I don't mean to be annoying, but this question now has four answers that all seem to me to answer a different question. One answers the question in the title, one discusses the Bohmian/orthodox mix, one is about time evolution, and the newest is about why we don't have a probability distribution in QM.
And I am still unjustified in saying it is not clear what is being asked?
@ACuriousMind You are (were), on my view, not (never) unjustified in saying that. Having said that, I see that the question has been edited since I first read it but I suspect that my view will not change upon reading the edited version.
Basically, they don't like the idea of a metric and such, and want to work with just a structureless set of events and the invariant intervals between them, I think.
"Adding up these subdistances gives the proper distance $$d_\text{prop}(t)=\int_0^{r_1}\sqrt{g_{rr}}\,dr=R(t)\int_0^{r_1}\frac{dr}{\sqrt{1-kr^2}}$$Obviously, no one is going to organize this sort of cosmic conspiracy, so the proper distance is not very relevant to observational cosmology."
But I'm not really sure, I never had the patience to read what this distance geometry is about, because, although the Wiki article claims it is "immediately relevant" to many things, I've never seen it anywhere else.
@0celo7 They've also been known to insist that not only is their choice of language better than everybody else's, but that it is so much better that everybody else is simply wrong.
Following Synge's description of a "five-point curvature detector" 1 and its generalization (e.g. as indicated in [2]), the curvature of five participants ($A$, $B$, $N$, $P$, $Q$) who were and remained (chrono-geometrically) rigid to each other (i.e. finding constant ping duration ratios) is mea...
Yeah, it's not really crackpottery because this distance geometry and the Cayley-Menger determinants and whatnot are actually things people have thought about
And you can (probably) recast some of relativity in that language
It's just so utterly tedious and unenlightening that I don't see the point at all
@ACuriousMind As you know, my knowledge of analysis is rudimentary. I thought the metric defines our notion of distance. How could you possibly get rid of it?
12262: Let's measure the circumference of a string! :: Measuring device has quantum wobbles :: 12262: More mass! :: Measuring device turns into a black hole ::
Quantum wobbles = uncertainty principle or something.
If you want to measure on the order of the Planck length, your measuring device will turn into a black hole. Or something like that.
I'm gonna go check that calculation in Zee.
Seems legit. It argues from the uncertainty principle and uses the speed of light and the mass of the measuring device to bound the uncertainty in length.
0celo7: "@MBN [An arbitrary curve can ... switch from timelike to spacelike.] True." -- So: Do we agree that the "Wikipedia prescription: the sign in the square root is chosen once for a given curve" does not provide a general and satisfactory definition of "arc length"? Then I'd be surprised/shocked if others had not arrived at this conclusion before. Thus I ask: Is there an established name and notation for the particular "solution to the problem" I described? (Else let's use what I made up.) — user122626 mins ago
"As a rigorous alternative of the (frequently but not convincingly) in- voked argument of the uncertainty relation to infer the existence of a nonvanishing zero-point energy for H, show (without solving explicitly the Schr¨odinger equation) that the energy of the system is bounded be- low by a positive constant"
Well that's important
usually a curve would be a map $\gamma: I\subset \mathbb{R}\to M$ with $\gamma(0)=A$ and $\gamma(1)=B$ for instance, if it's a curve between two spacetime events $A$ and $B$
The only thing I could imagine is a family of curves $\gamma_\lambda$ between $A_\lambda$ and $B_\lambda$ such that for certain $\lambda\in I$ the curve is timelike while, for other $\lambda$, it is spacelike
I am dissatisfied with the presentation (not to say "definition") of "arc length", in its "Generalization to (pseudo-)Riemannian manifolds", as given in Wikipedia. (Who isn't?. But I'll sketch it here as a starting point anyways.) Namely:
[arc] length of curve $\gamma$ as $$\ell[~\gamma~] :...
Obviously, as one varies the parameter within $I$, the domain of definition, one gets to different parts of the curve where its tangent vector may be either space- or timelike
This is not the curve 'changing', it's just the curve not being boring :P
@Danu This needs to be resolved. Let $\gamma(t):[0,1]\rightarrow M$ be a curve. For $t\in[0,\tfrac{1}{2})$, the tangent vector is timelike. For $t\in(\tfrac{1}{2},1]$ the tangent vector is spacelike. It is perfectly reasonable (English-wise) to say that the curve changes from timelike to spacelike at curve parameter $t=\frac{1}{2}$.
@Danu But $\sqrt{-g(\dot\gamma,\dot\gamma)}$ is imaginary for spacelike curves.
"It's kind of hard to fathom spending that kind of money on a sweater, but these are the times we live in," Vince Lombardi Jr., Vince's son, told the Asheville Citizen-Times earlier this week. "Whoever gets it I hope treasures it."
haha
@KyleKanos I agree
@0celo7 anyways, in things like 'the distance between two points' these things do not happen
that's the take-home message
because the generalization of a straight line is of course a geodesic
How does one determine the eigenvalues of a differential operator, i.e. the Laplacian? Zeidler just states that the eigenvalues of $\Delta$ on the unit circle are $\lambda_n=n^2$ where $n=0,1,2,...$
The collapse cannot be solved by many worlds, because it is not known what causes it. It is not sure that the decoherence at the contact with the macroscopic apparatus, produces the collapse - see entanglements where we have more than 1 apparatus, and we can't even say at which time are the worlds generated. But it won't help, because who wants those worlds at any price would argue endlessly, and invent new and new ad-hoc arguments. So, pleasant journey in other worlds.
@ACuriousMind my dear one, probably you are right. I placed my comment here because many people visit here, just for being sure.
@ACuriousMind I placed comments also at the respective site. It's on my tongue to say to all those science fictioners, "learn some physics" (the answer that von Neumann gave John Nash when the latter came with some QM proposals).
@Sofia: While I am not defending (or attacking) MWI, your phrasing is a bit weird - MWI denies that collapse happens, but instead has only decoherence, so you attacking MWI for not explaining collapse sounds strange.
I think your argument is one that is commonly brought against MWI, phrased differently - the mechanism of creating worlds is not explained, many inaccessible but existing worlds are wasteful by Occam's razor, and how "we" end up in any particular world is similarily mysterious at first.
@ACuriousMind Ah, yes! But when can be created that worlds? If we have two entangled particles (the photon/spin singlet), three entangled (GHZ), when do the worlds appear? And how can we get entangled worlds? Two, three, four, as many as we wish, entangled worlds. What a splendor!
@KyleKanos Aaaa! She was a lawyer. I like it. Thanks!
@ACuriousMind I wanted to tell you but I changed my mind in the last moment. After our long talk a couple of days ago (it touched mainly the collapse) I somehow began to hope that Bohm's interpretation would triumph. I believe that there is some truth in it. It seems to me that the thing can be checked experimentally, but I can't begin to work on that proposal for the moment. And I will need Alain Aspect's help. Hmmm! I have a good friend in France, but she is a biophysicist, not QM.
@KyleKanos and @ACuriousMind weren't you who told me about Lutheranism? What was the 1st name of Luther (the German one)?
Unrelated: Could one of the experimental physicists take a look at this question and find out whether it is on-topic and/or has enough information to be answered?
Having done some (minor) experimental work in undergrad (working with Raman spectroscopy), it does appear on topic. Whether it has enough information to be answered, I cannot say.
@vzn I saw "Little Buddha", very beautiful. I like to learn about traditions, religions, culture of different nations. It teaches a lot of interesting things.
@sofia :) glad you like it, its way cool stuff, very cutting edge, so far not widely known, some wont like it, others will, think its defn the birth of an entirely new paradigm answering decades old questions in a dramatic, sound, near revolutionary way...
@vzn I agree that the bouncing droplets are nice. But they can only reproduce single-particle quantum mechanics
Multi-particle quantum mechanics is where all the truly difficult conceptual issues arise.
(In my opinion)
So I'm definitely waiting to see what they can do with multiple droplets. But note that there is no way that they can reproduce entangled statistics with two droplets sharing the same fluid. This is already ruled out by Bell's theorem.
@Mark fully concede its a very nascent/ embryonic theory at this pt. as any serious student of sci history is aware, theories do not arrive on the doorstep full-fledged. think it will take literally decades to work out the specifics. agree these are near "toy" theories at this point. but intuition plays a role. the near eerie, uncanny explanatory power cannot be denied by anyone who looks at them closely. it seems a general theoretical answer to the notorious "spooky action at a distance..."
@vzn It is a mathematical theorem. Forget about Bell the person. Unless you believe that mathematics goes mouldy over time, then I do not understand what you mean.
but its interesting to note that all new theories can regarded as walking through "small/ subtle loopholes" (in prior theories). taking a very kuhnian pov.
bells analysis is "correct" in the context of its assertions.
eg the difference between einsteinian relativity & newtonian physics only exists in "extreme edge cases".
Right, but those are all the assertions for a nice theory with out any weirdness. If you relax them then you might not have spooky action, but you have something else equally philosophically repugnant.
so a lot of initial/ healthy skepticism is entirely warranted. do not deny that.
agreed the theory is esp going to be difficult to advance past the simple cases already studied. (if possible) it will require amazing math insight eg on the level of what von neumann did for axiomatizing QM. possibly even more.
Yeah. But the point is, I'm not even really excited about this as an explanation, because it will make things even more confusing if it is true. It doesn't really "resolve" the philosophical issues, they are always going to be there. Obviously if there were experimental evidence I would be enormously excited. But also daunted by the prospect of a theory that is even more confusing than QM.
@vzn That is not a "Kuhnian" point of view at all. Kuhn regarded Newtonian and Einsteinian physics as incommensurate. Although Newtonian physics is the (mathematical) limit of general and special relativity, their concepts of space and time are remarkably different.
MM my hopes are (justifiably) quite high :) but also have to be very patient on the very ambitious long term goals. its a research program, not a full fledged theory yet.
bell/ bohm work can be seen as valuable stepping stones.
@vzn Yes, he regarded them as incommensurate. He certainly would not have thought that they were only different in extreme edge cases. They have incommensurate notions of space, time and simultaneity.
From an operationalist viewpoint, however, you are correct about the "loophole" interpretation of scientific progress. But then there is also often an associated conceptual shift.
afaik nobody has made the "official list" of kuhnian shifts, not even kuhn himself.
its all a shift. conceptual etc., it can take decades for these shifts to fully play out. they are like massive waves.
let me dig up a ref for you MM, you may not like it, but it attempts to directly address the spooky action at distance issue "inherent" in fluid mechanics.
am just a messenger here guys so ofc feel free to shoot indiscriminately :p
my feeling is that simulations have massive potential to highly advance this area, but nobody else has noticed/ realized that yet.
I am just confused to death; it seems too hard to make progress without experimental input, so I'd rather spend my time thinking about physical models and systems which probably do exist!
Just demonstrating that a macroscopic hydrodynamic analogue can reproduce Bell correlations given some loopholes does not constitute any progress at all./
can expand on their basic explanation sometime. but arguably spooky action at a distance is a basic feature of classical wave systems combined with a probabilistic measuring rule of wave amplitude (borns rule).
no question its counterintuitive to current understandings.
lets note that almost no bell experiments have been done with electrons/ particles. its almost all photons.
admittedly there are some rare particle experiments.
@vzn I'll take care that this article be known to my acquaintances, and I'll ask them to handle it further. It is an important article and has to be well studied. I'll stay with it, probably on the week-end.
imho kuhn is brilliant but more coming from humanities than science. hes an expert science historian which is quite different than a scientist.... he has been seriously challenged by some scientists, imho quite credibly so.
for example, this is a subtle but key point, kuhn did not seem to believe in "true" theories. or one theory as being "more accurate" or a "truer picture" than another.
he didnt seem to acknowledge how new theories "mesh perfectly" in some sense with prior ones.
@vzn he was a philosopher and historian of science. i don't think you've grasped his ideas. he understood that e.g. that the mathematical low-energy limit of general relativity is newtonian gravity. he argued that they didn't "mesh" because they didn't share commensurable concepts or vocabulary. a newtonian and an einsteinian don't, for example, have a shared concept of space or time.r
am not an expert on the details of his philosophy...
ofc they mesh.
physicists are neither newtonian or einsteinian, they are both. after the paradigm shift. during the paradigm shift, there is a conflict. but the conflict is eventually resolved as no actual conflict.
How big a difference does gpa make in grad school applications? If I have a cgpa of about 3.83-3.85 (my current cgpa, on a 4.0 scale), will I stand a significantly lower chance of getting accepted than someone with a 3.9-ish cgpa?
kuhn probably didn't believe in "true" theories (does any philosophy of science?), but he does discuss theory confirmation towards the end of structures. he did believe it possible that one theory could be said to be more probable than another (though he thought it was problematic in practice).
i'm surprised you've chosen that criticism. e.g. popper certainly didn't believe in true theories or that one theory could be said to be "truer" than another.
physicists are keenly interested in the truths of nature. scientists in the same way. dont know another word for it. its a concept that humanities critics seem surprisingly wobbly/ weak on.
the universe has (eternal) truths associated with it. that is a fundamental precept of science/ scientific method etc.
whose scientific method! there is no neutral, null method. can't you see that you're invoking particular ideas about the philosophy of science just by saying that?
there is no universally agreed upon scientific method. the dominant method of science - popper's falsificationism - doesn't meet your desiderata. it has no concept of "eternal truths" or a single true theory, or even the idea that one theory is "truer" than another. it rejects theory confirmation.
popper wanted to build a philosophy of science on deductive reasoning only. theories could be rejected, but never confirmed or even considered "probable" or likely to be true.
(skimming popper wikipedia entry) to me its a bit of a philosophical technicality to say that theories cant be proven "true".
"there is no universally agreed on scientific method"... this is philosophical hairsplitting. a basic method has existed for thousands of years. there is some experimental science by the greeks although admittedly they were weak on "scientific method" from a philosophical pov.
no, it is not a technicality. it was one of popper's important insights. out of interest, what exactly do you mean when you say "the scientific method"?
ofc popper might not be familiar with it, apparently (unlike Kuhn phd physics) and maybe like other humanities "science critics" never having personally engaged with it, only hearing 2ndhand accounts :p
anyway my arguments are reflected by other eminent thinkers.
popper wasn't particularly concerned by the practice of science, you are right. he wanted to build a logically robust, normative idea of science. kuhn, on the other hand, wanted to understand and describe how science was practised.
anyway, what exactly do you mean when you say "the scientific method"?
anyway re "other eminent thinkers" try pinker vs the humanists, he makes a better case on this that me, admit some affinity for his "arguments" (and it is indeed an "argument" going on)
so are you now trying to trap me like a modern socrates? admittedly induction is a massive problem to philosophy but used every day in science :)
Is it just because it'd be very expensive?
Or are there serious problems that need to be dealt with, studied and solved? If so, what are they?
