Heisenberg Uncertainty Principle

[edpell]

Is the Heisenberg Uncertainty Principle as statement about the state of a particle or only a statement about what can be observed about a particle?

 

[chafelix]

Rather the second one. Actually it simply says that you start with a state. Acting with an operator on it measures whatever the operator corresponds to (energy, momemntum,position etc) After the measurement the particle is in an eigenstate of that operator(one that corresponds to the eigenvalue you just measured). Now you want a second measurement, so you act with a second operator, different from the first. If the two operators commute, they may have a common set of eigenvectors(i.e. states), so acting on an eigenstate of the second operator with the second operator will measue the eigenvalue of the second operator, but not change the state. If they do not, then you will force the state to CHANGE into an eigenstate of the second operator and after your measurement you know the state and the value of the observable correspoinding to the second operator. But then, you do not know the value of the first, because the state that occurred when you did the first measurement has CHANGED

 

[Entropia]

The Heisenberg Uncertainty Principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously know the precise position and momentum of a particle. This principle arises from the very nature of particles at the quantum level, where their behavior is governed by probabilities rather than definite outcomes.

To answer the question, the Heisenberg Uncertainty Principle is both a statement about the state of a particle and about what can be observed about a particle. It tells us that the state of a particle is inherently uncertain and that we can never know both its position and momentum with absolute certainty. This is not due to limitations in our measurement tools, but rather a fundamental property of particles at the quantum level.

At the same time, the Heisenberg Uncertainty Principle also tells us that the act of observation itself can affect the state of a particle. This is because the very act of measuring a particle's position or momentum changes its state, making it impossible to know both quantities with complete certainty.

In summary, the Heisenberg Uncertainty Principle is a fundamental principle that applies to both the state and observation of particles at the quantum level. It highlights the inherent uncertainty and probabilistic nature of the quantum world and has significant implications for our understanding of the physical universe.