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What is the main takeaway from the Heisenberg Indeterminacy Equation?? I am still a little confused about this equation after listening to the lecture. Like what is this "uncertainty" that this equation is trying to find?
Stated in words, the Heisenberg uncertainty equation is: the uncertainty in the position of an object times the uncertainty in its velocity is more than or equal to Planck's constant divided by 4*pi. The uncertainty (or as Professor Lavelle often refers to it, the indeterminacy) is a measure of the range of values that the position and momentum could be. In other words, it refers to the distance between the minimum value and the maximum value of either of these variables (position and momentum).
The indeterminacy equation gives the general idea of where the electron may be. It is impossible to tell with certainty where an electron is located, because of its wave and particle properties, so this equation is used to estimate position, velocity, and momentum.
The main takeaway from the Heisenberg Indeterminacy Equation is that we can never measure an electron's exact momentum and position because, by measuring these values, we change them. Therefore, there is always some element of uncertainty in an electron's measured position and momentum. Heisenberg's equation basically quantifies that uncertainty, therefore allowing us to see the spread of where the electron might be/what its momentum might be. I hope this helps!
The more certain you are of a particle's position, the less certain you can be of it's velocity. The more certain you can be of it's velocity, the less certain you can be of it's position. For really big things this uncertainty is negligible, but once it gets to subatomic particles, it means that you can really only know one of the two.
Thank you for talking about the conceptual underpinnings of the Heisenberg uncertainty principle; it really helps me understand to when it is explained conceptually.
The uncertainty part comes from the fact the we don't know the change in velocity of the electron from area to another, because we know the time takes to travel from one distance to another but NOT the distance itself (velocity= distance/time). This is due to the fact that an electron is so small in mass that if it is hit by a photon, it will be pushed off course and we cannot determine (are uncertain) which direction it will be specifically go and the direction determines the distance as some paths or shorter or longer. That is why in the equation that change in p can be as mass times CHANGE in velocity instead if just mass times velocity. So, the larger the mass of the object, the more predictable and certain the distance it travels it since it is not blown off course by a random photon hitting it.
The thing that really helped me conceptually understand this concept was Lavelle's light detector example in class. When the experiment is done with a ball, the ball travels in one known path after hitting the first light beam. However, when it is done with an electron, a photon in the first light beam throws the electron off course, so we can no longer be sure what path the electron took in between the two sensors. When we are uncertain of the value of x, we are uncertain of the value of velocity, and therefore momentum as well.
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