Jake1

Hi everyone, I'm working on a pretty relaxed end-of-the-year school project, the only objective of which is to explain a mathematical concept to the class. I've chosen quantum cryptography. By Monday, I would like to be able to: Define quantum mechanics for the class. Explain the math behind photon polarization. Explain how the BB84 (sending photons with laser pulses) and Eckert (communicating with two entangled photons) quantum key distribution protocols work. Explain the applications of quantum cryptography. I can accomplish all but the second objective by myself. I understand Wikipedia's explanation of the BB84 protocol pretty well, but I do not understand the actual mathematics behind photon polarization. I don't know what "rectilinear" or "diagonal" base states are, I don't know how photons are actually polarized, and I don't understand why measuring a rectilinear photon as if it were diagonal forces it to assume a random diagonal state. I can't simply settle for a qualitative understanding of these concepts, either, as this project must have a firm basis in actual math. So, as a student with a firm understanding of calculus and a very light understanding of physics, which online resources can I use to learn about the mathematics behind photon polarization? I need to be able to actually explain polarization in terms of the functions physicists use to describe quantum mechanics. Thanks in advanced for your help.

Yes, I've already read that FAQ, and it does a nice job of explaining virtual particles, but I'm still confused as to what uncertainty is. Does uncertainty in time decrease as change in time decreases, because the particle can only exist in a shorter interval of time, so its position in time is less uncertain? And this is what causes uncertainty in energy to increase, resulting in virtual particles?

So, as I understand it, virtual particles can exist because they exist for such a short period of time, so as uncertainty in time decreases, uncertainty in energy increases, creating enough energy for a particle to exist for that time increment. But why does uncertainty in time decrease as the length of time decreases? Is uncertainty equal to change? Is that why uncertainty and change are both represented by delta? I'm very uncertain about what uncertainty actually is.

I'll reply to the rest of this when I get home, but I must point out that when you say there are some things scientists can't control, no one is disagreeing with you. Science is simply a method of investigation, not an attempt to control everything at all times.

This is much different than what you proceeded to propose. If you tell kids Heaven is real, you're promoting a belief for which there is very little evidence. Presenting different viewpoints, however, and giving an honest explanation of the evidence for those viewpoints, is not dishonest.

My original post was meant to point out that Iwonderaboutthings ignored chadn737's post (except for the first four words) when replying to it. I edited my post to further explain why I disagree with Iwonderaboutthings. I'd also like to point out that while you went with "vaguely troll-like" I went with "either a troll or too lazy to read entire posts". If you felt my wording was too strong, I'll try to use milder language in the future. Nevertheless, I didn't intend to insult or aggravate Iwonderaboutthings, but was simply providing two possible explanations for my observation that he or she blatantly ignores most of what people reply with.

In your ozone layer thread, I recently asserted that you were probably not a troll because you have too many posts on these forums. However, given that you don't seem to read more than the first few words of each post you reply to, you are either a troll who hasn't gotten bored after over a hundred posts, or you're just uncommonly lazy. And yes, we that know "love", or the feeling we define as love, exists. We feel it. We've decided to call it love. That's part of language and society, not part of science. And yes, scientists can provide evidence that all emotions (I don't know why you're so obsessed with love in particular) are connected to physical events in the brain. It's like asking "Do scientists believe in dreams, and can they prove they exist?" The answer is that although scientists have studied dreams and have explanations for how they work, almost everybody "believes" in dreams because almost everyone has dreams. You don't have to provide a scientific explanation for feelings and thoughts to believe in their existence!

Iwonderaboutthings has too many posts on these forums to be a troll, unless he or she is just a troll with a very long attention span. Perhaps he or she just doesn't understand what science and capitalism are.

No, replacing critical thinking in kids with stories about Heaven, God, Santa, the American Dream (kidding...) is not a good idea in the long term. I know teens who still wonder about Santa's existence. Teens.

Yeah, I understand basic chemistry, so most of this is stuff I already knew. I should have phrased my question, "What do our nerve endings detect when we touch other objects?" The answer seems to be that we are feeling the repulsion of our electrons by the virtual photons emitted by the other object's electrons, correct?

http://en.m.wikipedia.org/wiki/Esoteric_programming_language My favorite is Whitespace. As the name suggests, it only uses space, tab, and return.

As previously mentioned, we're reversing the problem, and we wouldn't even be able to do that without science. Science is a tool, and it can be used to fix mistakes that we make.

The way Benjamin Schumacher explains it, as uncertainty in energy decreases, uncertainty in position increases. So when helium is at such a low temperature, uncertainty in energy is very low, so uncertainty in position increases and is greater than the space between the helium atoms. Thus the atoms form one uniform liquid with zero friction because there is no definite space between the atoms. Or something like that. Someone should correct my misconceptions.

Love is real, as we can feel it. We know it's caused by the brain, but then again we don't know what causes consciousness, so we don't know why we are aware of love (or anything, for that matter). None of this has anything to do with God or a soul, neither of which is supported by much evidence. You don't have to know the exact cause of love to know it's real.

Considering the only example of consciousness we have is the brain, and the internet is not a brain, it seems unlikely it would gain self-awareness. But we need a better understanding of what physically causes consciousness.

No, I know that objects are held together because of the charges on electrons and protons. I'm talking about why objects can't pass through other objects. Is that because the electrons of object A are repelling the electrons in object B with virtual photons? I definitely remember Benjamin Schumacher explaining that his hand can't pass through a table because of the properties of Fermions, not because the electrons in his hand are repelled by the electrons in the table due to their charge. Or did I misunderstand Schumacher and he meant that his hand is solid due to the Pauli exclusion principle, but the interaction between his hand and the desk is still due to electrons' charges repelling each other?

My high school physics teacher told us that solid objects don't pass through each other because their electrons exchange virtual photons and repel each other as part of the electric force. But with my rudimentary understanding of quantum mechanics, it's not the electrons' charges that repel each other. It's the fact that electrons are fermions and fermions can't occupy the same quantum state (hence the Pauli exclusion principle), and thus electrons cannot occupy other electrons' orbitals. Is that correct? And does the negative charge on electrons have anything to do with the solidity of objects, or is that not a contributing factor at all?