Really, Truly, Virtually
And as imagination bodies forth
The forms of things unknown, the poet’s pen
Turns them to shapes and gives to airy nothing
A local habitation and a name.
Such tricks hath strong imagination,
That if it would but apprehend some joy,
It comprehends some bringer of that joy.
Or in the night, imagining some fear,
How easy is a bush supposed a bear!...................Midsummer Night's Dream, Act V, Scene 1
Sometimes the pen belongs to a physicist or a mathematician.
Are virtual particles real? Are imaginary numbers real? How about negative numbers?
As usual, it all depends on what we mean by real. Not many mathematicians, physicists, or engineers would quarrel with the reality of imaginary numbers, but most of us would admit, I think, that the natural numbers are a bit more "real" than all those other numbers, including the Real Numbers.
The world is constructed of such figments of our imagination, and close analysis shows that some of the most dependable realities of our world, like money, corporations, nations, and races are essentially mythical constructs that exist only because people believe they do.
In math and physics, the criterion for belief is, or ought to be, some combination of beauty, explanatory value and usefulness. The complex numbers are useful because they explain and simplify many things that would otherwise be more complicated and puzzling.
The same thing, I think, applies to virtual particles, though I'm happy to put them a bit lower on the reality hierarchy than imaginary numbers. One gift of quantum theory to thought is the idea that it might well take more than one model to comprehend reality, and our deeply intuitive notions of space, time, and reality don't fully coincide with our best understanding of how the world works. In quantum mechanics, metaphorically speaking, we don't really know whether it's a bush or a bear until it roars (or is otherwise measured).
I once had an argument with a semi-famous philosopher as to whether a table was more real than an electron. My point was that each was a theoretical construct that was convenient and explained a lot. He wasn't convinced.