# Explainer: Heisenberg's Uncertainty Principle

The term "uncertainty principle" suggests some grand philosophical idea, like "you can never be sure of anything", or "there are some things you can never be sure of" and sometimes people use it as if this is what is meant. In fact, this principle discovered by German theoretical physicist Werner Heisenberg in 1927, has a precise technical meaning that's typically relevant only to microscopic particles.

Picture by ModernDope

But it does have implications for how we understand the universe and our relation to it, and also to new technologies of the 21st century.

While the Heisenberg Uncertainty Principle (HUP) does not mean "there are some things you can never be sure of", it does imply "you can never be sure of everything". How can this be? If you can never be sure of everything, doesn't that mean there are some things you can never be sure of? Surprisingly, no.

In science we are ultimately concerned with what we observe. So when we say we are uncertain about something, we mean that we are uncertain about what we will observe when we do an experiment.

Of course, life would be pretty boring if we could always predict what was going to happen next, but for many centuries scientists dreamt they would be able to do this. The HUP killed that dream in a very interesting way.

The simplest example of the HUP is the following: You can never be certain of both the position and the speed of a microscopic particle. It is possible to arrange an experiment so you can predict the position of a particle. A different experiment would let you predict its speed. But you will never be able to arrange things so that you can be certain of both its position and its speed.

You might be jumping up and down at this point and saying "That's ridiculous. If I want to know both I just measure them simultaneously. Or I first measure the position, then the speed." In fact, neither of these options will work, and what rules them out is other forms of the HUP itself.

In the first case, there is the HUP that says it is not possible to simultaneously measure position and speed with perfect accuracy. In the second, there is the HUP that says if you accurately measure the position you will disturb its speed, making it more uncertain, and vice versa. So you can't get around it.

## Is It A Principle?

Before getting into the details, one thing to get clear is that Heisenberg's "uncertainty principle" is not really a principle at all. A "principle", in science as in everyday life, is a fundamental simple idea from which all sorts of other things can be derived, such as the principle of freedom, or the principle of fairness.

Heisenberg's principle is not like that — it's actually a consequence of something more fundamental. That thing is quantum mechanics, a theory that applies to all forms of matter and energy (as far as we can tell).

Unfortunately, although quantum mechanics seems fundamental, it's not simple, and so cannot be encapsulated as a principle. But from it follow all forms of the HUP.

## Precisely Uncertain

For the example given earlier, Heisenberg's principle can be precisely stated as:

(1) Δq x Δv > ħ/m

Here Δq is the uncertainty in the position of the particle (in metres), Δv is the uncertainty in its speed (in metres per second), m is its mass in kg, and ħ is a constant (Planck's constant).

Note that the two uncertainties are multiplied together in equation (1), and the result must be greater than some number. This means that, although Δq can be as small as you like as long as Δv is large enough, or vice versa, they cannot both be arbitrarily small.

The HUP in its looser form ("you can never be sure of everything") is thus a consequence of the fact that Planck's constant is not zero. But Planck's constant is very small. In the units used here, ħ ≈ 10-35 ; that is 0.00…001, where there should be 35 zeros here. This smallness is why we don't have to worry about the HUP in everyday life.

You may have heard the anecdote about a woman who is stopped by a policeman who says: "I just measured your speed as 53.9 km/hr when you were in a 40 km/hr school zone." She retorts: "Are you familiar with the Heisenberg Uncertainty Principle? If you are so sure about my speed, you can't possibly know where my car was."

It's a cute joke, but let's see what the HUP actually says. When the policeman says the speed was measured as 53.9 km/hr, he presumably just means it was closer to 53.9 than to 53.8 or 54.0. This means an uncertainty of about 0.05 km/hr, which is about 0.01 metres/second. If the mass of the car is 1,000kg then the HUP implies:

Δq > ħ/(m x Δv) ≈ 10-35 /(1000x0.01) = 10-36 metres

Thus the minimum uncertainty in the position of the car implied by the HUP is much, much smaller than the size of an atom. So this is obviously irrelevant when it comes to the question of whether the car was in the school zone or not.

Although the HUP doesn't have much to say about speeding tickets, it's ubiquitous at the scale of atoms and sub-atomic particles. The mass of an electron is extremely small (m ≈ 10-30 kg) so that ħ/m ≈ 10-5 on the right-hand-side of equation (1) is no longer ridiculously small.

In fact, some simple arguments involving the motion of electrons around the nucleus of an atom let us derive the approximate size of an atom as the minimum Δq ≈ 10-10 meters implied by the HUP. The HUP in one form or another is a useful principle in almost every field of science dealing with very small amounts of matter or energy.

## Applications In Technology; Implications In Philosophy

Since quantum mechanics underlies almost all modern technology, the HUP turns up all over the place. It also plays a more direct role in the quantum technologies of the 21st century, which are just being developed now.

Quantum communication allows the sending of encoded messages that are un-hackable by any computer. This is possible because the messages are carried by tiny particles of light called photons.

If an eavesdropper attempts to read out the message in transit, they will be discovered by the disturbance their measurement causes to the particles as an inevitable consequence of the HUP.

The HUP also raises fascinating and difficult philosophical questions. The most obvious question is: what's the reason for this uncertainty?

In everyday life we could be uncertain about whether the cue ball will end up going into the top pocket because we are uncertain about its speed or position. But we would not doubt that the ball has a speed and position.

In the regime of quantum experiments, by contrast, we are uncertain about the results of experiments because the particle itself is uncertain. It has no position or speed until we measure it. Or so Heisenberg thought, and most physicists still follow this line.

However, others strongly disagree with this conclusion and the debate is not over — that's for certain.

Howard Wiseman is the Director of the Centre for Quantum Dynamics, Griffith University, and an Executive Research Leader in the Centre for Quantum Computation and Communication Technology (an Australian Research Council Centre of Excellence). His research group is also funded by the ARC through Discovery Projects, by the Templeton Foundation, and by the Perimeter Institute for Theoretical Physics (Canada). He has no other relevant affiliations, funding sources, or financial interests.

You might want to double check the "intro" text that shows when you view the LH front page. The description is almost the whole article and you have to scroll right down to see the previous article published!

Yeah... came here to say this... I think they missed a tag somewhere.

Ha! I came here to just say that too.
tl;dr

While commonly misnamed as Heisenberg's principle, the article actually discusses the principle as presented by Earle Kennard and further generalised by Howard Robertson. For many years physicists have wrongly thought that Heisenberg's formulation was equivalent.

The difference was that Heisenberg was talking about the measurement errors while the other two physicists discussed the intrinsic fluctuations. To derive a proper uncertainty principle, both effects need to be taken into account. For details see http://www.scientificamerican.com/article.cfm?id=heisenbergs-uncertainty-principle-is-not-dead or the original article http://www.nature.com/nphys/journal/v8/n3/full/nphys2194.html.

The above article discusses how to violate (misnamed) Heisenberg's principle and how to derive a proper uncertainty principle.

With a bit of luck, that dude that does the cartoon explanations of this kind of thing will do one on this subject. Much easier to digest when he explains it..! :)

Everyone loves the RSA cartoons!

Whenever I hear the name Heisenberg all I think of is Breaking Bad.

+1

I always have problems with this principle of uncertainty, as its truth has many implications for reality.
If I have a 6-sided dice, could I ever roll a 7? Uncertainty says that there is a non-zero probability of that actually occuring. In fact, there is a non-zero probablity of ANYTHING happening.

AFAIK no, you can never roll a seven. A 6-sided die will always roll a 1, 2, 3, 4, 5, or 6.

If you somehow made a Q-Dice (whatever that is), Quantum Theory states that until you "look" at the result, the die is a 1, 2, 3, 4, 5, **AND** a 6 at the same time. When you then actually go and measure the result, then it will be one, and only one, of these results.

Where's Schrödinger's cat :)

Just a quick point. The statement presented below is not quite accurate:
"Quantum communication allows the sending of encoded messages that are un-hackable by any computer."

There have already been successful demonstrations of hacking quantum communications. As far as I know, however, all of these rely on exploiting weaknesses in the implementation / engineering of the system, rather than some sort of fundamental weakness of the Science itself. I realise that what was probably meant was that the Science (as we know it) is unhackable, but the way it is written is slightly ambiguous.

Apart from that, good article! I think you managed to explain the basics reasonably well for something so complex and counter-intuitive!

*huge wall of text attacks and scores 5000 damage*

It's over 9000!!!!

NINE THOUSAND!?!