Computer scientists prove that heat destroys quantum entanglement(quantamagazine.org)
quantamagazine.org
Computer scientists prove that heat destroys quantum entanglement
https://www.quantamagazine.org/computer-scientists-prove-that-heat-destroys-entanglement-20240828/
144 comments
It's consistent with that interpretation (which is actually the line of reasoning which leads to the many-worlds interpretation). What it shows is that if you take the quantum description of the state of the system, above a certain temperature it turns into a state which can be described as if it were multiple overlapping systems which can be explained purely classically (i.e. no entanglement wierdness). This is what many-worlds is derived from: if you model a quantum system interacting with a big and hot system, you will find that for each outcome of 'collapse', there is a part of the resulting quantum state that corresponds to that observation, and it doesn't interact further with the opposite state. Hence the interpretation that actually the waveform never collapses, it's just the states of the measurement apparatus and the people running it seperate into two states that cease to interact (i.e. many 'parallel universes' inside the same wavefunction: they weren't made up just for fun).
So many-worlds says that the waveform doesn't collapse to a kronecker-delta, but to an average of multiple ones that 'don't interact'.
Is this conjecture, do we see this in some specific toy systems, or do we know this is how all 'collapsed' waveforms behave? In other words, to what degree is the many-worlds interpretation just an interpretation of the waveform, or is it also a conjecture about how the waveform behaves?
edit: it also sounds like the 'many worlds' are separate, but the 'real' waveform actually still has the information of all the worlds. That suggests the information in that waveform is huge. It also feels like the 'non-collapsed' things from the different worlds could still interact. How much of what I said here is wrong (I presume it is a lot)?
Is this conjecture, do we see this in some specific toy systems, or do we know this is how all 'collapsed' waveforms behave? In other words, to what degree is the many-worlds interpretation just an interpretation of the waveform, or is it also a conjecture about how the waveform behaves?
edit: it also sounds like the 'many worlds' are separate, but the 'real' waveform actually still has the information of all the worlds. That suggests the information in that waveform is huge. It also feels like the 'non-collapsed' things from the different worlds could still interact. How much of what I said here is wrong (I presume it is a lot)?
It's a bit of both: it's an extrapolation from the results of smaller systems (backed up by experiments like the delayed-choice quantum eraser, which creates an 'observer' which is in a superposition with respect to the experimenter-observer), but it's also reasonably well backed up by theoretical results that large, hot systems will tend to decohere or separate (the result in this paper is interesting because it shows that for this kind of state there's a hard shutoff where quantum effects completely disappear, instead of things just getting less and less 'blurry')
And yes, in many ways the conjectured real waveform is quite a beast. Though you could also argue that the information content is actually very low, in that it is fully specified by the boundary condition of the big bang (well, at least any quantum-like correct theory of everything, remember gravity isn't explained by QM). Thus it's any given universe that actually represents a lot of information because it's the result of many different 'decisions' as that initial state starts to become very complex as it evolves (in a similar way to which pi can be simply defined but contains infinite digits, and if it's 'normal', you can find any string of digits in there, but it'll almost certainly take more digits to specify the position of the sequence in pi than are in the sequence). There's often similar objections on the basis of energy/mass which can be addressed in a similar way.
And, as far as I understand it the interactions between 'worlds' can only really happen for things that are 'close by', in terms of how much the states have separated (that is, in order to observe quantum effects you need to have isolated the system well enough it hasn't already entangled with you. Once it has you can't undo that). I think one general challenge with conceptualizing it is that in practice the correlations in the waveform are extremely messy: the whole universe is not entangled all at once. The 'splits' suggested in the interpretation are basically creating a potentially infinite amount of universes every time any entanglement occurs, which makes it really hard to reason about (indeed, there are philosophical issues that arise if you try to imagine what you should expect to see as a subjective observer in such a universe)
And yes, in many ways the conjectured real waveform is quite a beast. Though you could also argue that the information content is actually very low, in that it is fully specified by the boundary condition of the big bang (well, at least any quantum-like correct theory of everything, remember gravity isn't explained by QM). Thus it's any given universe that actually represents a lot of information because it's the result of many different 'decisions' as that initial state starts to become very complex as it evolves (in a similar way to which pi can be simply defined but contains infinite digits, and if it's 'normal', you can find any string of digits in there, but it'll almost certainly take more digits to specify the position of the sequence in pi than are in the sequence). There's often similar objections on the basis of energy/mass which can be addressed in a similar way.
And, as far as I understand it the interactions between 'worlds' can only really happen for things that are 'close by', in terms of how much the states have separated (that is, in order to observe quantum effects you need to have isolated the system well enough it hasn't already entangled with you. Once it has you can't undo that). I think one general challenge with conceptualizing it is that in practice the correlations in the waveform are extremely messy: the whole universe is not entangled all at once. The 'splits' suggested in the interpretation are basically creating a potentially infinite amount of universes every time any entanglement occurs, which makes it really hard to reason about (indeed, there are philosophical issues that arise if you try to imagine what you should expect to see as a subjective observer in such a universe)
The article doesn't make it clear, but what heat really destroys is, specifically, a type of long-range entanglement between electrons. Heat makes entanglement with containers greater, and entanglement with nearby particles is unavoidable.
A very hot cube of metal isolated in a vacuum wouldn't have any less overall entanglement than a cold cube.
A very hot cube of metal isolated in a vacuum wouldn't have any less overall entanglement than a cold cube.
This paper talks about Gibbs states, i.e., thermal states. These are very specific states that naturally occur if the system is in thermal equilibrium.
The other thing you talk about is true. If you have a system in quantum superposition, to measure it you need to entangle it with some macroscopic system. Macroscopic systems decohere very fast. This concept is well explained in excellent John Preskill's quantum computing lecture notes [1]
Note that the system for which wavefunction collapses is not in equilibrium with the measurements equipment (otherwise it wouldn't be measured), so the claims of the paper do not apply to this case.
[1] https://web.archive.org/web/20231005202201/http://theory.cal...
The other thing you talk about is true. If you have a system in quantum superposition, to measure it you need to entangle it with some macroscopic system. Macroscopic systems decohere very fast. This concept is well explained in excellent John Preskill's quantum computing lecture notes [1]
Note that the system for which wavefunction collapses is not in equilibrium with the measurements equipment (otherwise it wouldn't be measured), so the claims of the paper do not apply to this case.
[1] https://web.archive.org/web/20231005202201/http://theory.cal...
I feel like there is also a big misconception of 'waveform collapse' and the influence of a cognitive observer 'measuring' the final result, surely wavefunction collapse happens constantly due to several particles self interacting with each other and the environment. (not what your implying btw just needed to state it) and yes quite precisely the destroy entanglement point is the Decoherence process that permanently ties (correlates) that particle with the physical world around it. The future is inherently unknown to any observer and only advancing forward reveals the truth (at least on the Macro scale lol)
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A similar result for superposition would be huge, I guess, after a century we could finally understand what qualifies as a measurement device, why we do not observe quantum effects at macroscopic scales, what actually saves or kills Schrödinger's cat.
There's a result in quantum information that demonstrating a superposition of two states is at least as hard as switching between those states.
So designing an experiment to show that a cat is in a superposition of alive and dead is at least as hard as bringing a dead cat back to life (obviously in real life it would be much harder, this is just a lower bound).
So designing an experiment to show that a cat is in a superposition of alive and dead is at least as hard as bringing a dead cat back to life (obviously in real life it would be much harder, this is just a lower bound).
Isn't the cat experiment bullshit outside of illustrating a macro version of this? Like, there's no superposition in reality or the cat is too big to be subject to quantum mechanics where these shenanigans happen or something?
The problem is to isolate the box enough. If you can heard the cat meow, then it counts as a "measurement" and the superposition disappears. If you can hear there is no heartbeat of the cat, then it counts as a "measurement" and the superposition disappears. If the cats move and the box wags, then it counts as a "measurement" and the superposition disappears...
So in practice the experiment only works with very small systems with a few atoms. Each year there are experiments with bigger systems, but they are usually frozen and very small. Perhaps one day we will be able to do the experiment with tardigrades.
So in practice the experiment only works with very small systems with a few atoms. Each year there are experiments with bigger systems, but they are usually frozen and very small. Perhaps one day we will be able to do the experiment with tardigrades.
Hearing at all implies sound waves. If there are soundwaves there is air inside the box. If there is air inside the box the system can't be in a superposition because it has long since decohered.
In other words it's not the act of "listening" that collapses the wave function but the interaction of air molecules that creates the sound in the first place, even if no one is there to listen.
A "measurement" or an "observation" doesn't actually require a human, or a living thing. It's just a physical interaction.
In other words it's not the act of "listening" that collapses the wave function but the interaction of air molecules that creates the sound in the first place, even if no one is there to listen.
A "measurement" or an "observation" doesn't actually require a human, or a living thing. It's just a physical interaction.
This does not help at all, quantum systems - even messy complex ones, boxes containing cats and air - evolve unitarily and do not destroy a superposition. The box and the air and the cat can interact all they want, you will still have a superposition of cat dead - and box and air in some state - and cat alive - and box and air in some other state. And no point are we addressing how we get rid of one half of the entangled state. And even if I see the box wiggle a bit, we only declare that me watching the box somehow was an measurement and that collapsed the wave function without answering the question why I did not simply get entangled with the box, too.
> quantum systems - even messy complex ones, boxes containing cats and air - evolve unitarily and do not destroy a superposition
This is wrong, they do collapse, you can test this using the double slit experiment. No human has to be there for the wavefunction to collapse and thus break entanglement.
If what you said was true then this wouldn't be a part of physics, physics is only about stuff we can measure not nonsense that has no meaning.
This is wrong, they do collapse, you can test this using the double slit experiment. No human has to be there for the wavefunction to collapse and thus break entanglement.
If what you said was true then this wouldn't be a part of physics, physics is only about stuff we can measure not nonsense that has no meaning.
It's not at all clear how, when, and why wave function collapse happens. The only known quantity there, decoherence, is related to interaction between a coherent quantum system and a noisy decohered environment, which causes the original system to decohere itself.
Theoretically, as far as it is known today, it is possible for a quantum system of any size, and at any temperature, to remain in a coherent state, if it could be perfectly isolated from the rest of the world.
Any limits to this process, where a perfectly isolated system would undergo wave function collapse without any outside interference, would be a Nobel-prize worthy discovery and would constitute a new theory of physics: quantum mechanics and QFT allow no such process.
Edit: and the double slit experiment is unrelated - the screen and the slit are noisy classical systems that are not in any way isolated from the rest of the classical world. In principle, if you performed the experiment using a screen and slits made entirely of atoms entangled with the emitter, and isolated perfectly from the rest of the world and the CMB and everything, you'd get a different result: this is what QM predicts.
Theoretically, as far as it is known today, it is possible for a quantum system of any size, and at any temperature, to remain in a coherent state, if it could be perfectly isolated from the rest of the world.
Any limits to this process, where a perfectly isolated system would undergo wave function collapse without any outside interference, would be a Nobel-prize worthy discovery and would constitute a new theory of physics: quantum mechanics and QFT allow no such process.
Edit: and the double slit experiment is unrelated - the screen and the slit are noisy classical systems that are not in any way isolated from the rest of the classical world. In principle, if you performed the experiment using a screen and slits made entirely of atoms entangled with the emitter, and isolated perfectly from the rest of the world and the CMB and everything, you'd get a different result: this is what QM predicts.
> quantum mechanics and QFT allow no such process
Double slit experiments shows collapse happens without any outside interference, nothing outside of the room has to do anything for the resulting measurements to show collapse happened. You can then afterwards enter the room, look at the recorded data and see that collapses did happen.
So you must have misunderstood what those theories says about collapses. They don't say exactly when collapses happens or what causes them, that is the unsolved problem, but we can know that they do happen.
Double slit experiments shows collapse happens without any outside interference, nothing outside of the room has to do anything for the resulting measurements to show collapse happened. You can then afterwards enter the room, look at the recorded data and see that collapses did happen.
So you must have misunderstood what those theories says about collapses. They don't say exactly when collapses happens or what causes them, that is the unsolved problem, but we can know that they do happen.
In the normal experiments we perform, the screen is already a classical system, collapsed / entangled with the rest of the "classical world" (depending on the interpretation). When the particles interact with the screen, of course their wave function collapses as well.
But what if instead you had a screen that was itself a quantum system? You'd then use the Schrodinger equation without any collapse (without the Born rule) to describe the results. You'd have to perform other measurements on the quantum screen to obtain a classical result that can be interpreted, of course. But nothing in QM says that there is some size limit, so in principle it should be possible to prepare a quantum system of any size, including the size of a typical double slit experiment screen, that doesn't collapse.
But what if instead you had a screen that was itself a quantum system? You'd then use the Schrodinger equation without any collapse (without the Born rule) to describe the results. You'd have to perform other measurements on the quantum screen to obtain a classical result that can be interpreted, of course. But nothing in QM says that there is some size limit, so in principle it should be possible to prepare a quantum system of any size, including the size of a typical double slit experiment screen, that doesn't collapse.
Quantum mechanics, i.e. the Schrödinger equation, and wave function collapse are incompatible. While not measured a quantum system evolves unitarily, when measured the quantum system ends up in the measured Eigenstate which is a non-unitary change. But any measurement device is also a quantum system and therefore the combined system should also evolve unitarily. And now we have a serious problem to which nobody has a generally accepted answer.
What is deficient about the original explanation that the wave function is not real but rather a scientific theory? The issue has been unresolved for about a century now, it's relatively unsatisfying but hasn't held the science back in any way.
The problem with that idea is that we don't have any other model, and little room for it. We already know from Bell's inequality and the experiments that verified it that there can't be underlying variables that we haven't detected yet (or if they exist, we have to rethink special relativity and by extension QFT). It's also quite hard to explain why the wave function is so good at predicting the results of experiments if it's not a part of the underlying reality.
There is a thing we call the universe and it does what universes do. What physics does is searching for models - mostly described in the language of mathematics - that describe the universe or parts of it. Some parts of the universe are well modelled by the Navier-Stokes equations, we also call those parts of the universe water [1]. But upon closer inspection one notices that description is not perfect, one can obtain a more accurate model if one treats the water bits of the universe as a collection of an enormous number of particles, water molecules. And we can keep going, treat molecules as collections of atom, break atoms into electrons and nucleons, split the nucleons into quarks and gluons, who knows how deep the rabbit hole goes.
Maybe we will even eventually find the ultimate model, a model that describes every aspect of the world perfectly, even though it is not obviously clear how we would determine that we did not miss some aspect of the universe in our models. But even then the map would not be the territory, the model would not be the universe or a piece of it. Imagine a wave function would perfectly describe an electron, would we be justified to say that an electron is a wave function? No, because for them to be the same thing, it is not sufficient that the wave function has all the properties of the electron, it would also have to have only the properties of the electron. But the wave function is an equation, I can write it down or square it, things I can most certainly not do with the electron.
So the wave function is of course only a mathematical description of a quantum system and not a real thing out there in the universe. But that is not the problem, the problem is that we have two seemingly contradictory descriptions of quantum systems. We have the Schrödinger equation describing the unitary evolution of isolated quantum systems and it works really well. But we also have the Born rule and the collapse postulate which tell us the probability distribution of measurement outcomes and how measurement changes the state into the measured Eigenstate, a non-unitary change, and this also works really well. But there is the problem, on the one hand a measurement - whatever that exactly is - seems to change the state non-unitarily but on the other hand a quantum system together with a measurement device is just a bigger quantum system and should therefore evolve unitarily. Something has to give.
As you say, that is very unsatisfying, but it was also not a complete roadblock, shut up and calculate worked pretty well. But I would not confidently declare that this does not hold us back at all, who knows what progress can be unlocked by solving the issue? It might of course also be mostly inconsequential but I guess that is something we will only find out after the fact.
[1] Or fluids if you want to be pedantic.
Maybe we will even eventually find the ultimate model, a model that describes every aspect of the world perfectly, even though it is not obviously clear how we would determine that we did not miss some aspect of the universe in our models. But even then the map would not be the territory, the model would not be the universe or a piece of it. Imagine a wave function would perfectly describe an electron, would we be justified to say that an electron is a wave function? No, because for them to be the same thing, it is not sufficient that the wave function has all the properties of the electron, it would also have to have only the properties of the electron. But the wave function is an equation, I can write it down or square it, things I can most certainly not do with the electron.
So the wave function is of course only a mathematical description of a quantum system and not a real thing out there in the universe. But that is not the problem, the problem is that we have two seemingly contradictory descriptions of quantum systems. We have the Schrödinger equation describing the unitary evolution of isolated quantum systems and it works really well. But we also have the Born rule and the collapse postulate which tell us the probability distribution of measurement outcomes and how measurement changes the state into the measured Eigenstate, a non-unitary change, and this also works really well. But there is the problem, on the one hand a measurement - whatever that exactly is - seems to change the state non-unitarily but on the other hand a quantum system together with a measurement device is just a bigger quantum system and should therefore evolve unitarily. Something has to give.
As you say, that is very unsatisfying, but it was also not a complete roadblock, shut up and calculate worked pretty well. But I would not confidently declare that this does not hold us back at all, who knows what progress can be unlocked by solving the issue? It might of course also be mostly inconsequential but I guess that is something we will only find out after the fact.
[1] Or fluids if you want to be pedantic.
> evolve unitarily and do not destroy a superposition
Unitary evolution can destroy superposition of the small subsystem by introducing negligible amount of superposition into large system.
Unitary evolution can destroy superposition of the small subsystem by introducing negligible amount of superposition into large system.
Not sure if that is true, but assuming it is, does this really count as destruction instead of moving it around and spreading it? After all unitary evolution is reversible and I could therefore reconcentrate the superposition into the small system. It would however seemingly be a good explanation how to get from the decayed non-decayed superposition of a few atoms to an almost alive or almost dead cat. This is however also what makes me doubt your statement, if true, why are we still puzzled about Schrödinger's cat?
Well the naming is a different question, but it is consistent with observation of what we call wavefunction collapse.
In Schroedinger cat experiment, the evolution is not thermalization but rather entangling the whole cat with atom state. I don't think we're really puzzled about it now, since we know that macroscopic objects can be in superposition. So cat, theoretically, can be in superposition of alive and dead until measured. I don't think there is any contradiction or confusion here physics-wise.
In Schroedinger cat experiment, the evolution is not thermalization but rather entangling the whole cat with atom state. I don't think we're really puzzled about it now, since we know that macroscopic objects can be in superposition. So cat, theoretically, can be in superposition of alive and dead until measured. I don't think there is any contradiction or confusion here physics-wise.
This isn't quite right, wave function collapse is relative so while within the box an observer's wave function of the box will be in a definite eigenstate, the wavefunction of the box for an observer isolated from the box will still be in a superposition of its states.
In other words, the fact that an observation takes place from within the box and collapses the wave function for an observer in the box does not mean that the wave function for every observer also collapses. A wave function collapse for one observer does not imply a wave function collapse for any other observer.
In other words, the fact that an observation takes place from within the box and collapses the wave function for an observer in the box does not mean that the wave function for every observer also collapses. A wave function collapse for one observer does not imply a wave function collapse for any other observer.
> wave function collapse is relative
No it isn't, why do you think this? If it was we wouldn't be able to see it in our experiments, as where the particle ends up would depend on which observer is looking, which would get absurd consequences.
No it isn't, why do you think this? If it was we wouldn't be able to see it in our experiments, as where the particle ends up would depend on which observer is looking, which would get absurd consequences.
This is actually an open problem in QM. We don't understand what constitutes a measurement, and so we don't know if two perfectly isolated observers could disagree on the "state" of a system in this way (as in, collapsed or not collapsed). And given special relativity, it is definitely possible that two different observers could disagree on the order that two independent measurements of the same system happened.
Do note that the result of the experiments is not going to differ, it is guaranteed to be consistent by the fact that both experiments are measuring the same quantum system. It's just that one observer is unsure of what result they will get for a subsequent experiment, while the other observer can know it exactly.
And in the many worlds interpretation, it is indeed believed that apparent wave function collapse is a relative phenomenon, caused by entanglement with the classical environment, which spreads out at the speed of light.
Do note that the result of the experiments is not going to differ, it is guaranteed to be consistent by the fact that both experiments are measuring the same quantum system. It's just that one observer is unsure of what result they will get for a subsequent experiment, while the other observer can know it exactly.
And in the many worlds interpretation, it is indeed believed that apparent wave function collapse is a relative phenomenon, caused by entanglement with the classical environment, which spreads out at the speed of light.
> We don't understand what constitutes a measurement, and so we don't know if two perfectly isolated observers could disagree on the "state" of a system in this way (as in, collapsed or not collapsed)
We do know that they can't disagree as collapsed particles behave differently than uncollapsed particles.
> It's just that one observer is unsure of what result they will get for a subsequent experiment, while the other observer can know it exactly.
Quantum systems aren't about knowledge or statistics, the wave function is an actual physical thing that changes how the particle behaves. If the wave function has collapsed it no longer behaves the same as before, so what you said here is wrong.
We do know that they can't disagree as collapsed particles behave differently than uncollapsed particles.
> It's just that one observer is unsure of what result they will get for a subsequent experiment, while the other observer can know it exactly.
Quantum systems aren't about knowledge or statistics, the wave function is an actual physical thing that changes how the particle behaves. If the wave function has collapsed it no longer behaves the same as before, so what you said here is wrong.
After a measurement, the wave function of a particle, and of any particles entangled with it, collapses. But this isn't itself a measurable difference.
For example, when performing measurements on two entangled particles at very far away places, the wave function collapses instantly, across any distance, even light years away. After that experiment, the result on the other side is 100% determined (if performed in the same basis). But there is no experiment whatsoever that could be done to tell if the collapse has happened or not from the other side.
This is the resolution of the famous EPR paradox: wave function collapse is non-local (instantaneous), but it is probably impossible to send classical information with it faster than the speed of light limit.
For example, when performing measurements on two entangled particles at very far away places, the wave function collapses instantly, across any distance, even light years away. After that experiment, the result on the other side is 100% determined (if performed in the same basis). But there is no experiment whatsoever that could be done to tell if the collapse has happened or not from the other side.
This is the resolution of the famous EPR paradox: wave function collapse is non-local (instantaneous), but it is probably impossible to send classical information with it faster than the speed of light limit.
You're now arguing against claims no one has made, which is apparent from the fact that you seem to only quite very tiny snippets of what's said while ignoring the main argument.
You seem to just want to argue for the sake of arguing.
You seem to just want to argue for the sake of arguing.
Wasn't the argument that two observers can disagree whether a collapse has happened? I offered evidence that they can't, as otherwise they would see different results in the double slit experiment.
There is nothing in the double slit experiment that makes collapse necessarily an objective reality. There is in fact no way to check if collapse of the wave function has happened or not.
I imagine you're thinking of the version of the double slit experiment with a detector installed next to one of the slits, which prevents the interference pattern from forming. However, this only applies for a "measurement device" installed at the slits. That is, a classical system interacting with the photon/electron/etc before it hits the classical screen. But this is not mysterious at all: the classical device causes decoherence of the wave function and thus prevents self-interference of the beams traveling through the two slots. That is true even in interpretations that consider that wave function collapse is not a physical phenomenon, such as Many Worlds.
But this doesn't prove much. We already know that a photon hitting an atom doesn't cause wave function collapse, while a photon hitting a detector does. We can say that an atom is not a measurement device and an observer is, but this immediately raises the question of why. Or, we can choose the MWI route and say that the wave function never collapses, and the only difference between an atom and a detector is that we are not entangled with that atom, but we are entangled with the detector. And if so, it immediately follows that if we could get a detector that we are not entangled with, we would not see the same results as we do in the traditional double slit + detector on a slit experiment.
I imagine you're thinking of the version of the double slit experiment with a detector installed next to one of the slits, which prevents the interference pattern from forming. However, this only applies for a "measurement device" installed at the slits. That is, a classical system interacting with the photon/electron/etc before it hits the classical screen. But this is not mysterious at all: the classical device causes decoherence of the wave function and thus prevents self-interference of the beams traveling through the two slots. That is true even in interpretations that consider that wave function collapse is not a physical phenomenon, such as Many Worlds.
But this doesn't prove much. We already know that a photon hitting an atom doesn't cause wave function collapse, while a photon hitting a detector does. We can say that an atom is not a measurement device and an observer is, but this immediately raises the question of why. Or, we can choose the MWI route and say that the wave function never collapses, and the only difference between an atom and a detector is that we are not entangled with that atom, but we are entangled with the detector. And if so, it immediately follows that if we could get a detector that we are not entangled with, we would not see the same results as we do in the traditional double slit + detector on a slit experiment.
I provided my explanation for why this is the case. A measurement device only collapses the wave function for itself, it does not collapse the wave function for every other observer/measurement device.
Of course, a second measurement device that's completely isolated from the first measurement device can eventually interact with the first measurement device and the two will converge and share the same wave function. However, until the second measurement device interacts with the first one or with the original quantum system being observed, then from the point of view of the second measurement device, the first measurement device is in a superposition of all the possible states that it could have observed.
This can continue on and on, with a third measurement device which is entirely isolated from the second measurement device having a wavefunction that's a superposition of all the possible observations that the second measurement device will observer...
Of course, a second measurement device that's completely isolated from the first measurement device can eventually interact with the first measurement device and the two will converge and share the same wave function. However, until the second measurement device interacts with the first one or with the original quantum system being observed, then from the point of view of the second measurement device, the first measurement device is in a superposition of all the possible states that it could have observed.
This can continue on and on, with a third measurement device which is entirely isolated from the second measurement device having a wavefunction that's a superposition of all the possible observations that the second measurement device will observer...
> A measurement device only collapses the wave function for itself, it does not collapse the wave function for every other observer/measurement device.
Wave function collapse is a real measurable phenomena, what you describe is not measurable so just a belief, don't mix in your beliefs with actual results.
Wave function collapse is a real measurable phenomena, what you describe is not measurable so just a belief, don't mix in your beliefs with actual results.
Wave function collapse is one of many equivalent (so far as we know) interpretations of quantum mechanics and not all interpretations have wave function collapse whatsoever. With that said even in the Copenhagen interpretation which is the most popular interpretation of quantum mechanics, the moment in time when the wave function collapses is relative to each measurement device. It is not the case that just because some measurement device that has been entirely isolated from me happens to perform a measurement on a quantum system, that my wave function of that quantum system will also collapse. On the contrary my wave function remains exactly as is until the moment I perform a measurement on the quantum system which collapses my wave function of said system.
One common view is that there is THE wave function of the universe. If it collapses, it collapses, there is no way it can collapse for some observers and not others. You might not know that it has collapsed but that does not make it not collapsed.
There is a different view that the wave function is just an representation of the knowledge someone has about the state of the universe or some part of it, in which case it can collapse for some and not others. On the other hand there is not really any collapse at all in this case, it is just a fancy term for updating once believe about the state of the universe or some system.
It is also important to note that a collapse is not a total collapse into a point. Measuring different things will collapse the wave function along different dimensions, only measuring everything in the universe would collapse the wave function along all dimensions into a point, or as far as the uncertainty principle permits.
There is a different view that the wave function is just an representation of the knowledge someone has about the state of the universe or some part of it, in which case it can collapse for some and not others. On the other hand there is not really any collapse at all in this case, it is just a fancy term for updating once believe about the state of the universe or some system.
It is also important to note that a collapse is not a total collapse into a point. Measuring different things will collapse the wave function along different dimensions, only measuring everything in the universe would collapse the wave function along all dimensions into a point, or as far as the uncertainty principle permits.
Imagine you have a lamp that sends a single photon, a double slit, and a screen with silver or something to catch the photon. All of that is inside a black box. You press the button to send the photon, open the box and see the screen.
There are 5 possible scenarios:
1) The wave function collapsed when the photon colides with the screen. You can calculate the time using distance/c. All the other steps are classic. You just open the box and see where the spot was.
2) When the photon colides with the screen there is no colapse. You get a superposition of two screens. A few milliseconds later when the gas inside the box hits the screen there is a collapse and ow you have a classic spot in a classic screen. Later you just open the box.
3) When the photon colides with the screen there is no colapse. You get a superposition of two screens. A few milliseconds later when the gas inside the box hit the screen, the gas gets entangled and later the walls of the box get entangled. There is no collapse until you open the box. Anyway, when you open the box everything get's classic and you see the usual result.
4) When the photon colides with the screen there is no colapse. You get a superposition of two screens. A few milliseconds later when the gas inside the box hit the screen, the gas gets entangled and later the walls of the box get entangled. There is no collapse. When you open the box your eyes and brain get entangled. There is no collapse! Anyway, each of the versions of you see the expected result because each one is entangled with a screen that has a spot as expected.
5) Shut up and calculate!
I'm a strong proponent of 5 because people pay me to calculate the distribution of the probability of the spot and not to tell weird stories.
The easy way to get the result of 5 is to use the scenario in 1, and that is what is teach, and that is essentially the Copenhagen interpretation and anyone that is not insane will use that scenario to make the calculations because it's "obvious" that all the other add negligidle corrections and are infinitely more difficult.
Here the problem is to define what is a measurement. It's "obvious" that the screen is good enough, but there is no good technical definition of what "obvious" means.
The problem is that the only non magical scenario is 4, where there is no collapse and you get entangled too. There are still many technical details to solve, but if it's real you would see the same experimental results than in 1, 2, 3 and 4, but the advantage is that there is no magic rule of collapse. In this scenario, measurement does not collapse wave functions, it just an illusion when some of the parts is big enough to get decoherence and make all the versions so different that you get (almost) no interference effect.
Anyway we are still not sure, so you can believe any of them until someone solves the problem, probably in 50 or 100 years.
There are 5 possible scenarios:
1) The wave function collapsed when the photon colides with the screen. You can calculate the time using distance/c. All the other steps are classic. You just open the box and see where the spot was.
2) When the photon colides with the screen there is no colapse. You get a superposition of two screens. A few milliseconds later when the gas inside the box hits the screen there is a collapse and ow you have a classic spot in a classic screen. Later you just open the box.
3) When the photon colides with the screen there is no colapse. You get a superposition of two screens. A few milliseconds later when the gas inside the box hit the screen, the gas gets entangled and later the walls of the box get entangled. There is no collapse until you open the box. Anyway, when you open the box everything get's classic and you see the usual result.
4) When the photon colides with the screen there is no colapse. You get a superposition of two screens. A few milliseconds later when the gas inside the box hit the screen, the gas gets entangled and later the walls of the box get entangled. There is no collapse. When you open the box your eyes and brain get entangled. There is no collapse! Anyway, each of the versions of you see the expected result because each one is entangled with a screen that has a spot as expected.
5) Shut up and calculate!
I'm a strong proponent of 5 because people pay me to calculate the distribution of the probability of the spot and not to tell weird stories.
The easy way to get the result of 5 is to use the scenario in 1, and that is what is teach, and that is essentially the Copenhagen interpretation and anyone that is not insane will use that scenario to make the calculations because it's "obvious" that all the other add negligidle corrections and are infinitely more difficult.
Here the problem is to define what is a measurement. It's "obvious" that the screen is good enough, but there is no good technical definition of what "obvious" means.
The problem is that the only non magical scenario is 4, where there is no collapse and you get entangled too. There are still many technical details to solve, but if it's real you would see the same experimental results than in 1, 2, 3 and 4, but the advantage is that there is no magic rule of collapse. In this scenario, measurement does not collapse wave functions, it just an illusion when some of the parts is big enough to get decoherence and make all the versions so different that you get (almost) no interference effect.
Anyway we are still not sure, so you can believe any of them until someone solves the problem, probably in 50 or 100 years.
Double slit experiment disproves you here, the observed pattern is the same for every observer and shows a collapse happened.
Catch 22: and if there is no air inside the box, then you are certain the cat is dead.
(somewhat related) There are two infinities operating in QM when systems get big.
https://youtu.be/FrTq_m1pLz8?t=2188
Quantum mechanics forces two infinities upon us when attempting to make precise observations. The first is the need for infinitely many measurements, stemming from the probabilistic nature of quantum predictions. To obtain a sharp notion of probability, we must perform an experiment infinitely often, converging to the true probability in the limit. The second infinity involves an infinitely large measuring apparatus. This arises because any finite measuring device is itself subject to quantum fluctuations, introducing an intrinsic imprecision to measurements. The degree of imprecision scales as e^(-n), where n is the number of particles composing the measuring device. While the first infinity is often discussed and practically relevant in experimental settings, the second is less commonly addressed but conceptually significant. These infinities highlight fundamental limitations in our ability to make precise quantum measurements and become particularly problematic when gravity is introduced into the picture.
https://youtu.be/FrTq_m1pLz8?t=2188
Quantum mechanics forces two infinities upon us when attempting to make precise observations. The first is the need for infinitely many measurements, stemming from the probabilistic nature of quantum predictions. To obtain a sharp notion of probability, we must perform an experiment infinitely often, converging to the true probability in the limit. The second infinity involves an infinitely large measuring apparatus. This arises because any finite measuring device is itself subject to quantum fluctuations, introducing an intrinsic imprecision to measurements. The degree of imprecision scales as e^(-n), where n is the number of particles composing the measuring device. While the first infinity is often discussed and practically relevant in experimental settings, the second is less commonly addressed but conceptually significant. These infinities highlight fundamental limitations in our ability to make precise quantum measurements and become particularly problematic when gravity is introduced into the picture.
This seems to predicate what does or doesnt happen on the awareness of sentient observers. What is the evidence for that and why would the cats fate depend on whether anyone (or itself) is monitoring it in any sense of that word?
The cat isn't in some quantum state. Cat is locked in a box, with some poison and a Geiger counter. Poison is released when Geiger counter registers a particle.
Now, the process of atom decay that would be registered by a Geiger counter has some interesting properties and that's where the "quantum magic" happens.
(at least, that's my mental model of it; ask an expert, I'm not an expert)
Now, the process of atom decay that would be registered by a Geiger counter has some interesting properties and that's where the "quantum magic" happens.
(at least, that's my mental model of it; ask an expert, I'm not an expert)
the idea is that everything is in some quantum state, because quantum mechanics attempts to describe everything. The thought experiment is basically going from the well-observed (and explained in theory) superposition of a nuclear undergoing decay to the never-observed (but still valid in theory) superposition of a cat being both alive and dead.
Why should it be valid in theory tho? What is the purported bottleneck in physical reality that is supposed to exist whose presence makes the Schrodinger cat thought experiment realistic? How does sentient observation get the ball rolling and why couldn't that happen in the absence of such observation at this scale?
The quantum magic properties are thought to transfer to the poison and the cat.
Schrödinger's thought experiment was supposed to demonstrate that superposition itself (and/or the whole of the Copenhagen interpretation) was a nonsense concept… but every test so far says it's real, that he was wrong, and that the cat would be in both states "until observed".
But nobody knows what "observed" even means.
But nobody knows what "observed" even means.
As far as known physics goes, nothing is too big to be subject to quantum mechanics.
It is very hard to demonstrate that fact though, the obvious way of doing it is to build a large quantum computer.
It is very hard to demonstrate that fact though, the obvious way of doing it is to build a large quantum computer.
Schrödinger never believed it; he gave that as an example of something that could never happen in real life.
Cat observes itself.
That defeats the point of the exercise. The whole point was about the state of some isolated system. Otherwise we could say that the detector observes the state of the system without even needing the poison or the car
It doesn't defeat the point of the exercise, it just shows that the exercise is nonsense. The cat is an observer therefore collapses the quantum wave function and is either alive or dead.
In what sense the cat is an observer? Having eyes and a brain doesn't really mean anything in QM.
If the particle interacts, that collapses the superposition. Cats aren't any more or less blessed as observers than physicists. If either of them can observe the outcome, then both can.
Hmm. Maybe what "counts as an observer" is relative to your reference frame, and so is the concept of "superposition". And thus, though the cat is making observations within its environment, since the environment is sealed off, the cat is not "an observer" from our reference frame because there is no interaction between us and the cat. From the cat's reference frame it is probably not in a superposition - If it is observing anything, it is alive, and if it is dead, it is not observing anything. But if we observe the cat, the wave function is collapsed from our reference frame and the cat is in one or the other state.
My understanding of quantum mechanics is pretty shallow so take this with an ocean of salt.
My understanding of quantum mechanics is pretty shallow so take this with an ocean of salt.
If the particle interacts, that collapses the superposition.
Not at all, the superposition spreads to the interacting particles. What destroys superpositions are measurements and we do not know what measurements really are.
Not at all, the superposition spreads to the interacting particles. What destroys superpositions are measurements and we do not know what measurements really are.
We do know what measurements are. "Superposition" and "collapse" are only really valid concepts in a particular reference frame. A "measurement" is an interaction in your preferred reference frame. The cat cannot "collapse" anything from your perpective - only its own. Indeed the cat itself does not experience superposition.
You can't measure something without interacting with it. So either it's the interaction that collapses it, or it's some sort of soul mumbo jumbo. If it's somehow the latter, there's no justification beyond shear anthropocentrism to suppose that physicists can do it but cats can't.
Therefore, the cat observes itself.
Therefore, the cat observes itself.
The result is the same if you replace the cat with a physicist. The relevant distinction is whether the animal in question is inside or outside the sealed box - not species.
Doesn't necessarily tell you anything about what you would observe. The cat's observations of itself would still be in superposition in theory.
> The cat's observations of itself would still be in superposition in theory.
Not anymore, not according to this theory.
Not anymore, not according to this theory.
No, the results of this paper are still 100% compatible with the interpretation that the cat is in a superposition: all it says is that the two states (cat alive and cat dead) can't interact with each other at all (or more specifically, can't interact in a way that's distinguishable from random noise).
[deleted]
We have this result already. Interaction with thermal noise ruins wave coherence, and causes classical physics to emerge. This comes when you in a sense replace waves with their average values.
It's not so much a question of scale, but of statistical noisiness. Quantum effects are primarily observable in the low-temperature domain (this is not necessarily "thermometer temperature", but a statistical measure)
It's not so much a question of scale, but of statistical noisiness. Quantum effects are primarily observable in the low-temperature domain (this is not necessarily "thermometer temperature", but a statistical measure)
I am not a physicist, but I thought that it is generally accepted that decoherence does not solve the measurement problem. It explains why quantum effects are not observable in a noisy environment but still does not explain the non-unitarity of measurements.
It does not solve the measurement problem, but it does explain why you don't see quantum phenomena such as superposition or tunneling at the classical limit.
Even lasers deal with weird temperatures: they're negative.
This doesn't answer the question. We know how classical physics emerges from a large number of quantum events through statistics. That was not the point of Schrödinger's cat though experiment! The idea is to link a macroscopic event to a random subatomic event that is in a superposition. When or how does the wave function collapse, does it even collapse?
How is thermal noise different from heat?
[edit: found another comment which you replied to, and now I see that you already knew all this. Oops.
Original comment follows]
Maybe you know the thing I’m about to say and just consider it to be too pedantic, but:
The question to ask of a system is not [whether it is “in a superposition” or “not in a superposition”], but rather, [whether it is “in a superposition of these different states” or “in a specific one of these states”].
Suppose I have a particle which I know is spin up (ignore the position aspect of things, considering only the spin). Is it “in a superposition”? One might be tempted to say “no, it is spin up.”, but the correct response is “A superposition of what? Anything? If so, then trivially yes.” . Because “spin up” can be regarded as a superposition of “spin left” and “spin right”, or as “spin northeast” and “spin southwest”. Likewise, “spin left” can be regarded as a superposition of “spin up” and “spin down”.
To usefully ask whether something is “in a superposition”, you have to specify what states you are regarding as the basis, as far as the question is concerned (or, alternatively, with respect to what observables, where “in a superposition with respect to those observables” would mean that if those observables were measured, the result would be random* ).
Now, why don’t we observe superpositions of states of macroscopic things which differ according to ordinary observables such as “x coordinate of center of mass”? In don’t know. That may be something still not understood. I don’t really understand these attempts, but I think there are things called “pointer states” and a process known as “einselection” which are supposed to help explain that? (Though it has been argued that this explanation involving einselection may be somewhat circular?)
Maybe you know the thing I’m about to say and just consider it to be too pedantic, but:
The question to ask of a system is not [whether it is “in a superposition” or “not in a superposition”], but rather, [whether it is “in a superposition of these different states” or “in a specific one of these states”].
Suppose I have a particle which I know is spin up (ignore the position aspect of things, considering only the spin). Is it “in a superposition”? One might be tempted to say “no, it is spin up.”, but the correct response is “A superposition of what? Anything? If so, then trivially yes.” . Because “spin up” can be regarded as a superposition of “spin left” and “spin right”, or as “spin northeast” and “spin southwest”. Likewise, “spin left” can be regarded as a superposition of “spin up” and “spin down”.
To usefully ask whether something is “in a superposition”, you have to specify what states you are regarding as the basis, as far as the question is concerned (or, alternatively, with respect to what observables, where “in a superposition with respect to those observables” would mean that if those observables were measured, the result would be random* ).
Now, why don’t we observe superpositions of states of macroscopic things which differ according to ordinary observables such as “x coordinate of center of mass”? In don’t know. That may be something still not understood. I don’t really understand these attempts, but I think there are things called “pointer states” and a process known as “einselection” which are supposed to help explain that? (Though it has been argued that this explanation involving einselection may be somewhat circular?)
> what qualifies as a measurement device
Anything, really. There are no "classical devices", after all, all of them are quantum systems, aren't they?
Anything, really. There are no "classical devices", after all, all of them are quantum systems, aren't they?
Quantum systems evolve unitarily, measurement devices collapse the wave function which is not unitary. And there is no accepted consensus how those two things fit together, just several ideas like Everett's many worlds which solves the problem by declaring that the wave function never actually collapses but instead splits the cosmos into many worlds.
Everett's idea was merely that the measurement device gets entangled with the thing being measured, so we now the wave-function of the (combined) device-thing system is the superposition of states <thing is in pure state Ai| ⊗ <device is in "measured Ai" state|; but for the measurement device it of course "looks" like it measured a pure state. That's it. That's basically what the decoherence suggests anyway. The "cosmos splitting" was proposed by Bryce DeWitt which IMHO turned a perfectly straight-forward and reasonable interpretation into a needlessly philosophical statement.
The measurement device gets entangled with the spin - which is in a superposition - and then I get entangled with the measurement device and for got measure the entire environment. How does this avoid the many worlds? If the measurement device only sees half of the entangled spin state and I only see half of the entangled measurement device - say I see the spin measured up because the measurement device saw the spin up - how does this avoid the necessity of a second world where the spin was down? What breaks the symmetry? What makes the spin down half of the entangled state go away?
There is also another weird asymmetry. For the spin we say that its superposition exists in my [slice of the] world but for the measurement device we say only half of the entangled state, the outcome I become aware of, is part of [my slice of the] world, what justifies this?
There is also another weird asymmetry. For the spin we say that its superposition exists in my [slice of the] world but for the measurement device we say only half of the entangled state, the outcome I become aware of, is part of [my slice of the] world, what justifies this?
> What breaks the symmetry?
Nothing. It keeps existing, and (1/sqrt(2) * <I think spin is down|⊗<device shows spin is down|⊗<spin was down| + 1/sqrt(2) * <I think spin is up|⊗<device shows spin is up|⊗<spin was up|) keeps evolving, and since QM is linear, the summands evolve independently.
Yes, to the outside observer (the one who could look at the whole of the universe from the side/above without interacting with it) this does look very similar to MWI. But we are not outside of the universe, we exist inside it as a part of it, so for us it looks like spontaneous collapse of the wave function.
Nothing. It keeps existing, and (1/sqrt(2) * <I think spin is down|⊗<device shows spin is down|⊗<spin was down| + 1/sqrt(2) * <I think spin is up|⊗<device shows spin is up|⊗<spin was up|) keeps evolving, and since QM is linear, the summands evolve independently.
Yes, to the outside observer (the one who could look at the whole of the universe from the side/above without interacting with it) this does look very similar to MWI. But we are not outside of the universe, we exist inside it as a part of it, so for us it looks like spontaneous collapse of the wave function.
Maybe I am wrong, but that is exactly what I always assumed the many world interpretation to be. Especially I think many worlds also requires an outside of the cosmos observer to look at all the worlds, I do not think I ever heard someone claim that many worlds allows you and me to see or even move between different worlds.
> Everett's idea was merely that the measurement device gets entangled with the thing being measured
That idea is almost as old as quantum mechanics itself. (von Neumann, 1932 - if not earlier.)
That idea is almost as old as quantum mechanics itself. (von Neumann, 1932 - if not earlier.)
Entanglement means that the states become macroscopic in noisy (and not too high-temperature, apparently) environments. Whether you call those states “worlds” or not doesn’t change the philosophical implications.
Isn’t this just ontological then. It doesn’t seem like a novel observation that “measurement devices” collapse a wave function (Schrödinger) if you’ve defined a measurement device as such.
Yes, as far as anyone knows the different interpretations of quantum mechanics are just ontological.
If I recall there was nothing ontological about the actual Copenhagen group's interpretation. They aimed to develop a predictive theory and nothing more. One of their key insights was that ontology simply doesn't play a role anymore. This led quickly to the discovery of QM, while ~100 years of fussing over the "reality" of the wave function has led to nothing.
The "Copenhagen interpretation" as we understand it, in which some thing "collapses" when measured, trades under the same name but was invented later. As a result the original interpretations of Bohr/Heisenberg and their philosophy of science have somewhat exited the discussion, even though they had the only defensible epistemology -- the rest as you say is just ontology.
The "Copenhagen interpretation" as we understand it, in which some thing "collapses" when measured, trades under the same name but was invented later. As a result the original interpretations of Bohr/Heisenberg and their philosophy of science have somewhat exited the discussion, even though they had the only defensible epistemology -- the rest as you say is just ontology.
The problem is that you can't "fix" superposition. I [1] like to explain it with the https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experime... .
For some strange reasons [2] it's enough to consider atoms with spin |up> and |down>. But if you put the device sidewide, you would preffer to use |right> and |left> instead. But if you are forced to use |up> and |down> then
The same idea of expressing a state using superposition/sums of states in other base is very fundamental to Quantum Mechanics and appears everywhere.
[1] The idea of using Stern–Gerlach experiment is stolen from Feynman, not a brilliant idea of me.
[2] Too much algebra and the SU(2) group. Just bear with me.
For some strange reasons [2] it's enough to consider atoms with spin |up> and |down>. But if you put the device sidewide, you would preffer to use |right> and |left> instead. But if you are forced to use |up> and |down> then
|right> = ( |up> + |down> ) / sqrt(2)
|left> = ( |up> - |down> ) / sqrt(2)
The same idea of expressing a state using superposition/sums of states in other base is very fundamental to Quantum Mechanics and appears everywhere.
[1] The idea of using Stern–Gerlach experiment is stolen from Feynman, not a brilliant idea of me.
[2] Too much algebra and the SU(2) group. Just bear with me.
Sure, if you would know the spin direction before the measurement, you could align your measurement device accordingly and get a predictable answer and spin state would remain unchanged as the particle is not in a superposition for that measurement basis.
But if measurement basis and spin direction are not aligned, then the measurement result will be random in proportion to the misalignment and the spin state will be non-unitarily changed by the measurement, projected onto the measurement basis.
It the second scenario that lacks proper understanding, the first one seems much less interesting, you measure something that you already know and you get the value that you expect. It is certainly an interesting fact that being in a superposition is not an absolute statement, but it also seems not to uncommon. In additive color mixing magenta is a combination of red and blue, in subtractive color mixing it is one of the base colors.
But if measurement basis and spin direction are not aligned, then the measurement result will be random in proportion to the misalignment and the spin state will be non-unitarily changed by the measurement, projected onto the measurement basis.
It the second scenario that lacks proper understanding, the first one seems much less interesting, you measure something that you already know and you get the value that you expect. It is certainly an interesting fact that being in a superposition is not an absolute statement, but it also seems not to uncommon. In additive color mixing magenta is a combination of red and blue, in subtractive color mixing it is one of the base colors.
Rhere are a few interesting cases where superposition is inevitable.
A) In a molecule with two electrons, the wavefunction of the electrons is written as |aa> + |bb> + ... combining one electron with spin up and one with spin down. [1] [2]
It would be nice to choose the base carefully and write only |aa>. That is the Hartree-Fock method [3] and the result is like 95% or 99% accurate, sometimes you get 100% accurate, but it's not usual.
To get the small difference, you must allow combinations like Sqrt(99%) |aa> + Sqrt(1%) |bb>. [4]
It would be very nice to be able to use the simple form because calculations would be much faster.
B) In a different area, IIUC the neutrino osculation is caused because it's impossible to choose the bases for leptons and neutrinos and their transformations in a way there is no superpositions.
[1] Actually, in some cases you must use |ab> + |cd> + ... , but the simple version is good enough.
[2] And with more electrons it's even worse.
[3] https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method
[4] https://en.wikipedia.org/wiki/Electronic_correlation
[5] https://en.wikipedia.org/wiki/Neutrino_oscillation
A) In a molecule with two electrons, the wavefunction of the electrons is written as |aa> + |bb> + ... combining one electron with spin up and one with spin down. [1] [2]
It would be nice to choose the base carefully and write only |aa>. That is the Hartree-Fock method [3] and the result is like 95% or 99% accurate, sometimes you get 100% accurate, but it's not usual.
To get the small difference, you must allow combinations like Sqrt(99%) |aa> + Sqrt(1%) |bb>. [4]
It would be very nice to be able to use the simple form because calculations would be much faster.
B) In a different area, IIUC the neutrino osculation is caused because it's impossible to choose the bases for leptons and neutrinos and their transformations in a way there is no superpositions.
[1] Actually, in some cases you must use |ab> + |cd> + ... , but the simple version is good enough.
[2] And with more electrons it's even worse.
[3] https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method
[4] https://en.wikipedia.org/wiki/Electronic_correlation
[5] https://en.wikipedia.org/wiki/Neutrino_oscillation
(not a physicist) One thing that I always wondered about that I never see "debunked" anywhere is any discussion about whether or not entanglement is actually just because the two entangled particles are put into a pretty predictable state (opposite of each other). If one is measured "up" the other will measure "down".
To me that just screams "particle physics are predictable(determinant) as long as the particles are shielded from outside noise, not because they are connected/bound together by some mysterious force or law of physics."
I suppose a thought experiment to prove/disprove that would be to send one of the entangled particles, particle A, around a black hole to slow it's time down and then afterwards measure if the entangled particles still give opposite results but consistent with the time delay.
To me that just screams "particle physics are predictable(determinant) as long as the particles are shielded from outside noise, not because they are connected/bound together by some mysterious force or law of physics."
I suppose a thought experiment to prove/disprove that would be to send one of the entangled particles, particle A, around a black hole to slow it's time down and then afterwards measure if the entangled particles still give opposite results but consistent with the time delay.
You want to read up on Bell's Inequalities, which were experimentally confirmed[1] by Alain Aspect who won the physics nobel prize for it.
In short, you can never properly describe what happens by assuming the particles states are already determined after being entangled.
[1] https://en.wikipedia.org/wiki/Aspect%27s_experiment?wprov=sf...
In short, you can never properly describe what happens by assuming the particles states are already determined after being entangled.
[1] https://en.wikipedia.org/wiki/Aspect%27s_experiment?wprov=sf...
There is a very important and often forgotten caveat to the Bell's inequalities: it covers local hidden states. If we are to assume that measurement and particle creation apparatuses are entangled with each other (after all, they had plenty of opportunities since the big bang), then we have a global hidden state and the quantum measurment randomness becomes a simple artifact of removing global state from the picture. This interpretation of QM is usually called "superdeterminism" and, personally, I like it much more than the black vodoo measurement magic with collapsing wave functions or creation of whole new worlds on each tiny measurement. This video can be a good introduction to this topic: https://youtube.com/watch?v=dEaecUuEqfc (don't mind the clickbaity title, the video itself is good)
superdeterminism is deeply weird, just in a different way that most of the other quantum mechanics interpretations are deeply weird. The main thing is that it implies that this global quantum state is just-so arranged that no matter how you make your decisions about what to measure, it's always correlated with the underlying quantum state.
I would say it differently. Suprdeterminism opposes to the deeply ingrained assumption that we can design experiments in a way which removes influence of a measurement apparatus (including experementators themselves) on the measured process.
It's more than that, though. Just 'having an influence' on the measured process doesn't explain the bell inequality. Super-determinism basically requires that there is some common state from the big-bang which means that if I were to decide to e.g. seed the random number generator I'm using in an experiment with a description of what I had for breakfast that morning, the particles in that experiment (which could in principle come from far enough away they had no way of causally interacting with me or said breakfast) somehow 'know' that I had made that decision, what I had for breakfast, and the details of the random number generator and act accordingly. Absent some mechanism by which this might occur, it requires an incredibly complex kind of setup to the universe to create that result, one that has so many free variables it could explain almost any universe with any physics.
It's not a some sort of particle conspiracy. The idea is not so different from the Laplace's demon. We have an initial state of the Universe at the moment of Big Bang (a PRNG seed, if you will) and a set of differential equations (QM is not different in this regard). Theoretically, it allows the demon to predict everything in the Universe. The wave nature of QM equations introduces a certain quirk to it, but, effectively, with your example the breakfast was already "preordained" at the moment of the Universe creation.
Surprisingly, this idea makes many physicists very umcomfortable and they start to object to SD using philosophical arguments about "free will".
Surprisingly, this idea makes many physicists very umcomfortable and they start to object to SD using philosophical arguments about "free will".
It should make anyone uncomfortable (a trait it shares with all other known interpretations of QM). It implies a degree of correlelation across many different levels of abstraction which basically nothing else in physics does. As the name implies it's not just an abstract sense of determinism but one which tips the scales of everything at every level towards a specific outcome.
>one which tips the scales of everything at every level towards a specific outcome
According to the SD, this is nothing more than an artifact of splitting an entagled system into an "observer" and an "observed" parts. The linked video covers this part relatively well, the "randomness" of quantum measurment is nothing more than an artifact of artificial split of the Universe done by humans.
According to the SD, this is nothing more than an artifact of splitting an entagled system into an "observer" and an "observed" parts. The linked video covers this part relatively well, the "randomness" of quantum measurment is nothing more than an artifact of artificial split of the Universe done by humans.
And since that precludes it from ever being testable, falsifiable, or making predictions different from a Bell's Inequality based theory, it just isn't physics
It's no different from any other interpretation.
Just to try and summarise the issue. It turns out measurements of one of the entangled particles (particle A) are correlated to the settings of the measurement apparatus. For example the axis on which the polarisation of a photon is measured affects the measurement you get.
That setting is not known when the particles become entangled, and so in principle cannot affect the state of particle B. However since the setting does in fact correlate with the measured state of particle A, it also correlates with the state of particle B.
That setting is not known when the particles become entangled, and so in principle cannot affect the state of particle B. However since the setting does in fact correlate with the measured state of particle A, it also correlates with the state of particle B.
You're looking for the Bell Experiment: https://en.wikipedia.org/wiki/Bell_test
It proves there's no "local hidden variable"--the state is indeterminate until they are measured. It's proven through some pretty simple probability theory, and is (relatively) easy to follow. There's a great video of Leonard Susskind explaining it somewhere
It proves there's no "local hidden variable"--the state is indeterminate until they are measured. It's proven through some pretty simple probability theory, and is (relatively) easy to follow. There's a great video of Leonard Susskind explaining it somewhere
Imagine I send you a box. The box has three buttons: one on the top, one on the front, and one on the side. You can press only one of these buttons. When pressed it will either light up green or red. Pressing other buttons afterward causes no effect, the box is disabled.
I send your friend a copy of the same box. I tell you that the result of pressing each button is random but no matter what, if you both press the same button you will see the same result. If you press two different buttons, the results will be uncorrelated.
You ask me to send you and your friend a bunch of these paired boxes and start testing. You then both press random buttons on each box and record your results.
Comparing notes afterward you can see that every time you happened to press the same button you received the same result. You confirm that if you pressed two different buttons, you get uncorrelated results. No problem, you think. I have obviously preprogrammed each box to be one of GGG, GGR, GRG, GRR, RGG, RGR, RRG, or RRR.
But then you notice something strange. If this theory was true, for 2/8 boxes you would have an RRR/GGG box and would see the same answer no matter what. The remaining 6/8 boxes you should get the same answer 2/3 of the time. This means that your answers should agree 3/4 of the time. Even if you surmise that I never send you a box set to the same three values, your results should agree 2/3 of the time.
You crunch the numbers and find that your results agree precisely 50% of the time.
I send your friend a copy of the same box. I tell you that the result of pressing each button is random but no matter what, if you both press the same button you will see the same result. If you press two different buttons, the results will be uncorrelated.
You ask me to send you and your friend a bunch of these paired boxes and start testing. You then both press random buttons on each box and record your results.
Comparing notes afterward you can see that every time you happened to press the same button you received the same result. You confirm that if you pressed two different buttons, you get uncorrelated results. No problem, you think. I have obviously preprogrammed each box to be one of GGG, GGR, GRG, GRR, RGG, RGR, RRG, or RRR.
But then you notice something strange. If this theory was true, for 2/8 boxes you would have an RRR/GGG box and would see the same answer no matter what. The remaining 6/8 boxes you should get the same answer 2/3 of the time. This means that your answers should agree 3/4 of the time. Even if you surmise that I never send you a box set to the same three values, your results should agree 2/3 of the time.
You crunch the numbers and find that your results agree precisely 50% of the time.
The interesting thing about entanglement is not the correlation per se. You can take a pair of hand gloves, put each one into a box, and send them to opposite ends of the universe. When you open one box at one end of the universe and see the left glove, you immediately know that someone at the other end of the universe will find the right one. The interesting thing about entanglement is that decision which glove goes into which box is not made when you prepare the boxes before sending them to opposite ends of the universe but only at the moment you look into the first box.
And if it doesn't fit...you must acquit.
If all you could measure was "up" and "down" then I think entangled particles would be indistinguishable from unentangled particles that were created as up/down pairs. But particles can be measured in other directions, and that's where the determinism goes away.
A nice thought experiment is the CHSH game. It's a two player game where the players (player A and player B) cooperate to beat the house. It is played as follows:
1. Each player is assigned a referee.
2. The players, accompanied by their referee, go to separate rooms. Before going to the separate rooms the players can confer. They may also bring any equipment with them that they want. The rooms are shielded to block any communication between the players during their time in the rooms. You may assume that the communication blocking is 100% effective.
3. Each referee uses a true random number generator to generate a bit, and tells the player the value of that bit.
4. The player then generates a bit, by any means, and tells it to the referee.
5. The referee records the bit they generated and the bit provided by the player.
6. Steps #3-5 are repeated 999 more times.
7. After both players have gone through #3-5 1000 times, the referees confer and check their records. For each round the players win $100 in these two cases:
In a quantum universe the players can do better. They can generate 1000 pairs of entangled particles and each take one particle from each pair. Let's assume that the particles are linearly polarized photons polarized in the up/down direction.
When player A is given the referee's bit, A sends their particle from the first pair through a polarizing filter and reports a 1 if the particle makes it through the filter, and a 0 if it is blocked.
If the referee's bit was a 0 the player orients their polarizing filter along the up/down axis. If the referee's bit was 1 they orient their filter rotated 45° to the right.
Player B does a similar thing, except their filter is rotated 22.5° to the right if they got a 0 from the referee and 22.5° to the left if they got a 1.
Here's a diagram of their measurement angles, where X0 means player X got a 0 from the referee and X1 means they got a 1:
Note that if either player receives a 0 from the referee the angle they use will be 22.5° apart from the angle the other player uses no matter what bit the other player got from the referee.
When the measurements on a pair of entangled particles are taken at an angle θ the results match the result you'd get at a 0° difference cos^2(θ) of the time.
For 22.5° that's 85.4% of the time, so when either referee generates a 0 they players will win 85.4% of the time.
If both referees generate 1, B measures at -22.5° and A measures at 45°. That's 67.5° apart and the player bits only match 14.6% of the time, but when both referees generate 1 the players want to generate different bits so that's good. They players win 85.4% of the time in this case.
That's an 85.4% win rate in all cases, which beats the 75% that they can get in a classical universe.
If you try to make some sort of classical-only thing that can take the place of entangled particle pairs you'll find that you can't make it work. You won't get past 75%.
Another thought experiment that might be clearer (or might just muddle things) involving two mysterious devices that you are trying to reverse engineer is here [1]. That puts it more mechanical/computational terms which may be easier to play around with.
[1] https://news.ycombinator.com/item?id=35905284
A nice thought experiment is the CHSH game. It's a two player game where the players (player A and player B) cooperate to beat the house. It is played as follows:
1. Each player is assigned a referee.
2. The players, accompanied by their referee, go to separate rooms. Before going to the separate rooms the players can confer. They may also bring any equipment with them that they want. The rooms are shielded to block any communication between the players during their time in the rooms. You may assume that the communication blocking is 100% effective.
3. Each referee uses a true random number generator to generate a bit, and tells the player the value of that bit.
4. The player then generates a bit, by any means, and tells it to the referee.
5. The referee records the bit they generated and the bit provided by the player.
6. Steps #3-5 are repeated 999 more times.
7. After both players have gone through #3-5 1000 times, the referees confer and check their records. For each round the players win $100 in these two cases:
The players generated different bits and the referees both generated 1
The players generated the same bit and at least one referee generated 0
In a quantum universe the players can do better. They can generate 1000 pairs of entangled particles and each take one particle from each pair. Let's assume that the particles are linearly polarized photons polarized in the up/down direction.
When player A is given the referee's bit, A sends their particle from the first pair through a polarizing filter and reports a 1 if the particle makes it through the filter, and a 0 if it is blocked.
If the referee's bit was a 0 the player orients their polarizing filter along the up/down axis. If the referee's bit was 1 they orient their filter rotated 45° to the right.
Player B does a similar thing, except their filter is rotated 22.5° to the right if they got a 0 from the referee and 22.5° to the left if they got a 1.
Here's a diagram of their measurement angles, where X0 means player X got a 0 from the referee and X1 means they got a 1:
B1 B0
| | |
| | |
+--------+--------+--------+
|-22.5 |0 |22.5 |45
| | | |
A0 A1
Note that if either player receives a 0 from the referee the angle they use will be 22.5° apart from the angle the other player uses no matter what bit the other player got from the referee.
When the measurements on a pair of entangled particles are taken at an angle θ the results match the result you'd get at a 0° difference cos^2(θ) of the time.
For 22.5° that's 85.4% of the time, so when either referee generates a 0 they players will win 85.4% of the time.
If both referees generate 1, B measures at -22.5° and A measures at 45°. That's 67.5° apart and the player bits only match 14.6% of the time, but when both referees generate 1 the players want to generate different bits so that's good. They players win 85.4% of the time in this case.
That's an 85.4% win rate in all cases, which beats the 75% that they can get in a classical universe.
If you try to make some sort of classical-only thing that can take the place of entangled particle pairs you'll find that you can't make it work. You won't get past 75%.
Another thought experiment that might be clearer (or might just muddle things) involving two mysterious devices that you are trying to reverse engineer is here [1]. That puts it more mechanical/computational terms which may be easier to play around with.
[1] https://news.ycombinator.com/item?id=35905284
> what actually saves or kills Schrödinger's cat
If the cat is not definitely dead (or alive) until you look at it, I think the mainstream consensus is that curiosity killed the cat.
If the cat is not definitely dead (or alive) until you look at it, I think the mainstream consensus is that curiosity killed the cat.
Isn't heat transmitted by photons? In that case, isn't it inevitable that heat destroys entanglement? Because the transmission of heat means some photon has to interact with one of the entangled particles.
> Because the transmission of heat means some photon has to interact with one of the entangled particles.
Interaction doesn't necessarily destroy entanglement, it can also entangle the new particle with the others. Meaning the photon would just get entangled with the rest instead of breaking the entanglement.
Interaction doesn't necessarily destroy entanglement, it can also entangle the new particle with the others. Meaning the photon would just get entangled with the rest instead of breaking the entanglement.
If one of a pair of particles gets entangled with others, it means that the entanglement of the original pair of particles will be broken.
you’re thinking of radiant heat. There’s also heating by conduction
… which is usually mediated by electric field interactions, involving virtual photons.
Right?
Right?
Isn't that induction? Asking as I am not sure.
Great question! It's literally all the same process! There's only a difference on a macroscopic scale. On an atomic scale, atoms are tiny vibrating charges held together (and apart!) by electric forces (well, by all forces, but the electric force is by far the strongest). A vibrating charge can emit a photon; we call this radiation. This radiation can be reabsorbed somewhere and induce a new vibration. This is technically induction (though I've never seen it referred to as such, more commonly radiative transfer). If we step back so that we no longer view individual atoms, we just see vibrations moving around within a material; we call this conduction but it's still happening via radiative transfer. If your material is a fluid and moves around for some heat-related reason (say, a change in density), we call this convection.
https://en.wikipedia.org/wiki/Radiative_transfer
Confusingly, inductive heating is a completely different process involving no heat transfer! You induce a current in material, and this current causes resistive heating.
https://en.wikipedia.org/wiki/Induction_heating
You might be wondering: "then what's resistive heating?" Well, electrons are also tiny moving charges. Care to hazard a guess how they interact with their environment?
https://en.wikipedia.org/wiki/Radiative_transfer
Confusingly, inductive heating is a completely different process involving no heat transfer! You induce a current in material, and this current causes resistive heating.
https://en.wikipedia.org/wiki/Induction_heating
You might be wondering: "then what's resistive heating?" Well, electrons are also tiny moving charges. Care to hazard a guess how they interact with their environment?
For practitioners, a rough description of their argument is on pg 7 (note: separable=unentangled, β =1/kb T) of https://arxiv.org/pdf/2403.16850
This state [rho] is the Gibbs state at infinite temperature, and is in the interior of the convex hull of product states. So, as β tends to zero, ρ will eventually enter the interior of this convex hull, making it separable. This happens at a finite β which depends on system size.
This state [rho] is the Gibbs state at infinite temperature, and is in the interior of the convex hull of product states. So, as β tends to zero, ρ will eventually enter the interior of this convex hull, making it separable. This happens at a finite β which depends on system size.
Been a while since I've been working in the field, but wouldn't we expect this finding through the model of dissipation and decoherence? Seems like Caldeira & Leggett all over again.
I think the naive expectation would be that a hot state would be highly entangled and non-separable. The non-separability is what leads to decoherence when you do a partial trace. You can arbitrarily split any multi-part Hilbert space into a "system" and an "environment" and then trace out the environment. If they are highy entangled with one another then the resulting system-without-environment will be decohered.
Alternatively formulated, this suggests that an entangled state, if weakly coupled to a bath at high temperature and allowed to thermalize, will become fully disentangled at a finite time. (p1)
hinting that something different is happening here (from the C&L model mentioned below.)
Indeed the CS guys are probably looking for a way to redefine entanglement (entropy, as you summarized above), to essentially “work” in the same way as what they have in their preprint, but also cover the prethermalized cases..
hinting that something different is happening here (from the C&L model mentioned below.)
Indeed the CS guys are probably looking for a way to redefine entanglement (entropy, as you summarized above), to essentially “work” in the same way as what they have in their preprint, but also cover the prethermalized cases..
Hmm, C&L argument involves taking a classical limit, does it not? This paper seems “fully quantum” (provided that you agree that the maximally mixed “Gibbs” state should not be considered a “classical” limit, only an infinite temp limit)
Yeah maybe that's what's bothering me, what is the high temperature limit if not the classical limit?
Heh, you might be additionally bothered that for the C&L model, the strong coupling (to heat bath) limit can also be considered the (/a?) classical limit, e.g.
https://arxiv.org/pdf/1603.07495
https://arxiv.org/pdf/1603.07495
For those interested in some quantum stuff and interested in watching a kindred spirit do approachable practical experiments I highly advise watching this guys stuff [1]. Consider it a psa
[1] https://youtube.com/@HuygensOptics
[1] https://youtube.com/@HuygensOptics
I have the suspicion that there are several very simple experiments we have yet to think up that would give incredible revelations with the inner workings quantum mechanics.
I have a mental model for entanglement that's probably very wrong, and I would love to devise a proper test to falsify it.
I have a mental model for entanglement that's probably very wrong, and I would love to devise a proper test to falsify it.
Something related from the og computer scientist, though does their new result have impacts on the quantum zeno effect?
[I]t is easy to show using standard theory that if a system starts in an eigenstate of some observable, and measurements are made of that observable N times a second, then, even if the state is not a stationary one, the probability that the system will be in the same state after, say, one second, tends to one as N tends to infinity; that is, that continual observations will prevent motion. Alan and I tackled one or two theoretical physicists with this, and they rather pooh-poohed it by saying that continual observation is not possible. But there is nothing in the standard books (e.g., Dirac's) to this effect, so that at least the paradox shows up an inadequacy of Quantum Theory as usually presented.
— Quoted by Andrew Hodges in Mathematical Logic, R. O. Gandy and C. E. M. Yates, eds. (Elsevier, 2001), p. 267.
I skimmed 5 pages down looking for the darn temperature of disentanglement with no luck. Could one of you more perseverant readers enlighten me?
Please note that the entanglement here are on spin states in equilibrium with a mean temperature bath - this doesn't apply to e.g. a pair of (or sets of) entangled photons (which aren't interacting with anything on the way to the detectors.)
<ctl>+f entropy didn't return anything, so I went looking for the paper. It looks like it is: "High-Temperature Gibbs States are Unentangled and Efficiently Preparable" [0] but maybe it is "Structure learning of Hamiltonians from real-time evolution" [1]
0. https://arxiv.org/abs/2403.16850
1. https://arxiv.org/abs/2405.00082
0. https://arxiv.org/abs/2403.16850
1. https://arxiv.org/abs/2405.00082
What is the implication for high temperature superconductors? Does this mean that they can't exist?
How do they come up with those amazing illustrations?
Quanta Magazine always impresses me with the illustrations for each article
Quanta Magazine always impresses me with the illustrations for each article
I’d assuming paying and working with good artists
Which illustrations are you referring to? I only see one illustration (at the top) and it looks like AI-grade material.
I'm guess they're referring to the illustration that's clearly attributed to Quanta's Visual Designer Kristina Armitage.
The illustration matches the tone and content of the piece, while also being visually consistent with her other Quanta illustrations. Seems like Ms. Armitage is only 2 years out of college, but is literally (illustratively?) crushing it [0].
Knee-jerk criticism like this in response to someone putting out heart-felt praise is so, so unnecessary. There's a time for putting down AI-assisted work, maybe, but this isn't it.
0 - https://www.behance.net/moodboard/179460311/illustration
The illustration matches the tone and content of the piece, while also being visually consistent with her other Quanta illustrations. Seems like Ms. Armitage is only 2 years out of college, but is literally (illustratively?) crushing it [0].
Knee-jerk criticism like this in response to someone putting out heart-felt praise is so, so unnecessary. There's a time for putting down AI-assisted work, maybe, but this isn't it.
0 - https://www.behance.net/moodboard/179460311/illustration
When is there ever a time for putting down AI assisted work? Serious question.
I can think of a few situations... Like when it's flooding your board / group with ultra-low-effort crap, or when it's clearly a barely-digested regurgitation of an artist's style that they spent decades developing at great personal cost. When it's used to scam people, or when it's used to smear them.
I find it upsetting that a company can steal the essence of thousands / millions of people's life's work, "transform" it with an algorithm, and then sell it to people without any recognition of the theft whatsoever. I don't like that a generation of creatives is being undercut, all during a time when inequality and wealth capture are rampant due to out-of-control mega-corporations - which immediately make moves to buy and/or copy said company...
Like, I love creativity. I love AI. I think AI will be a part of our future whether we moan about it or not. At the same time, the world is awash with the worst type of scams, to the point where making a living is hard even if you work a steady 9-5. Even if you work two.
Damn near every artist, writer, musician is scrabbling ridiculously hard to stay afloat as it is. Some aren't making it. I can see why they're pissed. And I think that for the most part, being angry at 'AI' is pointless, except as a means to distract from the true parasites of our age.
I find it upsetting that a company can steal the essence of thousands / millions of people's life's work, "transform" it with an algorithm, and then sell it to people without any recognition of the theft whatsoever. I don't like that a generation of creatives is being undercut, all during a time when inequality and wealth capture are rampant due to out-of-control mega-corporations - which immediately make moves to buy and/or copy said company...
Like, I love creativity. I love AI. I think AI will be a part of our future whether we moan about it or not. At the same time, the world is awash with the worst type of scams, to the point where making a living is hard even if you work a steady 9-5. Even if you work two.
Damn near every artist, writer, musician is scrabbling ridiculously hard to stay afloat as it is. Some aren't making it. I can see why they're pissed. And I think that for the most part, being angry at 'AI' is pointless, except as a means to distract from the true parasites of our age.
I didn't claim that it was generated by AI.
I didn't say you did, and it doesn't matter.
The point was, it's rude to call someone's work "AI-grade material"; especially in response to a compliment about it, and when it's actually pretty good stuff, and all without making the slightest effort to figure out whose work you're shitting on.
The point was, it's rude to call someone's work "AI-grade material"; especially in response to a compliment about it, and when it's actually pretty good stuff, and all without making the slightest effort to figure out whose work you're shitting on.
Some day, when I have moree time, I will work on proving my theory that the entanglement doesn't really exist, and the whole quantum weirdness is just bs. But know I have to finish coding that data acquisition system. Priorities..
I've heard Sean Carroll answer the question:
"Why don't more physicists worry about
the foundations of Quantum Mechanics?"
"They first say they have no time,
and it doesn't affect their work anyway."
"Then they imply that if they stopped their work
and thought hard for 20 minutes
they could solve all the problems."
Kind of like my plan to prove flat earthers wrong using long range rifles and the Coriolis effect at different places north and south of the equator, still waiting on Argentina to give me permission to bring a bunch of rifles to Tierra del Fuego.
coincidentally the flat earth movement is imploding a bit, as their 'thought' leaders were invited to visit the south pole to observe 24h day as witnesses.
A thing technically impossible for flat earth 'model'. But they just started attacking each other as not reliable enough to go.
Anyhow they would claim time near the edges slows down the time or the whole thing was a virtual 3d future tech used to fool them
A thing technically impossible for flat earth 'model'. But they just started attacking each other as not reliable enough to go.
Anyhow they would claim time near the edges slows down the time or the whole thing was a virtual 3d future tech used to fool them
>coincidentally the flat earth movement is imploding a bit, as their 'thought' leaders were invited to visit the south pole to observe 24h day as witnesses.
Got a link? That sounds hilarious but I couldn't find any articles about it (though I didn't search terribly hard).
Got a link? That sounds hilarious but I couldn't find any articles about it (though I didn't search terribly hard).
I found this which is I think what they were referring to: https://www.the-final-experiment.com/
yup thats the one
You could always two time it. Earn enough money to do physics. Then do enough physics while living on ramen to extend the runway. Repeat it till goal is achieved. Quantum Silicon Valley.
Is this concept debunked by this paper, or could it be that 'destroys entanglement' actually means 'becomes entangled with almost everything else'?