Q: Does quantum mechanics really say that there’s some probability that objects will suddenly start moving or that things can suddenly “shift” to the other side of the universe?

Physicist: In a word; nope.

The Heisenberg Uncertainty Principle is a statement about how “certain” some combinations of quantities can be.  The most commonly referenced is the “position and velocity” version of the Uncertainty Principle, that says that the more exact the position of a thing (any thing) the less certain its velocity, and vice versa.  It’s basically because of the Uncertainty Principle that you’ll hear about how quantum mechanics predicts that “particles have some small chance of jumping across the universe (position uncertainty)”, or “there’s some possibility that all the atoms in a book will suddenly start moving and it’ll jump off the shelf (velocity uncertainty)”.

And in fact, if you apply Schrödinger’s equation directly (which essentially describes how quantum wave functions change with time), it does seem as through there should be no problems with things suddenly jumping around.  If you apply it directly you find that if you have a particle confined to a particular region, then any amount of time later there’s some chance (no big) that it can be anywhere else, which is pretty exciting.  Unfortunately, Schrödinger’s equation is an approximation in very much the same way that Newton’s equations of motion are approximations of the (correct) relativistic equations of motion.

The wave function of a particle, which describes its position, tends to spread out like this

Soon after a particle’s position has been measured to be near zero, the wave function of a particle (which describes the probability of it being found at that position) tends to spread out like this, getting wider and wider as time goes on.  According to Schrödinger’s equation the tails on both sides approach, but never quite reach, zero.

Schrödinger’s equation was a massive break through and provided a lot of insight into a lot of problems.  But despite that, it doesn’t work perfectly.  In general, if you have a theory and it doesn’t line up perfectly with special relativity, then you only have part of a theory.  The fact that Schrödinger’s equation is “non-relativistic”, as evidenced by the fact that it predicts that sometimes particles will blink from place to place faster than light, made a lot of physicists extremely nervous.  It took a couple more years (1926-1928) until Dirac fixed the problem with the Dirac equation, which is more or less the same, but adheres to relativity.

The Schrödinger Equation (top) and the Dirac equation (bottom).

The Schrodinger Equation (top) and the Dirac equation (bottom).  The Dirac equation takes into account relativity.  Heck, it’s even got a “c” for light speed in there.

Newton’s equations of motion are very accurate, but only up until they disagree with relativity.  For example, they imply that there’s nothing special about light speed, and you can totally go faster.  Similarly, Schrödinger’s equation is remarkably accurate in most day-to-day, electron-shell type calculations, but makes big mistakes when relativity needs to be taken into account.

Long story short, even when considering the Uncertainty Principle, nothing can ever end up someplace else that would normally require faster than light travel.

As for books suddenly jumping off of shelves; the universe according to the laws of quantum mechanics is a seriously weird place.  But ultimately, laws are laws.  In this case, the conservation of momentum and energy.

If you take the predictions of quantum mechanics at face value (and why not?), everything that can happen does (in a very specific, many-worlds, sense).  But that “can” is pretty iron-clad.  Something that’s possible, even if it’s very unlikely, will happen in one some versions of the world*, but a book (or any other object) suddenly moving involves some extra energy suddenly being added to the universe, which is no good.

So, winning the lottery 75 times in a row, while making blind free throws for a couple weeks: sure.  Books jumping off of shelves: ridiculous.

* “World” is definitely not the right word for this, because it evokes images of other dimensions à la Sliders and leads to general confusionNeil Stephenson uses “narrative” which seems like as good a word as any, and hits a little closer to the mark.

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  1. Nolan says:

    Is it also not possible for an electron to jump from one place to another faster than light?

  2. John says:

    But a book could jump off of a shelf if enough atoms in the shelf were to all vibrate in the same direction at once, which is highly improbable (even ridiculous), but not prohibited by the laws of conservation of momentum and energy. I’d expect the shelf to get a little cooler and have a slight recoil, but no big, and it’s entirely classical.

  3. The Physicist The Physicist says:

    Exactly right. It is not possible for an electron to jump from one place to another faster than light.

  4. larry walden says:

    Well as usual it looks like fiction is being mixed with science in the attempt to explain how things work. As a long time student of physics i am wondering if i should re read the works of Conklin (science fiction writer) or Feynman (Nobel physicist)…one at a time or together.

  5. larry walden says:

    After thought. My point is: that if you are dealing with “probabilities” of the numbers that are impossible to achieve, then why even mention them since they are beyond comprehension. In my opinion here we can gain a better sense of “reality” from philosophy and religion….quantum physics appears to be having a nervous break down.

  6. Greg says:

    I thought the question was referring to the way Quantum Electrodynamics is described where it assumes that at the ‘next instant in time’, the electron is allowed the possibility to be anywhere in the Universe?

  7. Since it is not possible to determine the path of trajectory as well as the momentum of an electron as govern by Heisenberg Uncertainty principle….!!! Therefore, we use the concept of probability in order to determine its certainty…… Does the concept of probability breaks down ” Einstein Special Theory of Relativity “, by predicting that a particle can occupy two different position at the same time… which means that a particle has to travel(i.e. move back and fort) faster then the speed, for an observer to visualize that the same particle has occupied two different position at once !!!

  8. Dan says:

    At the scale that quantum mechanics is usually applied, The Physicist is totally right; everything that can happen does, and the universe is a pretty weird place. However, there is a “non-zero probability” that the exact right conditions will spontaneously occur to make a book jump off of the shelf. So in a way, yes, quantum mechanics says it is possible for some crazy stuff to happen (except, of course, for randomly jumping to a place before light). However, when we discuss the scale of books, the probability function would have to give the probability of every conceivable course of events. So, while the chance of the book flying off the shelf is “non-zero”, there are practically an infinite number of other non-zero probability outcomes that could happen. And, given that there must be a significant probability for the book to just sit there and do nothing (let’s assume it’s 99% in a hypothetically silly world), you can imagine that the probability for each crazy outcome would be (assuming each is equally likely) 1%/infinity (may actually be slightly smaller than infinity), because the 1% is divided among all the infinite random outcomes. So, it’s true, there’s a chance the book will fly off the shelf, but the chance of it doing specifically that is so small that I’d think it was crazier if I saw someone waiting for it to happen than if I saw it happen.

  9. Alistair STewart says:

    You say an electron can move faster than the speed of light. This only appears to be the case because all electrons are identical. Imagine a long tube filled with electrons. The tube stretches across across the universe. Now you squeeze in another electron at one end of the tube. This causes an electron to be squeezed out of the other end. The electron hasn’t travelled across the universe – it’s different but identical electron

  10. kweqnfj says:

    @Alistair Nope, the main interaction of electrons with eachother happens through the electromagnetic field, whose gauge boson is the photon. The electron on the other side of the tube won’t pop out until light had the time to travel all the way through the tube.

  11. ExLibertas says:

    So is there or isn’t there a possibility (no matter how infinitely small the probability is) of an object shifting locations? I didn’t quite get that from this post

  12. The Physicist The Physicist says:


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