Q&A: The Uncertainty Principle
The Uncertainty Principle
Question
Recently a thought passed through my mind (that doesn’t happen to me very often) that the term "Heisenberg’s uncertainty principle" is confusing. After all, the claim is not that we lack the ability to know *with certainty* two different properties of a particle (velocity and position? position and momentum?) but that we cannot know the two properties at the same time at all. Not knowing is not the same thing as knowledge that lacks certainty.
Given that, would you agree with me that the term "uncertainty principle" is indeed misleading?
Answer
Absolutely not. You do not understand what this principle says. There is uncertainty in the value of the position and uncertainty in the value of the momentum. The smaller the first is, the larger the second is, and vice versa. And that is exactly what it means to say that there is uncertainty in knowing those values.
Discussion on Answer
There is no inverse relation between the value of the position and the momentum. The inverse relation is between the uncertainty in the position and the uncertainty in the momentum. For example, if the value of the position has an uncertainty of 1%, then the uncertainty in the value of the momentum will be large (say 90%), and vice versa.
I understand. But if so, someone who claims something like:
"It is impossible to know simultaneously both the value of the position and the value of the momentum"
is making an incorrect claim.
That is because it is possible to know both of those values, except that this knowledge will have a different probabilistic status.
Am I right?
Precisely. Just note that if you know one value with certainty, the information about the other is worthless. So it is also correct to say that you cannot know it.
So it follows from your last remarks that there are indeed situations in which the description "uncertainty" does not really fit them…? Because the information about the second one "is worth nothing."
That is an extreme case, where the uncertainty is absolute.
Sorry, I can’t understand why to call this uncertainty. If, as you say, there is an inverse relation between the value of the position and the value of the momentum (the smaller the first is, the larger the second gets), then what exactly is "uncertain" here? Is it uncertain that there is such an inverse relation?
Again, from what I read in the past I understood (maybe mistakenly) that we simply cannot know anything about the value of the position if we know the value of the momentum (and vice versa).