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GiorgioP's answer is great. I want to address the final part of your quote though.

the spread here refers to the fact that measurements made of identically prepared systems do not yield identical results.

I don't think this part is specifically about the HUP. Even for just single measurements of indentically prepared states $|\psi\rangle$ we will not always get identical results. For any observable $A$ with eigenvalues $a$ there is always a probability of measuring a value of $a$ of $$P(a)= |\langle a|\psi\rangle|^2$$ If for more than one $a$ value $\langle a|\psi\rangle\neq0$, then you cannot expect the same result for each measurement. This has nothing to do with an uncertainty principle; it's just a consequence of the probabilistic nature of QM measurements.

Contrary to what many people think, the HUP doesn't show that spreads in measurements exist, rather it just shows how for certain pairs of measurements, their spreads (more specifically the product of the standard deviations) are constrained to be no larger than a certain value. In other words, the HUP doesn't explain uncertainty, it just characterizes it.

GiorgioP's answer is great. I want to address the final part of your quote though.

the spread here refers to the fact that measurements made of identically prepared systems do not yield identical results.

I don't think this part is specifically about the HUP. Even for just single measurements of indentically prepared states $|\psi\rangle$ we will not always get identical results. For any observable $A$ with eigenvalues $a$ there is always a probability of measuring a value of $a$ of $$P(a)= |\langle a|\psi\rangle|^2$$ If for more than one $a$ value $\langle a|\psi\rangle\neq0$, then you cannot expect the same result for each measurement. This has nothing to do with an uncertainty principle; it's just a consequence of the probabilistic nature of QM measurements.

Contrary to what many people think, the HUP doesn't show that spreads in measurements exist, rather it just shows how for certain pairs of measurements, their spreads (more specifically the product of the standard deviations) are constrained to be no smaller than a certain value. In other words, the HUP doesn't explain uncertainty, it just characterizes it.

GiorgioP's answer is great. I want to address the final part of your quote though.

the spread here refers to the fact that measurements made of identically prepared systems do not yield identical results.

I don't think this part is specifically about the HUP. Even for just single measurements of indentically prepared states $|\psi\rangle$ will not always give identical results. For any observable $A$ with eigenvalues $a$ there is always a probability of measuring a value of $a$ of $$P(a)= |\langle a|\psi\rangle|^2$$ If for more than one $a$ value $\langle a|\psi\rangle\neq0$, then you cannot expect the same result for each measurement. This has nothing to do with an uncertainty principle; it's just a consequence of the probabilistic nature of QM measurements.

Contrary to what many people think, the HUP doesn't show that spreads in measurements exist, rather it just shows how for certain pairs of measurements, their spreads (more specifically the product of the standard deviations) are constrained to be no larger than a certain value. In other words, the HUP doesn't explain uncertainty, it just characterizes it.

GiorgioP's answer is great. I want to address the final part of your quote though.

the spread here refers to the fact that measurements made of identically prepared systems do not yield identical results.

I don't think this part is specifically about the HUP. Even for just single measurements of indentically prepared states $|\psi\rangle$ we will not always get identical results. For any observable $A$ with eigenvalues $a$ there is always a probability of measuring a value of $a$ of $$P(a)= |\langle a|\psi\rangle|^2$$ If for more than one $a$ value $\langle a|\psi\rangle\neq0$, then you cannot expect the same result for each measurement. This has nothing to do with an uncertainty principle; it's just a consequence of the probabilistic nature of QM measurements.

Contrary to what many people think, the HUP doesn't show that spreads in measurements exist, rather it just shows how for certain pairs of measurements, their spreads (more specifically the product of the standard deviations) are constrained to be no larger than a certain value. In other words, the HUP doesn't explain uncertainty, it just characterizes it.

GiorgioP's answer is great. I want to address the final part of your quote though.

the spread here refers to the fact that measurements made of identically prepared systems do not yield identical results.

I don't think this part is specifically about the HUP. Even for just single measurements of indentically prepared states $|\psi\rangle$ will not always give identical results. For any observable $A$ with eigenvalues $a$ there is always a probability of measuring a value of $a$ of $$P(a)= |\langle a|\psi\rangle|^2$$ If for more than one $a$ value $\langle a|\psi\rangle\neq0$, then you cannot expect the same result for each measurement. This has nothing to do with an uncertainty principle; it's just a consequence of the probabilistic nature of QM measurements.

Contrary to what most people think, the HUP doesn't show that spreads in measurements exist, rather it just shows how for certain pairs of measurements, their spreads (more specifically their products) are constrained to be no larger than a certain value. In other words, the HUP doesn't explain uncertainty, it just characterizes it.

GiorgioP's answer is great. I want to address the final part of your quote though.

the spread here refers to the fact that measurements made of identically prepared systems do not yield identical results.

I don't think this part is specifically about the HUP. Even for just single measurements of indentically prepared states $|\psi\rangle$ will not always give identical results. For any observable $A$ with eigenvalues $a$ there is always a probability of measuring a value of $a$ of $$P(a)= |\langle a|\psi\rangle|^2$$ If for more than one $a$ value $\langle a|\psi\rangle\neq0$, then you cannot expect the same result for each measurement. This has nothing to do with an uncertainty principle; it's just a consequence of the probabilistic nature of QM measurements.

Contrary to what many people think, the HUP doesn't show that spreads in measurements exist, rather it just shows how for certain pairs of measurements, their spreads (more specifically the product of the standard deviations) are constrained to be no larger than a certain value. In other words, the HUP doesn't explain uncertainty, it just characterizes it.