[randomguy1254]

Can you give me some hints on what virtual particles actually are if its not too complicated? I keep reading that they are not actually real particles, only useful for calculations/as a simple way to understand what is going on. How does something like Hawking radiation work if they are not real particles?

[aroberge]

(Apologies to Quantum Field Theorist for the gross simplification below.)

I'm going to assume you know about basic calculus and Taylor series; if not, I'll explain what these are in a subsequent answer if you are interested.

In Quantum Field Theory, we cannot do exact calculations ... only (better and better) approximations. The way we do these calculations is very much similar to doing a Taylor series in Calculus. However, the calculations involved many complicated multi-dimensional integrals

Feynman found out a way to represent these complicated mathematical expressions that occured in those approximate calculations as pictures (known as Feynman diagrams). In these pictures, one could represent (real) particles interacting as lines (straight, curvy, etc., depending on the rules) that end in open space..

As we increased the order of expansion in the approximation (think of powers of the variable in a Taylor series), the terms corresponded to more and more diagrams, each increasing in complexity with the order of expansion.

Well, it turned out that, using the Feynman rules for translating mathematical expressions into parts of a pictures, that lines (straight, curvy) similar to that of "real" particles appeared inside the diagrams; however, these lines were all connected to others and did not end in open space: they do not correspond to any particles that we can measure directly.

However, we can think of these lines as representing "virtual" particles, that we cannot probe directly.

One thing to keep in mind (and that many that mention the "virtual particle" explanations often forget to mention): these diagrams are, in a very strong sense, an artifact of the way we do calculations using the best approximation techniques we know. These are useful computational tools. But individual diagrams should not be thought of as representing an actual precise interaction that is taking place. And virtual particles are just a way to make a connection between what we think we know ("real" particles interacting) and what our approximative way of calculating things give us.

[randomguy1254]

Thanks! That's an interesting fact about Feynman diagrams. If we had a hypothetical machine which could perform these calculations with infinite precision, would the "virtual particles" disappear from the diagram, or is it impossible to know this?

[aroberge]

Let me answer your question first very obliquely. We know that we can represent the sine function near x=0 as the following Taylor series:

sin(x) ≈ x - x^3 / 6 + x^5 / 120 - ....

With more and more terms, we can can calculate it more and more precisely. Does this means that this function really contains all of these powers of x?

Well, suppose we want to calculate sin(pi/2) (angle in radians, which is required for the Taylor series). We know that it is exactly 1. There are no powers of (pi/2) appearing in "1". The Taylor series gives us a convenient way to calculate the value of the function (technically: inside a radius of convergence), but it is not the same as the function itself.

Now, to give an example from Quantum Field theory: let me quote from a wikipedia page [1]:

_In a perturbative approach to quantum field theory, such interactions may require the calculation of hundreds of Feynman diagrams. In contrast, twistor theory provides an approach in which scattering amplitudes can be computed in a way that yields much simpler expressions._

So, these hundreds of Feynman diagrams would lead us to think of many virtual particles describing an interaction. The Amplituhedron type of calculation is done completely differently, in a way that does not lead one to think of interactions through virtual particles.

Now to answer your question: I do believe that, if we were smart enough to find a way to compute things exactly, "virtual particles" would not appear as intermediate steps of computations. But, then again, to be perfectly honest, the same would likely be of "real" particles which are just a convenient way of thinking of excitations in quantum fields ...

[1] https://en.wikipedia.org/wiki/Amplituhedron

[randomguy1254]

Very interesting, good analogies and information for me to think about.

[DavidPlumpton]

In Many Worlds virtual particles are simply other universes (other parts of Hilbert space) that have electrons in different positions. They are nearby enough to contribute some amplitude to have an observable effect. Edit a word.

[randomguy1254]

Interesting, thanks!

[Florin_Andrei]

The main challenge in understanding QM is the fact that we are all intelligent animals whose brains developed in what is for all practical purposes a classic newtonian universe. When you were one year old, crawling on the floor at your parents' house, your brain was learning to operate within the realm of classic physics.

In such a universe, things are very clear-cut. An object must be either here, or there. Something must be either in this state, or the other. Particles behave like billiard balls, and waves behave like, well, waves. Things either exist, or they do not. Space and time have perfect accuracy, there's no "smearing" of coordinates either in space or in time.

The problem is, that is not at all the case at microscopic levels. You've learned what a marble is as a kid, and you think of electrons as little marbles racing around the nucleus - but that's utterly wrong. You've watched water waves on a pond and you think that's how a beam of light behaves, but that's ridiculously simplistic.

The fundamental reality at the quantum level is the awkwardly named wave function (awkward because there's no wave proper there). That's what electrons, and photons, and neutrons, etc, are. It's a function that describes a probability amplitude as a complex number. That's it. They're not little marbles - although sometimes they kind of behave like that. They're not little waves - although they kinda-sorta look like that. They are bundles of probability amplitudes smeared out over space and time intervals. This is not a metaphor. This is stark reality.

The familiar classic universe with crawling floors and marbles and water waves is just an epiphenomenon. It's a collateral that emerges on top of the quantum world if you zoom out a trillion-fold and ignore all the little details.

The "smearing out" of space, time, momentum and energy parameters at the quantum level simply means these are not the truly fundamental things you think they are on that level. Take energy and time; in a quantum system, you could measure energy with infinite precision, but then you can't say anything about the time intervals. Or you could measure time very precisely, but then you don't know anything about energy. That's not a limitation of your equipment. It simply means neither energy nor time are the precious snowflakes you thought they are - but their combination is.

A particle that does not exist has exactly zero energy and exists for exactly zero seconds. But wait, this is the quantum world. That means a deviation from zero energy is permissible, as long as it does not take place longer than a correspondingly short interval. The higher the energy deviation, the shorter the duration of the blip. That means, in completely empty space, you will be able to measure that particles seem to appear out of nowhere, exist a very short time (the more massive the particle, the shorter the time), then vanish.

But do those particles actually exist? In QM, that's meaningless. Remember, there's no such thing as a particle? Only bundles of probability density? Remember that? And those bundles obey the basic relations about energy/time and momentum/location. As long as you're talking about fluctuations the size of an electron, then yes, pure vacuum would seem to produce electrons continuously, but they only blip in and out of measurement for a very short time.

But are they "real"? If you can measure it, it's real. Full stop. But classic categories such as "it exists" or "it does not exist" get blurred at the quantum level. Anything could potentially, and does actually, exist - provided it does not violate basic QM relations.

---

So that "quantum fog" exists in a vacuum all the time. Usually it's completely chaotic. But magnetars have such strong magnetic fields, they impose a structure over those short-lived virtual particles. And then when light passes through, it interacts with that structure and gets polarized.

So do those virtual particles exist? Well, they changed the light, didn't they? But realistically - "exists", "does not exist", that's newtonian bullshit. At the quantum level, which is the basis of reality as far as we can tell nowadays, it's all about probability functions.

---

If you feel compelled to visualize this stuff, think of quantum particles as little "clouds" of probability. More dense in the middle regions, getting thinner and thinner towards the periphery - but basically it keeps going on an on, it's just a stupendously small value far from the thickness. Of course, this is just a poor visualization, but for some folks it's better than nothing.

[halpiamaquark]

>That's what electrons, and photons, and neutrons, etc, are. [...] They are bundles of probability amplitudes smeared out over space and time intervals. This is not a metaphor. This is stark reality.

Aren't you describing a representation of atomic particles, not the particles themselves?

Edit: I'm not looking to get into a discussion about what constitutes "existence". I am just wondering if you are conflating a scientific-mathematical model for a thing with the thing itself.

[Florin_Andrei]

> you are conflating a scientific-mathematical model for a thing with the thing itself

Bohm would say yes. Others would say no.

[SomeStupidPoint]

You mix facts about the mathematics with opinions about interpretation and philosophical positions pretty freely, and that equivocation in science communication is what puts a lot of people off QM.

Scientists are too comfortable presenting philosophical positions or opinion as fact just because it's consistent with a model.

See the split between Copengahen, MWI, and Bohmian views about how to interpret the underlying calculations.

[Florin_Andrei]

Meh. It was just an intuitive description for laypeople, not a dissertation on the differences between Copenhagen and many-worlds.

Yes, I do take sides - but only for ease of explanation. The "sides" I'm taking are not even the ones I actually prefer.

Get people started first, then they can read rigorous analyses on their own.

[randomguy1254]

Thanks! That's a really nice explanation. I keep forgetting that particles don't really exist so much as a wave function does in the Copenhagen interpretation, so that gives me a new way to think about virtual particles, and helps tie it in with the article. Also a lot of other nice tidbits in this explanation for me to mull over...