# Transition of Electric Charge In Collision Between Proton And Antiproton

I know that

$$p+\bar{p}\to 4\pi^++4\pi^-+(\gamma)$$

Before the collision, the sum of absolute electric charge value is $2$.

$$\left | +1 \right |+\left | -1 \right |=2$$

After the collision, the $p$ collapses to $4\pi^+$, and $\bar{p}$ collapses to $4\pi^-$.

After that, $4\pi^+$ collapse to $4\mu^++(\nu)$, and $4\pi^-$ collapse to $4\mu^-+(\bar{\nu})$.

$$\pi^+\to\mu^++\nu$$ $$\pi^-\to\mu^-+\bar{\nu}$$

And then, $4\mu^+$ collapse to $4e^++(\nu+\bar\nu)$, and $4\mu^-$ collapse to $4e^-+(\nu+\bar\nu)$

$$\mu^+\to e^++(\nu+\bar\nu)$$ $$\mu^-\to e^-+(\nu+\bar\nu)$$

The result is

$$p+\bar{p}\to 4\pi^++4\pi^-+(\gamma)\to 4\mu^++4\mu^-+(\gamma) \to 4e^++4e^-+(\gamma)$$

In this situation, the sum of absolute electric charge value is $8$.

$$\left | +4 \right |+\left | -4 \right |=8$$

Question. How could it possible that the sum of absolute electric charge value has increased?

Added. 'So, what's the significance?'

Electric force bwtween $p$ and $e^-$

$$F=k\frac{e^2}{r^2}$$

Electric force bwtween $4e^+$ and $e^-$

$$\sum_{n=1}^{4} k\frac{e^2}{(r_{n})^2}$$

$p$'s electric charge is +1, but after this collision, $p$ collapses to $4e^+$, it means the total electric charge has increased $+1$ to $+4$.

• I didn't downvote, but I'll offer my opinion. I think that even with the "Added" part, the question's very unclear. You're asking why the total absolute value of charge fails to be conserved, but I don't really know why you'd expect it to be conserved in the first place! Commented Jul 21, 2011 at 17:39
• Like Ted Bunn, I don't feel that the "Added" part clarified anything. The electrical force would actually be a vector sum, not a sum of magnitudes like $|F_1|+|F_2|+\ldots$, and in any case, it doesn't seem to connect to your statement that "the total electric charge has increased +1 to +4." There is no family tree of relationships between the initial particles and the final particles. It's not as though the p is the father of the four e+'s.
– user4552
Commented Jul 21, 2011 at 22:35
• @ks0830: I assume you're talking about me, but what would make you think that I downvoted your question? (For what it's worth, I don't think it's a good question for the same reason Ted mentioned. You haven't explained why you would expect the absolute value of charge to be conserved.) Commented Jul 22, 2011 at 5:36

## 1 Answer

It's certainly possible to have an absolute electric charge value that increases, as long as total charge still sums up to 0. After all - this is why virtual particles (which consist of a pair of positive/negative charges) can be created

Is there any physical significance to the absolute electric charge value? Also - I'm just curious - where did you get the reaction equation from?

• What book though? Commented Jul 21, 2011 at 4:12
• Hm, what's the chapter/page number? I have a hard time believing that the book would ask a paticle physics question like this (but I haven't looked at the book too closely yet) Commented Jul 21, 2011 at 4:47
• @kso830 sit tight, because this is actually the right answer; also, absolute charge does not have any physical meaning, and more importantly, it is experimentally known to not be conserved, precisely by the mechanism that InquilineKea tried to explain to you Commented Jul 21, 2011 at 16:10