Thanks for the kind words Curt! Great explanation of what the path integral approach is, and importantly, isn’t. It isn’t a truth we must accept about the world, it’s just a (useful) tool. Very excited to read more from you!
Thank you Curt, this is a great rundown. But with regard to time evolution specifically, it should be noted that we can in fact treat imaginary time evolution as "physically real" in a PT-symmetric framework. Specifically, T∗ restricted to domains where PT-symmetry is preserved admits the action:
T∗ψE(x) = −iħ(d/dE)ψE(x)
where ψE(x) are energy eigenfunctions. The deficiency indices may be calculated by solving:
T∗ϕ±(x) = ±iϕ±(x)
In PT-symmetric quantum theories with appropriate boundary conditions, these equations yield n+ = n-, typically with n± = 1 for systems with one-dimensional energy spectra. By von Neumann's theory, when n+ = n-, there exists a one-parameter family of self-adjoint extensions Tu parametrized by a unitary map U: 𝒦+ → 𝒦-.
Therefore, even with H bounded below, T admits self-adjoint extensions in the PT-symmetric framework through appropriate boundary conditions that preserve the PT symmetry, giving us:
This is a good question! I'd just say that this applies to the PT-specific structure with its modified inner products and still doesn't automatically grant physical reality to the imaginary time parameter coming from Wick rotation used in standard, Hermitian theories. Again, fully interpreting PT-symmetric theories still leaves open the question of the operational meaning of measurements at, say, 3 seconds + 4 imaginary units. What is that exactly? Additionally, the SM is a CPT symmetry in QFT with Hermitian Hamiltonians and is distinct from these PT QM guys. These are my present deliberations and are subject to change! Thank you Alex.
Thank you very much for this detailed and thorough response! You raise several important points. I will try to go through them in order:
(1) PT-specific structure: this is true; however, for reasons elaborated on elsewhere (happy to share!), we treat PT symmetry the wider category, containing CPT-symmetry as a special case. Hence, our PT-symmetric theory recovers more or less the same empirical predictions as the Standard Model, give or take some tunable parameters (especially on the SM's end—as a general matter, methodologically, we avoid curve-fitting and instead put geometry and topology first).
(2) Modified inner products: essential to the formalism, but effectively a variation on a Frobenius inner product, which is to say, totally standard mathematics. In general I am trying to spare anyone having to go through proofs of sesquilinearity etc., but these are available upon request.
(3) To me the question is most fundamentally: what do we mean by "time"? I was listening to your recent episodes with Julian Barbour and struck by the many structural affinities between our approaches, especially regarding the "snapshot" momentariness (kṣaṇikatva), a crucially important technical term which is absolutely essential to Buddhist philosophy as such and explored at length in my forthcoming book.
But anyway, structurally speaking, in terms of the underlying theory or physical picture we're proposing, the idea is that just like how an electron "just is" the minimal representation of the first cohomology group U(1), Wick rotation "just is" how temporal evolution works. Fundamentally, there is no difference between t as physical proper time, and t as some real-valued holomorphic parameterization of the complex plane—Minkowski spacetime is a useful heuristic, especially when dealing with large regions, but Wick rotation is the better way to think about what is actually ("physically") happening.
(4) "3 seconds + 4 imaginary units": this is a truly great point that bears much more analysis than I can devote to it here. But in brief, the imaginary time parameter can be understood as encoding information about the phase structure and coherence properties of the system, rather than directly corresponding to a physically measurable time interval (which is important in terms of the underlying ontology, because we deny that there is any such thing as "temporal duration" outside of some highly restricted and narrowly circumscribed sense restricted to the Planck scale).
It might be helpful to consider a comparison to the role played by imaginary phase in the Schrödinger wave function, which also encodes the interference and superposition properties of quantum states, without itself being directly physically measurable.
Thank you again for having taken the time to respond with such thoughtful questions! I look forward to discussing further in the future.
I'll have to go watch the Veritasium video again, but I didn't notice literal ontological pronouncement, even if it made the point many times that there is no actual evidence that such actions are NOT happeneing. As I say I have to watch it again with your objections in mind. ... and I'm usually very tuned into ontology sneaking into QM videos. My question for you, Curt, is, do you ascribe to an ontology which applies to QM? I think I did make it through all of your two Jacob Barandes interviews, and completely loved his "car salesman" faceoff against Scott Aaronson, where Scott wasn't buying it, and clearly isn't in the market for an ontology that doesn't actually offer some way of going beyond the Dirac-Von Neuman postulates for the sake of just adding another "could be" plausible materialist model.
I'll add as an ontologically-related tanget that I watched with great interest your whole consciousness iceberg, and was disappointed that while you showed pictures of Husserl in the slideshow, you only referred to Heidegger in the transcript. I feel this is showing your ontological hand, and in this way it is a little heavy handed. Husserl rigorously hangs on the knife-edge of the "Epoché", the phenomenological reduction, which aspires to make no judgement about the nature of the world impinging on the senses. Ontology is the essence of what is being bracketed by the reduction, and that is the linchpin of phenomenology. If you require ontology to BE the essence of consciousness (as Heidegger does) then you can never get past that, and it will color forever the nature of consciousness as experienced. Husserl insists that one must even put aside ontology and know consciousness in its naked essence FIRST in order to map the structure of consciousness, before presumptions, and even before the categories of Being. This is why Jacob's objections to QBism are missing the point. QBIsm is aspiring like Husserl to actually try to understand "What Quantum Mechanics is trying to say" (David Mermin has some great pre-QBism papers on this point) before turning up the noise of our own social chatter.
While I appreciate the efforts done by people like David Bohm and Jacob Barandes to try to describe what "happens" between measurements (the Many Worlds nonsense is a different matter), I think that Bohr's and Heisenberg's position (that we can't really say anything meaningful about what "goes on" between measurements) was closer to the truth.
Of course, for a materialistic mindset this doesn't feel satisfactory. But materialism is probably wrong anyway.
The only problem with the Copenhagen interpretation is that it doesn't give a clear definition of what constitutes a measurement. The answer to this problem, in my view, is quite simple. But it requires stepping out of physics into the realm of biology: all measurements imply sensations experienced by living organisms. If I'm correct, life is more fundamental than matter.
Really good article, but it raises some philosophical questions for me. How do you determine which mathematical description is the correct one with respect to ontology? For example, why should I weight my belief towards the description using wave optics rather than using the path integral? Is it an Occam's Razor argument and we choose the simplest explanation? Or is it predicated on the fact that the wave optics description just requires wave mechanics and R^3 both of which are things we observe daily, while the path integral description seems to suggest things really counter to our every day experience? I don't have very much experience with either of these descriptions, so if I'm missing something I hope someone points it out to me. It seems like we descend into the realist vs. anti-realist debate quickly.
There’s value in challenging overused language in physics—especially when popular interpretations oversimplify complex mathematical tools. The phrase “particles take all possible paths” is certainly one of those cases, and it’s true that path integrals are computational in nature, not literal diagrams of physical reality.
But in correcting that surface-level confusion, some deeper misunderstandings are quietly reinforced—just as a much larger shift in theoretical physics is beginning to emerge.
-- Wave-based systems do evolve in physical space
Yes, in standard quantum mechanics, multi-particle wavefunctions live in configuration space. But that doesn’t mean this is a universal requirement. There are rigorous physical models where field evolution happens in ordinary 3D space and time, and the resulting structures can replicate everything we interpret as “quantum behavior”—including interference, nonlocality, and measurement dynamics.
These models don’t rely on path summation metaphors or imaginary-time regularizations. They’re built on deterministic or semi-deterministic wave evolution—meaning interference patterns aren’t symbolic, but real physical structures in space.
-- The double-slit isn’t just optics—it’s ontological
It’s fine to say that classical wave optics can explain the double-slit experiment. But that’s a bit like saying Newtonian mechanics can explain orbits—it’s true, but it leaves out what’s changing underneath.
In some emerging formulations, what travels through the slits isn’t a particle making a decision or a wave sampling every path—it’s a localized, coherent wavefront, stabilized by nonlinear field interactions. These wavefronts don’t “collapse.” They interfere, reconfigure, and localize again—depending on the environment and boundary conditions.
This is not just semantics. It’s a different ontological picture—one rooted in real field behavior, not probabilistic bookkeeping.
-- Cundamental physics is not where it was 10 years ago
There is a quiet but profound shift happening across theoretical physics. The idea that the core behavior of matter and interaction can be described through nonlinear field dynamics, rather than discrete probabilistic events, is gaining ground—quietly, but with increasing mathematical rigor and experimental relevance.
These formulations don’t deny quantum theory—they complete it by embedding it in something deeper: continuous field evolution, coherence-based behavior, and phase-structured causality.
The path integral works. But it’s not the foundation. It’s a shadow of something coming into view now—and the shift from symbolic to structural understanding is already underway.
Physics is about to change. Not because new metaphors are needed—but because new structure is being revealed.
Please take this seriously. I can show how the illusion is projected. However, the revelation also shows how it's projected TROUGH physics.
The entire mathematical/scientific endeavor has been IN ERROR.
And I can prove it to anyone who is capable of letting go of every single thing they believe about mathematics and physics. It's all wrong people, and that's why humanity is so fucked!
When the vacuum in the spaces of structurality is understood as a coherence of standing waves, as an updating physical network of zero geodesic fibers that exist even though no energy is transmitted along them, we get a total environment in which both the structures as closed zero geodesics and the vacuum as open zero geodesics organize themselves and update each other, in good correlation. We get the QED path formalism of Bohm's piloting idea.
When an energy quantum is then fed into the environment, there is already an updated zero geodesic situation waiting there and an output fiber, open or closed, into which the quantum is absorbed and realizes a solution that has already been interfered with or that is still being updated with delays.
There is really no superposition and Bell's inequalities become unnecessary. Quantum mechanics takes place in the field of memories, not in structures, without intersecting with GR. The field also preserves opposites, momentum, and quantum states - in good rhythm.
As a Mathematics student currently taking a Quantum Mechanics course, stumbling upon your video on this topic could not have come at a better time! I'm finally seeing someone address mystifying claims in Physics as presented in popular science, much like I've come to understand how Mathematics is being mystified online.
I know very little about Physics, and I struggle to find a good place to read about it. Most content on Physics I've interacted with assumes little understanding of Math and so proceeds to discuss certain topics quite vaguely. Would you be so kind as to refer me to a good book/resource on Quantum Mechanics, or maybe even Physics in general, where I could as a Math student better understand the current situation of Physics, perhaps better explain certain axioms and assumptions made in theories, and also something which doesn't make controversial claims that need debunking the way they do in your video?
I'm sorry if this is something you're asked about a lot and if you have an easily accesible answer I haven't yet seen somewhere! Also thank you for your video, I'll be sure to check out more of your content in the future!
I remember that "electron going through both slits" isn't based on any math or quantum theory. It is based on experiment: if you fire one electron at a time through screen with two slits, they will form interference pattern. If you close one slit, they won't. So there are two possible way to explain this: either electron final trajectory point at a screen knows about other electrons that were launched in other times, or it knows about second slit being open or closed. Moreover, any detector placed at slits will break interference pattern.
2. Quantum Mechanics is done in a configuration or hilbert space which does not necessarily need to mean physical space.
3. We cannot talk about the ontology of a thing based on it's math.
I agree problem 1 is a problem, but it doesn't mean the formulation is wrong, it just means possible needs some more thought.
For problem 2 we could just it takes paths in whatever hilbert space it is in. Of course it becomes less intuitive, but this doesn't make it false. Also, couldn't you say light in a way already explores all possible paths? In the sense of paths contained by the laws of light? This is literally how we determine the amplitudes of the waves on a detector in optics.
For problem 3, I think especially with the advent of representation theory, there may be a way of making these representations equivalent. There is clearly instances (most instances) where matrix mechanics is more expediant, but they could be connected still in ways I don't feel like trying to sustain our in a comment.
Also I think your approach is a bit self-contradictory. You say the math doesn't show ontology, but then say that things like the Heisenberg uncertainty principle are explained by the math. It's a bit inconsistent on mathematical realism. What if I find a representation of quantum mechanics where the Heisenberg uncertainty principle is explained by the mass of an electron or something. You would say the math doesn't show ontology there.
Curt, the reason for “distances below Planck length are meaningless” is given here: https://www.motionmountain.net/minimumlength.html The statement is a strict consequence of the maximum speed c, the maximum force c^4/4G, and the smallest action value h-bar. Combining the three yields that all lengths are larger than twice the Planck length. A smaller length value would disagree with all of physics. So, the correct statement is "distances below Planck length do not exist".
As you see, I disagree with you, but I would like to read your point of view in more detail. Where can one do so?
As a trained physicists some... years ago, I notice with videos like yours that there has been so much misinterpretations of the quantum world fed into my mind. I also suppose that professors did not even ha a clue what was happening 'for real' so to say (and still we have no idea). Anyway, physics I understand is about building the best model of perceivable/measurable phenomena and making predictions, and NOT about what is really going on (ontology). Are we back to the Copenhagen interpretation, full stop?
"then it’s likely they’ve just inherited it from hearing other people say it."
I think this above actually applies to everything we know and say... So far, I read as far as the above quote (I will read it through today, I promise). Yet, I find myself disagreeing with lots and lots already. I will share some of my non-physicist's (and math dumb) bewilderment afterwards. Best Regards, Julio.
Thanks for the kind words Curt! Great explanation of what the path integral approach is, and importantly, isn’t. It isn’t a truth we must accept about the world, it’s just a (useful) tool. Very excited to read more from you!
"To make these path integrals mathematically well-defined and convergent, you often have to do tricks. These tricks aren’t for kids."
Pure gold.
Thank you Curt, this is a great rundown. But with regard to time evolution specifically, it should be noted that we can in fact treat imaginary time evolution as "physically real" in a PT-symmetric framework. Specifically, T∗ restricted to domains where PT-symmetry is preserved admits the action:
T∗ψE(x) = −iħ(d/dE)ψE(x)
where ψE(x) are energy eigenfunctions. The deficiency indices may be calculated by solving:
T∗ϕ±(x) = ±iϕ±(x)
In PT-symmetric quantum theories with appropriate boundary conditions, these equations yield n+ = n-, typically with n± = 1 for systems with one-dimensional energy spectra. By von Neumann's theory, when n+ = n-, there exists a one-parameter family of self-adjoint extensions Tu parametrized by a unitary map U: 𝒦+ → 𝒦-.
Therefore, even with H bounded below, T admits self-adjoint extensions in the PT-symmetric framework through appropriate boundary conditions that preserve the PT symmetry, giving us:
[T,H] = iħ·I
This is a good question! I'd just say that this applies to the PT-specific structure with its modified inner products and still doesn't automatically grant physical reality to the imaginary time parameter coming from Wick rotation used in standard, Hermitian theories. Again, fully interpreting PT-symmetric theories still leaves open the question of the operational meaning of measurements at, say, 3 seconds + 4 imaginary units. What is that exactly? Additionally, the SM is a CPT symmetry in QFT with Hermitian Hamiltonians and is distinct from these PT QM guys. These are my present deliberations and are subject to change! Thank you Alex.
Thank you very much for this detailed and thorough response! You raise several important points. I will try to go through them in order:
(1) PT-specific structure: this is true; however, for reasons elaborated on elsewhere (happy to share!), we treat PT symmetry the wider category, containing CPT-symmetry as a special case. Hence, our PT-symmetric theory recovers more or less the same empirical predictions as the Standard Model, give or take some tunable parameters (especially on the SM's end—as a general matter, methodologically, we avoid curve-fitting and instead put geometry and topology first).
(2) Modified inner products: essential to the formalism, but effectively a variation on a Frobenius inner product, which is to say, totally standard mathematics. In general I am trying to spare anyone having to go through proofs of sesquilinearity etc., but these are available upon request.
(3) To me the question is most fundamentally: what do we mean by "time"? I was listening to your recent episodes with Julian Barbour and struck by the many structural affinities between our approaches, especially regarding the "snapshot" momentariness (kṣaṇikatva), a crucially important technical term which is absolutely essential to Buddhist philosophy as such and explored at length in my forthcoming book.
But anyway, structurally speaking, in terms of the underlying theory or physical picture we're proposing, the idea is that just like how an electron "just is" the minimal representation of the first cohomology group U(1), Wick rotation "just is" how temporal evolution works. Fundamentally, there is no difference between t as physical proper time, and t as some real-valued holomorphic parameterization of the complex plane—Minkowski spacetime is a useful heuristic, especially when dealing with large regions, but Wick rotation is the better way to think about what is actually ("physically") happening.
(4) "3 seconds + 4 imaginary units": this is a truly great point that bears much more analysis than I can devote to it here. But in brief, the imaginary time parameter can be understood as encoding information about the phase structure and coherence properties of the system, rather than directly corresponding to a physically measurable time interval (which is important in terms of the underlying ontology, because we deny that there is any such thing as "temporal duration" outside of some highly restricted and narrowly circumscribed sense restricted to the Planck scale).
It might be helpful to consider a comparison to the role played by imaginary phase in the Schrödinger wave function, which also encodes the interference and superposition properties of quantum states, without itself being directly physically measurable.
Thank you again for having taken the time to respond with such thoughtful questions! I look forward to discussing further in the future.
I'll have to go watch the Veritasium video again, but I didn't notice literal ontological pronouncement, even if it made the point many times that there is no actual evidence that such actions are NOT happeneing. As I say I have to watch it again with your objections in mind. ... and I'm usually very tuned into ontology sneaking into QM videos. My question for you, Curt, is, do you ascribe to an ontology which applies to QM? I think I did make it through all of your two Jacob Barandes interviews, and completely loved his "car salesman" faceoff against Scott Aaronson, where Scott wasn't buying it, and clearly isn't in the market for an ontology that doesn't actually offer some way of going beyond the Dirac-Von Neuman postulates for the sake of just adding another "could be" plausible materialist model.
I'll add as an ontologically-related tanget that I watched with great interest your whole consciousness iceberg, and was disappointed that while you showed pictures of Husserl in the slideshow, you only referred to Heidegger in the transcript. I feel this is showing your ontological hand, and in this way it is a little heavy handed. Husserl rigorously hangs on the knife-edge of the "Epoché", the phenomenological reduction, which aspires to make no judgement about the nature of the world impinging on the senses. Ontology is the essence of what is being bracketed by the reduction, and that is the linchpin of phenomenology. If you require ontology to BE the essence of consciousness (as Heidegger does) then you can never get past that, and it will color forever the nature of consciousness as experienced. Husserl insists that one must even put aside ontology and know consciousness in its naked essence FIRST in order to map the structure of consciousness, before presumptions, and even before the categories of Being. This is why Jacob's objections to QBism are missing the point. QBIsm is aspiring like Husserl to actually try to understand "What Quantum Mechanics is trying to say" (David Mermin has some great pre-QBism papers on this point) before turning up the noise of our own social chatter.
While I appreciate the efforts done by people like David Bohm and Jacob Barandes to try to describe what "happens" between measurements (the Many Worlds nonsense is a different matter), I think that Bohr's and Heisenberg's position (that we can't really say anything meaningful about what "goes on" between measurements) was closer to the truth.
Of course, for a materialistic mindset this doesn't feel satisfactory. But materialism is probably wrong anyway.
The only problem with the Copenhagen interpretation is that it doesn't give a clear definition of what constitutes a measurement. The answer to this problem, in my view, is quite simple. But it requires stepping out of physics into the realm of biology: all measurements imply sensations experienced by living organisms. If I'm correct, life is more fundamental than matter.
Really good article, but it raises some philosophical questions for me. How do you determine which mathematical description is the correct one with respect to ontology? For example, why should I weight my belief towards the description using wave optics rather than using the path integral? Is it an Occam's Razor argument and we choose the simplest explanation? Or is it predicated on the fact that the wave optics description just requires wave mechanics and R^3 both of which are things we observe daily, while the path integral description seems to suggest things really counter to our every day experience? I don't have very much experience with either of these descriptions, so if I'm missing something I hope someone points it out to me. It seems like we descend into the realist vs. anti-realist debate quickly.
There’s value in challenging overused language in physics—especially when popular interpretations oversimplify complex mathematical tools. The phrase “particles take all possible paths” is certainly one of those cases, and it’s true that path integrals are computational in nature, not literal diagrams of physical reality.
But in correcting that surface-level confusion, some deeper misunderstandings are quietly reinforced—just as a much larger shift in theoretical physics is beginning to emerge.
-- Wave-based systems do evolve in physical space
Yes, in standard quantum mechanics, multi-particle wavefunctions live in configuration space. But that doesn’t mean this is a universal requirement. There are rigorous physical models where field evolution happens in ordinary 3D space and time, and the resulting structures can replicate everything we interpret as “quantum behavior”—including interference, nonlocality, and measurement dynamics.
These models don’t rely on path summation metaphors or imaginary-time regularizations. They’re built on deterministic or semi-deterministic wave evolution—meaning interference patterns aren’t symbolic, but real physical structures in space.
-- The double-slit isn’t just optics—it’s ontological
It’s fine to say that classical wave optics can explain the double-slit experiment. But that’s a bit like saying Newtonian mechanics can explain orbits—it’s true, but it leaves out what’s changing underneath.
In some emerging formulations, what travels through the slits isn’t a particle making a decision or a wave sampling every path—it’s a localized, coherent wavefront, stabilized by nonlinear field interactions. These wavefronts don’t “collapse.” They interfere, reconfigure, and localize again—depending on the environment and boundary conditions.
This is not just semantics. It’s a different ontological picture—one rooted in real field behavior, not probabilistic bookkeeping.
-- Cundamental physics is not where it was 10 years ago
There is a quiet but profound shift happening across theoretical physics. The idea that the core behavior of matter and interaction can be described through nonlinear field dynamics, rather than discrete probabilistic events, is gaining ground—quietly, but with increasing mathematical rigor and experimental relevance.
These formulations don’t deny quantum theory—they complete it by embedding it in something deeper: continuous field evolution, coherence-based behavior, and phase-structured causality.
The path integral works. But it’s not the foundation. It’s a shadow of something coming into view now—and the shift from symbolic to structural understanding is already underway.
Physics is about to change. Not because new metaphors are needed—but because new structure is being revealed.
And it’s happening right on schedule.
Please take this seriously. I can show how the illusion is projected. However, the revelation also shows how it's projected TROUGH physics.
The entire mathematical/scientific endeavor has been IN ERROR.
And I can prove it to anyone who is capable of letting go of every single thing they believe about mathematics and physics. It's all wrong people, and that's why humanity is so fucked!
When the vacuum in the spaces of structurality is understood as a coherence of standing waves, as an updating physical network of zero geodesic fibers that exist even though no energy is transmitted along them, we get a total environment in which both the structures as closed zero geodesics and the vacuum as open zero geodesics organize themselves and update each other, in good correlation. We get the QED path formalism of Bohm's piloting idea.
When an energy quantum is then fed into the environment, there is already an updated zero geodesic situation waiting there and an output fiber, open or closed, into which the quantum is absorbed and realizes a solution that has already been interfered with or that is still being updated with delays.
There is really no superposition and Bell's inequalities become unnecessary. Quantum mechanics takes place in the field of memories, not in structures, without intersecting with GR. The field also preserves opposites, momentum, and quantum states - in good rhythm.
Sorry translation-gibberish; zero-geodesics = null geodesics.
As a Mathematics student currently taking a Quantum Mechanics course, stumbling upon your video on this topic could not have come at a better time! I'm finally seeing someone address mystifying claims in Physics as presented in popular science, much like I've come to understand how Mathematics is being mystified online.
I know very little about Physics, and I struggle to find a good place to read about it. Most content on Physics I've interacted with assumes little understanding of Math and so proceeds to discuss certain topics quite vaguely. Would you be so kind as to refer me to a good book/resource on Quantum Mechanics, or maybe even Physics in general, where I could as a Math student better understand the current situation of Physics, perhaps better explain certain axioms and assumptions made in theories, and also something which doesn't make controversial claims that need debunking the way they do in your video?
I'm sorry if this is something you're asked about a lot and if you have an easily accesible answer I haven't yet seen somewhere! Also thank you for your video, I'll be sure to check out more of your content in the future!
I remember that "electron going through both slits" isn't based on any math or quantum theory. It is based on experiment: if you fire one electron at a time through screen with two slits, they will form interference pattern. If you close one slit, they won't. So there are two possible way to explain this: either electron final trajectory point at a screen knows about other electrons that were launched in other times, or it knows about second slit being open or closed. Moreover, any detector placed at slits will break interference pattern.
So it sounds like you have three problems
1. What do we mean by possible?
2. Quantum Mechanics is done in a configuration or hilbert space which does not necessarily need to mean physical space.
3. We cannot talk about the ontology of a thing based on it's math.
I agree problem 1 is a problem, but it doesn't mean the formulation is wrong, it just means possible needs some more thought.
For problem 2 we could just it takes paths in whatever hilbert space it is in. Of course it becomes less intuitive, but this doesn't make it false. Also, couldn't you say light in a way already explores all possible paths? In the sense of paths contained by the laws of light? This is literally how we determine the amplitudes of the waves on a detector in optics.
For problem 3, I think especially with the advent of representation theory, there may be a way of making these representations equivalent. There is clearly instances (most instances) where matrix mechanics is more expediant, but they could be connected still in ways I don't feel like trying to sustain our in a comment.
Also I think your approach is a bit self-contradictory. You say the math doesn't show ontology, but then say that things like the Heisenberg uncertainty principle are explained by the math. It's a bit inconsistent on mathematical realism. What if I find a representation of quantum mechanics where the Heisenberg uncertainty principle is explained by the mass of an electron or something. You would say the math doesn't show ontology there.
Curt, the reason for “distances below Planck length are meaningless” is given here: https://www.motionmountain.net/minimumlength.html The statement is a strict consequence of the maximum speed c, the maximum force c^4/4G, and the smallest action value h-bar. Combining the three yields that all lengths are larger than twice the Planck length. A smaller length value would disagree with all of physics. So, the correct statement is "distances below Planck length do not exist".
As you see, I disagree with you, but I would like to read your point of view in more detail. Where can one do so?
As a trained physicists some... years ago, I notice with videos like yours that there has been so much misinterpretations of the quantum world fed into my mind. I also suppose that professors did not even ha a clue what was happening 'for real' so to say (and still we have no idea). Anyway, physics I understand is about building the best model of perceivable/measurable phenomena and making predictions, and NOT about what is really going on (ontology). Are we back to the Copenhagen interpretation, full stop?
I am presuming that all possible paths is the same basic concept as superposition?
"then it’s likely they’ve just inherited it from hearing other people say it."
I think this above actually applies to everything we know and say... So far, I read as far as the above quote (I will read it through today, I promise). Yet, I find myself disagreeing with lots and lots already. I will share some of my non-physicist's (and math dumb) bewilderment afterwards. Best Regards, Julio.