Beginners Question Uncertainty Principle

[GarciasMuffin]

Hi,

I just finished taking my first look at some quantum physics material and need some confirmation on a point which was not clear within the material, which I think will be pretty easy for you to answer.

The measuring of a particles position/momentum:

If in theory a piece of apparatus existed that allowed you to measure the position of a particle without affecting its momentum, would you then be able to record these values with absolute certainty, and it is only due to this theoretical apparatus not existing (if it ever will) that means the uncertainty principle exists.

Or is that there actually is some weird universal law that exists that means no matter what is invented you are never ever under any circumstances able to know both values at the same time even if the equiptment existed that should allow you to do this ?

As I said probably an easy question for most here, but I just wanted to get this answered before I go any further.


Many thanks in advance for all answers.

 

[Vanadium 50]

The uncertainty principle is a statement about nature, not a statement about our ability to engineer a measuring device.

I find it most enlightening to think of the HUP as a statistical statement. If I have a large number of identically prepared particles, and I measure the position of some of them, and the momentum of some of them, it is a statement about the relationship between the distributions of those two numbers.

 

[GarciasMuffin]

The uncertainty principle is a statement about nature, not a statement about our ability to engineer a measuring device.

I find it most enlightening to think of the HUP as a statistical statement. If I have a large number of identically prepared particles, and I measure the position of some of them, and the momentum of some of them, it is a statement about the relationship between the distributions of those two numbers.

Ok, but it certainly came across as being to do with the measuring device at the point where it said the momentum could not be measured precisely due to the momentum of the particle you are using to measure with (in the example a photon). This suggests to me that the principle only exists due to a lack of technology which allows us to do measure it correctly (ie a measuring device which has zero effect on the particle being measured).

I'll be honest here, I'm not sure you've actually told me which one is correct (if either).

 

[mikelepore]

There has been a case that uncertainty is due to the measurement apparatus. Erwin Schrödinger, in his book _What is Life?, and Other Scientific Essays_, explains that trying to measure both the position and momentum of a subatomic particle is "like trying to feel a ping-pong ball with a bulldozer." To use analogies of this type implies the opinion that the uncertainty is due to the disturbance of the measured thing that is produced by the measurement procedure. However, even in that version of the theory, the uncertainty can never be avoided in the future by using a different procedure or different equipment. So, to comment on the phrase in the original post, "this theoretical apparatus not existing (if it ever will)" -- the theory says that there is no "if" about it.

 

[I_am_learning]

I have read few times in this forum that the modern version of Uncertainty Exists and that it implies not that we can't measure a particles momentum and position with precision but that the particle itself don't have them precisely.

Having said that, I myself have got one question. If so, then our restriction to measuring methods, as said in the OP has to increase the uncertainty the particle already had. Then the uncertainty principle would be
<X><p> = h/4PI + h/4PI = h/2PI. Isn't it?

 

[GarciasMuffin]

There has been a case that uncertainty is due to the measurement apparatus. Erwin Schrödinger, in his book _What is Life?, and Other Scientific Essays_, explains that trying to measure both the position and momentum of a subatomic particle is "like trying to feel a ping-pong ball with a bulldozer." To use analogies of this type implies the opinion that the uncertainty is due to the disturbance of the measured thing that is produced by the measurement procedure. However, even in that version of the theory, the uncertainty can never be avoided in the future by using a different procedure or different equipment. So, to comment on the phrase in the original post, "this theoretical apparatus not existing (if it ever will)" -- the theory says that there is no "if" about it.

Ah right.

Are you able to explain to me in not overly complicated terms why it can never be avoided, which as you say means that the machine will never exist ?



Cheers

 

[Feldoh]

Ah right.

Are you able to explain to me in not overly complicated terms why it can never be avoided, which as you say means that the machine will never exist ?

Cheers

The uncertainty principle is a mathematical consequence of the statistical interpretation of QM. Basically from the math we know that (incompatible) observable quantities cannot be known to arbitrary precision in the same state, regardless of if we measure them or not. The measurement limit is just a result of the mathematical description of QM.

Or if you like as a result of the mathematics:

If we measure a particle's position we know it is well defined in some region, but the cost of this is that the wave function collapses to a localized spike.

State 1 is particle somewhere -> State 2 the wave function is a localized spike around the value you measure.

So now say you measure the momentum from the collapsed wave function (state 2) the wave function will again change and collapse to a localized spike in momentum. So now we know the momentum to arbitrary precision.

State 2 -> State 3 localized momentum spike

But the problem is that in measuring the particle again we've changed the state. So even though we know the momentum, we only know the momentum of state 3, where as we only know the position for state 2.

States 2 and 3 are distinct states, so in fact we have not really measured a corresponding pair of position momentum.

(position in state 2 = x, momentum in state 2 = ?)
(position in state 3 = ?, momentum in state 3 = y)

 

[mikeph]

^ Very neat description. The particle can never be in a state with stationary position AND momentum eigenvalues, only in one or the other. The act of "measurement" (operation of the position operator) on the particle fixes the position but a subsequent act of measurement of momentum will fix the momentum of the particle, but each time, the other variable is not certain.

The two observables are not "compatible" and the two operations are mathematically non-commutative (operating position then momentum does not give the same as operating momentum then position), and I think out of this comes your factor of h-bar/2 in the uncertainty.

 

[DrChinese]

Ah right.

Are you able to explain to me in not overly complicated terms why it can never be avoided, which as you say means that the machine will never exist ?

There are 2 things you should know additionally (if you don't already) which will help you to see that the issue is not due to the measurement apparatus imparting a physical change to the particle in question (so as to bring the Heisenberg Uncertainty Principle into play):

a. You CAN measure pairs of commuting observables WITHOUT running into the HUP. So surely it was not the measuring apparatus in this case that messes things up.

b. You CAN measure pairs of NON-commuting observables on two DIFFERENT entangled particles and you WILL see the HUP in action. I.e. if Alice and Bob are entangled photons, and you measure the momentum of Alice and the position of Bob: the HUP will be respected. If this were not the case, then you could learn something about Alice by measuring Bob, and vice versa. The HUP prevents you from accomplishing this. (So surely the measurement apparatus used to test the momentum of Alice did not change the position of Bob.)

The HUP seems to be a universal phenomenon, fundamental to quantum particles.