Could High Energy Virtual Particles Destroy a Starship?

[mrspeedybob]

I am told that the space surrounding me is filled with virtual particles, popping into and out of existence. I could believe that they exist for such short times and at such low energies that sophisticated equipment is needed to detect them. However, a collision between even 1 virtual electron and a starship going 0.99999999999999999999999999 c would have a significant effect on the ship because in the ships frame of reference the electron would have a large kinetic energy. Since all reference frames have equal claim to be "at rest", why are we not constantly bombarded by virtual particles that may be at rest relative to the afore mentioned starship, but would tear us apart?

 

[Bill_K]

mrspeedybob, Couple of misconceptions here. In the first place, virtual particles do not "pop into and out of existence." The vacuum state is time independent, there are no time dependent things happening. This is no more true than the idea that an electron "spins" on its axis or "orbits" about the nucleus. The vacuum does not boil with activity. This popsci idea results from forcing a classical interpretation of a quantum situation. The vacuum is a quantum state in which virtual particles exist with a certain (constant) probability amplitude.

Second is the implicit notion that "you can violate energy conservation if you're quick about it." Not so. Energy is exactly conserved at all times, even by virtual particles. Virtual particles can only transfer energy from one object to another. In order to be struck by a high energy virtual particle, that energy does not simply materialize out of the vacuum, it must have come from somewhere else. Whenever one particle gains energy, another (real) particle loses energy.

 

[Ken G]

I'm not sure I agree that we can state categorically that energy is exactly conserved at all times. I agree it is exactly conserved in any measurement, but all measurements "take awhile." I would say that time is a rather weird beast in QM (for example there isn't a formal time operator but there can be operators that function like time in given situations), so we need to talk about it carefully. There is a parameter "t" in QM, that we loosely regard as time, but it is actually only time in the sense that it will correspond to real time over the real time it takes to make a measurement to be able to say what happened. That really doesn't afford us the liberty of being able to talk about "at all times", because the ability to establish this correspondence over some given time t will always require an energy E~h/t, and that energy might simply not be available to test the expectation. It could easily hold that the correspondence breaks down at some energy scale that is so far undiscovered, and it is even expected to break down at the Planck energy scale.

So I would agree that saying that virtual particles "pop into and out of existence" is a very awkward and informal picture, but I don't think we can say they don't do that either. I would simply say that the universe takes no position on the existence of virtual particles because it is never called out to take such a position, and the question that is never asked is also never answered. So I would say the whole question of "what exists" becomes murky at the scale of virtual particles, and it may be as wrong to exclude them from a transitory existence as it is to assert they do have a short-term existence. Can't we just say we don't have an empirical language to even talk about existence or non-existence at that scale?

 

[TrickyDicky]

Second is the implicit notion that "you can violate energy conservation if you're quick about it." Not so. Energy is exactly conserved at all times, even by virtual particles. Virtual particles can only transfer energy from one object to another.

But apparently precisely that is what virtual particles are there for. They are the representation of how "you can violate energy conservation if you're quick about it" and get away with it. But this is not so weird due to the fact (as Ken pointed out) that it is not clear at all that energy is exactly conserved at all times, certainly that is not the case in GR where as Hilbert liked to say: general relativity has only improper energy theorems. And the HUP for time and energy precisely allows for energy not being exactly conserved at all times at certain energies. Virtual particles are just a visual device (and a calculational one) to justify this energy conservation violations.

 

[Bill_K]

Well, KenG and TrickyDicky, it's difficult to believe that anyone would seriously entertain the nonconservation of energy, but that seems to be what we're doing. Energy conservation is the bedrock of all of physics, and it holds exactly in quantum mechanics, and in relativity too. Not only is energy conserved "at all times", it is conserved locally, meaning "at all points in spacetime." When you draw a Feynman diagram, the four-momentum at each vertex must add to zero. There is no "missing energy" feature that will let energy disappear at one point and magically reappear at another.

Please do not confuse this with measurement, or the Heisenberg uncertainty principle. Uncertainty is not the same as nonconservation. If the energy of particle A is uncertain, fine; but that same uncertainty must be present in the opposite sense somewhere else, in particle B. The sum of the two must in all cases be exactly equal to the initial energy.

Quantum mechanically, energy conservation can be thought of as analogous to charge conservation. The fact that electromagnetism is gauge invariant demands that it couple to a locally conserved current J^μ, meaning that electric charge is conserved, not just globally but locally at each spacetime point. You cannot have charge disappear in one place and pop up somewhere else later. Likewise, the fact that gravity is gauge invariant (general covariance) demands that it couple to a locally conserved quantity T^μν, meaning that energy-momentum is rigorously conserved at each spacetime point. Without this property the theory cannot be inconsistent.

 

[TrickyDicky]

Well, KenG and TrickyDicky, it's difficult to believe that anyone would seriously entertain the nonconservation of energy, but that seems to be what we're doing. Energy conservation is the bedrock of all of physics, and it holds exactly in quantum mechanics, and in relativity too. Not only is energy conserved "at all times", it is conserved locally, meaning "at all points in spacetime." When you draw a Feynman diagram, the four-momentum at each vertex must add to zero. There is no "missing energy" feature that will let energy disappear at one point and magically reappear at another.

Please do not confuse this with measurement, or the Heisenberg uncertainty principle. Uncertainty is not the same as nonconservation. If the energy of particle A is uncertain, fine; but that same uncertainty must be present in the opposite sense somewhere else, in particle B. The sum of the two must in all cases be exactly equal to the initial energy.

Quantum mechanically, energy conservation can be thought of as analogous to charge conservation. The fact that electromagnetism is gauge invariant demands that it couple to a locally conserved current J^μ, meaning that electric charge is conserved, not just globally but locally at each spacetime point. You cannot have charge disappear in one place and pop up somewhere else later. Likewise, the fact that gravity is gauge invariant (general covariance) demands that it couple to a locally conserved quantity T^μν, meaning that energy-momentum is rigorously conserved at each spacetime point. Without this property the theory cannot be inconsistent.

Bill_K, this is kind of funny because until a few weeks ago I used to be firmly convinced that "Energy conservation is the bedrock of all of physics", but in this time interval and after some sour debates with several science advisors in these forums I have to say that I have come to understand the fact that energy is not strictly conserved in GR (see the cosmology FAQ "What is the total mass-energy of the universe? " that starts with the phrase "Conservation of energy doesn't apply to cosmology"), or the article by Sean Carroll: "Energy is not conserved" http://blogs.discovermagazine.com/cosmicvariance/2010/02/22/energy-is-not-conserved/
At the very least it is something debatable and there are contradictory views even from reknown physicists.
Now keep in mind that what you have talked about in your post is actually "momentum-energy" conservation, and absolutely everybody agrees that that is an exactly conserved quantity. But in general relativity at least the distinct quantities energy, mass, momentum and angular momentum on their own are not globally conserved, (some of them according to some authors not even well defined yet).

 

[TrickyDicky]

Please do not confuse this with measurement, or the Heisenberg uncertainty principle. Uncertainty is not the same as nonconservation. If the energy of particle A is uncertain, fine; but that same uncertainty must be present in the opposite sense somewhere else, in particle B. The sum of the two must in all cases be exactly equal to the initial energy.

Also I don't think anybody is confusing uncertainty with nonconservation, even if some people conflates the general meaning of uncertainty with the HUP. What is true is that it is a known fact that what allows virtual particles to have at least mathematical existence is the energy-time uncertainty principle.
And I don't think measurement and HUP should be confused.

 

[byron178]

But apparently precisely that is what virtual particles are there for. They are the representation of how "you can violate energy conservation if you're quick about it" and get away with it. But this is not so weird due to the fact (as Ken pointed out) that it is not clear at all that energy is exactly conserved at all times, certainly that is not the case in GR where as Hilbert liked to say: general relativity has only improper energy theorems. And the HUP for time and energy precisely allows for energy not being exactly conserved at all times at certain energies. Virtual particles are just a visual device (and a calculational one) to justify this energy conservation violations.

so what your saying is that virtual particles don't in reality pop in and out of existence?

 

[Vanadium 50]

It's very difficult to have a discussion about virtual particles. There are 100x as many people whose understanding of virtual particles comes only from popularizations as those who have actually studied them. Unfortunately, when someone from the second group says something in conflict with the popularizations, people from the first group inevitably jump all over them telling them they are wrong.

 

[Ken G]

Let me give you a different perspective. The issue at hand is not whether conservation of energy works essentially exactly "at the end of the day" when we compare to observations, it's whether it should be regarded as a fundamental truth underpinning everything that can be conceived of as having some claim on existence, or if it is just a kind of emergent truth that results from the more fundamental theory in the appropriate limits. To me, the beating heart of quantum mechanics is the concept that what actually happens is a kind of coherent sum over a vast number of barely conceivable things, and what culls out the actual from the barely conceivable is just one thing-- constructive interference. That's essentially the Feynman path integral picture, in spacetime a path integral involves paths that correspond to completely different energies, so the very principle of conservation of energy emerges from other possibilities that don't conserve it. The same idea underpins the principle of least action in classical physics. In this view, energy is conserved because nonconservation of energy gives rise to destructive interference, and for no other reason.

However, constructive interference is not a fundamental law, it emerges from the sheer vastness of the number of contributing amplitudes, and it comes at a price-- it isn't instantaneous, it takes a little time to happen. Every example Bill_K gave above, albeit good physics, all involves outcomes that were fully time integrated over the interactions they refer to, so do not suffice to answer the question that was posed-- is energy conserved at all times. By that we don't mean was it in 1956 and will it be in 2012, we mean at every moment in time in the evolution of a system, because we are wondering if "virtual particles" can have some claim on existence during the short intervals of time where that constructive and destructive interference is actually happening, those intervals when what can happen and what cannot is still being decided.

 

[jtbell]

It's very difficult to have a discussion about virtual particles. There are 100x as many people whose understanding of virtual particles comes only from popularizations as those who have actually studied them. Unfortunately, when someone from the second group says something in conflict with the popularizations, people from the first group inevitably jump all over them telling them they are wrong.

See for example the following threads:

https://www.physicsforums.com/showthread.php?t=302923

https://www.physicsforums.com/showthread.php?t=75307

https://www.physicsforums.com/showthread.php?t=460685

https://www.physicsforums.com/showthread.php?t=506228

 

[Ken G]

So it's a topic that you are tired of hearing about. What is demonstrably correct, and seems to be agreed on by all experts, is the quote from the field theory textbook:
"The correspondence between the integrals that make up the Dyson series and Feynman diagrams is perfectly precise and well-defined. However, it is customary to go further and think of the Feynman diagrams as schematic pictures of physical processes, and here the interpretation acquires a more imaginative character. ... They are, in short, the infamous virtual particles that are so ubiquitous in physicists' discourse. In the final analysis, the only existence they possesses for certain is as picturesque ways of thinking about the ingredients of the integrals in the Dyson series."
Now, what does this mean? Apparently, physics can now be divided into two categories, ontological constructs that are actually real, and those that are "picturesque ways of thinking about the ingredients of the integrals." Just stop for a moment and think about this interesting dichotomy we have within physics, and you see how quickly it falls apart. In actuality, anything that is a picturesque way of thinking about the ingredients of integrals is just precisely what is meant by ontology in physics. But yes, you are tired of the question.

Also, the suggestion that descriptions that take virtual particles seriously, or more correctly, as seriously as any of the many ontological crutches that we physicists routinely adopt without apology, is just pop sci, might seem insulting to well-known physics pedagogs like John Baez. Consider what he has to say about virtual particles:http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html. Is he saying they are really real? Of course not, no physicist ever needs to say that about anything but the outcomes of measurements. Is he saying they have as good a claim to existence as any of the many other ontological elements that are invented to help us understand the observable phenomena we encounter? Yes, I think he is saying that, but only in the usual "virtual", ephemeral, or too-short-lived-to-call-real sense of existence. So they are ephemeral, or they are just terms in an expansion, what difference does it make? Why is it so important to reject them as fantasy? Pedagogy is more of an art than anything else in physics. This doesn't make anyone wrong about virtual particles, it makes the issue quite nebulous, and perhaps that's what it is supposed to be when we are at the edges of what we can really describe.

 

[FrediFizzx]

Hmm... nobody here even mentioned that in particle physics "virtual" has a very specific meaning for particles. It simply means "off mass shell". It is a real particle that doesn't obey the Einstein relation. However, they are only indirectly detectable.
Fred Diether

 

[Ken G]

That was my impression also, that in the spirit of a Feynman path integral, virtual means contributions from processes that cannot persist "at the end of the day", but can contribute to the amplitudes on short times, essentially timescales over which the interference emerges. So if something contributes to what actually happens, then it is "kind of" a real contribution, but not quite as real as what actually happens, ergo "virtual." I get that many other people just see it as labeling terms in approximate expansions, but I would say this just comes down to language, and whether or not one wants to use language that makes the Feynman path integral (or whatever correlation function calculation is needed) sound like it is "really happening", or if it is just some kind of calculation that has no direct correspondence to what is really happening. I'm not sure that issue can be adjudicated, it seems like "tomato tomahto" to me, but perhaps the field theorists have a stronger view about the evils of virtual particle language.

 

[Vanadium 50]

Pedagogy is more of an art than anything else in physics.

There is very little to be gained with a model that allows people to learn wrong things quickly.

Two points:

• Any problem that can be solved using virtual particles can be solved some other way.
• There are problems that cannot be solved by the virtual particle paradigm that can be solved some other way.

These are facts, and because of these facts, it is difficult to ascribe some sort of independent reality to virtual particles. In many ways, they are a lot like the Method of Images in E&M.

Unfortunately, writers of popularizations either do not know or gloss over this, and people get the idea that these are real entities, with measurable quantities like velocity and mass.

 

[chaszz]

There is a good deal of ontological talk going on here. What about the Casimir effect, supported by a relatively simple experiment, which offers evidence that virtual particles really exist in a demonstrable way?

 

[Vanadium 50]

No, it doesn't. Read the threads that JT Bell posted.

And you see the problem? People who have read some popularizations think they know things that simply are not true.

 

[chaszz]

"No, it doesn't. Read the threads that JT Bell posted.

"And you see the problem? People who have read some popularizations think they know things that simply are not true."

With all respect, I have read those threads and do not see what you are talking about. Is it possible you could avoid bidding me to look through scores (or hundreds) of replies and simply address the issue of the Casimir effect directly here?

 

[jtbell]

See the following post, which references a paper that calculates the Casimir effect without using virtual particles:

https://www.physicsforums.com/showthread.php?p=3370377#post3370377

(I've just added this thread to the list in my earlier post. It wasn't there when you looked at the post earlier, and I'm not trying to make you look stupid for not having seen it before. I found it by doing a Google search for "casimir effect virtual particles site:physicsforums.com".)

 

[FrediFizzx]

Well, I would like to see how Vanadium 50 would model decay of pions and muons without virtual W bosons. The Casimir effect is actually still a bit contraversial.

Fred

 

[Ken G]

Two points:

• Any problem that can be solved using virtual particles can be solved some other way.
• There are problems that cannot be solved by the virtual particle paradigm that can be solved some other way.

I don't dispute these statements, I'm just wondering about the body of ways that virtual particles get invoked. When people ask how a particle theory of gravity could allow a black hole to influence its surroundings, I've heard mention that a particle theory of gravity would use virtual gravitons to mediate the gravitational force, and virtual particles would not be barred from leaving the black hole (akin to John Baez's use of them in the link I gave above). It's also common to state that mundane electrostatic forces are "mediated by virtual photons", though this is such an everyday application that you probably have a pretty good reason for not thinking that way. It would be useful to hear though. I've also seen a certain value in imagining that other mundane processes are mediated by virtual particles-- such as spontaneous emission of light from an atom. That process acts just like the spontaneous emission is stimulated by the photon that ends up being emitted, and if one adopts a kind of "it takes a quantum to make a quantum" approach, there's some value in imagining that the energy of the transition "promotes a virtual particle to real status" when spontaneous emission occurs. So we're not necessarily just talking about Hawking radiation or the Casimir effect, we have neon lights and static electricity invoking virtual particles sometimes. I don't claim we need virtual particles for these, but do you really see such potential for misconception that the virtual particle picture is not useful in these applications?

 

[Polyrhythmic]

Has anybody of you promoting the existence of virtual particles every seriously studied quantum field theory (no, that doesn't mean you've read the Wikipedia article on virtual particles)? Because if you did, you wouldn't have that opinion. Vanadium and jtbell are right and this has been discussed to death.

 

[Ken G]

Has anybody of you promoting the existence of virtual particles every seriously studied quantum field theory (no, that doesn't mean you've read the Wikipedia article on virtual particles)? Because if you did, you wouldn't have that opinion. Vanadium and jtbell are right and this has been discussed to death.

That's all a very nice stance and everything, but here's the problem-- it isn't true. Those who haven't studied QFT wouldn't have the vaguest idea what a virtual particle was if the concept hadn't come to them from those who did (look at, for example, the John Baez link I cited above). Furthermore, we all know that virtual particles are a kind of picture that gets used to communicate the theory, but that's just exactly what ontology is in physics, the same could be said about "particles", "fields", etc. This is nothing new in physics-- we create pictures to help us motivate the mathematics of our theories. Thus, if your sole argument is going to be "virtual particles are just pictures invoked to help motivate the calculation", my response would be "what else is new?" The actual way to defeat a pedagogy is to replace it with something better.

 

[chaszz]

That's all a very nice stance and everything, but here's the problem-- it isn't true. Those who haven't studied QFT wouldn't have the vaguest idea what a virtual particle was if the concept hadn't come to them from those who did (look at, for example, the John Baez link I cited above). Furthermore, we all know that virtual particles are a kind of picture that gets used to communicate the theory, but that's just exactly what ontology is in physics, the same could be said about "particles", "fields", etc. This is nothing new in physics-- we create pictures to help us motivate the mathematics of our theories. Thus, if your sole argument is going to be "virtual particles are just pictures invoked to help motivate the calculation", my response would be "what else is new?" The actual way to defeat a pedagogy is to replace it with something better.

The nature of reality, and of the relationship between the models we make to describe reality and whatever reality itself is, is not an easy topic, to be airily summarized as if it were a settled issue rather than a partly philosophical (therefore unsolved) one. Einstein for one disagreed with many of his peers on issues connected with this. I would suggest also that some scientists create pictures to help the unwashed non-math people who fund their work have some far-removed idea of what they are doing. As one of the unwashed whose considerable income taxes over a long lifetime have helped fund physics, I take a certain measured exception to the sneers and scorn which often greet us unwashed on this forum ("Have you read the scores of reams of sticky posts in which your primitive concern may somewhere be addressed in mathematical language which you cannot understand, or not? If not ((sniff)) please do not post"). As an artist (http://charleszigmund.com) I am generally gentle with unwashed art lovers who do not understand my painting or sculpture or art in general. I try not to treat them with scorn. If you experts do not want us here, say so outright, with respect not sneers, and perhaps devise a test which forum members must pass before posting. If not, please treat those of us who make your livings (at least the pros among you) possible with some respect and not scorn.

 

[Ken G]

I would suggest also that some scientists create pictures to help the unwashed non-math people who fund their work have some far-removed idea of what they are doing.

Right, and the issue for me is, some people talk as if there was a clear line between "pictures that physicists take seriously as part of their theories" versus "pictures that are purely for the consumption of the unwashed." Distinctions like that can be made, but there really is no such line, it's a very murky continuum there (and is not even agreed on by experts). I'd say this is an important element of our "art" to recognize-- the mathematics are fairly straightforward, but the ways of picturing them and interpreting them vary a lot from person to person, even from expert to expert. If we talk to experts, I'll bet we could find some who take both particles and fields literally, some who think particles are real but fields are just placeholders for interactions between particles, some who think fields are real but particles are just placeholders for interactions between fields, and some who think neither particles nor fields should be taken seriously, it's something more fundamental and abstract that lies underneath both those topics (and they think they know what is the "fundamental" underlier there). I understand that many field theory experts are tired of the misconceptions they see around the virtual particle concept, I'm not taking anything away from that, all I'm asking for is recognition of the complexity of this issue-- it's an amazing thing about physics that it has this quality, even though some seem so bothered by this aspect they would rather believe it isn't there.

 

[FrediFizzx]

Well, I would like to see how *anyone* here disputing that virtual particles aren't real would model decay of charged pions and muons without virtual W bosons. This is the Standard Model of particle physics, folks. Well established even by the LHC now.

Fred

 

[alxm]

Well, I would like to see how *anyone* here disputing that virtual particles aren't real would model decay of charged pions and muons without virtual W bosons.

I think you're either missing the point or trying to cloud the issue here.

Nobody's disputing that perturbative quantum field theories work. The point (which has been repeated ad nauseum in the many threads on the topic) is that the fact that they work does not in-itself justify interpreting the terms of a perturbation series as an objective description of the real physical processes involved (which itself already assumes a particular ontological position).

That's without precedent. I mean, refer to introductory QM and what PT actually is: A mathematical approximation method, where you describe some mathematically-intractable 'perturbed' system in terms of the states of an 'unperturbed' one that you have the solutions for. Let's say it's the ground state you're after. Well, by the variational theorem, it's obvious that the excited states of your unperturbed system will contribute to the description of the perturbed ground state. But doesn't mean it's physically meaningful to say that the interaction represented by whatever-term-you-neglected is caused (or 'mediated') by these 'virtual excitations'. And in most cases, such as with MBPT for electronic systems, nobody talks about those things as if they were anything other than an artifact of your starting point of working from an approximate basis.

To apply the argument to a common textbook example, you might calculate Helium's electronic ground state by taking hydrogen wave functions as my basis (thus, neglecting the electron-electron interaction) and proceed with a PT or variational calculation, summing contributions from 'virtual' excitations. That works to get the correct result. But if you interpreted that as being a physical description of how the e-e interaction worked ("Electrons in atoms interact through virtual hydrogenic states"?) rather than a feature of a mathematical description, people would say you're crazy. Asserting that you get the correct result as 'proof', would not convince many. Which of course doesn't mean you can't talk about these things, or use it as a visual or diagrammatic representation and so forth. (bear in mind that Feynman-and-related diagrams are equally applicable to other contexts where PT is used, yet where this interpretation of them is absent).

I don't why this should suddenly become a valid interpretation when the same general method is applied to quantum field theory.

 

[Polyrhythmic]

Well, I would like to see how *anyone* here disputing that virtual particles aren't real would model decay of charged pions and muons without virtual W bosons. This is the Standard Model of particle physics, folks. Well established even by the LHC now.

The existence of W bosons is well established, that's true. Not the existence of virtual W bosons though, because there is nothing to establish. Decay is modeled in terms scattering states. You have incoming states, you have outcoming states. You can calculate those matrix elements in terms of a perturbation series, which gives a certain result. You don't need the interpretation of virtual particles for anything. Any physical quantity in quantum field theory can be calculated without the need to invoke the reality of virtual particles.

 

[Polyrhythmic]

Right, and the issue for me is, some people talk as if there was a clear line between "pictures that physicists take seriously as part of their theories" versus "pictures that are purely for the consumption of the unwashed." Distinctions like that can be made, but there really is no such line, it's a very murky continuum there (and is not even agreed on by experts). I'd say this is an important element of our "art" to recognize-- the mathematics are fairly straightforward, but the ways of picturing them and interpreting them vary a lot from person to person, even from expert to expert. If we talk to experts, I'll bet we could find some who take both particles and fields literally, some who think particles are real but fields are just placeholders for interactions between particles, some who think fields are real but particles are just placeholders for interactions between fields, and some who think neither particles nor fields should be taken seriously, it's something more fundamental and abstract that lies underneath both those topics (and they think they know what is the "fundamental" underlier there). I understand that many field theory experts are tired of the misconceptions they see around the virtual particle concept, I'm not taking anything away from that, all I'm asking for is recognition of the complexity of this issue-- it's an amazing thing about physics that it has this quality, even though some seem so bothered by this aspect they would rather believe it isn't there.

The issue with virtual particles is different from other interpretational matters, like the nature of fields, or the wavefunction in quantum mechanics. Let's take the wavefunction: it is in one way or another a mathematical fundamental quantity of quantum theory, it is needed to calculate certain measurable observables. Since it is a fundamental object at the core of the theory, a possible physical interpretation beyond its mathematical nature is justified. As such, there can be opinions, there can be different points of view. This is not the case for virtual particles: they are neither needed for calculations nor are they fundamental in any way. The only reason that they around is the fact that Feynman diagrams can be used to visualize terms in a perturbation series. (Note that this visualization doesn't change anything about the outcome, the concept of the virtual particle has no influence on anything.)

Imagine this:

We have a natural logarithm acting on an exponential function:
ln(e^{x})=x.
Now I describe this mathematical operation in terms of a monkey eating a banana: I choose to visualize the logarithm acting on the exponential function as a monkey eating a banana. It's a perfectly valid picture, if it helps us memorize this fundamental relation between ln and exp. But does that mean that if I have such an operation in a physical calculation, an actual monkey eating a banana in real life contributes to the result of the calculation? I don't think so.

 

[FrediFizzx]

The existence of W bosons is well established, that's true. Not the existence of virtual W bosons though, because there is nothing to establish. Decay is modeled in terms scattering states. You have incoming states, you have outcoming states. You can calculate those matrix elements in terms of a perturbation series, which gives a certain result. You don't need the interpretation of virtual particles for anything. Any physical quantity in quantum field theory can be calculated without the need to invoke the reality of virtual particles.

If that is true, then there should be an online reference you could post for the decay of a muon to an electron and neutrinos. Let's go for the muon lifetime. The calculations I have seen all use the mass of the W boson. Well, unless you want to go back to Fermi's original theory of beta decay. :-)

Fred