I read Feynman's QED back in high school and was fascinated by it, but always had a lingering question.
Sure the math works out by summing all possible paths, and then most of them usually cancel each other out, and so you're left with the ones that mostly contribute to the actual probabilities, as complicated as those can still be.
But I always suspected... surely that just has to be one mathematical way of looking at it. That at some point we'd discover that turns out to be mathematically identical to something else that would be a bit more local, a bit more intuitive, a bit more straightforward. That never even had to deal in the first place with the infinity of paths that all wind up cancelling each other out anyways.
So now that I'm on a forum with smart people, the kind I didn't have access to back in high school... has there been any progress towards something like this at all? Are there any directions for this? Or is there a conceptual reason I'm missing why this fundamentally isn't possible, why the sum of all possible paths is the only way to account for certain behaviors?
In the past 10 or so years, a combinatoric approach to particle interactions has shown surprisingly good results. Simple algebraic calculations have been able to give answers that requires hundreds of pages of math through the feynman diagram approach.
This is the amplituhedron, led by Nima Arkani-Hamed, here's an article also by quanta magazine about it
In addition to giving exact simple calculations to particle scattering amplitudes, the most important aspect is that it does so in a way that does not require notions of space or time. Leading to the notion that there are more fundamental aspects to reality and space and time may be emergent phenomena.
This is the third formulation I've come across that sounds like this with space and time emerging from particle interactions. The other two are from Stephen Wolfram and Carlo Rovelli. Are the formulations related do you know?
I've struggled to get beyond their popular science descriptions to the actual theories, I find descriptions like the amplituhedron being 'a multidimensional jewel' distracting, if you have any suggestions where to start for a deeper understanding of this one I'd be interested.
Until we get evidence of such a thing, those ideas have little credibility though they are nice thought experiments.
What they're really seeing is that mathematically something can be expressed with less dimensions or degrees of freedom than what you observe in the real world, and then make the conclusion that therefor the dimensions and properties etc. that we observe are some emergent property and not fundamental.
But you can't make this conclusion from the mathematical model.
For example, if I have a finite sized two dimensional plane where each point is associated with some function f(x,y),you can trivially express it as a one dimensional system where all the rows of the plane are sort of unwound onto a single line.
This trick does not work for infinite 2D spaces but there are other ways to remap infinite sized spaces onto finite ones (e.g. via tan).
Yet there's nothing fundamental about this, it's just a mathematical modelling trick.
this trick works for infinite sets of the same cardinality and in fact works continuously for the case you are describing. there is a surjective continuous function fron R to R^n for any n
The biggest clue we have right now is illustrated by last year's nobel prize. Particles in an entangled state can interact instantaneously, disregarding space and time entirely.
It's a common thing to see in theories that try to unify QM with GR because in GR spacetime is dynamic, while in QM it's static. For QM to produce GR, there needs to be some way of generating space and time instead of taking it as an assumption.
You can find quite a few lectures by Nima Arkani-Hamed on YouTube including some on the amplituhedron. But they are mostly not gentle introductions and require some knowledge of physics to follow along. I think this one [1] provides a lot of background and explains the motivation.
I used to follow his lectures, but in the past 3 or 4 years he's become really quiet. I wonder if people stopped inviting him because he always overruns his time limit, or if he's too busy making progress on his theory.
Theoretical physicists are, on the whole, not a silly bunch and there do exist various "mathematically identical" ways to look at quantum field theory. But by the very definition of "mathematically identical" one can find the path integrals somewhere in these alternative descriptions anyway.
Contrary to your stated desire, I actually think that the path integral formulation is in some sense the most "intuitive" and "local". I apologize for not taking the time to explain that here, but let me instead try to convince you that "locality" is not at all obvious in quantum field theory.
One intuitively non-local process is the following. If I start with a state with one electron at the origin at time 0, what is the probability that I measure an electron one lightyear away one minute later? Naively this probability is zero, because the electron that you started with cannot move faster than light. But the actual (and measured, in a less idealized setting) probability is not zero, since vacuum fluctuations can create an electron exactly one lightyear away and you end up measuring that one. That, a physicist would say, is perfectly cromulent with locality of the underlying theory.
I hope this gives a glimpse of how subtle causality (and hence locality) really is, and why at least some believe that path integrals may actually be the most "intuitive" description available.
That's like looking at distant synchronized clocks and concluding they communicate faster than light. Your wish to make it look nonlocal isn't supported by physics.
> Theoretical physicists are, on the whole, not a silly bunch
... at least until the workday ends.
My own feeling is that it's obviously local if you consider that there really are virtual particles taking the non-critical paths. I know this is a bit interpretation-dependent though. GP may be interested to read e.g. https://en.m.wikipedia.org/wiki/Double-slit_experiment#Inter...
Of course the simple way around this issue is the best: "shut up and calculate".
Yes, this always bothered me as well. It happens to annoy some physicists too, so there has been a resurgence of interest in alternative (less magical?) interpretations of quantum mechanics in the past decade.
There are other very interesting, and intuitive, features of this line of modeling. I think it's better to have a realistic mental model of the microworld even if the overall QM predictions aren't (obviously, yet) affected. Maybe there's more here than immediately obvious to the mainstream physics community.
Physics is a model of the way the universe works. There's no reason to be sure that it does work the way that we model it. Practically speaking though it doesn't really matter as long as the model gives us accurate predictions. At that point you are entering the realm of philosophy.
A model can become a cage. Although the QM "infinite trajectories" interpretation is fine at explaining what happens in a quantum system from the perspective of an observer. But it doesn't provide any intuition about how the systems really behave. There may be ways to get access to more realistic interpretations. If we had them they might help us work with quantum systems.
That's a fascinating philosophical presupposition you have there: That there is such a thing as a difference between the observable* behavior of a system and its real* behavior. I won't agree or disagree with you. Just pointing it out because it's really interesting to me.
*You used essentially those words ('observer', 'really'). I won't try to pin you down into a particular definition of them, but I'm guessing we at least approximately agree on what they mean.
You could make a similar but less controversial statement by substituting "low-fidelity observer" & "high-fidelity observer" for "observer" & "reality". I wonder if that's what you mean, or if you meant what you said?
Hm... I suppose this could be mathematically/logically equivalent, but the thing that bugs me in GP's answer (and the way I hear QM talked about in general) is the very concept of an observer. I've never heard a good explanation of why an observer would be a thing - I'm not sure if there could be, without creating some kind of magical realm for it to live in, detached from the rest of physics.
What "an observer" really means, in the context of QM, is a large, approximately classical system interacting weakly with the system being "observed" (such that the interaction can be modeled perturbatively). Humans "observe" photons, but so does a pail of water.
It's a way of framing certain classes of problems, not a distinct sort of entity.
We, humans, are limited in our understanding of the worlds by what we can perceive and conceive. What does it means to understand how a system really behave when we are so limited? That’s an interesting metaphysical question but we have left the realm of sciences by asking it. Sciences care about what can be experienced.
The aim of sciences is to accurately predict the results of experiments. A model doesn’t have to be simple or intuitive, just accurate.
Obviously everyone would like a simpler model predicting the same things but not because it would be more real, just because simpler is nicer.
Feynman's QED talks pretty extensively about this as well. An intuitive mental model that humans can picture in their heads is a nice to have, not a requirement. Understanding how a system "really works" is also not really a goal of physics - the science is about predicting physical phenomena - and we generally choose whatever is the simplest equation we have currently available that does that. If you want to define the bar for explaining how a "system really works" as being able to give you an intuitive human-centric mental model you can fully understand and capture in your head - well, you are moving the goal posts over what physics really is and quantum physics has already left you far behind.
> Understanding how a system "really works" is also not really a goal of physics - the science is about predicting physical phenomena
I have to point out the above is a rather strong and debatable claim. I think most people who study science do want to understand how things really work.
Even if we accept that physicists only want to predict phenomena as opposed to understanding them, the same can't be said of other sciences (let's say astronomy, or molecular genetics). Mathematicians seek almost exclusively to understand things rather than predict them. So the claim attributes a certain lack of curiosity specifically to physicists, that doesn't apply to biologists, mathematicians, etc. To me, that makes it even more peculiar. So I'm skeptical.
I put "really works" in quotes because the definition of how to get to the bottom of how something "really works" is up for debate itself. The original context for claiming something like path integrals can't be how the system "really works" because it is some combination of being too complex, lacking an intuitive mental model for how to conceptualize it, and invoking things that seem extraneous to the person making the claim (possible paths that aren't necessarily realized).
I would agree that physicists have the same, or perhaps even more, curiosity regarding discovery as other fields (partly why they are drawn to understanding the nature of the existence/universe itself) - but there is certainly an error with this narrow definition of "this can't be how it really works because X" is simply wrong - we choose the simplest explanation which meets the scientific criteria for the time, and up until something new is discovered - that is de facto how the system "really works".
Ultimately people have this assumption from classical mechanics that everything can neatly fit into intuitive thought experiments to understand the nature of reality, but quantum mechanics has not followed the same human-centric intuitive modeling. Does it mean we haven't figured out how the system "really works"? Ultimately, it's a philosophical question, not question directly related to physics which is showing the way through predictable repeatable science.
The path integral formulation doesn't sound that counterintuitive to me, though I don't know anything about it in terms of actually computing with it. Aren't there similar integrals in statistical thermodynamics, where what is "really going on" is random motion of molecules and the math has to consider every possible path, though in Euclidean space? I'd like to understand this stuff better someday. The "really going on" of quantum mechanics is perhaps more mysterious, but that doesn't mean physicists don't want to find it.
You mean you don't understand when you don't know something? If you had no problem reasoning about quantum physics, you wouldn't say it's a philosophical question.
My post is not a statement about animal sentience. Until we can have a discussion about empiricism with another kind of sentience, I think beginning sentences with "we, humans" will be fine. I would appreciate if you could go farm PC points somewhere else than in reply to my comments and kept condescending winks out of it.
Unless you are making a pun about AI bots and I’m just having a bad day, in which case, I will have to ask you to be kind enough to bear with my rudeness.
My comment was not motivated by any notion of politics. Notice I didn't say "organism", but something far more general. A galaxy is a subjective agent in the sense that experiences incident upon it are subjective in nature (localized in time and space vs its environment, subject to some notion of "interpretation", broadly defined, on the part of the receiver).
Besides, there is nothing about a public-facing forum that prohibits anyone commenting on your posts for whatever reason. Since you brought politics into this, I will just say we live in a society and you have to accept that if you are to avoid such unhealthy and reactionary outbursts in the future.
There is no politic in my post. You were literally trying to correct my use of language. My previous comment is a polite way to tell you it’s unwelcome.
> But it doesn't provide any intuition about how the systems really behave.
In physics, intuition is much more of a cage than the models.
In fact, I would argue that our intuition itself is such a model. It's just one that vertebrates evolved over 100s of millions of years that enabled their brains to optimize Darwinian fitness.
It has layers upon layers of simplifications and heuristics to reduce complexity to a levels it can use to compute viable behaviour.
Models answer the questions What? and How? They do not answer the question Why?
The simplest model explaining all observed behavior, and even better, making new predictions that are then confirmed, is the model we tend to call "reality." But it's just a model. When you step back to think about it - everything is a model: colors, sounds, the table you're sitting at, the chair you're sitting on. We've just become so accustomed to these models we think of them as "reality" and it's super convenient to do so. I think that's a big point the Buddha was trying to get across.
Such a "truest" formula doesn't really exist, or at least what you determine to be the truest is just a matter of definition and taste.
For any equation it's mathematically trivial to come up with a different set of equations that produce the same result, e.g. for example just via approximating the original function with some infinite series that is guaranteed to give back the original result in the limit.
But even beyond such trite examples, it's not unlikely that there will simply be multiple competing ways to model the same data that the equation takes in and spits out that are very different in form and function, and perhaps even in mathematically incompatible ways (this could happen if e.g. the equations model more than what exists in reality but all of reality is described by some subset of the parameters of these equations, like how gravity works for negative masses but such a thing does not exist from what we know).
You could then decide on some reasonable criteria which of all your models is the truest one, but the criteria themselves will be up for subjective debate.
It isn't the only way. I would argue that the "sum over paths" is more of a convenient language for categorizing QFTs than an actual statement of physical reality. Path integrals have the benefit that they can be easily connected to correlation functions by a Wick rotation, are naturally invariant under relativity, and work (kinda) well with gauge theories (well better than any other way we know).
However, in practice they are not used directly. Instead, the path integral is either treated perturbatively giving you Feynman diagrams, or by working out the Hamiltonian prescription (probably closest to what you are thinking of), or by using Monte Carlo approaches (there are probably other approaches I don't know of too). All of these approaches are easier to calculate with, but are a less natural language for abstractly describing a QFT.
Alright fair enough, I'm not an expert on how those work. I was under the impression that there is quite a bit of work that has to be done to turn a path integral into something amenable to Monte Carlo though.
Well it depends on what you mean by "quite a bit of work"! Wick rotate, focus on a finite volume of spacetime, and discretize the spacetime. That's all. The first step changes a difficult-to-sample distribution exp( i S ) into an easy-to-sample exp( – S ). The other two steps keep you from needing infinite RAM.
The discretization and finite-volume approximations may be removed by doing calculations with different spacings and volumes and extrapolating. The Wick rotation is more subtle, and typically means only some observables are accessible. To study the path integral with real time causes a very difficult sign problem [essentially: you need an exponentially large number of samples in order to get cancellations under control], which is why real-time quantum dynamics is an exciting potential application of quantum computers.
You can take an amplitude-vs-time representation of a signal and via a Fourier Transform instead represent the same information as a sum of weighted complex exponentials in the frequency domain. It works mathematically, sure- but does that mean that- physically, at the core of existence- every RF, acoustic, seismic, or financial data ripple is actually a bunch of sines and cosines which are getting summed together to create the real phenomena?
99% of modern physics was developed for pen & paper mathematics, not numeric simulations. Even when computers became readily available it was seen as somehow "less than" symbolic solutions. More practically, special-case solutions that were tractable symbolically require far too much computer power if approached from a fully general "local" simulation perspective.
QED is essentially a Monte Carlo simulation, just like ray tracing in computer graphics. The difference is that QED will correctly model diffraction (and other more complex physical effects) that the simplified graphics-only model doesn't bother with.
Both QED and raytraced computer graphics rely on a mathematical dualism where a wavefront can be tracked either as a surface OR as a vector perpendicular to the wavefront. The whole "summing up but mostly cancelling" is just accounting for the wavefronts. The use of complex numbers is mostly also just a method for tracking the cyclic nature of wavefronts.
If you skip the "waves" part, it becomes traditional computer graphics. Less accurate, but essentially the same.
Computer graphics could also simulate light transport by using a 3D volume, which is roughly speaking how some diffuse light simulations work in real-time games like the Unreal engine. The problem is that to get decent accuracy, you need a lot of memory to store that 3D volume. For low-resolution scene lighting this is fine.
Monte Carlo enables a solution to be built up incrementally with much less memory required, needing only a 2D accumulator in the image plane instead of a 3D simulation in object space. This allows a vastly more complex and detailed simulation to be calculated, which is important for the tiny wavelength of physical light instead of some non-diffracting idealisation of it.
For a physics problem the memory requirements of any non-trivial system would be gigantic, that's why everyone just ignores this approach even though it makes a lot more intuitive sense.
> that's why everyone just ignores this approach even though it makes a lot more intuitive sense.
- No one ignores the correspondence between QFTs and stochastic processes (which is what I assume you're talking about, since the claim that QED is just Monte Carlo is extremely false if taken literally), any halfway decent intro QFT class will cover it.
- It only "makes more intuitive sense" because you've papered over all the gory details. There's very little intuitive or natural about analytic continuation in C^{\infty}, for instance.
Stochastic processes is one thing. But most calculations in QFT is done using various perturbation theories (kind of like Taylor series expansion), instead of by using exact calculation.
That could be interpreted kind of like ray tracing with finite resolution and a finite number of reflections.
EDIT: Feynman diagrams serve as an attractive way to rationalize the various perturbations, but it may be that a "true" theory needs to be able to solve the (for us) unsolvable integrals directly.
Especially since the perturbation theory integrals (that we can solve) diverge, and require renormalization to avoid infinities.
While in principle you can evaluate certain path integrals by using MCMC, in practice you run into all kinds of issues like the sign problem, which even with things like complex Langevin dynamics can't be resolved to this day completely.
Even if the insult is unintended, or is plausibly deniable, if the person ends up being insulted anyway, then it is unlikely to go well.
In totally unrelated news, it might be worth noting that "being right" is not a relevant defence against the charge of "being an asshole". It's entirely possible to be one without being the other.
> I understand that you are fine being called an idiot and that the proper response is a smile and nod of understanding. Some do not. I do not.
Because the only possible responses are "smile and nod of understanding" and "call the professor an idiot in return", and no middle ground exists where you can draw attention to someone's mistaken beliefs without escalating the situation, or even without putting them on the defensive?
> you can draw attention to someone's mistaken beliefs without escalating the situation, or even without putting them on the defensive?
This requires a will to discuss (both sides). I have had plenty of such discussions where the other side arguments sinked in or not, but where the was will to actually listen and think.
I don't believe you only met such people, and if so congratulations (I am not being cynical - it would really be great).
Unfortunately this was not the case, not even close. He was an asshole using his power to dominate others, something which works in some places where there is a medieval structure.
I did not friends on him and he said that we would meet at my defence where he will remember that. To what I said that I don't do, but wish him all the best.
He was childishly ridicule at the defense where he absolutely wanted to be part of the jury.
The world is sadly what it is. My life motto is "always be nice twice" (stolen from Irving) and I like to be the one extending the hand after a failed first meeting. Some take this as weakness or submission, and well, b it does not go well indeed.
The path integral formulation is possibly the most local theory you could come up with - it's incredibly simple and does not require any nonlocal effects! The relativistic lagrangian is even more elegant than the classical one - it's just mass! What kind of theory would be more intuitive and straightforward?
When you look at quantum mechanics from Schroedinger's equation point of view, it is very simple. The implications of it are not, which is true of many simple systems. What is difficult in quantum mechanics is trying to understand how those equations have anything to do with what we see.
The path integral interpretation actually does give us an intuitive picture of why we see classical physics. If you zoom out, the stationary point of the Lagrangian is all that survives, with other things mostly canceling out as you mentioned. This explains why in lagrangian mechanics of clasical physics we are told, without reason, that the equations of motion are the stationary point of the Lagragian.
You don't say this, but I think people think quantum mechanics is weird just because it is different from what they see. People also had trouble with the idea of us moving around the sun, one reason being because it looked like everything was going around us. Of course, if we did go around the sun, it would still look like things went around us. In the end though neither is really true. The sun in the center is just a better model. Likewise, quantum mechanics is probably just a better model to "reality" than classical physics.
I'm tempted to go check, I read that too around the end of HS or very start of college, but isn't QED the one that starts off with a story about counting physical beans in jars to do familiar arithmetic operations like summing and multiplying? Then the rest of QED is presented as describing how QED works using a similar counting-beans approach that everyone can understand vs. the more sophisticated methods that working physicists use that require a few years of undergrad training at least. That both end up having infinities at the core is an important part of being able to accurately (mathematically) describe nature, like counting beans vs. just using a calculator both involve numbers at the core to accurately describe to other humans what's going on -- and numbers can seemingly be "canceled out" when removing beans from a jar! (Or perhaps adding a different color bean does the canceling.) Without thinking about it further I suppose this falls under the umbrella question of whether reality is fundamentally continuous (as we assume when we model things with calculus) or discrete.
Why wouldn't summing all possibilities be the simpler solution?
Thing about Monte Carlo simulations - it's simpler to just try all possibilities than to figure out what is the formula of the correct result.
Neural networks also work like that - you randomly do things and propagate errors with simple rules instead of figuring out the complex formula that would give you the answer.
There seems to be a lot of power in summing up all the things.
If our universe is a computation, our practical experience seems to suggest that a Monte Carlo like simulation of it would be more efficient than a closed-form formula.
Summing all the things is similar to just a big "OR" right? It lets the important signal through (you don't know which it is) and the other ones just have to be suppressed or suppressed enough to not interfere. For example all the other ones might as well be as if stochastic, so on average you get it right.
>is there a conceptual reason I'm missing why this fundamentally isn't possible, why the sum of all possible paths is the only way
It's not so much a conceptual reason it isn't possible so much as that's just the way the universe is. If you have your particle going from A to B, changing things at some possible other path C simply does change the way it arrives at B, like it or not.
Feynman's take was:
>If you will simply admit that maybe [nature] does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possible avoid it, "But how can it be like that?" because you will get 'down the drain', into a blind alley from which nobody has escaped. Nobody knows how it can be like that.
Personally though I actually like pondering how it can be like that as an interesting puzzle. But it's the way the universe is, not a conceptual thing. My guess as to why is that reality at the most basic level is more like a path integral than like objects whizzing around.
Many-Worlds probably fits what you're looking for, that conforms with orthodox quantum mechanics. How to bootstrap probability seems like the only open question there.
If you want something less orthodox, then superdeterminism is seeing a bit of a revival. For instance, Tim Palmer's Invariant Set Theory (Invariant Set postulate on Wikipedia).
Born rule postulates that probabilities exist at sample size 1, which is not supported by reality: in reality probabilities are unobservable at sample size 1, which better corresponds to MWI than copenhagen. MWI shoves it in your face why probabilities are unobservable at sample size 1.
> So now that I'm on a forum with smart people, the kind I didn't have access to back in high school... has there been any progress towards something like this at all? Are there any directions for this? Or is there a conceptual reason I'm missing why this fundamentally isn't possible, why the sum of all possible paths is the only way to account for certain behaviors?
It certainly not the only way. One easy trick: you put it under multiple layers of definition, and at the lowest layer you just do the integral without calling anything "paths" or so. (Equivalent theories can be seen as bastardization of each other, that's why none of them says anything meaningful about ontology.)
It kind of feels like the epicycles that were used to make geocentrism work. Sure, they make the math work out correctly, but the equations for the motion of the planets become needlessly more complex than if you just take the sun to be the center.
The canceling out part is the reason quantum computing works. We basically just avoid computing a bunch of bad answers making the actual problem faster to solve. So it has some observable examples.
The summing over all paths is basically already there when you do the two slit experiment. In that case you sum over two possible paths. So it is already right there in the basis of quantum mechanics.
I think the fact that the oddest approaches work aren't exactly a measure of how the particles actually work in physics. I think it proves that math isn't the language of the universe no matter how much mathematicians and physicists want to say it is. It just proves we're good at modeling but not good enough to actually know what we're seeing/measuring (a natural limit to our knowledge). I don't know why this position is considered controversial or out of the mainstream when it seems to be the logical answer.
I don't see why it's logical to conclude that difficulties modeling hard problems means we can't model them using math. These difficulties are not uncommon in the history of science, and we've eventually solved them all before with math, and we should expect such problems to become more and more difficult as the low hanging fruit has been plucked. I see literally no reason to jump to the conclusion that the core problem is trying to use math at all.
>I don't see why it's logical to conclude that difficulties modeling hard problems means we can't model them using math.
That's not what I'm stating though. I'm stating that the math involved is a model but it isn't ever going to be identical to the thing being modeled. Meaning that math isn't the "language of nature" as we don't have a direct means to truly comprehend it (direct realism has a whole has been discarded by philosophers for a long time now).
>I see literally no reason to jump to the conclusion that the core problem is trying to use math at all.
Again, that's not what I said, please read my post again.
> I'm stating that the math involved is a model but it isn't ever going to be identical to the thing being modeled.
I don't know what "identical" means in this context. Either a mathematical model can capture all of the information in the system, or it can't. We know that we can reproduce a function on a long enough timeline just by observing its outputs via Solomonoff Induction.
The only escape hatch here is if reality has incomputable features. There's no evidence of this at this time. That's why it's confusing that you would go from "we have persistent hard problems" to "mathematical models can't exactly correspond to reality".
The only progress I would say is more and more people realising it's a waste of time. Why should we expect reality on a scale very different to everyday experience to behave like everyday experience?
(And frankly I've never found it particularly counterintuitive. It's just a wave bro. It behaves like any other wave)
Flash storage uses QM [1]. Who knows what other advancements could be made with a better grasp of reality, at these scales. It doesn’t seem like a waste of time.
Grasping reality is better done by grappling with it directly than by trying to force it into your everyday intuitions. I'd bet the people who made flash work were many-worldsers.
I skimmed the article, and admittedly didn't understand much. Action principles and path integrals are unfortunately one step above where my knowledge of physics stops.
But seeing a headline that reads, "Our reality may be a sum of all possible realities", I wonder whether the point is to (a) explain new experiments, (b) develop simpler mathematics, (c) close the gap between intuition and theory, or (d) whether this is all unfalsifiable speculation.
A charitable interpretation might be (c), but a skeptic within me thinks that this might be (d).
I think one problem here - physics and the philosophy of physics are two different things, but a lot of people (even professional physicists) fail to treat them as distinct in practice. So long as we are talking about math, observation and experiment, that’s physics. But many of these “multiverse theories” are moving beyond that into philosophy, because they are not about the math, but rather how to interpret it; not only are existing observations or experiments are insufficient to determine their truth or falsehood, but we often have no idea of any practically feasible way to test them.
There’s nothing wrong with doing philosophy-but let’s be honest when we are doing it, rather than pretending it is still just physics. Furthermore, your average professional physicist has indubitable expertise in physics, their expertise in philosophy (even the philosophy of physics) is much more variable.
If you have a quantum-mechanical system that you describe by specifying a Hamiltonian, I can always write down an exactly equivalent path integral. A failure of equivalence between these two descriptions would be extremely exciting, as it'd be evidence of some paradigm beyond quantum mechanics.
The mathematical equivalence of Hamiltonians and path integrals, by itself, doesn't tell us anything about a "multiverse", however.
Since the mid-20th century, many philosophers have come to analyse everyday talk about possibility in terms of "possible worlds" or "possible universes". However, those who invented that language (such as Carnap and Kripke) weren't claiming that all those possible worlds were just as actual as this one – that claim only arose later (David Lewis). Similarly, the originators of the path integral formulation of QM (Dirac and Feynman) weren't claiming that all those paths were "equally real". By contrast, the majority of proponents of "multiverse" theories, are claiming those other "universes" are ultimately just as real as this one, as as opposed to merely being some theoretical construct, a mathematical metaphor.
You can understand these "paths" in two ways – either as just a useful mathematical tool for analysing past observations and experimental results, and predicting future ones, but passing no judgement on their ultimate ontological status; or, as a claim that in some sense, all these paths "really exist". And, if you adopt the later reading, you can then argue whether they are all "equally real", or maybe one of them is "actual" and the others "non-actual", or even just maybe that some are "more actual" than others. Nothing wrong with those debates – but when we start engaging in them, we are no longer doing physics proper, we are doing the philosophy of physics.
Agree with your first paragraph and the first half of your second paragraph. But if you listen to Feynman talk about the path integral, he emphasizes that all the paths are real, are in fact critical to describing experimental results, and that it is simple to construct experiments to get those paths to coherently add to produce classically-unexpected results! I don't know about Dirac's "philosophy"; what you say of his stance may be correct.
I don't think Feynman would say any path is actual or non-actual. It's not the case that ONE of them "really" happens and the others are a calculational trick. It's that the thing that happens is a sum of alternatives. The sum is real, full stop. If you leave out terms in the sum you get the wrong answer. Is that enough to mark them as "real"?
THAT is philosophy. Certainly you may find another description for the same sum which does not discuss a sum over paths at all. Perhaps that means that the terms in the sum are not real? But we can all agree that the sum itself comes out right, whichever picture of the world you want.
> But if you listen to Feynman talk about the path integral, he emphasizes that all the paths are real, are in fact critical to describing experimental results, and that it is simple to construct experiments to get those paths to coherently add to produce classically-unexpected results!
Okay, but is he claiming that the paths are "real" in the exact same sense as the actual experimental results are? We (in principle) add up an infinite number of paths, and that infinite sum produces a probability amplitude, which gives us a probability, and then we expect that if we repeat the experiment enough times, and sufficiently control the sources of experimental error, the observed probability should converge to the calculated one. Even if he says that all those paths are "real", I don't think he is claiming that they are "real" in quite the same sense as the actual experimental results are "real". Whereas, a proper "multiverse theory" would be claiming something like that.
OK, I think I appreciate the issue: “multiverse” is overloaded. When people talk about the many worlds of quantum mechanics, or alternate histories, they’re talking about the terms in the path integral sum.
But multiverse can also mean, separately, at least two additional things. First, different bubble universes that may be a part of cosmology. Second, alternate quantum field theories (with different actions, or fundamental parameters, or different gauge groups, or whatever).
The standard quantum-mechanical path integral is a sum over histories / a many-world theory in the sense that the different histories / parts of the wave function can be detected via interference experiments. Other meanings of multiverse are speculative (though maybe a cosmologist will come and tell me that bubble universes are a direct prediction of inflationary cosmology and are not optional either).
> When people talk about the many worlds of quantum mechanics, or alternate histories, they’re talking about the terms in the path integral sum.
Hugh Everett's original "many worlds" theory wasn't just "talking about the terms in the path integral sum" – he saw all the "worlds" as "real" in exactly the same sense that the actual experimental results are "real". Everett believed in "quantum immortality", which only makes sense if you interpret the worlds in a much more literal sense than mere "terms in the path integral sum" suggests. By contrast, even though Feynman calls the paths "real", it isn't clear if he means them to be "as real" as the actual experimental results they are used to predict. People who reinterpret many-worlds as just "terms in the path integral sum" are cutting the theory down to be something far less metaphysically grandiose than its originator intended.
To quote Max Tegmark:
> Atheist or not, Everett firmly believed that his many-worlds theory guaranteed him immortality: His consciousness, he argued, is bound at each branching to follow whatever path does not lead to death —and so on ad infinitum. (Sadly, Everett's daughter Liz, in her later suicide note, said she was going to a parallel universe to be with her father. [149a])
I realise you are being somewhat flippant, but it is still sad, because (among other reasons) it appears that Liz Everett misunderstood her father's theory.
If the theory of quantum immortality is true, then while from our perspective, Hugh Everett died from a heart attack in 1982, from his own perspective, he's living on in some other branch of the multiverse in which he somehow survived that heart attack. Similarly, while from our perspective, his daughter Liz died from suicide in 1996, from her own perspective, she's living on in some other branch of the multiverse in which she somehow survived that suicide attempt. Indeed, if the theory is true, then no matter how many times 1996 Liz tries to commit suicide, from her own viewpoint she will never succeed – but she never gets to see her father again either – he's living on in a different branch of the multiverse from her, one which diverged from hers all the way back in 1982. And even that other Liz, whose father didn't die in 1982, is doomed to eventually watch her father die, and her father to watch her die, even as both go on living forever, trapped in different branches.
Quantum immortality promises us a somewhat bleak afterlife in which we all live forever, but none of us ever get to see each other again. Eternal loneliness is our universal doom.
The only way in which she actually could see her father again, would be if quantum immortality is false, but some other afterlife theory is true instead.
Well, it depends on what you mean by "two systems". If they are described by one Hamiltonian the result is one path integral. In a relativistic quantum field theory, for example, one may describe systems of any number of particles. The path integral captures all the interference effects.
Sometimes the discussion I observe among scientific experts resembles the type of discourse I've seen from Marvel fans debating the finer points about multiverses and incursions within their comic book canon.
At some level this is just the application of wave mechanics to reality. "A vibration on a guitar string is just the sum of the vibrations of its harmonics." You are decomposing a system into a mathematically favorable basis, performing a calculation in that basis, and recovering the original basis (by linearity).
You can do this in a hamiltonian way (find the eigenvectors of the hamiltonian, decompose your system into those, step them forward [easy] and add them back together) or in a lagrangian way (treat each point in the system as the source of a sort of spherical wavefront). Feynman is doing the latter - he's just asking "what if we treated other fields the same way we know we can treat the EM field via Huygens-Fresnel?" Calculate the progression of wavefronts through the field, using euler-lagrange to find the parts of the wavefront that don't fade away into random noise.
So, in the framing of your question, I think it's mostly B and C, with maybe a bit of D (it's not clear if we have any kind of tool besides aesthetic preference to distinguish between extrinsically equivalent models). However, your framing might be a bit uncharitable.
If we falsified quantum mechanics we might expect some formalisms (Hamiltonian, Lagrangian, path integral, whatever) to continue to work while others don't. So it's perfectly possible to falsify the idea that path integrals do not describe the world; doing so would demonstrate a failure of quantum mechanics and would be extremely exciting to physicists.
Path integrals are for (a) and (b), but take that with the knowledge that Feynman came up with them maybe 70 or so years ago, so that anything we say about it now tends towards (c) and (d) by virtue of a lot of the (a) and (b) questions already being taken care of.
As if I’m a ten year old, because I kind of am when it comes to this kind of stuff… how in the world could adding up all alternate realities end up with a single reality? How would that work?
The path integral suggests that all of the possible realities are like waves. When these waves are added up, they can interfere with each other in a way that only one of the possible realities can be seen. It's like when you throw two stones into a pond at the same time. The waves created by the stones will interfere with each other and create a single pattern on the surface of the water. In the same way, the path integral suggests that all of the possible realities can interfere with each other and create a single reality.
Alternative realities may have alternative people living in them - will they observe different laws of physics since their reality is not a sum of all realities, as opposed to ours? Or would they have the same conclusion about sum of realities?
A) these realities can't have people - they're not real enough to be called that
B) physics will be different - that would be a great scientific revelation
C) physics will be the same - making the premise meaningless
The problem here is the word "realities" because it doesn't in any way mean an alternate reality where you're there doing something else.
This is from the math model where the resulting path of a particle can be figured out by finding all possible paths. Then what follows is the conjecture that because the math works maybe those particles really do travel by every possible path. There's no proof of this, and it's very hard to test because the result has to be the same.
So maybe our reality is the sum of particles taking every possible path. Or may be it isn't. Wake me up when the article title is "Our reality IS the sum of all possible realities."
If we station ourselves outside of the quantum system, then the answer is that each reality puts a complex number on every outcome, which get summed into a single complex number. Then, the magnitude squared of that sum becomes the probability with which we will observe that outcome.
If we put ourselves inside the system then saying anything about it comes with a lot of implied philosophy about what "we" are.
"Our" reality is not necessarily the only one, or is somehow special: under the many-worlds interpretation, every "quantum event" forks the universe. It should look somehow similar to "updating" a typical immutable data structure (a tree, a list) so that a new copy is created, sharing most data with the old copy.
You wouldn't necessarily end up with a single reality, but if there was some kind of process "sampling" a finite number of realities from the wavefunction (either continuously, e.g. if quantum collapse is ontic, or e.g. at some time in the distant future god takes a look at the state of the wavefunction) where the sample probability was calculated in the normal way (square of the wavefunction magnitude), that would explain how probability "gets into" quantum mechanics. This is kind of an open question, though - you can find plenty of papers (mostly bad) wondering out loud how you get the appearance of "discrete" realities with things like probability when quantum mechanics appears to be continuous.
I don't have a good answer for you, but the best advice I'd say is to read Feynman's book "QED: the Strange Theory of Light and Matter" (it's really just a four part lecture series).
It’s also surprising at first that infinite series can add up to a specific, finite number. If I go halfway to X, halfway again, and so on, where do I end up?
All next realities are weighted based on their probability given the current one. The probabilities are based on our knowledge of the equations of physics. Some realities are more likely than others and adding this all up results in an average outcome. At the smallest scales the average outcome is not actually what happens, but time is a great equalizer.
It seems like Woit is kind of intending this to serve as a refutation of PIF, but I don't really see why - this sounds more like a description of some problems that are hard in PIF, rather than anything wrong with the underlying theory.
As an organizational scheme for approximate numerical calculations, the path-integral formulation is fine. But path integrals can't serve as a rigorous foundation for QFTs, because for the most part they don't actually exist. The high-frequency behavior Woit describes is one obstacle; the fact that no infinite-dimensional Lebesgue measure is possible is another. There are others.
Presumably there's some mathematical object out there that captures all the data a path integral ought to have without its pathologies, but no one knows what it is yet.
This title really irks me. Basically it is saying that quantum states or possible paths are realities. But the very definition of reality is what we experience, so how can a quantum state, be a separate reality? The article mentions reality 5 times, not explaining what it even means by the word "reality".
While there may be some philosophical content to the statement, it is not a well-defined physical statement and moreover, the article doesn't show any "evidence" for it assuming that there is even a valid way to interpret the title.
I've come to expect this type of artilce from Quanta Magazine though.
> But the very definition of reality is what we experience
If you're an anti-realist when it comes to science. I suspect a lot of scientists think there's plenty of reality we don't experience, such as quarks, dark matter or the interior of black holes. Or what lies beyond our light cone (probably a lot more of the same), given the flat topology that's been measured.
Sean Carol has argued for the Many Worlds Interpretation being a true description of reality, even though we can only experience the decohered branch (world) we're on.
One way to look at this is that there is no difference between possibility and reality. If there was, then the question would arise why only this one particular possibility is real, while the other possibilities aren’t. If there is a necessary reason for why this particular possibility is real, then that would mean that the other possibilities aren’t actually possible after all. If, on the other hand, there isn’t any such reason, then that would mean that the fact that this particular possibility happens to be real is fundamentally arbitrary.
Personally, I find it more plausible, in a parsimonious Occam’s razor sense, that everything that is logically possible actually exists, because the only other option is arbitrariness, the lack of any explanation even in theory.
Whether summing up path integrals makes sense, is however a different question.
The problem with that, is how can you ever be certain that, there isn't always such a reason? Just because no reason is found (yet), is not proof that there does not exist any such a reason.
To me, accepting that everything logically possible actually exists, is accepting arbitrariness, as all of logic is fundamentally built upon arbitrary assumptions. It seems like rather accepting that things aren't inherently arbitrary (that not all logical possibilities exist / there always is such reasons), is the only way to avoid arbitrariness. It's just a matter of finding the theory that explains it.
It irks me, because I find the title reads similar to: "Our possibilities may be a sum of all possible possibilities". Or shorter "What's possible is the sum of all that's possible". It's like, well no duh?
If it doesn't read like that, then I too find it irksome for the aforementioned reasons.
Well if it’s about QED I’m always drawn to the paper : “There’s something rotten about the state of QED” by Oliver Consa (https://arxiv.org/pdf/2110.02078.pdf). Since I’m in CS, not physics could anyone let me know if the paper above is making stuff up. If not, then it does paint QED in a very bad light and indicates something wrong with that field
Errr, that reminds me of a paper I reviewed. It was a favour for my daughter who doing a post-doctoral Uni course, who was asked to write a review of it for an assignment. She could not make head nor tail of it, which was surprising as she is is pretty strong at maths.
After maybe two days or dusting off my old statistics text books and numerous google searches I came to the conclusion the statistics they used were, as far as I could tell, complete rubbish. It looked like someone got themselves a (very small) data set by posting out a questionnaire, crunched the data by mashing together a grab bag of sampling techniques + distributions + significance tests, polished the result them by using the usual academic style of a numbered lemmas and "proofs", and served up the result which happened to match the latest management fad.
But we were both full of self doubt - why would a Uni course ask read something like this? Fortunately her father-in-law had a PhD in statistics, and had lectured at a major Uni for a while. So we asked his opinion. It was the same.
Which left us in a difficult position. We both suspected the point of the assignment was to demonstrate she could read complex material and learn from it. I' afraid I wimped out with "I'm an engineer, I'm not cut out for this sort of thing". I'm not sure what she wrote, but she got a distinction for the assignment. Oddly, I now think it was a good learning experience in management.
But the maths of QED has always been beyond me so I always just taken what the physicists said about the accuracy of their models at face value. If I had of read "calculated that the sum of all positive integers is not infinity but -1/12 ... and this is precisely the value that is used in the equation of the Casimir effect" a little earlier, I might have been a little less sanguine.
There’s an aspect of path integrals that’s always bugged me. They rely on an underlying classical field configuration space to integrate over. But, this seems problematic to me, since properly the objects of classical physics should emerge as limits of quantum physics. Shouldn’t we be able to start with “pure” quantum mechanics (a state space, a Hamiltonian operator), with no mention even of “paths” and get out classical physics? I.e. it seems backward to speak of a particle trying out different paths since a “path” is a classical notion; it’s as though quantum mechanics is merely a superstructure on top of an underlying classical layer rather than the other way around. Know what I mean?
Quantum and Newtonian physics are both just conceptual models to help ourselves understand and predict the things around us. They're useful for describing reality but neither of them are accurate representations of the real deal. All models break down at some limits.
To imagine one model "being merely a superstructure" on another implies that the limit doesn't exist and the two models are, in fact, the same thing. If you expand that idea to all other models, they would all eventually merge into one grand unified theory that accurately explains every single occurrencence in the universe. A nice idea conceptually, but we're at best no where near that and at worst have brains that will find the nuance of the universe impossible to comprehend in totality.
Any model that is useful for understanding and predicting the universe is worth sticking with, as long as you understand the limits where it applies. If path integrals happen to unlock some new insight that seems evidentially correct, it doesn't really matter if it ties into other theories.
Articles on this topic always remind me of Leibniz's philosophical optimism, which stemmed from considering all possible worlds through the lens of his theological motivations (https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz#Theo...). This was famously criticized by Voltaire in Candide.
But, even earlier, the Scholastics wrestled with alternatives to reality as we know it, which seems to have found its best articulation by Luis de Molina (https://en.wikipedia.org/wiki/Molinism).
Even Calvin seems to resurrect his influence through superdeterminism (most recently championed by Sabine Hossenfelder).
I'm not claiming that these thinker prefigure modern physics, only that intellectual history sometimes rhymes, even if it doesn't repeat.
My interpretation of the double-slit experiment has been that the presence of physical matters in a certain configuration imposes some sort of probabilistic "reality field" that propagates at light-speed. The superposition of these "reality fields" at a certain point in space(-time) determines the probability of the particles' behaviour at that point, not unlike how support vector machines with a RBF kernel work.
This interpretation has the benefit (I think) of bypassing the problems with the "observers" --- any apparatus that is able to discern the path a particle had taken just so happens to impose a field such that, when superposed with the original "reality field" the double-slit imposes, the mixture field no longer exhibits the interference pattern.
Of course I am not a physicist by training, so the above could be completely nonsense (or it could have already been an established theory).
I would love for someone to clarify this for me: My understanding is that the physical act of observing, as in, with the specific machine we use, is what causes photons to suddenly behave different. Like if decided to gently touch a marble rolling down a ramp in darkness to measure how fast it was rolling, the act of touching changes how the marble rolls. It's not that we're actually observing the marble's behavior, is that's we're interfering with its behavior when we measure it.
Is this accurate? Or is the observation of the photon not physically impacted by our observation, and through some magic of quantum behavior, it somehow "knows" it's being observed and changes because of that?
I'd thought direct observation of the photo would mean physically interact with it (and thus changing its behaviour). My understanding is that there are also other experiment designs which allow identifying which path a photon went after it passed the slits; in such cases the interference pattern disappears too.
It was Feynman’s excellent QED (basically the ELI5 for quantum physics) that introduced me to the concept that the photon I shine on my wall with a flashlight did a few orbits around Jupiter too, it just cancelled out. I believe the “dippy” process to do that is called renormalization. Feels like it’s time for a reread.
This is a pretty common misconception of path integrals from how Feynman explains them to a non-physicist audience. The path integral formulation cannot work from a particle-based approach, where you integrate over all possible trajectories of electrons, photons... . Instead, you are actually integrating over all possible configurations of fields, the electron field, the photon field... . As far as I know, there is no way to view the universe as being fundamentally made of particles that is compatible with our modern understanding of QFTs.
Also, the path integral really shouldn't be taken too literally. It's not reality, it's just an equation.
> The path integral really shouldn't be taken too literally. It's not reality, it's just an equation.
While it's always important to point out that the current paradigm might be overthrown tomorrow, it is ALSO important to understand different ways of describing what the current paradigm says!
The "bizarre" trajectories that contribute to the path integral are not optional; they're really there and you can arrange interference experiments to make their physical importance clear.
> the photon I shine on my wall with a flashlight did a few orbits around Jupiter too
This is a very confusing way to essentially say that an integral of exp(−iS) is taken over all possible paths for the action S. Your flashlight's photons don't literally do a few orbits around Jupiter. In fact, photons are quantum objects (not billiard balls) and they are "smoothed out" over spacetime, meaning they don't really have paths to take in the first place.
One absolutely astounding aspect of the path integral is that it ascribes amplitudes to trajectories that don't obey the (classical) equations of motion. If you like: the classical paths are at turning points of the action (loss function) but all other paths have some associated imaginary loss. In the path formalism we sum every possible path, weighted by the imaginary loss.
Since the classical paths are at turning points, small deviations around that path tend to sum coherently, while large deviations tend to have neighboring paths that contribute with opposite phases.
If you write the amplitude for a photon going from your flashlight to your wall, the path integral tells you to sum up all possible paths, not just the classical ones. So yes, the path integral formalism really does say that a photon goes from the flashlight, around Jupiter, and to the wall. But not in 48 minutes! In time = (distance to wall)/c! It goes every which way without caring about the classical law. The "insane" ones cancel.
Well, if all the insane ones cancel, what's the point of all this? Just forget about them, they're a huge surplus of nonsense in the theory! However, it's perfectly possible to construct experiments where it's clear that photons really do "smell out" alternatives. Diffraction gratings, the double-slit experiment, etc., all show this quantum weirdness.
It gets even worse if one starts thinking about the flashlight's filament or semiconductor, the wall, stratified Jupiter with its optical depth, the flashlight-wielder's visual system, and everything in between all being (sets of) quantum objects.
Maybe the thing to do in this example is to assume correspondence and think classically, and insist on using a fewer-quantum-number example if one wants to think quantumly. However I tend to admire detailed wrestling with everything-is-quantum in an example like this. Maybe start by remembering that the spot-on-wall-to-retina is relevant, not just the flashlight-to-wall.
There are two different "circle around distant bodies" here that are probably causing some confusion.
Classically, if near your appliance you can see stars and Mars through the window on a cloudless night, a flash of light from your appliance can in principle be seen (e.g. by a really good telescope orbiting one of those bodies). Indeed, some of the light from a laser pointer shining out your window will go to infinity, and has some astronomical chance of being stuck the photon ring around a black hole. It works just like you being able to see through your window starlight or (in principle) a bright flash on the surface of Mars. However, this is not the sort of "goes around Jupiter" that we are talking about; we are talking about something like the probability of one microscopic component of your appliance's flash of light scattering off or being absorbed by a microscopic component of said window (for example, in part of the spectrum in which the window is not transparent), where calculating that probability considers an infinity of possible paths.
Indeed, an infinity of the path-integral trajectories of one such photon (that classically is definitely intercepted by the window) will go out to infinity, an infinity of those trajectories will go out to Jupiter, an infinity of them will go to somewhere very near the window pane, an infinity of them will speed up and slow down along the way rather than travel at the speed of light at all times, etc. We then want to assign a probability to each of these paths.
The idea is that trajectories that are not like a classical path between appliance and window are suppressed because (somewhat technically) they [a] have the same magnitude of probability amplitude, but [b] have different phases, [c] different changes in trajectory have different changes in phase, and [d] for "longer" paths compared to the classical one, a small change of trajectory makes a big change in the action compared to Planck's constant, so [e] for sets of small changes in "longer" paths the phases change rapidly and thus are highly likely to cancel out. So most of those infinities are effectively irrelevant and we can focus on the smaller infinities that make a marginal-to-relevant change to the total probability amplitude and figure out a way to calculate it from them (e.g. by sampling).
All of them, including planets outside our observable universe.
Same with the flashlight and refrigerator.
Each photon also goes into and through all the planets, and near each of their electrons in an infinite number of ways. They also go through all the stars, all the vacuum, etc. And with all the speeds, all the accelerations, ...
Most of these infinite possibilities are a negligible contribution to the final probability that photon-detected-at-B was photon-emitted-at-A. The non-negligible contributions come from the (still infinite) trajectories allowed by relativity and mostly from those near the lightlike geodesic.
The whole glow? Treat it classically, it's mostly a solid-state physics problem. One individual photon, treated quantum mechanically? From a single inelastic interaction between a free electron and a metal cation. That origin marks one end of the photon's worldline. Repeating for large numbers of photons will make you quickly bored, so you'll probably want to look into the Stefan-Boltzmann law (which still includes the constant c and Planck's constant) and the concepts in Bohr's correspondence principle and effective theory.
If you're going to talk about Feynman's equations and use the double slit experiment as an illustration instead of using Feynman diagrams (good explanation by pbs space time here https://youtu.be/fG52mXN-uWI), I'd say you're doing the concept a disservice. Extrapolating that to philosophy is usually risky, especially when doing it to a general audience.
Also, I feel we should stop trying to explain quantum physics approximately AND do philosophy based on it in short articles. It's too hard to convey that "a possible reality" may mean something else than you traditionally expect in quantum mechanics, or that it's an interpretation of what the math implies. A general public always leaves with an inaccurate impression of what was written.
Well, that seems vague, but here are some of the things about quantum physics that people find odd:
1) We intuitively think of the past as certain and the future as unwritten. You seem to be suggesting that both are written. But quantum physics says that both are unwritten. So it's exactly the opposite. Just as there are many possible futures from this point, there are also many pasts leading to this point, and that's why you get interference patterns and so forth.
So, it's not that there is one past and many futures, nor is it the case that there is one past and one future. There are many pasts and many futures, and they are all mathematically, measurably, equally real. (But not all equally probable)
2) Probabilities in quantum physics have a phase angle, which is why they can sum or they can cancel out.
If you mean why is quantum mechanics probabilistic? That's because it's the best model we have to handle many of the momentary variations in physical systems. But I'll say that determinism could still be true even if we can't make predictions. But equally, I believe that determinism can be false even if the observable universe seems well ordered. Chaos doesn't just mean random things happening without a cause that could be found. It just means that not all chains of causality can link backwards and forwards perfectly in time (i.e. some chains of causality maybe emergent at best).
It's not a predictive solution. It could very well be revealed to be true by some god type creature, but it defies the fundamentals of conducting the scientific method.
Why does it defy the fundamentals of the scientific method? I don't see what fundamentally changed just because that search is deterministic. Given all finite theories are recursively enumerable, and we clearly have enough degrees of freedom to enumerate all such theories, what's the problem exactly?
The scientific method is hypothesis testing. You must be able to make a hypothesis that is testable. What method are we using to make testable hypotheses?
Abductive reasoning, which is compatible with determinism. Even if we had to resort to blind trial and error after enumerating all possible theories, science would still work, just less efficiently. Like I said, I don't see the problem.
I think you might be joking. I assert that we cannot in fact enumerate all possible theories, even if you could write down a representation, they must be enumerated in meatspace to conduct an actual comparison.
Of course we can enumerate all possible theories, in principle. This is a trivial corollary of the fact that we can enumerate all Turing machines.
It's not practical but that's not the point. The point is that if we are free enough to enumerate all possible theories in a deterministic universe, then science can be conducted. Clearly we can enumerate all possible theories, therefore even if our universe is deterministic, we can do science.
Sorry but that sounds like the writing of someone who has never conducted an experiment in quantum physics. Obviously we aren’t just spitballing, there’s hard evidence for every equation.
This short story "Divided by Infinity" is a great exploration of similar ideas/ particularly the Quantum Immortality thought experiment. Definitely worth a read.
https://www.tor.com/2010/08/05/divided-by-infinity/
What I am not understanding is if all paths have an equal amplitude, and there are infinite paths, shouldn’t all paths cancel out? I’ve heard an example of throwing infinite stones in a pool, and the ripple that forms is what we perceive as reality. But how does our reality not have a counter-reality that cancels it out?
Calling it an "imaginary hack" is frustrating to me. Imaginary numbers are called that for derogatory reasons already, leaning in on that bias is ridiculous in the modern world.
This is approximately right, time-evolution of a spatially homogeneous system is convolution of its initial state against the propagator `K = \int e^{iS[x]} Dx` over all of space - with the caveat that none of this is quite true. These aren't really integrals, `Dx` isn't really a measure, and fully rigorous interacting QFTs in 4d may or may not exist.
i'm way too dumb to understand quantum mechanics and all its implications but i love to believe in quantum immortality and surfing all those possible realities to infinity - the most optimistic, while somewhat grounded in science, approach to thinking about life & death imho
Does that make me the mean me? Am I the most mediocre of me's? Or does this mean I'm the best me? Is everyones reality discreet to themselves? Or is this the sum of all possible observable realities by everyone?
Alternatively, just program the characters to be incapable of perceiving the gaps in the simulation. Which is totally possibly happening considering we are far from understanding the entirety of how the universe works.
Interestingly, Zeno had said the exact opposite, a hundred years earlier -- that since a 'whole' could be divided into an infinite number of smaller 'parts', which themselves could be divided ad infinitum, that these infinite parts when summed up must be far greater than the whole. Which was the basis for nearly all of his popular paradoxes.
(And then Newton and Leibnitz, some two millennia later, spoiled everybody's fun by developing the integral calculus such that whole categories of amusing philosophical conundrums became utterly mundane mathematical word problems with rigorously defined correct answers)
Sure the math works out by summing all possible paths, and then most of them usually cancel each other out, and so you're left with the ones that mostly contribute to the actual probabilities, as complicated as those can still be.
But I always suspected... surely that just has to be one mathematical way of looking at it. That at some point we'd discover that turns out to be mathematically identical to something else that would be a bit more local, a bit more intuitive, a bit more straightforward. That never even had to deal in the first place with the infinity of paths that all wind up cancelling each other out anyways.
So now that I'm on a forum with smart people, the kind I didn't have access to back in high school... has there been any progress towards something like this at all? Are there any directions for this? Or is there a conceptual reason I'm missing why this fundamentally isn't possible, why the sum of all possible paths is the only way to account for certain behaviors?