# What is uncertainty principle

#### Rico L

what is uncertainty principle?

thanks ppl..

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#### bapowell

This is an easily researched topic. Why not do some poking around on the web, and then come back here with more specific questions.

#### ansgar

standard deviation in position times standard deviation in momentum is greater than h-bar

simple

#### LostConjugate

greater than 1/2(h-bar)

HUP applies to other operators as well.

#### ansgar

greater than 1/2(h-bar)

HUP applies to other operators as well.
yes sorry forgot the factor of one half!

it applies to all operators which does not commute, eg. S_x, S_y

#### bapowell

You really shouldn't discount the energy-time relation just because time is not a canonical operator. Since the energy of a state is proportional to its frequency, the longer it exists (the more cycles it undergoes) the more certain the energy i.e. the sample variance of the system energy goes down as more cycles pass.

In any event, the energy-time uncertainty relation governs quantum vacuum fluctuations, whose existence has been experimentally verified.

#### stevmg

I have never understood the logic behind the Heisenberg Uncertainty Principle and neither did Einstein. One of those quirks between Relativity and Quantum Physics and I don't know if it has been resolved. I do know that if one follows the procedures in the calculations, it does work out...

"God does not play dice with the universe..." Einstein

"Don't tell God what to do..." Bohr

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#### physixlover

As Hesinbergsaid -particle position and momentum both cannot be known at the same time
the best explanation you would get at this link-

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#### Rico L

This is an easily researched topic. Why not do some poking around on the web, and then come back here with more specific questions.

just reminded me... lol. thanks

#### stevmg

That video
still begs the issue... It states that the electron is a cloud because of its small mass (and consequently less internal attrcation to hold it together) and then states that as you leave the tight proton nucleus (the H atom) you increase your probability of finding the electron. If the electron is the cloud, then once you hit the cloud you $have$ found the electron. No probability about it.

But the old big argument about the inability to know the position and the speed and direction of the electron at the same time because if you look at the electron you alter its momentum is pure bunk. That just means we have no way currently of figuring this out, not that it is impossible.

However, the statistical formulas do work so I won't argue with them.

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#### Anthony A

The notion that one will never be able to understand the exact location of a particle.

#### Fredrik

Staff Emeritus
Gold Member
It's not just that you can't know the particle's position and the momentum. It doesn't have a well-defined position or a well-defined momentum at any time. (In particular, the claim made in the video about electrons spending most of their time at a specific distance from the nucleus, is wrong). What I'm talking about isn't even a consequence of the uncertainty theorem*. It's just the standard interpretation of a wavefunction.

(I must have said this in at least 10 different threads. See any of them for more details).

*) The original idea could be described as a "principle", but the modern uncertainty relation is a theorem and nothing else.

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#### ansgar

You really shouldn't discount the energy-time relation just because time is not a canonical operator. Since the energy of a state is proportional to its frequency, the longer it exists (the more cycles it undergoes) the more certain the energy i.e. the sample variance of the system energy goes down as more cycles pass.

In any event, the energy-time uncertainty relation governs quantum vacuum fluctuations, whose existence has been experimentally verified.
that relation is derived in a more "non rigour" way than the HUP though...

#### ansgar

As Hesinbergsaid -particle position and momentum both cannot be known at the same time
the best explanation you would get at this link-
wrong, HUP is a statistical relation, not applicable to one measurment but to several

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#### ansgar

I have never understood the logic behind the Heisenberg Uncertainty Principle and neither did Einstein. One of those quirks between Relativity and Quantum Physics and I don't know if it has been resolved. I do know that if one follows the procedures in the calculations, it does work out...

"God does not play dice with the universe..." Einstein

"Don't tell God what to do..." Bohr

the logic is simple, the derivation is done in school, I can show it to you.

#### Born2bwire

Gold Member
I have never understood the logic behind the Heisenberg Uncertainty Principle and neither did Einstein. One of those quirks between Relativity and Quantum Physics and I don't know if it has been resolved. I do know that if one follows the procedures in the calculations, it does work out...

"God does not play dice with the universe..." Einstein

"Don't tell God what to do..." Bohr
I don't recall Einstein having a problem with the Heisenberg Uncertainy Principle. More over, he had larger problems with the Copenhagen interpretation and he was seeking for a local realism interpretation. The Heisenberg Uncertainty Principle falls out simple from the mathematics of quantum mechanics. It is not taken via empirically like the Pauli Exclusion Principle.

The Heisenberg uncertainty principle makes NO ascertations about the precision of a measurement. It is a consequence that describes the relationship between the statistical measurement of what are called incompatible observables. It does not mean that the measurements are inaccurate or incorrect. It just means that between certain observables, we will not get the same measurements over and over again over a statistical set.

Think of a machine that measures some quantum state. The machine projects the measurement in the form of marbles. Each measurement makes a sack of marbles that varies in color, number, and size. We will consider color and size to be compatible (or commutable) observables. That is, every marble that is 0.5 in in diameter is always green and vice-versa. However, color (and by extension size) is incompatible (noncommutable) with number. That is, if we measure the state and have the machine make our sack of marbles, we might get 5 green marbles, or 3 green marbles, or 3 red marbles and so on.

So make 10,000 measurements and we get 10,000 sacks of marbles of varying colors and numbers. If we were to separate out the sacks by groups of numbers, we would find that for sacks of 5 marbles we have 10% red, 50% green, and 40% blue. For sacks of 6 marbles we have 20% red, 30% green, and 50% blue. And so on. Thus, we measure the number of marbles EXACTLY, but because a sack of five marbles can be red, green or blue then we get a spread of colors in our set of measurement. This spread will be described by the wavefunction in terms of color for the given eigenvalue of N marbles. This is the same as when we get an eigenfunction of position for a given eigenvalue of E energy. If the system has energy E_0, then the eigenfunction describes the positional distribution of the measurements of the system in this state (assuming time-independence). So if we measure the position of a particle in a system of state E_0, there are many many positions that it could be in and thus we get a statistical spread of position measurements.

Likewise, if we arrange the sacks by color we may find that green came in sacks of 5 10% of the time, 6 40% of the time and so on. This is another eigenfunction that gives the distribution of number for an eigenvalue of color. In this manner, we see that the eigenfunctions that describe the system in terms of color are different than the eigenfunctions that describe the system in terms of number.

Heisenberg's uncertainty principle then gives us the relationship between the variance of color and number in all our measurements. If we go back to our sacks and map out the number and color of the marbles in the sacks, we will find that we have a mean color and number (if we can allow for a mean color, we could allow the color to gradually transist over the visual spectrum as opposed to being three discrete colors). However, there will be a spread in the measurements in numbers and colors. The minimum spread is related by the uncertainty principle.

The problems of measurement and precision do not come into the argument yet, this is purely a consequence of the mathematics of quantum mechanics.

#### bapowell

that relation is derived in a more "non rigour" way than the HUP though...
umm...so what? It's a valid relation. The OP asked about the uncertainty principle. He didn't ask that we critique which versions of it are most rigorously derived.

#### ansgar

umm...so what? It's a valid relation. The OP asked about the uncertainty principle. He didn't ask that we critique which versions of it are most rigorously derived.
it is only valid for some specific systems, that is why it is not properly to call it a principle

#### bapowell

really? who doesn't call it a principle?

EDIT: Anyway, there's little point debating what one calls it (I personally refer to it as a 'relation'). I don't think the OP is benefiting from this side discussion. However, given its importance in physics, and since it is typically discussed along with the position-momentum uncertainty relation, I think the energy-time relation is germane to the discussion and the OP would benefit from learning about it. It seems ridiculous to selectively withhold information because it's "not as rigorous" as something else, or is technically "not a principle". Is the Pauli exclusion principle not a 'principle' because it only applies to fermions?

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#### ansgar

really? who doesn't call it a principle?

EDIT: Anyway, there's little point debating what one calls it (I personally refer to it as a 'relation'). I don't think the OP is benefiting from this side discussion. However, given its importance in physics, and since it is typically discussed along with the position-momentum uncertainty relation, I think the energy-time relation is germane to the discussion and the OP would benefit from learning about it. It seems ridiculous to selectively withhold information because it's "not as rigorous" as something else, or is technically "not a principle". Is the Pauli exclusion principle not a 'principle' because it only applies to fermions?
now you are making a huge mistake, the pauli principle says that for FERMIONS so of course it is only valid for fermions...

#### bapowell

now you are making a huge mistake, the pauli principle says that for FERMIONS so of course it is only valid for fermions...
Exactly. So as long as we make it a point to identify the systems to which a principle applies, then we can still call it a principle. You seemed to suggest that because the energy-time relation doesn't apply universally to all systems, that it didn't qualify as a principle. This serves as a counter point. But, if you agree with the rest of what I said in the previous post, perhaps we should call it a day on this topic.

#### Fredrik

Staff Emeritus
Gold Member
The reason why the uncertainty theorem shouldn't be called a "principle" is that a principle is an idea, usually stated in non-mathematical terms, that you can use to find an appropriate mathematical structure for a new theory that you're trying to find. The "principle" restricts the number of mathematical structures you can use, because you're only looking for theories in which a mathematical statement that resembles the principle can be derived as a theorem.

The "HUP", or rather the statement that should be called the HUP, is a statement that predates QM. It was used to find QM. The inequality that people insist on calling "the HUP" is a theorem derived from the axioms of QM.

Other examples of "principles" in physics are "Einstein's postulates" (which are even more inappropriately named than "the HUP", because "postulate" is a synonym for "axiom", and these aren't even mathematical statements) and "the equivalence principle". The former can help you guess that Minkowski spacetime is an appropriate model of space and time, and the latter can help you guess that some other 4-dimensional smooth manifold with a Lorentzian metric determined by a bunch of fields on that manifold, might be an even better choice.

It bugs me a bit every time I see someone refer to the HUP, Einstein's postulates or the equivalence principle when they want to prove something. It sounds like they're referring to the ideas that led to the discovery of the theories, when they could and should be using the actual theories. But most of the time, what they have in mind are the actual mathematical statements that appear in the theories, and not the loosely stated ideas that predate the theories. So the arguments are usually not wrong. They just use annoyingly inappropriate terminology.

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#### stevmg

Fredrik -

I don't mean to be annoying and I know less about quantum mechanics than I did about simple relativity, which you and several others helped me comprehend to my limited degree.

So, I am not saying "no" to the "uncertainty" and in fact, I know that the statistics do work out.

If I can wrap my "brain" around that an electron is a "cloud" and not a distinct particle, then there would be no specific location. This is analogous to a cloud in the atmosphere - one can tell when he or she is within it but where is it? Is it the water droplets that are in colloidal suspension? Does it include the water vapor (molecular H2O) between the droplets? What? In this case (the cloud case) there is no specific location as i is spread out over a large space. So the use of statistical techniques to describe its qualities would be in order - to get the "mass" effect as there would be no specific particle effect.

#### stevmg

Ansgar

Originally Posted by stevmg
I have never understood the logic behind the Heisenberg uncertainty principle and neither did Einstein. One of those quirks between Relativity and Quantum Physics and I don't know if it has been resolved. I do know that if one follows the procedures in the calculations, it does work out...

"God does not play dice with the universe..." Einstein
"Don't tell God what to do..." Bohr

the logic is simple, the derivation is done in school, I can show it to you.
I will be interested in what you have to show...

Thanks,

Steve G