Why Quantum Mechanics?
scottaaronson.blog
scottaaronson.blog
There's an argument in string theory called the brandenberger-vafa mechanism that I think is pretty clever:
Imagine that a bunch of particles and antiparticles travel along in one dimension. Because they can't spread out, they'll eventually collide and annihilate. However in 2d that's not the case: they're more likely to just miss each other all the time.
If you increase the dimension of the "particles" to strings, you can make a similar argument. In 2 (compactified) dimensions, strings will find each other but not in three.
Then if you start with some compactified space of 10d with a bunch of strings wrapped around various 2d subspaces, they will naturally constrain that space so that it can't expand. However, as strings move around randomly they'll tend to collide and unravel, allowing various 2d subspaces to cease being constrained and therefore expand.
If you analyze this carefully you can show that in fact three of the spatial dimensions will tend to expand while the six remaining ones will remain compactified.
Haha, thank you, hahaha, but no, thank you very much.
> If you analyze this carefully you can show that in fact three of the spatial dimensions will tend to expand while the six remaining ones will remain compactified.
While 1 is the domain of time, I pressume.
Actually though, the universe is flat spread out, as is the surface of the earth, so the vertical axis, ie. gravity, also needs explained for the human experience to make sense. There are these types of questions like why is my right arm the left arm in the mirror but the head stays up?
I forgot the canonical answer but it's evidently the case that the brain automatically creates a recibrocal to the mirror image which denies the fact that the "left" arm is still on your right side.
Generally the argument goes as follows: the mirror doesn't invert left and right. The image of your right arm is still on the right hand side of the image, just like your head remains at the top of the image. Instead it just inverts front and back.
interesting reading https://en.m.wikipedia.org/wiki/Anthropic_principle#Dimensio...
1. https://www.reddit.com/r/askscience/comments/q8fmo/what_woul...
2. http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/2-D_Di...
Stable is not really the right word. "Well behaved" is better. In 2D all orbits are stable in the sense that escape velocity is infinite, but a consequence of that is that you don't naturally get nice (nearly) circular orbits that keep planets in habitable zones. That only happens in 3D.
Not sure if this is what GP was talking about. But the explanation there is excellent. It's in the chapter where curl is introduced for the first time. After you read it, you'll get annoyed whenever you see curls or cross products.
Also: https://en.wikipedia.org/wiki/Seven-dimensional_cross_produc...
In computing applications, if you want to find a vector perpendicular to two or more vectors outside of 3 and 7 dimensions, you would use the QR decomposition to do it. If on the other hand, you want to generalise the "directed area" properties of the cross product, you would use Exterior Algebra, or its elaborations like Clifford Algebra or the theory of differential forms.
So, if you want to make the argument that 3d is preferred for some reason you need to acknowledge that there are other universes out there with 2d, 4d, etc that just can't sustain life and that therefore life only finds itself in the subset of universes that have three dimensions.
Or you can make the argument that no other universes other than a 3D one can support life, i.e. that 3D is necessary for life. Then you can conclude if life, then 3D.
If you use Bayesian probability, you would in this case start with p(3d) = 1 since there's only one universe which is 3d and then end with p(3d | life) = 1. In other words, there's no explanatory power in the observation that there's life.
If instead you say that p(3d) = 1/1000 because maybe the multiverse has all sorts universes out there but you also say that life is only possible in 3d, i.e. p(life | 3d) > 0, but p(life | not 3d) = 0, then you go from p(3d) = 1/1000 to p(3d | life) = 1. In other words, the observation of life does have explanatory power.
Anyhow, in short, why 3 dimensions? Because it can be modeled that way and seemingly makes for a good model.
Your question is unbounded because you're asking us to imagine an alternative that doesn't exist; there could be infinitely many reasons because there could be infinitely many alternative possibilities you're asking us to imagine with no constaints
However, a more interesting and much simpler variation has just 5 dimensions, and was seriously studied by Einstein: https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory
So given:
> In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of a very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension.
I've read many times that the shape of the universe could be a loop i.e if you traveled in one direction, over a long period you could possible loop to your starting point.
From that pasted from Wikipedia, in a looped-shaped universe, would that be the size of the dimension of the universe you just traveled?
I would tend to say that unless it is logically necessary for the universe to be what it is, the question of why it is what it is necessarily lacks an answer. We should expect the universe to be improbable.
Well that's what he's asking and what I was asking with the 3D question: is it logically necessary? Maybe it is. It seems like it could be in the case of 3D.
scott is not asking what other universes were possible. he's asking to explain why QM must be true in the universe that we do observe.
thats what I wrote QM must be the obvious conclusion (compared to X)
He's asking why a creator/creation process would use QM in a universe rather than something else.
> Most importantly, people keep wanting to justify QM by reminding me about specific difficulties with the classical physics of the 19th century: for example, the ultraviolet catastrophe. To clarify, I never had any quarrel with the claim that, starting with 19th-century physics (especially electromagnetism), QM provided the only sensible completion.
But, to say it one more time, what wouldāve been wrong with a totally different starting pointāletās say, a classical cellular automaton? Sure, it wouldnāt lead to our physics, but it would lead to some physics that was computationally universal and presumably able to support complex life (at least, until I see a good argument otherwise).
Putting that misgiving aside, I think I get what you're saying (correct me if I'm wrong): the question is whether the "simpler" or at least more naive classical rules of physics could be the foundation for a world that looks and feels exactly like ours, e.g. one that forms a substance that has the precise properties of water, one that can support a stable form of DNA with which to assemble living beings, and so on.
The answer to that depends on how far exactly you are willing to depart from perfect fidelity. To put it another way: what is exactly the set of invariants that you aim to preserve from QM to classical? Do you need them to be exactly the same? Probably not feasible. Do you want water to behave exactly the same? I would tend to say it couldn't. Do you want it to have stars? To be able to evolve humanoids? To be able to evolve life? These are all interesting questions on their own, but they may all have separate answers.
I hear it over and over and still don't understand the premise. Classical mechanics is not something sacred. It is our first serious model of physics. Our first approximation is based on the scales at which we operate and our senses as humans. Furthermore, even "regular" quantum mechanics is a non-relativistic, low-energy approximation of Quantum Field Theory.
It is like asking why God created clouds, not just "waters above the filament"?
That said, Q2 minus Q1 is an interesting question.
Just a sidenote: it is at most our second serious model. Aristotle's Physics has a bad rap, but it's "a correct and non-intuitive approximation of Newtonian physics in the suitable domain (motion in fluids), in the same technical sense in which Newton theory is an approximation of Einstein's theory". See "Aristotle's Physics: a Physicist's Look" by Carlo Rovelli (https://arxiv.org/abs/1312.4057).
I think it should be required reading for anyone interested in the development of physics.
Sure I understand the theory of the water cycle. But the whole precipitation and evaporation thing is a complex mess. It doesn't look at all like the simplest possible form that could achieve the same job. Why not just water above the firmament?
When something in nature seems needlessly complicated, one has to ask what purpose the complexity serves. Why would a hypothetical universe engineer (dare I say "god") sit down and decide to have a universe that is indistinguishable from a classical one on nearly every length scale but is still quantum at the bottom? There's only a few possibilities:
1. The complexity isn't actually needless but it is arbitrary. There are other self-consistent laws of physics that are possible, but all the alternatives are just as weird and complex as QM.
2. The complexity isn't actually needless because QM is inevitable. There's some deep logical principle that forces the hand of the hypothetical universe engineer.
3. There complexity actually is needless. Our universe is quantum because that's just how it is.
The uncertainty principle and stuff like Noether's theorem should nicely limit how to ask the right questions. Now I'm not sure if Noether's is a proof by contradiction that would answer the question directly, I rather doubt it.
It's a valid question for the sake of didactics at least, how much can be simplified and explained in classical terms without catastrophic loss of precision. Conversely, the slit-experiments for example are a probably the most prominent display of quantum effects in the experiential domain.
With classical mechanics you need to timestep and integrate F=ma and all kinds of associated issues. In QFT you just generate all possible 4D configurations of all fields, assign a weight to each by a prescription, and estimate the ones you're interested in finding the probability for by adding together the weights, take their square, and normalize by the total sum of weights.
One may argue that "a state" is a simpler concept than "a superposition of all state".
Even in pure mathematics [1], I don't think that (say) real numbers are less fundamental than natural (unlike Kronecker in "Natural numbers were created by God, everything else is the work of men"). What's true for the set theory route, does not need to be true for any possible mathematics, including those created by other species.
For me, it is perfectly conceivable that some aliens use Hilbert space, and for them natural numbers are a particular concept (finitely dimensional vector -> n=1 -> zeros of sin(šz) = 0 & Ī(z+1) is finite, or something in that line).
In this sense, if you understand quantization as a map between a set (e.g. {0, 1}) and a vector space over a set (e.g. |psi> = a |0> + b |1>), then it is harder within this conceptualization. For aliens, "a basis state" (i.e. |0> or |1>) might be not an object worth studying on its own.
When it comes to the path from classical to quantum physics - yes, it is full of question marks. The only hints I know come from "Quantum principle of relativity" by Dragan & Ekert (previously on arXiv with a more inflammatory title, "Why devil plays dice?").
Yes, there is a contrast with cases, in physics, in which a more advanced theory could be deduced purely with the elimination of inconsistencies, or strive for mathematical beauty, e.g.:
E/M -(symmetry)-> Maxwell equations -(Minkowski transformation)-> Special Relativity
or
non-relativistic quantum -(SR)-> Dirac equation -(Klein paradox)-> QFT
At the same time, I think it is a wild hypothesis that "any physics theory point to a more advanced theory only with its own ugliness and inconsistencies".
Furthermore, like almost anyone, I used to believe that it is always possible to reduce a "more advanced" theory to a "less advanced" one. Sure, for SR you take v/c << 1 and you are done.
For anything dealing with emergent phenomena, well - it is (IMHO) not as straightforward as it may seem at the first glance. Decoherence is one of these cases. For even simpler ones - how to turn molecules of water into their macroscopic properties (temperature, pressure, viscosity). Yes, we can do it (well, with T and p, but still - not viscosity); but if we haven't seen any field in our life, we would not ask such questions in the first place. Even the concept of temperature would be some arbitrary, made-up quantity.
Anecdote on a students' conference there were two talks after each other - one on bubbles in beer, and the other - C-star-algebras. The latter claimed that it is the more fundamental, ergo better, way of dealing with physics. Iwo Bialynicki-Birula (theoretical physics) smiled and asked the second speaker: "And how would you derive the beer bubble from C-star-algebras?")
[1] Disclaimer: I believe that mathematics is created by humans, not something existing on its own. An abstraction of our language, and our sensory experiences. If we were a slime mold, maybe we wouldn't come with the idea of integers at all. Evolutionary speaking, integers are an abstraction over counting own offsprings, and perhaps - estimating strengths of groups when hunting or protecting.
As a side note, it was really fun to have a longer conversation with Penrose, having very different views (also: I am Everettian, and have a naturalistic view towards consciousness, in the spirit of Dennett). After that, I got a clear idea that "the root of all misconceptions" is the assumption that mathematics exists beyond a human concept.
As to your statement about platonism or mathematical realism, I'm curious about something. Surely most axiomatic systems are a choice, so I can understand why we would say they're man made (euclidean geometry, ZFC, etc).
However we also know about 'meta axioms', which seem to go beyond being a choice. There are simply some axioms that don't seem optional. Do you hold those to be also man made or is that a separate phenomenon?
For a moment, forget about "and" and use "zxhds" instead. You need to specify how it works.
There is nothing magic, intrinsic or natural about "truth" or "implies". It is all rules of symbol rearrangement.
As to your reply above, regardless of what you call axioms, semantically speaking there is an isomorphic subset in common for all useful axiomatic system is what I'm postulating. Can you think of an axiomatic system that doesn't have something iso to identity and equivalence for instance?
1. When it comes to the Gƶdel's incompleteness theorem - for non-recursive systems you may you can get without that, vide https://math.stackexchange.com/questions/3359878/what-is-som...
2. In general, you can do a lot without equivalence. For example, in set theory (ZF), you get only trivial equivalence (sets having the same elements are the same set). But you can still do a lot with "contains". A similar thing works with partially ordered sets, in which you have the "<=" operator.
What would that mean in the context of QM?
"A superposition" is "a state".
*firmament
Q2 minus Q1 is much more interesting: why this specific theory (i.e. quantum mechanics), rather than anything else.
Yes, as a reference for an alternative possible world. Other alternatives discussed are cellular automata.
So what I dont get is why QM you could argue that there is some hidden shared state. Guess this is a typical question. But anyway Iām somehow not convinced that it is really random.
Taking the standard example of an entangled pair of photons. Those must have opposite spin. We then move the photons rather far apart measure the spin on one side. Then because of entanglement and conservation, the spin someone will measure on the other side is guaranteed to be the opposite.
A 'local variable theory' explains this by saying that the moment the entangled pair of photons is created it is already determined what the two spins are. This variable (the pre-determined spin) then travels with both photons (hence being 'local' to the photon). And the one measurement does not affect the other measurement.
The bell inequality shows this to be false. Crucial to the bell inequality is that, when measuring spin, You don't get back the 'angle'. Instead you choose a reference plane, and measurement will tell you whether the spin is pointing above or below that plane.
Now in the bell experiment. You measure in two different planes at the two different ends. If you pick two planes at a 180 degree angle. You will always find the same result on both sides (perfect correlation). If you pick two planes at a 0 degree angle, you will always get the opposite results (perfect anti-correlation). If you pick the planes at a 90 degree angle, the results will be totally independent, and this completely uncorrelated.
On these 3 angles (0, 90 and 180), quantum mechanics and a 'local variable theory' agree on the correlation coefficient between the measurements. (-1, 0 and 1 respectively). Bells inequality concerns the other angles. In those cases quantum mechanics predicts a stronger correlation (either more positive or more negative) than the local variable interpretation can predict. This discrepancy is strongest around angles of 45 degrees. Where a local variable theory means the correlation cannot be above 0.5, but quantum mechanics allows a correlation of up to Ā±1/ā2 = Ā±0.7071.
These correlations were measured experimentally, and something close to the QM maximum of 0.7071 was measured. Hence disproving there are local variables.
>It's painfully easy to have a clear intuitive picture of quantum physics. You just have to ditch one concept.
>Universe is not made of little balls.
>So what I dont get is why QM you could argue that there is some hidden shared state.
Because when you measure one of the coins in a particular way, there's an established probability that you'll change it some percentage of the time. (I.e. if you measure in this way 100 pre-prepared heads, you'll get some percentage of tails. [think of this as say measuring polarization of some photons after they've passed through a filter oriented to 0 degrees, by then placing a filter oriented at 45 degrees and seeing how many go through)
However, even after you do that measurement, you'll find that the other entangled photons are still correlated with the result of the ones you measured. So there's something "extra" going on, which is QM entanglement. I.e. that shared state.
You can actually see the effect of the "changing states" (not really what's going on, but if you were assuming the behavior was classical, it's what you'd start with. If you place two polarized filters at 90 degrees to each other and shine a light through it, you'll get basically zero photons out. Then, without changing anything else, you can put a third filter in-between the two but oriented 45 degrees from the others, and all of a sudden, about 25% of the light will pass all the way through the three filters! It's pretty cool. You could explain THAT part classically by saying that you are "changing the state of some of the photons by measuring them". But then... if you do that, you can't explain the correlation that happens when you do that with entangled photons, and classical explanations just don't really cut it unless you give up something like non-locality.
1. It consists of a base unit and to hand-held units that can dock in the base unit.
2. Each hand-held unit has a counter, a button labeled "A", a red light, and a green light. The counter initially reads 0. The base has a button labeled "Reset".
3. If you put both hand-held units in the docks in the base and press "Reset", the counters in the hand-held units are set to 1000.
4. If you press the "A" button on a hand-held unit nothing visible happens if the counter is 0. If the counter is greater than 0, exactly one of the lights flashes briefly, and the counter goes down by 1.
5. If someone records the results of a large number of presses of the "A" button on one of the hand-held devices, every statistical test they can device will be consistent with the probability of getting the red light being 0.5. As far as they can tell it is completely random what color they get. This is true both within a run of 1000 presses after a reset, and across resets.
6. If two people compare their result from a run of 1000 "A" presses of two hand-held units that were last reset together, their results are identical. I.e., if person 1 got red on one of the units when the counter was 1000, blue for 999, red for 998, 997, and blue for 996, then so did person 2 on the other unit.
It would be pretty easy to build such a device. The hand-held units could simply have 1000 bits of storage. When the base unit resets them it merely has to generate 1000 random bits using a true random number generator and store that random bit sequence in both units. The units use that sequence to choose the light color when the "A" button is pressed.
Now suppose we want a more elaborate device. Same basic setup with the base and the two hand-held units, but now the units have three buttons, "A", "B", and "C". Still two lights, red and green. Pressing any button gives you a short light flash and decrements the counter.
Like with the single button device, if you play with one of the hand-held units alone every test you can think of is consistent with the light color being entirely random, with red and green equally likely.
If you record the results of your 1000 presses, and compare results with someone else doing the same with a unit that was reset when yours was, we want to see these results:
1. When you just look at your results, every statistical test you can device is consistent with it being completely random what color you get with the two colors being equally likely.
2. When you two pressed the same button with the same counter value, you find that you got the same color on your two units 100% of the time.
3. When one of you pressed "A" and one "C" with the same counter values, you find that you got the same color on your two units 50% of the time. It seems to be completely random whether or not you got the same color or different colors.
4. When one of you pressed B" and one of you pressed "A" or "C" with the same counter value, you get the same color 85% of the time. It seems to be completely random whether or not you got the same or different colors, but instead of being 50/50 like in #3, it is 85/15 for same color.
You might think this device could be built with just minor changes to the earlier "A" only device. Just expand the storage from 1000 bits to 3000 bits so it can have a table for each button saying what color to flash if that button is pressed for any particular counter value. That base can download values that give the desired distribution.
But when you try to actually figure out those tables you will run into a problem. You will find that you cannot devise values that will actually give the right distribution unless you know ahead of time which sequence the users are going to choose for their button pushes. If the users are free to decide which button to press for each of the 1000 rounds and they don't have to decide until after the tables have been initialized, there will always be sequences they can press that those tables won't give the right distribution for.
You will find that the only way, if you limit yourself to pre-quantum physics, to make the units actually work is to include some kind of communications channel between the units so that whichever unit gets a button pressed first for a given counter value can tell the other what it choose and the other can then adjust its response to make sure the right distribution happens.
That could work, but then you would have a limitation that your units only work according to spec if they are close enough together when the buttons are pressed for them to get a message from the first one pressed to the second one before it is pressed.
If two people took a pair of units, reset them together, separated them by say a light-hour, and then started pressing their buttons at the same time the devices would not be able to give the right correlations.
You can make the devices work, but instead of making your table use regular bits, you need to use a table of qubits. Use 1000 qubits in each device, with the qubit in each hand-held unit for counter value N entangled with the corresponding cubit in the other device. A button press measures the value of the qubit, with each button corresponding to a measurement in a different basis. With the right choice of basis for each button, you get the correlations given in the spec, and it works no matter how far apart the units are.
As far as I know nobody has built the specific devices described above, but there have been experiments done with entangled qubits or entangled particles that show that they do work that way yielding those correlations when measured in different bases, and that this works even if they are very far apart, so you could definitely build the devices described above.
Now lets allow entangled states between the kids (states that can only be specified if you have both subsystems, locally if you measured such a state your result will look at least a bit random or even completely random). Then you can prove that the two kids can do the task (that has classical success probability 75%) with success probability ~85% all of a sudden.
You can write down general inequalities that describe such behaviour and that's what Bell inequalities are. The fact that entangled states in quantum mechanics violate the classical bound (which you cannot break if you demand your two kids can only share states allowed by classical physics, even if you allow unspecified hidden variables), proves that nature is not classical. It doesn't prove that nature is quantum, it just proves that nature is not classical. Bell inequalities have also been unambiguously experimentally verified [1].
In conclusion, nature allows for two-party (or multi-party) states that cannot be described by just describing the local parts of it. There is no information in the local parts, but if you look at both parts together then there is information. Think "the whole is more than the sum of its parts". Classically, the whole is the sum of its parts. Classically, you read a book page by page. If your pages are entangled with each other, you could only read your book by looking at all pages together, because if you looked a single pages separately anything written there would look like random garbage to you.
The question that remains is: Where is the information then, physically? In some sense you could say it does not exist before measurement, because only when you look at the correlations between the local measurement results of the two kids will you find out that the underlying state must have been entangled (which you get to know if the state violates a Bell inequality). But that is just one possible interpretation, there still is a lot of scientific debate about what quantum mechanics really means.
These are exactly the scenarios that make quantum so weird but fascinating at the same time.
[1] https://en.wikipedia.org/wiki/Interpretations_of_quantum_mec...
If you multiply the left and right sides of schrodingers equation by its complex conjugate, do you still get an equation that the real valued square of the wave function solves? Can you do QM with just the real valued probability distribution? If you can, why not say that thatās the ārealā thing, and factoring it is just a convenient way to solve it, same as imaginary solutions to quadratic equations.
You can't. The key fact is that other observables, such as momentum, depend on the complex part of the wave function.
If you were to append some fictitious spin system to whatever quantum state, you could put all the real amplitude on the spin down state and all the imaginary amplitude on the spin up state.
Perhaps "the simulation" is on a quantum computer and some of the qubits are not directly encoding things we can touch.
More precisely a quantum observable is a map (a function) that takes in a quantum state and outputs a probability distribution, representing the probabilities of the various outcomes you could get if you measure that observable on that state. The equivalent statement is also true of classical observables and classical states.
Under classical rules it turns out that if you have many observables acting on the same system you can come up with a joint observable, that maps a state to a joint probability distribution for all the observables. For incompatible quantum observables this is emphatically not the case. Given two quantum observables there is generally not a joint observable representing simultaneous measurement of them.
QM has very specific rules when it comes to how two random variables are dependent. That specific rule comes up when you have quantum interference and this is best described by the conjugate square of two complex functions A^2 + B^2 + A*B + B*A. This is just a special case of the union probability: P(A) + P(B) - P(AB).
It's the interaction between variables that is key.
Sort of like string theory. Not exactly, but sort of.
Q2: because that's how the simulator works.
Joking aside, I wonder if there's some principle that: physics will always look like you'd expect it to look if it's a simulation. Perhaps that's what Yang-Mills Gauge Theory is about?
I've never been able to mentally put the "we're in a simulation" paper away. It's always been persistently plausible, and refuses to budge.
A friend of mine keeps insisting that a lot of the complexity we see in physics stems from floating point arithmetic rounding error.
I don't know much about the nuts and bolts of QM, but on the surface, entanglement and the observer problem lines up nicely with our universe being a lazily evaluated simulation, crunching numbers at the last second for our benefit like a game engine.
It's all personal though, a fisherman sees God in the ocean, why wouldn't a programmer see God in complex digital systems?
For instance, what is the simulation in? Is not being in a simulation even possible?
Btw, I recommend reading Permutation City.
Simulations can have explanatory power and can potentially have falsifiable predictions.
One prediction of a simulated universe is that any such computer would be built on a budget. As in, you'd expect all aspects of the the compute substrate to have finite "limits" that manifest at the extremes of the simulation. For example:
1. Finite resolution -- Plank length.
2. Finite information propagation speed due to simple "update next cell based on neighbouring cells" simulation -- Special Relativity.
3. Finite (maximum) information density -- black holes.
4. Finite precision -- particle decay, "inherent randomness", etc...
You can even explain General Relativity by saying that simulation chunks that are busy due to highly complex content fail to fully update their state and hence fall behind, appearing to have a slower progression of time. Neighbouring cells also need to "check" the state of the busy cells, and hence they're slowed down a bit also, which explains field curvature.
Etc...
He did. Physicists just never managed to properly grapple with the concept that classical mechanics involves action-at-a-distance.
Furthermore, action-at-a-distance (non-locality) makes classical mechanics inconsistent even with itself, so it's a non-starter (it implies grandfather paradoxes).
IF you assume that photons have mass and interact gravitationally (there are good reasons for making this assumption), then you can explain the double slit experiment classically via gravitational interaction.
No, you can't. The double slit experiment has nothing to do with mass or gravity. It is well known that it happens with electrons, protons, and has even been demonstrated with some large molecules (thousands of atoms). Gravity can't explain anything about it though.
And even if I can imagine some gravitation-based interactions in the case of a stream of huge numbers of particles (though not the actual quantitative explanation), the double slit experiment has been reproduced with things like 1 photon emitted every hour - over the course of a few days, the same interference pattern emerges IF the photon's path is NOT observed; but NO interference pattern emerges if the photon's path IS observed.
> You can look under the hood of any software that simulates orbits and see that this is the case. No time delay is assumed for gravitational interaction.
The fact that simulation software takes shortcuts to make its computations feasible is not proof that this is how the world works. Einstein's GR equations are famously intractable to solve in their base form, and approximations are strictly necessary. But given the distances and observational precision for the positions of planetary objects, I would bet the effect of gravitational waves having a finite speed is negligible for most predictions.
Not to mention, we have actually measured the speed of gravity: we have detected gravity waves and they are moving at the "speed of light", or as near to that as we have been able to determine. Definitely not instantaneously.
> the Poynting-Robertson effect also makes this obvious
That is a General Relativity effect, which assumes that gravity is a local interaction (i.e. no action at a distance). That is precisely Robertson's contribution to the Poynting-Robertson effect, per the WIkipedia article (Poynting first understood the effect, but described it in terms of the luminiferous aether).
It's a matter of scale. At the highest level, of the individual, if you present them with two options, they will chose one of the options. At that level, the question is a trivial: yes, obviously they have "the capacity [] to choose between different possible courses of action unimpeded."[1] Your description was just an explanation of how they choose. If you then ask if the individuals also have "the capacity to do otherwise"[2] then that depends on whether things are deterministic or probabilistic. If they're probabilistic, then yes, otherwise no.
In all three cases, yours and my two, the question is answered trivially and uninteresting. The real question philosophers are asking, I'm told, is whether people have moral responsibility or not. It's interesting psychologically too, should you really feel guilty if you couldn't have done differently?
This view is based on a misunderstanding of what moral responsibility is. Moral responsibility is essentially credit assignment [1]. It exists as a concept not because it matters whether or not you actually could have done differently before, but rather as a mechanism to teach you to do differently in a similar situation in the future. "You" is just a machine making decisions. When you make a bad decision, according to the other machines surrounding you (society) or your own brain's reward system, you are assigned blame or feel guilty because you should avoid making the same decision again in a similar situation.
To say that moral responsibility requires something supernatural doesn't make sense, since we successfully use the concept all the time. Its a mechanism for multi-agent learning.
But if free will does not exist then other machines (humans) aren't making these decisions either... it's turtles all the way down so to speak. You could go on to say that the entire system (of humans, society etc) is either determined or probabilistic, but still no free will exists. It is meaningless to say whether you should feel guilty or not etc. as it is just part of a system no one has any control over...
Edit:
What I meant to say is that moral responsibility exists like natural selection in evolution, it is there but we don't choose it to be there, it is part of the natural system we find our selves in.
It becomes a similar question as asking: if god or "something" created the universe, what created that something. Its turtles all the way down yes.
>"it is part of the natural system we find our selves in". Like exactly everything else that surrounds us :)
And here you eventually hit both the limitation that without abstractions you can only simulate a less complex system, and also how the information about the exact state of the system is fundamentally limited by the (quantum) uncertainty principle (which also allows the discretisation of information, via Planck's constant h) - entropy being a superfluous concept meaning just "lack of information" :
https://www.av8n.com/physics/thermo/entropy-more.html#sec-ph...
The open question is why and how humans can "feel" guilt. How can a machine have a subjective experience at all? What is a subjective experience? This is the so-called "hard problem".
I've come to the same conclusion. Even without free will, "punishment" is a crucial tool in teaching agents acceptable behavior. Perhaps there's a meta morality question of whether the gains from that teaching are worth the suffering of the individuals being punished.
To hear about it and to then decide "this absolves me of any guilt, because I couldn't have done it any differently" is also a choice your process made. Counterfactually, it could've made the opposite choice (though it didn't do so).
Now, me pointing this out presents yet another choice and opportunity for change. And these opportunities keep happening for the rest of your life.
In essence, even though you cannot change your actions in a very deep sense, concluding "I can't change myself because it's already determined" is always a premature conclusion, whenever it is made.
If a person with Tourette's said profanities to you during your Zoom meeting, would you hold them equally responsible as a person not having it? No, because it's a symptom and you assume it is out of their control and they didn't have a malicious intent. If both persons said "sorry it wasn't in my control", you'd think
1) the person A didn't do bad, because they have a tic and they definitely don't have negative feelings towards me
2) the person B has an anger management issues and may or may not have negative feelings towards me, maybe he's bad
We assume intent is malicious when a person has the capability to stop themselves from doing something negative towards us and yet they "chose" not to.
A CPU that doesn't work when power is off could be a good CPU, but a CPU that doesn't work when power is on is a faulty CPU.
We just established nobody chooses what they do or how they feel, so at best it's like a matter of degree and at worst it's completely arbitrary.
And "can choose to" with "can go to else{} if rx is true" - and social interaction and reward/punishment can make rx == true.
These questions are decided in legal contexts all the time, so you can look up precedent. Generally there are considerations of coercion, mental fitness, and age/experience, because your responsibility is proportional in some sense to how much you know/have learned. If you literally have never learned right from wrong, say you were raised by wolves, then you are generally not held responsible until you do (or rather, you are held responsible, but the penalties are teaching you right from wrong rather than something more severe).
> just as much as the people that you describe.
I'm not sure which people you mean. I'm saying that it is both true that you "cannot help it" in one sense and false in another sense.
There is always a causal level in which you could not have helped it. But it is never correct to conclude that there is nothing you could've done to help it, because this is also a choice and making it prevents higher-order changes.
Well in case of strong determinism, you donāt have a choice not to feel guilty. Also, you donāt a have choice to believe or not in determinism.
It's ironic since you'd have no choice whether you feel guilty or not
The idea "everything that is natural can only be everything we can objectively measure" should be problematic right? Of course whatever out there that is unmeasurable is rife with confusion, messiness, lies etc but that shouldn't mean it doesn't exist at all.
The old confounding variables problem. It's silly to believe there must be none, yet that's what the physics = everything worldview amounts to.
EDIT: I love Scott Aaronson. Of course he predicted this type of answer explicitly and is looking for a more nuanced one :)
I have a lot of trouble imagining any experiment which could completely rule out every other influencing factor. There are silly thought experiments such as what if the world has been objective for the last x00 years - prior to that and after, the laws we've observed during the period would bend; things will become inconsistent.
It's silly and I don't even believe it, but it does show that science is incapable of completely ruling out everything.
The truth could be endemic mystery. Endemic insanely and terrifyingly simple endless levels of understanding. In a way science is nothing unless that's the reality.
It's called Bell's theorem and it can even be tested at home[4]. There are no local hidden variables in quantum mechanics.[1][2][3]
1. https://en.wikipedia.org/wiki/Bell%27s_theorem
2. https://en.wikipedia.org/wiki/EPR_paradox
3. https://en.wikipedia.org/wiki/Hidden-variable_theory
What?
> To date, Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems do, in fact, behave.
Everyday posters on this website amaze me. I should really stop coming here...
Regarding speculation, that assumes there isn't steps to knowledge about other things which physicists do not take. Any scientist will easily change their mind with the right evidence. The only issue is that the evidence takes place in one's subjective experience. It may take place specifically in contexts where it cannot be convincingly demonstrated to the general population.
It sounds silly, but if that's the nature of the object of investigation, it's necessary.
I know many people are very uncomfortable with this, but I don't really know what they actually want. I think appealing to QM to wave an indeterminism wand and 'somehow' resolve the problem is wishful thinking. Randomness, as pointed out by others here, is no answer and if all QM contributes is randomness then it's no real help. I'm perfectly willing to accept that there's a certain degree of randomness in our choices, that's fine, but it's not the answer to the question of free will.
I also don't see how appeals to some non-material source of decisions helps either, surely such a source must also have a state? It's simply punts the question, and I see no reason to suppose it actually helps answer it. Aside from the fact that if a 'non-material' source of choices interacts with real matter, surely that makes it real, right? It's just nonsense on stilts.
IMHO we are real, material beings. Our state determines our actions, with some randomness sprinkled in, and I'm fine with that. Yes this has some uncomfortable philosophical implications, but that's ok. In fact I think it's a good thing. If we're all driven by our state, and that's determined by factors outside our control, it humanises us. We're flawed beings living in a dangerous universe. We need to stick together and learn to understand and tolerate our flaws and weaknesses. Coming to this realisation has changed my attitude to a lot of things, and to me that capacity for change is all the free will I need.
In general, the concept of reason for things (aka purpose) follows a hirearchy tree structure. X happens because Y wills it. Y wills it because Z wills it. And so on. Whenever we reach a node in this tree where we can't find the parent node, we are left with a free floating will.
So long as there are things about our likes and dislikes and how we spend our time which can't be correlated with anything measurable, there is no choice but to attribute those things to our free will. The moment some component of who we are becomes predictable by science, we stop attributing that component to our free will.
The best you can do is be evolved to use true randomness (if it exists) to choose between good-enough actions, so at least nobody else can predict what you're going to do.
āThis often takes the form of rejecting physical realization, affirming fundamental higher-level causal powers, or both.ā
I find it fascinating to wonder about causal powers in multiple directions. Does it even make sense? Does it conflict with physicalism? What is the physical anymore? Chomsky says there is no physical for the past few hundred years. Itās worth reading about at least.
Since you like SEP, "Backward Causation"[1] is sometimes attempted as an explanation for entanglement. I don't buy it but it could be related to your question.
Commenters: "So are humans going to be able to travel FTL? Let's talk about that hypothetical for 200 comments!"
Completely ignoring physics. Everything must be human centric, everything must be dumbed down and anthropomorphised and become absolutely boring to the core until there is no more low hanging fruit left to pick.
Free will could be framed as unpredictable behavior arising from the emergent system itself, where the selection of one choice among many is deterministic, but otherwise indistinguishable from a non-deterministic system to any other mind. This is a plausible scenario that aligns with chaos theory and implies that every mind is a unique occurrence.
The firing of a single neuron can be triggered by quantum circumstances affecting the location and energy of a single calcium ion, and that single neuron can be responsible for radically different states in the meta-patterns that comprise a mind at any given point in time. Even software on silicon could be subject to bitrot, cosmic bit flips, and other fundamentally unpredictable changes. How such randomness affects the system plays into whether free will can exist in this sense.
The idea behind free will is that the mind has the ability to make choices independent of any influence except itself. It's highly probable that minds are entirely abstract, dependent on the physics of its substrate but existing as an emergent result of the particular arrangement of particles and energy in the substrate. If the choices made by a mind are indistinguishable from a hypothetically independent system not dependent on the physics of the substrate, it could be seen as "free will." Is definitely not the religious/supernatural Free Will, though.
If a mind is perfectly replicable - if you can perfectly simulate the state and ongoing experience of the mind bit for bit, - then you should be able to perfectly predict its behavior and state over time. It could be that such replication is mathematically possible but fundamentally intractable. Such a result would mean minds exhibit behavior indistinguishable from free will. It would mean that perfect knowledge of the state of the mind could never be known outside the mind itself - an extension of Heisenberg uncertainty - and simulations would be inaccurate.
The emergent, entirely abstract meta-system comprising the mind and its subjective experience could also be seen as the non-physical soul or spirit. That doesn't make room for the supernatural or magic in the universe. It might mean that divergence from prediction by the outside exists but is vanishingly small. It could also imply high probability of divergence if compute capacity needed for simulation grows exponentially over time and capacity of the mind being simulated. The answers will depend on exactly whatever "minds" turn out to be and the mathematics that govern the phenomena.
I personally think that radical divergence is likely, for no better reason than to think the universe is a much more interesting and weird place should that be true. It would mean that minds will forever be surprising, however much we increase computation and efficiency.
We don't know what minds or qualia are, and until we know for sure - as opposed to hoping and guessing and "well obviously..." - these speculations are just hand-waving.
The problem is that all of physics is filtered through our minds. We literally have no way to experience reality without experiencing it through a human mind.
So although we've managed to persuade ourselves our experiences of science are "objective", all that really means is that other human minds are very likely to have similar experiences if we set up similar circumstances in similar situations.
Potentially our minds could be operating in the conceptual and experiential equivalent of the visible light spectrum, and the range of possible "objective" experiences is very much wider.
The @and@ part may answer the free will question. Not the a or b part alone.
There is no chance in the equations of quantum mechanics as the equations are fully deterministic. The probabilities appear only when we try to explain interaction of classical systems with quantum ones. Traditional explanation is that those probabilities are inherent to the world. But this rise the question how this can be as there is no in reality classical systems, everything is quantum with deterministic equations. So more natural interpretation is that at classical level the system looses access to some information about global properties of the system and probabilities are just a natural consequence of this.
This is (to me) a highly appealing model for what is going on, but we still don't really know how to go from this viewpoint to what we observe in experiments, which is the Born rule.
If it was just classical physics, then you get yourself into the thinking that you can rewind time and all the "billiard balls" knock into each other the same way, which is why you order a soup and not a sandwich every single time on that day.
That eliminate free will. There is something about the uncertain nature of the universe at its fundamental levels that allows for consciousness to arise and actually does give us freedom to choose. Plugging in some parameters and letting the simulation run doesn't allow for this.
What is life if we are all truly just experiencing a "movie" and have no say in how it plays out? It's utterly meaningless and may as well not exist at all. And it raises very strange questions when we may not like the "movie" we are currently participating in. We have no ability to switch to another theatre?
What makes life "life" is consciousness and individual experiences.
I don't understand this line of reasoning. If I ordered a soup for lunch, and then time is rewound and I order a sandwich instead, it would appear that my choice is in fact random and therefore I most definitely do not have free will. If rewinding time is sufficient to change my past choices, doesn't that utterly demean them? I might as well flip a coin.
I think the problem with arguments regarding free will is that it's very hard to define (like consciousness for that matter). I am my brain. My brain controls what I do. Therefore, I control what I do. Only if we lift up our consciousness or free will as something higher than our brain does this become a problem.
The fact that my free will is deterministic, that is, a consequence of how the brain is structured and how the environment looks, does not change the fact that I, that is, my brain, controls what my body does. If anything, randomness makes this worse - then it is not my brain controlling my body, but some random result of a wave function collapse.
I think that the whole determinism vs randomness debate boils down to the fact that when we make a choice, for example whether to order soup or a sandwich, we have to hold the belief that either choice is possible. We can simulate ourselves in our mind taking either decision, evaluate pros and cons, and use the results to act. In that sense, because it is compatible with many counterfactuals, our internal self-model is decidedly non-deterministic. And if you think about it, it has to be non-deterministic in order to be a useful decisional tool: considering what would happen if you did X or Y is the foundation of deliberation.
The trick, though, is that ultimately this is just epistemological non-determinism: you don't know what is going to happen, and you can't know, because you are in the process of figuring it out. When I am looking at the menu, I think it is possible that I will order a soup or a sandwich, just like I think it is possible that they are out of soup, even though there is a definite answer to whether they do or not. I just don't know it. Our misstep is to (intuitively) extrapolate that if we can't know what we will choose, then no one else can.
Super determinism is the unpopular answer that solves many problems in quantum mechanics and relativity.
It also makes a lot of sense if you think of the universe as pre-rendered, just like you would a CGI movie. Determine where all the particles land upfront throughout time and then play it back like a movie.
Life can still be fun even it is pre-rendered. Like a movie you don't know what's going to happen next anyways.
It could be like an atheist's version of God, taking in comfort in knowing whatever happens was going to happen anyways. Enjoy the ride.
It's that mind-blowingly unlikely coincidence with no explanation that scientists object to.
Scott doesn't believe it's possible for them to be different though.
What if my life isn't "fun"?
A lot of people live out lives of complete suffering. Childhood cancer? Poverty? Disease? Genetic mental health issues? Inbreeding? Childhood trauma? That list goes on and on.
That isn't a movie I signed up for.
Does determinism think this is supposed to be a lesson of some sort?
Actually it does.
Your movie is going to play out the way it plays out, regardless of whatever you do. Throw your feet up in the recliner or struggle for that next promotion, doesn't matter. Brain cancer.
I just find this rubbish.
You rejecting superdeterminism, deciding that your fate is up to you, and making positive decisions to improve your life, is great. Do that.
It may be though, that those positive decisions and deciding your fate is up to you, etc, was already printed on the film. Or if instead you just throw your feet up on the recliner and decide to do nothing, then that would have already been printed on the film as well.
If in a trillion years the universe ends and thereās a complete story to tell about everything that happened, and some external observer were to watch that story, theyād see you making whatever decision you made and your life turning out in a particular way. But they wouldnāt expect that if they rewound the film that things would somehow turn out differently.
However, there isn't an explanation for why it's limited - seems like if the partial case could happen then the whole thing could happen too. (there's a long argument about this in the comments of Scott's post)
I disagree, I think quite the opposite.
Physicists often seem to adhere to a "religion" of sorts, that being atheism. Anything to get rid of the "God problem".
It's not all so cut and dry.
> āI believe in Spinoza's God, who reveals himself in the lawful harmony of the world, not in a God who concerns himself with the fate and the doings of mankind.ā - Albert Einstein
I'm not religious.
But even if fervent atheist physicists are trying to remove the God Problem, how does that mean they are selecting physical theories to make life meaningful?
For example you can have a system with two possible states, A and B. My decision to do experiments some superdeterministic setup is correlated with the state of the sytem so I only do experiments when the state of the system is A. I conclude that A is a physical law, but I'm completely wrong, its quite often B but I am only "choosing" to do experiments when it A.
(*) this is my opinion and the opinion of many, but absolutely not all physicists
The universe could still be entirely deterministic, in that your choice of experiment and measurement to make was fixed at the moment of creation. But you still believe that the results you are getting are a fair and accurate reflection of how the universe actually works.
Free will (in the philosophical sense) is irrelevant. Your choice of measurement is only influenced by what is happening locally to you at that time. The game isn't rigged to produce misleading results from the very moment of creation for all time.
The reason that super determinism is rejected is because (in the usual understanding) that it requires that the initial state of the universe is set up incredibly precisely to make all subsequent measurements appear to violate Bell's inequality, even though reality isn't actually like that.
So if we set up a quantum measurement and make a decision based on photons of light emitted from distant stars, the experimenter deterministically chooses to make just the right measurement that would make the universe look like it was violating the inequality. Including all the matter between us, and the atoms in the neurons in the experimenters brain, and the photons that were emitted before any of that existed.
This is why super determinism is rejected. It would mean that we are not "free" to choose the experiments and measurements we perform. The universe would be essentially conspiring to deceive us at all levels, including what science we do, the results we receive and the conclusions drawn from it. Which is why it would invalidate the scientific method itself. We couldn't trust anything we thought we knew.
Sabine has a different take from what I can tell. If you allow backwards causality, the measurement act is not independent of the thing being measured. See this blog entry and the comments:
http://backreaction.blogspot.com/2019/07/the-forgotten-solut...
Just observing that historically religion tends to select theories of the physical world that align with its moral and religious belief.
If you were to make a decision that is not in some sense pre-determined by the structure of your brain (as shaped by biology and past experiences), it would be essentially random and just as meaningless as an uranium atom "deciding" to decay at some specific moment and not another.
In other words I want it to be true that looking at the system doesn't tell you anything about when / whether I'm going to be performing experiments on it today, and more specifically I don't want you to be able to predict which measurements I'm going to do based on the system alone (i.e. without asking me).
This notion of free will is (as far as I can tell) completely necessary in order to meaningfully do physics at all.
I am of the hard determinist camp but I'm pessimistic about if we're ever going to be able to predict chaotic systems. Even if someone could predict what I'm about to do, this information would be fundamentally out of reach for me since getting this information would influence the outcome (also, maybe the predicting machine itself would causally perturb me enough to not be able to make meaningful predictions).
When prey are faced with predators on the open savannah, they may be in "unconscious mode" when grazing the grass, but if they glimpse a predator, ears and tail go up, head swings, and they have to make a decision.
I think it's important for everyone to keep in mind that "free will" is used differently in different contexts. In scientific contexts, it's more along the lines of experimental freedom, and free will and determinism are incompatible.
In ethics and law, it's more about moral responsibility and free will and determinism can be compatible (depending on who you ask).
He also had this theorem: https://en.wikipedia.org/wiki/Free_will_theorem
They are axioms. We have never looked beyond these axioms nor will we ever in your lifetime.
I mean we may find a deeper mathematical model for quantum mechanics but the question of "why?" will never be answered. It may not even be the right question.
Not exactly. It's only true in flat euclidean geometry. If General Relativity holds then we're only in a flat spacetime if the total energy content of the universe is in some range of values, otherwise the universe could be the 3d equivalent of a sphere or it could be a hyperbolic shape. In neither of these configurations do right triangles behave the way you learnt in primary school.
So a^2+b^2=c^2 if and only if the big bang happened to have some particular initial conditions. It's not axiomatic, and studying _if it's even true_ tells you a lot more than you'd expect.
Pythagorean theorem is not an axiom. It's a theorem.
>Not exactly. It's only true in flat euclidean geometry
It's a theorem for Euclidean geometry.
>So a^2+b^2=c^2 if and only if the big bang happened to have some particular initial conditions. It's not axiomatic, and studying _if it's even true_ tells you a lot more than you'd expect.
For theorems and the entire concept of math to even work all forms of mathematics from Euclidean geometry to hyperbolic geometry rest on universal axioms of logic. At best we have built higher forms of logic from the universal axioms and mathematics from arbitrary assumptions but we have never delved deeper than the 3 "laws" of logic.
The other weird thing that we don't understand, and this is likely connected with logic is probability. We don't know why it works. It seems foundational just like logic but the weird thing is, formally probability is just like another math theory with random axioms at it's foundation and the rest of the theorems built up from logic.
>If General Relativity holds then we're only in a flat spacetime...
This is part of science. Observed phenomena then statistically matched to a arbitrary mathematical model. The OP's article is talking about something more fundamental... he asks "why?"
When you ask that kind of question you have to really deep. Deeper than the science, deeper then the math all the way to the bottom. Everything stops at logic and probability. There is nowhere left to go to even move the needle closer to answering the question "why?"
Can you elaborate on this or provide further reading?
Probability seems like it's connected to logic. For example "if A then B" is a statement that is part of logic. But if you say "if A then 40% chance of B" then the statement is still logical but you can now see the connection with probability.
It could be probability is the foundation of all causal connections and the logic itself is just a a special case of: "if A then 100% chance of B." But the weird part it, probability theory itself is built upon logic. You can't have probability as a formal mathematical theory without logic to derive theorems from axioms.
Under very carefully controlled circumstances, even a die becomes deterministic and feasible to predict. Just drop it sufficiently low to the ground with as close to 0 angular and linear velocity as you can. Does something intrinsic or fundamental change as you increase the height at which you drop the die? I'd say no.
You aren't thinking deep enough. WHY is it an approximation? How come this random mathematical set of theorems and axioms happens to approximate these things?
When we DON'T look at the experiment in a controlled circumstance what is the fundamental process driving it to follow the laws of probability?
We in fact do not know. The phenomenon of probability is assumed... aka axiomatic. We have no further explanation for it. In fact it's encoded into a fundamental physical law. The second law of thermodynamics: Entropy must increase.
It's actually a misnomer. Increasing entropy is not the law, it is the consequence. Entropy increases because disordered configurations of particles are more probable then ordered configurations. Thus over time the more probable configuration dominates the system. Hence the system becomes more and more disordered. Note the word "Probable." Thus Probability is the fundamental axiomatic law here.
I understand why this is hard to process. It's because seemingly it seems like that if we understand the exact physics of a single particle it means we will understand the aggregate macro behavior of a billion particles by deriving the macro behavior from the physics of each individual particle. Turns out the aggregate behavior obeys axiomatic laws of entropy that we have no deeper explanation for. Even if you have a physics engine simulate the rolls of 10000000 physical dice approximately 1/6 of those dice come out to be 6. Why? We don't even know why the simulation behaves that way let alone the real world.
It seems easy to imagine a non-quantum world. I can't imagine a world where predicate logic doesn't work.
But the buck stops there. Even the very thought of predicting that there's a hidden layer has to involve logic. To get at the hidden layer we have to remove the upper layer of logic and therefore the process of thought itself. How is this even possible?
We can't go further. It's beyond us.
But I get what your saying. You think the answer exists on the side or the upper layers. Science and beyond.
My original point was: say logic is false. That's hard to concieve of, and if so we basically can't reason. The rules of logic are independent of the physical world in a way the physical world following QM is not. I wouldn't say it is gradual layers but a hard line between physical and non-physical theories.
As to your point - i disagree although i think we have different conceptions of "why". We'll never answer it in the sense of some creator saying "because i thought it'd be funny", but we can motivate the choice. We can make arguments that it is the most "natural" or "simple" system that meets requirements. Or most "elegant". Arguably that would probably all be post-hoc justification, but its still an interesting exercise.
You're saying finding attributes of a mathematical model to be simple or elegant answers this question of "why?".
For me such an attribute is arbitrary. If we determine something to be elegant it doesn't mean anything at all. But "why" is it elegant means something.
1. We may still glean insight by reflecting on them, and
2. There may be unknown processes by which we can explain these axioms
2. You mean Logic? The foundation which axioms and theorems themselves rely on? Logic is like a recursive axiom. We assume logic is true (aka an axiom) then, logic allows us to create axioms themselves and build theorems off the axiom.
The thing with logic is that it's almost a thought driven endeavor. We don't need to observe the world to go deeper. But we can't. The buck ends here. To answer the question "why?" we have to go deeper, but there's nothing left.
Okay then, can you explain the math behind that solution?
How in the world does the words āGodā, ājustā and ābe done with itā in anyway whatsoever help elucidate this issueā¦?
Scott's aim is to understand QM better.
Could easily be done without any references to an omniscient, omnipresent and omnipotent concept with exactly zero scientific evidence. Even worse the whole concept of God literally defies logic, so mixing god into this discussion is laughable, if it didnāt come from an authority in the field of QM. I have a lot of respect for Scott, but IMHO he would be more persuasive if he left his religious beliefs out of this argument.
>Scott's aim is to understand QM better.
How does referencing god help with this endeavor?
Btw, the comment you linked commits the exact same fallacy of assuming anthropomorphic qualities behind whatever created the universeā¦
Q: Because consciousness is all there is.
Q2: Because you need consciousness to observe the universe as classical.
Q3: Way over my head.
But then the question becomes, why exactly is consciousness manifesting in exactly this way as quantum mechanics? There is no escaping addressing this question somehow.
Seems like an absurd, conceptually-crippling stipulation, analogous to asking why [the fine-structure-constant is exactly 1/137](https://en.wikipedia.org/wiki/Fine-structure_constant#Numero... ).
I mean, while one might reasonably wonder why alpha~=1/137, wondering why alpha=1/137 exactly doesn't seem like a simplification but rather a different question that'd invite a different sort of reasoning.
This limitation is because Scott is wondering "Is there a way to explain QM in a way that makes QM an obvious conclusion". That is an interesting question regardless of whether QM is true.
#4 is about limiting the discussion to QM as opposed to dealing the claim that QM is incomplete - that maybe the only reason it gives us probabilities for events is because its incomplete, and maybe theres a deeper theory that would supersede QM; this line of reasoning would not be productive to scott's initial question, which is focused on the nature of QM, given that it is true in a fundamental way.
Best quote from the article right there. I love Scott's writing style... highly recommend his book "Quantum Computing Since Democritus" if you're into his blog.
I fee confused when an article begins with a blatant exaggeration about a subject I am cognisant in right off the bat because then Idon't know how much I can trust it when it speaks of subjects I don't know.
To wit, Turing did not win WWII and didn't found CS. Turing wrote a seminal paper in early computer science, but he didn't found the field of research called "computer science". To be honest, I have no idea who would rightfully deserve to be recognised as the founder of computer science, when there have been many contributions of the same value as Turing's, the most obvious examples being Church and Von Neumann, less well-recognised ones being Charles Sanders Peirce and Henry M. Sheffer, Claude Shannon, Conrand Zuse and others (Church described a theory of computation equivalent to UTMs; Von Neumann proposed the accursed Von Neumann architecture; Peirce and Sheffer described logic gates and showed the completeness of the NAND gate; Shannon proved the completeness of Boolean logic circuits; Zuse made the first programmable computer -Babbage only designed the first). And so on. In my mind, trying to ascribe feats to heroes that they never performed, diminishes, rather than exalts, the hero. Turing doesn't need any extra serving of praise for things he didn't do to be known for ever as one of the greats of CS.
On the actual meat of the post, Scott Aaronson is a definite authority figure (among others) on these topics especially as they relate to computing.
To make a comparison, the laws that determine the movement of celestial bodies are closer to classical physics. There is no order in these bodies: galaxies all look very different. But molecules all look very similar, thanks to QM. You need this property for life to exist (you need e.g. replication, which can only happen if things easily turn out to be the exactly same, as with molecules).
Therefore, my question: show me a theory simpler than QM that can explain chemistry. And then we can talk.
Why mention God? If you're attempting a scientific stance, starting your initial question with an unproven deity who doesn't want us to eat meat on Fridays part of the year, why? Why include that, it's an instant turnoff to any evidence-based reader.
I'm an atheist myself and find no issue in the use of the word God here. We don't know with any certainty how the universe was spawned into being, using God as a sort of shorthand to state as much isn't a problem.
I don't think there is a problem in mentioning God as a shorthand for "whatever caused the universe to be the way it is and cannot be proven". Like axioms in maths, you need some unproven assumptions to do something, otherwise you get ridiculous situations like Boltzmann brains.
Q1 could be understood as "why is the universe so weird as to require quantum mechanics?" It is undecidable, just like god is, but it makes the point that quantum mechanics may take us a bit too far. For example, it may result in said Boltzmann brains, and once you get to that point, the science become meaningless.
The maths of quantum mechanics check out, this is unquestionable, but the article is about the deeper implications, at the limit of philosophy. If you are in the "shut up and calculate" camp (which is fine), it may be meaningless to you, but I don't think it is an unscientific debate.