Spacelike particle propogation

[jamievicary@gmail.com]

Dear all,

In conventional quantum field theory, particles have an
exponentially decaying, but nonzero, amplitude for spacelike
propogation. (Peskin & Schroeder derives, in the section named
"Causality" in chapter 2, that D(x,y) = <0|phi(x)phi(y)|0> is
proportional to exp(-mr) for x, y spacelike separated by r.)

Have any experiments been done to test this? It would be simple: a
laser flashes a brief pulse (event 1), and an opaque barrier between
the laser and a radiation detector briefly flickers open (event 2),
such that events 1 and 2 are spacelike separated. High-frequency pulsed
lasers could repeat this at a very high frequency, and the intensity
reaching the radiation detector monitored. (Presumably the relevant
expression for the propogation amplitude here would be exp(-Er/c^2).)

What is the status of this phenomenon? Is it physical? Has it been
experimentally detected? Is it as interesting as it seems?

Thanks,

Jamie Vicary.

[Oh No]

Thus spake jamievicary@gmail.com
>Dear all,
>
> In conventional quantum field theory, particles have an
>exponentially decaying, but nonzero, amplitude for spacelike
>propogation. (Peskin & Schroeder derives, in the section named
>"Causality" in chapter 2, that D(x,y) = <0|phi(x)phi(y)|0> is
>proportional to exp(-mr) for x, y spacelike separated by r.)
>
> Have any experiments been done to test this? It would be simple: a
>laser flashes a brief pulse (event 1), and an opaque barrier between
>the laser and a radiation detector briefly flickers open (event 2),
>such that events 1 and 2 are spacelike separated. High-frequency pulsed
>lasers could repeat this at a very high frequency, and the intensity
>reaching the radiation detector monitored. (Presumably the relevant
>expression for the propogation amplitude here would be exp(-Er/c^2).)
>
> What is the status of this phenomenon? Is it physical? Has it been
>experimentally detected? Is it as interesting as it seems?
>

You have only a grasped part of the argument. The process of a particle
created at x and annihilated at y is indistinguishable from that of an
antiparticle created at y and annihilated at x. When both amplitudes are
combined the complete process does have a zero amplitude for space-like
separations. The point is that it is impossible to keep these processes
out of the mathematical model event though they are unobservable.

Regards

--
Charles Francis
substitute charles for NotI to email

[Eugene Stefanovich]

jamievicary@gmail.com wrote:
> Dear all,
>
> In conventional quantum field theory, particles have an
> exponentially decaying, but nonzero, amplitude for spacelike
> propogation. (Peskin & Schroeder derives, in the section named
> "Causality" in chapter 2, that D(x,y) = <0|phi(x)phi(y)|0> is
> proportional to exp(-mr) for x, y spacelike separated by r.)
>
> Have any experiments been done to test this? It would be simple: a
> laser flashes a brief pulse (event 1), and an opaque barrier between
> the laser and a radiation detector briefly flickers open (event 2),
> such that events 1 and 2 are spacelike separated. High-frequency pulsed
> lasers could repeat this at a very high frequency, and the intensity
> reaching the radiation detector monitored. (Presumably the relevant
> expression for the propogation amplitude here would be exp(-Er/c^2).)
>
> What is the status of this phenomenon? Is it physical? Has it been
> experimentally detected? Is it as interesting as it seems?
>

This effect has been discussed a lot, usually under the name
"superluminal spreading" or "instantaneous spreading".
See, for example,

G. C. Hegerfeldt, Instantaneous spreading
and Einstein causality in quantum theory, Ann. Phys. (Leipzig) 7
(1998), 716; quant-ph/9809030

In terms of experiment, there is probably no chance to observe this
effect, because it is very small. For example, in the paper

Ruijsenaars, S.N.M. "On Newton-Wigner localization and superluminal
propagation speeds" Ann. Phys. 137 (1981), 33

it is estimated that the probability of finding the electron
at spacelike separation is something like 10^{-100000000}.

Nevertheless, some people claim that "instantaneous spreading"
immediately disqualifies any relativistic quantum theory of particles.
In their opinion, only quantum field theories are good. See for example

Halvorson, H.; Clifton, R., No place for particles in relativistic
quantum theories? quant-ph/0103041

Eugene.