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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…

Life would be pretty boring if we could predict what was coming next. ModernDope

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. 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.

Uncertainty about what?

Werner Karl Heisenberg (1901 - 1976) Wikimedia

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 divided by 2*pi).

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^-34; that is 0.00 … 001, where there should be 34 zeros here. This smallness is why we don’t have to worry about the HUP in everyday life.

AAP Image/Alan Porritt

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.

See more Explainer articles on The Conversation.

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19 Comments sorted by

  1. Giles Pickford
    Giles Pickford is a Friend of The Conversation.

    Retired, Wollongong

    Things you will never ever know
    Inspired by Heisenberg’s Principle of Uncertainty

    The moment you are born and first see your mother
    The moment when you die and last see your lover
    The moment when sleep shuts the curtains of your mind
    These are the moments you will never ever find

    Nor will you ever know the nature of time
    Nor the depth of space, nor the number nine
    The Quark and the Lepton will not be understood
    Nor will you comprehend the nature of The Good

    Some people know that they are always right
    That certainty is real does not cause them fright
    But some are relaxed to know it is also true
    The sum of one and one is approximately two

  2. George Fink

    Professorial Research Fellow

    HUP may have considerable relevance to our understanding of brain functioin that it is it is difficult to be certain when certain nerve cells will begin and terminate Sponteneous firing. We understand reflex induced firing. Or externally induced firing...but spontaneous firing remiains uncertain. Resaerch on clusters of nerve cells in culture is ongoing to ask the question as to whether in fact there Are leader cells which once fired trigger firing in the other surrounding neutrons. Unfortunately, the presence of a recording electrode highlights the significance of HuP

    1. Craig Savage

      Professor of Theoretical Physics at Australian National University

      In reply to George Fink

      There is plenty of uncertainty, and randomness, in scientific measurements, and most of it is not due to the Heisenberg uncertainty principle. This is because, as Howard makes clear, it only acts on the atomic scale.

      Uncertainty in nerve cell firing is unlikely to be due to the Heisenberg uncertainty principle. It is more likely to be due to everyday kinds of uncertainties, such as in molecular concentrations.

      The broader question of the role quantum mechanics plays in biology, beyond explaining molecular bonding etc., is a hot topic. There are hypotheses that deeply quantum mechanical processes, like entanglement, are involved in photosynthesis and in certain sensory functions, such as the sensing of magnetic fields by birds, and the sense of smell. However the validity of these hypotheses remains under investigation.

  3. Alex Cannara

    logged in via Facebook

    It's always good to go back and see where geeky ideas like inevitable uncertainty arise. Bohr & Heisenberg bullied Einstein into going along with their concept of how atomic-scale things work. It became the Copenhagen Convention. It was religiously taught by generations of uncritical profs.

    Many physicists have considered that it wasted about 70 years of scientific research and development of Quantum Mechanics.

    Recent experiments using "weak" measurements have actually disproven some bullying…

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  4. Gil Hardwick

    anthropologist, historian, novelist, editor and publisher at eBooks West

    Yes, we had quite enough of this bullshit when seeking to implement demonstrably beneficial remedial works supported by ongoing monitoring in plainly degraded environments, to be told by the Greens and Conservation Council activists that because we cannot be precisely sure of the long term outcome the Uncertainty Principle applies, so the work was prevented.

    My considered opinion then and now is that if the Uncertainty Principle were applied to itself in this setting it would spontaneously disappear up its own dot, right where it belongs. Right up Bob Brown's arse would be better, and a few others I could name.

    Some people in politics should be banned from reading scientific papers, especially when they are smoking the green stuff and delude themselves into believing that the addition of a few high-fallutin' words to their limited vocabulary imparts some sort of authority and prestige.


    Howard, thanks for the clarification . . . .

    1. Alex Cannara

      logged in via Facebook

      In reply to Gil Hardwick

      But how do you really feel, Gil?
      Actually, I've long hoped to get a program going under which we could send the kind of folks you mention to an island that they would all have to share -- we'd airdrop necessities but they'd have to stay on the island and leave us alone. My guess/hope is that they'd wipe each other out.

    2. Berthold Klein

      Civil-Environmental engineer

      In reply to Gil Hardwick

      When more and more people realize that the pretend scientist aka "climate scientists " have been lying to them, they stopped listening to the Henny Pennies!
      Mann-made global warming is a total hoax. The weather thought out the world has shown that the "models used by the "climate scientists"are just crap.
      The world has been lied to by the "environmental whachos" and the money being spent to "correct" a non exist problem is hurting every country in the world. People are tired of having their…

      Read more
    3. Alex Cannara

      logged in via Facebook

      In reply to Berthold Klein

      Wow! I didn;t know so many thousands of scientists, even at our own NASA, USGS, NOAA... were all carefully coordinating lies to deceive the world's populace into understanding why the earth doesn't freeze over and why it is in fact warming!

      I guess you have an explanation of why we see tide gauges rise and pH meters in the sea fall, Berthold? Love to hear it.

  5. George Fink

    Professorial Research Fellow

    In response to Craig Savage

    Thanks for this. Re olfaction, as you probably know, each odor or class of odorant has its own while there may be some uncertainty at odorant-receptor interaction, there is a distinct 'landline' for each odor which ensures robust transmission. To have a single protein for each odor is remarkably heavy duty (genetically) in neurobiology where frequency and amplitude coding are the main signaling mechanisms. Teleologically, it possibly reflects the importance of "smell" for all metazoa from C.Elegans to man and might reflect stepwise evolutionary add-ons?

    1. Alex Cannara

      logged in via Facebook

      In reply to George Fink

      The number of genes dogs have to define their smell sensing makes our smellers look primitive.

    2. Yoron Hamber


      In reply to Alex Cannara

      Yeah, HUP is weird :)
      But I like it, as well as indeterminism.

      Somehow I always come down to thinking of 'free will' when i think of HUP. It's a quite thought provoking 'principle', and to me it seems as a principle in fact, relating not only to the microscopic? I'm not altogether sure but I think there are some experiments relating to HUP 'above' the microscopic? Wasn't there some guys in Vienna? As well as where planets will be :) in some future moment. If I now remember right there?

    3. Howard Wiseman

      Professor in Physics at Griffith University

      In reply to Yoron Hamber

      Indeed Yoron, the HUP applies to everything. As I said it is "typically relevant only to microscopic particles" but if you work very hard as an experimenter it can become relevant to objects that are slightly less microscopic than atoms. The "guys at Vienna" have done experiments with molecules containing >100 atoms. But that's still only about a nanometre across (a millionth of a millimetre).

    4. Yoron Hamber


      In reply to Alex Cannara

      :) heh.

      You know Alex, one of the things that really are under discussion ever since Heisenberg defined it is whether it is about a real uncertainty, as in being truly probabilistic, or if there is some underlying 'real' component defining it. And there it comes back to what one believe to be most probable. If one finds 'weak measurements' to define that reality then there should be some such 'underlying reality' defining it, don't you agree?

      If you on the other hand find what we classically…

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    5. Yoron Hamber


      In reply to Yoron Hamber

      But it also comes down to how you define your reality. If you as me use 'locality' as the real measure of it, then a meter always will be a meter for you. It will only be your neighbor disagreeing, and neighbors do have that tendency at times :)

      And doing that and using Planck scale as a definer of what we possibly can define as measurable? We can't really measure 'down there', but theoretically it still is a sound principle, as I understands it. Then we find at that small scale 'reality' disappear replaced by probability. And now we just need to put those two together. Locality as in your wristwatch and your ruler, and 'probability as the focus for that 'macroscopic' definition of 'time', the arrow, and 'your' reality (locality)..

    6. Alex Cannara

      logged in via Facebook

      In reply to Yoron Hamber

      Yoron, the wisest thing I've heard personally was from my fist boss: "The electrons know what they're doing. It's up top us to try to find out."

      And "probability" is not reality. Probability and statistics are math models we use when we're ignorant of how things really work. And math is not reality either. It's just an accounting tool that can't even model everything either, as Godel & Turing showed.

    7. Yoron Hamber


      In reply to Alex Cannara

      I agree on mathematics being limited by our current ideas and imagination :) It still seems as the best tool there is for physics though? And I agree on that we still are largely ignorant about 'reality'. The question though isn't about what we think it is, based on what we know from our daily life, but what experiments can show us. Then we search for the math describing it best, or go the other way around and test our hypothesis (as in the mathematics) with a experiment to see if it fits.


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