Physics on Such geek. Wow.

Where does mass come from?

Wed, 18 Mar 2020 00:00:00 +1300

I’m a bit over halfway through a brilliant set of particle physics lectures by Don Lincoln, called The Theory of Everything: The Quest to Explain All Reality. Don has spent many years as an experimental particle physicist, and has worked with particle accelerators at both at Fermilab and at CERN. You may remember him from his co-discovery of the top quark in 1995, or from his membership on the CERN team when they discovered the Higgs boson in 2012. Or heck you might have seen one of his TED talks. Either way you have this set of lectures, Don Lincoln, and Don’s moustache to thank for today’s episode.

This fascinating (to me) lecture series takes us on a journey through the four known forces of the universe – the strong nuclear force, the weak nuclear force, the electromagnetic force, and the gravitational force. I’ve spent literally hundreds of hours reading on this esoterica (glares pre-emptively at autocorrect), and I know it’s a baffling area, so I’m really just going to skirt around the edges of this. But one particularly outstanding part really got my interest, and I think I can write it in an understandable form here. Wish me luck… ☘️

This post is on the topic of mass. To start looking at this we go down to the foundations of matter – let’s take a quick journey through mass:

What are things?

To get us started, I’ve put the below into a bulleted list – every level is the next step down in matter:

You, a standard human being, are made up of molecules (mostly water), along with a collection of bad ideas and faulty memories. I’m not judging.
- Those molecules in your body are made up of atoms – mostly carbon, hydrogen, and oxygen.
  Let’s look closer at hydrogen. *squints*
  - A hydrogen atom is the simplest atom. It has the atomic number of 1, meaning its nucleus has only a single proton, which is balanced by a single electron.
    
    Side-note: Hydrogen is a little special because it doesn’t have a neutron in its nucleus. In contrast, heavy hydrogen – known as deuterium – has a proton, an electron, and a neutron.
    - A proton is, in turn, made up of three quarks, and weighs roughly 938 MeV/c². (that’s megaelectronvolts… more below)
      - An up quark (carrying a positive electric charge of “plus two-thirds”) has a mass of roughly 2.3 MeV/c² (ignore that part)
      - The down quark (carrying a negative electric charge of “minus one-third”) has a mass of roughly 4.8 MeV/c² (ignore that too, the fun bit is coming)
        
        (Quarks appear to be made up of strings, but that’s too deep for this article. Extra credit: String theory, superstring theory, and M theory)
        
        Holding the quarks together are the Gluons, which are the particles which mediate the strong nuclear force. These are massless*-ish*, coming in at almost exactly 0 MeV/c².
      - A proton is made of two up quarks and a down quark, which gives it a total electric charge of +1. (four-thirds from the up quarks, minus a third from down quark)
    - The electron is not made up of quarks – it appears to be a primary particle (specifically, a lepton) that cannot be subdivided. It has an electric charge of -1, and a mass of about 0.5 MeV/c².

What’s a MeV, and has it been approved by the FDA?

Okay, so you’ve probably never seen mass described in MeV/c² before. That’s because people live in the world of Relatively Big Things™, so we generally think of mass as what you might measure on a set of bathroom scales (also known as m’ass). But when you’re looking at particle physics, things get way fuzzier… SO fuzzy, in fact, that we don’t weigh things in grams – we weigh them in energy! Specifically, in electron-volts.

For example, a proton weighs 938 million electron-volts (/c²), and an electron weighs about 500,000 electron-volts. CBut… how does *that* work? How on earth do we measure mass in energy? You wouldn’t say “this glass weighs 500 calories”, would you?

HECK YEAH, you would! It’s the formula most deeply burned into your brain from high school: E=mc². Energy (in joules) = Mass (in kilograms) * the speed of light (in metres per second) squared. Einstein’s been saying it for over a hundred years… mass is energy, and energy is mass! And mass contains a whole honkin’ bunch of energy. So much energy that a single gram of matter – about the mass of a business card – looks something like this:

Energy (joules) = 1 gram * speed of light^2
Energy (joules) = 0.001 * 300000000 * 300000000
Energy of 1 gram of matter = 9,000,000,000,000,000 joules

… or about 2,151,051,625,239 calories.

So yep, you can definitely weigh things in energy … and because subatomic particles are so small, energy is a totally sensible measure to use. So let’s get back to the world of the extra-tiny.

Those numbers look fishy…

Yes, those numbers are weird. And I’m not talking about my equations above, I’m talking about the mass of an atom. Check it out again:

Proton = 2x up quarks + 1x down quark = 938 MeV/c²

But the two up quarks only bring 4.6 MeV/c² to the party, and that down quark is only 4.8 MeV/c², adding up to a mere 9.4 MeV/c². In fact, when you put together the mass of all the components of a proton, you still only see about 2% of the mass of the proton. So… where’s all that other mass coming from?

Well, okay. Those quarks aren’t just sitting stationary – they’re moving around at nearly the speed of light, within an incredibly tiny area. In fact, these quarks are fizzing around in an area approximately one-quadrillionth of a meter.

And here’s the whole idea that got me writing this post:

Our quarks, zooming around near the speed of light, and confined within such an incredibly tiny area… Well heck, that’s a whole lot of energy.

And what is energy?

It’s mass.

And that is where most of the mass of an atom comes from. From this kinetic energy, found within in the quantum foam, and expressing itself in our universe as mass.

fin.

What's so weird about lightspeed, anyway?

Thu, 16 Jan 2020 00:00:00 +1300

Have you ever experienced that thing where you’re in your car, stopped at a traffic light - you suddenly get the sensation that you’re rolling backward, so you slam on your brake… but you already had your brake on, and you weren’t moving! It was the car beside you rolling forward, but your brain misinterpreted it as your own - backwards - motion.

So, another mental image: imagine that you find yourself suddenly transported to a quiet, peaceful mountaintop. There’s a monastery here, and Monks are quietly meditating. There is no sound, no wind, just silence and calm. You would probably say you’re standing perfectly still.

Now, remembering that perception of stillness, think about the example in this tweet:

Take a kid & explain to him the true fact that the Sun is so far away that it would take a car going 100 mph a 100 years non-stop to get there. And then tell him to picture that same distance BEYOND the Sun! And then tell him that he and you were at that very spot 6 months ago.

– @KevinPaulGregg

… your peaceful mountaintop really wasn’t that still at all. In fact, it was hurtling through the galaxy at … (cough) … an astronomical rate. And on top of that, it’s spinning wildly: at the equator, the earth’s surface is moving at almost 1700km/h.

This speaks to the very basis of an important question: What is speed?

Over 400 years ago, Galileo Galilei’s Principle of Relativity (not to be confused with Einstein’s Theory of Relativity) emphasised that the concept of speed requires a frame of reference. That is, speed is always relative to something else. If you’re driving at 100km/h, that speed is relative to the road under your tyres - but compared to a motorbike passing you at 120km/hr, you’re moving backwards. Or … from a different perspective, you’re sitting still, and the motorbike is only travelling at 20km/hr. And no matter how fast you’re driving, your steering wheel isn’t really moving relative to you.

OK I think I’ve explained that point to death now. Speed is always measured between two points in space. But here’s the interesting bit.

Maxwell’s Equations, published in the 1860’s, can be used to calculate the speed of light - exactly 299,793,458 metres per second in a vacuum. But there’s something missing: that all-important frame of reference; the OTHER point in space to measure the speed against. What’s going on there? Lots of theories and experiments were floated to figure out where this missing factor was, but everything was shown to be incorrect… that is, until Einstein looked at the problem.

Einstein - in typical Einstein fashion - simply looked and said, “if the speed of light doesn’t have a frame of reference, that must mean that the speed of light is the same in any frame of reference”. That is, if you shine a torch forward, the light is travelling away from you at 300,000km/s. If you keep the torch on and hop into a speeding car, the light is still travelling away from you at 300,000km/s. If you turn around and point the torch out the rear window, the light is travelling away from you at 300,000km/s… and towards someone else, still at 300,000km/s. So what’s happened to the speed of your car??

Okay, so the speed of light is weird. But the weirdest part is what happens when you look at what that means. Let’s go back to my earlier question – what is speed? In one way, this is easy: speed is simply the distance travelled over a certain duration. But take a closer look at what those words mean: distance refers to space; duration refers to time. So, speed is the rate of movement through spacetime. Fine, semantics, whatever.

But these semantics matter. Because what we’re seeing here isn’t just light being weird: now we’re actually seeing space and time moving weirdly - dancing around themselves in a big conspiracy to force the speed of light to be 300,000km/s, no matter what your frame of reference is.

It’s time to wrap up this episode - mostly because I’ve reached the limits of my knowledge. Earlier in this article, I asked “what’s happened to the speed of your car” and, frankly, I have no idea. When it comes to the warping of spacetime I get really confused. If you’re travelling in a train at 200,000km/s, and point a powerful laser in the direction of travel, that laser’s light is going 300,000km/s relative to you. But … then we get silly business, like Lorentz contraction squishing the length in the direction of travel, time dilation starts messing with things, and we get space bending. So to the outside observer, the laser is going … 300,000km/s. ¯\_(ツ)_/¯

“People assume that time is a strict progression of cause to effect, but actually — from a non-linear, non-subjective viewpoint — it’s more like a big ball of wibbly-wobbly… timey-wimey… stuff.”

– The Tenth Doctor, Doctor Who, “Blink”

The tension between classical and relativistic mechanics

Thu, 09 Jan 2020 00:00:00 +1300

When I was considering writing my post on time dilation, I expected precisely zero feedback… just on the basis that nobody would read it. I’m really pleased with the feedback I actually got, and you’ve all spurred me to write another post on the topic. So today, I’m going to give you a brief glimpse into what caused all this ruckus: Einstein’s general theory of relativity.

If you remember, Einstein first came up with the special theory of relativity in 1905, and it took another ten years to get to the general theory of relativity. This alone should show you that the jump from the special theory to the general theory was a major leap - but let’s step back and see what this is all about.

Our very good childhood friend, Isaac Newton, published his Prinicpia in SIXTEEN EIGHTY SEVEN, which is… like… aaaaages ago. With this, he laid the foundation of “classical mechanics”, which are the physical concepts and mathematical methods that describe the motion of objects under a variety of forces.

Classical mechanics worked well - really well. There were tweaks here and there there over the ~~centuries~~, but overall, classical (or “Newtonian”) physics had things pretty much nailed… That is, until we started thinking about things that were really heavy, really small, or really fast… at that point, classical mechanics started to fray at the edges.

One of the earliest recognised failures of classical mechanics was the “precession of the perihelion of Mercury”. Don’t worry what those words mean; basically, Mercury’s orbit didn’t behave quite the way that classical mechanics said it should. The effect is suuuuper tiny: classical mechanics says that Mercury’s orbit should change by 5557 arcseconds per century, but in reality it changes by 5600 arcseconds per century… a difference of 43 arcseconds.

How big is 43 arcseconds? It’s about two-thirds of one degree. If you stand on a flat field and imagine a soccer ball on the ground, a kilometer away, the angle drawn from the ground under your feet to the top of that soccer ball is bigger than the 43 arcsecond discrepancy.

… I’m gonna say that again in case you missed it: that was per century. Less than a kilometre-away-soccer-ball every hundred years. Yikes.

Where did this discrepancy come from? It all started from a very fair assumpiton of Isaac Newton’s: he perched his calculations on the basis that things were consistent. Well, the universe Does Not Roll That Way™. Space warps; time stretches; light falls into gravity wells. But because these effects aren’t really visible in our day-to-day life, it took almost two hundred years - and the genius of Einstein - before classical mechanics was overturned by the general theory of relativity in 1915.

Okay this has become a little long and rambling now, so I’m going to take a break and come back to the topic next week! :)

Spacetime, and Time Dilation

Sun, 10 Nov 2019 00:00:00 +1300

I remember reading Stephen Hawking’s A Brief History of Time back when I was about 16 years old - a bit over 20 years ago. I didn’t even come close to understanding it then. I re-read it on Audible a year ago and I can report that I still didn’t understand it at all. Either way, I’ve been interested in physics and spacetime for a huge chunk of my life, and I wish I’d spent more time on mathematics when I was younger, because I’d have really loved to be a theoretical physicist. I shit you not. The universe just seems to be more predictable than computers.

Einstein published the special theory of relativity in 1905, and it took him another ten years to bring this into the general theory of relativity (which incorporated gravity) in 1915. The special theory is only “special” in the sense that it assumes a flat spacetime; it was the general theory which extended relativity to allow for the curvature of spacetime - for example, the curvature caused by massive objects.

Today I’m going to share my understanding of time dilation, based on what I’ve learned from Dr Brian Greene, Dr Michio Kaku, and my favourite astrophysicist Marcus Chown. I’ll start with a disclaimer: I don’t understand any of the calculations behind any of this. I’m familiar with some of the words, and I have a vague grasp of some of the concepts, but I’m mostly limited to regurgitating things I’ve read and then swearing loudly to distract people from asking questions.

I’m also quite conscious that this is around step three in the age-old progression:

Primary school: “This is how the weather works.”
High school: “That wasn’t quite right - this is how the weather works.”
Undergrad: “That wasn’t quite right - this is how the weather works.”
Postgrad: “That wasn’t quite right - this is how the weather works.”
Doctorate: “Nobody knows how the weather works.”

… Nevertheless, the actual concept is pretty simply stated, once we get everything laid out. In brief, time dilation is when time appears to slow down for an object, when that object is moving very quickly. There are three important parts to that:

the slowing of time;
the fact that it looks to you as if time has slowed for the object;
the object travelling quickly relative to you.

That means, if your twin travels (around Europe, say) at the speed of light for “ten years” (your time), you will age ten years, but they will hardly age at all.

That’s pretty weird - why does that happen? We can understand where time dilation comes from by remembering a few things:

We all know that the universe’s speed limit is the speed of light, c.
We’re all familiar with the three dimensions of motion.
We’ve probably heard someone say “time is the fourth dimension” (aka “Minkowski spacetime”).

Here’s the thing about speed limits: they apply whether you’re moving in a straight line, or if you’re moving on an angle. Imagine a box, a hundred kilometers square. If you travel a hundred kilometers from left-to-right, you will start at one edge of the box, and finish at the other. But if you start at the top-left corner of the box, and travel towards the bottom-right corner of the box, and still travel a hundred kilometers, you will end up only about 70% of the way to your destination… because some of your motion has been ‘used up’ travelling in the up/down direction, instead of just the left/right direction.

Now, here’s the thing: you’re always travelling at c. It’s just that mostly you’re travelling through time at the speed of light. Any movement in the other three dimensions will ‘use up’ your speed through the time dimension (because your total speed can’t be faster than c). Quick examples:

You, sitting here now reading this:

Speed in x dimension: 0km per second
Speed in t dimension: 299,793km per second

You, 20 years from now, travelling away from Earth at a currently-safe velocity of 3G’s (29.42 meters per second):

Speed in x dimension: 0.02942km per second
Speed in t dimension: 299,792.97058km per second

You, 200 years from now, travelling away from Aldeberan at a somehow-safe-by-then velocity of 300G (2942 meters per second):

Speed in x dimension: 29.42km per second
Speed in t dimension: 299,763.58km per second

You, never, travelling away from the milky way at 95% of the speed of light:

Speed in x dimension: 284,803km per second
Speed in t dimension: 14,989km per second

So, as you get faster in one dimension, you necessarily must move more slowly through time! Time dilation comes down to that, plus the hard-to-grasp concept that you’re only either accelerating or stationary in your own frame of reference… but that’s a story for another day.

That pretty much exhausts everything I know about time dilation… I hope you enjoyed reading it. Huge thanks to Ellie for finding me a friendly physicist to check over this for me!

In case you’re looking for some good books on the science of the very fast, the very big, the very heavy, and the very small… Here are some books that I really enjoyed reading:

Brian Greene - The Elegant Universe
Marcus Chown - Quantum Theory Cannot Hurt You
Michio Kaku - Einstein’s Cosmos