Virtual Particles: What are they? (2011)
profmattstrassler.com
profmattstrassler.com
I am adding this framework to my set of tools to explain (and intuit about) QFT. And going back for a reread now. Well done!
The same with particles. They are as real as the red circle. A convenient illusion which simplifies things and computations.
I’m wondering what this looks like if you observe these fields from a distance. Are ‘echoes’ of these perturbations and interactions detectable at a distance? In the diagrams in the article representations of these perturbations are shown between the particles, but do these perturbations propagate outside the scope of these interactions? If so, I’d have thought these would count as e.g. photons.
I suppose not necessarily, not all energy levels in a quantum field are achievable, hence discrete discontinuities like absorption lines and electron shells, and in fact particles like electrons themselves. You can’t have a half strength perturbation in the electron field that adds up to half an electron. Do these perturbations fail to propagate outside the local interaction then?
> a “virtual particle” disturbance is different from a real particle. If something makes a real particle, that particle can go off on its own across space. If something makes a disturbance, that disturbance will die away, or break apart, once its cause is gone. So it’s not like a particle at all, and I wish we didn’t call it that.
Another comment here mentioned Hawking radiation. Isn't Hawking radiation when a pair of virtual particles appears just at the event horizon of a black hole, with one "falling in" and the other escaping out? Is it not in fact going "off on its own across space"? Or as the Wikipedia article[1] on Hawking radiation puts it: "the other escapes into the wider universe ('to infinity')". I fail to see the difference here, especially when both pages use very similar language about particles traveling the universe. If the one that escapes is "not like a particle at all", how is it different? Does it not behave exactly like any other particle of the same kind?
Or is the article calling a "disturbance" the creation and annihilation of a pair of virtual particles? I certainly see how that's different from a particle, but it's also pretty clear that it's not one particle but a pair. Of course this very special pair of particles that spawns and disappears is not like "a" particle.
The article is saying that neither "virtual particles" nor "particles" are good descriptions of reality. Those are better understood as just names for different shapes of ripples in a field. In the field picture, there are no particles as you would normally think of particles, but there are ripples which a variety of behaviours.
In the article's suggested model, "particles" are ripples that travel away from whatever caused them and carry on. They retain structure that they carry with them, so as they move away from the process that caused them, we think of them as objects in their own right.
"Virtual particles" are ripples, but they don't propagate away. Think of the difference between evanescent and propagating waves. Evanescent waves are ripples or shapes in a medium that don't propagate. Virtual particles are like these. There's still a ripple, a bit like the wake near a boat, but the shape of the ripple means it doesn't propagate away from whatever caused it as if it was an object in its own right.
"Virtual particles" is unhelpful terminology, because they don't behave or even exist the way we imagine a particle. Descriptions of virtual particles popping in and out of existence are misleading, as they are not particles, don't behave like particles, and there are no sudden events. There's no popping.
In Hawking radiation, when they say a pair of virtual particles appears, it means certain non-propagating ripples form in the field. That part happens normally without a black hole as well. It means there's a local ripple in the field that is non-propagating (like evanescent waves).
But in Hawking radiation, the interaction between these quantum field ripples and the distorted geometry of spacetime caused by black hole gravity means part of that local ripple ends up propagating away. The geometry of spacetime turns what is normally a local, non-propagating ripple into a propagating ripple.
In the language of "virtual particles", we wouldn't say the virtual particle propagates away. Rather, we'd say a process takes place where a virtual particle interacts with event-horizon gravity to create a (non-virtual) particle.
But it's more accurate to stop thinking about particles, and say what is normally a non-propagating ripple becomes propagating in the presence of spacetime geometry distortion, and that carries away energy. All these processes and geometric distortions still conserve energy, so any field configuration which produces a propagating ripple away from the black hole also results in the black hole itself losing a little energy, and therefore losing a little mass (because energy and mass are equivalent), which is why Hawking radiation causes black holes to shrink.
Black holes and event horizons are pretty screwy anyway, as the very notion of whether something exists or not, and whether something happens or not, can depend on your frame of reference.
> Or is the article calling a "disturbance" the creation and annihilation of a pair of virtual particles? I certainly see how that's different from a particle, but it's also pretty clear that it's not one particle but a pair. Of course this very special pair of particles that spawns and disappears is not like "a" particle.
It's the other way around: When a text (or mathematical abstraction) says creation and annihilation of virtual particles, it's misleading picture because virtual particles don't exist, and they don't pop into and out of existence. The compound operation you might call "creation-and-annihilation" is a way of describing a non-propagating local ripple, which has some mathematical subcomponents that it's convenient to call creation and annihilation of virtual particles, but the parts always co-exist in any event. There are no separate creation and annihilation events of these; they always co-exist.
Then in Hawking radiation that picture isn't quite right. One way to describe it in virtual particle language is add gravitons to the picture, but that might be a hack. Another way is to drop the virtual particle language altogether, as they are a mathematical tool and nobody has found a way to make them work consistently with gravity anyway. Even looking directly at the behaviour of fields might not give the right answers: Famously QM and GR have yet to be reconciled.
In the article Strassler says: "A 'virtual particle', generally, is a disturbance in a field that will never be found on its own, but instead is something that is caused by the presence of other particles, often of other fields."
So if a virtual particle (disturbance) can only exist in the presence of another particle, what other particles are involved in the generation of magnetic field lines? I didn't think there were any.
That should very clearly explain what "virtual" particles are.
But the idea is: the scattering matrix (https://en.wikipedia.org/wiki/S-matrix) is a matrix that says for each possible input and output state, what the amplitude of that transition happening.
The perturbation expansion is roughly a Taylor series in the number of interactions that occur in a scattering problem. So: no interaction is order-0, exchanging one particle is order-1, etc.
The first dozen terms or so then tell you the dozen or so highest-amplitude processes that occur in a given interaction. Most of these will involve virtual particles.
The elements of the scattering matrix determine how two (or more) colliding particles will interact and emit zero or more particles as a result. These elements are defined by an integral that has no closed form. For certain fields (electromagnetic being the prominent example) the integral can be approximated by the sum of terms in an infinite series.
Each term in the series includes a multiplicative factor of the coupling constant (typically denoted by alpha which is approximately equal to 1/137) raised to a certain power. Since this number is quite small, the higher the power, the less the term contributes to the overall sum.
Additionally, there is a bidirectional mapping of each term in the series to a Feynman diagram (you are likely familiar with examples of these diagrams). The number of vertices in the diagram correspond to the power of the constant mentioned above. So, the terms that dominate the integral are the ones that have a small number of vertices, but you can keep going, adding more and more vertices to get a more accurate sum.
These additional vertices can be added as long as you satisfy the rules of the diagram for the particular field you are considering (different fields have different constraints on invariants that must hold at each vertex). For EM, you can add additional photon/electron vertices as long as the overall electric charge is preserved.
These additional photon edges in the diagram are "virtual" particles. Nothing more than a pictorial representation of a term in an infinite series that approximates an integral.
(First order response might regular 6DOF motions (motion spectra) in response to wave spectra)
Here the analogies are pretty fun, because you are scattering and radiating waves in the water. Very physical!
https://www.amazon.com/Guide-Feynman-Diagrams-Many-Body-Prob...
Accessible to anyone who can sum a geometric series and take a Fourier transform!
(Feynman diagrams for dummies basically, for any who run across this comment - yes I’m being cheeky about “dummies” but I believe it calls itself something similar in the front matter. A self interaction term, then.)
Of course that was many years ago, and maybe they're fathomable now. There may even be code for it.
Are gluons virtual particles then? And all the other heavier, unstable particles? What distinguishes them from the other disturbances?
"A virtual particle is not a particle at all. It refers precisely to a disturbance in a field that is not a particle."
So from that I gather, it's a term in physics to describe things that look like particles but aren't.
Matt Strassler was among several theorists who helped me, as a graduate student, to develop a deeper intuition for quantum fields -- it is important to develop an understanding of the strengths and weaknesses of both the simplistic and nuanced ways of thinking about and discussing these interactions.
It is tempting to regard Feynman diagrams as if they are actually what is happening. One should only use them as guides to intuition. They are actually compact expressions of successive terms in a perturbative expansion, terms that can interfere with one another sometimes. Theorists (like Matt), who work with these things every day come to develop a more-nuanced understanding, generally one that places greater weight on fields (not just the bosonic force-mediating fields, but the fields for the fermions, too) than understood by even many practicing physicists in other specialties.
Another helpful insight that may aid understanding of virtual particles as you start to understand things more-deeply: the photons we observe with our eyes from distant stars need not be exactly on-shell, just very (very!) close.
It is not the most-useful/calculable way to think about it, but it is an evocative way to motivate the idea of fluctuations of quantum fields.
On atom and molecular level, chemistry also provides distributions of predictability and even more outcome certainty.
This follows the general pattern of interesting chaotic systems, and the side-effects of "chaotic attractors". We find areas of stability, where big numbers tend to converge to stable and predictable values/surfaces. We also find chaos and unpredictability between the stable surfaces in outcomes. Without full information, we can approximate using ML, though how they generalize and explain could also be an iterative ML task.
The 3-body problem means that even on macro scale we run into problems calculating some orbits (ie. asteroids). It's just that over time, most chaotic orbits tend to stabilize, so we don't run into this too much. With full information, everything can be calculated theoretically. So it is both the fundamental problem of the differential calculus itself, though inaccurate information compounds the fundamental.
Virtual particles sound like constructs bridging some of the gaps, though still unsolved on most 3+ body problems. Maybe it is correct to assume they "work" for stable/semi-stable areas of simple models, but break down in between states of chaotic systems?
I sense that we search for simple foundational relationships and understandable constants. However, the problem itself seems intractable using reductionism, the more you seek to encompass the whole across scales.
Ie. given two random real numbers between 1.0 and 10.0, human beings expect to find integers. We seek to construct perfection, while blinded to the environment sustaining us.
The expectation is not totally unwarranted, if you look at the distribution of 2+ random numbers.