I'm still worried about phase. The argument is that he can represent any phase he wants. I challenge him to represent different phases of his Nyquist frequency without the reconstruction losing power. He keeps saying "band limited", which I don't believe to be exactly true. I agree, the ear can only detect powers at frequencies below 22.1k, I'm not convinced it's ability to detect phase shifts is limited in the way you would expect with a digital signal with a cutoff at that frequency. For instance, the human ear can localize an impulse with accuracy down to about 10 microseconds. I can't see how a Dirac function can be localized that accurately by a sampled wave unless the system acted like a 100K sampled system. The latter, IMHO, is supported by the neuro-anatomy. There are different mechanisms for identifying pitch and onset. The quote-unquote Calyx of Held neurons carry the phase information, and are designed to fire with astonishing precision. Much more temporal precision than would be predicted from the "nyquist frequency" of the place coding subset of 8th nerve ganglia. I understand that this is what he was trying to address with his bit at the end, but he kept insisting on "band limited" inputs. Pressure waves aren't band limited dodge-rammit.

There are many models which have their own proofs. Without wave-particle duality, there would be not electron microscopes. One definition of a wave is the probability of a particle being at a certain time t. This is one topic where Einstein disagrees with de Broglie, who also disagrees with Feynman, and so on, hence the Copenhagen interpretation. They all agree on the differential equations behind the wave-particle model, but their interpretations of the equations are all in violent disagreement. Great topic though

>> ^offsetSammy:

According to Feynman's QED, there's no such thing as "wave-particle duality", it's just all particles. The behavior of the particles, however, is very strange, and that's what accounts for their wave-like characteristics. QED came after Dirac and Schrodinger (it was a refinement of their theories), so I'm not sure why it doesn't get acknowledged in these kinds of discussions.
QED also predicts exactly the results of things like the double slit experiment without ever resorting to the "well the wave collapses into a particle when we observer it" kind of thing.

According to Feynman's QED, there's no such thing as "wave-particle duality", it's just all particles. The behavior of the particles, however, is very strange, and that's what accounts for their wave-like characteristics. QED came after Dirac and Schrodinger (it was a refinement of their theories), so I'm not sure why it doesn't get acknowledged in these kinds of discussions.

QED also predicts exactly the results of things like the double slit experiment without ever resorting to the "well the wave collapses into a particle when we observer it" kind of thing.

Dirac on religion:

I cannot understand why we idle discussing religion. If we are honest—and scientists have to be—we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions.

I can't for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit.

Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards—in heaven if not on earth—all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins.

>> ^siftbot:
"All this sounds like science fiction..."
Am I the only one whose sick of hearing this used all the time in consumer level science programs?


No, you're not. This whole video is... wait a minute, I'm talking to a freaking robot. *ahem* Sounds like science fiction...

Energy has mass too, though it's probably more correct to say that mass and energy are equivalent.

>> ^dag:
Yes, my mistake- I think my high school science is insufficient. And as they have mass, albeit a very tiny amount- I guess they are "matter" and not energy? >> ^rychan:
>> ^dag:
From the video "he had discovered particles of anti-matter"
Wouldn't positrons be "anti-energy" as they don't have any mass? - and if they follow the same rules as an electron - not quite a "particle".

Electrons (and positrons) have mass.
http://en.wikipedia.org/wiki/Electron

Comment hidden because you are ignoring dag. (show it anyway)

Yes, my mistake- I think my high school science is insufficient. And as they have mass, albeit a very tiny amount- I guess they are "matter" and not energy? >> ^rychan:
>> ^dag:
From the video "he had discovered particles of anti-matter"
Wouldn't positrons be "anti-energy" as they don't have any mass? - and if they follow the same rules as an electron - not quite a "particle".

Electrons (and positrons) have mass.
http://en.wikipedia.org/wiki/Electron

>> ^dag:
From the video "he had discovered particles of anti-matter"
Wouldn't positrons be "anti-energy" as they don't have any mass? - and if they follow the same rules as an electron - not quite a "particle".


Electrons (and positrons) have mass.
http://en.wikipedia.org/wiki/Electron

>> ^MaxWilder:
When I heard about the seemingly spontaneous creation and destruction of particles, as described by this theory, I was immediately struck that this is probably related to the big bang. The universe as we know it, spontaneously created from nothing and eventually disappearing again, on a time scale unimaginable by we who popped up in the brief moment between.


They're probably not related at all since "before" the big bang, space and time didn't exist, which is not the case for spontaneous appearance of matter and antimatter pairs. Also, we have no theory that describes what happens at the time of the singularity, or "before" it, as opposed to QED.

Your video, The Dirac Equation and QED: Part 2, has made it into the Top 15 New Videos listing. Congratulations on your achievement. For your contribution you have been awarded 1 Power Point.

I love that they covered this. The derivation of the Dirac equation is one of the masterpieces of modern physics and it rarely gets talked about.

Your video, The Dirac Equation... What is antimatter?, has made it into the Top 15 New Videos listing. Congratulations on your achievement. For your contribution you have been awarded 1 Power Point.

It's a bit simplistic to say that the conservative physicists like Bohr and Dirac rejected Feynman's diagram because they loved their complex mathematics so much. Fact is that Feynman diagrams are very dumbed down versions of reality, as quantum particles do not move in such simple straight lines as implied by the diagrams. Their power lies in how they are an exquisite intuitive tool for keeping track of how the complex equations should be put together. When you first hear of them there is a danger of mistaking them for being meant as accurate pictures of reality, and I think this was a big part of Bohr and Dirac's misgivings.

Anyhow, when you keep in mind that the diagrams are always to be used in conjuntion with the complex mathematics, they are perhaps the most useful tool ever discovered in physics.

Here is the second part.

http://www.videosift.com/video/The-Dirac-Equation-and-QED-Part-2

The Dirac equation is a pretty incredible step in physics. Dirac made a huge leap from standard quantum mechanics to modern day field theory.

Dirac tried to rectify quantum mechanics with relativity and in the process proved that negative energy - i.e. antiparticles - had to exist. But there was still a major problem. The Dirac Equation didn't take into account electrodynamics. A great question here is how can macroscopic electrodynamic fields be justified for point particles like fermions and bosons... The answer is that the are understood as spin, torque, and charge. QED was the next big step. But it all started with the elegant and simple dirac equation.