Why is there Heisenberg's uncertainty principle?

Then you're getting so far from reality that the question becomes meaningless.

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The point I was trying to make was that if the velocity after t1 is completely unknown, then there is no basis to correlate the event at t2 with the same particle. Besides, even if the two events do relate to the same particle, that still doesn't tell you the velocity after t2, and that is the important point. Heisenburg is talking about the state of the particle _after_ the measurement, as that is what is predictive for the future.

 

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I'm afraid I don't understand why the Heisenberg uncertainty should not hold for a world with a single particle. And why do you think that I don't know the velocity of the particle after I measure it with total precision at t2? The velocity should not change during or after my measurement at t2.

 

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In a "world" that consisted of nothing but a single particle there would be no observer and no decoherence. There would be neither measurement nor anything else similar to the collapse of a wave function. I believe it's the quantum mechanical version of the question "If a tree falls in the forest, but no one is there to hear it, does it make a sound"

Also, in a single particle world, how coul anyone ever determine a "position" or a velocity. as those are relative concepts?

Plus the very existence of a space without anything in it violates the uncertainty principle. At the very least you space should be teeming with virtual particles in addition to the one "real" particle.

 

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Part of what Heisenburg was saying is that measurement perturbs a particle position/velocity. So assuming you can restrict to a single particle, At t1 you know the precise position of the particle and nothing about it's velocity. At t2 you can hypothetically determine the velocity from t1 to t2, but that is in the past and does no good because after the measurement at t2 you have no idea of the velocity from t2 to t3. And so on.

 

Considering the fact that they now bend, fold, spindle, and mutilate photons, and encode data onto individual photons, I would have to say that this uncertainty principle only works in special cases.