Is there a limit to the precision of a photon's target?

[md65536]

Suppose you fire a photon from some ideal source to a target point on a flat surface 1 m away.

Suppose that the smallest distance from the target that you can theoretically hit, with probability P, is epsilon.

 

Is P < 1 for any finite epsilon? Is there a remote chance of missing a target no matter how big it is?

 

Is epsilon related to the Planck length?

Is it related to the photon's wavelength?

 

If the target were moved to say 10^100 m away, would epsilon be scaled by a factor of 10^100?

[Xittenn]

 

"Normally, light cannot be focused to a spot smaller than half its wavelength – something known as the diffraction limit. However, in recent years, scientists have succeeded in compressing light down to the nanoscale by coupling it to the electrons that oscillate collectively at the surface of metals – called surface plasmons. The resulting excitations of light and electrons are known as "surface plasmon polaritons" or SPPs.

 

- Belle Dumé

 

 

"Plasmonic Laser Puts the Squeeze on Light"

 

Bachor, H. A. "Manipulating The Quantum Properties Of Continuous Laser Beams." Applied Physics B: Lasers & Optics 81.7 (2005): 889-896. Academic Search Premier. Web.

 

Nicolas Treps, et al. "Teaching A Laser Beam To Go Straight." Contemporary Physics 46.6 (2005): 395-405. Academic Search Premier. Web.

 

Is there a remote chance of missing a target no matter how big it is?

 

As far as I understand this is a fundamental property of quantum mechanics. Why are you relating precision to the Plank length?

 

http://en.wikipedia.org/wiki/Transverse_mode#Laser_modes

 

http://arxiv.org/pdf/1105.5970v1.pdf

 

That last step it's a doozy!

Edited March 8, 2012 by Xittenn

[md65536]

As far as I understand this is a fundamental property of quantum mechanics. Why are you relating precision to the Plank length?

 

Thanks for the links. Actually I don't know what my point was.

http://en.wikipedia.org/wiki/Beam_divergence says that all beams diverge, proportional to wavelength and inversely proportional to smallest beam diameter. I'd mistakenly thought a narrower beam (with a waist limited by Planck length?) could be aimed more precisely.

 

My poor understanding of QM is the same. Even for an extremely large very close target, the photon could miss, meaning it would essentially shoot out perpendicularly to the beam, if the photon is moving in the general direction of the target at all. I would assume then that there's also a tiny chance that the photon would travel backward away from the target.

 

Actually these questions come from thinking about "what the universe would look like to a beam of light", which I know is not really a valid question because light doesn't "see" or experience anything. But if all beams diverge, and there is the possibility of a photon going anywhere, then from the source it's not possible to know for certain which way a single photon will go. The single photon, travelling as a wave, also diverges. In a sense it might be thought of as travelling in all directions at once. A'ight now I've fully digressed into "Speculations" territory, but I was looking for a rationale for the idea that the universe isn't squashed in one direction to light, but all directions. I don't think that the universe is squashed into a plane according to light, but into a point.

 

Anyway... if a laser's divergence could be minimized with a large enough beam "waist" and a small enough wavelength, then the beam could be aimed precisely on a small and distant target, but the individual photons could still go anywhere, I guess with decreasing probability with increasing precision.

 

 

[elfmotat]

[questionposter]

I think the more energy a photon has, the more localized it is, and since there's no limit to how much energy a photon can have, there is no limit to how localized it can be.

From there on, the question is whether you can control it, because even with that video, photons can be so localized that their 3 dimensional probability function only spans over 1 nano meter, so you can have some pretty precise results. The laser that guy is using looks very low energy, and low energy photons are much less localized so it is easier for them to span out over large distances. You wouldn't see the same thing with gamma-rays.

Edited March 21, 2012 by questionposter