@AccidentalFourierTransform On a more practical ground, they also led to the development of tools that were then applied in other contexts, such as the calculation of one-loop effective actions and other anomalies for QFTs in curved background space. (e.g. worldline formalism)
@ACuriousMind too long to explain here, but the issue is that if you are not very careful, your math can reflect certain assumptions about how information is obtained in the physical world, and those assumptions are not always physically realizable due to factors such as SR. I mention SR because any measure of length is also a measure of time.
@111: the direction of the field lines for an electric field is easily defined because it's the direction of the force they exert on an electric charge. The problem is that this doesn't work for magnetic fields because (as far as we know) there are no magnetic charges. Hence the rather convoluted definition.
@JohnRennie it's actually a funny image, which is why his more recent history makes it more disturbing. Kind of like one of those LMN movies my wife watches where someone's husband turns out to be a secret but very discrete ax murderer.
After a lot of Google and asking professors about the two quantization methods, I have learned that first quantization is what you use to quantize classical particles, while second quantization is what you use to quantize classical fields or a large number of classical particles.
If, according t...
First quantisation cannot accommodate pair-production, which is non-negligible at energies comparable to the mass of the particle. Therefore,
First quantisation only works for massive particles, and only in the range of energies that make motion non-relativistic.
Of course, this doesn't mea...
"We apologize for any inconvenience, but an unexpected error occurred while you were browsing our site. It’s not you, it’s us. This is our fault. Detailed information about this error has automatically been recorded and we have been notified."
@DanielSank While I agree with your basic sentiment that QFT and SR should for pedagogical purposes be seen as separate, I wonder where you get that impression from. Which questions receive answers that are "prejudiced toward relativity"? Keep in mind that many askers when they say "QFT" actually do mean "relativistic hep QFT".
@DanielSank I'm going to switch oddly on you, but I think it's related: I still find it fascinating that Dirac's ocean-of-electrons explanation of positrons is blithering nonsense in a continuous vacuum, but works incredibly well for explaining holes in semiconductors. It's like he was channeling/predicting solid state without understanding why or how.
*" I mean, you can to an extent, but it feels forced, the whole reason being Gauss' law forbidding a position eigenstate, but why does something similar not happen for other particles' fields?
I'm interested in why the localization problem applies to the photon and not to, say, the electron: Why can you (in principle) exactly locate an electron in space, if you can't do it for the photon? They are both fields, shouldn't they follow similar rules? Obviously they don't, so what is the difference?"*
@JohnRennie thx for Verlinde ref. (rats missed mtg.) have been hearing more about verlinde lately & was wondering what others think. think general concept of "emergent gravity" is important/ plausible shift in general & have long mused along those lines. quantamagazine.org/20161129-verlinde-gravity-dark-matter ... as far as "doing away with dark matter" its probably regarded as somewhat radical at moment...
@ACuriousMind ah, we are all in agreement that the concept of exact physical location of anything is non-physical, right? You can only drastically reduce wave packet sizes up to the wavelength of the probe used, but no further. Even calculating a true exact particle is non-physical, as it would require a computer within infinite memory.
@vzn I would love something like Verlinde's theory to start making real experimentally verified predictions. Suddenly quantum gravity would start making a lot more sense if GR was just an emergent theory. However we're still miles away from that goal. Don't get your hopes up yet.
@JohnRennie ok, fair point, but the paper essentially says there are (now) "real experimentally verified predictions" (albeit a "1st step")... agreed this could be a very long process, years at minimum, presumably over a decade... anyway nice to see a measurable advance along the lines... maybe a milestone already...
@DanielSank The problem is also that the first half is somewhat ill-defined - depending on your personal preference QFT is constructed from the elementary notion of particles a la Weinberg, so it's non-sensical to ask why it should be compatible with the particle interpretation
@JohnRennie (Hossenfelder is informative.) in general think physics is much more emergent than anyone realizes right now & will continue to go in that direction (emergence), think it still has some hangover from reductionism aka "looking under streetlight for keys because thats where the light is"... :|
I hope that I am using appropriate terminology. My confusion about quantum theory (beyond my obvious unfamiliarity with its terminology) is basically twofold:
I lack an adequate understanding of how the mathematics of quantum theory is supposed to correspond to phenomena in the physical world
@AccidentalFourierTransform Ah, see, that's the terminology problem here I think. "Second quantization" is, by those who think the term is useful, not used as equivalent to "quantizing a system with infinite degrees of freedom". See the answer Daniel posted and you'll see that.
@DanielSank Well, yes, that's what you call "second quantization". I was introduced to "second quantization" as "quantizing the wavefunction", i.e. promoting the solutions of the Klein-Gordon equation (the SE eq. analog in relQM) to operators, thereby "again" quantizing a theory that was already quantum. This usage is somewhat historical, but it still muddles the water when talking about "second quantization".
@ACuriousMind you've several times mentioned Weinberg's approach to constructing QFT starting with particles rather than the traditional free scalar field. Is there an informed amateur description of this available anywhere?
@AccidentalFourierTransform I don't either, I'm actually contra-Tegmarkian. I simply think that our real physical universe enables interesting and simplifying limits, which in turn makes the kinds of abstractions needed to enable computation (and so living organisms that compute for advantage, and what we call "real math") possible. And yes, that's both multi-verse-ish and anthropic.
@JohnRennie Not to my knowledge; the issue is that Weinberg very carefully has to develop a lot of group theory in the typical sloppy physicist's way in order to be able to classify the possible sorts of particles we can in principle have. After that, the construction of the actual free fields isn't that hard, you just build them as the transforms of the c/a operators on your Fock spaces.
@AccidentalFourierTransform In the classical vein of Wigner's "The unreasonable effectiveness of mathematics", I see
@JohnRennie The advantage is that you are not quantizing a classical theory. You start from a premise that the world is quantum and contains certain quantum objects we call particles and develop QFT purely from that and symmetry consideration + some locality.
@AccidentalFourierTransform It's silly to argue about what is and isn't intuitive because it's a personal thing. But we learm about (classical) fields from early days of science lessons. That makes it intuitive to me.
@AccidentalFourierTransform that's the anthropic selection part. You sort of can't be here to talk about it unless it's true, but it also makes the not-physically-accessible limits seem "more real" than they actually are. Computation e.g. works better if you don't assume precision first, and stop wasting cycles by tossing away results that never meant anything.
@JohnRennie in that case it becomes intuitive a posteriori, once you've solved the problem. It's like magic. In the end it works, yes. But in order to build the theory from scratch, it is not intuitive at all that fields might be useful in the end
Verlinde's theory of emergent gravity is a MOND derivation?? Wow, @JohnRennie, I've definitely got to take a closer look at that. Some of MOND data fitting needs explaining, even if there are other parts that are weak.
@JohnRennie I'm heading off now, but you caught my attention with that one. I happen to think that space is computational in nature, very much not a given... but why would that even be odd? Why would something as complex as space with isotropic real SO(3) symmetry be a "given", and not an emergent property of much simpler math?
@JohnRennie I should tell you about what happened to the US back in early November...
The following experiment is a simple one that can be tried at home. First pick up a ball in your hand and then release the ball above the ground. If you observe carefully you may see the ball moving closer towards the Earth. This is evidence of the mysterious gravitational force.
> German Baron Karl Drais von Sauerbronn invented an improved two-wheel version of the celerifere, called the laufmaschine, a German word for "running machine." The steerable laufmaschine was made entirely of wood and had no pedals. Hence, a rider would need to push his or her feet against the ground to make the machine go forward. Drais' vehicle was first exhibited in Paris on April 6, 1818.
The Mendip Hills (commonly called the Mendips) is a range of limestone hills to the south of Bristol and Bath in Somerset, England. Running east to west between Weston-super-Mare and Frome, the hills overlook the Somerset Levels to the south and the Chew Valley and other tributaries of the Avon to the north. The hills give their name to the local government district of Mendip, which administers most of the area. The higher, western part of the hills, covering 198 km2 (76 sq mi) has been designated an Area of Outstanding Natural Beauty (AONB), which gives it a level of protection comparable to a...
By the way @JohnRennie I didn't read that paper but I did note that most of the authors are from Dutch universities (some from the same as Verlinde) and thus it's highly likely that Verlinde checked with them and possibly fine-tuned based on their data before publishing his proposal. Therefore I don't find it a super convincing "check" of his theory.
I ordered some graphene off ebay to test on some applications and I am unable to get continuity.
I applied a layer of graphene on some two sided tape, made sure the adhesive was completely covered, then removed the excess with cello tape.
Is there something else you're supposed do to graphene...