Ask a physicist anything. (3)

[Cabal]

Is there any practical use to quantum cryptography? I heard that, once the next prime number is discovered, we'll have uncrackable public keys, or something like that.

I don't think there's anything that allows one particular prime number to be crackable and the next not to be. There's infinitely many, although I suppose they will be harder to find at higher powers of 10 (or whatever base you're working in.)

Classical cryptography is not technically uncrackable, it's just so time-consuming for a classical computer to do it may as well be. Quantum computing, on the other hand, will be able to crack it much faster, so I'd say the industry standard will need to shift to quantum cryptography eventually if quantum computers become standard.

The advantage about quantum cryptography is that for generating key exchange, the quantum mechanical nature of the transmissions mean that it's hard to intercept. If the data is encoded via superpositions or entanglement, you can't look at the data, copy it, and re-transmit it, because you can't recreate quantum states in an exact, deterministic way. If you attempt to bluff anyway and send up randomly encoded data packets, the people communicating will notice errors in their data when they meet to finalise the key exchange.

My knowledge of cryptography is limited to a book on it that I've read, and Darren Brown's Digital Fortress, so I'm probably wrong on all counts

Hey, at least this isn't a particle physics discussion. I've had people ask me suspiciously about antimatter bombs before

 

[Wiccan_Child]

I don't think there's anything that allows one particular prime number to be crackable and the next not to be. There's infinitely many, although I suppose they will be harder to find at higher powers of 10 (or whatever base you're working in.)

I think it's because the next prime, whatever it is, will push brute force decryption time from a maximum of a matter of days to a length of time that is several orders of magnitude longer than the age of the universe. That seems like way too big a leap, but, who knows.

Classical cryptography is not technically uncrackable, it's just so time-consuming for a classical computer to do it may as well be. Quantum computing, on the other hand, will be able to crack it much faster, so I'd say the industry standard will need to shift to quantum cryptography eventually if quantum computers become standard.

So the 'uncrackable' prime becomes somewhat fragile? Kewl.
Is there any estimate on the computing power of a commercial quantum computer?

The advantage about quantum cryptography is that for generating key exchange, the quantum mechanical nature of the transmissions mean that it's hard to intercept. If the data is encoded via superpositions or entanglement, you can't look at the data, copy it, and re-transmit it, because you can't recreate quantum states in an exact, deterministic way. If you attempt to bluff anyway and send up randomly encoded data packets, the people communicating will notice errors in their data when they meet to finalise the key exchange.

If there's one thing computer piracy has taught me, is that there will be a way to crack it. As a clandestine government agent one said, it is inevitable.

Hey, at least this isn't a particle physics discussion. I've had people ask me suspiciously about antimatter bombs before

What? You mean Dan Brown's completely factual books are erroneous?! And here I thought Christ's daughter was roaming the English countryside.

 

[Cabal]

I think it's because the next prime, whatever it is, will push brute force decryption time from a maximum of a matter of days to a length of time that is several orders of magnitude longer than the age of the universe. That seems like way too big a leap, but, who knows.

I was under the impression it was already at this stage, but I'm not sure how much parallel computing was assumed when I saw that factoid being presented.

So the 'uncrackable' prime becomes somewhat fragile? Kewl.
Is there any estimate on the computing power of a commercial quantum computer?

Depends on the number of qunits, really. Saw a great couple of lectures on quantum computing over the summer, need to dig them out.

It's not so much computing power per se, as the means by which it operates. The running time of quantum computation is polynomial, rather than linear, which I think makes it a lot faster for factorising into primes. The first thing we were told in those lectures I saw was that there is no difference between a classical and a quantum computer in what they can do - only in how they do it.

f there's one thing computer piracy has taught me, is that there will be a way to crack it. As a clandestine government agent one said, it is inevitable.

Oh sure, I wasn't saying it wasn't crackable. It's just a lot harder to crack because it's quantum information, so the laws of the universe are against you on that one. Best approach I imagine would be to tackle the key transfer via a classical channel. I imagine there are other quantum mechanical ways of bettering your odds as an eavesdropper also - think there's definitely a few papers on arXiv about that, but not sure how widely considered they are.

What? You mean Dan Brown's completely factual books are erroneous?! And here I thought Christ's daughter was roaming the English countryside.

See, every time I think I might have the stomach to face a Dan Brown novel, someone summarises a plot point like that and.....urgh.

The Yahtzee quote about how one could vomit over a typewriter and come up with something equivalent to a Dan Brown novel springs to mind.

 

[Maxwell511]

That said, I maintain what I said: semiconductor physics is a semi-classical approach, like modern thermodynamics. It's a classical approach to a quantum problem (instead of classical particles, you have spin states, energy bands, etc).

But the statistics used to formulate the behaviour is not classical. It is based on Fermi-Dirac Statistics. It is entirely quantum mechnical in origin. If it were based on Maxwell-Boltzmann statistics I would given you that it is a classical approach, but it is not.

 

[Maxwell511]

Oh sure, I wasn't saying it wasn't crackable. It's just a lot harder to crack because it's quantum information, so the laws of the universe are against you on that one. Best approach I imagine would be to tackle the key transfer via a classical channel. I imagine there are other quantum mechanical ways of bettering your odds as an eavesdropper also - think there's definitely a few papers on arXiv about that, but not sure how widely considered they are.

Also modern cryptography is largely based on the premise that NP-Complete problems are not within the set of P problems. This is not known for sure to be true. If a polynomial algorithm was found for NP-Complete problems quantum cryptography would be the only option.

 

[Chesterton]

<bump>

I often think...fish must get awfully tired of seafood. What are you thoughts, Hobson?

 

[AV1611VET]

What keeps electrons from crashing into the protons they are orbiting; especially since they have opposite charges?

Is it centrifugal force?

 

[Cabal]

What keeps electrons from crashing into the protons they are orbiting; especially since they have opposite charges?

Is it centrifugal force?

That's what the Rutherford and Bohr models were based on, and as the electric force between an electron and a proton is an attractive central force, it's not unreasonable to formulate it as such.

However acceleration of charge causes the emission of electromagnetic radiation as a result of draining the electron's energy - which isn't what we see happening with atoms. Bohr didn't even really attempt to explain this with his model, his postulates basically amounted to a "they just don't, OK!"

As I understand it, the stable atomic configurations we observe arise as a result of quantum mechanical uncertainty. Electrons don't occupy defined orbits as that would violate the uncertainty principle, so their orbitals are more rough shapes where it's very likely we'll find an electron. The zero point energy of the system prevents electrons from falling into the nucleus.

 

[AV1611VET]

That's what the Rutherford and Bohr models were based on, and as the electric force between an electron and a proton is an attractive central force, it's not unreasonable to formulate it as such.

However acceleration of charge causes the emission of electromagnetic radiation as a result of draining the electron's energy - which isn't what we see happening with atoms. Bohr didn't even really attempt to explain this with his model, his postulates basically amounted to a "they just don't, OK!"

As I understand it, the stable atomic configurations we observe arise as a result of quantum mechanical uncertainty. Electrons don't occupy defined orbits as that would violate the uncertainty principle, so their orbitals are more rough shapes where it's very likely we'll find an electron. The zero point energy of the system prevents electrons from falling into the nucleus.

--- What?

 

[Cabal]

--- What?

Short answer - no.

If it were purely centrifugal/centripetal force, the electrons would spiral into the nucleus as they'd lose their kinetic energy as it was converted into light (same thing happens on a radio mast, you're accelerating charge to create a signal).

The fact they have opposite charges hasn't really got anything to do with it - in fact it's usually what's said to cause the centripetal acceleration, which means it'd be responsible for the atom losing charge.

The atom is a quantum mechanical system, which means that you can't really describe it using classical mechanics - centripetal forces and general Newtonian stuff like that. Instead of well-defined orbits (which would violate the uncertainty principle as it implies definite knowledge of both position and momentum), you deal with somewhat nebulous regions where an electron is likely to exist. It isn't "moving" in the strictest sense of the word.

In quantum mechanics, the fact that a system has specific energy levels (as opposed to being able to exist in any arbitrary energy state), and that the lowest of them isn't zero, means that an electron can't really "collide" with the nucleus.

 

[AV1611VET]

In quantum mechanics, the fact that a system has specific energy levels (as opposed to being able to exist in any arbitrary energy state), and that the lowest of them isn't zero, means that an electron can't really "collide" with the nucleus.

Would they @ absolute zero?

 

[Cabal]

Would they @ absolute zero?

Nope. The zero point energy is the energy a system has when all other energy has been removed - so even if there's no heat, no potential energy sources, nothing - there'll still be that energy present. It physically can't get any lower than that amount.

So for a hydrogen atom, at absolute zero you'll still have the electron separate from the proton (most likely value is the Bohr radius, which is about 10^-11 m)

 

[AV1611VET]

Nope. The zero point energy is the energy a system has when all other energy has been removed - so even if there's no heat, no potential energy sources, nothing - there'll still be that energy present. It physically can't get any lower than that amount.

So for a hydrogen atom, at absolute zero you'll still have the electron separate from the proton (most likely value is the Bohr radius, which is about 10^-11 m)

Okay, thanks --

 

[Wiccan_Child]

What keeps electrons from crashing into the protons they are orbiting; especially since they have opposite charges?

Is it centrifugal force?

Any deviation from their orbit requires energy. Like marbles moving in a circular groove on a piece of wood, you have to knock them particularly hard to shift them out of their path.

 

[Wiccan_Child]

Would they @ absolute zero?

Temperature gets a bit wiffy on quantum scales. As Cabal said, absolute zero amounts to the zero-point energy of the system - the minimum energy, which isn't quite zero.

 

[AV1611VET]

Any deviation from their orbit requires energy. Like marbles moving in a circular groove on a piece of wood, you have to knock them particularly hard to shift them out of their path.

Good analogy --

 

[alexacker]

Why does radioactive decay occur? From what i have read in wiki unstable nuclei release energy in form of radiation and particles.
Up until now i thought that the coulomb force ,in atoms with less neutrons than normal, is slowly breaking the atom apart... But i couldnt give an explanation for atoms with more neutrons than usual..

 

[Wiccan_Child]

Why does radioactive decay occur? From what i have read in wiki unstable nuclei release energy in form of radiation and particles.
Up until now i thought that the coulomb force ,in atoms with less neutrons than normal, is slowly breaking the atom apart... But i couldnt give an explanation for atoms with more neutrons than usual..

Neutrons hold the atom together, but protons push it apart. If you want more protons in an atom, you need more neutrons. Stable atoms have sufficient neutrons to keep the atom together forever, while very unstable atoms have so few neutrons that electromagnetic repulsion rips it apart.

There are quasi-stable atoms, like Uranium-235 and Carbon-14, which are on the verge of being ripped apart - like a pendulum that's somehow been balanced so the weight is at the top, it only takes a little push to knock the whole thing over. This can happen when a neutron quantum tunnels outside the nucleus, or turns into a proton, or when extra protons and neutrons are shoved into the atom.

Uranium has a couple hundred nucleons (protons and neutrons), and, occasionally, four of them will come together to form a stable 'mini nucleus'. This can then tunnel outside the main nucleus as a whole - such a nucleus is a Helium atom, otherwise known as an alpha particle.

So, basically, it's a question of stability. Coulomb repulsion plays a part, but radioactive decay in things like Uranium is governed principally by quantum mechanical hooey.

 

[alexacker]

thanks man i hope i get into the physics university to learn more about all these exciting stuff !!

 

[Wiccan_Child]

thanks man i hope i get into the physics university to learn more about all these exciting stuff !!

Yay, another physicist in the making! Have some cake!