For simplicity, let's assume that it's the wave function of an electron, but this applies to any particle.
The first problem is the question. What does "detection" means?
The technical term is "measurement", and the most important idea is that you can measure different things, for example the position of the electron, or the speed of the electron, or the energy of the electron, or ...
If you measure the exact position of an electron, the wave function collapses to a point.
But you can measure other thing, for example if it's inside a box or outside the box. In this case the wave function that initially is spread perhaps in all the universe, will collapse to a smaller wave function. In some cases to one that is completely inside the box, and in other cases one that is completely outside the box.
Knowing the initial wave function it's possible to know how the wave functions inside or outside the box will be, but the details are quite technical.
What is not possible to know if after the measurement you will get the wave function that is inside or outside the box. As fas as we know this is a random choice. Nobody likes it, some people thing there are not random rules, but most people think it's sadly random.
Note that the probability to get the wave function that is inside or outside the box are not equal. It may be la loaded "dice". The exact numbers can be calculated if you know the initial wave functions, but the details are quite technical.
Very informally, if the box is small, the probability of getting the wave function that is inside is small. If you have an electron inside the box and open it for a very short time and close it, then the probability of getting the wave function that is inside is big. To get a formal definition, you must read all the nasty technical details.
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The idea is that you can somehow detect that the electron is inside or outside the box, but it does not collapse the wave function completely. You still have a complicated wave function inside or outside the box. And you can make this wave function colide with other wave functions and get some weird quantum mechanics results that are impossible if you assume that the wave function has collapsed for a very short time to a single point inside or outside the box.
Or you can generalize this with two boxes and the rest of the universe. It's possible to measure if the electron is in box A, box B or outside. It's also possible to measure if the electron is in any box or outside. In this case you get entangled boxes that are even weirder.
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The experiment in the link use photon in a one or two slits experiment. The physical details are very different but the calculations and the idea is very similar. The box is the slide, and outside the box is the screen.
The notion of the wave function collapse is very specific to Copenhagen interpretation of quantum mechanics that tries to reconcile classical and quantum world. But everything is quantum so there is no classical measurement device, just its wave function interacting according to fully deterministic equations with the wave function of the electron.
The catch is that appearance of classical objects is still unsolved problem in QM. There are various approaches that in theory can explain the experimental results, but in practice explaining, say, quantum split experiments from pure QM view of multiple interacting wave functions still not possible.
No, it doesn't. Decoherence explains why self-interference of a single wave-function doesn't happen after interaction with the environment. But it doesn't explain two important things.
1, which is very practical, is that it doesn't explain why the wave function always decoheres in the same way. In experiments, you can always chose the basis of measurement, and get some definite results in that particular basis, while the properties in another basis remain indefinite. But, in classical reality, all objects have definite properties in the same basis (say, positions in the same Cartesian coordinate system). This is known as the preferred basis problem, and decoherence can't explain it.
2, which is somewhat more philosophical, decoherence doesn't explain the quantitative relationship between the wave function and the probability of observing a particular outcome. Indeed, in MWI it's very hard to even define probability in a coherent way, since all outcomes actually happen and there is an uncountable (in the mathematical sense) number of outcomes.
The many worlds interpretation works better with quantized probability. Imagine a huge computer running a monte carlo simulation with a probabilistic current state, and a set of transition states (the wave function). With quantized probability and a universe with finite "memory" the amplitude of the wave function basically maps to the amount of system memory being utilized for a portion of the simulated state space.
Well, quantized probability doesn't really make sense, there are extraordinarily improbable events happening every second. It's easy to create an event that has less probability than many things that have never been observed (flip 10,000 coins - whatever result you get has probability 1/2^10k).
You could perhaps create a version of QM with a quantized amplitude for the wave function in some basis.
It's also important to remember that the Schrodinger equation of a system has an infinity of solutions - for any solution, any linear function of that solution is also a solution. You need to choose a particular basis of measurement - choose a decomposition of the solutions - to be able to apply the Born rule and get from the wave function to a probability distribution.
By quantized probability, I assume you mean something like "there is a minimal probability p for any possible event; if the probability we compute for some event is q < p, then that event is impossible".
If this is the right definition, then it's easy to disprove: for any p you chose, I can construct a series of events that each have probability q < p, but one of which is guaranteed to happen. This was the meaning of the examples I gave with the 10 thousand coins - the probability of any particular result after flipping the coins is extraordinarily small, and yet one of the results is guaranteed to happen.
Edit to add: to be clear, even if the universe itself were quantized, all measurable physical quantities, probability still wouldn't need to be quantized, as it's not a physical quantity, it's just a mathematical abstraction. Still, even in QM, not all physical quantities are quantized. For example, space (position) is not quantized in QM, and neither is time. They are both continuous quantities in all of the equations normally used. Planck time and Planck distance are only the shortest possible distances to measure precisely, given the Heisenberg uncertainty principle, but that doesn't require them to actually be quantized. In contrast, the quantization of mass, energy, spin etc are actually necessary for the theory to work, they are not just measurement artifacts.
Why do you think this is a result of an unquantized wavefunction rather than due to the mathematical edifice we use to model it? It's not clear to me that things like the product rule for probabilities would still hold if you're not transforming and normalizing amplitudes.
> In experiments, you can always chose the basis of measurement, and get some definite results in that particular basis, while the properties in another basis remain indefinite.
Can you give some examples of such bases? Position is one, for sure. In "Quantum Mechanics 101" we are told that momentum is another, but I'm sceptical that there is a real experiment that can measure momentum without also measuring position.
Even for position, you can measure less than a point-like position. For example, you can check if a particle is inside this box or outside it. After this measurement, the particle will either be inside the box or outside it, but it will not be at some fixed position inside the box (or some fixed position outside it). For example, if it's determined to be outside the box, it will definitely not interact with any particle that was inside the box at the same time, but it may interact with any particle anywhere else in the entire universe - and according to MWI, it WILL interact with every other particle everywhere else in the universe, in some part of state-space.
While quantum decoherence explains appearance of classical objects in simple models, predicting the results of real experiments still not possible. And given this has not changed much as far as I know for the last 20 years, I started to suspect that decoherence alone may not be enough.
Classical objects are not explained in Quantum Mechanics, they are a fundamental part of the theory itself. (Measurement is an interaction with an apparatus which is a classical object.)
The notion of a 'Classical Object' in this particular framework of QM is an assumption, not a prediction.
Since all objects are composed of quantum particles, all objects are quantum objects. So a complete theory of QM needs to be able to explain, not assume, why some objects behave classically.
To summarize: a measurement need not give enough information to convert a wavefunction into an impulse (point) function. Not all measurements give you point information. A measurement could provide enough information to constrain the wavefunction to a more restricted (knowledgeable) form (lower entropy if you use integrate over the wavefunction -- that is Integral(-P(x)*Log(P(x))))
This is especially the case with entanglement. By measuring one entangled observable, we often increase our knowledge but not absolutely like in the naive explanations that have you believe it is always an entangled pair of spin up and spin down..
All measurement does is reduce uncertainty/entropy of the wavefunction. The strange part is that one can actually undo this restriction by erasing any traces of the measurement. See the Delayed choice quantum eraser experiment. Collapse doesn't really exist.. It's more like expressions that can be reduced, appear reduced, until they cannot be reduced..thus they appear expanded. Imo, entanglement is evidence that all interactions are lazily computed and are copy-on-read or lisp expressions that gradually become larger as interactions continue, and are beta or alpha reduced when possible.
I like it. Dont confuse tgis entropy with the von neumann entropy which increases (or at least stasy the same) when a measurement is perfomed (pure state turning into mixed state)
> If you measure the exact position of an electron, the wave function collapses
to a point.
Note, though, that in reality you can never measure the exact position of an electron (or anything else); the best you can do is to measure that the electron is inside some finite-sized (possibly very small) region. The "exact position" measurement is an idealization that can be useful for pedagogy but can't be realized in any actual experiment.
I assume that by 'you can never measure the exact position of an electron (or anything else)', they meant 'you can never measure the exact position of an electron (or the exact position of anything other than an electron)', not 'you can never measure the exact position of an electron (or any other property of an electron)'.
As moonchild posted, I was only saying that you can't measure the position of an electron exactly. I was not saying that you can't measure any properties of electrons at all.
The more general statement is that you can't measure exact values for any observable with a continuous spectrum; you can only measure that a quantum system is within some finite range of values. Spin has a discrete spectrum, so you can measure exact values for spin.
If you are intrigued as to what it means for the wave function to collapse, and related questions such as at which speed does it collapse, etc, you must consider what it means to measure something.
If you want to know the property of some particle you need to interact with it ... at least with another particle. The system of those two particles is described by a wave function. This wave function evolves according to the Schrödinger equation and it will tell you that after the interaction you have a superposition of two states: one where the particle you're measuring is inside the box and the measurement probe particle is carrying that information, and the other state that tells you that the particle is outside the box *and* the measurement probe tells is carrying that information.
The wave function of the system hasn't really collapsed to a single state.
Now, let's say that your measurement apparatus records the information of this test particle by e.g. printing it out to a piece of paper or whatever (bits in hard disk)
The wave function of the whole system now captures the superposition where the measured particle was in one state and the paper contains black ink in some places and not in other places, superimposed with the other state where the measured particle was in the other state and the paper carries ink in other locations.
Nothing has collapsed yet; you just have a very complicated wave function. By processing the measurement you effectively introduced a "causality amplification" process, but one that operates on the whole of the wave function.
But, you may protest: "I see only one outcome of the measurement!"
The wave function of the universe is in a superposition of your body (and thus brain) being in a state where you have observed ( and recorded such observation) one measurement outcome and another state where you have observed the other outcome.
Both states are equally real and present in the wave function of the universe. But each of the brain states in the superposition doesn't interact with the other states do each future though you have in one of the superimposed states are effectively independent from the others, giving the impression that the wave function has "collapsed".
Some people like to say that the "universe has split" into independent world lines or something like that. Some people find this terminology helpful, some find it confusing. But the thing is, this just follows from applying the Schrödinger equation without making arbitrary exceptions when humans get involved.
> But surely the wave function is smeared across both slits
That's the whole point of the experiment - you can't get an interference pattern if it does not.
> and the act of detecting which slit the photon could go through, if it were a particle
The whole point of the double slit experiment is that there is only one photon, and which slit it goes through is irrelevant.
Whether a photon is a wave-function is missing the point entirely - the point is how do you get an interference pattern if the photon/wave-function only goes through one slot?
The point of this experiment is to show that sometimes light behaves like a continuous wave, while other times it behaves like a particle of sorts.
In short, QM might have produced some nice mathematics models, but it's claims about objective reality are contested. Some people don't agree there is any paradox, and that the double-slit experiment correctly identifies light as a wave, and that claims that the photoeletric effect proves light is a "particle" are based on false inference (particularly that energy quantization implies packetization). Some people still seriously propose that consciousness affects basic particle physics (as if particle know when they are being measured).
Despite all that the cool smarty pants brigade who have read some 1st year QM books (while understanding only a fraction) come away all puffed up that QM actually provides deep insight and wide consensus as to the underlying interpretation of reality. The fact is, it's as paradoxical today as when the great physicists up to the last of them (Feynman) correctly identified it as such. Quite sad really.
Does a wave function collapse if there is no conscious entity to measure that?
It is a philosophical question, but philosophy is precisely designed for dealing with what is technically unfalsifiable in hard science—the “far lands” of modeling the system from within itself.
There's a difference between strong and weak quantum measurements. Experimentally we can now even apply feedback on quantum states to stabilize them, which requires making partial, non-destructive measurements of a quantum state and then applying signals to correct deviations.
The whole talk about "wave function collapse" originated from the beginnings of quantum mechanics where the measurement process was poorly understood, in my opinion it should be replaced by the modern understanding, in which a measurement is a combination of an entanglement process between the system under test and a large external system, followed by decoherence caused by the many degrees of freedom of the external system. That produces wave form collapse, but it's not an abrupt or absolute process but rather a continuous, controllable one.
I think the most reasonable explanation is that unobserved things do not happen, at all, or only happen on some abstract statistical level.
That doesn't imply that consciousness is special. The reason why you are aware of reading this, if you are indeed aware of reading this, is that your life matters for some future event, which on the fundamental physical level has already happened, but its exact results depends on how your life unfolds in some way. If I locked you up in an impenetrable box that is to be completely obliterated at some future point in time, so that whatever you do in the box would make no observable difference, the rest of your life in the box would not happen.
That's an observation.
Schrodinger cat isn't both dead and alive. Nothing happens in the box while it's closed.
Really think about how this is an elegant solution that makes it completely un-paradoxical, excluding that events happen out of order compared to our intuition.
Does anyone have a link to a real world example of the double slit experiment where the photons are observed at the slits, causing the wave function of the light to collapse so the light acts as a particle beyond the slit, ending up in two piles on the detector screen, rather than the wave pattern.
Every time I ask this, some do-gooder will not read a word I wrote and send me a video of the basic slit experiment and think they've somehow educated me. Every time. It's amazing.
What I'm looking for is a photo or video of a real experiment showing just two groupings. There a million photos/videos of the wave pattern. I'm looking for an example with exactly two clumps of photons because the light is observed as it passes each slit. In real life, not a computer simulation.
You are asking that the screen be moved back to the slits - less than a slit-slit distance away.
The wave aspect of the EM field remains downstream of the slits. The photon aspect is only exhibited at the screen.
There may be no such images, because it’s not interesting to observe two bright spots. There has to be enough path length difference to allow the phase difference causing the interference. Think about the classical case.
The mystery is not the interference, it’s that the photon density at the screen tracks the predicted interference pattern, even if they arrive at one per second.
Bohm’s pilot wave theory has an explanation for this.
> There may be no such images, because it’s not interesting to observe two bright spots.
*Seriously?* There are an unlimited amount of uninteresting pictures on the internet, but no one has bothered to take a picture of a fundamental claim of quantum mechanics because it's so trivial as to be boring?
If you try it yourself and continue moving the 'screen' closer towards the two slits, the wave pattern will eventually disappear and you will have the two 'piles' of photons you refer to.
There's nothing like testing it yourself in 'real life' if you remain unconvinced.
If you're trying to say there's something that seem suspicious about such claims then I agree with you. I don't know what it means to "observe" a photon at a slit without completely invalidating the experiment.
Ah, well the video is about electrons, and it's somewhat more plausible to "observe" them going through one slit or the other, since they will emit an electromagnetic field. There do seem to be such recent experiments, for example https://phys.org/news/2011-01-which-way-detector-mystery-dou...
Derp, sorry... Electrons and photons are completely different types of particles. I'm getting things mixed up. And I had just skimmed that video again! I need to pay attention.
Still, I would have loved for the authors of that paper to get a pic of the setup and results on the computer monitor next to it or something.
Also, isn't this stuff fundamental to theoretical quantum encryption? If we try to observe information as it flows by, we always alter it in detectable ways because of the observation effect? I think?
(In some ways it's absurd that here we are, everyday people, chatting away trying to get a mental hold on the weird, abstract yet fundamental way the universe works, as dreamed up by literal scientific geniuses a century ago. But in reality, getting a general grasp of this stuff is knowledge you need to have in so many fields, from suburban electrician to anyone working in high tech. Crazy.)
I don't have the link handy but IIRC the result of the experiment when you have minimally invasive detectors at the slits is that depending on the distance of the slits from the final plate and the separation of the slits you'll see either two broad smears, or one wide smear with just a few interference patterns in the middle.
The confusion with the Copenhagen interpretation comes from two main sources in my opinion:
1. What can count as a measurement?
2. Quantum ‘thing’ interacting with a classical world
One of my favorite talks on this subject is by Sean Carroll and offers the ‘many worlds ‘ interpretation as an alternative, mainly for its simplicity. Recommend watching the whole thing but if you want just the “debunking”: 25:11
https://youtu.be/5hVmeOCJjOU
Interpretation is a crutch, gives nothing extra, and only obfuscates things; it should be discarded.
Let's just accept that (1) we don't know the objective reality, and (2) there is something that ensures consistency of information across fairly large distances -- entanglement experiments have been done up to 1000+ km's -- maybe even across the entire universe, though the latter has never been tested.
> entanglement experiments have been done up to 1000+ km's
Do you have a link to more info on that? I've never heard of such an experiment and I'd be interested how you send entangled particles 1000+ kms without disturbing them in a way that invalidates the experiment.
This is the video that finally made it click for me[1]. Despite the somewhat click-baity title ("What Popularizers of QM Don't Want You to Know") it actually goes into quite a bit of detail of what is and isn't a measurement, in the sense of interactions in a quantum mechanical system that strongly resemble classical behavior (it can be said that the quantum mechanical world is a simulator that can run classical mechanics).
It's perhaps not surprising an approaching quantum "paradoxes" as classical "computer" trying to analyse the quantum computer it is running on appeals to computer programmers. It sure appeals to me.
Isn’t a wave function essentially just a representation of all possible answers? Like a (perfectly flat) coin flip would be something like 0.5h + 0.5t = 1, where if t is 1, then h is zero, and vice versa?
There is an intuitive way to picture what particles are and what their measurements is. So simple even a 5-year could play with it.
You take a shoe lace. You tie a loose knot in it. Prevent the extremities of the lace to move, by placing your feet on them (or rocks, or whatever). Put your finger inside the knot and slide the knot along the rope.
You have just played with a "particle". The knot is the particle.
Pinch the rope with your left hand somewhere along the rope. Pinch the rope with your right hand somewhere along the rope. Slide your fingers along the rope to bring them together. This will progressively tighten the rope between the fingers. Alternatively you can just tighten the rope by pulling on it.
If there is knot in the region you just tighten, congratulation you have just measured your first particle. If not, try again by placing your finger at different spot, and try again you may get lucky. Quantum physics is a matter of probabilities.
Now that you have caught your particle, you have to loosen the knot, so you can explain the uncertainty principle.
Once you have played with one knot. Try adding a second knot, move them. Can you get one to go through the other ? Is the number of knots on the rope always conserved ?
Now that you have played with knots, here is a fun twist. You need to have a flat lace or a belt though. Lay the flat lace flat. Do a half twist on an extremity of the lace. And like you did with the knot before, slide the half twist along the lace between your fingers, tightening and loosening it as you like. Congratulation you have discovered another type of particle. Try adding another half-twist. How do the twist interact along the rope ? Did you succeed in making them disappear. And can you create a pair of particle out of nothing by twisting the lace in the middle ?
If it feels too easy for your 5-year old, you can now show him the belt trick to continuously rotate a cube attached by its faces https://en.wikipedia.org/wiki/File:Belt_Trick.ogv and he will have a better grasp on what an electron is than 99% of high-school students.
This analogy can be extended for more complicated kind of knots, twists, elements of lie algebras... And you can also extend it from the 1d case of the rope to 2d case of a fabric (twist along one dimension, twist along the other dimension...), 3d case.
If you want to learn more about physics, don't throw the lace away, you can play with it in a ton of different ways (vibrating modes of energy...), even before needing to introduce springs; but that's a story for another day.
I’m not sure if this is the same concept: There’s the idea that an observer, through something magical about consciousness, collapses a quantum state on observation, forcing the universe into that state. This sounds interesting until you realize the question: what is the speed of observation/collapse? And then the idea of an observer forcing a collapse doesn’t make sense anymore.
Which is fine and dandy if calculation is your goal.
If "understanding the nature of reality" is your goal then engaging with various interpretations of QM is unavoidable.
(which is not to say it will be fruitful. This stuff might be genuinely beyond the reach of science. We might be hitting the brick wall of the unknowable. But that's not an excuse to stop trying. Some current formulations of the question are probably meaningless or based on false premises but philosophy, theoretical physics and experimental physics creep forward hand in hand)
Contrary to what used to be hammered into people, it must be observed by the observer, that is, by you. Any random interaction will not trigger the collapse. An interaction must itself be observed by the observer, otherwise it will not cause a collapse.
It seems that the universe works pretty much as Haskell does. Things that don't matter to anything else do not happen.
It has nothing to do with consciousness, but the event must matter, or it doesn't happen. Even your consciousness only exist if it matters and will be observed.
For simplicity, let's assume that it's the wave function of an electron, but this applies to any particle.
The first problem is the question. What does "detection" means?
The technical term is "measurement", and the most important idea is that you can measure different things, for example the position of the electron, or the speed of the electron, or the energy of the electron, or ...
If you measure the exact position of an electron, the wave function collapses to a point.
But you can measure other thing, for example if it's inside a box or outside the box. In this case the wave function that initially is spread perhaps in all the universe, will collapse to a smaller wave function. In some cases to one that is completely inside the box, and in other cases one that is completely outside the box.
Knowing the initial wave function it's possible to know how the wave functions inside or outside the box will be, but the details are quite technical.
What is not possible to know if after the measurement you will get the wave function that is inside or outside the box. As fas as we know this is a random choice. Nobody likes it, some people thing there are not random rules, but most people think it's sadly random.
Note that the probability to get the wave function that is inside or outside the box are not equal. It may be la loaded "dice". The exact numbers can be calculated if you know the initial wave functions, but the details are quite technical.
Very informally, if the box is small, the probability of getting the wave function that is inside is small. If you have an electron inside the box and open it for a very short time and close it, then the probability of getting the wave function that is inside is big. To get a formal definition, you must read all the nasty technical details.
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The idea is that you can somehow detect that the electron is inside or outside the box, but it does not collapse the wave function completely. You still have a complicated wave function inside or outside the box. And you can make this wave function colide with other wave functions and get some weird quantum mechanics results that are impossible if you assume that the wave function has collapsed for a very short time to a single point inside or outside the box.
Or you can generalize this with two boxes and the rest of the universe. It's possible to measure if the electron is in box A, box B or outside. It's also possible to measure if the electron is in any box or outside. In this case you get entangled boxes that are even weirder.
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The experiment in the link use photon in a one or two slits experiment. The physical details are very different but the calculations and the idea is very similar. The box is the slide, and outside the box is the screen.