Can we find the definite path of electron?

Question

Light can crisscross in all directions.
Source: Can photons pass through each other?

In a given volume, we can have light throughout, such that there is no space with no light in it (with the electron which is to be seen).

Light gets scattered or reflected from the electron, in either I hope we can expect absorption and re-emission of photon (and thus use this to see the electron with appropriate technology).

Source (covers only an idea of quantum picture of reflection) : http://arxiv.org/abs/1207.0998

(I couldn't find better source on this, any related source or suggestion of reading w.r.t this, particularly on the difference between quantum picture of reflection and scattering, will be of interest to me)

Absorption and re-emission involves time delay (around $10^{-23}$ to $10^{-20}$ s).

Source: http://arxiv.org/abs/1207.0278

This time delay won't affect if the photons are incident continually. With this thought experiment, can we track the electrons definite path?

Answer 1

If your electron is very fast you can track its trajectory in a ionization chamber. But if the electron is slow, its wave-like (quantum) character enters into the scene.

About absorption and re-emission of a photon, please check if such things are possible, i.e. write the laws of conservation of energy and momentum as if these two bodies are billiard balls, $$ \frac{mV^2}{2}+\hbar\omega=\frac{mV'^2}{2} $$ $$ mV+\frac{\hbar\omega}{c}=mV' $$ where $V$ is the electron velocity before collision, and $V'$ is after. Dividing the 1st equation by $c$, then subtracting it from the 2nd equation, you get $$ mV\left[1-\frac{V}{2c}\right]=mV'\left[1-\frac{V'}{2c}\right] $$

So, the solution is $V = V'$, which introduced in the equations gives $\hbar\omega=0$. I.e. impossibility.

Now, a few words about the electron with small velocity. First of all it becomes a wave-train. Still, we can apply the conservation laws (why so? - this is the dual character, particle and wave, of the quantum objects). Since the electron mass is also very small, the linear momentum $p = mV$, is also small. Collision with photons - if we try to irradiate the electron with light for observing its movement - may be destructive for the electron path. Each collision would kick the electron in some arbitrary direction.

Answer 2

In a given volume, we can have light throughout, such that there is no space with no light in it (with the electron which is to be seen).

Note that in this view you can hardly talk of photons as particles localized somewhere and somehow bouncing around. If you consider a given volume with a given amount of electromagnetic radiation in it you are talking of an electromagnetic cavity, which will contains "photons" as (non-localized) normal modes with defined momentum. See e.g. wave and modes. This does not mean of course that you cannot have scattering with electrons or such.

Light gets scattered or reflected from the electron, in either I hope we can expect absorption and re-emission of photon (and thus use this to see the electron with appropriate technology).

Scattering and reflection are basically the same thing. "Reflection" is the electron (or whatever) scattering at 180°. Scattering events are generally described in Feynman diagrams as absorption-emission events. For example in the case of electron-electron scattering (also called Møller scattering) you can describe (to first approximation) pictorially the process as the following:

There are a number of ways in which an electron can scatter with another electron or a photon or whatever, as you can see for example here.

Absorption and re-emission involves time delay (around $10^{-23}$ to $10^{−20}$ s). This time delay won't affect if the photons are incident continually. With this thought experiment, can we track the electrons definite path?

I'm not sure I understand what "thought experiment" are you referring to. The time delay between absorption and re-emission is the cause of the slower velocity of light inside matter, i.e. of the refractive index (see slow light for a nice consequence of this).

To detect the path of an electron there are a number of ways, for example Cloud Chambers are used to detect charged particles, and produce images like the following (these are alpha-particles, not electrons, but the concept should be the same):

To use the time-delay alone as a mean to detect the path of an electron seems hard, but maybe if you explain better what you are thinking of (incident continually where? among each other?) it will be easier to answer you.

Answer 3

I read what is written in the physicsforums.com/threads/ that you indicate. So, you speak of the electron as of a QUANTUM particle. That means that it has a linear momentum of the same order of magnitude as that of the particles with which you want to test its movement.

If the linear momentum of those particles were much smaller, s.t. the collision with them wouldn't practically modify the electron's linear momentum, the study of those particles after collision could give information on electron's trajectory, because the latter weren't be modified.

But, I understand that this is not the case. Now, in quantum theory, position and linear momentum QUARRELL, due to the uncertainty principle. The velocity has indeed an operator, which is the derivative of the position operator, but that doesn't mean that in any experiment the velocity is a CONSTANT OF MOTION. You have to see what happens in the experiment that you study.

In short, whenever you measure the position with a precision (Δx, Δy, Δz) you disturb the linear momentum by Δp_x = ħ/Δx, Δp_y =ħ/Δy, Δp_z = ħ/Δz. So, your electron will pick, arbitrarily, one of the new linear momenta and after Δt you will find it at the corresponding point on that path. As you correctly noticed, making Δt smaller, won't help.

Maybe now I answered your question,

Sofia

P.S. Let me quote Dante Alighieri's saying (about what was written on the gate of the "Inferno") : "Abandon any hope thee who enter". This is one of the disappointing things in the quantum mechanics - and there are MUCH, MUCH worse ones.