“In this quantum Universe, every particle will have properties that are inherently uncertain, as many of the measurable properties are changed by the act of measurement itself, even if you measure a property other than the one you wish to know. While we might talk about photon or electron uncertainties most commonly, some particles are also unstable, which means their lifetime is not pre-determined from the moment of their creation. For those classes of particles, their inherent energy, and therefore their mass, is inherently variable, too.
While we might be able to state the mass of the average unstable particle of a particular variety, like the Higgs boson or the top quark, each individual particle of that type will have its own, unique value. Quantum uncertainty can now be convincingly extended all the way to the rest energy of an unstable, fundamental particle. In a quantum Universe, even a property as basic as mass itself can never be set in stone.”
Create an electron, and there will be a certain set of properties that you’ll know for certain, irrespective of any quantum uncertainty. You’ll know its mass, its electric charge, its intrinsic angular momentum, and many other properties as well. But that’s because the electron itself is a fundamentally stable particle: it’s lifetime is infinite, with no uncertainty. This isn’t true for many of the particles of the Standard Model, though, with the heaviest particles like the Higgs boson, the W and Z bosons, and the top quark having the shortest lifetime. Well, there’s also an energy-time uncertainty relation, and that means that the shorter your lifetime is, the bigger your inherent uncertainty in your energy is. Now, combine that with the knowledge that E = mc^2, and what do you get?
An inherently uncertain mass. Yes, it’s true: every top quark you create has a unique mass that’s different from every other top quark. Come find out the science behind this remarkable property of nature!
“I would be very interested in a post about quantum fields. Are they generally/universally believed to be real and the most fundamental aspect of our universe or just a mathematical construct? I’ve read that there are 24 fundamental quantum fields: 12 fields for fermions and 12 for bosons. But I’ve also read about quantum fields for atoms, molecules, etc. How does that work? Does everything emerge from these 24 fields and their interactions?”
When you think about the Universe, you probably think about it in a very particular fashion. There’s spacetime: the backdrop upon which the matter in the Universe exists, and then there are particles and antiparticles, which make up everything we can conceive of in the cosmos. Only, the quantum nature of reality is very different from this intuitive picture, and quantum field theory goes a few steps farther than even the unintuitive pictures we have in our heads. What if Heisenberg uncertainty, the Pauli exclusion principle, wave-particle duality and more were all just manifestations of something very basic: quantum fields themselves?
“It’s one of the most remarkable and counterintuitive results of the quantum Universe, that every unstable particle that you make has an inherent uncertainty to the most seemingly fundamental property of all: mass. You can know what the average mass of a typical particle of any particular type, and you can measure its width, which is directly related to its mean lifetime through the Heisenberg uncertainty principle. But every time you create one new particle, there’s no way to know what its actual mass will be; all you can do is calculate the probabilities of having a varieties of masses. In order to know for sure, all you can do is measure what comes out and reconstruct what actually existed. Quantum uncertainty, first seen for position and momentum, can now be convincingly stated to extend all the way to the rest energy of a fundamental particle. In a quantum Universe, even mass itself isn’t set in stone.”
There are a few properties you can say intrinsically belong to a particle: things like mass, spin, electric charge, and certain other quantum numbers. If your particle is completely stable for all eternity, there’s no reason to question any of this. But if a particle you create, even a fundamental one, has an inherent instability and can decay, all of a sudden Heisenberg comes in to mess everything up! Suddenly, the fact that you have an uncertain lifetime means you have that pesky energy-time uncertainty, and the energy of your particle is intrinsically uncertain, too. Because E = mc^2, that means your mass is uncertain, too. And the shorter-lived your particle is, on average, the more uncertain your mass is. This means when you make a top quark, for example, it could have a mass of 165 GeV, 170 GeV, 175 GeV, 180 GeV, or anywhere in between those values. (Including some values outside of that range!)
“Explain to me what information is gained from the quantum mechanical commutation relation. There’s more to it than, “we just can’t measure both properties at the same time.””
It’s absolutely true that, in quantum mechanics, there are certain pairs of properties that we simply can’t measure simultaneously. Measure the position of an object really well, and its momentum becomes more uncertain. Measure its energy, and its time becomes more uncertain. And measure its voltage, and the free charge becomes more uncertain. Although this is disconcerting to some, it’s a fundamental part of the quantum nature of the Universe. But there’s also more to it than that! Not only are pairs inherently uncertain, but each component has some built-in uncertainty that you can never take away. Moreover, it arises from a simple fact that isn’t true classically: the order of operations – whether you measure position or momentum first – makes a fundamental difference in what you get out. This quantum commutation relation is where so much of the fundamental quantum weirdness in our Universe comes from.