heisenberg uncertain principle

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Farcus

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Ok the principle states its impossible to pinpoint the exact location of an electron at any given point in time, or "the momentum and position of an electron exactly." Ok why exactly is this?

I know we can't find the exact location of any atom but only the relative area of its existence with about 95% accuracy. WHy is it that we can't find the exact location and momentum of it? I read somewhere its due to the fact that in order to find the position of an electron you must use force/energy and this force/energy consequently alters the momentum of the electron thus its like a catch 22 thing. I don't know if i'm wrong I just want to get some verification.
 
Ok the principle states its impossible to pinpoint the exact location of an electron at any given point in time, or "the momentum and position of an electron exactly." Ok why exactly is this?

I know we can't find the exact location of any atom but only the relative area of its existence with about 95% accuracy. WHy is it that we can't find the exact location and momentum of it? I read somewhere its due to the fact that in order to find the position of an electron you must use force/energy and this force/energy consequently alters the momentum of the electron thus its like a catch 22 thing. I don't know if i'm wrong I just want to get some verification.

It is both of those.

Think of taking a picture of a moving object with a camera. You either get a streak (exposed for a long time) or a dot (fast exposure). As you get a longer streak, you can tell more about where it is going and thus its momentum. But you lose accuracy in its location. If you get a dot picture, then you have a better idea of where it is, but you lose insight as to where it's going and how fast it's going.

You can either take a picture that tells you location or trajectory, but not both. An electron is damn small and damn fast, so we have to come up with approximations and time averaged pictures to describe its probable whereabouts.

I hope this analogy helps.
 
Ok, I will explain it exactly. The statement is actually an inequality: delta_position*delta_momentum > h/4*pi where h is planck's constant.

This is how it goes down. You've probably heard of wave-particle duality that says that all particles have wave-like properties or vice versa. In reality objects are neither waves nor particles but have a mix of properties that we associate with both.

So, you are familiar with the fact that the frequency of a wave is related to its energy by E=hf. Momentum is also related to properties of a wave(it's wavelength) by this equation where p stands for momentum:
debrog5.gif
.

Now, if a particle can be described by a wave then what property of the wave is related to its position? Well, the obvious guess is that the location of the wave is related to the location of the particle. If you find the wave the particle will be there! So the position of the particle is given by the location of the wave itself.

So a particle traveling through space would have a wave that looks sort of like the wave on the right with the lines going flat on both sides. :
unc2.gif


So what does this have to do with uncertainty? Well, if you have a wave that starts and ends like the wave above you can't precisely define it's wavelength because its changing from peak to trough. But you DON'T run into this problem if you have a wave that looks like any one of the ones on the left. All these waves have precisely defined wavelengths because they never start or stop. So the only way to know the momentum precisely is if you say that the wave goes forever which means you have no idea where the particle is located. It could be anywhere! But if you try to trap the particle in a region in space then it's wavelength changes every peak to trough so you don't have a precise wavelength for it...which means you don't know the momentum precisely!

From this strange behavior you can reach the conclusion mathematically that the particle's position and momentum are related with a precise amount of uncertainty.

This is only one way of looking at it--the wave way. You can describe quantum mechanics in tons of ways including the matrix way. You can reach the same conclusion using matrix mathematics. If you go even deeper to quantum electrodynamics(graduate physics stuff) you would see that you can do away with the wave and matrix interpretation altogether and use something called path integrals and come up with a completely different interpretation of uncertainty. I won't go further but a layman's book on the topic that is incredibly short and requires no mathematics is called "QED : The Strange Theory of Light and Matter" by Richard Feynman.

Additional Info: If you look at the DeBroglie equation you might make the clever insight that DeBroglie did so long ago that anything that has momentum has a wavelength. So a basketball has a wavelength associated with it in proportion to its momentum. That means that basketballs exhibit all sorts of phenomenon that you can't see because the phenomenon is so small. One property would be that basketballs can diffract because waves diffract. You would be able to see this if planck's constant were larger...but it's actually very small and 'close' to 0. Ok, time to stop nerding out here.
 
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It is both of those.

Think of taking a picture of a moving object with a camera. You either get a streak (exposed for a long time) or a dot (fast exposure). As you get a longer streak, you can tell more about where it is going and thus its momentum. But you lose accuracy in its location. If you get a dot picture, then you have a better idea of where it is, but you lose insight as to where it's going and how fast it's going.

You can either take a picture that tells you location or trajectory, but not both. An electron is damn small and damn fast, so we have to come up with approximations and time averaged pictures to describe its probable whereabouts.

I hope this analogy helps.

Oh god this really has been the best damn analogy ever and its so damn practical.
 
I agree, the best explanation of the principle I have ever heard of. Its up there with the explanation of relativity - an hour with a hot girl seems like seconds, while seconds with your hand on a hot stove feel like hours, courtesy of LL Cool J.
 
Ok the principle states its impossible to pinpoint the exact location of an electron at any given point in time, or "the momentum and position of an electron exactly." Ok why exactly is this?

I know we can't find the exact location of any atom but only the relative area of its existence with about 95% accuracy. WHy is it that we can't find the exact location and momentum of it? I read somewhere its due to the fact that in order to find the position of an electron you must use force/energy and this force/energy consequently alters the momentum of the electron thus its like a catch 22 thing. I don't know if i'm wrong I just want to get some verification.

This 95% thing is wrong, btw. So is the part about the force/energy altering the momentum. The heisenberg uncertainty principle is a fundamental part of quantum physics and has nothing to do with the act of observing the electron. Also, it is not a catch 22 because it is not a paradox. There is nothing paradoxical going on with the uncertainty principle. It is unusual, but not paradoxical.

BRT's analogy is great for someone who refuses to accept that you can't know momentum or position precisely but it peddles an inaccuracy that the heisenberg uncertainty principle is a result of experimental limitations and not a fundamental physical limitation. Everyone knows that you can't measure position or momentum exactly using an experiment...you could always use more resolution(read: decimal places). The uncertainty principle says that there is a physical limit of how well you can determine the position and momentum of a particle. Even if you design the perfect experiment you still can't know the precise momentum and position because they don't exist! All you have is probabilities that a particle has a certain momentum or a certain position. When quantum mechanics was first developed heisenberg got bombarded with criticisms from people who were saying things like "your theory can't predict the position of the electron" or "your theory can't predict the position of the electron or even what hole the electron goes through in the double slit experiment". Heisenberg responded that his theory did not have to answer such questions because you can't ask such a question with an experiment. Genius.

Analogies usually fail at describing quantum physics because nothing we experience has similar properties and it goes against common sense intuition of what you know about the world.
 
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One relevant consideration is that whenever you make a measurement, you impact the thing you are measuring. Happenings at the atomic and nuclear level are particularly sensitive to anything you can do to try to measure specific properties, which results in an inability to fully describe every property of the system.
 
One relevant consideration is that whenever you make a measurement, you impact the thing you are measuring. Happenings at the atomic and nuclear level are particularly sensitive to anything you can do to try to measure specific properties, which results in an inability to fully describe every property of the system.

No, this is wrong. As I stated before, the uncertainty principle deals with measurement not observation. The uncertainty is not caused by an experimental limit due to the observer affecting the system. The observation of the position or the momentum is not what is causing the uncertainty. Read my last post...

Btw, when I say observer I don't mean the person watching. I mean the particle that interacts with the particle you are trying to observe. You are not the observer. A classical example is if you throw a ball at a wall with a certain speed and then calculate how far the wall is by how many seconds it took for the ball to get there then the ball is the observer. Not you.
 
Analogies usually fail at describing quantum physics because nothing we experience has similar properties and it goes against common sense intuition of what you know about the world.

For the MCAT, I'm pretty sure a good basic understanding of the fundamentals from general chemistry and general physics is good enough. Graduate level quantum mechanics, impressive as it may be, is seriously over the top and overkill for the simple purpose here: to get a better MCAT score.
 
For the MCAT, I'm pretty sure a good basic understanding of the fundamentals from general chemistry and general physics is good enough. Graduate level quantum mechanics, impressive as it may be, is seriously over the top and overkill for the simple purpose here: to get a better MCAT score.

True, but the OP did seem genuinely interested in where the mechanism behind the uncertainty principle comes from. I don't take to answering his question in an MCAT context because he already seemed to grasp the implication of the statement that you can't measure both position and momentum precisely. That's about as much as you need to know for the MCAT.

The analogy is a still a seriously incorrect representation of the mechanism. I would rather know that I don't know why something works than have the wrong idea about how it works. So far all of you guys are saying that measuring the position changes the momentum or vice versa...that is not true. Particles with a precise position and momentum simply do not exist. It's this gem of knowledge that makes the uncertainty principle interesting and important. If they didn't want you to learn this there is absolutely no reason it should show up anywhere in life science physics...you will never see a physicist use it in any calculation. It's just a conceptual tool that highlights how different quantum physics is from classical physics.

Reading http://en.wikipedia.org/wiki/Uncertainty_principle#Uncertainty_principle_and_observer_effect is pretty enlightening. I mostly just post here to hone my own knowledge of this stuff...I don't care much if I spend two hours writing out a reply that no one will read.
 
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True, but the OP did seem genuinely interested in where the mechanism behind the uncertainty principle comes from. I don't take to answering his question in an MCAT context because he already seemed to grasp the implication of the statement that you can't measure both position and momentum precisely. That's about as much as you need to know for the MCAT.

Just wondering what does "OP" stand for? I've seen it occasionally on the forum.
 
This is not on the MCAT, but the real reason is that the position and momentum operators don't commute, hence you can't find simultaneous eigenstates of both; so it'd be impossible for a system to have both definite position and definite momentum. When two operators (A, B) don't commute, the product of the uncertainties in their observables is given by &#916;A&#916;B >= (1/2)|<[A,B]>|
 
This is not on the MCAT, but the real reason is that the position and momentum operators don't commute, hence you can't find simultaneous eigenstates of both; so it'd be impossible for a system to have both definite position and definite momentum. When two operators (A, B) don't commute, the product of the uncertainties in their observables is given by &#916;A&#916;B >= (1/2)|<[A,B]>|

That's an equivalent reason...although I doubt anyone knows the abstract operator approach here. I don't like using it because there is no intuitive way of understanding px - xp = i*h-bar.
 
That's an equivalent reason...although I doubt anyone knows the abstract operator approach here. I don't like using it because there is no intuitive way of understanding px - xp = i*h-bar.

I look at it as a measure of the overlap of their two spaces.
 
I look at it as a measure of the overlap of their two spaces.

Reminds me of the old joke...

A mathematician and an engineer attend a lecture by a physicist. The topic concerns Kaluza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The mathematician is sitting, clearly enjoying the lecture, while the engineer is frowning and looking generally confused and puzzled. By the end the engineer has a terrible headache. At the end, the mathematician comments about the wonderful lecture.

The engineer says "How do you understand this stuff?"
Mathematician: "I just visualize the process."
Engineer: "How can you visualize something that occurs in 9-dimensional space?"
Mathematician: "Easy, first visualize it in N-dimensional space, then let N go to 9."
 
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