to it in our high level world. Thus, analogies play the part in giving meaning to the maths, and by use of analogies we can share our understanding and meaning to others.

Written by Thomas Stainer who likes to develop software for applications mainly in maths and physics, but also to solve everyday problems. Check out my GitHub page here.