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Comment by jcims | Hacker News Reader

If you trace the path of individual photons it seems implausible. That somehow a photon leaves the sun, travels possibly weeks until it strikes some nanoscopic face of a crystal on the surface of this object, which is rotating and travelling tangentially at several km/sec, and departs at such a resolved and precise an angle that it makes it almost all the way back to the sun, passes through the atmosphere of an orbiting body travelling 30km/sec, lands on a finely curated layer of aluminum where it is reflected yet again and lands on a square likely smaller than an index card.

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I mean, yeah, it's an incredibly unlikely scenario for a single photon, but on the other side of that equation is a whole heck of a lot of photons.

Enough chances makes almost anything likely.

There may be more photons than you think. 10^^17 per cm^^2 per second at the surface of the earth.

https://www.reddit.com/r/askscience/comments/2n6zo0/comment/...

What do you mean by the double caret (cm^^2) ?

I think that's a plain text way of saying "square centimetres" - `^` often means `xor` thus `^^` to mean exponentiation (and is less obtuse than `cm2`)

Ah, I didn't think of it being to disambiguate from xor.

I would usually expect 2^3 to mean 8, and 2^^3 to mean 16

Perhaps too much time reading people talk about 3^^^^3 dust specs

I've never seen '^^' to mean exponentiation. In Python (and probably other languages), exponentiation is denoted with '', so 23 = 8.

"You know, the most amazing thing happened to me tonight... I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!" —Richard Feynman

If you select a random point from [0, 1] segment, then probability of selecting that particular point is zero. Not "very close to zero", but "exactly zero".

Actually, to be pedantic, the probability is one. Not "very close to one", but "exactly one".

P (X | X) = 1.

Yep. That's why one speaks of probability density functions and not just probability functions.

I want your random number generator.

Good thing telescopes aren't 0 in size.

It is not equal to zero. It is infinitesimal. There is a difference.

Infinitesimals don't exist in standard analysis. There exist no positive numbers smaller than all positive real numbers. The probability of picking any given real number from [0, 1) is exactly zero, there's no other number it could be. Rigorously, the measure of any countable subset of real numbers is zero.

Honestly, I don't really "like" real numbers, exactly because they are defined as classes of equivalence of converging sequences of neighborhoods.

But I'm pretty sure even in rational numbers probability would be exactly zero, because that's how probability there is defined (as a limit of a sequence, and limit is zero).

The thing is 9 light hours out. It's 9 light hours back. What's the photon doing in the meantime? A little R&R on the beaches of Neptune, taking in the sights of floating diamonds?

It's travelling at the speed of light. From its reference frame, the trip is instantaneous.

Given that OP - our observer - is presumably on earth, it's a different reference frame. We'll still have to account for the difference of "possibly weeks" and and 18 hours.

And it's a really sorry state of affairs for photons that their vacations pass instantaneously.

(IOW: I was poking fun at the OPs statements of the photon travelling "possibly weeks", not making a statement of fact. I thought the "beaches of Neptune" bit gave it away, but I guess not)

That may or may not be accurate. The limit of time dilation function as velocity approaches speed of light is zero, but the function itself is discontinuous. It hits a division-by-zero.

I really enjoyed this description. Very colorful.

I'm not smart enough to have that kind of doubt: you really got me thinking! And you made me think of the wave/particle duality. Detection over this distance seems much more plausible with the light-as-waves model; the waves behaving like er... waves and our detection of them working more like radar/echo-location.

It doesn’t make any difference - the probabilities would be the same. You can treat it as a bunch of photons (with the expected photon density that the sun emits) or as a light wave that collapses to a photon in the detector with probability given by the Born rule. The probability will work out the same.

That breaks my mental model of waves (which probably means my model needs improving). I imagined the probably of the wave reaching the detector was proportional to the energy of the original signal. Does that map directly to photons and probability? I suppose it must... woah.

Well since we still don't have any great explaination for the 200 year old double slit experiment, how do you know it is photons moving around? Could be star sized tsunami waves of light trashing about collapsing into photons when finally measured.

In fact, we do have an explanation for it - its called quantum theory and it explains and predicts not only the double slit experiment but many other much more complicated phenomena.

Meh. Predicts, yes. But I expect you could poll massive support for the proposition "the standard model is an accurate description of what happens, but not an explanation of why things would be like that".

>Well since we still don't have any great explaination for the 200 year old double slit experiment

I'm duty-bound to point out that this is only true in a philosophical, interpretive sense based on the aesthetics of explanations. Scientifically it's completely understood.

We can only predict the outcome of the double-slit experiment. We do not know how that outcome comes to be, nor do we know "why" the rules are the rules.

I think you are asking for answers beyond what science can offer. Our current understanding of mathematics and logic suggest that every scientific theory will always have some axioms that we will have to take on "faith". Moreover, contrary to popular belief, science is process of eliminating the false theories leaving behind a set of _possibly true_ theories. Our current understanding of the philosophy of science suggests that we will never be able to infer the "true" laws of the universe. How can you answer the "why" if you don't even know if the current physical laws are the "true" ones.

Science is just a way of compressing what we perceive with our senses into compact descriptions that our easy to memorize and understand by human beings. That is all. In the words of Neil Bohr, "Physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods of ordering and surveying human experience.".

>Our current understanding of mathematics and logic suggest that every scientific theory will always have some axioms that we will have to take on "faith".

I don't think this is true. The axioms can be testable, in which case you can do a little better than faith and say that "well, this is how it seems to work." For example I could have a theory that when I press the gas pedal my car moves forwards. Later on I could discover another theory that explains why that theory is true, but in the meantime I'm better than faith but worse than complete fundamental knowledge. That's where physics is - if we had complete fundamental knowledge many of us would go home, having nothing left to do.

What you say is indeed true and I did not mean my comment to imply that axioms are not testable.

Why can be a rather unscientific question. As long as the observation matches reality the just so story used is rather meaningless.

That's even cooler, photons popping into existence like whitecaps on a wave as the energy coalesces to a point after travelling independently for hundreds of billions of miles.

A detected photon is just a wavefunction that isn't there any more.

It's just a wavefunction that your wavefunction is entangled with; it only looks like it isn't there because you're now inside rather than outside.

As a matter of fact we do have, and it's quite understandable by anyone with an understanding of high-school physics if you can spare a few (<10) hours to study.

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