Heisenberg principle: how can you find an electron's speed without finding it's location?

[ElasticCollision]

If you are able to measure the time taken for an electron to move from point A to point B in order to find it's speed, surely you also know it's location at both point A and point B, as these points are where you are measuring the electron passing through.

[derek w]

If you are able to measure the time taken for an electron to move from point A to point B in order to find it's speed, surely you also know it's location at both point A and point B, as these points are where you are measuring the electron passing through.

 

 

 

If you have an electron that was going to travel from an emitter at point( x,y,z=0) to a point on a detector at point (x=10,y=0,z=0).

Measuring it's position at point A, you find it's position to be(x=3,y=0,z=0),however you have interfered with it's momentum.

when you measure it,s position at point B,you find it's position to be(x=7,y=2,z=1),however once again you have interfered with it's momentum.

you cannot predict at which point it will arrive at the detector(x=10,y=?,z=?),or if it misses the detector then (x=?,y=?,z=?).

[ElasticCollision]

you cannot predict at which point it will arrive at the detector(x=10,y=?,z=?),or if it misses the detector then (x=?,y=?,z=?).

 

I see. Would it not be possible to simply use a detector which only measures a space that is the size of one electron though?

Surely that would allow it's position to be known with accuracy, as well as it's speed?

[derek w]

I suppose that you could say that for a fleeting moment in time the Large Hadron Collider at CERN,does what you are asking.

[ElasticCollision]

I suppose that you could say that for a fleeting moment in time the Large Hadron Collider at CERN,does what you are asking.

 

But then, if it does, doesn't that disproved Heisenberg's principle, because it proves that you can know both it's speed and location precisely at the same time, as long as the device you are measuring with is accurate enough?

[MigL]

Another way to look at it is that momentum is related to the energy of a particle. If you try and confine the particle to smaller and smaller spaces, it bounces around much more violently, so that its energy, and so its momentum becomes more and more indeterminate.

[swansont]

Would it not be possible to simply use a detector which only measures a space that is the size of one electron though?

I think what you will find is that even if such a device were possible, if you measured an ensemble of identically prepared electrons you would get a range of answers, because the position of an electron is not well-defined.

[ElasticCollision]

I think what you will find is that even if such a device were possible, if you measured an ensemble of identically prepared electrons you would get a range of answers, because the position of an electron is not well-defined.

 

I'm not sure I understand. If the same electrons were detected at both point A and point B, their position and speed will have been defined with certainty, wouldn't they?

[derek w]

The electron does not behave like a single point like object,it behaves like a wave function,therefore each electron will behave differently when detected at point A,point B will be different each time.

[ElasticCollision]

The electron does not behave like a single point like object,it behaves like a wave function,therefore each electron will behave differently when detected at point A,point B will be different each time.

 

I'm still not sure I completely understand. It will be different at point B from point A in what way?

[swansont]

I'm not sure I understand. If the same electrons were detected at both point A and point B, their position and speed will have been defined with certainty, wouldn't they?

You don't know what the uncertainty is from one measurement.

[derek w]

I'm still not sure I completely understand. It will be different at point B from point A in what way?

 

 

 

Point B will be at different places each time,each electron will travel away from point A in a different direction,because it was interfered with at point A.

You cannot predict where point B will be.You can only say where point B is after the event.

 

If you know point A and you know point B,and you know how much time it took to travel between A and B,you know it's position and velocity,but you don't because you interfered with it at point B.

Edited October 14, 2012 by derek w

[ElasticCollision]

Point B will be at different places each time,each electron will travel away from point A in a different direction,because it was interfered with at point A.

You cannot predict where point B will be.You can only say where point B is after the event.

 

I see. But in theory, could you not fire hundreds of electrons from a set point A to a set point B, and wait for one which happens to pass through A and B (given that A and B are both measuring an area the size of only one electron), allowing you to know that one particular electron's position and speed with certainty.

[swansont]

I see. But in theory, could you not fire hundreds of electrons from a set point A to a set point B, and wait for one which happens to pass through A and B (given that A and B are both measuring an area the size of only one electron), allowing you to know that one particular electron's position and speed with certainty.

You get a number, but you don't really know how that reflects the reality of what the position and momentum were. If you did a series of measurements on an identically prepared sample, the numbers would not be the same.

[ElasticCollision]

You get a number, but you don't really know how that reflects the reality of what the position and momentum were. If you did a series of measurements on an identically prepared sample, the numbers would not be the same.

 

Seems I'm getting a bit out of my depth, but as I'm fascinated I can't help but ask: What number do you get? what does it represent? and why doesn't it reflect the reality?

[derek w]

Because you interfered with the electron a point B,you don't know it's speed and momentum.

[swansont]

Seems I'm getting a bit out of my depth, but as I'm fascinated I can't help but ask: What number do you get? what does it represent? and why doesn't it reflect the reality?

I don't know what number you get, but I do know if you repeat the experiment, the chances are excellent that you will get slightly different numbers.

[EquisDeXD]

If you are able to measure the time taken for an electron to move from point A to point B in order to find it's speed, surely you also know it's location at both point A and point B, as these points are where you are measuring the electron passing through.

 

Are you sure you aren't confusing "speed" for "momentum"? Because the word "momentum" comes up in quantum mechanics almost infinitely more than "speed", and it doesn't mean the same thing as speed. "Speed" is almost meaningless in quantum mechanics, because particles are naturally in a state of superposition, which means they can occupy all possible states at once, and when you measure an electron, all you have is the measurement, you don't actually see it traveling distance over time.

Edited October 16, 2012 by EquisDeXD

[ElasticCollision]

Are you sure you aren't confusing "speed" for "momentum"? Because the word "momentum" comes up in quantum mechanics almost infinitely more than "speed", and it doesn't mean the same thing as speed. "Speed" is almost meaningless in quantum mechanics, because particles are naturally in a state of superposition, which means they can occupy all possible states at once, and when you measure an electron, all you have is the measurement, you don't actually see it traveling distance over time.

 

I need a better answer to my original question before I can start thinking about this.

[EquisDeXD]

I need a better answer to my original question before I can start thinking about this.

What's better than speed which you like to have continuous measurement for, you can I guess measure velocity instead, which is the change in position over time, but an electorn may not always travel in a straight line, or a predictable manner.

[ElasticCollision]

What's better than speed which you like to have continuous measurement for, you can I guess measure velocity instead, which is the change in position over time, but an electorn may not always travel in a straight line, or a predictable manner.

 

But I don't understand how you get a different "number" each time. Whatever that number even represents still hasn't been explained to me.

If electrons were the size of footballs and you had a device measuring an area the size of a football in two points, whether it moved through point A and point B in a straight line or in a wave motion, wouldn't you still get a precise reading of it's position and momentum/speed/velocity?

[swansont]

But I don't understand how you get a different "number" each time. Whatever that number even represents still hasn't been explained to me.

If electrons were the size of footballs and you had a device measuring an area the size of a football in two points, whether it moved through point A and point B in a straight line or in a wave motion, wouldn't you still get a precise reading of it's position and momentum/speed/velocity?

You get a different number because there is an inherent uncertainty in the value. Electrons are not footballs, so you can't think of them as such.

[ElasticCollision]

You get a different number because there is an inherent uncertainty in the value. Electrons are not footballs, so you can't think of them as such.

 

Right, I wasn't directly thinking of them as such, it was just an analogy.

And I don't see what is uncertain: If you have detected an electron within the maximum space an electron can fill, at two points, then how have you not detected both it's position and momentum with certainty?

[swansont]

Right, I wasn't directly thinking of them as such, it was just an analogy.

And I don't see what is uncertain: If you have detected an electron within the maximum space an electron can fill, at two points, then how have you not detected both it's position and momentum with certainty?

Are you sure the electron is exactly where you measured it to be? Especially when you repeat the experiment and you get a different answer?

[ElasticCollision]

Are you sure the electron is exactly where you measured it to be? Especially when you repeat the experiment and you get a different answer?

 

How can you be uncertain? if you are measuring an area that is only the size of an electron, then if the electron is anywhere other than in the path of the detector, it will not be detected.