Since we're linking to comments from Reddit: people also found out that this solution was known since at least 1860, and was published in a modern journal in as recently as 1977.

It's great that a 16 year old discovered this, and it could have been a cute (but not as flashy) story. But the reporter didn't even bother to talk to someone familiar with the field.

A lot of people seem to feel that way. If was even common among physicists in the beginnings of Quantum Mechanics (Einstein -- among many others -- was never satisfied with the theory, and tried without success to find something better).

I'm not sure myself, but it seems that when you begin to understand the math, you realize that it's actually very simple at the bottom -- the same very basic rules predict and explain so many wildly different things we can measure -- interference (the wave-particle duality stuff), the uncertainty principle, entanglement, quantum tunneling, etc. -- that it seems unlikely that there's some simpler explanation that will fit everything as well as Quantum Mechanics.

But one can never be sure :)

No, see the intermediate states in the step-by-step walkthrough of quantum teleportation in Wikipedia. Immediately after the first peer (called "Alice" in Wikipedia) does the measurement, the destination qubit (called "Bob's qubit" in Wikipedia) is in one of 4 the states described after the paragraph that begins with "Notice all we have done so far (...)". The state of Bob's qubit is represented to the right of the tensor product sign (the circle with the cross inside, for those not familiar with this notation). The states are completely different -- in fact some of them are orthogonal (the first is orthogonal to the last and the second is orthogonal to the third; that's easy to see because alpha*beta-alpha*beta=0).

What this means is that, if Bob doesn't use Alice's result to perform the right measurement in his qubit, he might as well have a random qubit. That's not surprising, since entanglement can't be used to transmit information. It's only with the information from Alice's measurement that Bob can select the right measurement to perform in his qubit to put it in the desired state (i.e., the state "teleported" from Alice's initial qubit).

[ouch -- overly long comment ahead... I wonder if anyone will read it :( ]

I have also never seen a good popular explanation of entanglement: either they go full weirdo saying things like "instantaneous something" or don't really explain entanglement, like your example about numbers in a hat. The problem is, to understand exactly what physicists understand by "quantum entanglement", you first must understand measurement, and in particular, that you can choose many different ways to measure each particle from the entangled pair. If you're willing to spend some time, I recommend the excellent series of lectures starting in this video. The material is pretty self-contained, except some matrix algebra and complex numbers. The lectures are given by Leonard Susskind, a famous physicist.

Now, if you just want to understand why entanglement is different then your "numbers in a hat" example, I'll try to explain as simply as I can with a simple example (which has the basic idea of Bell's inequalities and their violation, you can search wikipedia if you like).

OK, consider a "game" with these elements:

• (1) two people, Alice and Bob, the players in the game
• (2) both Alice and Bob each have a coin. Their coins are fair (i.e., 50/50) and, when flipped, give the result "0" or "1". Call the results of Alice and Bob flipping their coins ca (for "Coin-Alice") and cb (for "Coin-Bob"). Clearly, ca and cb are completely unrelated, because the coins are fair. Alice can see the result of her coin, but NOT Bob's, and vice-versa.
• (3) the hat from your example, which generates either two "0"s or two "1"s. You'll always give one of the numbers to Alice and the other one to Bob, and each of them can NOT see what the other one got. Call the two generated numbers ha and hb (for Hat-Alice and Hat-Bob). So, you'll always have either ha=hb=0 or ha=hb=1.
• (4) both Alice and Bob each have a piece of paper where they have to write either "0" or "1". Call the two written numbers pa and pb (for Paper-Alice and Paper-Bob). Each of them can't see the other one's paper.

The game is played by Alice and Bob collaborating to win -- either they both win or they both lose. To play, they can discuss their strategy, after learning the rules which I'm about to explain. But once the game starts, they can't talk anymore (i.e., no information can pass between them).

The rules of the game are as follows: when the game starts, Alice and Bob are given the numbers from the hat (ha and hb), then flip their coins (ca and cb) and write in their papers (pa and pb). They win if the resulting numbers satisfy the following equation:

pa XOR pb = ca * cb

and lose otherwise. Here, XOR is the usual XOR operation on bits, and "*" is the usual multiplication. Remember that all numbers in the equation (pa, pb, ca, cb) are either "0" or "1"). Also note that the numbers from the hat are not used to determine if they win or lose, but they can use the hat numbers to write their answers, according to whatever strategy they decided.

Now, note that if they both always write "0" in their papers, ignoring the hat completely, they win 75% of the time, because 0 XOR 0 = 0, and ca*cb will only be different than 0 if both coins are 1, which happens only 25% of the time. It's not too hard to prove (mathematically) that if their coins are indeed completely fair, any strategy they use will give them at most 75% of chance to win, it's impossible to do better without cheating.

So far, nothing involves anything quantum, and there's no entanglement. What I described is called a "Bell inequality" (win probability <= 75%), you can look up Wikipedia for a much more complicated explanation of basically the same thing.

Now, the real reason for all this business is this: if you replace the hat with a source of entangled photons (or a pair of anything that's entangled), then it's possible to do better than 75%, if Alice and Bob have a strategy for deciding what measurements to make on the photons that came out of the hat based on the result of the coins. This experiment has been done in the laboratory by many different people, and it shows that nature does indeed behaves like this, i.e., it's not really behaving like "numbers from a hat" (the actual possible win rate is about 82% with the right "strategy", as predicted by the theory that explains entanglement, i.e., Quantum Mechanics).

Unfortunately, to understand that you must understand what exactly is meant by "measurement", how you define a measurement, etc. That's what's explained in the lectures starting in the video I linked at the start of this (now extremely long) comment.

I hope this helps to at least give a hint about how entanglement can be different than the hat in your example.

It's actually worse than that. You could send the photons ahead of time (i.e., you could stock photons and use them to perform teleportation whenever you need it), but teleportation is still not "instantaneous".

The problem is that, to perform the teleportation, you must first measure the source, and then send the result of the measurement to the destination (that's just 2 bits of classical information). Given this information, the person in the destination chooses one of four measurements to perform in the corresponding destination photon, and then the teleportation is complete. Wikipedia has a more detailed explanation, including the measurements performed.

That's not really true. The real motive is explained in this other comment.

That said, I think that what you mean is (and this is true): to perform quantum teleportation, you still need a classical channel. But the reason for the satellites in this case is not that: the satellite is being used to send entangled photons (i.e., it's a quantum channel). The classical information could have been sent in any other way (over the Internet, for example), but to send entangled photons, there must be no measurements of the photon along the way.

SSH doesn't use SSL, it has its own transport layer protocol (which is described in RFC 4253).

(To confuse things a bit, OpenSSH does use OpenSSL, but only the cryptography functions. The SSL part of OpenSSL is completely untouched by OpenSSH).

This result shows nothing wrong with relativity or quantum theory.

Neutrinos have so little mass (less than 0.28 eV, compared to, for example, about 510000 eV for the electron and about 940000000 eV for the proton) that they're expected be found traveling *very* close to the speed of light. This experiment is simply not precise enough to detect the difference between the speed of the neutrinos and the speed of light.

It's great to study, understand and use Feynman's path integral, especially since it leads to new insights about the nature of Quantum Mechanics (plus, seeing the familiar face of the principle of least action in the quantum world is just awesome). But it seems counter-productive to limit yourself to it. For example, some problems that are relatively simple to solve using the "usual" methods (i.e., thinking about waves and using the Schrodinger equation) can become intractable math nightmares with Feynman's path integral. I'm sure there are problems for which the reverse is true, too.

Most people who work with QM seem to take a very pragmatic approach when dealing with problems outside the foundations of QM: use whatever works for you for the problem at hand. Peter Shor (the guy who invented the quantum algorithm to factor numbers in polynomial time) once wrote:

(Source)

And I agree that people should read QED: it's very easy to read, and it's great.

This discussion is mixing two different things: the decimal expansion of irrational numbers and infinite random sequences.

I won't argue about random sequences, but Hatta is right about irrational numbers in general (an pi in particular). It's perfectly possible (as far as we know today) that the decimal expansion of pi does not contain, for example, any "1"s after the n-th digit (for some n).