Alexis asked in Science & MathematicsPhysics · 2 months ago

# What is the Heisenberg's Uncertainty Principle vs Observer Effect? They seem to describe the same thing?

What system does this explain here.

‘’that you can never know with absolute certainty where the particle is and it’s speed.” .....””You may know it’s speed but not where the particle is or know where the particle is but not it’s speed””

If so why is it the case that you cannot know where the particle is and it’s speed at the same time? You may know where the particle is but not it’s speed or you may know it’s speed but not where the particle is.

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• 2 months ago

A particle doesn't have a definite position and momentum at the same time. It isn't that we can't measure it, but it doesn't have those properties at all. Before a measurement, the particle has neither property. After a measurement, it has either position or momentum or a combination of both. But not both completely.

• 2 months ago

Walter Heisenberg was once pulled over by a traffic cop who said to him "do you know that you were doing more than 65 mph back there ?"  Heisenberg replied "well, thanks a bunch, now I have no idea where in hell I am!".

• 2 months ago

The uncertainty principle and observer effect should not be confused with each other.

The observer effect states that measurement of a physical system cannot be made without affecting the system itself. It is about the inherent imprecision of our measuring equipment.

The uncertainty principle is something else. It's not about the imperfection of observing equipment, it is an inherent property of nature. There are several interpretations, one of which comes from wave mechanics.

According to de Broglie, every object in the universe is a wave. The position of the particle is described by a wave function

Ψ (x,t)

Max Born interpreted this as a probability density function

p (x,y,z) = |Ψ (x,y,z,t₀)|²

of finding the particle in a certain area.

The measures of the (im)precision of position and momentum are then standard deviations σₓ and σₚ, respectively.

With a simple plane wave, the position of the particle is very uncertain - it can be practically anywhere along the wave packet. To increase the accuracy of position and reduce σₓ we can superimpose several waves. The cost is that the wave becomes a mixture of waves of many different momenta and that increases inaccuracy σₚ of momentum ---> σₓ and σₚ have an inverse relationship.

The Principle of Uncertainty is quantifying the tradeoff between the respective precisions of the two by stating

σₓ σₚ ≥ ℏ / 2

where ℏ is the reduced Planck constant, ℏ = h/(2π)

In layman's terms, this is a consequence of dual nature of matter - it is both matter (in common sense) and wave (energy). On the macroscopic scale, we can use equations to simultaneously, at least in theory, predict the position and momentum of bodies like snooker balls. As we get smaller, the wave properties of matter become increasingly more pronounced, to the level of subatomic particles, when matter is "so much wave" that we cannot talk about exact position and momentum at the same moment. The more precisely we determine one of them, the less certain the other is. We then apply statistical probability to predict the outcome of the experiment.

Einstein's famous quote that "God does not throw dice" is from his debate with Max Born and Niels Bohr who advocated the probability approach.