joigus

I love pasta.

No. That's one good reason, and a pretty important one, but not the only reason. Any initial-condition wave function of any shape you like --not necessarily a function for which Ax+By+Cz=K (plane) is a surface of constant phase, and let it propagate freely. Eventually, it will get close to a plane wave if you leave it alone, but it never reaches that profile. It's curved and contorted for a long, long while, ever so slightly less so as time goes by, but never totally plane. It takes infinite time to do so, and then the multiplicative constant must become zero. "Plane" is what they tend to be, given enough time, but not what they are. Plane waves are extreme simplifications. Their localisation probabilities produce an infinity, so they're not the actual representation of a physical state. They're toy models. Plane waves are, eg, what the amplitude looks like in some region when you prepare the state having it go through infinitely many collimating screens, and then let it "relax" until it reaches this situation in some region of interest. OTOH, there has been extensive study of states which propagate in one direction, but package orbital angular momentum in the directions perpendicular to the propagation direction, so they're not plane waves. Look up for Bessel and Airy packets. They're very interesting, and quite a surprise when you're used to this simplifying idea that free waves are plane waves. Many people say it, but it's very old, sloppy, non-rigorous QM. We understand it better now. Another more realistic approach to a free Schrödinger wave is a Gaussian wave packet. Another one is the wave function of a particle coming out of a slit. It's never plane, although once it's got out of the slit, it's totally free. So V=0. But even more simply. Take the free Schrödinger equation: \[ i\hbar\frac{\partial\psi}{\partial t}=-\frac{\hbar^{2}}{2m}\nabla^{2}\psi \] Now suppose you know, for some reason, that the momentum is in the z-direction. So you can do the separation \( \psi\left(x,y,z,t\right)=e^{-iEt/\hbar}e^{ip_{z}z/\hbar}\varphi\left(x,y\right) \). Now plug it into the time-independent Schrödinger equation: \[ -\frac{\hbar^{2}}{2m}\left(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial y^{2}}+\frac{\partial^{2}}{\partial z^{2}}\right)\psi=\frac{p_{z}^{2}}{2m}\psi \] So your Schrödinger equation splits into, \[ \frac{\hbar}{i}\frac{\partial}{\partial z}\psi=p_{z}\psi \] and, \[ \left(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial y^{2}}\right)\varphi=0 \] The second one is the Laplace equation, so any harmonic function in the variables perpendicular to the selected momentum will do as a perfectly valid --and actually much more realistic-- solution to the Schrödinger equation. This is why people have been studying for some time now these very interesting states with orbital angular momentum packaged in them that I like to call --privately-- fusilli or tagliatelle electrons. They are free particles, and they are not plane waves.

This is incorrect. It's what some/many freshman or sophomore "introduction to quantum mechanics" books suggest say, and it's badly, badly wrong. Wanna know why?

Eigenstates of what? Position eigenstates could not be farther from being oscillatory. Waves do not have to be oscillatory. But the question actually all depends on how you define a wave, and what you wish to include in the definition. Perhaps you should actually read what I posted, as I provided a somewhat restrictive one, although by no means necessarily unique: You could, of course, weaken this definition and therefore expand the concept to include non-linear phenomena, like solitons or gravitational waves. In that case, it would be just any solution to a field equation that admits particular solutions that propagate as a travelling disturbance, \[ u\left( x-vt \right) \] Being "oscillatory" --most certainly-- is not a requisite in any definition I know. You are confusing the particular case with the general one. You are confusing the pieces into which we analyse waves with what is is an analysis of --the waves themselves. In fact, no realistic interesting solution of a wave equation is "oscillatory." Most waves suffer dispersion. What you are referring to is a monochromatic wave. The classical wave equation, the equation for the vibrating string, for example, has infinitely many oscillatory Fourier components, while the overall solution doesn't have to be oscillatory in any sense --even though every one of the pieces oscillate with its particular frequency. Welcome to the forums. I don't think chemists are mere. Not anymore than isomers are mere "isos." I think in Chemistry you're mainly concerned with electrons being comfortably set in stationary states. Either atomic or molecular wave functions with a given energy. This dispersion is still going on, but due to the peculiarities of the function being complex, and the "diffusion coefficient" being imaginary, the stationary situation, when it's spatially confined, allows for states going back and forth withing a small volume. Like --another Wikipedia image--,

You're absolutely right. +1. An image is worth a thousand words: The image is not mine, of course. It's from Wikipedia, and it represents the time evolution of a free quantum-mechanical wave packet. You can actually see how dispersive the non-relativistic regime is. The low-down is: Even empty space somehow operates as a dispersive medium for Schrödinger waves. Although you can get a similar behaviour for waves that are actually waves --same order in time and space derivatives-- by having them propagate through a dispersive material. The diffusion equation is, \[ \frac{\partial n}{\partial t}=-D\nabla^{2}n \] with D being what we call the diffusion coefficient. The Schrödinger equation, OTOH, is, \[ i\hbar\frac{\partial\psi}{\partial t}=-\frac{\hbar^{2}}{2m}\nabla^{2}\psi \] So it's exactly mathematically equivalent to the evolution of a complex space-time valued function with complex values and purely imaginary diffusion coefficient, \[ D\rightarrow\frac{i\hbar}{2m} \] Whether something is a wave or not is, of course, a matter of definition. I would be happy enough with an equation that's linear in the field variable and admits travelling solutions being in some sense a wave. Travelling solutions meaning, \[ \psi\left(x,t\right)=u\left(\omega t-kx\right) \] If the equation is linear, we can do a Fourier analysis of the wave, and an arbitrary solution is a linear superposition of infinitely many travelling solutions like these. But the problem of whether our equation is dispersive or not is coded in the relation, \[ \omega\left(k\right) \] That's why it's called dispersion relation. Fourier components with different frequencies have different velocities. The velocity of propagation for each component of wave number k depends on that particular value of k. That's why the wave spreads out as it evolves. In the case of the Schrödinger equation, the dispersion relation is, \[ \hbar\omega=\frac{\left(\hbar k\right)^{2}}{2m}\Rightarrow \] so that, \[ \omega\left(k\right)=\frac{\hbar k^{2}}{2m} \] The phase velocity for Schrödinger waves being, \[ v_{p}=\frac{\omega}{k}=\frac{\hbar k}{2m} \] And their group velocity being, \[ v_{g}=\frac{d\omega}{dk}=\frac{\hbar k}{m} \] For light in a vacuum, there's no dispersion, or the dispersion relation is linear, so group velocity and phase velocity coincide. If we enter a medium, then we have dispersion. For relativistic (massive, matter) waves, the dispersion relation is very interesting, giving a group velocity that's subluminal, and a phase velocity that's superluminal, the product of both giving exactly c2. The problem with relativistic equations is that they cannot be consistently interpreted in terms of one particle. They are multi-particle systems from the get go.

There you go again. There is no "first." None of them comes first, and then the other. It'd better not. That's why those people in Taiwan that you mentioned earlier are just measuring the speed of nothing. It is a non-speed. That's why Ghideon's analogy is so brilliant. There's no speed at which the woman becomes a widow. Or it's infinite, whatever way you want to say it. It's a logical fitting between both ends. Nothing travels. No Cramer, I'm sorry. It's the "speed" at which infinitely many propositions are anticorrelated, and infinitely many other propositions are totally non-correlated. I am. Let me give it a try. Let's introduce another Ghideon-observable: If I destroy their house while they're away, they "instantly" become homeless. In the classical world, It's possible to know whether a person is "widowed" and "homeless" at the same time. In QM those could be incompatible observables. What's interesting in your analogy is that you've introduced a world of potentialities: Legal bindings, conditions, attachments, etc. This is, in the analogical space, playing the part of the wave function.

You guys are forgetting that sometimes we are surprised with a gem by other members. I personally find @Ghideon's analogy of the widow/widower very illuminating. I've been trying for years to find an analogy that illustrates this particularly difficult point that you can instantly obtain information about a remote thing without physically affecting it, and there you are --and the example not being quantum mechanical. To me, it's worth all the effort spent. Here it is again:

A Zen master once said, Light is what allows you to see the elephants. Light is not the elephants. Dark is not light. Light is not dark. Light is light. And there's nothing lighter than light.

Our goal is to have goals. Our purpose, to have purpose. May I also point out that there is such a thing as too much reproduction... 🤷‍♂️

Cosmology is of no relevance here. Experimenters doing quantum interferometry, quantum teleportation, and the like, do not refer anything to the CMB. That would be silly. The CMBR is distinguished from a cosmological POV, not from a POV of local quantum mechanics. Seems trivial to you only because you do not understand, and looks now as if you will never do. The experimenters decide who does the measurement: One of them, the other, or both. And they also decide when that happens, in their respective local reference frame. OTOH, observers moving with respect to them, see the measurements happen in different temporal order, depending on their state of motion. Will you at some point understand this? You have a flair for getting everything backwards like I've never seen before. Everything is together --non-separable, that's why I say it's "hardwired," and it comes apart after we do the measurement --the particles become disentangled, and the density matrix goes from pure state to strict mixture state. Nothing is observed until it is observed. There is no signal. Filtering measurements carry no signal either. In this way, it's similar to a non-interaction measurement, like counterfactuals --Elitzer-Vaidman bomb tester-- or filterings.

Seems to me that this is an insurmountable objection. It is what I would call a zero-order problem with the OP's idea. IOW: The hypothesis is not even designed to do the job it's intended to do.

Man oh, man. That's a great analogy!!! +1 It's freakin' brilliant. You've made the other person a widow or widower, without actually doing anything to them. You have learnt something about them because of what you've done at one point. You know something about the other person's future. But the other person, and those around her or him, are clueless until the "classical data" are sent to them. Those classical data are under the constraints of delay, because they do have to use a signal.

Yes, you're saying this since day one. I will repeat: SR always applies in sufficiently small regions of space-time. There is no known experimental exception to it, and there's no reason to expect any. Quantum entanglement is every bit as compliant with SR as every other physical process we know. If you think this not to be the case, explain why with theoretical arguments from mainstream physics, or direct us to the experimental evidence. So far you're just parrotting unsubstanciated claims by other people. We are all aware of the existence of these claims, as we are aware of the existence of bad music. There's a thin line separating serious science from free-floating fantasy, and some people take every oportunity wherever they find ambiguity, or a grey area, to cross that line. There's bad science too, you know? I wasn't born yesterday. No. An Entanglement is a property that only very special many-particle states satisfy. It's not a set of entities having properties according to which we can do statistics. The statistics of such properties is hardwired in the state without them being "real" properties of the individual entities. The entangled state is the entity as far as the current theory understands it. No quantum numbers of spin make up the Bell state. The individual quantum numbers are totally undetermined. The eigenstates are totally undetermined. The particle identities are totally undetermined. There's no cohort. There's no set of internal colours, markers, tags. So far as we know today, there isn't. Maybe in the future someone will come up with an idea to weaken the criterion of reality to define these variables and make it all consistent with known physics, but so far it hasn't happened. Entanglement is a property in itself (the ending "-ment" should give it away). A cohort is a set of individuals with properties (like, eg, people aged between 16 and 20, unemployed, and single.) So no, you're not dealing with this topic with any degree of scientific of philosophical care. You're obviously ignorant of relativity, as well as of how and why it's critical in this discussion. Yes. At least @MigL has told him, you @Eise have told him --and he's telling you again--, and I have told him. I had no objection to that anthropomorphic expression either. I think everyone involved in this thread understood it is just a manner of speaking.

I think this is more or less equivalent to what @Janus already mentioned about the old "tired light" hypothesis: More or less what I meant when I said, Although I don't know how light being red-shifted amounts to it becoming 6 times the mass of baryonic matter through the billions of years. Red shift is not the same as photons "staying around." This argument, or similar ones, are bound to be reborn in the minds of people who think they understand the problem. It was ruled out long ago, and I must confess I've never considered it because it's so off the mark in so many directions. DM is a big unknown today. It could be exotic matter, or it could be "quintessence" or... who knows. But it's not light. We do know that much today. Astrophysicists say it's not baryonic, nor EM --so no photons--, nor weak-interacting[?] The Wikipedia quote is, in fact, incomplete: It does not appear to interact with charged particles. Keep in mind the EM field interacts with itself only too weakly. It does not scatter off electrons or ions AFAWK. DM does not interact electromagnetically at all. Photons do. Maybe a mixture of different things... Perhaps. It's either something that clusters very, very loosely, or just a deviation from Einstein's equations. I don't know and, so far as I can tell, you don't know either.

LHC gets tons of data about QCD background and rules out wrong hypotheses and ideas about how matter behaves. It provides an excellent school for engineers and experimental physicists. It fosters collaboration among nations. But maybe you're right. We should throw money at other --more worthy-- causes. Here's another one that's in sorry need for more money:

SR is relevant to everything physics. It's the local limit of GR, it's the basis of QFT. There are no known experimental exceptions to it. Analysis and theoretical discussion on how nothing about QM can contradict its salient facts has been the subject of study for decades. I suggest you study thoroughly how it underpins all of physics. It will be very illuminating. You cannot just say "oh, but this is not SR," and get away with it. About "bickering," If people tell you there are non winged lions, that's not bickering. That's stating something that's very likely to be true. It's for your own intellectual good when people tell you so. There are no winged lions, and there is no contradiction to special relativity. You can take that to your grave. I'll take it to mine.

Oh, don't worry about the words. It could be arranged if you show some equations. What about the virial theorem? It is essential to understand the velocity distribution of objects moving around in a gravitationally-bound cluster. Everything you've said so far is inconsistent with what I know about the virial theorem for galaxies. And you don't need GR for it. A classical calculation would suffice, as the speed of the galaxies is safely within the non-relativistic regime. Mind you, photons themselves are always relativistic, and red-shifted, and subject to gravitational lensing, but the speed of the galaxies due to the presence of photons is not, and could be treated non-relativistically. I want to see how visible radiation from galaxies accounts for a big whopping bulk of mass that represents most of the mass and goes far and far away, well outside of the galactic halos, and somehow stays thereabouts. What you propose is so amazing that I --for one-- demand no less than extraordinarily convincing proof for this extraordinarily outlandish claim. How is the light emitted from a lamp almost 6 times the mass of the lamp? You tell us. (When I say mass I mean energy.)

What do you mean by this? What does it mean "light climbs out more and more the farther away from the source it is?" I don't think that's physics.

This sentence doesn't make sense gramatically, let alone physically. A cohort is a set. I'll get back to you later.

It is insufficient, and exceedingly so: https://en.wikipedia.org/wiki/Dark_matter (My emphasis added.)

This is incompatible with the inverse-square law for any conserved stuff that escapes from a source. You seem to be suggesting that more photons are being created the farther away from the source. It's the other way aroung: The farther away from a source, the rarer and rarer the "stuff" becomes, the quantity of stuff per unit of solid angle being approximately constant. Not consistent with the distribution of velocities we observe. Apply the virial theorem and you'll see. Do a google search "virial theorem for galaxies" and get familiar with it. You'll rule out your idea in a matter of minutes. Visible, infrarred, and UV light etc, is how we know there's visible matter there, not the bulk of the matter that we don't see.

That gives a 1/r2 dependence with distance, as Swansont said. Not consistent with the virial theorem for the galactic speeds. And still it is a tiny "contamination" compared to the barionic matter. Crudely, but hopefully clearly, you need a much much bulkier thing, non-interacting --except gravitationally--, and reaching substantially well out of the galactic halos. I don't think that's the issue at all. That would be a minor rearrangement (in the cosmological model) of the matter/radiation/etc terms in the density. The photon having a mass, OTOH, would be something more than just a nuisance, because it would break gauge symmetry, as Markus said, and you would have to spontaneously break it with the Higgs mechanism. By the way, individual photons don't have a mass, but a bunch of photons escaping away from each other do have a centre of energy, so you can infer a collective "mass" for them. They would have a collective speed of the centre of mass less than c. If you want to see it as a mass, that's OK. But that's not the issue. The most important issue IMO is that photons are a fluffly nothing thing in comparison with the enormous bulky mass that DM must be in order to explain galactic velocity distributions. It has to cluster, but it has to do it very dilutely. I'm no expert on this, and I will re-read all the arguments and think more about them, and document more, but to me this attempt is hopeless, has been beaten to death many years ago as a possibility, and would require a total re-vamping of the standard model. I don't even want to start considering what it would do to the electroweak mixings. And on top of that, it's an ugly alternative. But that, and that alone, is just my taste. It's as if --if you allow me the joke-- you detected that there are 70 invisible elephants in your living room by using gravimetric methods, and the explanation you're offering is that somebody left the lights on.

Also, visible light is a tiny fraction of total energy content of the universe, plus it comes in every direction approximately equally. So the idea is really a non-starter. More than likely Kelvin, and many others, in the 19th century already considered it, and ruled it out almost immediately. Radiation does not cluster. I think the idea fails on so many levels that it's difficult to give a complete account of all of them in a few words...

That's exactly the point. Quantum systems do not have "internal cohorts." No internal cohort of elements with attributes can explain their correlations. Read it again, and you may finally understand this. If you insist on these properties to arise from any kind of internal cohort, whatever the wave function represents --either our knowledge of the system or some "real wave" carrying our knowledge of the system-- would have to be updated non-locally. "The internal cohorts" would have to change their composition in a coordinated way, at a distance, even when separated by space-like intervals. But none of this represents any interaction. It represents updating of your knowledge of the system. You now know more about the system than you knew before, that's all. The fact that the position variables play no role, and you can conduct the experiment at one small region of space, and the results would be exactly the same, should give it away.

Dark matter is thought to be about 85% of the total mass in the universe. Radiation from a lamp is certainly not an 85% excess of the lamp's mass when it's turned off. Also, DM is known not to interact electromagnetically, or strongly, or by weak decays. That's what people mean by "dark." If DM interacted as photons do, it would cluster much more than it's known to do. I was about to say more, but I think that's enough food for thought for the time being. And Janus has given a pretty good account of it.