I’m back. My holiday was wonderful, and I’m really glad I was without the Internet, e-mail and whatnot for about two weeks. Because of that, I have to catch up to what has happened over here. So far, nothing much to report, but I have a lot of work waiting to get done. In the meantime, I’ll send you to interesting stuff out there.
Bee discusses the dullness (or lack thereof) of modern scientists. In my opinion the statement “Most scientists are dull” is dead on. It is the same statistic of “Most people are dull”, but it does not really say scientists are more dull than other people. Of course, the interesting scientists are so interesting that they make it up for the rest. By the way, don’t take these comments seriously. I’m not well rested enough to make a real point.
On this topic, over at Cosmic Variance, there is a discussion on whether learning philosophy makes you a better scientist. Sure, learning anything extra makes you a better scientist. That does not mean that we should all go back to the middle ages and read Thomas Aquinas and revel in discussions about Kant, Hegel and all those guys with beards (and some without). I grew up in places where people really spent way too much time doing philosophy and science was dropped by the wayside because trying to sound deep was ‘cool’. I’m really not convinced that all this rhetoric is all that useful for science per se.
Clifford discusses fundamentals. Whether doing things that are `fundamental or not’ is that important. Lubos has a rebuttal. So what’s my opinion? Seems to me that this is a discussion about semantics and the proper usage of words. Using the ‘fundamental’ label seems to inspire religious feelings somewhere in my subconscious.
Also, here you have a new entry by Oswaldo Zapata. He discusses the topic of beauty (in science, and in particular in string theory).
In the meantime, Michael Jackson is dead, which seems to be more important than however many people have died in other places of the world in various riots, protests and wars (at least if you take into account how much press coverage there is of this event). Also, I found out that Billy Mays passed away very recently. I had just read an article about him in an airline magazine. My cats were happy to see me again after my holiday and I got some really good peaches in the market. Now, there is this workshop at the KITP on the interface between Condensed Matter Physics and Gravitational Physics in higher dimensions. With two talks per day, I will be very busy.
It’s not learning per se that will necessarily make one a better scientist – it’s learning about things you are PASSIONATE about that will make you a better scientist. If you’re not passionate about philosophy, but you start learning about it for the sake of being better, well, will you get that much out of it other than how to argue better (and when you only have a hammer everything looks like a nail).
If you start learning about it and *find* passion, that’s one thing.
For instance, when playing music more of your brain is active than when doing any other thing, even neuroscience or brain surgery. (This is your brain on music, http://www.brainonmusic.com). But if you don’t have the passion for it, will you get as much out of it as someone who does? When you have the passion for it, your amygdala lights up, your reward centers trigger, and you want MORE.
And that ravenous desire for more is what propels a person to true greatness, whether it’s world-shattering like Einstein and Hawking and Erdos or just personally touching like a great relative or friend.
And, of course, it all has to do with what you’re exposed to as a youngun. The brain tends to trim for brevity around the time of puberty, so if you don’t experience it young you are less likely to have an aptitude for it – not impossible, you just have to work harder for it. The brain likes predictability.
Hi Neko:
You misunderstand me… Philosophy is a lot of fun, but it usually does not really help in science (per se). My comment referred to people who prefer to do `philosophizing’ over science, even though they call what they are doing science and basically their actions prevent people from learning how to do science properly.
It’s nice to talk about philosophy of quantum mechanics, but for crying out loud, people need to learn how to calculate, not just talk about it.
Hi,
Just happened on your blog and was initially captivated by the name – ‘Diracseashore’.
I wonder if you have ever pondered (philosophicaly or mathematically) on the existence of this said ‘shore’.
Incidentally the picture portrayed looks very Aegean to me, which would be a tad ironic as this is where the whole Ionian birth of natural philosophy occurred.
Hi Des:
Nice of you to stop by. The picture is taken of Anacapa Island, near the coast of California.
The Dirac sea is by itself a very old fashioned way to deal with relativistic quantum mechanics of fermions (electrons for the most part). It is a relativisic version of the Fermi Sea and helps stabilize the system against electrons falling to ‘negative energy states’. This concept was replaced by modern quantum field theory, where there is no need to talk about the Dirac sea any longer. Instead, we have a vacuum, particles and antiparticles.
The hypothetical shore of such a sea would require some type of end of the world where the sea ends… so one would be breaking some of the symmetries of the relativistic system.
The reason why I chose the name is completely different. A shore of a sea is where you tiptoe into the sea without getting in too deep: you can have fun getting splashed by the waves but don’t have to commit to swimming in deep waters. As such, it is much more of an artistic concept than a philosophical one.
Oh, I see. So the shore is actually a Lorentz-breaking cutoff – at some large value of the 3-momentum – a limitation of the existence of negative-energy states of fermions in the vacuum? I am sure that the Dirac sea shore in this form doesn’t exist and it is bad science. 😉
I have thought that the shores you had in mind appeared in some ordinary setup with a nonzero density of fermions and the Dirac sea shore was just the Fermi surface for the holes. 😉
Hi Lubos:
I thought what you were describing was the Fermi surface: the boundary between sea and ‘air’.
Then again, a shore might be the boundary conditions of fermions on some brane, or the distortion of the Fermi-Dirac sea near the boundary of some graphene device.
For some unknown reason I’m hungry for fish right now 😉
I see you are busy but in a spare moment if interested.
Sean Carroll of Cosmic Variance, California Institute of Technology and David Albert-Columbia University
I thought not being of the trade that this talk might reveal a most appropriate stance in regards to science with regards to David Albert’s positioning of philosophy of science, while speaking with Sean. What do you think?
Best,
David, I think I’ve already mentioned this but again why these KITP talks are so badly recorded?
They are out of synchronization and you can’t follow what is happening in the blackboard. You can only listen the speaker which is not very helpful. It’s a pity because there are many interesting talks in KITP. Why can’t they fix this?
Hi Giotis:
I think fixing it well costs too much: you need ‘production staff’.
Most of the times if the talks are available as pdf files and one has the audio stream it kind of works. But I would not expect full synchronization.
If its a blackboard talk, all bets are off.
I rarely have the patience to see such talks online anyhow.
Hi David,
I like your artistic metaphor usage – there is another physical/mathematical aspect of shores that I’m sure you’re subconsciously alluding to; the fractal nature of shorelines. Even the simplest metaphor has hidden depths!!
Best Regards,
Des
Management is about process not product. Scientists are as dull as grant funding demands. Young faculty are starved because they might be wrong. Old faculty are gorged because they are guaranteed to discover nothing. Management seeks that perfect world in which every PERT chart, every spreadsheet, every business plan is mundane and zero-risk.
Mediocrity is a vice of the doomed.
Dear David, I was describing the Fermi surface and the Fermi surface is the boundary between the air and the sea!
The only other fact that is true but apparently ignored by you is the fact that there is no Fermi surface of the Dirac sea in the vacuum.
The occupied states – whose holes manifest themselves as positrons – exist on the full half-hyperboloid i.e. mass semi-shell with E<0, E^2-p^2=m^2.
So in the vacuum, there are no shores, no Fermi surface, and no boundary between air and the sea – and all of them are really the same thing. 😉
How do I know that? First of all, positrons in the high-energy cosmic rays exist at least up to the Planckian energy (coincidence…) so the hypothetical shore would have to be behind the Planckian "E".
But if there were such a shore, the vacuum would become unstable. At least if you really talk about the "air" behind the sea – i.e. unoccupied states. 😉 It would be energetically favored for Nature to fill the states in the air right behind the shores.
Even if you replaced the "air" by non-existent states (let me call it a vacuum, but it is a different vacuum than the complicated state in QFT!), one would get inconsistencies. Positrons with energies in the sea but near the shore couldn't be further accelerated by the electromagnetic field.
If you studied the theory describing positrons near the shores, you would get a contraction of your QFT which would be a nonrelativistic theory where the longitudinal momentum (transverse to the shores) is constrained to be positive for all excitations – an independent positivity theorem from the energy. Try to write down such a possible theory near the shores and embed the result in a theory that respects Lorentz invariance far from the shores.
At any rate, I think you will fail. This is a very stupid, qualitative way of breaking the Lorentz invariance, the kind of demagogic special relativity (DSR), and it's inconsistent with physics.
Huh?
I though the Fermi energy of the Dirac sea was exactly zero. All states below E_f are filled, and all states above E_f are empty. This is an old fashioned way of thinking, that as I said, was replaced by proper quantum field theory. It is useful in the theory of solids to think this way.
For a mockup of the relativistic theory, there is a band structure, so states between -m and m don’t exist: there is a gap. This vanishes for massless fermions, in which case one has arbitrarily small energy excitations.
Are we calling a surface of the Fermi sea a location where arbitrarily small energy excitations can occur?
There is such a Fermi surface for the theory of massless fermions in a ‘Dirac sea’ then.
Otherwise I’m rather confused by your statements.
Lets get this straight: I never said any such shore existed as a project in physics. Nor do I research on the possibility of such a shore. My comment was on trying to figure out what a definition of such a hypothetical shore would entail after a question was asked and trying to make some statements about it that make some semblance of making sense. By the way: I never said one had a hard UV cutoff or such. I was imagining one might have a spatial location where something might happen to the Dirac sea (the brane, so to speak) that one could call a shore.
Any such spatial prefered locus would break
translation invariance in at least one direction without the need for such a hard UV cutoff as you are describing.
I think we have a different ‘picture’ that we are visualizing in our heads and that is leading to this heated non-argument because my first description was rather vague and prone to misrepresentations. I completely agree that such a UV cutoff would be extremely problematic in the senses you are describing and that’s why I don’t go and pursue such an idea.
Dear David, although the differences can’t surely be that big, I think that one of us is confused about the meaning of these basic words such as Dirac sea and Fermi energy, and I think it’s not me.
The Fermi energy is normally defined as the highest energy of an occupied state, see http://en.wikipedia.org/wiki/Fermi_energy
So it can’t be zero because there are no states of electrons in the vacuum with E=0 because that couldn’t satisfy the mass-shell condition, E^2-p^2=m^2 with real E,p. The same is true for all massive fermions. And there are no strictly massless fermions in Nature, so let me omit this singular case.
According to the strictly applied conventional definition above, the Fermi energy for electrons’ Dirac sea in the vacuum is minus mc^2.
But this answer is meaningless because there is no Fermi surface so we shouldn’t be talking about Fermi energy. The Fermi surface is the boundary of the volume of occupied states in the momentum space. But the whole component with E being negative and with E^2-p^2=m^2 (the whole half-mass-shell) is occupied and this occupied region has no boundary, except for the boundary at infinity (with E equal to minus infinity). So there’s no Fermi surface and it is meaningless to talk about the Fermi energy.
So the Dirac sea, which always refers to the in-vacuum relativistic solutions for massive fermions, see http://en.wikipedia.org/wiki/Dirac_sea , has no shores.
Your idea to make the Dirac sea space-dependent is new and was not mentioned previously but I think it is a no-go idea, too. It seems to neglect the uncertainty principle and the continuity of the laws of physics. The Dirac sea – and the Fermi surfaces – are located in the momentum space. The density of states is V/h^3 per unit volume in the momentum space.
If you want to study the Dirac sea’s shape with accuracy better than “m” in the h=c=1 units, you can’t distinguish distances of order 1/m, the Compton wavelength and the spectrum of states near the hypothetical “shore” would still have a discrete and continuous component.
The continuous component would have to exist in the same interval without the shore, while the discrete component could indicate additional and/or missing states at the very locus of the brane. The only “deformations” due to the brane can be new (or perhaps missing) states stuck at the codimension-q locus in space. But that’s something different than a domain wall that could be called a “shore”.
In other words, I think that there can’t be (spatial) domain walls in physics behind which states suddenly disappear, like in a qualitative change of a Dirac sea. The gravitons exist behind this domain wall, by definition (because there’s space over there), and I think that this means that all other bulk excitations must exist there, too. If you think otherwise, do you have a counterexample (where modes of gravitons exist in a region but excitations of other particles locally disappear or otherwise qualitatively change)? It would be interesting. I think that such a singularity would really mean a discontinuity in the laws of physics and can’t be obtained from anything like a soliton or any generalization of it I can imagine.
Lubos:
Fine you win.
I don’t have the patience for this type of argument right now.
Classic Lubos Motl: a simple joke has to be turned into a long boring diatribe against his physics enemies. Next Prof Berenstein will be accused of being a crypto-communist for thinking that all positrons are equal.
Back in the real world: that string/condensed matter conference looks absolutely fascinating. We would all be very grateful if Prof B. could find some time to make some comments on the talks he hears!