死亡恒星不辐射：关于Hawking辐射的讨论

Azimuth

死亡恒星不辐射

有三位研究者声称，任何大质量物体都会发射 Hawking 辐射，即使它不是黑洞：

现在他们通过宣称这意味着宇宙将比我们预期的更快地消亡，获得了更多的关注。他们声称，一颗死亡的、寒冷的恒星也会发射 Hawking 辐射，从而缓慢地失去质量并最终消失！

他们承认，这将违反重子守恒：毕竟，恒星中的质子和中子必须以某种方式消失！他们承认他们不知道这将如何运作。他们只是说，恒星的引力场会产生粒子-反粒子对，这些粒子-反粒子对会缓慢地辐射出去，迫使死亡的恒星以_某种方式_失去质量，以保持能量守恒。

如果专家们认为这甚至有一丝可能是真的，那将是自切片面包以来最重大的事件——至少在量子引力领域是这样。每个人都会写关于它的论文，因为如果这是真的，那将是革命性的。它将推翻专家们的计算，这些计算表明静止的物体不会发射 Hawking 辐射。这也意味着弯曲时空中的量子场论只有在重子数不守恒的情况下才能保持一致！这将是令人震惊的。

但事实上，这些新论文对物理学几乎没有产生任何影响。这里有一个简短的反驳：

它解释说，这些人使用了一个粗略的近似方法，即使在更简单的问题中也会给出错误的结果。类似观点见于此：

不幸的是，关于弯曲时空中的量子场论的真正专家似乎并没有站出来提及思考这个问题的_正确_方式，这种方式至少从 1975 年起就已经为人所知。对他们——或者也许我应该敢于说“我们”——来说，只是_众所周知_静态质量的引力场不会导致粒子-反粒子对的产生。

当然，审稿人应该拒绝 Wondrak, van Suijlekom 和 Falcke 的论文。但显然这些审稿人中没有一个是手头主题的专家。所以你不能仅仅因为一篇论文出现在一家据称信誉良好的物理期刊上就相信它。你必须真正理解这个主题并自己评估这篇论文，或者与你信任的一些专家交谈。

如果我是一位科学记者，要写一篇关于像这样所谓的令人震惊的进展的文章，我会给一些专家发电子邮件，看看这是不是真的。但是现在很多科学记者都不再费心去做这件事了：他们只是相信新闻稿。所以现在我们被大量像这样的懒惰文章轰炸：

这样的例子还有很多；这只是其中三个。我说的话不可能对如此大量的信息产生太大影响。正如马克·吐温所说：“当真理还在穿靴子的时候，谎言已经绕了世界一圈。” 实际上他可能并没有这么说过——但每个人都一直说他这么说过，完美地说明了这一点。

不过，可能还是有一些既关心又尚未了解这些内容的人。与其在这里尝试举办一个迷你课程，不如简单地指出一个关于事物如何真正运作的解释：

它是技术性的，所以如果你没有学习过量子场论和广义相对论，那么阅读起来并不容易，但这是不可避免的。它表明，在静态时空中，有一个明确定义的“真空”概念，并且真空是稳定的。 Jorge Pullin 指出了当前目的的关键句子：

因此，如果底层时空承认一个处处类时的 Killing 场，那么真空态确实是稳定的，并且诸如粒子的自发产生之类的现象不会发生。

拥有“处处类时的 Killing 场”的这个条件表明，时空具有时间平移对称性。 Ashtekar 和 Magnon 还假设时空是全局双曲的，并且质量为零的粒子的波动方程对于给定的平滑初始数据具有平滑解。所有这些都让我们为这个方程的解定义能量的概念。它还让我们将解分解为正频率解（对应于粒子）和负频率解（对应于反粒子）。因此，我们可以按照我们习惯的方式在 Minkowski 时空中建立量子场论，其中有一个明确定义的真空，不会衰变成粒子-反粒子对。

描述静态黑洞的 Schwarzschild 解也有一个 Killing 场。但是这个场在地平线上不再是类时的，所以这个结果不适用于它！

如果需要，我可以详细说明，但您可以在这本标准教科书中找到更具教学性的处理方法：

特别是，转到第 4.3 节，该节是关于静态时空中的量子场论。

我也忍不住引用我一位学生的这篇论文：

这篇论文涵盖了电磁学的情况，而 Ashtekar 和 Magnon，以及 Wald，为了简单起见，侧重于质量标量场。

所以：已经严格证明了静态物体的引力场不会产生粒子-反粒子对。这已经为人所知几十年了。现在有些人做了一个粗略的近似计算，似乎表明情况并非如此。近似中的一些缺陷已被指出。当然，计算的作者不相信他们的近似是有缺陷的。我们可以为此争论很长时间。但这几乎不值得思考，因为不需要任何近似来解决这个问题。它在 50 多年前就已解决，而这项新工作并没有为这个问题提供新的启示：它比旧工作更具有猜测性。

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11 Responses to Dead Stars Don’t Radiate

  1. Clive Scott's avatar Clive Scott says: 17 May, 2025 at 3:23 pm Journalists measure their success by their ability to sell newspapers and get clicks. It follows that they have a perverse incentive to sensationalize any story. Reply
  2. duetosymmetry's avatar duetosymmetry says: 17 May, 2025 at 3:41 pm In their defense, some science journalists do check with experts! I know of at least one journo who asked my colleague about this very paper, and correctly took the advise that the paper was wrong. PRL clearly asked the wrong referees about this manuscript… Reply
    • John Baez's avatar John Baez says: 17 May, 2025 at 4:27 pm I’m glad some journalists did check with experts. Unfortunately the journalists who did , did not publish articles with attention-grabbing headlines like PHYSICISTS PUBLISH FALSE CLAIM THAT THE UNIVERSE WILL END SOONER THAN EXPECTED So, it’s like how experiments that report unsurprising “negative results” tend not to get published, while those that report surprising “positive results” do… leading to a a bias toward surprising but false papers. We do now have the Journal of Negative Results. But we need the Pop Science Magazine of Incorrect Discoveries. Reply
  3. Toby Bartels's avatar Toby Bartels says: 17 May, 2025 at 3:45 pm So we have a rigorous proof that 2 + 2 = 4, but some people noticed that 2.3 + 2.4 = 4.7, did a rough approximation, and concluded that sometimes 2 + 2 = 5? Reply
  4. Wyrd Smythe's avatar Wyrd Smythe says: 17 May, 2025 at 4:18 pm Nice of you to lay it out like this, thanks. The way I had it explained is that an event horizon is necessary for Hawking radiation because it presents a “wall” that affects the QFT vacuum. It makes perfect sense that mere gravity wouldn’t do it. Perhaps they took too seriously the (as I understand it, utterly incorrect) metaphor about one of a particle-antiparticle pair generated near the event horizon getting lost behind the horizon? Reply
    • John Baez's avatar John Baez says: 17 May, 2025 at 4:39 pm Sort of. In their mild defense, a static electric field can create positron-electron pairs: • Wikipedia, Schwinger effect. This is true even for a weak electric field, though the effect is exponentially suppressed and it’s never yet been seen (see the article). So, you might think a static gravitational field could do something similar. The original paper, the rebuttals, and the attempted rebuttal to the rebuttals are all about this. Unfortunately, no amount of fiddling around with approximate calculations will take you to the truth. Or maybe it eventually could, but it’s very inefficient. It’s better to start with the correct answer as found by Ashtekar, Magnon and others, and then use that to study the approximations and see how well or poorly they do. That could be somewhat interesting, though I don’t have the patience to do it myself. The key fact is that the geometry of spacetime affects our definition of what counts as a particle. If you don’t handle this correctly you’ll get nonsense. Luckily you can learn how to do it by reading Wald’s textbook. Reply
      • Wyrd Smythe's avatar Wyrd Smythe says: 17 May, 2025 at 6:15 pm I’d never heard of the Schwinger effect. Very interesting! And I can see how an electric field would accelerate electrons and positrons in opposite directions. But for gravity to have that effect, it would seem the particles and antiparticles would need to be oppositely affected by gravity. And wasn’t there just a recent experiment showing anti-hydrogen falls downwards just like hydrogen? (Thanks for inserting my missing word.) Reply
  5. John Baez's avatar John Baez says: 17 May, 2025 at 5:21 pm I had a nice conversation on this topic with Tobias Fritz here. We got into some of the technical issues. Reply
  6. Gregor's avatar Gregor says: 17 May, 2025 at 5:32 pm This might be a stupid question, but couldn’t I read the claim that massive things dissipate as saying that there is not a timelike Killing vector field in the first place? After all, such a thing would generate an isometry that takes points prior to dissipation to points afterwards, which clearly can’t exist. In other words, when you say ‘static spacetime’, aren’t you assuming what you want to prove? Reply
    • John Baez's avatar John Baez says: 17 May, 2025 at 7:16 pm It’s not a stupid question, it’s a very clever one. In computations of the Hawking radiation for black holes, the assumption of a timelike Killing vector field is an approximation. The approximation is justified by the fact that the change in mass of the black hole is so slow. This sort of approximation is typical in physics. However, people have gone further and computed what happens when you consider the ‘back-reaction’: the effect of the changing mass of the black hole on the Hawking radiation it emits. This back-reaction effect is tiny until near the end of the black hole’s life, when it’s losing mass quickly. For the case of a static dead star, I believe the assumption of a timelike Killing vector field is fine and exactly correct, since it leads to a perfectly self-consistent result: no radiation and no change (unlike the case for black holes, where this assumption leads to radiation and a slowly changing mass of the black hole). The skeptic (like you) could argue that while we get a self-consistent solution, the reasoning is circular. Such skeptics should do a calculation where they allow the dead star’s mass to slowly change, and see if there’s also a self-consistent solution where there’s a little radiation and the dead star slowly shrinks. I don’t think there will be. But if there were, there would then be two self-consistent solutions to the same physics problem, an unusual situation. Then one could try to study whether one solution was ‘better’ than the other. Of course we already have one reason the (known) static solution is vastly better than any (purely hypothetical) alternative solution: in the static solution, protons and neutrons don’t disappear into thin air! Any ‘slowly shrinking star’ solution would violate conservation of baryon number—and in a completely mysterious way, since nothing about the process of particle-antiparticle creation that supposedly drives this hypothetical solution violates baryon conservation. Reply

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