# B Uncertain position and momentum -- A property of particles?

1. Sep 29, 2016

### Prem1998

I could completely understand the fact it it was just a limit to our observations but how can it be a property of the microscopic particle itself? Here's how I understand about probabilities:
Before a die is thrown, the probability of a certain number coming up is 1/6. But, it's before the die is thrown. But, when the die has been thrown, there is a definite outcome. And, we can't say that the outcome is uncertain or what is happening is uncertain. So, before we observe a microscopic particle, we can calculate the probabilities of where it would be. Before any time instant 't' has happened, we can calculate the probability of where the particle will be at 't' by the wave function but that when 't' happens it has an outcome and the particle has a definite position. So, uncertainties only exist when predicting the future, but the present existence of a particle must have definite position and momentum. Future is uncertain before it happens, but when it happens it must give an outcome.
Then, why is it said that microscopic particles posses uncertain positions and momentum?

2. Sep 29, 2016

### Staff: Mentor

You may be misunderstanding what the uncertainty principle says.

We can measure the position of a particle as accurately as we wish, and we can measure the momentum of a particle as accurately as we wish. (In practice,we are limited by our budget - eventually we run out of money to buy or build more precise instruments, but that has nothing to do with the uncertainty principle).

What the uncertainty principle does say is that for any pair of non-commuting observables (position and momentum are one such pair, but by no means the only one) we cannot set a particle up (the scientific technical term is "prepare the state" of the particle) so that if we measure its position to infinite precision we will get exactly x AND if we measure its momentum we will get exactly p. If you set the particle up to have a particular position, then there will be some uncertainty about what will come out of an infinitely precise momentum measurement, and vice versa. We test this by preparing a large number of particles in a state of exact position, and then measuring the momentum of each one - and we get different momentum values even though the particles were all created in the same state.
That is one of the most natural and intuitive assumptions you might make... But it's not correct. It turns out that this assumption has some subtle statistical consequences that can actually be tested in experiments; the experiments have been done; and the results are inconsistent with these statistical consequences so the assumption is wrong. You can google for "Bell's Theorem", and also take a look at the website maintained by our own @DrChinese : http://www.drchinese.com/Bells_Theorem.htm

3. Sep 29, 2016

### Prem1998

Let's just talk about an experiment which does not involve any external observer.
Let's just say that I'm an electron. A living electron in an orbital. Now, what would I observe about what's happening to me? How would I interpret my uncertain position and momentum?

4. Sep 30, 2016

### Staff: Mentor

There's no such thing as a living electron actively observing its surroundings, so this hypothetical doesn't have an answer. We can measure the position of an electron, and we can measure the momentum of an electron, but we cannot sensibly talk about the electron itself observing its position and momentum.

We can also run experiments to see if what quantum mechanics says we will measure under various conditions matches what we do in fact measure. Quantum mechanics has been abundantly confirmed by many different observations under many different conditions, so our confidence that it accurately describes the universe we live in is very high.

Last edited: Sep 30, 2016
5. Sep 30, 2016

### Prem1998

I've nothing against quantum mechanics. I know that all its predictions have been correct.
I'm just talking about what quantum mechanics says about the electron frame of reference. Let's think of electron as a planet. How do the living creatures on it see things? How do they interpret their uncertain position and momentum? How do things look from the electron frame of reference? An electron is not just a thing to observe. It must have existence when no one is looking it or striking it with photons. So, how does an electron observe the universe? And, I surely don't mean an electron is alive by saying it is observing things. You know what I want to ask. Maybe a better wording would be: How does an electron interpret the universe?

6. Sep 30, 2016

### Staff: Mentor

A planet is a big classical object; it has a surface, it has a shape, it has a size, it moves on a definite trajectory through space, and so forth. We've spent a lifetime surrounded by such classical objects, some large like planets and others small like pebbles and grains of sand, so it is very easy to think that an electron is the same sort of thing, except even smaller. However, it turns out that a quantum particle is not like that at all; it doesn't have a trajectory, the electron doesn't orbit the nucleus the way a planet orbits the sun, it doesn't behave at all like a little tiny classical ball.
It exists, yes. And if it were a classical object "it exists" would imply that it has a definite position and momentum even when nothing is interacting with it. But it's not a classical object, so it doesn't.

7. Sep 30, 2016

### Demystifier

I disagree. According to the Bohmian interpretation of QM, the particle has both position and momentum. The experiments do not rule this interpretation out. We cannot measure both position and momentum, but it is logically possible that particles still have both.

8. Sep 30, 2016

### Prem1998

But, how does the universe look from the electron frame of reference?

9. Oct 1, 2016

Staff Emeritus
Asking the same question over and over is not going to help. If there is something specific in one of the answers that you didn't understand, you should raise that point,

10. Oct 1, 2016

### Prem1998

All of the questions which I wasn't much focused on have already been answered. My questions about how can uncertainty exist in particles have been answered. But the question on which I was focused is:
How does the universe look from the electron frame of reference?
Now you tell me where this question has been answered in any of the answers.

11. Oct 1, 2016

### Staff: Mentor

Part of the difficulty here may be that a frame of reference is not what you think it is, so asking "how does the universe look from" a frame is just a meaningless agglomeration of words - as far as your chances of getting a satisfactory answer are concerned, you might as well be asking how much the Pythagorean theorem weighs.

But it may be that your real question is not about frames of reference....
That sounds as if you are asking: How would a very small but classical observer (the living creatures) that has the same position as the electron (implied by being "on" the electron) see things? However:
- There can be no such observer. Anything that small is small enough that quantum effects cannot be ignored so it's not classical.
- The electron has no definite position, so "has the same position" is not meaningful. (There are techniques for finding reference frames in which the electron can be treated as if it as at rest; but this has nothing to do with any notion of seeing thngs from the electron's point of view).
So if that's what you're trying to ask, the answer is that there is no answer. You are trying to use the laws of physics to say something about a situation in which the laws of physics don't apply, and that cannot produce logically consistent results.

12. Oct 3, 2016

### Prem1998

You should better say that we can't understand how things look from the electron point of view. But you sound like the point of view of electron does not exist. I understand that electrons are not billiard balls. But whatever it is, let's just say that I am the same thing. I have the same size, I have wave properties, I have everything that makes an electron an electon. Now how would I interpre my uncertain position and momentum? If there's not an answer, just say no.

13. Oct 3, 2016

### houlahound

If you were the same viewpoint of the electron I doubt you would have much uncertainty about your own position in relation to yourself.

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14. Oct 3, 2016

### Prem1998

Does that mean that for an electron, it's position and momentum are certain and specific?
This sounds like uncertainties are just for observers and are not a property of the particles. This is clearly against what quantum mechanics says.

15. Oct 3, 2016

### Prem1998

Does that mean that for an electron, it's position and momentum are certain and specific?
This sounds like uncertainties are just for observers and are not a property of the particles. This is clearly against what quantum mechanics says.

16. Oct 3, 2016

### vanhees71

This is all wild philsophical speculation, and philosophy is rarely helpful in understanding physics. To the contrary philosophers tend to distort simple things to something very complicated just for sake of the argument. It can be fun, but it's not helpful.

From a purely scientific point of view an electron and any other object never has a certain position or momentum, according to the uncertainty principle. That macroscopic things seem to have a determined position and momentum is just because you don't look that accurately at these quantities but only on a macroscopic resolution, and usually the accuracy with which you know a macroscopic body's position (say its center of momentum) and momentum is much worse than the restriction by the uncertainty relation.

17. Oct 3, 2016

### PeroK

It's perhaps more accurate to say that position and momentum are only well-defined as the result of a measurement. And a measurement requires an interaction with something that isn't the particle itself.

I suspect you are thinking an electron must be somewhere at any given time and that QM is, therefore, an incomplete theory, which provides only probabilies where a better theory would say precisely where the particle is at any time.

I suggest you read a little about an electron's spin, as this (in my opinion) is a better example than position of the role of uncertainty in QM. A brief summary is:

If you pick an axis, any axis, and measure the electron's spin about that axis you always get one of two values $\pm \frac{\hbar}{2}$. This is, in fact, about 1/3 of the total spin (which is also always the same when measured).

Now, if the electron really had a definite spin (like a classical object), then you could get many different values for the spin about your chosen axis. And, every now and again, you would get a spin about that axis equal to 0, as you would have - by luck - picked an axis about which the electron is not spinning.

The conclusion must be that the electron does not have a definite spin until you measure it. And, even then, you only have the spin about one axis: the spin about the other two axes remains probabilistic. Note that this isn't QM - this is the experimental evidence - so any theory that you may replace QM with would have to explain this experimental evidence.

In particular, no theory could say: the electron is definitely spinning about the x-axis. Because, if you measure the spin about the y-axis, you will always get a value of $\pm \frac{\hbar}{2}$. And, in fact, if you had measured the spin about the x-axis you would, likewise, get only $\pm \frac{\hbar}{2}$ and never the full amount of spin the electron has.

18. Oct 3, 2016

### Prem1998

But it still comes down to our measurements of the spin which contain uncertainties.
For example, I could have two definitions of velocity ofanelectron:
1 The velocity of an electron is the velocity measured by observers. This one contains uncertainties.
2 The velocity of an electron is the distance travelled by electron per unit time.This one is observed by the electron itself and we don't know if this one contains uncertainties.
And until we don't know if the electron is also uncertain about itself, we can't favor the first definition. And I like to believe that the electron knows more about itself, so I'm gonna favor it's measurement about which we don't know if it too is uncertain.
And, correct me if I'm wrong but I think that assuming that an electron's observations are not uncertain produces no contradiction to the experimental results. And, the fact that we can't know about electron's observations due to uncertainty principle does't imply that an electron too is uncertain.

19. Oct 3, 2016

### vanhees71

2. is nonsense since it's not observable at all. I also still don't get the idea what should "an electron's observations" mean.

20. Oct 3, 2016

### houlahound

Basis for this assumption?