Built on Facts

Time-Reversal

Posted by Matt Springer on October 15, 2010
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Generally speaking, if you play a movie backwards everything that happens is still physically possible. If I throw you a baseball and you catch it, reversing the video is just the equally plausible situation of you throwing the baseball followed by my catching it. If entropy is changing in the video – e.g., breaking an egg – the time-reversed video will not be especially likely. But it doesn’t break the laws of physics.

This is called time-reversal symmetry (sometimes T-symmetry for short). If you’re looking at planets orbiting in uniform circular motion about the sun, you know from your physics class that they have to satisfy a particular relationship between their velocity and the force F of gravity that the sun exerts on the planet:

i-d4bb9fe09d6b78eb832985821d8a307f-1.png

The gravitational force doesn’t make any reference to time – if you have two masses, they attract. On the other hand, time reversal changes v to -v, since the planet is now moving in the opposite direction*. But the equation involves the square of v, and so the minus sign vanishes and the law retains the same form despite the time reversal.

This T-symmetry holds very generally in physics. both in Newtonian mechanics and Maxwellian electrodynamics. It came as a bit of a shock therefore when it was discovered that particle physics (the weak interaction, specifically) is not time-reversal invariant. It does hold to a more general CPT-symmetry where the laws are invariant if you flip the direction of time, flip left and right, and change matter into antimatter. Exactly why this is so is not so well understood.

Which is a long way of introducing an interesting APS article about a violation of T-symmetry in electromagnetism. This certainly raised my eyebrows when I read the headline, but as it turns out the symmetry is indeed broken in the device itself under the influence of a magnetic field. But magnetic fields do reverse direction under time reversal (because they’re generated by moving currents), and so the symmetry is preserved if you take the magnetic field into account. Still, it’s a pretty snazzy paper – both the summary and the paper itself are freely available online. Give ‘em a look!

*This is sort of handwaving since v in this notation is usually defined as a strictly positive magnitude in the first place. If this bothers you, define the quantity v^2 = v.v and it’s a little more clear.

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Comments

  1. #1 Eric Rodriguez
    October 15, 2010

    Where are these studies being found? is it accurate information? Are there proffesional scientist reviewing these studies?

  2. #2 Chris Crawford
    October 15, 2010

    Make a movie of an electron’s probability cloud of positions immediately after being measured by collision with a photon. The probability cloud expands with time; that’s what we expect. Now play the movie backwards. The probability cloud contracts – time irreversibility.

  3. #3 Russell
    October 15, 2010

    The puzzling thing is that the Schrödinger equation is time symmetric, too. What is violating it?

  4. #4 Raskolnikov
    October 15, 2010

    There is nothing strange about that. You just started in a very special initial state, one which is unlikely to be realized and that’s why you feel the time reversed motion seems strange. But it doesn’t violate any fundamental law.

  5. #5 Carl Brannen
    October 15, 2010

    Glad to see you blogging again. The symmetry of time reversal violation is equivalent to CP violation under the (fairly reasonable but possibly a bit dated due to anti-neutrino mass measurement) assumption that CPT is a perfect symmetry. My latest paper shows that CP violation in the CKM mixing matrix (i.e. weak interactions) can be attributed to Berry / Pancharatnam / quantum phase. The paper had a strange rejection at Foundations of Physics. Both reviewers said it should be published, but one suggested it was too mathematical and more suited to Journal of Mathematical Physics. The FoP editor agreed, so I’m getting it ready for JMP.

  6. #6 Chris Crawford
    October 15, 2010

    I’m not sure whether comments #3 and #4 refer to my own comment or to the main post, but I’ll assume that they are. If so, then here are my responses:

    #3: Yes, Schrodinger’s equation is time symmetric. The Uncertainty Principle (when applied over a period of time) isn’t.

    #4: What’s so special about measuring a particle with another particle? Do that with a zillion particles and you’ve got a gas in which the behavior is macroscopically irreversible. You can argue that, classically, the behavior of the gas is microscopically reversible, but if you use QM instead of classical mechanics, all those particle collisions are really just “measurements”, and are not reversible.

  7. #7 Uncle Al
    October 17, 2010

    Consider the difference between pseudovectors (axial vectors, e.g., magnetic field H) and chiral systems. Reflecting a current-carrying solenoid trivially reverses the direction of current flow and coil helicity, but field direction does not reverse if the mirror plane is parallel to the field axis. Normal to the field axis the field reverses, solenoid helicity reverses… but what of current flow? Reversing two of three axes in a chiral system does not reverse its chirality. One reflection or all three axes’ reflections reverse chirality.

    It’s complicated and subtle. Footnotes are a rich source of wonder.

    1) Entropy is a weak arrow of time for it is only statistical.

    2) Angular momentum is a strong arrow of time. Feynman’s sprinkler only spins in one direction, blowing water out but not aspirating it.

    3) Chirality is coupled to moments of inertia. Chirality is also a strong arrow of time – and it don’t need no stinkin’ magnetic field,

    Nature 463 210 (2010)
    “Chiral spin liquids are a hypothetical class of spin liquids in which the time-reversal symmetry is macroscopically broken in the absence of an applied magnetic field or any magnetic dipole long-range order. ”

    Phys. Rev. D 71 057501 (2005)
    “The so-called time-reversal odd distribution functions are known to be nonvanishing in QCD due to the presence of the link operator in the definition of these quantities. I show that T-odd distributions can be nonvanishing also in chiral models”

    Chem. Phys. Lett. 173(5-6) 485 (1990)
    time-reversal symmetry of chiral systems

    Phys Rev Lett. 91(24) 247404 (2003)
    Broken time reversal of light interaction with planar chiral nanostructures.

    4) Gravitation does not get off the hook. Though physics cannot imagine a universe non-identical to its mirror image (perfect theory derived from fundamental symemtries, then furiously ad hoc patched with inserted symmetry breakings), this universe does it everywhere. Physics denies emergent obervables can be fundamental. Nobody has examined gravitation for chiral divergence. Physics knows no structural chemistry. Cowards – two opposite geometric parity atomic mass distribution Eotvos experiments,

    http://www.mazepath.com/uncleal/erotor1.jpg

    Theory predicts what observation tells it to predict.
    Somebody should look. The worst it can do is succeed.

  8. #8 wingcodavid
    February 17, 2011

    Where can I access more information on Time Reversal?
    Time slipping and the Dimension of Timelessness?