Friday, February 05, 2016

Me, Elsewhere

I'm back from my trip. Here are some things that prevented me from more substantial blogging:
  • I wrote an article for Aeon, "The superfluid Universe," which just appeared. For a somewhat more technical summary, see this earlier blogpost.
  • I did a Q&A with John The-End-of-Science Horgan, which was fun. I disagree with him on many things, but I admire his writing. He is infallibly skeptic and unashamedly opinionated -- qualities I find lacking in much of today's science writing, including, sometimes, my own.
  • I spoke with Davide Castelvecchi about Stephen Hawking's recent attempt to solve the black hole information loss problem, which I previously wrote about here.
  • And I had some words to spare for Zeeya Merali, probably more words than she wanted, on the issue with the arXiv moderation, which we discussed here.
  • Finally, I had the opportunity to give some input for this video on the PhysicsGirl's YouTube channel:

    I previously explained in this blogpost that Hawking radiation is not produced at the black hole horizon, a correction to the commonly used popular science explanation that caught much more attention than I anticipated.

    There are of course still some things in the above video I'd like to complain about. To begin with, anti-particles don't normally have negative energy (no they don't). And the vacuum is the same for two observers who are moving relative to each other with constant velocity - it's the acceleration that makes the difference between the vacua. In any case, I applaud the Physics Girl team for taking on what is admittedly a rather technical and difficult topic. If anyone can come up with a better illustration for Hawking-radiation than Hawking's own idea with the pairs that are being ripped apart (which is far too localized to fit well with the math), please leave a suggestion in the comments.


  1. "To begin with, anti-particles don't normally have negative energy (no they don't)."

    Surprisingly, I found the same mistake in a semi-popular book by someone who has way too many credentials to get this wrong. I emailed him, pointing this out, and he said that he would think about it. Huh?

    I often send lists of goofs, typos, and mistakes to authors so that they can get corrected in future printings (easier with eBooks and print-on-demand (many books are, even if not marketed as such) than it used to be back in the days of lead type and print runs). Some are really thankful. Some at least acknowledge my effort. Some don't even reply. Separates the wheat from the chaff.

  2. It's only half the fun if you don't tell us whose book it was :o)

  3. OK, so a bit of help please. The Dirac equation is often said to have negative energy states, and these were associated with the discovery of antiparticles. So what's right?

  4. "It's only half the fun if you don't tell us whose book it was :o) "

    Half the fun for you. Perhaps no more fun ever again for me if I do. :-|

  5. "The Dirac equation is often said to have negative energy states, and these were associated with the discovery of antiparticles."

    Yes, this idea played a role in the early development of QED, but it is not the correct way to think of it. For one thing, it is asymmetric with regard to matter and antimatter. (OK, there is some asymmetry, but not in this context.) Like the Bohr model of the atom, it gives the right answer in some cases, without being a good model. But perhaps this is the root of the false belief antiparticle = negative energy.

  6. Andrew,

    Yes... and already Dirac noted that it would be very problematic if these states did indeed have negative energy, because that would mean you could produce real particle pairs out of nothing, causing the vacuum to decay. That's why he introduced the Dirac sea, which is still (I think) the most useful way to think of it. Though in QFT the problem kind of doesn't occur, you have annihilation and creation operators for particles and antiparticles, and they all have positive energy. You still have, of course, to renormalize away the (technically infinite) vacuum energy (which you can interpret as the Dirac sea if you want). In any case, I subscribe to instrumentalism and don't really care how people interpret QFT, but we know for sure that anti-particles do not carry negative energy. If they would, then particle-antiparticle pairs would annihilate to nothing and not to (eg) photons (which carry the energy of the particle pair). Best,


  7. "anti-particles don't normally have negative energy"

    It has already been mentioned in comments, but in trying to understand Hawking radiation I read what seemed like dozens of online articles without seeing this explained, and somewhere previously I had gotten the idea in my head that (virtual) anti-particles did have negative energy, so none of the articles made sense to me. Finally I did find the crucial piece of information (probably it was here, thanks) and then finally I got it. (Except of course it's not actually true - but if it was, it would make sense!)

  8. JimV,

    In the standard treatment for Hawking radiation the anti-particles which appear there indeed have negative energy, but this is an artifact of the calculation in a fixed background, and not a property of anti-particles in general. If the background is fixed, you cannot get energy from anywhere, consequently the only way to create particle pairs is to have them with a net-energy of zero. It is, in a sense, indeed as if the vacuum was slowly decaying (what Dirac wanted to avoid). In any case, one shouldn't confuse this negative energy (which is a consequence of the black hole geometry) with the energy of anti-particles in general.

  9. Thanks very much for your responses.

    I don't think it's quite so clear-cut though. It seems to me like we have to look at the big picture, energy-momentum, the four-vector in space tine. Energy is then just the time component of the energy-momentum vector. But instead of considering just the energy of a particle or antiparticle, we really have to consider the energy-momentum vector, and that always has a positive magnitude - even if the energy component might be negative. So we can have a particle with negative energy, but a positive magnitude energy-momentum.

    So in particle-antiparticle annihilation, it is the energy-momentum which must be conserved. So we should not expect nothing to result - as that would break conservation of energy momentum. Instead, the energy-momentum of both particles (the magnitude of which is positive for both particles) gets converted into the momentum of the photon. But, yes, the energy component vanishes completely, cancels out, so we can have positive energy and negative energy cancelling, but a ton of momentum emerging instead.

    But I might well be completely wrong!

  10. Andrew,

    What I mean is simply that v + (-v) = 0. I don't know what you mean, sorry.

  11. " If the background is fixed, you cannot get energy from anywhere, consequently the only way to create particle pairs is to have them with a net-energy of zero."

    But even here, it doesn't have to be the antiparticle with the negative energy.

  12. Hi Bee, it was a bit of a stream of consciousness thing! Sorry.

    A last point though, if we consider antiparticles as particles moving backwards in time (which I suspect you don't agree with), does that not suggest negative energy?

  13. Crank bait: "…come up with a better illustration for Hawking-radiation…"

    OK, I'll bite!

    Assume each particle radiates as two parts, and that each can re-localize/collapse separately (via an intermediate vacuum interaction). You'll then get two independent events (having anti-particle signature, coupling to the alternate Dirac phases) some distance from the source. Repeat the process for those new particles. It's then possible to (a) have the original particle re-constitute, using the same parts, or (b) it fails to re-constitute, and the parts go their separate ways, forming other couplings.

    For black holes, the vacuum density (a statistical measure of discrete bosons) would be high, and the collapse would be more local, but coherence is less likely. Low-(mass-)energy radiation would result, likely observed as an increased vacuum flux (manifest as an increased gravitational field, on interaction), rather than emitted massive particles. If you're wondering what happens to high-mass, inner element: it simply forms other couplings with the vacuum flux, likely forming a 'plasma' in high-energy conditions. I see the interior of a black hole as chaotic and non-classical.
    (Not asking for evaluation! Remember, I'm pretending not to be a crank)

  14. Andrew,

    You can (with some fineprint) interpret negative energy antiparticles as positive energy particles going back in time because E*t remains the same. It's the same thing. You lose nothing but gain nothing either.

  15. JSV,

    I think this is a misunderstanding... I am looking for a metaphor or image that gets across the standard calculation for the Hawking radiation better than the picture with the pair-production at the horizon and yet not quite as vague as the attempt in the video (which is correct, but not particularly catchy).

  16. Thanks, Bee. I'm looking forward to your new book.

    (I'm also interested in whether antimatter is gravitationally repulsive or attractive)

  17. Hi Sabine,

    Personally I would put my money on superfluid dark matter (or similar idea). Interesting to see what comes out from the computer simulations. Next step... read the blog post of yours about the topic.

  18. Is it better to say that, in terms of quantum fluctuations (or vacuum energy, as discrete radiation), a particle pair is less likely to annihilate in the presence of a flux gradient (ref: stress-energy tensor), because the gradient makes one part more likely to collapse independently of the other? It then doesn't depend on an actual event horizon, and can happen anywhere in the influence of the black hole. Once free of its partner, it radiates until collapsed by other means.

    There's more that can be said here (like multiple steps, to avoid the anomalous blue-shifting back-trace), but it diverges from the standard stuff, and assumes quantum-chaotic, rather than classical mechanisms.

  19. Andrew,

    Antimatter is gravitationally attracive. We know this - I don't understand why people are still discussing this. We know that matter-antimatter pairs have a positive gravitational mass because they add to quark masses (among other things).

  20. Thanks. My impression was it was still undecided.

  21. The challenge with Khoury's model of Dark Matter is that it relies on axion-like particles.

    Despite a host of claims to the contrary, there is no firm experimental evidence for axions, as well for other nearly massless scalars advocated by symmetry breaking scenarios, at least for the time being.

  22. "superfluid dark matter" is degenerate, located at the galactic gravitational potential minimum, perhaps at disk minima, violating Tully-Fisher. Fermions stack, but then density distribution (Rydberg atoms).

    Milgrom acceleration replaces dark matter. It is testably sourced in bench top existing apparatus - via chemistry. Physics rejects experiments falsifying accepted empirically sterile theory.

    "there is no firm experimental evidence for axions" Observation efforts fail single photon detection downstream (CAST at CERN re solar axions). No observation sensitivity exhausts Yukawa potential graphs.

    Dark matter is a streetlight fallacy. Look elsewhere.

  23. The popular Hawking particle / anti-particle thing also suggests negative energy because the black hole is supposed to lose mass and evaporate. If both particles have positive mass, one would assume that the black hole was gaining mass by "eating" the vacuum energy even as it emitted radiation.

    I would love to see a better metaphor. There seem to be two pieces. One says that an accelerating observers see the vacuum energy differently so strong acceleration makes it appear that the vacuum is radioactive. (Would it be reasonable to consider acceleration making virtual vacuum particles look like real particles?) Since acceleration warps the space time in the same way that a black hole does, so a fixed observer watching a black hole sees the same radiation.

  24. An interesting way to drive home that second point is to hook up an three axis accelerometer chip. Many laptops and cell phones have these. At rest on your desk, it will report an acceleration towards the center of the earth. If you wiggle the device around you see other accelerations. You can even raise and lower the device to make the vertical acceleration change, though one should be careful doing this lest it slip out of one's hands.

    Combine the idea of virtual particles in a vaccum with "it's like the red/blue shift which is a result of relative velocity except it's a result of acceleration. So, of course you'll see black holes emitting particles. Even the earth emits particles, though so few as to be irrelevant.


COMMENTS ON THIS BLOG ARE PERMANENTLY CLOSED. You can join the discussion on Patreon.

Note: Only a member of this blog may post a comment.