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Does the measurement of the particle change it's physical state? Or does it only seem to do that?
Ex. if a particle was measured before the slits, would we see an interference pattern, or a particle pattern?
And if the wave function is physically collapsed does it say like that forever or does it ever revert back to it's "superposition" state.
Quantum mechanical entities are described by solutions of the Schrodinger equation, the wave function, with specific boundary conditions. A measurement changes the boundary conditions and thus the subsequent wavefunction describing the particle measured will be a different one.
A measurement picks an instant from the probability distribution describing the entity, and this is called "collapse" to confuse people. It is one entry in a distribution
Lets take the simple example of the harmonic oscillator:
On the right is the square of the wave function, and one sees oscilations in the probability distribution in the displacement x.
Suppose we have one atom the electron's dependence described by a harmonic oscillator . If we measure the displacement, it means we probed the atom and we will get one value in the distribution. A second atom will give a second point etc, and we will develop histograms that will have the shapes on the right. Each atom-electron after the measurement will be described by different wavefunctions because the boundary conditions will have changed, for example "scattered out" , "on a different energy level, etc. It will be very hard to follow what happens collectively from then on to determine the new probability functions because the boundary conditions will depend on the scatter.
Measurements of elementary particles, quantum mechanical entities, usually manifest the particle side . In this electron double slit one at a time one sees the particle
as it leaves a spot on the screen, and each spot with its relevant probability looks random. The accumulation of spots though shows that the probability of finding the screen has a wave nature. This is analogous to the example above. When the electron hits the screen the problem changes because the boundary conditions change due to the screen
Ex. if a particle was measured before the slits, would we see an interference pattern, or a particle pattern?
It will depend on the boundary conditions of the measurements before. If it is a screen it is self evident . If the experiment is set up that the boundary conditions after the first measure allow again a coherent wavefunction plot with the boundary conditions of "two slits electron" the experiment will be the same as in the picture. There have been experiments interfering with the incoming beam statistically and maybe you can understand them.
And if the wave function is physically collapsed does it say like that forever or does it ever revert back to it's "superposition" state.
It always hinges on boundary conditions of the experiment changing the wavefunction solutions relevant to the experiment.
The double slit experiment basically shows these results, which is quite extraordinary in my view.
If an electron is fired from a gun one at a time towards a double slit, we will see interference pattern (vertical bars), which kind of shows what water wave will show if it hits a shore for instance. Because of interference, some systematic areas on the board are much higher because waves are interfering and interfered areas have high probability of catching the electron.
Here is the tricky part.
Because the sheet behind the slits are trying to measure the electron, the sheet itself collapses the wave like nature of the electron, and nature says since it hit the sheet/detector, wave function collapsed and electron acted like an object. Looking at the electron while in flight, it exactly appears like one electron. When not looking at the electron while in flight, the electron is everywhere at the same time and interfered with itself (because it is at all possible locations at the same time in flight, kind of like a wave) at the same time and landed/wave function collapsed on the back detector.
I think therefore in my opinion not observing the electron, the electron is a wave. Once it collapses on the sheet/detector, it is over and collapsed. But if the electron went through the sheet/detector and detector catched the electron at (X, Y) coordinate and flew out the other end and we not measure that passed through electron, the wave function is again back. I think this WFC is a reaction to observation. When not observing, it will revert back in my opinion. WFC is not the end, it reacted to observation bounced back and reverted to its superposition of states and continue. The critical thing is observation is measurement. I look at a chair and see that this chair is this far from the table and this far from the wall, which is observation and it is measurement. But according to quantum mechanics, this chair is at all the place at the same time when I turn around and instantly collapses to one chair when I look (from this distances from table and wall), in my humble opinion.
According to Quantum mechanics a particle exists in a state $|{\Psi}\rangle$ which belongs to a hilbert space of states. When you make a measurement, you act on the state with an operator, say $A$. And by doing this you project the state $|{\Psi}\rangle$ onto the subspace spanned by the eigenvectors of $A$, so now your state is one of the eigenvectors of $A$ with a corresponding value of the measurement being the eigenvalue corresponding to that eigenvector. So your state has now changed to $|A\rangle$.
No a measurement doesn't have to change the state of the system, but it has to at least has the possibility to change the apparatus; otherwise you wouldn't call it measurement. The change to the environment(the apparatus , the scientist and everything that interact with it) is what cause you to lose interference pattern. This is usually called decoherence procedure and a large number of publications are available.
If you do not like to think about it inside the system/ environment scheme, you can also look at it this way: Wave function is the function of coordinates of all particles. In simple terms, to interfere all particles have to line up at the same time, and this includes all the particles on the apparatus. Say there are two possible states of the system, and you make a measurement and get definite information, then in the two schemes particles in your apparatus will very likely be in different places, and when you try to interfere the system there'll be no coherence . On the other limit, if the apparatus are the same in both schemes, then you likely don't know anything from the measurement. A real measurement is usually somewhere in between.
Does the measurement of the particle change it's physical state?
A measurement, as an evaluation of given observational data, does not have any direct physical effect other than being accompanied by a change of state by whoever carries out the evaluation; the state changing from not yet knowing the result value (or indeed whether one could be obtained at all), into knowing the value (or knowing that the given observational data is insufficient or unsuitable for a successful evaluation). As a comprehensive example consider
Consider as an example the measurement of the invariant mass of a (short-lived) particle which had been produced and which decayed within a particle detector: its decay products must have been identified by analyzing the detector data collected for the recorded event under consideration, their energies and momenta are (generally) determined separately, and finally the evaluation of the quantity to be measured.
Changes of state (such as "decay", or various "interactions") are instead generally involved in the generation and collection of observational data.
Ex. if a particle was measured before the slits, would we see an interference pattern, or a particle pattern?
Considering experiments in which particles are emitted by a source and being detected (and spatially resolved on) a screen, obviously it should be possible to conclude (as a measured result) that each such particle had been emitted initially at the source; regardless of which pattern would eventually be determined at the screen.
And if the wave function is physically collapsed [...]
A specific wave function serves as a statistical representation of (consistent, "coherent") observational data, usually involving numerous individual trials. Speaking of any individual trial as "a collapse" doesn't add to this understanding.
