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Heisenberg's uncertainty principle is one of the most fundamental principles on which quantum mechanics is based on. But it is also one of the most confusing laws we encounter. My doubt is whether the uncertainty is due to observation error or due to dual nature of matter ?

Dual nature of matter states that a particle exhibits properties of both particle and wave. My question is whether at any given time a particle exists both as a particle and a wave combined. I mean quasi-state. Statistically we can say a given ensemble for a given time interval is 80% matter and rest wave. But my question is in terms of extremely precise measurements i.e., particle is observed for time interval which is given by an impulse function. If time interval is large we wont get result in absolute(discrete) terms but as a statistical graph. In more technical terms does a particle follow a Gaussian distribution as mass and wave for a given time interval. The significance of gaussian distribution is that it is applicable only for mutually exclusive events.

Is the existence of particle nature and wave nature mutually exclusive events for time period tending to zero?

anuraag
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  • i have answered something similar recently here http://physics.stackexchange.com/q/107397/ . The particle nature of the wave nature appear as a function of the experiment looking at the quantum mechanical "entity" within the HUP constraint. Outside it it is classical particle behavior. also answer to another similar question here http://physics.stackexchange.com/q/103294/ – anna v Apr 12 '14 at 15:00
  • There are some relevant commentis in my answer to another question. This is about photons, but the comments apply to any particle. – John Rennie Apr 12 '14 at 15:04
  • @user38515 I could also recommend reading Heisenberg's The Physical Princple's of The Quantum Theory. It has some very nice descriptions of this from the man himself! – Flint72 Apr 12 '14 at 15:08

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Uncertainty principle is due to intrinsic uncertainty of nature.

Yes, at any given time a particle exists both as a particle and a wave combined. Following part of your question is related to the complementarity principle (of the most accepted Copenhagen interpretation of quantum mechanics) claims that wave and particle are similar to two sides of a coin. That's to say, you can show the wave characteristic or the particle characteristic by measurement, but can't show both of them.

Qianyi Guo
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  • Is existence of quasi-state(both particle and wave as a state) ruled out? Is the measurement of such a state ruled out? – anuraag Apr 12 '14 at 15:15
  • All matter exhibits the properties of both matter and wave at any time. Measuring it in some way may reflect matter properties more and measuring it in some way may reflect wave properties more. – Qianyi Guo Apr 12 '14 at 15:25
  • Can you be more elaborate. If quasi states exist then we get complex solutions i.e., e^(i theta). Many systems can measure these complex results. – anuraag Apr 12 '14 at 15:26
  • For measurement I have taken a time period tending to zero(impulse function). If the quasi state does not exist I get reading as either mass or wave. If quasi state exists we can get both mass and wave as a complex solution. – anuraag Apr 12 '14 at 15:27