Our reality may be a sum of all possible realities

I think the current state is very much “the formulas work, don’t get too philosophical with them though”. IANAP.

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.

Pilot wave theory

Note: I don't have a good grasp of quantum physics

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.

Perhaps the most striking is experimental evidence that particles follow "surreal" trajectories: https://doi.org/10.1126/sciadv.1501466

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.

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

https://www.quantamagazine.org/physicists-discover-geometry-...

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.

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)

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?

This!

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.

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?

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.

You are never going to get the locality you're hoping for, because of Bell's theorem.

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.

Welcome to philosophy

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.

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.

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.

> 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.)

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.

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.

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.

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).

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.

>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.

This is probably the best explanation you're going to find https://www.lesswrong.com/posts/apbcLXz5zB7PXfgg2/an-intuiti...

>the sum of all possible paths is the only way to account for certain behaviors?

It isn't?

Also you put too much hope into mathematics, it only calculates, nothing more.

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.

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.

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.

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.

Most of them cancel out. Think of it like summing an infinite array of an equal number of 1 and -1 and then a 2. The sum of that array is 2.

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.

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).

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.

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.

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."

"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.

https://en.m.wikipedia.org/wiki/Many-worlds_interpretation

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.

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.

The title irks me for a different reason. An improvement would be "Reality Considered As a Sum of All Possible Realities".

This is an interpretation/model you can choose. It doesn't seem falsifiable or provable.

"The sweater I wear today may be a sum of all sweaters is my wardrobe" - yeah, it is if you choose to think of it that way.

> 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.

That's a definition of solipsism, not reality.

Yes, there are historical issues with that calculation, and field theories in general. I've become very suspicious of continuous formalisms period:

https://arxiv.org/abs/1609.01421

I think many problems in physics will be solved by moving to more discrete formalisms.

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.

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?

You think that when you turn on there are actual photon particles that traveled 48 minutes to jupiter and back?

> 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.

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.

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.

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.

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).

Indeed, then the fundamental object would be a kernel much like the cosmological polytope or amplituhedron

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.

Each year is just another round of stochastic gradient descent, optimizing for the darkest timeline.

That's what the article says.

If they're too different, they cancel out.

Sounds like the TVA - https://en.m.wikipedia.org/wiki/Time_Variance_Authority

We can’t even agree on an objective version of reality and you want someone to determine which ones are “bad.”?

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)