danR said:
Now it's over my head. The way Randall puts it sounds similar to Asimov's popular description 40 years ago, and ran something like: virtual particles shouldn't exist because they are contrary to the laws of physics, but because of Heisenberg, they can get away with breaking the law because they are so short-lived no one is around soon enough to enforce it.
But that's no evidence they do exist. I find it odd that two physics heavyweights find them parsimonious enough to let them live, though the SA (2006) argument sounds deplorably pop-sciencey, something like: 'Well, the Casimir effect shows they exist.'
Here's another layperson-way of weighting the evidence: do the proponents depend on internally consistent, well accepted, standard theories for VP's 'reality' (loosely defined)? How similar is their definition of 'real' space that virtual particles inhabit to that of educated average people's realist views of space? Or is it a momentum-space that is so familiar to physicists that it seems real enough, like mathematician's imaginary number 'i' is to mathematicians? (This was an educated argument against acceptance, in lay terms, of the 'proof' of Fermat's last theorem.)
Do critics depend on the gratuitousness of VP by cherry-picking theories that specifically invoke alternative mechanisms, which theories contradict each other, or mainstream theories? Or are less parsimonious than the offending VP themselves? That's not something I would be able to figure out.
Naturally, scientists aren't required to satisfy public understanding of esoteric things, however. In my own area, there is something called 'Optimality Theory' that has gained wide acceptance for explaining the abstract representations of sound in the mind, but it is hopelessly hard to explain. Students spend the first few weeks scratching their heads over it.
I have a course starting soon, and can't do much more on PF for a while, regrettably.
Well first of all Isaac Asimov certainly was not a "heavy-weight" of physics, he wasn't even a physicist. He was a bio-chemist and a science fiction writer. Also, virtual particles are not needed to explain the Casimir effect. Essentially the issue is something like this. Imagine the function
e^x
the exponential of x, it'll be on any scientific calculator you can just pick various values of x to see what its value is. Now what if I told you that for any value of x the following will give exactly the same answer:
1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \frac{x^4}{24} + \ldots
where the ellipsis means you keep adding terms, to make things easier only consider values of x that are less than 1, then a number less than 1 raised to some power becomes an even smaller number. Thus we see that each of these terms (the next would be
\frac{x^5}{120}
then
\frac{x^6}{720}
and so on) is going to be a smaller number (try it on a calculator if you like, try something like 0.3 so you'd type in exp(0.3) and get the answer and then you try the infinite sum and you'd get
1 + 0.3 + \frac{0.3^2}{2} + \frac{0.3^3}{6} + \ldots
and you'll see as you add more and more terms you'll get closer and closer to the answer exp(0.3) gave. This is called a TAYLOR SERIES or TAYLOR APPROXIMATION. If you actually include and infinite number of terms (i.e. x^5,x^6,x^7,x^8,\ldots) it is EXACTLY e^x. However, if you only care about, say only the first 5 decimal points, then you can get away with only having to calculate a dozen or so terms, the terms after that are so small they only effect decimal positions further away.
This is basically the situation, no dumbing down, we have an equation like
e^x
and we want to do something to it (what's called a functional integral) but we can't. We don't know how. However, we CAN do it to each of the terms in the series form:
1 + x + \frac{x^2}{2} + \ldots
and the more terms we do it to the more accurate we are (obviously we could never ACTUALLY sum all the infinite terms). Now, imagine the math of x looked kinda but not really like the math of a particle moving in a vacuum and the math of \frac{x^2}{2} looked kinda but not really like that of two particles moving with opposite momentum or some such and so it goes for the next term and the next term.
Now, saying that virtual particcles are "real" is basically saying that these terms represent real-life goings on of magical new particles. The thing is, if we could just integrate e^x in the first place then there'd be nothing to debate and we'd never have even heard of the concept of virtual particles much less insist that they're part of reality. However, since we CAN'T write down the answer to that guy and have to move to an approximation scheme than, allegedly, the very nature of reality magically changes. Now, let me ask you Does it make sense to say that reality changes because your math skills aren't good enough to get the direct answer you want so you're forced to move to approximations? I would say no. Virtual particles are a calculational tool, not reality, they're a way we can mathematically get the answer we want to arbitrary accuracy, they're not new physics.
… you can't just string words together, you need to be able to insert the idea into a theory
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