1. ## iNow

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2. ## exchemist

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3. ## TheVat

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## Popular Content

Showing content with the highest reputation since 11/04/22 in all areas

1. ## Putin has attacked Poland?

I know exactly what you mean. Those Nazi Ukrainians, and their jewish President, will stop at nothing in an effort to implicate those innocent Russian victims and make them look bad in the eyes of the World. Those well-intentioned Russians should just leave the Ukraine to their evil ways, and stop trying to help and denazify them.
4 points
2. ## crowded quantum information

Let’s look at this whole quantum entanglement business systematically, because I really don’t think it requires 22 pages of discussion and argument to understand this. It may be counter-intuitive, but it really isn’t that complicated. Suppose you have - to begin with - two completely separate particles, which aren’t part of a composite system; their states are thus entirely separate, and denoted by $|A\rangle ,|B\rangle$ Don’t mind the precise meaning of this mathematical notation; it simply denotes two separate particles being in two separate states, where the outcome of measurements are probabilistic, and not in any way correlated at all. No mystery to this thus far. Now let’s take the next step - we combine the two particles into a composite system. The state function of that composite system is then the tensor product of the states of the individual particles, like so: $|\psi \rangle =|A \rangle \otimes |B \rangle \equiv |AB \rangle$ Again, don’t mind the precise definition of these mathematical operations; the idea here is simply that our two particles A and B form a composite system. Let’s, for simplicity’s sake, assume that each particle can only have two states, ‘0’ and ‘1’ - the physical meaning of the tensor product above is then that it combines each possible state of one particle with each possible state of the other, so the overall combined system can have four possible states: $|00\rangle ,|01\rangle ,|10\rangle ,|11\rangle$ Thus the overall combined state of the particle pair is (I will omit the coefficients here, as the precise probabilities aren’t important): $|\psi \rangle =|00\rangle +|01\rangle +|10\rangle +|11\rangle$ This is an example of a system that is not entangled - the combined state function can be separated into the individual states of the constituents, and all combinations are possible (though not necessarily with equal probability). Non-entangled states are separable into combinations of states of the individual constituent particles - they are tensor products of individual states - which means physically that there are no correlations between outcomes of measurements performed at the constituent particles. If you get state ‘0’ for a measurement on particle A, then you can get either state ‘0’ or state ‘1’ for a measurement on B, and these outcomes are statistically independent from each other. Mathematically, the tensor product makes no reference to the separation of the particles, ie it is not a function of their position, hence neither is the overall combined state. An entangled 2-particle state, on the other hand, looks like this: $|\psi \rangle =\frac{1}{\sqrt{2}}\left(|01\rangle +|10\rangle \right)$ Notice three things: 1. Compared to the non-entangled state, two of the possible measurement outcomes are missing; the set of possible outcomes is reduced 2. The combined state cannot be uniquely separated into tensor products of individual states; it is non-separable 3. The form of the combined state does not depend on the spatial (or temporal) position of the particles - it is purely a stochastic statement, not a function of spacetime coordinates. What does this physically mean? Because the set of possible measurement outcomes in the overall state is reduced as compared to the unentangled case, there is now a statistical correlation between measurement outcomes - with emphasis being on the term statistical. There are now only two possible combinations, as opposed to four in the unentangled case. This is the defining characteristic of entanglement - it restricts the pool of possible combinations of measurement outcomes, because the overall state cannot be separated, due to there being extra correlations that weren’t present in the unentangled case. This is purely due to the form of the combined wave function - the outcome of individual measurements on each of the constituents is still purely stochastic, and not (!!!) a function of distant coordinates. Because the outcome (statistical probability) of local measurements is not a function of coordinates or any distant states, it is completely meaningless to say that this situation is somehow non-local, or requires any kind of interaction, be it FTL or otherwise. The entire situation is fully about statistics and correlations, which is not the same as a causal interaction; in fact, any interaction between the constituents (including FTL ones) would change the combined wave function and preclude the possibility of there being a statistical correlation while at the same time maintaining the stochastic nature of the outcomes of individual measurements. This is evident in the fact that the entanglement property of the above state function isn’t encoded in any kind of coordinate dependence, but rather in a reduction of terms, ie in a reduced pool of possible outcomes. This hasn’t got anything to do with locality at all, but is purely a statistical phenomenon. Hopefully the either helps, or possibly it might spark off another 22 pages of discussion
4 points
3. ## Minkowski space and geometric intuition

I think it is best to just keep the situation fully classic, and consider only physical clocks to begin with, rather than wave functions. The question of evolution operators in RQM is complex and very non-trivial, and does little to illuminate this underlying question. Time dilation is a relationship between reference frames, and not something that physically “happens” to a single clock. Asking for a mechanism that “slows down” some clock is thus meaningless - clocks always tick at the same rate within their own frames. So the correct question would be why inertial frames are related via hyperbolic rotations in spacetime - that’s a very valid question, but it isn’t one that any of our present theories can answer. So to make a long story short, we don’t have an explanation of why this happens, only a description of it. That’s not the same thing at all. The length of a world line between given events in Minkowski spacetime is defined to be equivalent to the proper time of a clock travelling between these events that traces out that world line. In other words, it’s simply the total elapsed time that’s physically measured on a clock that travels along a specific spatial path between events. Intuitiveness is not a necessary condition for a mathematical model to be valid and useful. It just needs to be internally self-consistent, and produce results that can be verified using the scientific method. I think you would agree that SR does this quite well. Beside, something being intuitive (or not) is a very subjective measure - many things I find intuitive might appear otherwise to you, and vice versa. I would, by and large, agree with you - though I wouldn’t put into such strong terms. I just think many depictions of physical concepts get the differences between what is an explanation and what is a description muddled up, especially within pop-sci publications. We do not yet know the underlying mechanism of why spacetime is what it is, but we do have an excellent description of its features. To fully understand why spacetime gives rise to the phenomenology we see, we’d have to figure out first how spacetime itself comes to be, and if it can be broken down further into more fundamental concepts. Such attempts are under way, but at present they are just ideas and conjectures. I disagree. Physics makes models of the world around us, but not all of these models purport to be a fundamental explanation in ontological terms. As such, SR is a very good model that is in excellent agreement with experiment and observation. It’s just important to not confuse a model with an (ontological) explanation, because they are not the same.
4 points
4. ## Dropping Like Flies Worldwide

In the US there are many more Republicans dropping dead than Democrats. Just guess why... Two hints: Which group was more vaccinated? Which group did take social distancing and masks more serious? The risks of Covid vaccination are negligible compared to having Covid. From More Republicans Died Than Democrats after COVID-19 Vaccines Came Out
3 points
5. ## What Gives a Particle Charge and Spin?

In quantum field theory, particles are characterised as irreducible representations of symmetry groups. Symmetry transformations are different ways to look at particles that leave the quantum state unchanged. When these transformations can be expressed in terms of a finite number of parameters, these groups of transformations help us classify the particles according to their so-called Noether charges. When the system is symmetric under one of these groups --also called Lie groups--, Noether's theorem guarantees that these "charges" are conserved. Some transformations have to do with space-time symmetries. Examples are translations and rotations, which have the corresponding conserved quantities that we're familiar with under the name of linear momentum and angular momentum. In any quantum theory, charged particles are represented by complex wave functions. Everything observable depends on quadratic expressions of the form (field)*(field), where the asterisk represents complex conjugate. Because the physics is indifferent to a global phase change, a conserved quantity exists --by virtue of Noether's theorem-- that we call electric charge. In the case of angular momentum --due to symmetries under rotations--, it so happens that the spatial coordinates are not enough to represent all the rotational states of particles. Internal variables must be specified describing the orientation of a particle that allow no representation in terms of spatial coordinates. That's what we call spin. Spin has to do with rotation, although it's not nearly as intuitive as the rotation of a spinning top, eg. Charge has to do with something even more abstract, which is a phase shift in the wave function. This transformation is sometimes called "internal." Isospin invariance is not exact, it's only approximately conserved. It is an analogue of electric charge, and also occurs in this "internal space" of elementary particles. It so happens that, if you ignore electromagnetic interaction, a proton and a neutron are very similar when you only consider the strong nuclear force. You can kind of rotate the states smoothly from "being a proton" to "being a neutron." This is in close analogy with electric charge. There are other analogues of electric charge: baryon number, lepton number, hypercharge... Colour charge is similar, but more complicated, as the previous charges depend on a 1-parameter group called U(1), while colour is defined in terms of a 3-parameter group SU(3). Mass is very different. It is not a conserved quantum number like the other charges. So I would say that what gives a particle its charge and spin are its properties under global gauge transformations (global phase shifts), in the case of charge; and rotational properties, in the case of spin. This is a summary of the present theoretical understanding of these things within the context of the standard model of particle physics.
3 points
6. ## Why does everyone believe in particles?

As a general reminder, I think it is wise to remember that the concepts of ‘particle’ and ‘field’ are first and foremost mathematical models - to be precise, they are irreducible representations of symmetry groups. In physics, when we say that something ‘is’ a particle or field, then the verb ‘is’ should not be understood in a strictly ontological manner, but rather in the sense that these concepts are useful models for some observable aspect of reality. They are ways to make useful and functional models of the world, not irreducible ontologies. Consider the following effects: 1. The Unruh effect: for a given volume of space, the number of particles contained therein depends on the observer. An accelerated observer will figure that the volume contains more particles than does an inertial observer, even though they are looking at the same 3-volume. 2. The Aharonov-Bohm effect: there are measurable physical effects on charges due to an electromagnetic potential, even though the charges are located in a region where the electromagnetic field is absent (F=0). So clearly, our naive intuitions of what ‘particle’ and ‘field’ might mean can be very misleading. Ultimately, the question as to what exists in an irreducible way on the most fundamental level is very much open, in physics as well as philosophy. To me, it isn’t even clear what ‘exists’ and ‘most fundamental’ actually means, since these terms would need to be defined in a completely observer-independent way, which is difficult to say the least. Modern physics takes quantum fields and spacetime to be the most fundamental categories of (physical) existence that we know of, but there is certainly no claim that there couldn’t be something else that is even more fundamental - in fact, it is quite safe to claim that there most likely will be. There are also other ways to make models of what we already know - Rovelli’s relational QM, where the central category is a network of interactions rather than a collection of entities with given properties, is a good example. With all that being said, particles and fields are far to useful as computational models in order to simply abandon them.
3 points
7. ## Can intuitionist math bridge the QM/GR divide?

https://www.quantamagazine.org/does-time-really-flow-new-clues-come-from-a-century-old-approach-to-math-20200407/ (This is a pull-quote, but I have to warn that reading the full article may be necessary to follow what Gisin is up to. I can't cut/paste everything on this device, sorry.) Over the past year, the Swiss physicist Nicolas Gisin has published four papers that attempt to dispel the fog surrounding time in physics. As Gisin sees it, the problem all along has been mathematical. Gisin argues that time in general and the time we call the present are easily expressed in a century-old mathematical language called “intuitionist mathematics,” which rejects the existence of numbers with infinitely many digits. When intuitionist math is used to describe the evolution of physical systems, it makes clear, according to Gisin, that “time really passes and new information is created.” Moreover, with this formalism, the strict determinism implied by Einstein’s equations gives way to a quantum-like unpredictability. If numbers are finite and limited in their precision, then nature itself is inherently imprecise, and thus unpredictable.
3 points
8. ## crowded quantum information

In the quantum realm, when you talk to a wall, there is a small but non-zero probability that at least some of what you say gets through to the other side: $T^{-1} =1+\frac{V_{0}^{2}}{4E( E+V_{0})} sin^{2}\left(\frac{2a}{\hbar }\sqrt{2m( E+V_{0}}\right)$ This thread here, alas, appears to be a purely classical situation.
3 points
9. ## What would be the most important thing than humans should try to achieve in priority in your opinion ?

waste control arms control birth control self control IOW, maturity: GTFU
3 points
10. ## This book lays out a greater justification for belief in its doctrine than any other holy book in history and is the greatest threat to the Abrahamic religious systems

If it's based on astrology, that's all we need to know: it is guaranteed to be crap.
3 points
11. ## What are you listening to right now?

Fleetwood Mac's Rumours album. Not really my kind of music, but they were a part of my 'growing up' and the passing of Christine Perfect/McVie has knocked me a bit off kilter. A tear in the eye when I listen to 'Songbird'.
2 points
12. ## Decarbonising Fizzy Drinks

It's not the element carbon but dissolved carbon dioxide, CO2, that makes drinks fizzy. And it's not exposure to oxygen that makes them go flat, but the reduction of pressure on exposure to the atmosphere. When you open a bottle of fizzy drink, the pressure above the liquid drops. Since the amount of gas the water can dissolve depends on the pressure of CO2 above it, you then have a supersaturated solution, which is why it fizzes. Any nucleus for bubbles to form on will accelerate the rate at which the CO2 comes out of solution. A classic way is to put in a sugar lump. This has a large surface area with many sharp edges, which promotes the initiation of bubbles. Sand would also do the job, but not so good if you want to drink it later. The reason why you need a nucleus to start the bubbles off is because of the energy needed to pull apart the water molecules. The excess pressure inside a bubble is 2T/r where T is the surface tension of the liquid - a measure of the strength of the intermolecular forces - and r is the radius of the bubble. From this you can see that the smaller the radius, the higher the pressure, so in the limiting case this formula predicts an infinite pressure is needed to blow up a bubble of zero radius i.e. at the start. While this formula is not accurate at very small radii, it gives an idea of the problem. Sharp edges reduce the intermolecular forces in their vicinity, as the water molecules are not entirely surrounded by other water molecules, making it easier for gas molecules to push them apart and start off a bubble.
2 points
13. ## Could circuit board, electronic components tdust and dirt to some extent by design?

Most electronic circuits are pretty dust and dirt proof by nature. The main threat to these circuits is that they attract dust and dirt and that dust and dirt will coat the circuit board, components etc with a layer of dirt that sticks. This layer then thermally insulates the board and components and may cause some of them to overheat and fail. Most circuit boards can also be taken out and scrubbed in mild soapy water (or scrubbed in situ). So long as the assembly is thoroughly dried out before power is again applied everything will be OK.
2 points
14. ## The Lagrangian equation...

bump I would like to get back to this took a break
2 points
15. ## What would be the most important thing than humans should try to achieve in priority in your opinion ?

You're in luck, since I've heard some very convincing arguments lately that laziness, at least the way we typically think of it, never existed in the first place. It's simply a way to judge people who aren't doing something you think they should. The idea that people would rather do nothing than anything else is patently untrue. What we've always thought of as laziness is often just smart people refusing to do something in which they see no value, or smart people doing their jobs with the least amount of effort. Some jobs have been so dumbed down that they're almost insulting. Personally, I've always bragged about working smart rather than working hard. Does that make me lazy? This is one reason why I think the term is being misused. Right now, lots of business owners are screaming about lazy workers bringing conflict and problems, but I know a lot of those folks are just fed up with being underpaid. Productivity has been through the roof for the last 50 years, but wages have stagnated for workers and they're sick of working for a pittance while the rich sit on fat stacks of cash, waiting for the worker to falter so they can buy up their assets at twenty cents on the dollar. Again I think you're off by a bit. It's not the comforts that makes us less smart or want to work less, because historically, saving up for the comforts made us work harder to earn them. I think it's the convenience. Convenience seems to promote an attitude where people should do dumb things in order to save time. Spend an extra 25% on items from a small store so you don't have to spend the time dealing with a bigger store. Or shop online thinking to save some time but end up researching 20 products and their comments sections for three hours. Convenience lets you drive on fresh asphalt AND ensures you'll have potholes next year. I think "lazy" is a pejorative whip used by those who want us to work harder on their terms. Humans in general aren't lazy at all. We're ultra smart and curious, and we all prefer to do the things we want to do as opposed to the things we may HAVE to do. Nobody teaches us when we turn 18 that we have to parent ourselves from now on, and the real job of parents is to get us to do things we don't want to do. Practically everybody wants to do things as opposed to not doing anything, but they often don't want to do what everyone else thinks they should be doing. I remember being called lazy once because I arranged my work area to where everything was a bit closer to me. The boss hired me to make fittings and put them into boxes, not walk around unnecessarily, but when I tried to do a better job he called me lazy for not wanting to walk those extra steps. I pointed out that it saved me a LOT of time, but he still thought it was lazy. Said a young man shouldn't mind a few extra steps. I thought he was crazy.
2 points
16. ## crowded quantum information

I have to amend my previous statement. They can interfere under other situations, depending on the kind of entanglement. https://www.nature.com/articles/s41598-020-68181-1 Interference does not affect the frequency.
2 points

2 points
18. ## Do you have some movies to suggest please ?

The Thirteenth Floor is a special favourite - as noted by TheVat it was based on a German TV series called World on A Wire. If you enjoy VR based SciFi theme films, then you might also enjoy Avalon (2001) which is Japanese/Polish collaboration directed by Marmoru Oshii - who is probably better known for his original animated version of Ghost in The Shell (1995). Avalon was made on location in Poland with a Polish speaking cast and crew. A stand alone sequel called Asssault Girls set in the same world was released in 2009
2 points
19. ## Do you have some movies to suggest please ?

Flesh Gordon (1974)
2 points
20. ## Do you have some movies to suggest please ?

Debbie does Dallas Rumple Foreskin Penelopes Phallus Palace Hard Folks, Clean Strokes The Flintstones
2 points
21. ## Do you have some movies to suggest please ?

Old Westerns. Specifically Sergio Leone 'spaghetty' westerns. ( what were you expecting ? )
2 points
22. ## What would be the most important thing than humans should try to achieve in priority in your opinion ?

I disagree, but that’s off-topic
2 points
23. ## crowded quantum information

No I cannot think of any other example of non-locality. As far as I know, no other effects require that the outcome of an event at a specific point is determined explicitly on what happens at another point, unless there is a transfer of information. And relativity explicitly states that information is constrained to transfer at speeds not exceeding c . So non-locality is not just unproven yet, it is actually not needed; not even for entanglement.
2 points
24. ## Psychology is a soft science (split from Childhood hyperactivity; what makes it a bad thing?)

I wouldn't characterize psychometrics as the staple of psychology; I would rather call it a branch. Psychology was not born as a science; it's more a convergence of medicine (as medicine grew and became more sophisticated and compartmentalized in the 20th century) and ministry (spiritual guidance, usually provided to a community by its shaman or religious guardian). People have always suffered from disturbances of the mind, but these were not always considered medical conditions. They are insubstantial - no boil to lance, no rotten tooth to yank; no fever, shooting pains or vomiting; no spots or rashes or lumps to examine. They manifest in ordinary behaviours in what is considered inappropriate situations - except what is considered appropriate and inappropriate varies by culture and situation. It manifests in moods and feelings that are normal in some situations, in some degree and duration, but are considered abnormal in excess - except that the assessment of excess is also cultural and situational. It manifests in distress felt only by the patient, but judged by other people, who cannot see, touch or feel it themselves. Consider the range of intelligence, sensitivity, temperament and resilience of human beings. Project that onto a big white wall. Superimpose the range of normal emotions, reactions and ideation of which beings are capable. Superimpose the range of philosophies and attitudes of societies to what is considered 'normal'. Superimpose the range of parenting style, influences, expectations and circumstances of childhood. Superimpose the list off the 'aberrant' behaviours people display. Superimpose the symptoms of exposure to chemicals in food, the environment, therapeutic and recreational substances. In front of that great big busy wall, put one young man who says: "Help me. I'm afraid to go to sleep." Where do you start? Trying to address that kind of dis-ease, to classify, codify, diagnose, trace to its cause and alleviate it is never going to be a slide-rule kind of problem.
2 points
25. ## Mathematics is Inconsistent!

No, it doesn’t. What it does say is that you can decompose a Euclidean 3-volume into a finite number of subsets, each of which is itself a non-measurable collection of infinitely many points, and then reassemble these subsets in a new way. The crucial point here is that you cannot uniquely and self-consistently define the notion of ‘spatial volume’ for a non-measurable infinite collection of individual points, so this decomposition does not preserve the original volume, contrary to naive intuition. It’s a subtle ‘trick’ of sorts to do with Lebesgue and Banach measures. IOW, the Banach-Tarski paradox breaks down and reassembles a 3-volume in a way that does not itself preserve the original volume. Thus it is hardly surprising that you can turn a ball into two balls in this manner - in fact you could turn a ball into anything at all in this manner, no matter how big or small. It isn’t a true paradox, and most certainly not an inconsistency in mathematics. Also, don’t forget that unfortunately we do not really live in an infinitely sub-divisible 3-dimensional Euclidean world where such a procedure could in fact be implemented - it would be a neat little trick with lots of interesting applications!
2 points
26. ## Science of gasses in Earth atmosphere.

Consider dG = dH - TdS For a column of atmosphere at uniform density & pressure under a gravitational field, a downwards vertical flow is favoured (supporting the argument of @studiot) since the release of gravitational energy increases total enthalpy sufficiently to counter the reduction in entropy due to reduced occupancy of the higher levels of the column. So we have established an equilibrium condition with a vertical density/pressure and entropy gradients much as the atmosphere we see around us. But for further gravitational settling of, say, CO2 to take place, the gravitational potential energy released is now countered not only by the entropy gradient, but also the necessary displacement of an equal volume of lower density gases previously below it generating an adverse temperature gradient and expansion of the lower levels due to both the temperature gradient and the reduced mass of the upper part of the column. In short, while dH is likely not zero for a perfectly uniform gas mixture (constant mole fractions) it becomes so small that it can support only a tiny mole fraction gradient. I therefore suspect that while @exchemist and @Ken Fabian are not quite 100% accurate in their assertions, in practical terms they are very close to measurable reality. It's certainly an approximation I used throughout my working career without a qualm. The 'phosgene' counter argument simply reflects the very low rate of diffusion of high molecular weight gases. The thermodynamic equilibrium remains an (approximately) evenly dispersed mixture. It's just that these cases take their time about reaching equilibrium.
2 points
27. ## Minkowski space and geometric intuition

The length of a world line between given events in Minkowski spacetime is defined to be equivalent to the proper time of a clock travelling between these events that traces out that world line. In other words, it’s simply the total elapsed time that’s physically measured on a clock that travels along a specific spatial path between event Excellent short answer +1 I would like to add to the second answer to the question "what does it mean....?" Minkowski imposes a cartesian coordinate system, which as Eddington pointed out a century ago, actually adds unneccessary mathematical structure. The same result could be achieved by a set of events and a set of the invariant intervals between them. This would form a network of linked events, with no cartesian structure superimposed. The sum of these invariants connecting any pair of events as a mathematical 'graph' (since this thread is partly about geometry, whch includes geometrical graph theory) then includes the shortest path. Ref Eddington The Mathematical Theory of Relativity pages 8 - 16, Cambridge 1923 (my ed 1954)
2 points

2 points
29. ## Complex or real wave function?

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.
2 points
30. ## Complex or real wave function?

Energy eigenstates are states where x and t can be separated in the time-dependent equation, so the solutions can be factored into two terms, as f(x)exp(iwt). Solutions with no potential-energy function (V(x,t) = 0) are traveling plane waves, and solutions with an infinite potential well are not dispersive. So calling the Schrödinger equation a "diffusion equation" seems misleading to me, and "wave equation" seems reasonable. I think the linear time derivative in the Schrödinger equation is misleading because its coefficient is imaginary. I think it has more in common with a real-valued second derivative from a physical or dynamical point of view, even though it superficially looks like a diffusion term. Traveling waves aren't defined in terms of oscillation, but standing waves are certainly associated with it, and classical diffusion is a completely different phenomenon, with no oscillation at all. PS: How do you edit equations here?
2 points
31. ## Putin has attacked Poland?

By all accounts it seems to have been Ukrainian AD system that went off course. The argument could be made for giving Ukraine mor emodern AD, like the Patriot or ( Israeli ) Iron Dome AD systems, so similar incidents are not repeated.
2 points
32. ## Complex or real wave function?

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.
2 points
33. ## The Official JOKES SECTION :)

It doesn't matter if they aren't spotted. The interesting question is which side of a zebra has the most stripes? And of course, it's the outside. Last time I bought zebra, the clerk scanned the wrong barcode and I got charged for rhino.
2 points
34. ## crowded quantum information

Maybe not intended but I see this as yet an analogy for entanglement. Assume a couple is married and then separated by some (great) distance. When one (random) individual of the married couple dies we immediately know that the other party has become a widower or a widow. The immediate change from wife to widow (or husband to widower) does not need a signal.
2 points
35. ## Complex or real wave function?

Indeed so. In fact the naming of the equations is somewhat arbitrary and discipline dependent. Classically both the wave equation and the diffusion equation were derived from the more general telegraph equation by setting some of the coefficients to infinity or zero.
2 points
36. ## My point of view on religion

I like and agree in most part the basic premise of the views of the OP. In fact if that is all religion is designed to do then I'm in. Anything that promotes a healthy and happy standard of living for all life is surely a good thing, no? I also agree that "if" god is real then I would imagine god to be unimaginable, as I have stated before. But I'm also happy with the notion that there is no requirement for god in the first place.
2 points
37. ## My point of view on religion

Certainly there are creators and those created by them, but the physical evidence seems to show that the religious have the identities reversed.
2 points
38. ## Artificial brain, mind uploading : what level of difficulty ? what do you think about it ?

Computational neuroscience would cover most foundations.
2 points

2 points
40. ## LHC costs money, is it worth it?

Google: CERN annual budget. Voila. https://cds.cern.ch/record/2799091/files/English.pdf
2 points
41. ## This book lays out a greater justification for belief in its doctrine than any other holy book in history and is the greatest threat to the Abrahamic religious systems

What if someone were born on Mars at the same time? The whole system seems to fall into incoherence. If planets were in a certain relative position when someone was born on Earth, those positions would be different from the perspective of Mars's surface. I'm a Feces - it's a small cluster of stars under Taurus the Bull.
2 points
42. ## LHC costs money, is it worth it?

That is equivalent to the unit cost of four B-2 bombers; not including operational costs. The US SAC has a fleet of about 20. Shouldn't Thewowsignal be bitchin' about the cost of something else ?
2 points
43. ## Dark matter found?

Some issues with your idea: It fails to explain why DM(Dark matter) is concentrated as spherical halos surrounding galaxies. Our own galaxy's DM halo only extends out to 210 thousand parsecs (compared to the 27 thousand parsec diameter of the galaxy itself). It is within this radius that the "extra mass" is needed to explain galaxy rotation curves. If the majority of light is contributed by other galaxies, then it would not be concentrated in a region around us (or any other galaxy.) But the vast amount of dark matter mass would be evenly spread out through the universe. Andwith this being the case, it would have no gravitational effect on individual galaxies' rotation. ( Mass evenly distributed throughout the universe has no effect locally, as the combined effects cancel each other out over "small"(compared to the size of the universe) regions. Put another way, for things to work the way we see them happening, the extra mass of DM has to be mostly clumped around galaxies, and not spread out evenly through the universe. And if that much light was concentrated in the region around galaxies, we would see it. Even intergalactic space isn't completely empty, and the little material there would scatter enough of that light to produce a visible "glow" It fails to explain why we have found some galaxies that seem to show little to no indication of DM. They produce just as much light as other galaxies, and are being bathed in just as much light, but do not behave the same. Then there are observations like the Bullet cluster, where we are looking at the aftermath of galactic collisions. Here we can use gravitational lensing to locate concentrations of mass, and have noted that after the collision, there is a region that shows a concentration of mass that is separate from any visible light source. This is what one would expect if the DM was separated from its parent galaxy by the collision. This is not something that could occur if DM was the result of the mass of light.
2 points

2 points
45. ## The Official JOKES SECTION :)

I just thought the pronoun thing wasn't very funny. We are allowed to react to the jokes, right? For example, my SpaceX/SpaceY joke was tasteless and crude, and I would support anyone's right to say so, or reject it any other way. Personally I find the pronoun choice for nonbinary folks a poor one that's kind of been forced on them by the fact that people are unable to adapt to new pronouns which would surely work better and without ambiguity. Instead of she and her, why not assign a new NB set of pronouns like de and der? This would eliminate what would seem to be a chronic source of confusion with they/their/them.
2 points
46. ## McCarthy said it will be "hard" not to hit Pelosi with gavel

The Meidas Touch news site recently produced a viral super-cut video after Fox anchor Laura Ingraham asked "Which Republican official or candidate has ever condoned or encouraged any form of violent physical assault ? Can you start naming them ? I can't think of any". The video was featured by Stephanie Ruhle on MSNBC last night as her sign off to the 'The 11th Hour".
2 points
47. ## Are you atheist?

Did you just come here to fight?
2 points
48. ## Why cooking oil runs faster when heated?

There are intermolecular forces acting between the molecules in the liquid, which have to be overcome in order for molecules to slide past one another. At higher temperatures, a greater proportion of the molecules have enough kinetic energy to overcome at least some of these forces, reducing the resistance to them moving relative to one another.
2 points
49. ## Are you atheist?

You played your hand and I'm no longer engaging with you. Google Bertrand Russell if you find yourself ignorant of his philosophy. For those following along - this is a particularly tricky game of shifting the burden of proof - e.g. 1: "Some people believe in bigfoot, I personally don't" 2:"Please provide evidence that bigfoot doesn't exist" 1: "You're asking for me to prove a negative, that's a logical fallacy" 2: "You made the positive claim bigfoot doesn't exist. The burden of proof is on you to prove bigfoot doesn't exist." That's not how the burden of proof works. 1 is claiming a null state. 2 is then demanding proof of the null. If this were a hypothesis test, 1 demonstrates a result not supporting the test hypothesis. 2 is then demanding statistical proof of the null. That's not how a hypothesis test works - one tests the test state and either supports it or does not (refracting to the null). Nothing about this preposition provides support for the test state, nor that retaining the null state demands a burden of proof. E.g. Say I dropped a pencil and it fell to the ground. Demanding proof it didn't fly into the Sun is not a logically valid premise. If someone demands that it is, they are intellectually dishonest, and not worth engaging. As demonstrated.
2 points
50. ## Are you atheist?

That's probably the most elegant shifting the burden of proof I've ever seen. Well done. I can't prove that every belief system is developed by humans any more than I can prove that none of the pigeons in New York City are robots, or that none of the "humans" in West Virginia are bigfoot. We've done a big circular dance to the logical fallacy where you demand that atheists prove God isn't real. To illustrate; Could you prove that there isn't a single mushroom in the world that a fairy doesn't sleep under? Does that mean the only logical premise is to accept the existence of fairies? Why or why not?
2 points
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