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How can two particles be drawn together by exchanging other (force carrier) particles. Both reactive components of exchange and absorption logically seem to support repulsion. How are these particle exchanges responsible for attraction of the exchanging parent particles? Unable to find an online answer after considerable effort. Help

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Unable to find an online answer after considerable effort.

The reason is that this is a strictly quantum-mechanical feature, and satisfactory glib pictorial metaphors for QM are really hard to make. R P Feynman has written a popular book about it, and he was a stickler against misinterpretation of his (eponymous) "Funny diagrams", as he'd mordantly refer to obnoxious abuses of them: so there are no bad metaphors in that book.

Now, you may extract an attractive or repulsive force between two suitably charged particles exchanging a virtual photon, for instance, through a QM perturbative calculation, whose covariant expression is symbolically summarized by a Feynman diagram. That's all it is: a mnemonic for calculating technical QM amplitudes. It strictly conserves momentum and energy along its lines and at the interaction points, except the virtual particle has a counterintuitive ("unphysical") mass, attributable to the properties of intermediate states in QM.

But many, including professionals, picture this as a spacetime diagram, so, simultaneously in coordinate space and with well-defined momenta, which you know QM will take its revenge on you if you don't know when to blink and shrug. Specifically, for example, they often think of, without acknowledging it, two canoes on a lake converging, when a canoe throws a ball at the other one, shedding momentum in it, and reversing its momentum direction, the ball captured by the other canoe and reversing its direction of motion. The two canoes have exchanged their momenta.

This is clearly a repulsive force interaction, the source of your picture:

Both reactive components of exchange and absorption logically seem to support repulsion.

But this picture looks like science fiction when the virtual particle (the ball) actually transfers momentum opposite to what you thought was its direction of motion. This is what you cannot picture. How two canoes drift apart, and one canoe throws a ball to the other, which sucks its momentum and makes it change direction, and the ball hits the other canoe sucking off the same amount of transferred momentum to it, changing its direction. So the two canoes originally diverging, exchange momenta and now converge, a net attractive interaction.

The math has no trouble with it. The Feynman diagram mnemonics conserve momentum and energy at every step, and all is fine, but super-certain momenta imply undefined positions, so you might as well think of the ball hitting the other canoe from the opposite direction from where you imagined it came from. Pros are trained to avoid such mind-bending fantasies and shrug, but popular science has spread enough logical damage around that needs deconstruction. Feynman used to be furious at the nonsense vulgarizing he felt made responsible to undo.

So, the takeaway is that there is no good metaphor for virtual particle exchange; it is a "Twin Peaks" dream, and it might, or might not, give you a meaningful impression. To make its dysfunction even more apparent, the sign of the force depends on the relative signs of the "charges", labels of each canoe, so a feature of the ball coupling to the canoe. But how do you convince people to not think about a blue elephant on a cliff?

So there is no good answer to your question within the terms it was posed, which is why you couldn't find one online.

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  • $\begingroup$ Cosmas Insightful well presented answer to a widely popular question that fits a category of questions, of which there are many. I got a million of em! Thanks for your time. $\endgroup$ – RaSullivan Aug 8 '20 at 22:49

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