The slit experiment is the modern embodiment of the wave partilce debate. In it we take a wall and cut some holes or slits in it. Then we shine a light or shoot a beam of electrons at it. The pattern that the light takes on the other side of the wall indicates whether it is acting like a particle or a wave. first we cut just one slit in the wall.
The two slit experiment
When we cut two slits in our screen and shoot particles through we can expect therefore to get out a simple scattering pattern. A similar pattern to the one we got for the single slit. If however the particles that are coming through the slits are not really particles but waves then the waves emanating from the two holes will interfere with each other creating a great many peaks and dips in the distribution. This is indeed what we observe when the experiment is carried out. From this experiment we can take an important lesson about the wave like nature of all particles. Not just light but electrons protons neutrons xenon atoms all have wave properties. And at the same time can be considered to act like particles whichever is more convienient for the mathematical representation at the time. The wavelength of such particles can be found by a simple relation and this wavelength is called the de broglie pilot function. it is
where h is planks constant p is the momentum of the particle (mass times velocity) and lambda is the particle's wavelength. but quantum physics is more than just the wave/particle duality. we can still learn from our simple slit experiment.
low density slit experiment
What happens in our simple slit experiment if we only run one electtron through it at a time? Since there is only one electron it can't be expected to interfere with any other waves. So it should act like a particle again and give us the simple diffusion pattern. Again the quantum world surprises us because when we actually run the experiment with two slits and one electron we get an interference pattern. When we wait to send a lot of electrons one after another through the machine slowly the image of an interference pattern builds when we mark all of the elctrons collision points on our screen. The electron is somehow managing to interfere with something while going through the machine even though it is alone. The fantastic explanation that quantum theory gives to us is that the electron is interfering with itself. You see this is where the observer starts to come into quantum mechanics. remember schroedinger's cat? well this electron is going trhough much the same thing we send the electron through a box inside which we have no idea what it is doing. It has two possible options it can go through one hole or the other schroedinger tells us that we cannot know what it does until we open the box to look. Until we look it exists in both states. In the case of the slit experiment we never do open the box to see which hole the electron goes through it could go through either one and we would get the same distribution on the other side. But since we don't measure its passage it goes through both slits at once and then interferes with itself because it exists in both states at once. This property of the quantum mechanical world is called the superposition principle. It means that a system can be in two states simultaneously even when they are contradictory. But the superposition principle only allows contradictory states to occur when no measurement is being taken. like the cat when we actually open the box up and look to see what happened we will see one outcome or the other not the superposition of both.
The two slit measurement experiment
The final slit experiment is based on what exactly happens when we put a device next to each of the slits so that the device triggers when an electron passes through its respective slit. Now we know which slit the elctron passes through and they act like particles again and when we pass an electron beam through the system we get a simple scattering pattern again. the importance of the observer in quantum mechanics is made clear. so if a tree falls in the forest and there is no one to hear does it make a sound.
Heisenburg uncertainty
The heisenburg uncertainty principle states that you can never measure a particles momentum and its position with perfect accuracy at the same time. The principle is more exactly stated by saying that the product of the uncertainties of momentum and position must be greater than planks constant divided by 2 pi.
h <. Pu*xu
where h is planks constant pu is the uncertainty in momentum and xu is the uncertainty in position. But this is only one face of the heisenburg uncertainty principle momentum and position is just one pair of quantities that cannot be known simultaneously. The key to understanding what pairs of things cannot be known to greater certainty than h/2PI these pairs are things that have dimensions that can be multiplied together to produce action. Action is the product of energy and time. So it comes in units of Kg*m2/s anything that multiplies together to give those units makes an uncertainty pair. For instance take momentum and position, momentum comes in units of kg*m/s and position comes in units m so when multiplied together they give action. But the uncertainty principle is not just a statement about what we can know about objects but what properties objects can have. It is not enough just to say that we cannot know the position and momentum of an electron exactly both at once but rather we must say that an electron cannot have a well defined momentum and position at the same time. This is the fundamental fuzzyness of the quantum world but it is not due to an out of focus lens or inadequate measurements but nature herself is fuzzy. Take for instance the example of empty space. Space that is completely devoid of everything cannot be said to be absolutely empty. To say that space is completely empty we must measure the energy in that space and find it to be exactly zero. But the heisenburg uncertainty principle demonstrates that the uncertainties in time and energy are related it is impossible to know one with absolute certainty without knowing the other with no certainty at all. In the case of time and energy the relation can be interpereted that to know the energy that something has to a certain accuracy we cannot know the exact moment that it had that energy to an accuracy that would violate the uncertainty principle. The principle allows us to know that a space is exactly empty that is to say completely devoid of energy just so long as the amount of time we take to measure the energy in the space is infinitely long. However for any length of time shorter than infinity we will measure slight fluctuations in the energy of the empty space. If these variations were truly just noise in our detectors and actually had no real existience then they would have no effect on objects in that space. However there are experiments that have been carried out in which casimir forces due to fluctuations in the quantum vaccuum have actually been observed to exist, proving the reality of quantum uncertainty. The casimir experiments consist of two metal plates held very very close together. Electromagnetic waves cannot exist inside a cavity bound by conductive boundaries if the cavity does not resonate with the waves and is too small to allow many wavelengths inside it. So when two metal plates are brought very close together in an appearently empty space they are pushed together. You see they exclude some electromagnetic waves that arise because of uncertainty and exclude others but since the fluctuations inside are devoid of waves that cannot exist inside the cavity but the space outside produces a complete spectrum of waves there are more waves outside than inside and the extra waves outside push the plates together.
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