I am newb please explain this about Electrons

[tundra]

Okay I don't know anything about physics and I'm trying to understand Heisenbergs (sry spelling) uncertainty principle, they say you can't measure the position and momentum at the same time (of an Electron let's say), I want to know WHY?

I mean how does an electron move in the first place? does it teleport randomly around an atom is that why?

can you measure a trajectory of an electron? because if it orbits around in a trajectory and has a constant mass how is it uncertain where it's going? I would understand if it's teleporty-ish you know?

 

[granpa]

the whole concept of the electron 'orbiting' the nucleus is considered to be primitive if not completely wrong.

the electrons position cont be determined because it really is spread out.

dont know about momentum. someone else will have to answer that.

 

[Danger]

As for the uncertainty aspect, it's because the mere act of trying to measure something changes its state.

 

[LURCH]

This is one of those times when it might be more helpful to think of the electron as being more like a wave. You could point to the peak of a wave, and then the trough, and then several other places in between, and asked the question, "is this the location of the wave?" And the answer each time would be, "yes."

You see, according to the theory, it isn't just that we cannot know the exact location of the electron. It would seem that an electron actually does not have an exact location.

Here is an analogy that I frequently use, but please bear in mind that it is only an analogy:

Suppose you see a photograph of a baseball. The ball has just been thrown, and you are seeing it in flight between the pitcher's mound and homebase. The camera is looking straight down from overhead, and you are seeing the ball against a uniform background of grass. How can you tell which direction the ball is traveling?

Well, if the camera was using high-speed film and a very fast shutter speed, it would be nearly impossible to tell which way the ball is going. You could point very precisely to the edges of the ball on the photo, and say that you know the location of the ball. You could tell very definitely where in the picture the ball is and where it is not. But you could not say where the ball is headed.

Now, no matter how fast the shutter speed, if the ball was traveling when the photo was taken, there will be some blurring along the leading and trailing edges of the ball in the photo. If you blow the photo up to a very large size you might be able to see that blurring. Then you could point to the edges that are slightly blurred and say that the ball must of the have been traveling along that path, but it would only be a very vageu notion odf the direction of travel. However, due to the blurring at the edges, you have now lost the very sharp line along which you could say, " here there is baseball, and here there is none."

On the other hand, you could have the picture taken with low-speed film and a very long exposure. Then you would see the baseball as a long streak across the photo, and you have a very excellent idea of its path of travel. However, you would've lost any notion of its location. You could point to any spot along that streak and ask, "was this the location of the ball at the time the photo was taken?" And the answer would be, "yes."

Again, I will mention that this is only an analogy illustrating the mutually exclusive nature of knowing both the location and the momentum of nearly anything. In this analogy, for instance, the ball has a definite location and a definite path of travel, and we are simply unable to pin down both. In particle physics, it is generally believed that this is not the case. The particles literally have only a probability of being in a certain location and a probability of traveling a certain path. One can calculate the locations with the highest probability, but never come up with a single location with a 100% probability (definitely the exact location of the particle). Neither can one calculate any location in the universe that has a 0% probability. So, you could point at any place in the whole universe and ask, "is this the location of the electron from my example?" And the answer would be, "probably not, but maybe."

I think that a lot of the difficulty people have with this theory is not that they couldn't understand it, but that their mind rejects it. Our everyday experience tells us that objects cannot exist in such a state. Because no one has "everyday experience" with particles on the Quantum level, some of their behaviors tend to go against what we have learned to accept as possible. So it may help you to start out by trying to convince yourself to believe that electrons really do exist only as clouds of probability, not as the little plastic ball you've seen orbiting the nucleus in models in the classroom. After accepting and believing, understanding should come more easily.

 

[jtbell]

I mean how does an electron move in the first place? does it teleport randomly around an atom is that why?

can you measure a trajectory of an electron? because if it orbits around in a trajectory and has a constant mass how is it uncertain where it's going?

Fundamentally, we do not know how the electron moves around an atom, in the sense that you are talking about.

The mathematical formalism of quantum mechanics does not address the question "what is the electron really doing before we observe it?" It only gives us a method to calculate probabilities for the result of the observation.

There are various interpretations of QM that attempt to answer the question "what is the electron really doing?" They all reduce to the same mathematics, as far as calculating probabilities is concerned, so it is impossible to decide which interpretation is correct, by experiment.

 

[DaveC426913]

Fundamentally, we do not know how the electron moves around an atom, in the sense that you are talking about.

The mathematical formalism of quantum mechanics does not address the question "what is the electron really doing before we observe it?" It only gives us a method to calculate probabilities for the result of the observation.

There are various interpretations of QM that attempt to answer the question "what is the electron really doing?" They all reduce to the same mathematics, as far as calculating probabilities is concerned, so it is impossible to decide which interpretation is correct, by experiment.

Is this the gist of Feynman's famous line: "Shut up and calculate"?

 

[Gear300]

it means we don't know everything

 

[jobyts]

Is the uncertainity principle mathematically proved?, or it is an assumption due to our limited knowledge on particle physics.
There could be many things in the physics that is unknown to us. Why is it that only for the electron movement, we have an uncertainity principle and not for all others?

 

[Hootenanny]

Is the uncertainity principle mathematically proved?, or it is an assumption due to our limited knowledge on particle physics.
There could be many things in the physics that is unknown to us. Why is it that only for the electron movement, we have an uncertainity principle and not for all others?

The Uncertainty Principle is a special case of the Robertson-Schrödinger relation which results from the non-zero commutator between quantum mechanical operators. So yes, the HUP is mathematically proved, it is simply a special case of a mathematical relation.

 

[jtbell]

Or, to approach it from another direction, the HUP follows inescapably from the assumptions that particles are represented as waves whose wavelength is related to momentum via $\lambda = h / p$, and that these waves superpose (add) like other waves to form localized wave packets. The mathematics describing wave packets is part of Fourier analysis, which applies to all kinds of waves. The HUP has analogues in other kinds of waves.

 

[Minte]

I really like LURCH's examples. Kudos. ^^ That could be in a textbook.

Here's an elaboration, just because I can't let it go unsaid.

The exact location of an electron isn't known. It's more like a cloud of probability. It's "probably" in a certain range.

Electrons have more wave characteristics than "normal" (macro) matter, generally speaking. It's almost as if the electron is "smeared" over the general area, to quote Asimov.

 

[Crosson]

I really like LURCH's examples. Kudos. ^^ That could be in a textbook.

I second this sentiment, crediting LURCH for an apparently original and insightful analogy.

Why is it that only for the electron movement, we have an uncertainity principle and not for all others?

The uncertainty principle becomes more relevant when the object has a small mass. Electrons have a very small mass, but protons, atoms, and molecules obey the uncertainty principle as well.

 

[system downs]

As for the uncertainty aspect, it's because the mere act of trying to measure something changes its state.

This is true, don't be confused by the metaphorical responses.As for the orbiting the atom thing, completely ignore the guy who said the orbiting is wrong, he is stating a purely hypothetical theory with no experimental basis. The electrons travel as waves, but when the are at rest the act as particles.(planck's constant). This is why you can't measure the velocity and position of an electron at the same time. We are foced to use different methods for finding each, and only one method can be used at once. This is also what makes determinism currently invalid.

 

[Minte]

Oh! I found a really cool analogy of this the other day.

Imagine that you're blindfolded in a room, and you have to stay in one location and find a chair. All you have is a baseball to judge distances. So you throw the ball around a little bit (assume that it can come back to you), and you eventually hit the chair. But when you measured it, you moved it. So you can't be exactly certain of where it is, just the general area.

...It's not exactly it, but I still like the analogy.

 

[Crosson]

Oh! I found a really cool analogy of this the other day.

Imagine that you're blindfolded in a room, and you have to stay in one location and find a chair. All you have is a baseball to judge distances. So you throw the ball around a little bit (assume that it can come back to you), and you eventually hit the chair. But when you measured it, you moved it. So you can't be exactly certain of where it is, just the general area.

...It's not exactly it, but I still like the analogy.

This is an analogy of an analogy. It is universally recognized among physicists that the HUP is not caused in a semi-classical way by the measurement apparatus. It is a fundamental property of variables that don't commute, position and momentum are just one case.

If the HUP was merely a consequence of a crude measuring process, then its likely that physicists and engineers would find clever ways to overcome the limitation. Instead the HUP is a fundamental property of all measurements, a property of reality, unless quantum mechanics is wrong.

 

[Minte]

This is an analogy of an analogy. It is universally recognized among physicists that the HUP is not caused in a semi-classical way by the measurement apparatus. It is a fundamental property of variables that don't commute, position and momentum are just one case.

If the HUP was merely a consequence of a crude measuring process, then its likely that physicists and engineers would find clever ways to overcome the limitation. Instead the HUP is a fundamental property of all measurements, a property of reality, unless quantum mechanics is wrong.

Haha, I know. I just saw it and thought that it could be a representation with macro objects with fewer wavelike tendencies. =) Maybe it's because it was an old book...

 

[granpa]

It is a fundamental property of variables that don't commute, position and momentum are just one case.

now that is interesting. any connection to the non-commutative geometry suggested for double special relativity?

 

[HallsofIvy]

One crucial point that should be mentioned is that the energy contained by a photon depends on frequency and so on wavelength. In order to determine the position of a very small particle, you have to decrease the wave length to be smaller than the particle, so increase the frequency and thus the energy. The more accurately you measure the position, the harder you "hit" the particle with a photon and so the more you disturb its momentum.

 

[DaveC426913]

One crucial point that should be mentioned is that the energy contained by a photon depends on frequency and so on wavelength. In order to determine the position of a very small particle, you have to decrease the wave length to be smaller than the particle, so increase the frequency and thus the energy. The more accurately you measure the position, the harder you "hit" the particle with a photon and so the more you disturb its momentum.

Yah, but the trouble with this explanation is that is encourages exploration for more "passive" forms of observing.