(He kept insisting so much that he “didn’t believe God played dice with the universe”, that at some point Bohr lost patience and told him to: “Please stop telling God what to do”.) Bro, this is bombshell! INSANITY! LOL 😎
I’m delighted to see high-caliber mathematicians and theoretical physicists getting interested in the theory behind deep learning.
One theoretical puzzle is why the type of non-convex optimization that needs to be done when training deep neural nets seems to work reliably. A naive intuition would suggest that optimizing a non-convex function is difficult because we can get trapped in local minima and get slowed down by plateaus and saddle points. While plateaus and saddle points can be a problem, local minima never seem to cause problems. Our intuition is wrong, because we picture an energy landscape in low dimension (e.g. 2 or 3). But the objective function of deep neural nets is often in 100 million dimensions or more. It’s hard to build a box in 100 million dimensions. That’s a lot of walls. There is a number of theoretical work from my NYU lab (look for Anna Choromanska as first author) and in Yoshua Bengio’s lab in this direction. This uses mathematical tools from random matrix theory and statistical mechanics.
Another interesting theoretical question is why multiple layers help. All boolean functions of a finite number of bits can be implemented with 2 layers (using the conjunctive of disjunctive normal form of the function). But the vast majority of boolean functions require an exponential number of minterms in the formulas (ie.e. an exponential number of hidden units in a 2-layer neural net). As computer programmers, we all know that many functions become simple if we allow ourselves to run multiple sequential steps to compute the function (multiple layers of computation). That’s a hand-wavy argument for having multiple layers. It’s not clear how to make a more formal argument in the context of neural net-like architectures.
Vlatko Vedral is right to reject the pedagogical mythology of Copenhagen. Interference disappears not because of observers, knowledge, or “looking,” but because which-path information becomes physically encoded in correlations. Entanglement, not complementarity-as-metaphor, does the real work here. On this point, the essay is both correct and necessary.
Where the argument overreaches is in presenting this clarification as a closure. Entanglement explains how local coherence is lost under interaction. It does not explain why particular decompositions into subsystems become physically or epistemically privileged, why some correlations function as records, or why classical appearances stabilize at all. These questions do not reintroduce observers or collapse; they arise precisely after those notions have been removed.
Vedral’s claim that quantum mechanics is “as objective as Newtonian physics” is therefore true only in a restricted dynamical sense. Quantum dynamics is objective, but quantum theory does not itself specify the conditions under which objectivity emerges as a shared, stable structure. Entanglement is necessary for decoherence, but not sufficient for appearance.
In short, replacing complementarity with entanglement is progress. Treating entanglement as the end of the foundational story is not. The problem has not vanished; it has shifted—from dynamics to the epistemic conditions under which dynamics become reality for anyone.
Your articles are as clear as ever, Vlatko… and still confined to what I call the “upward look.” You put yourself in the place of quantum micromechanisms and therefore have no need for an observer. But there are two radically different stances within this “non-need.” The first is that the observer exists but is not necessary for quantum mechanics. The second stance is that the observer does not exist, that they are an illusion. I have the distinct impression, though you may well contradict me, that you subscribe to the second stance. That is to say, you yourself, as an observer, do not exist. You would be a mere quantum assembly.
If we do indeed adopt the first stance, then the fact that the observer exists still pushes a large number of physicists toward the Copenhagen interpretation, which is undoubtedly not the correct one but certainly facilitates the path toward this possibility. With the second stance, you carefully avoid ever mentioning this possibility, because no path is defined. Why would the observer be unaware of the fundamental multiplicity of the quantum universe if they were merely an emanation of it?
Ultimately, these magnificent demonstrations are rather inconvenient… given your absence from them.
The entanglement is between the detecting device and the consciousness of the physicist.
The device is not detecting pre-existing “particles”, it is PROJECTING THE APPEARANCE of a subatomic particle on the digital readout of a screen.
Hang with me here.
The physicist has been trained in a very specified, esoteric manner to be able to:
A. Build the “detecting” (actually projecting) device
B. Interpret the information displayed on the screen of the device
All electrons are EXACTLY alike because an “electron” is a mathematical entity, exclusively. It IS the wave function and the appearance of a particle ONLY exists WHILE the physicist interprets the information on the screen as representing what he's been programmed to see. While the thought “electron” or “particle” emerges in the consciousness of the physicist, that is the “collapse of the wave function”.
The entanglement is between the physical device and the person interpreting the information displayed on the screen of the device.
Listen closely
There's a Spiritual teaching, a thought experiment, within the Advaita Vedanta tradition that goes like this:
A farmer was working in his yard and was startled by the sight of a coiled up cobra. He leapt back and his heart was pounding in his chest. Upon a second look he recognized it as a wound up rope.
The appearance of the snake is the collapse of the wave function.
Understand this and you will be able to SEE and ACCEPT the correct interpretation I am showing.
I'm guessing you won't agree to the correct interpretation of quantum mechanics. If you did you would be intimately involved in the greatest revelation of the past 100 years.
Thank you for this wonderful clarification? of quantum physics that did not feel right - how and IF observers actually change outcomes. Your explanation sits much better..
(He kept insisting so much that he “didn’t believe God played dice with the universe”, that at some point Bohr lost patience and told him to: “Please stop telling God what to do”.) Bro, this is bombshell! INSANITY! LOL 😎
To live in interesting times (1927-2027) 🏹
https://claude.ai/public/artifacts/8c36b0aa-7cd1-4a49-af59-2fbc0306e13d
........Grace and peace to you!
I’m delighted to see high-caliber mathematicians and theoretical physicists getting interested in the theory behind deep learning.
One theoretical puzzle is why the type of non-convex optimization that needs to be done when training deep neural nets seems to work reliably. A naive intuition would suggest that optimizing a non-convex function is difficult because we can get trapped in local minima and get slowed down by plateaus and saddle points. While plateaus and saddle points can be a problem, local minima never seem to cause problems. Our intuition is wrong, because we picture an energy landscape in low dimension (e.g. 2 or 3). But the objective function of deep neural nets is often in 100 million dimensions or more. It’s hard to build a box in 100 million dimensions. That’s a lot of walls. There is a number of theoretical work from my NYU lab (look for Anna Choromanska as first author) and in Yoshua Bengio’s lab in this direction. This uses mathematical tools from random matrix theory and statistical mechanics.
Another interesting theoretical question is why multiple layers help. All boolean functions of a finite number of bits can be implemented with 2 layers (using the conjunctive of disjunctive normal form of the function). But the vast majority of boolean functions require an exponential number of minterms in the formulas (ie.e. an exponential number of hidden units in a 2-layer neural net). As computer programmers, we all know that many functions become simple if we allow ourselves to run multiple sequential steps to compute the function (multiple layers of computation). That’s a hand-wavy argument for having multiple layers. It’s not clear how to make a more formal argument in the context of neural net-like architectures.
Vlatko Vedral is right to reject the pedagogical mythology of Copenhagen. Interference disappears not because of observers, knowledge, or “looking,” but because which-path information becomes physically encoded in correlations. Entanglement, not complementarity-as-metaphor, does the real work here. On this point, the essay is both correct and necessary.
Where the argument overreaches is in presenting this clarification as a closure. Entanglement explains how local coherence is lost under interaction. It does not explain why particular decompositions into subsystems become physically or epistemically privileged, why some correlations function as records, or why classical appearances stabilize at all. These questions do not reintroduce observers or collapse; they arise precisely after those notions have been removed.
Vedral’s claim that quantum mechanics is “as objective as Newtonian physics” is therefore true only in a restricted dynamical sense. Quantum dynamics is objective, but quantum theory does not itself specify the conditions under which objectivity emerges as a shared, stable structure. Entanglement is necessary for decoherence, but not sufficient for appearance.
In short, replacing complementarity with entanglement is progress. Treating entanglement as the end of the foundational story is not. The problem has not vanished; it has shifted—from dynamics to the epistemic conditions under which dynamics become reality for anyone.
That is where the unfinished work remains.
Your articles are as clear as ever, Vlatko… and still confined to what I call the “upward look.” You put yourself in the place of quantum micromechanisms and therefore have no need for an observer. But there are two radically different stances within this “non-need.” The first is that the observer exists but is not necessary for quantum mechanics. The second stance is that the observer does not exist, that they are an illusion. I have the distinct impression, though you may well contradict me, that you subscribe to the second stance. That is to say, you yourself, as an observer, do not exist. You would be a mere quantum assembly.
If we do indeed adopt the first stance, then the fact that the observer exists still pushes a large number of physicists toward the Copenhagen interpretation, which is undoubtedly not the correct one but certainly facilitates the path toward this possibility. With the second stance, you carefully avoid ever mentioning this possibility, because no path is defined. Why would the observer be unaware of the fundamental multiplicity of the quantum universe if they were merely an emanation of it?
Ultimately, these magnificent demonstrations are rather inconvenient… given your absence from them.
The entanglement is between the detecting device and the consciousness of the physicist.
The device is not detecting pre-existing “particles”, it is PROJECTING THE APPEARANCE of a subatomic particle on the digital readout of a screen.
Hang with me here.
The physicist has been trained in a very specified, esoteric manner to be able to:
A. Build the “detecting” (actually projecting) device
B. Interpret the information displayed on the screen of the device
All electrons are EXACTLY alike because an “electron” is a mathematical entity, exclusively. It IS the wave function and the appearance of a particle ONLY exists WHILE the physicist interprets the information on the screen as representing what he's been programmed to see. While the thought “electron” or “particle” emerges in the consciousness of the physicist, that is the “collapse of the wave function”.
The entanglement is between the physical device and the person interpreting the information displayed on the screen of the device.
Listen closely
There's a Spiritual teaching, a thought experiment, within the Advaita Vedanta tradition that goes like this:
A farmer was working in his yard and was startled by the sight of a coiled up cobra. He leapt back and his heart was pounding in his chest. Upon a second look he recognized it as a wound up rope.
The appearance of the snake is the collapse of the wave function.
Understand this and you will be able to SEE and ACCEPT the correct interpretation I am showing.
I'm guessing you won't agree to the correct interpretation of quantum mechanics. If you did you would be intimately involved in the greatest revelation of the past 100 years.
https://open.substack.com/pub/roydopson/p/quantum-mechanics-correctly-interpreted?utm_source=share&utm_medium=android&shareImageVariant=overlay&r=1y5bkg
Thank you for this wonderful clarification? of quantum physics that did not feel right - how and IF observers actually change outcomes. Your explanation sits much better..