Yes.

You can actually do this experiment using a technique called ghost imaging.

What is interesting with ghost imaging is that you only need one double slit apparatus. The other entangled photon acts just as if there had been a double slit in its path.

Entangled photons obtained from a spontaneous parametric down conversion crystal are entangled in a number of different degrees of freedom. They are polarization entangled and momentum entangled. It is the momentum entanglement that is important for understanding the ghost imaging property.

Ghost imaging only works because you are detecting photon pairs, and the pairs must be momentum entangled. The double slit apparatus is a spatial filter that selects photons of a specific momentum. Because of the entanglement, the filter is actually selecting a property shared by both photons. That's how you get the ghost effect.

Using the ghost imaging effect, you can actually perform one of the “have your cake and eat it too”, types of experiment. You can detect one photon at the screen, where the interference fringes are formed, while detecting the other at the slits. Then you are effectively watching the slits and the screen with each pair detection.

So what do you see?

Each pair detection just results in a local point of light. On the slit side you see a detection in one or the other of the slits. On the screen side, you see a single point.

Have you really seen both the interference and the slit the photon passed through?

With a single detection pair you can't tell whether the detection on the screen corresponded to an interference pattern or not.

If you only select detections from the left slit, you find that after accumulating many detections, there is no interference. Same with the right slit. We could interpret this as the ghost arm detection collapsing the wavefunction.

Furthermore, if instead of looking at the ghost image of the slits, we erase all position information with a lens, then we find that after accumulating enough pair detections that we have an interference pattern.

Understanding how ghost imaging works can take some time. It's related to the property of the Fourier transform associated with momentum entanglement.

If you detect an entangled photon pair, they must have had a very precise momentum relationship. With photons, momentum corresponds to their direction of travel. Spatial location is a conjugate Fourier variable. Thus a photon with a well-defined direction of travel will not be spatially well defined. These properties can be used to understand ghost imaging. They also show that the particle picture of a photon can't apply. A photon only acts like a particle at the point of detection. It's best to consider the photon as a wave and use Fourier transform properties to understand the experiment.

Ghost imaging is a fascinating quantum technology using entangled photons. With a little lateral thinking, it can be used in a wide range of applications.

Ghost imaging - Wikipedia

Possibly.

Wavefunction collapse is an inference, as the wavefunction is related to the probability of obtaining a measurement result. This probability becomes an actuality on measurement, which means you need to update the wavefunction to one that reflects the actual measurement.

What you need to do is find a means of introducing this irreversibility into a mathematical formalism. One way to do this to consider entanglement with the environment that is unobserved. The environment is considered a state reservoir and the interaction with the reservoir is stochastic and irreversible. However, this stochastic and irreversible nature is an approximation. In particular, it is a locality approximation. That means the information of entanglement becomes irretrievably lost. This is called decoherence theory. It provides an effective mathematical formalism that uses entanglement to the environment to introduce the irrevsible element represented by the collapse. This is how you treat open quantum systems. Furthermore, one can also treat open quantum systems using the so-called quantum trajectory method, which specifically includes quantum jumps (wavefunction collapse). Both methods yield identical results, indicating that the entanglement with the environment approach is a way of introducing an effective collapse.

However, one should note that such open quantum systems approaches do employ approximations, and as such do not so much explain what a measurement is, but rather treats a measurement as something akin to a local approximation of a global system. In other words, the decoherence phenomenon is an apparent phenomenon for some local “observer” who doesn't have access to the non-local information of entanglement.

Answer: No.

Two points: 1. Collapse of the wave function is not an observable phenomenon. It’s an inference. 2. Photons do not “experience” time. The vacuum speed of light is not a valid rest frame, because it’s a frame that can never be at rest. That means that photons have no internal clock, which in turn means the internal degrees of freedom do not change.

Hold on to your hat, as I explain in more detail below…

The property of entanglement is an information property. The supposed collapse means that the information becomes apparent to an observer (only if they know that they are measuring an entangled photon). Thus if you know that you are measuring one of an entangled photon pair, and that pair have entangled polarizations, for example, then with a single measurement you can know the outcome of two measurements, given the prior knowledge. In fact, you only know the probable outcome of a second measurement, as the second measurement will most likely not have the same alignment as your experiment. It is that probability that indicates quantum entanglement, because quantum probabilities are calculated differently than classical probabilities. Thus you have the foundation of Bell’s inequality, which is a test of what is known as local realism. The nonlocality of quantum information violates this test because they result in probabilities that are different from what a classical theory would allow.

When a wave function collapses, it means that in your mind, you took one mathematical model of the universe, past, present and future included, which had the original wavefunction, trashed it, flushed it down the toilet, and replaced it with a different mathematical model of the universe, past, present and future included.

In the actual, physical world, nothing really changed. Sure, there was an interaction between two subsystems, one of which had a few degrees of freedom while the other had many uncorrelated degrees of freedom. The former, on account of its few degrees of freedom, is well described by Schrödinger’s equation. The latter, on account of its many uncorrelated degrees of freedom, is well described by classical physics.

Now we can’t really have both at the same time in the same, consistent set of equations, so one way or another, the mathematics has to give. One possibility is to accept the fundamentally nonlocal nature of quantum physics, and recognize that the Schrödinger equation may be constrained by future boundary conditions, such as the yet-to-happen interaction with the classical system. This has no observable consequences at present, in particular no violations of causality, but it does imply that the wavefunction evolves unitarily towards an eigenstate that will characterize its “measured” value when it interacts with the classical system.

Another possibility is to try to stay strictly local, reject the idea that the Schrödinger equation might be governed by a future boundary condition, let the wavefunction freely evolve towards that interaction which pretty much guarantees that it will not be in an eigenstate, and then “collapse” it into that eigenstate. The fact that this nonunitary “collapse” is mathematically ill-defined and far more dramatically nonlocal than the idea that the wavefunction is subject to a future boundary condition is then conveniently forgotten, or perhaps obscured by erudite philosophical discussions about the “measurement problem”.

Of course in the end, none of it matters, as it is all about how we, stupid humans, try to make sense of the equations. The only thing that actually does matter is whether or not the equations correctly describe reality. If it sounds dangerously close to the “shut up and calculate” school of philosophy, I am probably guilty as charged. But I am really just trying to be pragmatic here. Quantum physics is nonlocal, no matter how we try to twist it around. Bell’s theorem is what it is. How we make sense of it is our business. It does not affect the accuracy or validity of predictions, only our philosophical outlook concerning their “meaning”.

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The terms “measurement”, “observation” and “collapse” are merely summarized descriptions of a complex process of the quantum object interacting with the environment and the evolution of its superposition of states into a single surviving state that is now exposed to the environment. During that process and object that was in a supposition of, say, four states might change into three or two states but when it has reached only one state we declare it “fully collapsed”. As for which object will constitute a full collapse, a camera with 100% absorption rate will definitely collapse a photon but so would a chunk of black coal but there is a caveat for that coal. A mirror or a lens do not collapse the photon and even the coal might sometime let the photon pass nearby if the photon wave is abeam wider than the coal. What makes the camera a good example of nearly full collapse is the combination of a lens and an image screen. The lens focuses the photon into a small area in the image plane and the sensor thus absorbs the photon in a small area.

One of the critical misunderstandings concerning entanglement is the notion that the act of measurement somehow “causes” something to happen, especially something to happen at a distance.

So let us clarify a few things.

First, “entanglement” is not about A being entangled with B, our persistent misuse of the language notwithstanding. For starters, by default everything is entangled with everything else. When we casually discuss, say, an “entangled pair of photons”, what we really mean is that we somehow established an experiment in which those two photons are (at least temporarily) isolated from the environment, so they are only entangled with each other for the duration of that experiment.

Second, putting aside theories that postulate “objective collapse”, the act of measurement doesn’t do anything. It does not collapse any quantum state. The collapse of the wavefunction is a useful mathematical model, not a physical process. When we look at what the actual equations (Schrödinger’s) say, if we introduce into the system the notion of a “classical” instrument with which the measurement is being made, that instrument constrains the system, even if the actual measurement takes place in the future. This is really what it means when we are told (e.g., by virtue of Bell’s theorem) that the quantum theory is “non-local”.

And third, quantities related to entanglement must not be viewed as properties of one photon or another. This really is the most critical aspect of nonlocality. The conserved quantities in entanglement experiments are properties of the system, not of any individual particles. So we know, say, the total angular momentum of the system. We measure the angular momentum of one part of the system (e.g., a photon). That means that we know with certainty (because the quantity is absolutely conserved) the angular momentum of the rest of the system. When the rest of the system happens to be just a single photon, it means that all that remaining angular momentum “belongs” to that (second) photon. But it’s not because anything happened to that second photon as a result of us measuring the first photon.

Lastly, relativity theory has nothing to do with this at least not directly. These qualities of the quantum theory remain the same in both nonrelativistic and relativistic formulations. Of course when it comes to relativity theory, we are more concerned about influences that appear to travel faster than the vacuum speed of light. But, and I hope that I was able to clarify it at least a little bit, no influences travel whatsoever when parts of an entangled system are measured. The quantities involved do not travel; they are nonlocal to begin with, characterizing the system, not any individual particle in that system.

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Photons don’t have wavefunctions. Wavefunctions aren’t real things out there in the real world, they’re algebraic objects constructed in order that we can talk sensibly about parameters that have no definite values so that we can make predictions about what will happen in interactions. It’s something that quantum-mechanical operators act on.

Photons, and indeed all “particles”*, propagate in a manner that’s well modelled by the mathematics of waves, with a lot of the same features, like uncertainty, and superposition. Superposition sounds odd, but it just means that if you take a wave and another wave and add them together, you get a wave. The inverse of this is that any wave can be constructed as a sum of other waves and, ultimately, as a sum of sines and cosines.

The wavefunction is a complete description of the system, but it’s only a description. We evolve the wavefunction forward in time using the Schrödinger Equation (basically a quantum-mechanical version of all our conservation laws) and it gives us a distribution of probability density for, say, where a particle will be found. The wavefunction is in a superposition of all those places, with a given probability density that must normalise to 1 (because 1 is certainty, for a given statistical value of ‘certainty’, and because the particle had damned well better be somewhere).

When the particle actually hits something, all the other probabilities vanish, because we know where the particle is, because it’s right there where we registered it. The wavefunction now describes a single location with probability 1. That, right there, is what was canonically known as collapse of the wavefunction.

It’s really important to note that this term is really not well-regarded n modern theory, because we’ve moved on. It was a product of the earliest ontology of QM, and a poor description. We are so loaded with linguistic and terminological baggage from the Copenhagen days that it’s pervaded the public consciousness virally, and it’s really not helpful language. Nowadays we talk about decoherence. Decoherence is simple enough to grasp, if you’ve ever listened to a band and heard somebody play a bum note.

*There are no particles, an d no waves; there’s something else with behaviour that we associate with particles and waves respectively depending on the nature of our interaction with them.

When entanglement of two or more photons is being described, the wavefunction that collapses is the multi-photon wavefunction, not just the part of the wavefunction describing a single photon. Furthermore, wavefunctions and their collapse are parts of calculations. While I expect almost all physicists to feel as if there's something in the real world corresponding to the wavefunction, a similar feeling about collapse isn't so widespread. Some physicists think wavefunction collapse corresponds to a process in the real world, and others have another explanation for why it's ok to include it in a calculation. In either case, calculations are done by people, not photons. Suppose, for example, a calculation involves collapsing a wavefunction after dividing it by [math]\sqrt{2}[/math]. It makes no more sense to suppose a photon can collapse its wavefunction than to suppose it can divide its wavefunction by [math]\sqrt{2}[/math].

The particles are said to be in a superposition state because the wave function is but a statistical distribution of the states that an N-particle system finds itself in. When we observe any one particle, we find the obvious – that it has a well defined state – and so we discard all the other possible states. While early Schrödinger and Heisenberg formulations of quantum mechanics imply superposition is present in every particle singularly, the more modern Feynman path integral formulation of quantum mechanics shows that the trajectories of single particles are well defined and that all the possible paths are what make up the wave function.

One could argue my reasoning contains an ambiguity: Since spin operators in orthogonal directions do not commute, two consecutive, orthogonally polarized Stern-Gerlach apparatuses will yield different results depending on the order in which they are placed; hence implying observation does affect physical measurements. At first sight, this result may seem to work against the statistical argument aforementioned. However, using Feynman’s interpretation, we see that particles following different paths interfere with one another. The first Stern-Gerlach apparatus “filters out” some possible paths, hence changing the subsequent interference phenomena between the particles that reach the second Stern-Gerlach apparatus.

This creates the illusion that observing the system changes the state of the particles, when what is really happening is that the observed state is a result of the interference of the system’s eigenstates. Filtering out some of these eigenstates produces a different interference pattern.

An analogy we could use to exemplify this is the shadow cast by a rotating rectangular plane. Starting off with the rectangle parallel to the surface where the shadow is projected: If we first rotate the plane vertically and then horizontally with respect to the axis orthogonal to the projection surface, the shadow is a short vertical line. If we reverse the order of these two rotations, the shadow is a long horizontal line. This example does not only work as an intuitive analogy, but also as a rigorous mathematical framework for why spin operators in particular do not commute – “measuring” in quantum mechanics is defined as projecting the state vector onto the eigenbasis of the operator being measured.

Yes, two particles can become entangled by interacting with other particles even if not directly interacting with each other. The entanglement can be broken in just the same way as if it came about any other way.

This kind of thing will become much more familiar when quantum computing is common. Suppose we have just three qubits. One basic operation is to swap two qubits. Another is to do a flip of one bit based on another one, so that if they start out as having the bits [math]00[/math] or [math]10[/math] they don't change, but if they are [math]01[/math] they become [math]11[/math] and vice-versa. Those operations make just as much sense for a classical computer but they can do interesting things in a quantum computer.

So imagine we have a first qubits that is way to the west, a second qubit that is portable, and a third that is way to the east. We first flip first bit conditioned on the second one, then carry the second bit over to the third bit where we arrange to exchange their values. So if the qubits start out as [math]000[/math] or [math]100[/math]they just stay that way. The first bit is not flipped and the second and third were just the same anyway. If we start with [math]010[/math] we first flip the first bit to get [math]110[/math] then exchange the other two to get [math]101[/math].

Now say we decide actually to use the quantum properties of the qubits. Set the first one third qubits to [math]0[/math], but put the second bit into a quantum superposition of [math]0[/math] and [math]1[/math]. After we go through our two operations, we have the three qubits in a superposition of [math]000[/math] and [math]101[/math]. The first and third qubits are now entangled.

The entanglement can be undone in this example by reversing the process. Each of the steps is reversible.

Alternatively the first and third qubits can stop being entangled with each other by interacting with the environment, perhaps by our measuring whether the qubit is zero or one. Exactly what happens to cause the qubits to stop being entangled is a point of disagreement between views about quantum mechanics.

In some cases the qubits stop being entangled with each other because they have become entangled with something else. This could happen without a measurement. Suppose we bring in a fourth qubit and flip it based on the third. Technically this makes the first and third stop having a pairwise entanglement.

Others would say that if the interaction is a measurement, it collapses the wavefunction of the system which eliminates the entanglement.

I described the hypothetical situation in terms of qubits, but in principle the qubits could be the spin states of particles.

Think about it this way. There is an electron pair. These electrons have a spin vector that can virtually point in any direction in space. They have a spin direction but we don’t know what it is. It can point in 1 o’clock 2, 3,…….12 o’clock direction. This is called superposition. The only thing we know is the the two spin directions are exactly the opposite.

We send one of these electrons through a machine to determine its spin direction. This machine has a vertical magnetic field in 12–6 o’clock direction. When we send our electron with the unknown spin direction though this magnetic field three things can happen:

1. If the pre-measurement spin direction of our electron was somewhere above the horizontal, the vertical magnetic field will always reorient it to the 12 o’clock position.
2. If the pre-measurement spin direction of our electron was somewhere below the horizontal, the vertical magnetic field will always reorient it to the 6 o’clock position.
3. If the pre-measurement spin direction of our electron was was right on the horizontal, the vertical magnetic field will randomly reorient it to either the 12 or 6 o’clock position.
4. Same is valid for the other electron as well except in the exact opposite direction. And this is what creates the correlation between the outcome of the two measurements, not some spooky action at a distance.

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Good question! If there is no interaction with environment (interaction Hamiltonian is zero) then this will be the eigenstate and will remain that for ever according to Schrodinger equation. But this rarely if ever happens. The moment H(int) is non zero, it starts evolving according to the Schrodinger equation until you make the next measurement which will put it into a new eigenstate. So the answer to the second question is no. Repeated measurement gives you probabilistic results. As an example suppose you have a spin wave function 0.6 (spin+1/2) + 0.8 (spin -1/2) and the first measurement gives +1/2, next one will give randomly +1/2 or -1/2. But QM assures you that if you do the experiment say a million times, 360,000 times you will get +1/2 and 640,000 times you will get -1/2.

No, this won’t work. How does Alice know that Bob collapsed his particles? She’d have to look at them, which would collapse them.

Imagine this. You have an idea on how to communicate faster than light. You make four envelopes in two pairs. Each pair has a one or a zero. Bob takes two envelopes, one from each pair, and heads to Tau Ceti.

When he gets there after 11 years, Alice opens both her envelopes and sees a 1 and a 1. Now she knows that Bob must have a 0 and a 0. And when Bob opens his envelopes at Tau Ceti, he knows that Alice as a 1 and a 1.

But no information was transmitted faster than light. And Alice can open either one or two envelopes, but there is no way for Bob to know whether she opened one or two. No information is transmitted by opening or not opening the envelopes.

Yes… quantum entanglement does exist, and some quantum entangled sub particles do have strange polarization properties, or at least some sort of properties that are somewhat similar to polarization properties, but not really polarization properties.

I discovered these strange polarization-like properties one day while I was experimenting with quantum entanglement. No one has ever discovered this strange polarization-like property that exists when quantum entanglement exists, or I would have read about or heard about it.

This strange polarization-like property that I discovered in Nature, can be flip-flopped back and forth multiple times, in a short duration, and it always works. In polarization the waves of light are blocked out coming from a vertical component or a horizontal component depending on how you are using the polarized lens, and if you are using two polarized lenses at 90 degrees to each other it blocks out all light.

The new strange polarization-like property that I discovered years ago doesn’t need polarized lenses in order to change from one type of strange polarization-like property to another. What happens, is that the strange polarization-like properties are changed electromagnetically instead of with a lens, and it takes place at the speed of light.

For instance, if I aim my camera at anything, and then change the polarization-like property of the camera, it will suddenly show something else that exists in the filming of whatever it was filming, but without having used any type of special lens or polarized lens. I simple blanket the image, and there is something else hidden within the original image that suddenly appears within the image that can’t be seen otherwise in the image. Many times, there are multiple things discovered within the image that couldn’t be seen otherwise.

In other words, it's basically filming another dimension to what we see originally. No matter how many times I flip it back and forth, both films are just a little different from the other, but they are always the same for each dimension when viewed. It’s very interesting to see something else exists within the film, besides what we see with our own eyes while filming.

That is an excellent question! it was the apparent instantaneous nature of the collapse that fueled Einstein’s most constant complaint about Copenhagen-style quantum theory: the “Spooky action-at-a-distance”. He thought it would plainly violate relativity. Einstein wanted to remove any real physical collapse in favor of a mere epistemic change in the information one has about a system. That was what he was arguing for in the famous EPR paper, but in order to do that you have to admit that the quantum wavefunction of a system does not provide a complete physical description, so that there are some unknown facts about it you can come to know and then conditionalize on. Bohr and company (along with most contemporary physicists) want to insist on the completeness of the wavefunction, and so cannot consistently regard the collapse in this way. How they do regard it is—to say the least—unclear.

Einstein, of course, wanted a completely Relativistically local physics, but the observed violations of Bell’s inequality (which he knew nothing about, of course) rules that out.

The simple way to implement collapse physically is indeed to violate Relativity and postulate a preferred foliation in space-time. Trying is get away without that is possible, but rather artificial and tricky.

Sorry, we don’t do popular, only what works.

A wave function as a particle perturbation consists of a change function and a magnitude containing a sequence of absorption information. The change function allows for two spaces, each space being defined sequentially by the EMR-EMA information in that magnitude.

Understanding this, you can collapse or change the wave function several ways, none of which are reversible.

1. Each change function has a chiral anti-form that will neutralize it causing the wave to propagate as light.
2. You can use a charge potential (an identity with an available matching charge space) to steal the energy from the change function to observe it. Stealing it naturally subjects it to the information and change conditions of another identity.
3. You can subject the wave function to another wave or field function causing their fields to interfere and modify each other seeking an information and energy equilibrium. While this won’t collapse the wave necessarily, it will irretrievably alter it.
4. A virtual particle fitting the wave-particle description is dependent on the conditions perturbing its existence. Take away any element of those conditions and you will either alter the perturbation to something else or eliminate it altogether.

A tough question. It really shouldn’t be tough but…

There is a school of thought, under the heading “objective collapse”, that views wavefunction collapse as a physical process. Of course that becomes a thorny concept. Technically, when we look at the equations themselves, “collapse” quite literally means taking the entire universe, its present, its future, and its past included, throwing it away, replacing it with a different universe in which the original wavefunction is replaced by a wavefunction representing the collapsed eigenstate. So it’s more than instantaneous: it is retroactive!

Of course folks advocating “objective collapse” know this, so they have proposed various more subtle mechanisms that avoid this extreme interpretation.

But in mainstream interpretations of quantum mechanics, wavefunction collapse is not viewed as a physical process. The interaction between a quantum system and a classical “instrument” is necessarily an idealized model since no instrument is truly classical: a measuring apparatus, a video camera, a cat, even a human consists of a finite number of quantum particles after all. So maybe wavefunction collapse is just a piece of fiction that arises because we approximate that camera, cat or human by an idealized, classical representation.

All this takes us to the core of quantum physics: Namely that the theory is inherently nonlocal. Nonlocal in this context means that the physical system is governed, in part, by variables that cannot be nailed down to any specific point in space and time. These variables, e.g., some conserved quantities, are kind of ephemeral, representing the system as a whole, not any specific bits and parts of it at specific places and times.

This might indeed raise valid concerns about causality! But this is where something almost miraculous occurs when we take quantum physics to the next level, relativistic quantum field theory. Even though the theory is fundamentally nonlocal, any faster-than-light, backward-in-time influences in the system are canceled out exactly, leaving us with a theory that is manifestly nonlocal yet causal. Take two correlated electrons a great distance apart. They cannot communicate. Individually, their behavior is strictly random. It’s only after we observe them and bring the results together by conventional means or signals that we notice that they are correlated. No detectable influence passes between the electrons. One does not “cause” the other to behave in a certain way. The behavior of the two-electron system, however, is governed by those nonlocal variables that cannot be nailed down to either electron or any specific location or time.

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You have to be very careful with words like ‘exists’ and ‘collapses into a single physical form’, these are human terms linked to intuition. Also, quantum mechanics is not about ‘waves of possibilities’.

Let’s try this, sticking to quantum mechanics and not quantum field theory, which makes things a bit harder. But for normal things like a single electron in an atom, quantum mechanics is very accurate

• The electron exists. It exists all the time, it has charge and a lepton number and these are conserved in the universe. So the electron does not flit in and out of existence
• The electron is NOT a small lump of something. That is a intuition from human experience. You may have learned in classical mechanics that things are described by their mass and where they are in space and which velocity they have. That is not true in real life and only an approximation (but an excellent one for anything larger than a virus or so)
• A particle is instead described by a wave function, which is a complex function of space and time. Almost any wave function is a valid wave function, and the Schroedinger equation describes how that wave function evolves over time
• You may have heard that the square of the wavefunction (absolute value) at a point is the probability of finding the particle at that point. That is correct. But if you find it it does not mean that ‘the particle happened to be there at that moment’. Instead, this is a measuring process, which collapses the wave function into one where the amplitude in 1 (certainty) at that point and zero everywhere else. We then call that a ‘localized wave function’ and it describes that the particle is for sure at that point.
• But the particle is still described by the overall wave function. A wave function that is smeared out broadly still is the electron. It is very confusing to say - but frequently said in physics books for the general audience - that the particle is in multiple places at the same time. The particle wave function is non-zero in many places. But there is no ‘lump of stuff’ in multiple places. The electron is simply ‘spread out’.

It is very counter intuitive, but nature does not feel a need to follow our intuition.

Let's just take the most widely used source of entangled photons, called spontaneous parametric down conversion. This process is simpler than it sounds. A single photon enters a special crystal (called a nonlinear crystal) that induces the single photon to split into two photons of lower energy. Then the conservation of energy, momentum and angular momentum must be satisfied. That means that the converted pair are not independent of eachother. They share a common property that they together must satisfy the conservation laws. However, considered independently, they exhibit no evidence that they were emitted as part of a conserved process. They just look like any single photon. Therefore, the evidence that the two photons were emitted as part of a conserved process is a property that only becomes evident when both photons are detected and the results compared.

The entanglement is the property that the state of one photon will in fact determine the state of the other due to the requirement that the conservation laws must be satisfied.

If the state of the each photon were independent of the state of the other, there would be a violation of a range of conservation laws, which would be even bigger news and shatter our knowledge of physics as we currently understand it.

The conservation laws are a pillar of modern physics and really the origin of entanglement. The seemingly weird properties come from quantum mechanics.

Schrödinger's cat satire conveyed the message that there is no physics behind the imaginary superpositions and collapse/decoherences Born made up to make his 1926 probabilistic estimates seem more realistic. Born's probabilistic estimates are very useful, but the probabilities are not inherent in quantum mechanics itself: they're consequences of the electrodynamic incompleteness of all the Q.M. models so far. The 1910-1928 models are all purely electrostatic, and Born's probabilistic estimates give us at least some idea of the outcomes of the so-far entirely unmodeled atomic transitions: the electrodynamic energy exchanges between real bound atomic electrons and their surrounding electromagnetic field. Until we have an electrodynamically complete quantum mechanics able to render the dynamics of the electron-proton interaction, we can be grateful both for Schrödinger's deterministic but purely electrostatic hydrogen model and for Born's probabilistic estimates of possible outcomes of the so-far unmodeled electrodynamical energy exchanges.

The state of an isolated physical system at any moment determines the state of the system over the entire time span of the system (Boscovitch 1758; Laplace 1814). This isn’t as good as it looks. You have to maintain the isolation, and the system must have a sufficiently small number of degrees of freedom that you can keep track of everything at some moment. Small isolated quantum mechanical systems with only a few degrees of freedom are ideal for this purpose: that’s entanglement

A2A With “quantum collapse”, you mean the “collapse of the wavefunction”. In quantum mechanics system can be in a superposition of states. But, when you do a measurement only one of the states will be measured at a time, never two or more. This is meant with the “collapse of the wavefunction”.

Having a system prepared in a superposition one can ask how long it would usually take for it to evolve from a superpositon into a single (observable) state. This depends on many factors. What triggers this “collapse” is any interaction with the environment. This is much easier for macroscopic systems than for subatomic systems. A typical time is called the decoherence time. For a system of one gram at room temperature on length scales of one centimetre this time is very short, in the order of [math]10^{-40}[/math] seconds or less. Only for very small systems and/or at very low temperatures a superposition of states can be maintained for a long time.

In this text I put “collapse” in quotes because this term is quite ambiguous.

As others have said, the “collapse" is not a physical phenomenon. That's because the wavefunction cannot be directly measured, just inferred. What happens, when you measure one of an entangled pair, is that you gain knowledge about the possible measurement result of the entangled partner. However, that partner may never be measured. Moreover, if it is measured, the type of measurement may be different so that the measurement result is not even correlated. In any case, the agents making the measurements have no indication that another measurement may have been made. The only thing that really happens is that IF you know the particle is one of an entangled pair, then you know that your measurement will be correlated with the measurement result of the second particle. However, because you can't determine your measurement result, neither can you determine the correlated result. That's why you can't use the process to send information.

The whole point of entanglement is that the particles don’t have independent states. There is no such thing as “the state of particle 1” or “the state of particle 2”. A single state describes the system consisting of both particles, and it can’t be divided up. So, when you make any measurement on one particle, either partially or totally collapsing the wavefunction for the whole system, it affects the probability distribution for what will be measured for the other particle immediately.

You mention elsewhere the common misconception that this could somehow allow instantaneous communication. I have explained why this can’t work as part of Erik Anson's answer to Who can explain the no-go theorems in quantum mechanics in a simple way for someone with a basic knowledge of quantum mechanics?

This question posits two things: Objective reality of the wavefunction and that of the measurement.

If the wavefunction were to be some more abstract concept, such as a representation of all possible knowledge of a system and a measurement is then a process of retrieving knowledge, then what is it that is collapsing?

We can build an epistemic theory based on a few axioms, which is quantum mechanics. Here we're not concerned about the nature of reality, but just what we can know about it. By taking this approach, we skirt many of the really big questions. However, the wavefunction here is not considered as much more than an accounting tool.

I think it's wise to get off the bus at this stop. Indeed many of the people working on quantum information theory and quantum computing are pretty happy at this juncture. Pragmatically this is the place where you can actually do something with quantum mechanics.

The epistemic stop is also where decoherence theory explains the different behaviours of open and closed quantum systems. That is to say that decoherence theory offers less in the way of an explanation, than just an alternative calculation tool for open quantum systems. The epistemic stop treats quantum mechanics as the ultimate limit to measurement.

We don't need to ask if the wavefunction is real for quantum mechanics to work.

The problem is somehow related to the actual concept of a measurement. If we accept measurement axiomatically, then we have already gotten off at the epistemic stop.

There is a hell of a lot of literature on the topic of how measurements relate to and interface with reality. Much of it is philosophical and I am unfamiliar with it. Therefore I can only offer you some of my thoughts on this topic.

Quantum mechanics rests as the fundamental theory that describes reality. The problem seems to be that that implies that quantum mechanics must be self-referential. If that is so then just what is a measurement? Can a system measure itself? Exactly what is knowledge or information? These are really deep questions.

Physics has dealt with self-referential concepts before. In particular there is the self-interaction, which lies at the heart of renormalization theory. That was a major challenge that unlocked some of the most exciting physics of the mid to late 20th century.

The ontology of quantum mechanics is probably the greatest renormalization challenge remaining for the foundations of physics. If the success of the past renormalization efforts are anything to go by, a similar success with this foundational concept might unlock some major insight into the universe. Who knows?

Entanglement and Quantum collapse are terms that are used to describe an aspect of quantum theory. As an example, there are devices that generate pairs of photons. The net angular momentum of the pair is zero in order to conserve angular momentum.

Now it is possible to send each photon to destinations that are far apart, for example in space say 20 light minutes apart. Then at each destination, if we set up measuring devices to measure their spins, we find that angular momentum is indeed conserved, they will have opposite spins. So, you may then think that only goes to demonstrate that their actual spins were determined at the emission end.

But no, it is possible to measure photon spins not only along the direction of travel but along any direction in 3D space and when we do that, again we get perfect correlation provided both ends are measuring the spin on the same axis.

Now suppose each end point chooses to measure the spins choosing one of three perpendicular axes chosen randomly while the photons are in that twenty-minute flight. Again, we get perfect correlation when both ends chose the same axis and zero correlation otherwise.

This example demonstrates that the spins could not have been determined in advance at the source end and the two photon spins are said to be entangled. As a way of describing what happens, physicists describe this as entanglement and in terms of the wave particle duality as a wave collapsing at the time of measurement and becoming a particle.

So, in terms of that way of modelling the wave particle duality, the answer to the question that entanglement and collapse are part of the same model, so no not in this model.

It may be helpful when thinking about this to understand the role of the arrow of time. Time has a direction where there is increasing disorder, and physicists call this increasing entropy. For the universe at large the arrow goes in one direction. But when you zoom on very small parts aspects of this universe, there are situations where there is no arrow and even situations that can only be described as an arrow going in the opposite direction.

So, returning to the two photons in their twenty-minute flights, there is no arrow of time, there is perfect correlation between ends points, but no way for us to exploit that correlation, e.g. by sending a message back in time and use that information to make a winning bet.

No. The question itself is based on a flawed premise. In order to see diffraction, you need to know the phase difference between the slits. e.g. Diffraction requires a point source. But entanglement itself makes that an unknown. The uncertainty of where the entanglement happens is at least one wavelength. So you cannot run a diffraction experiment on both photons.

If you choose to run a diffraction experiment on a photon you can’t measure the phase difference first without ending the entanglement.

The only potential loophole is if you assumed the wave states could continue to evolve the same way after passing through a coherence filter. (e.g. a pin hole). But the No-cloning theorem tells us the quantum states will evolve independently.

There is a no collapse from one to the other. I have thought of a very simple, and obvious statement that clarifies this quickly:

You cannot entangle a state and still know the value of that state.

We cannot entangle phase of the two photons, and still know the phase of the two photons.

Lets take a look at how diffraction works:

I know it looks complicated, but notice on the left it shows the wave has a 0 degree phase difference between the two slits. To get the pattern on the screen, you need the paths to either slit to have a constant phase difference. If is a 0 degree difference you get the pattern shown. If it is a 180 degree difference then you get a complimentary pattern, where the bright and dark areas are swapped. If you overlay these two patterns on-top of each other, you see no diffraction pattern.

After you entangle produce a pair of entangled photons, you no longer know what the phase difference will be at the double slits because that property has been entangled. So you will not see a diffraction pattern on either screen.

Quantum entanglement tells us one, and only one thing. Measurements of the same value must be consistent. No matter which of the entangled particles you measure first, the measurement of the second will be consistent with what you would expect for a second measurement of the other. But here is a key point, if you don’t know the initial state, then the order of which photon is measured first does not matter.

Entanglement made the phase difference unknown so in order to see the pattern you need to measure that phase difference with one of the two photons. Then you can separate out the two complementary patterns and see the interference pattern with the other photon. The interference patterns exist always exist, if you have a way to sort them. There is no sudden “collapse” where suddenly you can see a pattern. This requires build the image photon by photon, typically with a digital device that recorded the where and when each photon was detected.

Something that gets really confusing, is something like the delayed quantum eraser experiment, the experimenters did not intend to measure the phase difference. But if you examine there setup closely, you’ll realise that is exactly what they did for the photons they did not measure which slit instead.

Now perhaps this image by Stigmatella aurantiaca - Own work, CC BY-SA 3.0 makes sense:

R01 is measuring building the image for the in-phase at the slits photons, and R02 is build the out of phase image. R03 and R04 are the overlap of the two patterns because those respective measurements did not tell us the phase difference.

Mark John Fernee brings up the interesting concept of ghost imaging and ghost diffraction. Ghost imaging is very easy to explain without the need to “collapse” the other wave function. After entanglement, you don’t know where the photons will hit the screens. That is an entangled property. But you do know they are correlated. So if you measure where one photon his the screen, that should tell you where the other photon will hit its screen. You form the image simply by which photons are reflected. So you are filtering based from one set of photons that hit the screen in certain location to another set to hit the screen in the same location.

So again, ghost imaging just proves that initial state of each photon is same. There is no evidence the states will not evolve independently.

Now ghost diffraction sounds more complicated. Because that is replicating the results of one weak measurement, onto the screen of the other. That does seem to imply both a transfer of information, and a violation of the no cloning theorem. However, I can find no reference to such an experiment having been performed. The only reference I could find is:

Experimental Limits of Ghost Diffraction: Popper’s Thought Experiment

Which is describing a thought experiment, not an actual set of observed results. If someone can find a link to an actual experiment, if the results mean what we think it means that changes everything!

If I understand the question correctly, no, you can't - if you only have one of the particles, you can't detect that the other one has been measured (this would allow you to use entanglement for FTL communication, or, indeed, for communication!). Both parties just get random results, and it is only through comparing the results that it can be determined that there has been entanglement at all.

But if you mean when you're in possession of both particles and just want to know whether decoherence has occurred, then yes - you'll see outcomes as if you're just sampling two uncorrelated random variables, instead of the correlated results that you see when there's entanglement.

The nature of wave function collapse is a matter of interpretation, and understanding it is a key aspect of the measurement problem of quantum mechanics. Some interpretations assert that there is no collapse at all: what appears as collapse is actually a result of decoherence. The phenomenon of decoherence provides a mechanism for understanding how, due to coupling of the system with the environment, the coherence of the system's wave function becomes for all practical purposes unobservable. However, the coherence can not actually be completely destroyed or lost by means of a continuous evolution in accordance with the Schrödinger equation. More importantly, decoherence merely produces improper mixtures (which can not be interpreted as reflecting our ignorance of an actual pure state). It can not produce a proper mixed state. Thus, decoherence alone does not provide a solution to the measurement problem, as it does not result in an actual collapse.

In the Copenhagen interpretation, and various other interpretations, wave function collapse is a discontinuous change in the state of a quantum system associated with measurement. In contrast with the continuous evolution of the wave function of an unobserved system according to the Schrödinger equation which produces a superposition of different states, when a system is observed it is not found to be in a superposition but in a single state (e.g., Schrödinger's cat is observed to be either dead or alive, but not a superposition of dead and alive states). The collapse of the wave function is the term used to describe this discontinuous transition from a coherent superposition of states to a single state upon measurement. It is an explicit violation of the Schrödinger equation and is associated with the fact that the system has been measured by an apparatus that is, by definition, not part of the quantum system. To study the measurement process as a physical process would require including the measurement apparatus in the system to form a composite system whose wave function does not collapse until it is measured by another measurement apparatus. So, collapse can never be treated as a physical process within a physical system, according to these interpretations.

Penrose has proposed that collapse is an objective event related to gravity, but that implies new physics of quantum gravity, and is highly speculative at this point.