[HN Gopher] What is quantum field theory and why is it incomplete?
___________________________________________________________________
What is quantum field theory and why is it incomplete?
Author : digital55
Score : 81 points
Date : 2022-08-11 14:16 UTC (3 days ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| kloch wrote:
| I suspect it's an approximation of much lower level deterministic
| processes that we don't understand yet.
|
| One serious issue is renormalization, a crude mathematical hack
| that nobody likes but has turned out to be a very useful
| workaround to our limited knowledge.
| tines wrote:
| Pretty sure it's been proven that no deterministic theory can
| reproduce all the predictions of quantum mechanics. That's the
| essence of Bell's theorem isn't it?
| drunkpotato wrote:
| The two explanations or interpretations I've come across that
| recover determinism are many worlds interpretation and
| superdeterminism. I don't think either are testable with
| current technology so it's not a very satisfying or
| experimentally useful explanation. At least not yet.
| kloch wrote:
| From wikipedia:
|
| > Consequently, the only way that hidden variables could
| explain the predictions of quantum physics is if they are
| "nonlocal", which is to say that somehow the two particles
| were able to interact instantaneously no matter how widely
| the two particles are separated.
|
| It's true that with our current theories, instantaneous
| action at a distance does not seem possible. Yet quantum
| experiments (wave function collapse over large distances)
| consistently suggest this might be possible at macro (non-
| quantum) scales. I think our knowledge is incomplete on this
| topic.
|
| Gravity is another area where I don't think non-local effects
| have been fully ruled out. Gravitational waves (energy
| emitted/thrown off by certain mass/momentum configurations)
| have been proven to travel at or near the speed of light, but
| the propagation speed of the first order gravitational
| effects an open question. This is an area I would love to see
| more experimentation done. To simultaneously measure the
| gravitational and optical positions of the Moon or Sun for
| example.
|
| https://en.wikipedia.org/wiki/Speed_of_gravity
| hprotagonist wrote:
| if you have instantaneous action, you no longer have
| causality.
|
| squaring that circle seems, uh, fraught.
| zmgsabst wrote:
| Sure you do -- but space no longer looks like the 3+1D
| hologram we see.
|
| Also, doesn't entanglement already punch that hole? ...in
| which case, assuming non-locality is the minimal
| assumption.
| thfuran wrote:
| >Also, doesn't entanglement already punch that hole?
|
| How so?
| russdill wrote:
| Unless the action can only have effects that do not
| effect causality and can only be "observed" once there is
| a casual connection.
| feet wrote:
| Unless they're acting on each other through another
| euclidian dimension that we can't currently perceive in
| our three dimensional perspective
| thfuran wrote:
| How could there be a higher dimensional, shorter path
| between the points?
| feet wrote:
| Why does the path have to be shorter?
| akomtu wrote:
| Wolfram speculated on this idea: if spacetime is a graph,
| it may approximate the 3+1 topology on average, but in
| some places two distant nodes can be connected by a
| direct link. I'd speculate further that such isolated
| links may be enough to entangle low-level quantum
| properties of two particles, but not enough to be a
| tunnel even for a single photon.
| thfuran wrote:
| That would not be a euclidean space.
| eurasiantiger wrote:
| Depends on the frame of reference.
|
| From the viewpoint of an electron, the moment it is
| emitted from an antenna as a photon and the moment it is
| absorbed in another antenna as an electron _are the same
| moment_ i.e. the photon travels zero distance in zero
| time.
|
| Somehow our communications equipment still maintains
| causality.
| fsh wrote:
| Antennas do not emit or absorb electrons at all. Radio
| waves propagate at most at the speed of light.
| eurasiantiger wrote:
| What? I never claimed that. Radio waves are
| electromagnetic radiation just like visible light.
|
| Radio amplifiers pump electrons into the antenna, which
| transmits them as photons, and the receiving antenna
| absorbs them, turning them into electrons, the flow of
| which then becomes the audible radio signal which gets
| (demodulated and) amplified by the receiver.
|
| The photons do not travel any distance and they do so in
| zero time. This can be mathematically proven.
|
| See e.g. https://phys.org/news/2014-05-does-light-
| experience-time.amp - the relevant parts:
|
| "The closer you get to light speed, the less time you
| experience and the shorter a distance you experience. You
| may recall that these numbers begin to approach zero.
| According to relativity, mass can never move through the
| Universe at light speed. Mass will increase to infinity,
| and the amount of energy required to move it any faster
| will also be infinite. But for light itself, which is
| already moving at light speed... You guessed it, the
| photons reach zero distance and zero time.
|
| Photons can take hundreds of thousands of years to travel
| from the core of the Sun until they reach the surface and
| fly off into space. And yet, that final journey, that
| could take it billions of light years across space, was
| no different from jumping from atom to atom."
| scatters wrote:
| Electrons are not transformed into photons; that would
| violate conservation of lepton number. Rather, an
| electron is accelerated by the antenna and as it
| accelerates it emits a photon. The electron still exists
| with the antenna afterward, with a lower energy.
| raattgift wrote:
| Under your conception, how does RADAR work? Consider
| bouncing a RADAR signal off two objects at different
| distances (1 m, 10 m; or the Moon and Venus [1] when the
| two are very close to each other in the early evening or
| early morning sky). Do the RADAR reflections return
| instantly, or at the same time, or at different times,
| according to the wristwatch of the RADAR operator, or the
| RADAR apparatus's computer clock? How does that work with
| your comment, "the photons do not travel any distance and
| they do so in zero time. This can be mathematically
| proven."?
|
| Can we agree that each of the RADAR and the two RADAR-
| reflecting objects definitely occupy different points in
| space?
|
| - --
|
| RADAR images (taken at e.g. Arecibo, here on Earth) of
| Venus, the Moon, and several other solar system bodies
| <https://www.naic.edu/~pradar/radarpage.html#venus>
| tines wrote:
| I believe the gp is correct, the closer you get to the
| speed of light the slower time passes. If a particle
| travels at the speed of light, no time passes for it.
| raattgift wrote:
| You're part-way there. First I'll explain how it works in
| standard textbook relativity, then I'll reword your first
| sentence a bit.
|
| p != p' are two points on a 3+1 dimensional Lorentzian
| manifold (M, g), modelling our spacetime.
|
| There is a minimizing geodesic from p to p', the
| "shortest straight-line path".
|
| In a Lorentzian spacetime, geodesics are classified into
| three groups: spacelike, null, and timelike. A null
| geodesic describes the freefall of the massless
| relativistic wave equation, which applies to e.g. photons
| (as the Maxwell equations using the Lorenz gauge); and a
| timelike geodesic describes the massive relativistic wave
| equation, which applies to e.g. neutrinos (as the Dirac
| equation) or the Higgs boson (as the Klein-Gordon
| equation). In a particle paradigm, photons move at c
| freely falling on null geodesics; neutrinos, electrons
| and so forth move at less than c freely falling
| (experiencing no accelerating force) on timelike
| geodesics.
|
| If p and p' are _timelike-separated_ , they can be
| connected by a timelike geodesic (e.g., a path that could
| be taken by a massive particle), then we can calculate a
| nonzero spacetime interval S in some coordinate basis,
| and divide by c, giving us the proper time \tau such that
| d\tau = dS / c in a patch of flat spacetime (the metric g
| enters into the definition through general curved
| spacetime: on path P, \Delta \tau = \int_{P} 1/c
| \sqrt{g_{\mu\nu} dx^\mu dx^\nu (= \int_{P} d\tau), which
| is invariant under changes in coordinates, and has the
| same problem with dividing by c.
|
| However, if spacetime points p and p'are _lightlike-
| separated_ , they cannot be connected by a timelike
| geodesic, but rather by a null one. The spacetime
| interval of a lightlike geodesic is defined such that dS
| = 0 (thus the name "null").
|
| Any path through spacetime can be parametrized by
| applying arbitrary labels to its points. A geodesic is a
| species of path. We can label any geodesic from A to B
| any way we like: Apple Zebra Xray 3.1415 1 86 Xray-again
| Manitoba Xray Xray-again ... 911. Arbitrary labellings
| are not widely useful, though, so we will probably want
| to label every point with a _unique_ value in such a way
| that there is a total ordering from A to B, and even more
| ideally so that there is some smooth monotonically non-
| decreasing function f on the geodesic, mapping all its
| points to unique values of the parameter.
|
| Proper time is just such a useful function on a timelike
| geodesic. It is not the only such function.
|
| On a null geodesic, proper time would give us a labelling
| 0 0 0 0 0 ... 0, which is obviously not useful, as the 0s
| aren't unique or ordered. However, we can use any
| monotonic function, setting out labels at every point
| along the path from p to p' where we would (if we
| measured) detect the photon.
|
| A good choice for a null geodesic is the _affine
| parameter_ , as that preserves the photon's tangent
| vector under parallel transport along the path. There is
| a unique affine parametrization satisfying the geodesic
| equation for every geodesic, including every null
| geodesic.
|
| One of the properties of the affine parameter on a null
| geodesic is that we can define a momentum k^{\mu} =
| \dot{X}^{\mu}, the dot representing the derivative with
| respect to the affine parameter -- the momentum k can be
| calculated at every point on the null geodesic, and in a
| curved spacetime k will _differ_ from point to point.
| This difference in momentum is exactly the gravitational
| redshift.
|
| So, it might be better to say: _proper time_ is an
| unsuitable parameter for a photon in free fall, or for
| labelling points on its path from point A to point B.
| Instead we can use _affine time_ (== the affine
| parameter) for a photon and for its path from point A to
| point B, and see that there is some definite timelike
| parameter for a photon on its journey that can [a] show
| where in spacetime it can be found during that journey
| and [b] what its momentum is at [a] and thus what its
| frequency, wavelength or energy is at [a] via the E =
| h{\nu} = \frac{hc}{\lambda} relation, and how those
| quantities change along the path in the presence of
| spacetime curvature.
|
| I would not say "no time passes for it", because we can
| always define such a time. Affine time is one such
| (useful) definition, but we can use any others we like.
| Although a proper time can be calculated for such a
| massless particle, the proper time is 0 everywhere, so
| not very useful. However that does not strictly speaking
| mean that there is no passage of time from the point of
| view of the photon. It just needs to "wear a different
| sort of wristwatch" than an electron might choose to.
| However there is an affine parameterization for an
| electron moving between points I and J, so electrons (and
| neutrinos and other non-massless waves, particles, or
| objects) can always "wear the same sort of wristwatch" as
| a photon. (Some mathematical details in Wald's graduate-
| level textbook _General Relativity_ SS3.3 and see ch. 3,
| problem 5).
| eurasiantiger wrote:
| It is not "my conception", it is scientific fact.
|
| From the frame of reference of a transmitted photon, the
| transmission is instantaneous, and the spatial distance
| traveled is zero.
|
| From our perspective, it is a different story. If you are
| having difficulty grasping this, perhaps you are thinking
| that photons are like tennis balls but with a very high
| velocity. Perhaps you even entertain the sci-fi notion of
| faster than light travel.
|
| However, speed of light in a vacuum is a much more
| fundamental limit than an inherent velocity limit of some
| particle.
|
| It is essentially the default propagation speed of all
| physical information. Interaction of light with matter
| causes absorption and re-emission of photons, which
| causes light to both slow down in a medium and pick up
| some information about whatever it went through.
| raattgift wrote:
| > it is scientific fact
|
| ...
|
| > If you are having difficulty grasping this
|
| I don't think I am. Compare my longer comment in this
| thread <https://news.ycombinator.com/item?id=32462046>
| which makes reference to Wald's standard textbook. It's
| not just Wald - any standard textbook will agree. I can
| give you chapter references for practically any of them
| if you like.
|
| What I was wondering was how you reconcile the difference
| in time at a RADAR station when receiving photons bounced
| off targets at different spatial distances with, quoting
| you, "the photons do not travel any distance and they do
| so in zero time".
|
| Surely time passes at the RADAR transceiver? Otherwise,
| wouldn't we get instant returns back from the Moon and
| Venus, instead of having to wait seconds to minutes?
|
| A broader question might be, "is there a 'best' clock for
| analyzing a RADAR detection, and if so, which clock?".
|
| Finally, you might want to wonder if an in-flight photon
| changes spin states or frequency. Doesn't a RADAR photon
| bouncing off a moving target (or returning to a moving
| transceiver) undergo a doppler shift, and thus change of
| frequency? How do police RADAR guns work if photons do
| not feel time?
|
| It strikes me that you didn't care to answer my earlier
| RADAR questions at all among your five paragraphs in
| reply. If you don't care to do so, or you don't want
| think about any of this, that's fine. But I think you
| should take care in judging how much or how little anyone
| on hackernews might know about relativity, or what ideas
| about sci-fi-like-concepts they might entertain.
| akomtu wrote:
| I've read somewhere that photons, while travelling,
| casually turn into electron-positron pairs and back to
| photons. It's quite possible that both are just
| distortions in the magnetic field.
| immmmmm wrote:
| Gerard 't Hooft would disagree
|
| https://arxiv.org/abs/quant-ph/0212095
| auntienomen wrote:
| Renormalization hasn't been a conceptual problem since Ken
| Wilson's work in the 1970s. Before that, it looked like a
| mathematical hack (rather like linear algebra without the
| geometric interpretation) and a lot of physicists who came of
| age in the postwar period never got over this.
| bowsamic wrote:
| > I suspect it's an approximation of much lower level
| deterministic processes that we don't understand yet.
|
| All current evidence heavily leans towards this not being the
| case
| zmgsabst wrote:
| What evidence do you believe shows that?
| bowsamic wrote:
| Basically that non-local hidden variables and
| superdeterminism do not seem like likely solutions to the
| violation of Bell's inequalities compared to just accepting
| that nature is random. You have to do a fair amount of
| reaching in order to hang onto the notion that the universe
| is deterministic
| zmgsabst wrote:
| Except that we know entanglement is non-local: this
| suggests that non-locality rather than non-determinism is
| the correct resolution to Bell's inequalities.
|
| Non-determinism is an extraneous assumption if we're
| forced to accept non-locality for other reasons.
|
| Edit:
|
| I've hit my posting cap, so replying in edit --
|
| If we know particles are entangled and subject to non-
| local effects, we're already concluding that there's a
| hidden non-local variable: the sum of all entanglements
| we don't know about.
|
| You can model that as a randomness distribution for
| calculations, but that doesn't make the universe non-
| deterministic.
|
| Edit 2:
|
| I think where we diverge is in the belief you're
| measuring "nothing" and so it's strange you're getting
| slightly varying results. I'll have to think about that
| aspect some more.
|
| I'll leave off here with a big thanks for giving such
| detailed replies!
| bowsamic wrote:
| Except non-local deterministic theories are much more
| complicated and almost impossible to use. That's why a
| lot of physicists regard the result as showing that
| reality is both non-local and non-deterministic. Very few
| suspect a non-local hidden variables theory.
|
| I think that non-determinism would be an extraneous
| assumption given the fundamental randomness apparent in
| quantum measurements. In my opinion, hidden variables are
| something extra to add to take account of this, and
| indeed it's very difficult to use Bohmian mechanics with
| relativity etc.
| bowsamic wrote:
| (replying to the edit) It's still just very unlikely. My
| work is based around reducing the fundamental quantum
| noise in gravitational wave detectors. This is the noise
| that arises from the following process: if you set up
| many copies of an experiment where you measure the
| electric field E in the vacuum state |0> (no photons) you
| will get a spread of results around E = 0. This is
| actually the largest noise affecting advanced
| gravitational wave detectors such as LIGO at their most
| sensitive frequencies (the classical noise sources have
| been reduced so much).
|
| If I have a situation where I take the quantum vacuum and
| get a different, random result every time I measure it,
| it seems like quite a stretch to conclude that it is
| _really_ deterministic.
|
| Further, if quantum states are described by wave
| functions then they must be intrinsically random due to
| the mathematics of the Fourier transform.
| photochemsyn wrote:
| There's a very good book on quantum physics, published in 1978,
| by PCW Davies, called 'The Forces of Nature', which discusses
| most of this in nice detail. One gets the sense that not a whole
| lot of new physical theories have been confirmed since this book
| was published.
|
| For example, the renormalization problem:
|
| > 'Fortunately the problem of infinite self-energy can be
| overcome... Manipulating infinte quantities requires some
| mathematical care, but it can be proved that all <observable>
| quantities are finite. The technique, developed in the 1930s and
| 1940s, of absorbing infinities into unobservable 'bare'
| quantities to get a finite answer, is called _renormalization_.
| It may appear like a trick, and nobody pretends that it is
| completely satisfactory, but without renormalization the
| predictive power of quantum electrodynamics would disintegrate.
| With it, the answers obtained have the legendary accuracy already
| described. '
|
| According to this book, the problems with renormalization are
| much more severe with weak interactions:
|
| > 'The renormalizability of QED can be traced directly to the
| masslessness of the photon. Like all massless particles that
| spin, it can direct its spin either parallel or antiparallel to
| its direction of motion, but not in between as well. In contrast
| the massive W can align its spin in _three_ different directions,
| for example, parallel, antiparallel and perpendicular to its
| motion. This seemingly innocuous property is the cause of all the
| difficulty, because it turns out it is the W particles with the
| perpendicular spin directions that prevent the infinities from
| being renormalized away. "
|
| > "These observations suggest that if the W particle were
| massless, it might be possible to construct a unified
| renormalizable theory of weak and electromagnetic interactions in
| which the photon and W are combined, like the hadrons, into a
| single family."
|
| Notably there's no mention of the Higgs boson in this book, which
| is nevertheless remarkable in how it covers the background of
| almost every physics story I've come across for years. However,
| is this basically the entry point to why the Higgs boson is
| important? For example:
|
| https://en.wikipedia.org/wiki/Electroweak_interaction
|
| > "In the Standard Model, the W+- and Z0 bosons, and the photon,
| are produced through the spontaneous symmetry breaking of the
| electroweak symmetry SU(2) x U(1)Y to U(1)em, effected by the
| Higgs mechanism (see also Higgs boson), an elaborate quantum
| field theoretic phenomenon that "spontaneously" alters the
| realization of the symmetry and rearranges degrees of freedom."
| syspec wrote:
| Accompanying podcast:
| https://pca.st/episode/af3ea556-c30b-4784-a901-404f7b8c03e5
| jmyeet wrote:
| This transcript doesn't mention it specifically but the most
| accurate prediction they're referring to is likely the anonalous
| magnetic dipole moment of an electron [1] where theory matches
| experimental value to at least 10 significant digits. The article
| talks about 12 decimal places so maybe they're referring to
| somethign else?
|
| At the other end of the spectrum is the s-called _vacuum
| catastrophe_ [2] where the predicted and actual values for the
| energy density of a vacuum diverge by as many as _120 orders of
| magnitude_.
|
| As for the incompleteness of QFT, this is well beyond my
| knowledge. I really wish this were an article instead of a
| transcript though. Transcripts are such poor means of conveying
| information.
|
| [1]:
| https://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_mome...
|
| [2]: https://en.wikipedia.org/wiki/Cosmological_constant_problem
| analog31 wrote:
| One sleight of hand is to write down g instead of g-2, in which
| case you pick up a couple more digits but haven't added any
| useful information because the value of 2 is already known.
| Eupraxias wrote:
| I would love to hear any critical take on David Tong's excellent
| video here: https://www.youtube.com/watch?v=zNVQfWC_evg "Quantum
| Fields: The Real Building Blocks of the Universe"
|
| I'm interested to talk to others who want to think about QFT past
| the maths. I had my own stab at making sense of related
| ontological implications here:
| http://www.katabane.com/mt/ontology.html#back8
| nyc111 wrote:
| "And cells, in turn, are made of molecules and molecules are made
| of atoms. Dig even deeper and pretty soon you'll find yourself at
| the level of electrons and quarks. These are the particles that
| have traditionally been considered to be the end of the line, the
| fundamental building blocks of matter."
|
| To me, the so-called "the end of the line" is a philosophical
| question not a physics question. For the simple reason that, we
| can never know, if something is really indivisible, or if we are
| unable to divide it because of our insufficient technology. We
| can never know this. The story of physics makes this clear. Each
| generation of physicists with new techology available to them
| take pride in showing that the previous generetion was lying, and
| that it is their atoms which are the real "end of the road". Then
| comes the next generation with a better technology...
| eurasiantiger wrote:
| To paraphrase Tesla, fundamental answers will elude us until we
| decide to abandon the particle model.
| peteradio wrote:
| Was this said prior to the formulation of modern QFT? I imagine
| Tesla would agree that QFT is the thing to be done to add
| waviness to the particular questions we humans like to ask,
| although he didn't exactly believe in the concept of electron,
| maybe he would see its formulation in QFT and say yes?
| eurasiantiger wrote:
| I think Tesla would still object to seeing quantum phenomena
| through such a classical lens. It is very much "not seeing
| the forest for the trees".
|
| In fact, Tesla might even object to the usage of the word
| "quantum", since it implies that same top-down view. Tesla
| would start from the field(s) and let whatever phenomena
| emerge from that, quantized or not.
| fsh wrote:
| Tesla may have been a capable engineer in his early years
| (before turning into a crackpot and/or fraud). However, his
| understanding of modern physics appears to have been extremely
| poor. He certainly has not contributed anything significant to
| the field.
| immmmmm wrote:
| Still the basis of the most precise prediction by a Physics
| theory:
|
| https://physicstoday.scitation.org/doi/10.1063/PT.3.2223
|
| I'm always amazed by quantum field theories, with a particular
| taste for the two dimensional ones (as string theorist :))
| formerly_proven wrote:
| Also the basis of the least precise prediction made by a
| physics theory:
| https://en.wikipedia.org/wiki/Cosmological_constant_problem
|
| > Depending on the Planck energy cutoff and other factors, the
| discrepancy is as high as 120 orders of magnitude
| immmmmm wrote:
| yes and no. physical theories always have a domain of
| validity where their prediction make sense and QFT and QM do
| not give an _absolute_ value of energy (density). sure you
| can do QFT on curved spacetime (Hawking had some success w /
| it) but comparing the QFT vacuum energy with the cosmological
| constant is sloppy at best.
|
| but yeah, sure, it doesn't work for that :)
| westurner wrote:
| And then what about fluids? Are there other descriptions
| for things that look like that?
|
| TIL superfluids have zero viscosity; and at that scale,
| galaxies are supposably superfluidic; at least one
| formulation of "superfluid quantum gravity" has Bernoulli's
| && GR and it supposably works.
| nobodyandproud wrote:
| This Q&A was extremely understandable.
|
| I really enjoyed how he broke down why the Standard Model--as far
| as we can tell--cannot be made mathematically rigorous.
| andrew_eu wrote:
| Probably the highest point in my physics "career" was when my
| advisor recommended Quantum Field Theory for the Gifted Amateur
| [0] to me. It was after I had basically decided to abandon hope
| at academia and become an engineer, but I was just barely past
| the threshold of being able to understand the contents. I worked
| through the book solo and really greatly enjoyed it; highly
| visual and well paced. I'd recommend it to any undergrad+ who has
| made it past bra-kets and wants to see how far the rabbit hole
| goes.
|
| [0] https://www.goodreads.com/book/show/18781406-quantum-
| field-t...
| sigmoid10 wrote:
| Another great book at that level is _Student friendly Quantum
| Field Theory_ by Klauber. Especially if you struggle with the
| incomplete math treatments in standard books like Peskin &
| Schroeder, where the first chapter basically assumes you
| already know all the weird complex contour integrals that you
| usually only encounter in QFT. If Klauber says "from this
| easily follows ..." then you can expect to understand it even
| if you're not yet an expert. Ofc that comes with less depth in
| total, but there's no point in talking about renormalization if
| you haven't understood field quantization.
| daniel-cussen wrote:
| I second the sentiment, that working through a book is the
| absolute best education. I worked through many.
|
| I copied down all the code in ANSI Common Lisp and answered all
| the questions in the book explicitly, wrote down my answers and
| everything. Except for the object-oriented part which the
| author says not to read. Says it was a requirement for the book
| in the 90s, he didn't want to include it. I didn't read it on
| his advice. That book also includes cryptic objections to
| political correctness, in a simulation you're supposed to run
| about a contest in an alien race that always ends in a tie or
| near-tie. The simulations the book proposes reveal equality of
| outcome in these contests is due to manipulation. You don't get
| even representation from fair contests. Whereas university
| admissions in general do end up with a lot of "underrepresented
| minorities"--and this Daniel Cussen saying that, my torturer
| said that I'm a "minority of one"--but the ties and near-ties
| are because of fixing. The game is rigged.
|
| But a book! That is an education! Then I attended Stanford and
| it was like, what is this shit? I gotta cheat to pass, the
| fuck? If you say I can't cheat and then you say I can cheat in
| a specific manner, eg asking a TA for all the answers, what do
| I do? My Chilean logic says, if they say you can't and say you
| can, you can't. Same rules as Magic: the Gathering, negative
| prevails over positive--and it's a matter of integrity, there's
| reasoning for this, both in Chile and in Magic, it makes
| perfect sense to me. Basically it's conservative. Not
| "negative" in the pejorative sense.
|
| Hell, weight loss is negative, is it bad to lose fat? Fatness
| is positive, bigger number on the scale. Why is negativity
| worse? Further I'm in the Southern Hemisphere, the negative
| hemisphere, there's a physical definition for its negativity.
| Is this wrong? Does negative magnetism translate to negative
| morality, which I truly do recognize as wrong? Manicheanism,
| yes, right is positive wrong is negative. I basically buy that.
| But with all physics? And of course technically positive
| current is incorrectly defined, it should be the other way
| around, electrons are what moves so they should be positive.
|
| Stanford I guess thinks _can_ prevails over _can 't_, should go
| over that in orientation. There shouldn't be contradictions
| like this in the first place, though. Admitted students have to
| be able to pass all courses without any cheating. I guess
| that's where I fucked up. Getting myself lobotomized, guess I'm
| no longer Stanford material despite having already been
| admitted.
|
| No longer have the brains. Literally no longer having the
| brains. That's literally it.
|
| But Stanford refused to protect me from lobotomy, I kept
| telling them how much harm I would go through, crying in my
| lynching meeting on February 6 2009, begging for a trial and
| always getting denied, going to every office I could, writing
| emails nobody gave any replies in writing to, telling my whole
| dorm I was getting lynched (apparently nobody does this).
| Stadmin only pushed me further into that system, jammed me
| further into the meat grinder. Meat grinder. Think of it like a
| blender, what happens to meat that goes in? Does it retain its
| shape? No it gets diced right?
|
| Just watched gloatingly as I got put through the system.
| Watched with relish. Young white man getting lynched. That is
| the consummation of the Civil Rights Movement, young white man
| getting lynched. It's not as platonic, abstract and noble as it
| pretends to be. White is negative. Young white man getting
| lynched? Justice.
|
| But back to my point: the book. It used to be, before
| universities monopolized annointing the intelligent as such,
| that it wasn't about going to the right schools. It was about
| being well-read. Universities didn't exist before AD 1000,
| University of Bologna. And even then it started slow.
|
| Books are better.
| m_a_g wrote:
| My undergrad is in Computer Science and Engineering, but I
| would love to read and understand this book. Any
| recommendations for what to know beforehand? Some prerequisite
| books or subjects, maybe?
| mhh__ wrote:
| If you have a talent for manipulating symbols before really
| understanding them, only a little bit of quantum mechanics.
|
| Realistically an undergraduate physics education
| andrew_eu wrote:
| It's been a while now since I've picked it up, but I think
| the main content it assumes your comfortable with is on the
| order of a semester of Quantum Mechanics. Otherwise, it
| definitely uses quite a few tricks in calculus (e.g.
| integrating probability amplitudes, variational calculus, and
| likely some higher dimensional stuff). The later chapters
| probably get even more exotic, but the book prepares the
| reader pretty well I think.
|
| For book recommendations, the ones that come to the top of my
| mind are:
|
| - Griffiths' Quantum Mechanics [0]. It's become a pretty
| standard undergrad QM text, and in my experience was very
| approachable.
|
| - Div, Grad, Curl, and all that by Schehey [1]. I don't
| remember how much into vector calculus the QFT book got, but
| this one turned the tide of my undergrad personally. For ~120
| pages it gave me a better intuition with 3D calculus than any
| other resource.
|
| - Something that covers calculus of variations, Euler-
| Legrange equation, etc. I first covered this in Classical
| Mechanics but don't remember the textbook. The Feynman
| Lectures of Physics [2] probably covers it, but I don't know
| for certain. Incidentally, Feynman is all over QFT, so his
| undergrad materials are probably excellent prep materials.
|
| I don't remember whether the book introduces bra-kets (Dirac
| notation) or assumes them, and I don't remember if Griffiths
| uses it at all. I first saw this notation in General
| Relativity, with Spacetime and Geometry [3], but I think
| there are definitely better materials that can explain the
| notation better.
|
| I'm pretty sure all of these books, and plenty more on these
| topics, should be widely (or freely) available. Good luck :)
|
| [0] https://www.goodreads.com/book/show/153908.Introduction_t
| o_Q...
|
| [1] https://www.goodreads.com/book/show/703104.Div_Grad_Curl_
| and...
|
| [2] https://www.goodreads.com/book/show/5546.The_Feynman_Lect
| ure...
|
| [3] https://www.goodreads.com/book/show/259680.Spacetime_and_
| Geo...
|
| Edit: newlines always get me
| funklute wrote:
| The Feynman lectures have a reputation for being very hit
| and miss. People who "get it" will find them really
| interesting and useful. But if you don't, then it might
| just confuse you.
|
| I know a condensed matter postdoc who told me he felt ready
| to tackle the Feynman lectures only after he had completed
| his phd....
| zinclozenge wrote:
| They're a great companion book, but you really need a
| book that guides you through derivations and
| computations. Some techniques are non-obvious like
| choosing coordinate systems to make integrals easier,
| clever contours when applying residue theorem, change of
| variables using orthogonal matrices to diagonalize
| symmetric matrices, etc.
| jasomill wrote:
| _Something that covers calculus of variations, Euler-
| Legrange equation, etc. I first covered this in Classical
| Mechanics but don 't remember the textbook. The Feynman
| Lectures of Physics [2] probably covers it, but I don't
| know for certain._
|
| Indeed it does:
|
| https://www.feynmanlectures.caltech.edu/II_19.html
|
| The original lecture recording is also available:
|
| https://www.feynmanlectures.caltech.edu/flptapes.html
| daniel-cussen wrote:
| Caltech is fantastic. They even have the old-form domain
| name there in your links, similar to Stanford CS
| department which is also exceptional in the nomenclature,
| but grandfathered in.
| kbr- wrote:
| > There is a mathematical theorem that forbids you from writing
| down a discrete version of certain quantum field theories.
|
| > (...)
|
| > You know, if you take this theorem at face value, it's telling
| us we're not living in the Matrix. The way you simulate anything
| on a computer is by first discretizing it and then simulating.
| And yet there's a fundamental obstacle seemingly to discretizing
| the laws of physics as we know it. So we can't simulate the laws
| of physics, but it means no one else can either. So if you really
| buy this theorem, then we're not living in the Matrix.
|
| I don't buy this reasoning.
|
| I can encode the continuous function f(x) = x^2 on a computer.
| Then I can calculate this function for any number up to any
| digit, if I allocate enough memory.
|
| I don't need to allocate a discrete domain up-front and then
| stick to it at all times. I can increase and decrease the
| accuracy as needed.
|
| In a similar fashion I could simulate a continuous universe
| encoded with continuous operators. I could simulate it on a
| discrete lattice with certain precision as long as nobody inside
| the simulation builds equipment that can measure things "in-
| between" the lattice points. And when somebody does, at that
| moment, I can simply pause the simulation, calculate the values
| of my operators using a locally-denser lattice, then unpause. The
| observer with their equipment wouldn't notice anything because
| the simulation was paused, they would just get the correct
| measurement.
| blueprint wrote:
| What theorem is he talking about though?
| kbr- wrote:
| > The theorem is called the Nielsen-Ninomiya theorem. Among
| the class of quantum field theories that you cannot
| discretize is the one that describes our universe, the
| Standard Model.
| blueprint wrote:
| ah. it talks about issues with putting fermions with spin
| on a lattice. there's more to fermions than a continuous
| exponential function though! :)
| [deleted]
| atty wrote:
| The point is that it can't be simulated on any lattice of any
| density. It doesn't matter how fine the lattice is compared to
| the sensitivity of the measurement. For your case you showed,
| it would be like if x^2 simply didn't exist on a lattice, and
| couldn't be calculated by a computer no matter how much memory
| you threw at the problem.
|
| Certain parts of QFT work fine in lattice based calculations
| (lattice-QCD, for instance, where it's simulated on a certain
| lattice scale, and then extrapolated to the continuous limit),
| and some seemingly don't work at all.
| kbr- wrote:
| > The point is that it can't be simulated on any lattice of
| any density. It doesn't matter how fine the lattice is
| compared to the sensitivity of the measurement.
|
| It feels like you want to do sth like: first discretize
| (choose a lattice), then simulate (do calculations on this
| lattice).
|
| I want to do the opposite: first simulate (do calculations on
| a continuous domain), then discretize (restrict my results to
| a lattice).
|
| > For your case you showed, it would be like if x^2 simply
| didn't exist on a lattice, and couldn't be calculated by a
| computer no matter how much memory you threw at the problem.
|
| So the functions we're talking about do exist on continuous
| domains - but they don't have a corresponding definition on a
| lattice?
|
| Couldn't we embed a lattice in the continuous domain, then
| restrict the function along the embedding, thus getting a
| definition on a lattice?
|
| Unless it's not possible to embed the lattice in a continuous
| domain - then my reasoning breaks.
|
| (note: I know nothing about physics, I'm a programmer with
| math education, talk to me like I'm an idiot)
| zmgsabst wrote:
| If you have an oracle that can tell you the answer, you can
| subsample that at lattice points.
|
| But how do you compute the continuous answer in the first
| place?
| kbr- wrote:
| I guess the (crazy, I know) assumption that I made is
| that I have some analytical, symbolic expression for a
| function that describes the state of the universe at
| every point. This "state" describes some fundamental
| quantity (not necessarily a quantity we have a name for
| yet).
|
| Then we express the value of any particle field at every
| point as a (potentially very complex) symbolic expression
| that only uses the state function from my previous
| paragraph.
|
| All of these expressions need only finite memory to
| store. They describe functions with domain R^n to some
| co-domain of operators or whatever.
|
| Then I can calculate the value of this complex function
| at any point with any precision I like, with finite
| memory, although unbounded - I need to allocate more
| memory when I want more precision.
|
| Point is, I delay the process of "latticization"
| (calculating the numerical values at each point of a
| chosen lattice) to the very end - only then I have to
| choose how fine-grained my lattice is.
| evanb wrote:
| > I guess the (crazy, I know) assumption that I made is
| that I have some analytical, symbolic expression for a
| function that describes the state of the universe at
| every point.
|
| This is the error. All you have is some partial
| differential equation. It has no known symbolic solution.
| atty wrote:
| I apologize I am actually running out the door at this
| point, so I can't reply in a ton of detail (I'll try to
| remember to do so later)
|
| But the point to remember is that these aren't normal
| algebraic equations, they're based on the quantum
| operators, right? And so we can always do symbolic math on
| them, but to get numeric results, they have to be
| instantiated at some point. The operators exist at every
| point in space, and some of the operators can be
| approximated on a lattice discretization, but some of them
| cease to be well defined as soon as there is any distance
| between the operators (so they require true real numbers,
| not floating point numbers - ergo, infinite memory).
|
| One point that i think is missing is that there's a bit of
| a difference between numerical solutions to QFT equations
| (like the calculation of g-2 referenced in the paper) and
| lattice calculations in that in general those numerical
| calculations are giving averaged quantities. We couldn't,
| for instance, take that average quantity and use it instead
| of the dynamically fluctuating quantity in a lattice
| simulation. We could run a lattice simulation and estimate
| the value of g-2 from the lattice to see how well our
| discretization -> continuum extrapolation worked. But we
| couldn't go backwards from the numerical solution to the
| lattice, so to speak.
| criddell wrote:
| Do analog computers have the same fundamental limitations?
| klyrs wrote:
| Pulling on this thread leads directly to quantum
| computation.
| atty wrote:
| Honestly I've never considered an analog computer, and I'm
| a physicist but not a lattice expert. While an analog
| computer would let you use real numbers, you'd still need a
| way to store state at every point in space, which would
| lead to the infinite memory problem (and you'd need
| infinite compute to operate on the infinite memory).
| Perhaps there's a clever way to get around that, but my
| suspicion is that if it were possible someone would have
| done it already.
| evanb wrote:
| I do lattice QCD. It's not that we have a problem because
| of float/double inexact and limited arithmetic. It's that
| we have a finite amount of RAM.
|
| So the thing we'd want is not continuous _values_ but
| continuous _registers_. Maybe this is possible with some
| very clever engineering but I 'd wager that your
| computation will develop other problems, such as thermal
| noise causing problems (whereas digital computers have
| error correction).
| mxkopy wrote:
| I don't think continuous and discrete-with-arbitrary-precision
| are the same thing, maybe even to the degree where we can't use
| the latter as a universal approximation for the former. I think
| there are some cases where approximating a continuous function
| on a lattice produces an error that isn't a function of
| precision (I think the Weierstrass function is one).
| hyuijk wrote:
| But who says the computer running the simulation must be exact?
|
| We are using a lot of low precision computations in graphics,
| neural networks, ....
|
| Pi also can't be calculated exactly to infinite precision, yet
| that doesn't stop us to compute circles and so on.
| x86x87 wrote:
| You cannot have arbitrary small precision past a certain point
| no matter how much memory you allocate.
|
| You will run into this limit and it's a physical hard limit.
| Lookup why it's called quantum (mechanics, physics, field
| theory, etc).
|
| Before you simulate an entire universe try accurately
| simulating one atom. Let me know how it goes (spoiler alert:
| the computing power needed to do this is beyond the computing
| power we have today)
| [deleted]
| machina_ex_deus wrote:
| The theorem mentioned is Nielsen-Ninomiya. A good analogy is
| aliasing in signal processing. It's not that you can't define a
| theory and compute it. It's that under certain conditions, you
| get more than one electron, you will get electrons that behave
| like electron does but they are different, and they are an
| artifact of the discretization.
|
| This is similar to aliasing in signal processing. A high
| frequency signal behaving like low frequency. And there are
| solutions to this problem, but it's hard to reason which one is
| the "right" solution.
| blablabla123 wrote:
| It's the current state of the art anyway. But also it's worth
| mentioning it's more complex than just a function x^2. When
| looking at a Feynman Path Integral you integrate an Operator
| (mapping a function to a function) over a an uncountable domain
| of functions. The other approach which is used to calculate
| probabilities goes with an approximation that cannot be used
| for simulations though. All this is not mathematically bullet-
| proof as Mechanics also speaking about Wightman axioms. (And
| even in Mechanics it's possible to construct infinities)
| quandumbspiels wrote:
| There are two main reasons why the theory is "incomplete"
|
| 1> human perception is not often considered; in many ways humans
| are like dogs trying to see in full color depth. Humans are
| "colorblind" to types of information.
|
| 2> structure of the flow is not often considered: the assumption
| is a flow through some X-dimensional space: what if this flow is
| defined according to a chaotic map: not just a fractal but a
| subset of other rules which create chaotic flows across multiple
| dimensions in time which collapse /retroactively/ along a chaotic
| Riemann geometry
|
| Quantum more like quant dumb
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