Quantum Mechanics is a set of laws that govern the really small, the realm of particles. It is a strange world were nothing is certain, particles taking multiple ways at once, things not being anywhere but just having probabilities to be in one place or another.

Introduction to the problems that lead to quantum mechanics

Black body radiation

The spiralling electron

The photoelectric effect

The Compton effect

The solutions to the problems

Black body radiation

The spiralling electron

The photoelectric effect

The Compton effect

Wave/particle duality

The world of probabilities

The heisenberg uncertainty principal

The wave function

The EPR paradox and Bell's theorem

Quantum tunneling

Electron orbital

The delayed choice experiment

Shrödingers cat...

...and decoherence

Interpretations of quantum mechanics

The shut up and calculate interpretation

The transactual interpretation

The many-worlds interpretation

The Copenhagen interpretation

The hidden variables interpretation

Inventions based on quantum mechanics

Quantum computers

Quantum teleportation

Quantum mechanics comes from the need to divide up energy, to quantify. There where problems with classical mechanics, dealing with energy.

You have a box, the box is filled with electromagnetic waves, which constitutes the temperature inside the box. Now, lets try to divide up the total energy inside the box between the various numbers of electromagnetic waves that would be inside such a box:

First the frequency of the waves can't have any number at all, the waves has to fit between both sides of the box and have a whole number wave length. Then we first have one large wave stretching from one side of the box to the next with one peak, then we can have a wave with two peaks in the same space, three and so on. You can cram what ever amount of peaks between the walls you want, there's no end to it, so there is a infinite numbers of possible waves, with the frequency becoming larger and larger. Now we have an infinite amount of possible waves and since the black body should treat all waves equal, not favoring any of them, the energy has to be divided up equally between all the possible waves. The dilemma is that no matter how small portion of the total energy you give to each wave, because of the total wave number being infinite the energy will also be infinite.

1. The intensity (amplitude) of the light wave.

2. The frequency of the light wave.

These two together decided what the energy level of the wave would be. That means that if you have a wave with certain energy you could turn down the frequency and turn up the intensity and you would have a wave with the exact same energy level as your original wave, there would be no difference. And then neither would there be any difference in the energy of the electron that was knocked off the metal. But scientists found to their great surprise that only if they turned up the frequency of the light was the energy level of the electrons affected. Instead if they turned up the intensity the number of electrons which where knocked off raised.

If you the treat the electron as a wave which produce an standing wave around the nucleus, it can create different interference patterns. A interference pattern arrise when two waves overlap each other.

An interference pattern can either be destructive, that's when the peaks and troughs of each wave are turned in opposite direction (as in the pic above). Or reinforcing, when they are turned in the same direction.

When you have the electrons round orbit around the nucleus, the standing wave it produce would also have to be wrapped in a circular shape around the nucleus. It was found that in order not to create a destructive but reinforcing interference pattern when the standing wave was wrapped around the nucleus, the number of oscillations had to be a whole number: 1, 2, 3 etc. If the number of oscillations where a fractal; 1.1, 2.2, 3.3 etc there would be a destructive interference. Thereby the orbits couldn't be anywere around the nucleus, but only at certain positions were they form standing wave with a whole number oscillations. Since if the interference pattern is destructive that orbit is forbidden, since it would be unstable, and nature always strives for stability.

As we've seen from the above examples light and electromagnetic waves in general has to behave like particles, if theory will match reality. But does this mean that light is particles? There is an experiment produced by a fellow named Young, called the double slit experiment. It involves a screen that doesn't let through any light; two parallel slits are cut in it:

And a light source put behind the screen so that light passes through the slits and gets projected against a white screen. If we covered over one stripe is easy to see that on the white screen we would see one bright spot, from the light coming out of the open slit. But if we uncovered the other slit, instead of seeing two bright spots bright and dark stripes would appear, a so-called interference pattern.

Why is that?

It's easy to understand this if you think of light as waves. As the original wave from the light source goes trough the two slits, it's just as two independent new waves arise from the two slits. Those two waves consist of peaks and troughs, and as the two waves spread out there peaks and troughs will meet, then two basic things can happen:

1. Two peaks or troughs from each wave can overlap each other. Then they'll reinforce one another, creating a bright stripe.

2. One peak and one trough from each wave can overlap each other. Then they'll cancel each other out, creating a dark stripe.

Beneath is a picture showing two peaks overlapping and therefore creating a bright stripe. The red circles are where the two slits are and where the waves come out. The green circle is where the two peaks overlap. To illustrate a dark stripe, where a peak and a trough overlap, simply turn one wave around so the two peaks that now point in the same direction point in opposite.

Now you should see why there are stripes. Below is a final picture showing the interference pattern. It's a bit difficult understanding what it shows, so you probably have to read this through a couple of times. Lets start from the bottom: First there's a dark grey area, this is a peak. Then a black line that is a border between a peak and a trough and then a light grey area, which is a trough (never mind the meaning of dark and light grey areas as peaks and troughs the meaning of the grey areas will change later, but black lines are still borders). Now, the second black line is a bit different, that's the screen with the slits, the slits being the two openings in it. And from those two openings the two "new" waves that create the interference pattern arise. Now remember; the following section is basically divided using black lined half circles, on one side of a black line half circle there's a peak on the other side there's a trough, lets start by saying that the first area emerging from the slit to the left (the area between the left slit opening and the following black lined half circle) is a peak(try to ignore the lines cutting through it), the next one above that is a trough. And it's the next one, the trough that is interesting. Since emerging from the slit right of it is also first a peak and above that a trough. If you follow those two troughs you'll see that they intersect and where they intersect there's a dark grey area (it's right between the two slits and shaped kind of like an egg). This grey are where the two troughs reinforce each other and bright stripe will be.

Lets keep focused one the same left trough as before. On the right side of it, above the trough that we used to earlier there is of course a peak if we follow that peak to where is intersect the trough on the left side, we find a light grey area. This light grey area is where the peak and the trough cancel each other out and creates a dark stripe.

If you continue like this, finding the peaks and troughs and see where they intersect, and remember that dark grey areas are where they reinforce and light grey is where they cancel. You'll find the same pattern as the picture shows.

Now you might ask if this wave isn't made up by the particles, the photon, much like a water wave is made up by atom. This way light would still be trusty old particles traveling in groups that behave like waves.

That's easy to test (easy and easy with the right equipment), you turn down the intensity on the light source to just firing one photon, say every second. If we then considered light to be classical particles this would, create just two bright spots of the screen, since the particle now wouldn't have anything to interact with and creating the interference pattern. But what we see now is rather strange; if we say that each photon leaves like a little burn mark where it hits the white screen, and if we left the machine going for quite some time, the same pattern will arise. That's strange, it's as if the photon went through both slits and interacted with it self! This can only be possible if you consider the photon as waves. And in fact you can say that the photons in the light beam, going through the slits doesn't interact with each other they only interact with them self! But there's another troubling thing that we can do to make quantum mechanics even more strange: If we place a photon detector at the screen which examines the way the single photon will go, then the interference patter will disappear. And this is not because the detector blocks of the slit or something, it's because if we know that the particle goes through one of the slits it can't go through the other and so it can't interact with itself. This means that if we want to know which path the particle takes then we can't see the interference patter and vice versa, our measurement forces the particle to take a specific path through space.

However there is something called Feynmans sum-over-histories which treats the photon as a particle. It says that the photon takes every possible path to the target (the white screen) therefore it can take both the paths thru the slits, and may other paths to, however this doesn't say that everything is fine and that light is particles. You can still say that the photon is a wave or that it takes every possible path, non of them are more right then the other and non of them brings everything back to normal since usually things can't travel two places at once.

(Curiosa: The interference pattern should in fact look slightly different: the should be peaks and troughs already existing should also have peaks and troughs in them. This is because there are actually four wave sources. The incoming wave scatters from the sides of the slits so two slits with two sides makes for four wave sources. I painted each slit as an individual wave source for clarity. It only requires one slit to make the interference in pictured above)

We start of with a simplified billiard ball analogy; if you have a billiard ball and wants to know it's position you could shoot another billiard ball at it and watch it's trajectory. Its trajectory will depend on where it hit the other billiard ball(if it was a direct hit or if it just nudged it) and also the speed of the other billiard ball , so by watching its' trajectory you can find out the other billiard balls' position and speed.

If you have a particle and want to know its position you would shine some light on it to see were it is. If we considered light to be waves, then as normal waves do we could say that the light would shatter and form ripples around the particle. But now we want to know which way the photon went(just like in the double slit experiment) so then the light wave collapses into a photon and it can't spread out around the particle, it has to go one-way or another, so which way will it go? This is where the uncertainty comes in; there is no way of telling exactly which way the photon will go or exactly what speed it will have. There is just a set of chances that it will go one way or another. So therefore you can't get an exact answer of the particles' position or speed since there are allot of different scenarios where the photon would have some chance of gaining a similar speed and position as the one you may observe in an experiment. This is one thing that creates uncertainties when looking for a particles position.

Now, the same thing goes for the particle that the photon will hit, since we now know that matter particles also behave as waves. So when the incoming photon collides with the particle it will give the particle a recoil which also will send it of in a random direction and at a random speed because of its' wave like character.

If you want to know the particles' position better you would use light with smaller wavelength, an increase in the wavelength is also an increase in the energy in the photon so this means that it will hit the particle harder. The thing is that if the photon hits the particle very lightly it will move away in a more uncertain way then if the photon would hit it very hard, in which case the particle would be set on the move in a much more predictable way and thereby you'll know it's direction and therefore it's destination better.

You can again think of normal billiard balls, if you only nudge the billiard ball the force in it's movement will be so small that any little disturbance in the rug will alter it's trajectory thereby making it hard to predict, but if you hit it hard it will take a large obstacle to stop or alter it's direction of motion. The same goes for particles, if the photon hits it very lightly it will be more easily affected by outside forces the if it were hit very hard.

Now back to the photon and the particle; if you smack the photon harder into the particle you'll send it of flying which means that you've altered it's speed allot and in a uncertain fashion. However if you just nudge the particle its' speed will hardly change and so it will be more uncertain. BR> So then you can see that this is sort of a trade off between position and speed.

But you shouldn't think that it is only because we "touch" the particle that this behaviour occurs. Say we put a particle in a shrinking box, the more the box shrink the better we know the particles position(since then we've narrowed down the places were it can exist). But we don't interact with it so therefore we shouldn't change its momentum. Wrong. The smaller the box gets, the more energetic and unpredictable the particles motion gets. This is because, as in black body radiation, the particles wave length has to fit between the sides of the box. So as the box shrinks the wave length has to get smaller and smaller, and a smaller wave length leads to higher energy values, thereby the chaotic motion. So there's no way to get around it.

It wasn't very welcome(and still isn't?) in the scientific world that properties didn't exist until measured which meant that we couldn't predict exactly how things worked. And there's a famous experiment devised by Einstein, Poldosky, Rosen to prove that quantum mechanics(or more specific the Copenhagen interpretation which was the leading interpretation at that time) was wrong:

This was resolved in Bell's theorem or also called Bells inequality. John Bell found that there should be certain differences between a theory, which is local and supposes that everything's predetermined and in and a theory, which is non-local and where things doesn't take on a special attribute until measured. Basicly in a world where every thing is determined you should be able to add together results from two experiments to make a prediction. But if that aren't the case (which is the case in quantum mechanics) then you can't add together results from different experiments since results aren't something constant, but has to be measured before they become something real to use. The verdict came in an experiment by Alain Aspect, and it was in the favour of the non-local. So the attributes of particles are uncertain and have to be measure to become real. But this doesn't mean that quantum mechanics is right, it simply means that our notion of one static world where every thing always exist is wrong, and that we need a new theory.

But as said above you can't know an object properties too a 100%. This is also true for the energy level of balls, here it's time and accuracy which is traded for each other. If you want to know the balls energy level with a high accuracy you'll have to examine it under a long time. If you just examine it for a brief period of time the energy level will be less well defined. This means that the balls energy can fluctuate up and down, and that the shorter time span the higher the fluctuations.

So in fact there is a small but existing possibility that the ball will momentarily gain enough energy so that a large part of its wave function spills right through the wall and passes right through it. And here comes the strange part; the ball wont really travel through the wall. Instead it will hit the wall and reappear on the other side, faster then light. Note, that balls have little probability to tunnel through anything since all particles in the ball have to gain energy at the same time. But particles do sometimes, e.g in alpha radiation the protons and neutrons which will form the radiation particle tunnels through the nucleus currently in, in order to escape.

Now you might wonder if a electron really can form a standing wave around sucha strange shape. The answer is that it doesn't have to adapt to the orbital, but infact it's the wave functions that arise from treating a electron as a standing wave which leads to the orbitals. But they aren't cicular as in the Bohr model, so then we can say bye bye to having nice division of the areas were the electron can be and not? Again not really, even though they aren't circular it's still largely a division of the areas were the electron can be, although it can as said above be anywhere. But since 90% of it's wave function(E.i it has a 90% chance) is within these orbitals it's still a division which keeps the electrons in place and the atoms functioning.

As seen above the orbital can take on different shapes, what shape the orbital has depends on the energy level of the electron or more specific on the three first quantum numbers. There are four quantum numbers:

NAME | MEANING | SYMBOL |

The principal quantum number. | In what shell around the nucleus the electron is. | n |

The orbital quantum number. | In what sub shell(there are shells within the normal shells) the electron is. | l |

The magnetic quantum number. | What energy level in the sub shell the electron has. | m |

The spin quantum number. | What spin the electron has. Can only have two values: +1/2 or -1/2 | s |

There can be two electrons in one orbital, but only if they have the opposite spin.

This experiment shows again that the quantum world does not act like our classical world. There are various different types of delayed choice experiments, but they all shows that the particle seems to have the ability to see into the future. Here I will take a fairly easy one.

In the experiment you have a photon emitter and the a mirror which lets though half of the light shone on it and reflects half of it(a so called half-silvered mirror). That is it splits the beam up into two paths. Later with the use of other mirrors, these two paths recombine to create the normal interference patter(instead of two slits there's two paths) so now it seems like the photon has traveled down two paths at once to create the interference pattern.

Then if we place a photon detector along one path to see which path the photon goes. This will, as with the slit experiment, destroy the interference pattern since this measurement collpases the photons wave function, gives it a certain position and now it can only go one path and not create a interference pattern. But then wait until the photon have gone through the mirror to switch it on then the photon has already made a choice to travel down two paths to create an interference patter or just one. But with the detector on the pattern will disappear, all the time. One can wonder, how could the particle know if the photon detector where going to be switched on or not? Whether to take two paths at once or just travel down one of them? Creepy.

We've talked about uncertainty in the thing measured and how the uncertainty principal never lets us measure every aspect with 100% accuracy. But why doesn't this affect our measuring devices? How can they give us definite results and not just probabilities? Do they stand above the laws of quantum mechanics? This is called the measurement problem.

There is a famous experiment called Shrödingers cat it goes something like this:

You have a cat in a perfectly sealed off container and in the container there is a gun, connected to a device which every hour measures a particles spin. If the particle has a down spin there will be an extra hole in the poor little kitties head. And if the particle has a up spin, well it just waits for another particle (BWA-HA-HA). Now we know that before the measurement the particles spin is 50% up and 50% down and it's first when the measurement is made it becomes definite up or down. But up till now we have assumed that the measuring device are a purely classical devise which is in a definite state so it can't show a 50% up, 50% down value. But if we treat the devise as quantum mechanical it is 50% up and 50% down until measured itself, and since it's in a sealed off container there is nothing which can measure it. So does this mean that the cat will be both shot and not be shot, do we have a both dead and alive cat here, until someone measure the measuring device and establish that it's either up or down spin? It seems this means that there is something strange and mystic about our consciousness, that in order for a system to be measured a human needs to look at it, and even if a human looks at it will the wave- function collapse for his brother or will it still be in a superposition to him?

Another strange thing is that, in a dead cat, the alive states will continue to evolve separately from the dead states, even though we only see the dead states. So even if we only see one state, all the separate states will continue to exist and evolve not caring about each other. So it's not only a averaging of the wave functions of the atoms in an object, but also a averaging from macroscopically waves functions of the object.

And this is quite interesting. You might have thought that when you measure a particles spin and it comes out up, the down state doesn't exist at least not anymore. But on a closer look this would violate Bells theorem, there are no definite states. You can see this in a example:

Suppose you(please don't involve me) measure a particles spin on a verticle axis, the spin can now come out either up or down lets say it comes out down. Then you measure the particles spin 90

However decoherence is a field under development and we can't be certain that it's right.

As you might have figured out, quantum mechanics doesn't exactly mesh with our intuition. In fact it doesn't look like anything we see in everyday life. There has been attempts to explian it's weirdness, so that it looks a bit normal, in various interpretations. The interpretations all offer a different explanation to the experiments mentioned above: the double slit, delayed choice, Shrödingers cat, Bells theorem etc. Here I will just discuss one or two experiment each interpretation which best brings forward its own attributes. There are a lot more of them but here I'll discuss the most popular ones. Also note that there might be different 'versions' of some interpretations but the basic ideas will be the same.

As you may have figured out this isn't exactly an interpretation, it's simply the brutal use of nothing but the calculations of quantum mechanics, no questions asked. This may seem like the only real way of doing things. But it's very philosophically disturbing, since we humans have a need to understand things on a deeper level.

E.g the EPR experiment could be explained so that when you measure one of the particles spin a wave will travel backward in time and give the other wave the opposite spin. This would give the impression of faster then light travel, but in reality the wave would travel at light speed. And also in the delayed choice experiment a wave traveling backward in time should "tell" the forward traveling if the photon detector will be on or off. The interpretation is still non-local though. It may seem like a backward traveling wave can mess up the past changing it in certain ways this wont happen since the advanced waves cancels out when the retarded wave gets measured and destroying all traces of their backward traveling business . So we wont find waves traveling to us from the future.

This means that every different situation that can happen, happens but in different universes.

This creates something known as the Tegmark quantum suicide experiment. In it there's two persons and they have one gun(sounds like two typical american 8 year olds to me) connected to a apparatus which measures the spin of a particle, if the particles spin is up then a shot is fired and if it's down it doesn't. Then one of puts the gun to the other ones head and pull the trigger. For the first couple of times the spin might be measured to be down and no shot is fired. But sooner or later a shot will be fired. At that point the universe splits and two different outcomes happen:

1. To the person pulling the trigger the spin was measured up and for the person which shot the other one, the other one of course dies.

2. For the person which gets shoot the gun doesn't ever fire, the spin will be always be measure down. So to him they all continue to live happily but their friendship might have been placed under strain.

This is because at each measurement the universe splits. And the person being in front of the barrel always continuse to live in one of the universes, since both spin outcomes happens.

It explains the interference patter by saying that it's created, not by one particle in our universe, but many particles each in different universes interfering with each other. The problem is that for the interpretation to hold we can't be able to communicate or travel into the parallel universes, they would only interfere indirectly with our universe via e.g. the double slit experiment, so we can't detect parallel universes.

The interpretation says that the wave function isn't a real thing; it isn't the particle itself. Which means that half of the particle doesn't go through one slit and half of it through another.

One thing with the Copenhagen interpretation which has been criticized is that it doesn't specify when a measurement is made or more commonly said: when the wave function collapse happen. This means that in the interpretation it doesn't say whether a particle takes on a specific property when the measurement occur or when someone looks at the measured particle or anywhere in between.

This has lead to the myth that the Copenhagen interpretation should treat consciousness different from something non-living. That is wrong Copenhagen doesn't need consciousness to work. The reason it doesn't specify it is because to honor the famous/infamous the-devil-may-care attitude of the Copenhagen interpretation, when the collapse occur doesn't affect anything, we can't see any difference in the real world and therefore isn't a sensible question. It can still be considered unsettling(in fact the entire interpretation can be found unsettling) The instantaneous collapse leads to non-locality.

However problems exist with the interpretation. It is non-local since the pilot wave have to know all information about the surrounding and measuring device instantly and transmit it to the particle instantly. No something alarming but think of this: When you measure a particle in the EPR experiment the wave function has to travel to the other particle so that the quantum potential can change it into the opposite spin. Even though this non-locality may not seem like such a bad thing since other interpretations like the Copenhagen also have it. But in the other interpretations the wave function isn't something physical, it still allows for faster then light communication but the wave function isn't real and doesn't travel any were. But in hidden variables the wave function is a physical entity and there for it travels faster then light, which can be found unsettling. Another problem with the wave function as a physical thing is with reference frames which exist in the theory of relativity. In relativity things doesn't happen in the same order as seen from different reference frames. So even though it may seem like the particles both gets defined spin when you measure one of them they may actually be measured in different orders in different reference frames, this creates a problem that if in your reference frame you measure one particle and then the wave function must travel toward the other particle. But as seen from another frame the particles may be measured in different order and so the wave function travels in the wrong direction so things happen in the wrong order. And also in classical physics a force also has a counter force in the opposite direction. Meaning that if the quantum potential exerts a force on the particle the particle would also exert a force on the quantum potential. But it doesn't. And if it would exert a force on the particle order to change its path, then according to classical laws the particle would then reach i.g the screen in the interference experiment with a different amount of energy then it had from the beginning. And this isn't observed to happen. So now it has been proposed that the pilot wave instead of exerting a force on the particle, sends information to the particle so that it knows were to go. Which seems to mean that the particle can somehow think.

But you shouldn't rule out this interpretation because of this. There is no direct proof that forbids a hidden variables interpretation.

Now that we've seen the most common interpretations it should be added that non of them are provable. Which means that you can choose which ever one you like and that you think seems reasonable. But won't have any scientific proof that the interpretation you choose is right.

All this strange stuff has got to make for some new exciting stuff, right? Yes it does, for example:

Now you might think that we only get the double capacity because we can store two numbers in one atom. But indeterminacy is sweater then that. Say we have two atoms; they are both in a super position and hold two numbers, 1 and 0. Then we have, because of the uncertainty, some probability of the pair together creating: 00, 11, 01 or 10, that is four numbers in two atoms. And they all exist, remember bells theorem, particles doesn't have determined attributes but they become determined only after measurement so since the particles are in super positions both states exist in the particles, and all the four states exist in the two particle combined. And it gets better, in three atoms we can store 000, 111, 010, 101, 100, 001, 110, 011, eight numbers in three atoms. So now we see an exponential growth which has the formula 2

But there are problems, the biggest one involves decoherence. The least interaction causes the atoms to come into a certain state and the computer is ruined. So you have to keep the computer completely sealed of. And more, you can only extract one answer from a preformed calculation, then the calculation gets destroyed, since to extract an answer you have to measure the particle, which will collapse its wave function and therefore destroy its super position.

But it was found that a liquid could work very well as a quantum computer. Then instead of having one particle hold one qbit you would have a whole bunch of particles holding the same qbit. Then you can interact with some of the atoms and some can get destroyed by decoherence, without affecting the computations.

In order to be able to control a quantum computer you have to be able to control the spin of the particles in the liquid. This can be done, if you have a static magnetic field present the particles spin either align itself with the applied field(the particles magnetic north aligns with the fields magnetic north and its south with its south), or not. You can say that if it's aligned it represents a 0 and if it's not it represents a 1. Then, using another magnetic field, you can "flip" the particles spins to either align them with the static field or not. Which means that you change the spins so to represent 0s or 1s as you like. But then of course you could turn the not-static field on for just as long time so it doesn't quite flip the particle in alignment with the statical field or leave it unaligned. But right in the middle, not aligned nor unaligned. Then you have the uncertain 0-and-1 spin which makes a quantum computer a quantum computer.

If you would like to teleport a particle you would of course first measure it to see in what state it's in, but as we've seen above, a measurement disturbs the particle you measure in such a way so that it might not even be the same particle before and after the measurement, since the measurement would disturb and change it's different states. But it seems that quantum mechanics itself offers a solution to it's own limitations.

Alice and Bob have one particle each. And these particles are entangled, they are EPR particles so they stand in a special relationship to eachother; e.g. they might have the opposite spin to one another. The way in which they are related to each other is called their Bell state. This pair will work as the transmitter.

Alice then has a original particle, which she wants to teleport to Bob.

Alice then measures the relationship between her EPR particle and the particle which she wants to teleport. E.g she might find out that they also have opposite spin of eachother but she doesn't get to know their actuall spin, this is a Bell state. The important thing is that she doesn't measure the particle directly themselves, so she doesn't disturb them. However Alice original particle still gets destroyed, this is because in the Bell state measurement, Alice EPR particle and her original particle also gets entangled, which means that the original particle looses it's own state and instead it's state now depends on Alice EPR particles and vice versa. EPR particles have no identity of their own any more but are now dependant of eachother.

She then sends the data recovered from the measurement to Bob. Bob can now, using the information Alice sent him, change his EPR particles state into the exact same state as the one Alice original particle had, since he now knows:

A: In what relationship his and Alice's EPR particles stands to eachother.

B: In what relationship Alice's EPR particle and the particle which she wanted to teleport stands to eachother.

This gives Bob the information he needs to change his EPR particle to Alice original particle. Say that Alice and Bobs EPR particles have the opposite spin of eachother, and then Alice finds out that the particle which she wanted to teleport and her EPR particle had the same spin. Then, because of the different relation between the particles, Bob would know that Alice's original particle had the opposite spin of his EPR particle, so he simply invert it's spin to the opposite and then he's got a copy of Alice original particle(note that to invert the spin to the opposite doesn't require him to know it's exact spin so he doesn't disturb the particle and also note that it's not only the spin that can be teleported). It might also be so that the particle will be teleported directly without Bob having to do anything. If Alice and Bobs EPR particles have opposite spins and Alice original particle had the opposite spin of her EPR particle then no change to Bobs particle had to be made since they would have the same spin immediately, but you still had to send a message to see it that really was the case. It is also possible to teleport super positions of states.

But in the teleportation neither Alice nor Bob(or anyone else) can ever know exactly what was transferred in the teleportation, the only thing that they can know is that the correct state

The important thing is that there's no real faster then light teleportation, there still has to be send a message(the one from Alice containing her particles Bell states) with slower then light means to perform the particle teleportation, and there already has to be two particles at the different places where you are and where you want to teleport your particle to, since no matter gets teleported only the particles state. And also that the original particle gets destroyed is important, since else you would have two particles with the same properties so you could measure one thing on the other and another thing on the other and in this way circumvent the uncertainty principal and know all the properties of the particle, this is something called the non-cloning theorem.

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