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Eh, it's ... both right in a sense, and wrong in a sense, to say that particles can be created out of energy.

Energy isn't a thing — it has no tangible, corporeal existence. It's not itself a particle, or a constituent of any system — for a given system, there's no part that you can point to and say "that's the energy, right there." Rather, energy is a number ... a property of the system, part of the physical description of a system (or in other words, "physical information"). Now, it's a very important number, since it is conserved in local interactions and that conservation law puts constraints on what is allowed to happen. But it's not itself a physical thing; it is a concept, and a fairly abstract one at that (you can't even directly measure energy, it always has to be calculated from other measurable properties such as mass, force, velocity, etc.). So it's not really correct to say that anything is "made up of" or "created out of" energy. What is correct is to say that systems have energy.

On the other hand, since energy is a property of systems, in order to create a physical thing, you need to imbue it with the necessary amount of energy, which has to come from some other system or process.

For example, in the process of annihilation, a particle and antiparticle collide and destroy each other. However, energy is required to be conserved, so they can't just both be destroyed and that's the end of the process, because then what would conserve the energy? So as a consequence of the law of conservation of energy, new particles must be created in order to carry that energy and conserve it.

So in that sense, you do need energy to create particles. They aren't "made up" of the energy, but they do have the energy that is carried over into them, and some energy is required to create particles (at a minimum, at least as much energy is required as the particle would have due to its rest mass).

Anyway, to get a bit closer to your main question about Matt Strassler's quote, the bottom line is that nature obeys what Murray Gell-Mann called the totalitarian principle: "that which is not forbidden is compulsory." Meaning, that if a hypothetical process is not forbidden, then it will/must eventually occur (unless something else that is not forbidden happens first). Or more accurately, if it is not forbidden, then it contributes to the path integral, and has some probability to occur within a given period of time.

So, this begs the question: what determines whether a process is forbidden or not? And the answer is: conservation laws. A process is forbidden if it would violate a relevant conservation law; otherwise, it is allowed. Any process you can think of, as long as all the conserved quantities balance out at the end of the day, that process is allowed, and has some probability to occur!

Now, for most systems, conservation of energy acts as a very big limiter on the allowed possibilities, which is why it's such an important and ubiquitous conservation law. For example, something like an electron can't just turn into a muon, because muons have a higher mass (and a higher associated energy), so you could only turn an electron into a muon if you also gave it enough energy to make up the difference in mass.

And essentially, that is what we do in high-energy particle colliders. By colliding particles together at extremely high speeds (where they have many, many times more kinetic energy than they have mass-energy), we can make them interact with each other while having a huge abundance of extra energy available. Because that energy is available, new particles can be created and processes which would create particles out of "thin air" can proceed, since there is enough extra energy available to satisfy the law of conservation of energy. If there is a lot of extra energy (which there is, in modern high-energy colliders), then even particles which have a really large mass can be created while still satisfying the law of conservation of energy.

And so, in particle colliders, there is so much energy available that lots of brand new particles can be created, including rare ones with very high masses such as the Higgs boson, or the top quark.

And that's essentially what is described by Strassler's quote. By colliding particles together and making them interact at high energies, they are allowed to interact in ways that create brand new particles using some of the available energy. They are allowed to interact this way because, with so much energy available, nothing forbids it anymore — all the conservation laws get balanced out and conserved, including the law of conservation of energy. If a conservation law might forbid it (such as conservation of electric charge), and there is enough energy available to create yet another particle to satisfy the conservation law, then multiple particles may be created — however many are needed to satisfy all the conservation laws. Or even more than are necessary; so long as the laws all are satisfied, it is allowed to happen, and will happen with some probability.

Hope that helps explain it! Cheers,

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This was great. Thanks for taking the time to write that

I'd like to say thank you for answering my question! I do have one follow up one though; if these particles are created "out of thin air" and contain mass, where does the mass come from? The Law of Conservation of Mass states that particles cannot be created.

By the way, I'd like to say that that totalitarian principle is really cool! I'd never heard of it before!

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To put it as simply as possible, some of the energy is converted into mass. The law of conservation of mass is in fact an approximation used under classical physics, and both quantum mechanics and relativity instead use mass-energy equivalence, in which mass and energy form a single conserved quantity.

>I'd like to say thank you for answering my question!

You're most welcome! :)

>I do have one follow up one though; if these particles are created "out of thin air" and contain mass, where does the mass come from?

From the energy of the particles that go into the interaction. Surely you've heard about Einstein's famous relation, E=mc^(2), yes? A given amount of mass is equivalent to a corresponding amount of energy, and vice-versa. So, if you have enough energy, you can create particles with up to however much mass corresponds to that much energy.

>The Law of Conservation of Mass states that particles cannot be created.

No, it doesn't, because there is no law of conservation of mass. There is only conservation of energy.

Mass is approximately conserved in chemical interactions, but even in chemical interactions there are small variations in mass for most interactions because of effects like binding energy and the mass defect, or the release of energy in exothermic reactions.

But either way, there really is no such thing as a "law of conservation of mass," and even if there was, such a law would only say that mass is conserved, it would not say anything about particles not being allowed to be created. Remember: mass and particles are different things. Particles are real physical entities; mass is just a numeric property that particles have, like energy, electric charge, or velocity. Mass is not some kind of physical, tangible thing. It's just a number — one that is involved in governing the behavior of objects which have it.

Hope that helps clarify,

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