[Physics] Uncertainty principle with two photons

heisenberg-uncertainty-principleMeasurementsphotonsthought-experiment

Imagine an experimental setup in which you have to measure the momentum and location of a particle. To measure it we know we will have to affect it, and the uncertainty principle would come into the picture, but I have a different setup. The classical setup is that you fire a photon to measure the location of the particle, but the particle will change its momentum due to the collision with the photon.

I decided to take two photons. I will shoot one photon from either side of the particle, so the effects of the two photons cancel each other, giving an accurate measurement. To understand this, see the picture below.

  1. The classic experiment

    enter image description here

  2. My thought experiment

    enter image description here

In the second experiment, we shoot a photon of the same energy as the first one and counteract the effect of the first photon, so the electron would continue on its original path. Please tell me where I am wrong.

EDIT

We will have to take multiple photons but equal from both sides and in opposite directions.

Best Answer

First of all, the uncertainty principle is more than just disturbance of observation.

From the Wikipedia article "Uncertainty principle":

Historically, the uncertainty principle has been confused with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems. Heisenberg offered such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty.

It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology. It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer.

Now, you've drawn 'the' path of the electron as if the electron has a definite trajectory and that two photons of equal and opposite momentum interact with the electron at a definite location.

However, the state of definite position has maximum 'uncertainty' in momentum! Not only can there not be a definite trajectory but, if the electron is localized by an interaction, one cannot escape the inherent uncertainty of that localized state.