Understanding the Meaning of Infinity in Uncertainty Principle

[spidey]

for ∆x ∆p ≥ ћ / 2 ..if ∆p = 0, then ∆x is infinity..what is the meaning of this infinity?
does this mean it exist everywhere or it don't exist at all?
my thinking is ..if we say it exist everywhere, then we are certain of its position which itself contradicts with ∆x is infinity..moreover,something cannot exist everywhere since absolute is prohibited in relativity..so we are left with second option..am i correct?
can anyone give meaning of this infinity?

 

[ZapperZ]

for ∆x ∆p ≥ ћ / 2 ..if ∆p = 0, then ∆x is infinity..what is the meaning of this infinity?
does this mean it exist everywhere or it don't exist at all?
my thinking is ..if we say it exist everywhere, then we are certain of its position which itself contradicts with ∆x is infinity..moreover,something cannot exist everywhere since absolute is prohibited in relativity..so we are left with second option..am i correct?
can anyone give meaning of this infinity?

I think you are carrying the same misconception of the HUP that I've described many times before on here.

If the momentum uncertainty is zero, then it means two things:

1. the statistical spread in the measured position is so wide that the repeated measurement of the position gives you the conclusion that standard deviation is infinite.

2. your ability to predict the position of the next particle is zero since the particle can be anywhere.

Zz.

 

[jtbell]

does this mean it exist everywhere or it don't exist at all?

QM (the mathematical formalism) does not address the question, "where does the particle 'really exist' before we observe/measure it?" That is the subject of interpretations of QM, of which there are several, and about which there is much heated debate in this forum and elsewhere.

As Zz notes, as far as QM is concerned (regardless of interpretation) the HUP is a statistical statement related to the probabilities that we will measure/observe various values for the particle's position or momentum, when we do measure/observe it.

 

[spidey]

I think you are carrying the same misconception of the HUP that I've described many times before on here.

Zz.

sorry Zapperz..ever since Heisenberg given this, many layman are having uncertainties in the meaning of uncertainty principle..i am one of them..