# I don't understand something

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?

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Hootenanny
Staff Emeritus
Gold Member
Is this thread wondering toward Heisenberg's Uncertainty Principle by any chance?

An electron is a charged particle... A time varying electric field produces an electro-magnetic wave perpendicular to it.
perpendicular to what ?

Sure, you would get measurements of positions and velocities.

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

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 what ?
perpendicular to the direction of motion of the particle.. thats what i meant...

Hootenanny
Staff Emeritus
Gold Member
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?
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.

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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??

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
Staff Emeritus
Gold Member
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??
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.

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... [=(]

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

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...

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Astronuc
Staff Emeritus
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.

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

Astronuc
Staff Emeritus
I was getting at -
then should we not be able to detect its presence as it moves around, courtesy this em-wave. Now if we can detect this..
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?

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
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.

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?
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.

ah... k... will do that surely tim_lou..

And.. hmmmm... k, i see your point NeoDevin, but what does the position of the wave have to do with the velocity and the position of the particle? all we need to measure is which angle its coming from to find its velocity (this can be done by measuring the energy we get at a static detector, when the magnitude is highest, then thats the position isn't it?) and the frequency shift to find out the velocity..

Am I right?

Oh... here's another question...
What if in the double slit, if we put this kind of a detector at the 2nd slit, then without doing anything! to the experiment we can measure which slit the electron goes through right...? So... if we did that.. then what pattern do we observe?

It doesn't matter what properties of the wave you are measuring, your measurements will have uncertainty greater than or equal to a certain amount, which means your inference about the position and velocity of the electron will have uncertainty.