Violation of uncertainty principle?

In summary, the conversation discusses the concept of uncertainty in quantum mechanics and how it relates to the ability to predict the exact location of an electron. It is explained that knowing the momentum with no uncertainty does not guarantee the ability to calculate the exact location of the electron, and that the uncertainty in position is infinite in this scenario. Therefore, there is no violation of the uncertainty principle.
  • #1
AlonsoMcLaren
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Suppose I have an electron gun that shoots electron with momentum p (no uncertainty) at t=0, then at t=t0 I can calculate the exact location of my electron, with no uncertainty.

Violation of uncertainty principle?
 
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  • #2
If there is no uncertainty in the momentum of the electron, then your gun will need to have an infinitely wide barrel.
 
  • #3
AlonsoMcLaren said:
Suppose I have an electron gun that shoots electron with momentum p (no uncertainty) at t=0, then at t=t0 I can calculate the exact location of my electron, with no uncertainty.

Violation of uncertainty principle?

A single measurement of the position tells you nothing about its uncertainty. Only if you make many measurements of position, and always get the same location, can you say there is no uncertainty in position. Quantum uncertainty is about predictability, not about an exact measurement. What we call the "uncertainty" in quantum mechanics is called the "standard deviation" in ordinary statistics:
The uncertainty in position is [tex]\Delta x = \sqrt {\left\langle {\left( {x - \left\langle x \right\rangle } \right)^2 } \right\rangle } [/tex]

If you know the momentum with no uncertainty (meaning that when you repeatedly measure momentum, you always get the same momentum value), then you cannot "calculate the exact location of my electron". Your assumption that you can do so is incorrect. In quantum mechanics, we can only calculate the probability of finding the electron at a particular location when we measure its position. If the electron is known to be in a momentum eigenstate, as in your example, the calculated uncertainty in position is infinite, not zero as you suggest! Quantum mechanics predicts an equal probability of finding the electron anywhere. If we do your experiment many times, each position measurement will most likely find the electron at a different location. There is no violation of the uncertainty principle.
 

FAQ: Violation of uncertainty principle?

What is the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, states that the position and momentum of a particle cannot be simultaneously measured with arbitrary precision. This means that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

Who discovered the uncertainty principle?

The uncertainty principle was first proposed by German physicist Werner Heisenberg in 1927. He was working on the mathematical foundations of quantum mechanics and realized that there was a fundamental limit to our ability to measure certain properties of particles.

How does the uncertainty principle affect our understanding of the world?

The uncertainty principle has significant implications for our understanding of the microscopic world. It means that we can never have complete knowledge or control over the behavior of particles. It also challenges our traditional understanding of cause and effect, as it suggests that certain properties of particles are inherently uncertain and cannot be determined.

Is the uncertainty principle proven?

The uncertainty principle has been extensively tested and is considered a fundamental principle of quantum mechanics. However, it is still an area of active research and there are ongoing debates and experiments to further understand its implications and limitations.

How does the uncertainty principle relate to everyday life?

Although the uncertainty principle is most commonly discussed in the context of quantum mechanics, it also has practical applications in everyday life. For example, it is the basis for the functioning of technologies such as MRI machines and electron microscopes.

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