Understanding the Meaning of Infinity in Uncertainty Principle

In summary, the HUP states that 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, and 2) your ability to predict the position of the next particle is zero since the particle can be anywhere.
  • #1
spidey
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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?
 
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  • #2
spidey said:
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.
 
  • #3
spidey said:
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.
 
  • #4
ZapperZ said:
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:frown:..
 

FAQ: Understanding the Meaning of Infinity in Uncertainty Principle

1. What is simple uncertainty?

Simple uncertainty is a scientific concept that refers to the lack of knowledge or information about a particular event or measurement. It is characterized by the absence of a definite and precise answer or outcome.

2. How is simple uncertainty different from complex uncertainty?

Simple uncertainty is typically associated with situations where there is a lack of information or understanding about a single variable or event. In contrast, complex uncertainty involves multiple variables or events that interact with each other, making it more difficult to predict outcomes.

3. What causes simple uncertainty?

Simple uncertainty can arise from a variety of factors such as limited data, measurement error, or incomplete understanding of a phenomenon. It can also be a result of inherent randomness or unpredictability in a system.

4. How do scientists deal with simple uncertainty?

Scientists use various techniques and methods to address simple uncertainty, such as collecting more data, improving measurement techniques, and conducting statistical analyses. They also strive to improve their understanding of a phenomenon through experimentation and research.

5. Is simple uncertainty always a bad thing?

No, simple uncertainty is not always a negative aspect in scientific research. In fact, it can lead to new discoveries and insights. By acknowledging and addressing simple uncertainty, scientists can identify areas for further investigation and improve their understanding of the natural world.

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