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The reason why we can't determine the precise value of position and momentum is because when the light (photon) is shown onto an electron, it will alter the course of the path the electron is traveling on. The light scattered from the electron will affect the electron's momentum and position because both particles are small enough and traveling at velocity where they can affect each other.
The precise value of the distance (x) and momentum (p) of an electron cannot be precisely known because the photons it is exposed to will affect the electron's path. Therefore, the distance of the electron is unknown, creating uncertainty in its velocity and momentum. The value of the position and momentum of an electron cannot be simultaneously known. For this reason, we have to account for difference in both (Δp and Δx ). Hope this helps!
I found the way that Professor Lavelle explained this concept in lecture today very helpful. Basically, if you passed something with large mass such as a baseball or human being through a stream of light, the distance and time could be accurately computed by multiple light beams because the track of the mass is known and direct from one beam to another. The light does not alter the course of the large mass, such as if you were walking past a light sensor in the doorway of a store. But for electrons as small particles this is not true. The light rather skews the path of the electron making the measurements not exact and creating the need for Heisenberg's Indeterminacy Equation.
We have to account for the difference in position and momentum because electrons have such small mass that the presence of electromagnetic radiation, or light, causes the electron to alter its path and momentum. We use the symbol delta p and delta x because delta represents change which shows that there could be some variance in the possible values of momentum and position due to the light that hits the electron. Therefore, we aren't able to determine the exact value of position or momentum, shown through the Heisenberg Indeterminacy Equation, (indeterminacy in momentum) x (indeterminacy in position) >= h / (4 x pi). This equation shows that if a more accurate value of one of those variables is known, then the indeterminacy of the other value is larger.
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