in phenomenon, Scientific

Ask HN: What scientific phenomenon do you wish someone would explain better ?, Hacker News

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                   Quantum Computers. Not like I’m five, but like I’m a software engineer who has a pretty decent understanding of how a classical turing machine works. I can’t tell you how many times I’ve heard someone say “qubits are like bits except they don’t have to be just 1 or 0” without providing any coherent explanation of how that’s useful. I’ve also heard that they can try every possible solution to a problem. What I don’t understand is how a programmer is supposed to determine the correct solution when their computer is out in some crazy multiverse. I guess what I want is some pseudo code for quantum software.

                   

                          I recommend Computerphile’s videos (https: //www.youtube.com/playlist? list=PLzg3FkRs7fcRJLgCmpy3o … . I had the same “problem” as you. What finally made me feel I sort of cracked it was those videos. The way I think of it now is: They let you do matrix multiplication. The internal state of the computer is the matrix, and the input is a vector, where each element is represented by a qubit. The elements can have any value 0 to 1, but in the output vector of the multiplication, they are collapsed into 0 or 1. You then run it many times to get statistical data on the output to be able to pinpoint the output values ​​more closely .             

                          In short I’d say you need to understand the underlying mathematics to intuitively understand the operations that underpinn the algorithms. And since this is quantum mechanics … there’s no real ELI5 version that can give you any useful understanding.

            

                          I had an aha moment with quantum computers a few months ago when reading an article that explained it as probability distributions. I don’t think I have the complete understanding in my mind anymore and I wish I had saved the article, but looking into how quantum computers essentially serve as probability distribution crunching machines might help with your understanding.

            

      

                   So can they still do traditional deterministic. (?) calculations? Or would that be somewhat akin to using machine learning to do your taxes; possible but just overkill? I’ve often heard it said that Quantum Computers can crack cryptographic keys by trying all the possible inputs for a hashing algorithm or something handwavey like that. Are they just spitting out “probable” solutions then? Do you still have to try a handful of the solutions manually just to see which one works?             

      
                   I would like to understand how cellular biology processes actually work. Like, how do all the right modules and proteins line up in the right orientation every time? Every time I watch animations, it seems like the proteins and such just magically appear when needed and disappear when not needed [0]. Sometimes it’s an ultra-complex looking protein and it just magically flys over to the DNA, attaches to the correct spot, does it’s thing, detaches, and flies away. Yeah right! As if the protein is being flown by a pilot. How does it really work?
[0] (https://youtu.be/5VefaI0LrgE)
            

      

                   The issue with these animations is that They’re getting rid of all the thermal noise. In reality, single proteins are flying around the whole length of the cell many times a second, just from their thermal motion. And when processes like DNA transcription happen, they’re not like a regular conveyor belt – a fraction of the time the machine will even accidentally run steps in (reverse) ! However, if any of this were shown, the animations would become impossible to understand.

                         

      

                   any time something “magically lines up “, it means that those molecules randomly float around until the right ones bump into each other.
Once they are in close enough proximity to bump into each other, intermolecular forces can come into play to get the “docking process” done.

For something like transcription, once they are “docked”, think of it like a molecular machine – the process by which the polymerase moves down the strands is non-random. there are also several ways to move. things around in a more coordinated fashion. Often you have gradients of ion concentration, and molecules that want to move a certain direction within that gradient. You also have microtubules and molecular machinery that moves along them to ferry things to where they need to be. You can also just ensure a high concentration of some molecule in a specific place by building it there.

            

      

                   (A few different things help everything work : 1) Compartmentalizing of biological functions. Its why a cell is a fundamental unit of life, and why organelles enable more complex life. Things are physically in closer proximity and in higher concentrations where needed.

2) Multienzyme complexes. Multiple reactions in a pathway have their catalysts physically colocated to allow efficient passing of intermediate compounds from one step to the next.

(https://www.tuscany-diet.net/) / / / multienzyme-complexe … 3) Random chance. Stuff jiggles around and bumps into other stuff. Up until a point, higher temperature mean more bumping around meaning these reactions happen faster, and the more opportunities you can have for these components fly together in the right orientation, the more life stuff can happen more quicky. There’s a reason the bread dough that apparently everyone is making now will rise faster after yeast is added if the dough is left at room temp versus allowed to do a cold rinse in the fridge. There are just less opportunities for things to fly together the right way at a lower temperature.

3a) For the ultra complex protein binding to the DNA, how those often work in reality is that they bind sort of randomly and scan along the dna for a bit until they find what they’re looking or fall off. Other proteins sometimes interact with other proteins that are bound to the DNA first which act as recruiters telling the protein where to land.

            

      

                   I recently started taking insulin. Check out the molecular structure for that. It blows me away how complex it is.

            

      

                   From a physics perspective I bet you have two things happening: 1. These molecules are moving around a lot

The kinetic energy of molecules at room or body temperature gives them impressive velocity relative to their scale, and they’re also rotating altogether and internally. 2. Compatible molecules are like magnetic keys and locks. They attract each other and the forces align with meeting points. The same way that proteins fold spontaneously. So the remaining part is getting concentrations appropriate for what you want to happen – and that’s a matter of signaling molecules and “automatic” cell responses to changes in equilibrium. It’s a really chaotic system and it’s a wonder it works at all.

I imagine that’s also one reason life is imprecise, ie no two individuals are alike even with identical genes. There’s a lot of extra “entropy” introduced by that mess of a soup.

            

                   I find most explanations of the Equivalence. Principle that lies at the foundation of General Relativity to be very lax. To wit, the idea is that you cannot distinguish whether you are in an accelerated frame or in a gravitational field; alternatively stated, if you’re floating around in an elevator you don’t know whether you’re freefalling to your doom or in deep sideral space far from any gravitational source (though of course, since you’re in an elevator car and apparently freefalling … I think we’d all agree on what’s most likely, but I digress). Anyway, what irks me that this is most definitely not true at the “thought experiment” level of theoretical thinking: if you had two baseballs with you in that freefalling lift, you could suspend them in front of you. If you were in deep space, they’d stay equidistant; if you were freefalling down a shaft, you’d see them move closer because of tidal effects dictated by the fact that they’re each falling towards the earth’s center of gravity, and therefore at (very slightly) different angles. Of course, they’d be moving slightly toward each other in both cases (because they attract gravitationally) but the tidal effect presents is additional and present in only one scenario, allowing one to (theoretically) distinguish, apparently violating the bedrock Equivalence Principle. I never see this point raised anywhere and I find it quite distressing, Because I’m sure there’s a very simple explanation and that General Relativity is sound under such trivial constructions, but I haven’t been able to find a decent explanation.

                   

      

point particles falling, the effect of gravity is the same for all particles. This suggests that we should model gravity as something intrinsic to spacetime itself, rather than as a field living on top of spacetime, which could couple to different particles with different strengths.
The second part of the argument, which is what you point out, is that gravity can have nontrivial tidal effects. (This had better be true, because if all gravitational effects were just equivalent to a trivial uniform acceleration, then it would be so boring that we wouldn’t need a theory of gravity at all!) This suggests that whatever property of spacetime we use to model gravity, it should reduce in the Newtonian limit to something that looks like a tidal effect, ie a gradient of the Newtonian gravitational field. That leads directly to the idea of ​​describing gravity as the curvature of spacetime. So both parts of the argument give important information (both historically and pedagogically). Both parts are typically presented in good courses, but only the first half makes it to the popular explanations, probably out of simplification.

            

      

            

      

            

      

                   Yeah the problem is that that the equivalence principle is a _local_ property that cannot really be expressed precisely in standard English. Clearly it will fail given a big enough lift to experiment in, Since a big enough lift would essentially include whatever object is creating that gravitational pull (or enough to conclude its existence from other phenomena). However these effects are nonlocal, you need two different points of reference for them to work (like your two baseballs). In fact most Tidal forces are almost by definition nonlocal.

The precise definition involves describing curved spacetime and geodesics, but that one is really hard to visualize as a thought experiment. The thought experiment does offer insight though, as it is possible to imagine that, absent significant local variations in gravity, you cannot distinguish between free-fall and a (classical) inertial frame of reference without gravity. This insight provides the missing link that allows you to combine gravity with the laws of special relativity and therefore electromechanics, including the way light bends around heavy objects, which provided one of the first confirmations of this theory.

            

                          The elevator car is a thought experiment. that draws attention to the equivalence in sensation of acceleration on one hand, and being in a (uniform) gravitational field on the other hand. As you correctly point out, this particular thought experiment breaks down when you consider that all of the gravitational fields that we are accustomed to are non-uniform, and have apparent tidal forces.

The real principle of relativity is a bit more subtle (sometimes called the strong principle): that the effects of gravity can be explained entirely at the level of local geometry, without any need for non-local interaction from the distant body that is generating the gravitational field. To describe the geometry of non-uniform fields, we need more sophisticated mathematical machinery than what is implied by the elevator car thought experiment, but nonetheless, the elevator example is a useful launching point for that type of inquiry.

            

      

                  > you’d see them move closer because of tidal effects dictated by the fact that they’re each falling towards the earth’s center of gravity, and therefore at (very slightly) different angles.

This point isn’t raised anywhere because it’s mostly a pedantic point that has nothing to do with the thought experiment. You shouldn’t try and decompose thought experiments literally, otherwise you’ll get caught up in unimportant details like this. Just assume the elevator is close enough to the earth such that the field lines are effectively parallel, or better yet, just pretend the elevator is in an infinite plate field.

            

      

                   I’m gonna assume that for purposes of the thought experiment you’re supposed to envision a point-shaped elevator, not one where you can place two baseballs next to each other.                          

                          I think the elevator scenario is imagining that the earth is a point source, and you are neglecting the (much smaller) gravitational forces for the sake of illustrating a more general phenomenon.

            

                   The twin paradox. All explanations seem to be just “something something one twin has to accelerate”

                   

                          Quantum spin. Electrons aren’t really spinning, right? But why do we call it spin? I know it has something to do with angular momentum. What are the possible values? Is it a magnitude or a vector? Is there a reason we call it “spin” instead of “taste” or some other arbitrary name? How do you change it? What happens to it when particles interact?             

       [2]                   > Electrons aren’t really spinning. , right? Correct. > But why do we call it spin?

Because it is a physical quantity whose units are those of angular momentum, and we have to call it (something) . > What are the possible values? /- h / 4pi where h is Planck’s constant. (It is usually written has h-bar / 2 where h-bar is h / 2pi.) > Is it a magnitude or a vector? It’s a vector that always points in a direction corresponding to the orientation of the apparatus you use to measure it. > Is there a reason we call it “spin” instead of “taste” or some other arbitrary name?

Yes. See above. > How do you change it? You can change an electron spin by measuring it along a different axis than the last time you measured it. The result you get will be one of two possible values. You can’t control which one you get.

> What happens to it when particles interact?

Their spins become entangled.

            

                          No, they are not really spinning. . However the spin quantum property does make the particle deflect as if it were spinning when it moves through a magnetic field, thus the name.
It is techinically a two-component spinor, which is why the direction of the spin ‘moves’ if you measure it along different x, y, z axes. It is also quantized unlike a normal vector: All fermions have quantized half-integer spin magnitudes and all bosons have integer magnitudes. (Magnetic fields can be used to change the spin.) When particles interact, opposing spins tend to pair up in each electron orbital which cancels the magnetic field. This is why permanent magnets must have unpaired electron orbitals.

            

       ()                    If you take some ball of charge and actually spin it, and then place in inside a magnetic field, it moves in a certain way. If you take a single electron and place it in a magnetic field, it moves in that same way as the ball of charge. Ergo, its natural to call the relevant intrinsic property of electrons “spin”.
            

      

                  
Annoyingly I’ve always struggled with the precise definition of spin, but to my understanding angular momentum is (only) conserved if you take spin into account as well. Being quantum mechanical there is some ambiguity in the direction, but in principle it is a vector (except it’s a superposition of several vectors, and this superposition is also equal to superpositions of (different) vectors, I think there is usually one ‘pure’ vector, but that might just be after measurement).

            

      

                  > angular momentum is only conserved if you take spin into account as well.
Do you know an example of a process that moves angular momentum from one kind of spin to the other? 		                         

      

                   Electrons have both angular momentum and magnetic momentum, these have fixed magnitudes and they are always parallel.
The situation is somewhat similar to a classical spinning charged sphare, although this similarity easily breaks down.
            

      
                   Fourier Transforms. I’d wish I had a intuitive understanding of how they work. Until then I’m stuck with just believing that the magic works out.
                         

      

                   This really depends on the level of math you’re expecting for your intuition, but for me it really clicked when I understood it in terms of linear algebra.
A function is like a vector, but instead of having two or three dimensions you have a continuous number of them. Adding functions component-wise works just like adding vectors.

Just like regular vectors, you can choose to represent functions in a different basis. So you choose a family of other functions (call it a basis) that’s big enough to represent any other you want. For a lot of reasons [1, 2], a very good choice is the set of complex exponentials g_w (x)=exp (2πiwx), for every real w. It’s an infinite family, but that’s what you need to deal with the diversity of functions that exist.

So you try to find the linear combination of exponentials that sum to your original function. You need a coefficient for each w, so call it c (w) for simplicity. After fixing the basis, the coefficients really have all the information to describe your function. They’re an important object, and we call c (w) the Fourier transform.

How do you find the coefficients? Just project your original function onto a particular exp (2πiwx), that is, take the inner product. Usually the inner product is the sum of the products of coefficients. Since functions are continuously-valued, you use an integral instead of a sum. This is your formula for the Fourier transform.

I known there are technical conditions I am glossing over, but this is the intuition of it for me. [1] There is an intuition for these exponentials. Complex exponentials are periodic functions, so you are decomposing a function in its constituent frequencies. You could also separate the exponential into a sin and cos, and will obtain other common formulas for the Fourier transform. [2] Exponentials are like “eigenvectors” to the derivative operation (taking the derivative is just multiplying by a constant), so they’re really useful in differential equations as well.

            

      

                   What’s the difference between the coefficients of the furier basis and the weights of a neural network? Both are ways to approximates functions, aren’t they?
            

                   the difference is the basis that is chosen. Fourier use sin and cos as a basis (or equivalently complex exponentials). You can choose other bases and get wavelets, or hermite functions, or any other particular independent functions.
Weights on neural networks don’t have to be independent functions. Gives you a set of mathematical guarantees that insure you fully cover the space you’re representing. For example that given a 2 dimensional space, X and Y are pointing in different directions. If they pointed in the same direction you could not fully decompose all vectors on the plane into two coefficients of X and Y.

      
                         

      

                   I had a professor describe a FT. as a “dot product of a function against the real signal space”. Thus a FT is valued higher at frequencies where the input signal is more “similar” or “in line” with that frequency. Conversely, the FT is zero where there are none of those frequencies in the input signal. If this helps, then it can also help with understanding other projections such as the Laplace transform (a dot project against the complex signal space).

While this analogy has helped me, I still have no clue why real valued signals result in an even FT.

edit: grammar

            

            
      

                   Every analytical function, like f ( x)=x ^ 2-log (x 1), or signal, like a radio signal, can be rewritten as as infinite sum of sines and cosines. The Fourier transform helps you break down these components for you

            

                   Bell’s theorem. It somehow proves that quantum physics is incompatible with local hidden variables, but I could never see an understandable explanation (for me at least) of just how it works.

      
                                                   

                          I started to read the first one but his insistence that Many Worlds is true was too frustrating. Many Worlds Theorem seems specifically useful at saying “the variables aren’t hidden because everything before wavefunction collapses actually plays out in different worlds.
But, we specifically have no way of proving that theory. So now we’re back to the essence of the original question – if these things seem random why do we know that they’re in fact deterministic without any hidden variables?

            

                   Well, I’d recommend to read the whole series. It’s not so bad as it sounds. There are so many steps from where you are to appreciating the utter (weirdness) of Bell’s experimental result. Not the weirdness of any theory (or an interpretation, which Many Worlds actually is) but of the basic experimental result.
If you are properly amazed by it, rejecting MWI or any crazy-ish borderline -conspiracy theory seems suddenly a lot harder. I feel the whole Yudkowsky’s QM series in fact served to deliver that one post.

                   

      

                   To be clear, I don ‘ t reject Many Worlds at all and in fact consider it a promising candidate due to it sort of “falling out” of the Schrodinger’s equations taken literally unless you add complexity.

But the fact remains that it is impossible to prove and it is conveniently well equipped to handle this situation. I’d prefer an argument that presupposes the Copenhagen interpretation as that is when my intuition fails.

            

      

                   I trust Yudkowsky on many things, but not on that explanation. It’s still quite complicated, and a couple of times I miserably failed to reconstruct it over a beer or two. A red flag. Plus, I’d rather expect at least one professional (QED) physicist exists able to explain it and he isn’t one. Mermin is, but the explanation is decidedly less clear.

BTW I came here to say Bell’s inequality as well. For me it’s as baffling as science could ever be.

                         

                   Subreddit / r / askscience does a good job at explaining science in plain words. I usually google “site: reddit.com/r/askscience/ __QUESTION __”. The StackExchange sites have less coverage and answers tend to be more technical. University websites return reliable answers, but often neither short nor accessible.

                   

                   What happens when you actually fall inside a black hole and what is the singularity.
I never really understood what happened really when the guy fell inside it in Interstellar and how come he started seeing all those photos. I just accepted it as Hollywood bs. I know my question is based on a movie but would still like to know what will someone witness (assuming of course they somehow live)

                   

                         > I never really understood what happened really when the guy fell inside it in Interstellar and how come he started seeing all those photos. I just accepted it as Hollywood bs.

Coupled with people saying “but they had scientists on staff! They talked with scientists that makes it so cool and accurate, lets ignore that other part “

                         

                          You should check out PBS Space Time. (on youtube), there are several episodes explaining this in different ways.

                                                                

                  
Flight. Apparently “air flows faster on the top side of the wing, lowering the pressure” is an incomplete explanation; I even heard we don’t completely understand why it works (?!?).
      
            

      

[2]             

                  
Aerospace engineer here: What a lot of people don’t know is that the wings are actually installed on a small upward incline, relative to the longitudinal axis of the body. Think of holding your hand out the window of a moving car, and then tilting your hand to catch air under your palm. In aerospace we call this the Angle of Incidence, and most aircraft have a small amount, usually in the 1-5 degree range. Now google any picture of an airfoil and notice that many of them are slightly concave on the underside. This is called Camber, and in a nutshell it creates a “cupping” effect under the wing that increases the amount of air deflected downward. Additionally, the teardrop shape reduces the tendency of air to billow off the trailing edge of the wing in favor of kinda sticking to the wing’s surface and following its curvature. This also causes downwash off the trailing edge. That’s really all there is to it, from a high level. The wings deflect air downward such that the total momentum change causes an upward force that is exactly equal to the aircraft’s weight, and that equilibrium of forces keeps the aircraft aloft. Obviously it gets more complex than that, because guys spend entire PhD careers researching edge cases, but there’s no magic involved. that wings don’t have to be of the classic teardrop shape. There are plenty of research papers about lift forces on flat plates. In fact that’s classic fodder for an undergraduate assignment. The airfoil shape is beneficial in several ways, some of them quite subtle, but you can think of the airfoil as being the most efficient cross-section for a wing known to science, whereas a flat plate is much less efficient (though it still works

      

                   It directs air moving horizontally downwards, by conservation of momentum the wing must get additional upwards momentum, called lift.

            

      

                   That can’t be the explanation. , otherwise wings wouldn’t need to be curved – flat wings could fly, as long as they’re tilted to redirect the air.
                         

      

                   I think this is actually a good explanation of the lift force, but lots of other factors come in to play for wing shape. Two other big factors are drag forces, which are dependent on the surface area, air density and the velocity of the craft, and so there’s a complicated optimization problem there, and turbulence, which depends a lot on the wing tilt, and the the shape of the wing. )

            

                   I’m not too sure it won’t work, but I’m pretty sure it won’t be efficient. Or maybe your plane will just rotate until the wings are horizontal again.
      
            

      

https: //fermatslibrary.com/s/how-airplanes-fly-a-physical-de … (the summary being:

– The vertical velocity of the diverted air is proportional to the speed of the wing and the angle of attack.

(The – The lift is proportional to the amount of air diverted times the vertical velocity of the air

It also debunks the myth of “air flows faster on the top side of the wing, causing lift”

            

      

                   Flight is EXACTLY like swimming except in air and without any component of floating. You’re welcome.

            

      

                   This is only a partial explanation. The effect you’re speaking of is pretty simple: The top of a wing is curved, making it longer than the bottom of the wing. This means that air takes longer to go over it, meaning it has to spread out further to go the same distance as the air under the wing. As a result, the air going over the top of the wing is less dense, (aka lower pressure). The wing tries to equalize the pressure by moving in the direction of the low pressure, which is Up. We call this Lift.
That accounts for some of the lift, but not all of it. For the rest of it, stick your hand out the window of a car doing mph and “fly” your hand up and down in the air. Wings do the same thing, just far more subtly.

            

      

                   (The> The top of a wing is curved, making it longer than the bottom of the wing. This means that air takes longer to go over it, meaning it has to spread out further to go the same distance as the air under the wing. As a result, the air going over the top of the wing is less dense, (aka lower pressure). The wing tries to equalize the pressure by moving in the direction of the low pressure, which is Up. We call this Lift. (% completely false.) Imagine you have two particles of air, and they are immediately adjacent to each other. Suppose now that one goes above the wing, and one goes underneath. In your example, the particle going upward goes further in the same amount of time.

But ask yourself this: Why do the particles of air have to arrive at the same time? What mechanism from physics requires that they end up at the far end of the wing?

()             

            
                   Hawking Radiation. I know just enough to know that the story of “anti-particle of virtual pairs happens to always fall in the hole” is a Lie Told To Children, but the explanations seem to go straight from there to rather dense math and I’ve never wrapped my head around it.             

                   

                   When two particles get closer, their mutual gravitational attraction increases. As the distance approaches zero, the force approaches infinity. In the limit of d -> 0, the energy released -> infinity. Obviously at some scale the notion of a point mass breaks down, but even quantum theory would be problematic if we think of a wave function as describing a (probability) distribution, wouldn’t it? What’s the “official” story on this?

                   

      

                   The official way this is handled is called renormalization. Basically, we just declare that we have no idea what is going on at such short distances, and put in some regulator by hand to get rid of the infinity. One very crude regulator (which nobody uses, but which is suitable for demonstration) would just be to say that particles are simply not allowed to get any closer than some fixed tiny distance. But what about the effects that occur when particles actually do get that close? Well, in most theories, whatever is happening can be parametrized in terms of a few numbers (e.g. it could shift the observed mass of the particles, or their charge, etc.). Our ignorance of what is actually happening prevents us from computing these numbers from first principles. But we can still make scientific progress, because we can treat them as free parameters and measure them – and after that measurement, we can use the values ​​to crank out perfectly well-defined predictions. Repeating this process through several layers was crucial to building the Standard Model, which Currently has about 1818 free paramet ers.

            

                          What follows is very hand-wavy. , and the renormalization sibling post may touch on it. An answer is that the d-> 0 approaches infinity presumes a nice, continuous analytic function . If d-> epsilon, you can’t get to that singularity.

There was an equivalent problem in the E / M space with “The Ultraviolet Catastrophe” [1], which turned out to go away if you assumed quantization. I’m not going to claim this is a perfect analog to the gravity problem, only that a lot of physics doesn’t quite work right when you determine continuity. (The Dirac delta is a humorous exception that proves the rule here, in that doing the mathematically weird thing actually is closer to how physics works, and it required “distribution theory” as a discipline to prove it sound.) https://en.wikipedia.org/wiki/Ultraviolet_catastrophe

            

                          This is definitely related, though not. the whole story. Quantization did get rid of some infinities, but as GP kind of states, it also introduced others. My comment focuses on what we do for those.

            

                  > In the limit of d -> 0, the energy released -> infinity. I believe the poster’s general premise to be false. While renormalization may be useful in resolving infinities in general, I don’t think it’s necessary for this one.

You can’t commute the dp dx of a Hamiltonian to be zero in a quantized world, so if gravity has quantum properties, you don’t need to worry about what happens when d -> 0. There is no “0” distance.

            

      
                          I guess, but it depends on how one parses the poster’s setup. You’re correct that for particles interacting under a 1 / r ^ 2 force, the energy turns out finite in quantum mechanics. My comment was referring to the fact that once you quantize the field that gives rise to that force, the infinities return, but for a different reason.

            

                   When I hear explanations like “space is expanding like the surface of a balloon ”it’s always confusing. Because a surface is an object, separate from anything on it, but space is the thing we’re all embedded in, so we’re like drawings on the balloon.

If space is expanding why aren’t the radii of fundamental particles and their orbits and molecules also expanding? And if that were the case we couldn’t notice space expanding.

            

      
                         > If space is expanding why aren ‘t the radii of fundamental particles and their orbits and molecules also expanding? And if that we’re the case we couldn’t notice space expanding.> Does space only expand somewhere else? Only between me and the Andromeda galaxy, and not _within_ me and the Andromeda galaxy? How would it know to do that? If you start with expanding space in general relativity, and then carefully take the limit where you get back to Newtonian gravity, then it just corresponds to a classical force, specifically a very tiny force that weakly pulls everything apart, growing with distance . This does not expand small objects, because they’re rigid. It’s the same reason that I can’t make my laptop get bigger by gently pulling on the ends. On the other hand, it would pull apart two independent, noninteracting objects (such as the Milky Way and Andromeda).

            

       [2]                    On top of that, FLRW spacetime is a large-scale approximation: More realistic models should probably follow the ‘swiss-cheese’ approach, where local conditions can look rather different.

            

                          The mathematics of training a neural network . I understand how they work once trained, but that you can train them almost seems too good to be true.                                                    

                   Why tardigrades are so hardy, how their biology is so different?
How immune system and medications work. Why some plastics are recyclable and others are not.
                   

      

                   I’ve been mulling making a youtube channel with ten minute videos on immunology; what would be a good starter video that might interest someone like you? I thought I’ll do something about antibodies as drugs!

            

      

            

                   Thank you and please please do it and post a link here or send me an email (in profile)! For me the most interesting is the recognition / pattern matching aspect: how antibodies find what to attack and what to leave alone.

      
                   Non-interactive zero knowledge proofs. ZK proofs have a number of good explainers, mostly using graph colorings. Non-interactive versions, however, require quite a bit more than that explanation allows – and despite asking experts, I still haven’t found a good, basic explanation.
                                      

                   Why bicycles stay upright.

For every authoritative-sounding, in-depth explanation, there is an equally plausible, yet conflicting and contradictory alternative.

      
                                      

      

https://pdfs.semanticscholar.org/bb 22989665 / d (c5a2ff) dd2a1a (f2 …)

            

                   Mach’s principle. Why is there a “preferred” rotational frame of reference in the universe? Or as stated in this Wikipedia article,
“You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don’t move? ”

https://en.wikipedia.org/wiki/Mach% (s_principle)

      
            

      

                   The two most obvious solutions to the thought experiment presented are either 1) space is absolute in some way (ie the classical Newtonian response) or 2) the behavior of space “here” is affected by the by distribution of matter “over there”. General relativity gives us a strong argument in favor of (2) by showing that a) many physical principles thought to be absolute are actually relative and b) showing that mass “over there” affects the shape of space “here”. To say anything more concrete requires requires defining the question much more precisely. I believe there is still some disagreement on the interpretation of Mach’s principle in light of general relativity. For example, see https: //en.wikipedia.org/wiki/Mach’s_principle#Variations_in … and a couple sections above, the 22989855 poll of physicists asking: “Is general relativity with appropria te boundary conditions of closure of some kind very Machian? ”

I hope that is helpful in some way.

            

      

                   The unsatisfying mathematical answer is that it It is impossible to have a uniform distribution of rotational speeds, therefore there must be a preferred one. It’s the same reason the universe has an average speed (unlike what you might expect from special relativity), although it is unclear if this is true for the (entire) universe or just the portion we can see. We can measure how fast we’re moving wrt the cosmic microwave background radiation though (it is red- / blue-shifted in a particular direction). [2]             

                   

                   Why does time slow down / go faster with movement compared to another object.
The well known example that if you travel into space you’d gain let’s say 5 years and people on earth 2000 in the same time or so. I just don’t get it and I can’t find any logic explanation. For instance: Two twins who came to live exactly at the same moment in the year and both die on their th birthday at the same time. One travels into space, the other stays on earth. Earth-brother dies on earthyear , space-brother dies in earthyear (or so …) I know its Einstein’s point but that just doesn’t instantly make it correct to me.