Why can’t we unstir our coffee?


Newtonian Physics (and pretty much all of Classical Physics) represents an elegant, minimalist set of ideas that allow us to very accurately predict the movement of pretty much everything you and I are likely to encounter on the human scale. The model is so successful that the English poet Alexander Pope wrote

Nature and nature’s laws lay hid in night;
God said “Let Newton be” and all was light.

But the equations, as wonderful as they are, have one odd feature that remains to be understood. According the theory, there is no preferred direction to the flow of time. I can do a mechanical experiment and let run forward in time, and I can run the same experiment backwards in time (imagine a movie projector running in reverse) and Newtonian physics gives the same, equally valid results.

Which is mostly what we see. Until we come to things like a coffee cup. If I put a spoonful of instant coffee into a cup of hot water (I know… ugh) and stir it, I get a cup of “coffee”. But if I reverse the direction of my stirring, attempting to unstir the cup, I can’t manage to separate the coffee crystals from the water.

Why is that? Newton’s Laws can’t explain this. Thermodynamics (the study of heat flow and energy) can, but to do it, one has to postulate a law (albeit based on experience) that disorder is always maximized. (Disorder within a system is the physical basis of what physicists call “Entropy”) But that’s really an observed law, not a law that we understand from basic physical reasoning. Because, if one goes to a small enough scale, it should be possible to reverse the process – just flip the switch on the project (effectively reversing the flow (or arrow) of time.)

Entropy, and the 2nd Law of Thermodynamics is presently the best explanation for what we observe as the unidirectional restriction of the “arrow of time” – the observed inability to go backwards in time. But why is it this way? How did the Universe pick which direction it decided to prefer? (Such a question is similar to asking why is there so much more matter than anti-matter in the Universe. Why did it choose one over the other?)

A small team of physicists think that perhaps we can understand the origin of this preference as being a result of small perturbations in the fabric of space-time in the early Universe. As is reported on the ArXiv Physics blog:

” Kiefer’s conjecture is that the direction of time arises when quantum mechanics is applied to the universe as a whole, a branch of science known as quantum cosmology.

Central to this idea is the Wheeler-DeWitt equation that describes the quantum state of the universe as a whole, including both its gravitational and non-gravitational states.


This equation does not contain any parameter that is equivalent to our classical notion of time. In the Wheeler-DeWitt formulation, spacetime does not exist in any classical sense and particles do not have traditional trajectories in spacetime, just as particles do not have traditional trajectories in ordinary quantum mechanics. Instead all the information about the universe is encoded in its wavefunction

So how might an arrow of time arise? While the universe is considered homogeneous to the first degree, there is no preferred direction of time, says Kiefer. But he shows that when small inhomogeneities are taken into account, an asymmetry arises in this wavefunction.

He even says that with slight elaborations, this idea could be applied to an arrow of time in the multiverse.”

Read the full article here. It’s a pretty straightforward explanation.

Which is a pretty neat idea. This gives a basic phenomenological explanation to the observed behavior of time in the Universe. (This is similar to the way that Cosmological Inflation is used to explain the asymmetry in matter-antimatter.)

The problem apparently is, as is often the case in Cosmology, there’s no obvious way to test the hypothesis. Someone more clever is going to have open that can for us. But, in the meantime, it’s a plausible explanation, even if it requires a bit more complexity and hand tuning than we’d like.

It’s the lack of that complexity and hand tuning of equations that makes Newton’s Laws so beautiful in the eyes of Physicists. Of course they’re not exactly correct, but they’re very pretty.

Perhaps the Universe though isn’t as simple as we want it to be.

The Author

Episcopal bishop, dad, astronomer, erstwhile dancer...


  1. ruidh says

    I’m sorry, but people over think this. It’s called “sensitivity to initial conditions” — the same quality that occurs in chaos theory. In order to have a time reversal, you need precise information about the current state of the system and a way to reproduce that exact state. Miss the 8th or 10th significant figure and it won’t reverse. It’s just not possible to have enough information about the system in order to be able to reverse it.

  2. Not according to Newton’s laws – they should be in principle allow one to calculate to the nth decimal place. Especially when we use infinite precision mathematics.
    Your argument bears weight if all we were doing was an approximation, but Newton’s laws are not an approximation.

  3. Paul Martin says

    When was the last time you used Newton’s laws without approximation? Frictionless pulleys, neglect air resistance, simplify the many body problem, it goes on and on ad infinitum. And let us not forget the infamous spherical horse. Sure, Newton’s laws by themselves do not include any approximations, but once you start applying them to a real problem, watch out. The problem quickly becomes unsolvable unless you are able to approximate somewhere.
    Sorry for the digression. My real point is that I don’t understand why one has to resort to quantum mechanics to explain the arrow of time. Your instant coffee strikes me as a macroscopic problem where quantum theory doesn’t really apply. I remember a very simple statistical physics explanation of diffusion which explains it all quite well. Perhaps I just need a better example before I look at this in quantum terms.

  4. Paul – the coffee stirring is an example of a unidirectional arrow in macroscopic physics. There are others. (I just like that example because people “get it” relatively easily.
    The real issue is that Newton’s equations, which do explicitly contain a time expression unlike the Wheeler De-Witt equation referenced above, are invariant under a time reflection transformation. (To use the proper mathematical language.) But while the equations are invariant, the physics observed is not. That’s the issue. Generally we argue that we can discard the solutions to the equation which are forced upon by time invariance by a hand-waving argument that discards them as being non-physical solutions.
    But if you push people about why they do that, they have to admit that’s it related to the “art” of physics rather than the a fundamental understanding of why the time symmetric equations should be solved in asymmetric ways.
    The arrow of time paradox is pretty well understood by the majority of reputable physicists. There’s more to it than the simplistic examples I’m using as way of illustrating it to a non-technical audience.

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