Hello everyone,
How convinced are we that the Uncertainty Principle is nothing more than a mathematical glitch, or a trick we use to get around the innermost abstruseness of mathematics? How can we resolve whether this principle simply acknowledges our inability to truly represent nature itself?
It has been asserted that the Uncertainty Principle’s implication that no particle can simultaneously possess position and momentum is a pure reflection of reality itself. I do not agree. I think we arrive at this principle simply because we are unable to truly represent nature itself.
As I have expressed before in this forum, I do not think our theories impeccably define the mechanisms that constitute reality. However, as I should reinforce my stance with an exploration into *something* deeper than my assertion alone, I shall examine the ‘essence’ of the Uncertainty Principle itself. If I can show that the Uncertainty Principle is somehow lacking, then I can affirm my stance.
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The Uncertainty Principle:
ΔxΔp>h
where Δ = uncertainty, x = position, p = momentum, and h = Planck’s Constant.
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1) “Δ” represents our inability to ‘nail it down,’ or as physicists say, uncertainty. In other words, “Δp” might be read, “how uncertain we are as to an object’s *exact* momentum.”
2) “x” represents position. Position is simply an object’s point in space.
3) “p” represents momentum. Momentum is mass times velocity.
4) “h” represents Planck’s Constant. This is perhaps the toughest of these concepts to grasp, as it represents the least ambiguous amount of ‘play’ between a particle’s presence in space and its action in space. As an illustration, imagine we have a machine operated by reciprocating gears. These gears turn for a bit, then stop, then turn in the other direction (i.e., they reciprocate). No matter how well we tune our machine, there will always be some amount of space between the teeth of the gears themselves (putatively *behind* each ‘active’ gear tooth/cog pairing). During gear reciprocation, this space will alternate during gear camming. The smallest universally possible value of this ‘slop’ in the fabric of reality is known as Planck’s Constant.
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Armed with more digestible definitions of the necessary terms, let’s reexamine the Uncertainty Principle:
ΔxΔp>h
In plain English, it means this: Since anything multiplied by zero is zero, and since Planck’s Constant (h) is a positive value, then neither momentum error (Δx) nor position error (Δp) can be zero. Therefore, the principle states, there is always ‘error’ in our calculations of a particle’s position and momentum (neither “Δ” can be reduced to zero).
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Some assert that this principle's repercussions go further than our measurement 'errors,' but in fact represent an inherent aspect of reality. I disagree, and can pose a dilemma with the third building block of this principle: momentum.
Look back at our definition of momentum. Momentum equals mass times velocity. Mass is an object’s quantity of matter, and velocity is its function of displacement. Displacement is a linear vector of separation between two fixed positions.
Therefore, as displacement requires a measurement of position, and velocity requires a measurement of displacement, and momentum requires a measurement of velocity, then momentum requires a measurement of position.
But does not the Uncertainty Principle state that the absolute measurement of position is untenable? Indeed, it does.
The Uncertainty Principle denies its very foundations, and therefore its own validity.
-LH |