From a point source of photons – perhaps gamma rays constantly smacking into something at a point and generating radiation – we can think of an expanding sphere of photons radiating uniformly away from the point being smacked. One way I visualize this is as a cork ball (the point source) with needles (each needle representing the path of a radiated photon) poking out from the ball in all directions. Sort of a perfectly spherical hedgehog.
Now, as one’s distance from the point source increases the perception is that the light – the portion of the sphere of photons we can see – gets dimmer. I assume this is because the density (number of photons per square meter) of photons has decreased with increased distance from the point. So far it seems to make sense.
But…if the density continues to decrease there must be a point or points where there are only, say, 42 or some other finite number, of photons in our square meter. Therefore, by judiciously moving our eyes or detector from side to side we’d find a spot where no photon will be detected (we’ve bound a spot “between needles”). My gut tells me that this is bushwa; we’d see a ray of light no matter how we wriggle. But this in turn suggests an infinite number of photons (needles) coming out of our point. I don’t see a way to resolve these two possibilities.
Yea, the number of photons/sec hitting a square meter is always somewhat probabilistic. For large number of photons, this variation is small compared to the number of photons and you can ignore it, and the number of photons seems to simply fall off with the square of the distance from the source.
Eventually, though, the average to the point where during many seconds, your seeing zero photons. So as you continue to move away from the source, the net result is that the number of photons per sec. drops. The total number per square meter integrated over time is still dropping with the square of the distance, but the instantaneous number of photons varies.
Think of it this way - the photon sphere will expand in a wave-like manner - as a sphere, but when it hits an object, it will contact it at a finite number of points - i.e. photons move like waves but impact like particles
So if you had a point source, only a finite number of photons would be observed when they interacted with something over a set amount of time
Your gut is wrong. Fewer photons is what “dimmer” actually means. Where I think you’re going wrong here is only thinking of a static situation with fixed photons. That’s the only way you can realistically place yourself “between needles”. In reality there’s a constant stream of photons with completely random directions.
If you want to really boggle your mind, if I don’t recall the numbers wrong, the speed of light, the size of a normal room and the number of photons emitted by a regular light bulb add up to no more than a single photon from the bulb being in a room at any particular instance.
Your numbers are off. A source emitting only one watt of visible light energy is emitting a photon approximately once every 10[sup]-20[/sup] seconds. Light is fast, but it only travels about 10[sup]-11[/sup] meters in that time. So unless your room is exceedingly small or your light is exceedingly dim, the numbers don’t work out this way.
ETA: I assume these are basically the same calculations you did in your head.
It sounds to me like you’re imagining each photon having some precise direction, so that when you’re down to 42 photons per square meter, your eye needs to be in the right location to catch one. The photons aren’t pre-determined like that. By the time photons have got that far away, each photon will have spread out over a very large area. Your eye has a very small probability of interacting with a photon that spread out.
A better way of thinking about it would be that by the time they are that far away, each photon covers, say, 10^20 square meters, and that there are 4210^20 photons involved in any given square meter. If your eye covers 10^-5 square meters, then you’ve got a 1 in 10^25 chance of intercepting each of those 4210^20 photons.
There, Chronos says (Post #4) that a well-lit room has just one photon at a time, but upon questioning, later recants that. Further discussion of that question ensued, but I didn’t get whether there was a clear answer. It was sort of tangential to the topic of the thread.
Do we have detectors that can detect individual visible light photons yet? I think detectors have a finite exposure time, which is too long to capture the granularity.
“Visible” is relative; if the sensor detects it, then the photon is “seen”. Nonetheless, google search provides a wikipedia article on a single photon detector and google indicates there is further research being explored.
We’ve had them since the 1930s or 1940s, and they are pretty routine items in industry, science, and medical imaging. The workhorse device is the photomultiplier tube, in which an incoming photon kicks an electron off a thin metallic layer and induces a cascade of ever-increasing numbers of electrons down a chain of “dynodes”, each held at a higher electrical potential than the last. There is a wide range of off-the-shelf photomultiplier tubes (PMTs) available commerically, ranging in cost from around $200 to $10,000, depending on the specs you want.
There are also avalanche photodiodes, microchannel plates, “intensified” charge-coupled devices, and more. There is always a pressure to improve photodetector capabilities and/or cost, so while there are plenty of options available, photodetector development is an active area.
Yes I know it’s easy to detect individual x-ray gamma ray photons, eg during a PET scan. Are you seriously saying “visible” means “able to be detected”?
I just wish I could remember whence I got that “factoid”, so I could similarly resent them.
And not only can we detect individual visible-range photons, we can do so with high efficiency. Even an off-the-shelf black-and-white CCD, like might be used in a digital camera, will have a quantum efficiency in the vicinity of 90% (that is to say, if a visible-light photon strikes the detector, it has a 90% chance of detecting that individual photon). Photomultiplier tubes are even higher, but they’re not used so much any more, since a CCD is almost always good enough, and can also produce an image.
My post is only about visible light (i.e., wavelengths in the few-hundred nanometer range).
Photomultiplier tubes have low efficiency, typically around 20%. There are wavelength-shifting tricks you can do (at some cost) to bump that up a bit, but even then you’re lucky to scrape into the upper thirties. Nonetheless, PMTs are still the go-to device in lots of applications due to their high gain, low noise, and good time and charge resolution. Where they lose to solid-state devices including CCDs is in physical size (and efficiency, when that matters).
