I don't understand something...

The_Thinker

An electron is a charged particle... A time varying electric field produces an electro-magnetic wave perpendicular to it. So when an electron moves, it should also produce an electromagnetic wave perpendicular to it. Isn't this true?

Now if this is true... then should we not be able to detect its presence as it moves around, courtesy this em-wave. Now if we can detect this.. then we should be able to find out its velocity through the shift in frequency and we should be able to detect its position by putting detectors at the right place.

Is this wrong?

Hootenanny

Is this thread wondering toward Heisenberg's Uncertainty Principle by any chance?

lalbatros

perpendicular to what ?

Crosson

Sure, you would get measurements of positions and velocities.

I don't know what you mean by "the position" and "the velocity".

The_Thinker

ah... yeah.. Hootenanny... thats what i was wondering about... if you can measure the position and velocity of the thing... then how does that not go against the uncertainty principle?

and lalbatros:
perpendicular to the direction of motion of the particle.. thats what i meant...

Hootenanny

Because the HUP doesn't say anything about whether or not you can measure both the position of momentum of something simultaneously. It does however, say that you cannot measure both to an infinite precision, regardless of the accuracy of your instruments. The HUP is a mathematical principle which come about because the momentum and position operators do not commute.

The_Thinker

so... hmmm... if it is just a mathematical principle... then how is it that people use it as a fundamental principle? I have read and heard of things where they say that the HUP also applies to energy and that is why QM states that a pair of protons and anti-protons can just appear and annihilate each other stating HUP as a reason...

Have I heard or read wrong??

tim_lou

the uncertainty principle is a mathematical one. It can be derived from Schrodinger's equation (the non-relativistic one... I don't know anything about the relativistic one though) and theories from linear algebra.

Hootenanny

No, you have heard correctly. Unfortunatly, I don't have time for a full explanation now (I've got spiderman 3 tickets ). However, I can say that it isn't just a mathematical principle, it is the fundemental principle that the whole of QM is based on. It is if you like, the basis of the mathematical formalism behind QM.

The_Thinker

cool k man... have fun...

(and do let me know how it is... ive been dying to see it myself...)

K... well ill just read up on it... physics sure is weird... [=(]

pallidin

I posit that that core problem is that we do not fully understand the nature of momentum; not that I have explanation.

tim_lou

even if you have electromagnetic fields to measure, I doubt the wave would have an exact value of momentum, and/or "position" to give you an exact value of the position of the electron itself.

I may be wrong though, as photon obey the relativistic Schrödinger's equation and the commutator of the position and momentum operator might be different. (I'm pretty sure the derivation based on Cauchy-Schwartz's inequality would still be valid though).

quantum mechanics is indeed a very abstract subject... as momentum and position become operators rather than definite numbers.... and you can only talk about the average of all the position and the average of all the possible momentum...

Astronuc

What is the magnitude of the electric field of one electron? Then think about what is the 'change' in the electric field of one electron as a function of its velocity.

The_Thinker

ah.. k... tim_lou, wish i knew what all those terms meant.. I just know a little of what ive read here and there... dunno in depth, will someday when im done reading all the books... but k... anyway.. thx for the reply...

but Astronuc
Im sorry... but i don't quite get what your getting at..

Astronuc

I was getting at - How does one detect a single electron? What is the sensitivity of the detector? Does the detection process influence the position, energy or momentum of the electron?

tim_lou

Neither do I before this semester... If you just grab Griffith's text on quantum mechanics, you'll know most of the terms in one week.

NeoDevin

We can determine both the position and velocity from this wave, but the wave does not have precisely defined properties itself. We can measure the properties of the wave emitted, but there will be some uncertainty to the measurements of the wave (because of it's wave nature, it doesn't have a well defined position, for example). The uncertainty of this measurement translates into an uncertainty about the inferred properties (position, and momentum) of the electron, which will be greater than or equal to the limit expressed by the uncertainty principle.

Astronuc:
This is independant of any particular measuring apparatus, or how that equipment may or may not affect the electron.