Heisenberg's Uncertainty Principle

[jimmy p]

Hi, my physics tutor was explaining to the AS physics class about Heisenberg's Uncertainty Principle, and having never been told about it in any great detail, I am intrigued. I vaguely understand part of it but i would be grateful if someone could explain the other part, which as far as i know has E and t involved in it, and if they could maybe the other part too.

I would have listened myself but I am in A2 physics and i have other things to worry about (SHM).

Thanx
Jimmy

 

[Fuego]

what i know is as follows:

heisenberg's uncertainty principle states that you cannot know the exact position of a particle and its exact velocity. as the certainty with which you know its position increases, the certainty with which you can know its velocity decreases, and vice versa. you can put this into an inequality which is something like this (i don't remember exactly):

pv > h/2

where p is the uncertainty in the particle's position, v is the uncertainty in its velocity and h is Planck's constant.

i believe you can substitute other quantities for position and velocity, such as energy and time.

i'm als doing A2 physics so you'd probably better wait for someone who knows more about this.

 

[Njorl]

The momentum/location relation has a more intuitively meaningful consequence - to know a particle's location, you must hit it with light, changing it's momentum.

The time/energy relation is a bit more abstract. Essentially, if you want to know the energy of a time-varying phenomenon, like a lightwave, you can make the measurement more accurately over long periods of time. An instantaneous measurement (dt=0) yields no information on energy. You might think measuring over one wavelength would yield perfect accuracy of photon energy, but it does not. A single photon is really of infinite length. Perfect measurements thus require infinite time, shorter measurements incorporate virtual photons necessary to form a finite pulse from superimposed wavetrains.

Njorl

 

[wolfgang]

Hi,
You mention the momentum/location and energy/time relations but what about the angular momemtum/angle relation Äl*Äè > h/2ð ?

 

[jimmy p]

huh??

What there's more? ARGH! please, if u really want to explain that u can but...well, I am happy with anything i suppose

 

[wolfgang]

I am not quite sure but Äl*Äè > h/2ð means that we can not know exactly the value of the angular momentum and its direction at the same time.

 

[jcsd]

Hesienburg's uncertainity principle in it's most precise form is (in terms of uncertainty in momentum and postion):

Δp_xΔx >= h/4π

though mostly it can be assumed that value is approximately h/2π

This relationship applies for any set of what are known as complementary pairs of measurments like energy and time for example (there is an equation known as the generalized uncertainity principle which is non-specific for the quantites measured, but the maths is beyond what is taught in a A2 level).

In the case of angular momentum, different components of the angular momentum form a complentary pair, so you cannot know both the value and the direcion (with respect to the z -axis for example).

 

[wolfgang]

Hi everyone,

I do not think that Äpx*Äx >= h/4ð is correct.

As we know a particle that is moving can have an orbital angular momentum which minimum value on a specific axis is h/2ð and an intrinsic angular momentum(spin) which minimum value on a specific axis is h/4ð.

In Äpx*Äx >= h/4ð the Äpx*Äx is the angular momentum because we are using the orbital velocity of the particle to calculate the momentum Äpx so the Äpx*Äx >= h/4ð is not correct.

Even if we say that Äpx*Äx is the intrinsic angular momentum of the particle then what Äpx and Äx would mean in the intrinsic rotation motion of the particle?

If anyone has any objection please to replay and correct me.

 

[jpritch]

hi jimmy p

I found a website you might want to check out.

http://www.aip.org/history/heisenberg/p08a.htm

 

[wolfgang]

o.k the site says that is Äpx*Äx>= h/4ð but can somebody explain me WHY ?

WHY is h/4ð and not h/2ð ?

 

[jcsd]

Originally posted by wolfgang
Hi everyone,

I do not think that Äpx*Äx >= h/4ð is correct.

As we know a particle that is moving can have an orbital angular momentum which minimum value on a specific axis is h/2ð and an intrinsic angular momentum(spin) which minimum value on a specific axis is h/4ð.

In Äpx*Äx >= h/4ð the Äpx*Äx is the angular momentum because we are using the orbital velocity of the particle to calculate the momentum Äpx so the Äpx*Äx >= h/4ð is not correct.

Even if we say that Äpx*Äx is the intrinsic angular momentum of the particle then what Äpx and Äx would mean in the intrinsic rotation motion of the particle?

If anyone has any objection please to replay and correct me.

As I said before an uncertainity of h/4pi is the most precise form of the HUP for most pratical purposes an approximate value of h/2pi is sufficent.

I see what you are saying, but you are incorrect, the value of h/4pi is well-known and appears in all QM textbooks.

 

[VBPhysics]

You guys are getting some things confused:

1)The HUP is not constricted to just one or two groups of quantities.

2)The HUP as you are speacking of it arises from the statistical interpretation physicist use when explaining quantum phenomenon.

Qualitatively what it means is that there are certain pair arrangments which represent observable quantities(like where something is, or how fast it is going) that you cannot measure at the same time, for example

Position and momentum / Energy and time

this has to do with the way in which physicist use probability to more or less average out an expected value for observable quantities.

quantitatively it has to do with a mathematical concept known as an "operator"(a mathematical operation unique to each observable quantity which helps physicist average out observable quantities), and with or not the are compatible. pairs are considered compatable if you get the same answer by doing the following 2 things:

take a particle, measure quantity one, measure quantity two
take a particle, measure quantity two, measure quantity one

for some observable pairs like energy and time or position and momentum the final measurements will not be the same, thus they are incompatable and have an uncertainty.

as a side note: there are compatablie operators momentum and energy have no uncertainty in this respect.

 

[VBPhysics]

also this h/2pi , h/4pi business

there is a quantity known as h-bar(it looks like an h but has a horizontal line through it about mid way up the vertical line on the left)

h-bar is defined to equal h/2pi

the uncertainty relations that yall are speaking of are
> or = h-bar/2, which is = h/4pi

I think someone is just getting confused about the bar part.

 

[jcsd]

VBphysics, you mean the generalized uncertainty principle, which can be used to calculate the uncertainty in any pair of physical quantities.

h-bar can be used as an approximate value for uncertainity in most situations.

 

[VBPhysics]

the only place I have seen that is in conceptual physics books. I have NEVER seen it in any analytical Physics books.

 

[jcsd]

My conceptual QM textbook doesn't have that value in it, but the approximate pratical for most situations of h-bar is given my physics dictionary.

 

[jimmy p]

Hey thanks for the website. I had a lookie and its cool lol! I love it when ppl type in comic sans! Oh yeah and the information was good too, how i like things explained