How does emergent spacetime work?

[PeterDonis]

I'm still a bit confused as to whether the particle/anti-particle pairs are just a myth or they really do exist, even if it's just for a fraction of a second.

And the answer to this is, neither. Virtual particles are a name for a particular mathematical feature of a particular mathematical approximation used in quantum field theory. (The simplest way I know of to point at this feature is to say that virtual particles are internal lines in Feynman diagrams.) So virtual particles are not a myth, because the mathematical approximation I refer to is really used and can make real predictions that match experiments. But virtual particles don't "really exist" either, because they can never be observed directly (that's what internal in "internal lines in Feynman diagrams" means) and the mathematical feature is part of a specific approximation scheme which is not the only mathematical way to do quantum field theory. So the question you are asking is really the wrong question; you should not even be thinking in terms of whether virtual particles "exist" or not.

virtual particles (if they exist) have positive and negative energy

While there is a sense in which this can be said to be the case, it is open to the same objections that I gave above to asking the general question of whether virtual particles "exist" or not.

Does that mean the virtual anti-particle has negative mass (Eg. -1 kg)?

Not in any useful sense.

 

[phinds]

This has nothing whatever to do with virtual particles or the (highly heuristic and often misleading) viewpoint in which some virtual particles have negative energy. Please don't confuse the OP any further.

He asked for a link to negative energy. I gave him one.

 

[PeterDonis]

He asked for a link to negative energy.

He asked for a link about negative mass in relation to virtual particles. That's not what you gave him. The concept of "negative mass" described in the link you gave has nothing whatever to do with virtual particles and is not the same concept as the concept of "virtual particles having negative energy" that was referred to in the Carlip article the OP linked to when he asked about negative mass. As I said, please don't confuse the OP further.

 

[valenumr]

And the answer to this is, neither. Virtual particles are a name for a particular mathematical feature of a particular mathematical approximation used in quantum field theory. (The simplest way I know of to point at this feature is to say that virtual particles are internal lines in Feynman diagrams.) So virtual particles are not a myth, because the mathematical approximation I refer to is really used and can make real predictions that match experiments. But virtual particles don't "really exist" either, because they can never be observed directly (that's what internal in "internal lines in Feynman diagrams" means) and the mathematical feature is part of a specific approximation scheme which is not the only mathematical way to do quantum field theory. So the question you are asking is really the wrong question; you should not even be thinking in terms of whether virtual particles "exist" or not.
While there is a sense in which this can be said to be the case, it is open to the same objections that I gave above to asking the general question of whether virtual particles "exist" or not.
Not in any useful sense.

I like to think of imaginary numbers as an analogy. I've never had 3i apples, but the concept is incredibly useful mathematically. Heck, even negative numbers were considered absurd until people started lending money. ..

 

[PeterDonis]

I've never had 3i apples, but the concept is incredibly useful mathematically. Heck, even negative numbers were considered absurd until people started lending money. ..

In other words, what kinds of numbers are going to be useful depends on the particular application. Yes, that's true.

In the particular application under discussion in this thread, namely General Relativity, negative numbers for mass has a very specific physical meaning, which does not apply to virtual particles.