Help! Is there a physicist in the house?

[sammythecat]

I just watched a video, Prof. Brian Cox - A Night with the Stars

, and about 36 minutes in he talks about the Pauli Exclusion Principle. My own slight understanding of this is that no two electrons "within an atom" can have the exact same energy level. If one changes than all others adjust, or don't adjust, accordingly. Prof. Cox, however, said this sort of status update occurred between every electron in the universe so that no two electrons in the whole universe could have the same energy.

I didn't misunderstand, he stressed this point and stated it very clearly. It was a building block for the rest of the lecture. Every electron in the universe was aware of, and would react to, the status of every other electron in the universe. Instantly. All the time. It's not a domino effect kind of thing where each reacts to its neighbor and so on down the line. It just happens all at once. Either way though, wouldn't this violate the speed limit of the universe, that no information can travel faster than the speed of light. These status updates would clearly be transfers of information, and it's just as clear that in order to have a coherent universe this would have to happen at speeds vastly exceeding the speed of light.

Maybe I somehow misunderstood what he was saying but he was speaking to a lay audience and it was an important point. If he was in error it was a huge error so its more likely I'm the one in error. Can anyone here enlighten me on this?

[valerief]

1. This site says within an atom, too.

http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html

Same here.
http://www.britannica.com/EBchecked/topic/447124/Pauli-exclusion-principle

But you're right. In the clip, he does say 'in the universe' multiple times.

[sammythecat]

4. I was too pressed for time to check more

than a couple sites and they too said "within the atom". Seems like he made a big mistake about something he surely knows inside and out.

[bananas]

11. Brian Cox is correct, he responded in the Wall Street Journal

http://blogs.wsj.com/speakeasy/2012/02/20/why-quantum-theory-is-so-misunderstood/

Feb 20, 2012
Why Quantum Theory Is So Misunderstood
By Brian Cox

I recently gave a lecture, screened on the BBC, about quantum theory, in which I pointed out that “everything is connected to everything else”. This is literally true if quantum theory as currently understood is not augmented by new physics. This means that the subatomic constituents of your body are constantly shifting, albeit absolutely imperceptibly, in response to events happening an arbitrarily large distance away; for the sake of argument, let’s say on the other side of the Universe.

This statement received some criticism in scientific circles. Not because it’s wrong, because it isn’t; without this behavior, we wouldn’t be able to explain the bonds that hold molecules together. The problem is that it sounds like woo woo, and quantum theory attracts woo-woo merde-merchants like the pronouncements of New Age mystics attract flies – metaphorically speaking.

<snip>

For some scientists, the unfortunate distortion and misappropriation of scientific ideas that often accompanies their integration into popular culture is an unacceptable price to pay. I share their irritation, but my strongly held view is that science is too important not to be part of popular culture. Our civilization was built on the foundations of reason and rational thinking embodied in the scientific method, and our future depends on the widespread acceptance of science as THE ONLY WAY WE HAVE to meet many, if not all, of the great challenges we face. Is the climate warming and, if so, what is the cause? Is it safe to vaccinate children against disease? These are scientific questions, in that they can be answered by the analysis of data, and therefore the answers are independent of the opinion, faith or political persuasion of the individual. If you would like to see the scale of the problem faced by those who wish to champion science and reason above rhetoric and knee-jerk prejudice, have a glance at the comments that are no doubt proliferating below this article because I mentioned climate change and vaccination.

The key words in the above paragraph are “widespread acceptance”. In democratic societies, progress is made through persuasion, and science has a most persuasive story to tell. Quantum theory tells us that the universe we experience emerges from a bewildering, counterintuitive maelstrom of interactions between an infinity of recalcitrant sub-atomic particles. To understand something as simple as a rainbow, we have to allow each single particle of light to explore the entire universe on its journey through the rain. This is magical, and there is plenty more in the library of science. We have landed on a world where the faint sun glints off methane lakes, seen stars the size of cities spin hundreds of times a second, and taken photographs of light from the beginning of time that has journeyed for over thirteen billion years to reach us. This is true wonder, with the power to deliver a dizzying feeling, the craving for which might be seen as the very definition of what it means to be human.

<snip>

[NYC_SKP]

2. Most physicists would secretly admit that there is no speed limit.

There are forces and actions in our world that behave with instantaneity.

I don't hear as many people challenge the speed of light limit theory as I'd like to.

[sammythecat]

5. I'd like to see some credible challenges too.

I think that'd be wonderful. That whole speed of light thing is a real bummer. Takes a lot of the fun away.

Maybe l can sail to Andromeda after all.

[NYC_SKP]

7. Sail to Andromeda? You're probably there right now.

And you just don't know it!

[eppur_se_muova]

3. No two electrons can have *ALL* the quantum numbers the same.

Two electrons in two different, NON-INTERACTING atoms will necessarily differ in their quantum states, so they might have the same numbers assigned to them if you write out the local quantum state for each, and use a different numbering system for each atom. And yes, they can have the same energy. In the absence of a magnetic field, all atoms have have what are called "degenerate" energy levels -- electrons in several different orbitals will all have the same energy, but will split into different energy levels in the presence of a magnetic field.

So far, all this refers to the non-relativistic approximation described by the Schrodinger equation. In a relativistic universe (like the one we live in) a more correct description is given by the Dirac equation, in which orbitals are replaced by "spinors" which include the spin in the wavefunction. Electrons having different spins actually have (*very* slightly) different energies in a full relativistic treatment. But in the absence of a magnetic field there are still degenerate orbitals having the same energy, even within the same atom.

[sammythecat]

8. Is there an interpreter in the house?

I'm just kidding about that although I have to admit I don't yet completely understand what you said. I feel I will understand once I look up a few definitions. Problem is I have to leave 10 minutes ago.

Judging by the content and the speed of your response you're quite comfortable with this subject and I'm sure this is the answer I'm looking for. I can easily look up Dirac's equation and spinoors but I wonder if you could tell me what you mean about "absence of a magnetic field". Is this a very rare state of matter? Would the atom have to be somewhere in intergalactic space or something. Sorry for my ignorance but I thought just about everything had a magnetic field. If the answer is much more complex than that you don't have to explain it. I can look it up (and should) if my understanding is wrong.

btw, I figured this forum would be sort of slow. I was surprised at how fast I got responses. And good ones at that.

[eppur_se_muova]

9. No, it's not a very rare state ... it's kind of the default state ...

If you heat a sample of a pure element and examine the spectrum, you will find a number of emission lines, which tell you something about the energy levels of the electrons in the constituent atoms. Add a very strong magnetic field and many of the lines will split -- the stronger field, the greater the splitting (known as the Zeeman effect). IIRC this effect was first observed in spectral (absorption) lines from the Sun, where the magnetic field is intense enough for the effect to be observed. From this it was deduced that the energy levels themselves are being split. For example, a second-row element like carbon has several electrons in three "p orbitals". Normally, these have the same energy and cannot be distinguished from each other. Add a magnetic field and these are split into different energy levels, depending on their orientation relative to the direction of the magnetic field.

[DetlefK]

6. Didn't see the video, but...

"Every electron in the universe" is limited by two things:
- The speed of light only allows for events up to a certain distance (the event horizon) to influence a certain spot
- The "networking" only holds for solid matter. In other states of matter, the atoms are so far apart, that the long-range-interactions between their electrons are negligible. The Pauli-exclusion drops even faster in influence than the van-der-Waals-interaction (which is electron-on-electron) which scales with 1/(distance)^6

And if you deal in such great distances, where speed-of-light becomes important, you have to treat your system relativistically. You have to switch from Schroedinger's equation to Dirac's equation of quantum-mechanics, which is nasty as shit:
- The electrons Prof. Cox is speaking about would no longer have a single-wave-function: They would have 4 different wave-functions at the same time. How do relativistic electrons interact in that way? I have no idea, try to find a guy specialized in theoretical particle physics.
- The wave-function no longer correlates to the probability that you can find the particle inside a certain volume. -> It has become even trickier to define the "location" of a particle.


"Every electron in the universe" is a dangerous simplification that can easily (well, for a physicist) be disputed.

[Beachwood]

10. Brian Cox misunderstands locality, Pauli exclusion principle

See this and other links:

Brian Cox misunderstands locality, Pauli exclusion principle


Update: See a wonderful Twitter confrontation between Carroll and Cox, as storified by storify.com – thanks to Jon Butterworth and Twistor 59




http://motls.blogspot.com/2012/02/brian-cox-misunderstands-locality-pauli.

Also, you might want to see this video.
Published on Mar 7, 2012

Was Brian Cox wrong?

[Chemisse]

12. I think he mucked up the point he was trying to make.

No two electrons in an atom can have the same exact energy state.

If, within an electron pair, one of the electrons changes, the other would change accordingly.

According to Quantum Theory, this would happen even if the two electrons were separated in space, that they would have instant communication with each other. And it would not matter how far away they were - speed limit be damned.

[FiveGoodMen]

13. He SEEMED to be saying that all electrons are quantum entangled with all other electrons

[Chemisse]

14. That seems a bit out there, but so much about Quantum Mechanics is

I guess you could say if everything in the universe was together at the Big Bang, then all is entangled.

It's a little creepy if you go too far with the entanglement premise. It makes me feel like every little thing I do is affecting the universe. Frankly, I don't want that much responsibility.

[Jim__]

15. Sean Carroll had a pretty interesting post on Cox's statement.

It's worth reading his entire post. An excerpt:

...

The point of this last statement is that when you say “When I heat this diamond up all the electrons across the universe instantly but imperceptibly change their energy levels,” people are naturally going to believe that something has changed about electrons very far away. But that’s not true, in the most accurate meaning we can attach to those words. In particular, imagine there is some physicist located in the Andromeda galaxy, doing experiments on the energy levels of electrons. This is a really good experimenter, with lots of electrons available and the ability to measure energies to arbitrarily good precision. When we rub the diamond here on Earth, is there any change at all in what that experimenter would measure?

Of course the answer is “none whatsoever.” Not just in practice, but in principle. The Hamiltonian of the universe will change when we heat up the diamond, which changes the instantaneous time-independent solutions to the Schoedinger equation throughout space, so in principle the energy levels of all the electrons in the universe do change. But that change is completely invisible to the far-off experimenter; there will be a change, but it won’t happen until the change in the electromagnetic field itself has had time to propagate out to Andromeda, which is at the speed of light. Another way of saying it is that “energy levels” are static, unchanging states, and what really happens is that we poke the electron into a non-static state that gradually evolves. (If it were any other way, we could send signals faster than light using this technique.)

Verdict: if this is what’s going on, there is an interpretation under which Cox’s statement is correct, except that it has nothing to do with the exclusion principle, and more importantly it gives a quite false impression to anyone who might be listening.

The other possibly relevant bit of physics is quantum entanglement and wave function collapse. This is usually the topic where people start talking about instantaneous changes throughout space, and we get mired in interpretive messes. Again, these concepts weren’t mentioned in this part of the lecture, and aren’t directly tied to the exclusion principle, but it’s worth discussing them.

...

[Chathamization]

16. There’s a pretty good discussion about it on Stack Exchange

http://physics.stackexchange.com/questions/18527/does-the-pauli-exclusion-principle-instantaneously-affect-distant-electrons

Mostly disagreeing with Cox. Yet another reason to proceed with caution when listening to these things.