Thread: Heisenberg Uncertainty Principle

Can somebody please give a clear explanation of the Heisenberg Uncertainty Principle? I understand that it states you cannot determine the position and the momentum of a particle cannot both be known to high accuracy. The greater the accuracy of the position, the less accurate the momentum and vice versa. Also, I believe this is also a physical limitation, not a technological limitation. The main issue is, I don't understand WHY you cannot determine both quantities with high accuracy. If somebody could clarify things, that would be great! Thanks

Ok, lets say that you want to know the position of an atom. In order to do this you will need to reflect light or particles off it to find out where it is. However, doing so will slightly affect its position because there will be a momentum transfer between the particle and the atom, so by the time the particle has returned to your detector, the atom will have moved slightly from where it was when it was hit by the particle, thus giving you a slight measurement error.

Yes, but if the particle I choose to use to measure the atom does not have a large momentum, the atom's position would not change very much, thus the position measurement should be within a high degree if accuracy. In addition, if the particle has a low momentum, then the collision with the atom should not change the atom's momentum very much either, and I should also be able to obtain the momentum measurement with accuracy. So, I don't see the contradiction between the position and momentum; they both should be able to be obtained with accuracy.

Originally Posted by MrRice5555

Can somebody please give a clear explanation of the Heisenberg Uncertainty Principle? I understand that it states you cannot determine the position and the momentum of a particle cannot both be known to high accuracy. The greater the accuracy of the position, the less accurate the momentum and vice versa. Also, I believe this is also a physical limitation, not a technological limitation. The main issue is, I don't understand WHY you cannot determine both quantities with high accuracy. If somebody could clarify things, that would be great! Thanks

"Why" is unfortunately not a question that science can answer. Science address "how" not "why".

You have the basic idea correct. When you make one measurement, say of position, you introduce and uncertainty in the momentum.

In terms of the quantum mechanical model it is because i.e. the position operator "x" does not commute with the momentum operator d/dx.

"Why" was the wrong word to use. I apologize for the confusion. What I meant was how is determining both position and momentum accurately impossible? If you can find the position accurately, and the momentum accurately, how is it possible for them to not be simultaneously accurate? I've done some research, and I believe its related to the wavelength and frequency of the particle you are measuring, however, from there my understanding stops.

Sorry, I don't understand your mathematical explanation as it involves derivatives and calculus, and I'm only a high school sophomore so I haven't had much experience with calculus yet.

I don't know, if it helps, but it can be reduced to a simple mathematical property, the Cauchy-Schwarz Inequality. In this way, the Uncertainty Principle can be regarded as a simple mathematical property of a vector space. Therefore, it is also a property of nature, and not a pure consequence of the act of measurement. Still, it reveals that property. Quantum mechanics do also work, if you do not observe its processes.

The Wikipedia article doesn't help?

I don't understand WHY you cannot determine both quantities with high accuracy. If somebody could clarify things, that would be great! Thanks

This is because a perfect momentum measurement implies an infinitely long wave (as particles are described by the wave function(schrodinger) in Quantum mechanics), so the particle could be anywhere. Similarly, if the energy is exact, you can have no knowledge of the time when it got there.

this is related to the Copenhagen interpretation, where it says that every particle is described by a wavefunction.

in fact the inequality represented in my forum image, is actually the quantum mechanical equation for the uncertantity principle, derived from the De Broglie relation.

I've never been very sure about Heisenberg's Uncertainty Principle.

All hail the Time Lord!

Originally Posted by MrRice5555

Sorry, I don't understand your mathematical explanation as it involves derivatives and calculus, and I'm only a high school sophomore so I haven't had much experience with calculus yet.

The unfortunate truth is that you will have a very difficult, probably impossible, task of understanding quantum mechanics in detail without a very strong foundation in calculus.

In fact, basic physics is not really understandable without calculus. Newton invented calculus for just that purpose.

My strong recommendation is to learn your mathematics through calculus at least before you try to understand the subtleties of physics. And quantum mechanics is very subtle.

Once you have the basic mathematics under your belt a very nice presentation of quantum mechanics at an introductory level can be found in The Feynman Lectures on Physics. There you will find a discussion of the uncertainty principle by a master of the subject, but you do need calculus.

The basic idea is that if you measure position, you change the momentum and vice versa. A very rough idea is that locating position usually means hitting the particle with a photon of light to find it and that imparts momentum. The more precise the position location, the shorter the wavelength of light involved and the greater the potential momentum change.

Ah I see, momentum and position are inversely related, therefore, the smaller the error of one, the greater the error of the other. I understand this subject better now, though I will continue to research it. Many thanks to those who contributed.

2500 years ago Dzeno proved, that if some variable is continuous then a system which consists of more then one element (e.g., for spatial variable - of Achilles and a tortoise) practically can not change. So the unique variant follows – if the variable at some moment becomes be uncertain (and so – the correct name of the principle should be "Zeno – Heizenberg Uncertainty principle").

Cheers

More about the uncertainty in QM and something else see -
http://arxiv.org/abs/0812.2819 , V5;

though it is rather desirable to have read the paper http://arxiv.org/abs/1004.3712 before/ also.

For example - as it seems the SR theory becomes be more understandable…

Cheers

Originally Posted by SSDZ

More about the uncertainty in QM and something else see -
http://arxiv.org/abs/0812.2819 , V5;

though it is rather desirable to have read the paper http://arxiv.org/abs/1004.3712 before/ also.

For example - as it seems the SR theory becomes be more understandable…

Cheers

Those ArXiv e-prints (apparently not to be published in a refereed journal) appear to be nothing but jiunk.

seriously ssdz, linking to an actual paper would be helpful. The links you provide contain no information, do you realize this?

I always just take it to mean that you can't know all 4 coordinates that describe an object's location in space and time. If you could accurately measure an object's location and the time at which it occupied that location at two separate moments, then, from that, you could easily determine what its velocity had been in the meantime.


Of course, there is also the problem of energy existing in packets/photons, which makes a totally precise measurement of any kind impossible. Your margin of error is always +/- one half photon.

To: DrRocket
- It seems you forgot t what SSDZ wrote (SSDZ posts in the thread "The informational physics" of Tue Dec 29, 2009 5:30 am and of Wed Dec 30, 2009 4:09 am.)

on your previous post of Mon Dec 28, 2009 6:26 am (after this post and post of Waveman28 of Tue Dec 29, 2009 5:40 am the thread was moved from “Physics” section on this forum to “Pseudoscience” section -http://www.thescienceforum.com/viewtopic.php?p=249137).

Or you didn’t read the posts. Would you be kind to read these posts, possibly again? – I can add to these posts nothing.

To: Arcane_Mathematician

- if you click on "PDF only" option in the link http://arxiv.org/abs/0812.2819 , you obtain "real" version V5.

Though, since you (as it seems) have read the http://arxiv.org/abs/1004.3712 paper,

you can pass the text till section 2.2. – this section is mostly modified comparing with V4.

On another hand paper's another sections are corrected somewhere also, e.g., - relating to misprints.

Though some minor misprints appeared – in two lines after Eq. (6b) , but they are evident and non – essential.

To: kojax

Indeed you cannot know all 4 coordinates exactly – since these coordinates are defined in Matter so that corresponding physical action (or angular momentum) is equal 1 Dirac action. More – see the link http://arxiv.org/abs/0812.2819 .

Cheers

There seems to be a lot of confusion here about what the Heisenberg Uncertainty principle actually says.

Imagine you have a laboratory filled with 1,000,000 little boxes containing a particle. You set up each particle in each box to be in the exact same physical state (so the wave functions are all identical). You go from box to box and measure the position of each particle (for simplicity, assume every state is time-independent and 1-dimensional).

After measuring all these positions, you calculate the standard deviation of the measurements. If you plotted these measurements on a histogram, the standard deviation measures how spread out the histogram is.

Next, you put all the particles back into their original states. You go from box to box, but this time you measure the of each particle. You calculate the standard deviation of all of these measurements and call it .

The Heisenberg Uncertainty principle states that, as the number of measurements (1 million in our case) gets larger and larger, the standard deviations are inversely related to each other in the following way:



So that's what it means. And it makes total sense if you recall that the position and momentum wave functions are Fourier transforms of each other.

The uncertainty principle is not related to technology but is an intrinsic property of QM. It relates 'observables' such as position and momentum by the accuracy to which they can be ultimately determined. Another two would be time and energy, which appear in theories of spontaneous pair creation, small black hole evaporation and even the creation of the universe.

I also recommend anything by Richard Feynman, he was excellent at popularising QM.