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Thanks for a Great Semester

Thanks to everyone for making this a great semester. Since this blog has a very specific purpose, I won’t continue to post here, but I look forward to getting term papers (soon!) from everyone enrolled in the class.

Virtual Particles and Hawking Radiation

Virtual Particles

The discussion of virtual particles in A Brief History of Time raises a lot of questions I can’t answer. However, the guys and gals at Scientific American seem to have it together:

Virtual particles are indeed real particles. Quantum theory predicts that every particle spends some time as a combination of other particles in all possible ways. These predictions are very well understood and tested.

Quantum mechanics allows, and indeed requires, temporary violations of conservation of energy, so one particle can become a pair of heavier particles (the so-called virtual particles), which quickly rejoin into the original particle as if they had never been there. If that were all that occurred we would still be confident that it was a real effect because it is an intrinsic part of quantum mechanics, which is extremely well tested, and is a complete and tightly woven theory–if any part of it were wrong the whole structure would collapse.

But while the virtual particles are briefly part of our world they can interact with other particles, and that leads to a number of tests of the quantum-mechanical predictions about virtual particles. The first test was understood in the late 1940s. In a hydrogen atom an electron and a proton are bound together by photons (the quanta of the electromagnetic field). Every photon will spend some time as a virtual electron plus its antiparticle, the virtual positron, since this is allowed by quantum mechanics as described above. The hydrogen atom has two energy levels that coincidentally seem to have the same energy. But when the atom is in one of those levels it interacts differently with the virtual electron and positron than when it is in the other, so their energies are shifted a tiny bit because of those interactions. That shift was measured by Willis Lamb and the Lamb shift was born, for which a Nobel Prize was eventually awarded.

Quarks are particles much like electrons, but different in that they also interact via the strong force. Two of the lighter quarks, the so-called “up” and “down” quarks, bind together to make up protons and neutrons. The “top” quark is the heaviest of the six types of quarks. In the early 1990s it had been predicted to exist but had not been directly seen in any experiment. At the LEP collider at the European particle physics laboratory CERN, millions of Z bosons–the particles that mediate neutral weak interactions–were produced and their mass was very accurately measured. The Standard Model of particle physics predicts the mass of the Z boson, but the measured value differed a little. This small difference could be explained in terms of the time the Z spent as a virtual top quark if such a top quark had a certain mass. When the top quark mass was directly measured a few years later at the Tevatron collider at Fermi National Accelerator Laboratory near Chicago, the value agreed with that obtained from the virtual particle analysis, providing a dramatic test of our understanding of virtual particles.

Another very good test some readers may want to look up, which we do not have space to describe here, is the Casimir effect, where forces between metal plates in empty space are modified by the presence of virtual particles.

Thus virtual particles are indeed real and have observable effects that physicists have devised ways of measuring. Their properties and consequences are well established and well understood consequences of quantum mechanics.

Read Gordon Kane’s entire piece on the subject here. And you can get the lowdown from the BBC about the relationship between virtual particles and Hawking radiation below.


Term Paper Due Date

Uddit pointed out that I’ve got May 10th as the due date for the term paper. But I won’t be done grading 310 and 395 finals until Wednesday, May 16. So let’s make COD May 16 the revised due date for the paper. Hope that makes your life easier; it certainly won’t make mine any harder!

(If you’ve already submitted a final draft and want to withdraw it to do more work, just let me know.)

The Makropulos Case


Bernard Williams’ famous piece of the tedium of immorality can be found in his Problems of the Self (Cambridge: Cambridge University Press). If the library doesn’t have a copy, you can borrow mine. Williams’ essay was published in the early 70s and has generated many responses. Some of the issues discussed by Williams were discussed around the same time by J.L. Borges in his “Utopia of a Tired Man,” which, I think was originally published in his Book of Sand. Julian Barnes, who often writes with an eye toward mortality and its consequences, also lends his considerable skills to this topic in the last chapter of History of the World in Ten and One-Half Chapters.

The Immortality Project


Those of you who are interested in writing about immortality might want to check out the Immorality Project, which is run by John Martin Fischer. Incidentally, Fischer has done some of the last decades best work on free will and moral responsibility as well as on the nature of death. According to the project’s website, “Questions about personal immortality are central existential concerns that know no geographical or cultural bounds.”

Such questions include:

  • whether and in what form(s) persons survive or could survive bodily death
  • whether and to what extent persons’ beliefs about immortality influence their behavior, attitudes, and character
  • why and how persons are (at least pre-reflectively) disposed to believe in post-mortem survival
  • whether it is in some sense irrational to desire immortality
  • and more besides.

Recently the scientific, philosophical and theological communities have paid serious attention to these themes. Interest in these issues is reflected in the popular press as well. Such interest in the project themes inside and outside the academy signals the present time as an auspicious one to launch a unified, organized, and open-minded project that will

(1) stimulate research from across the disciplines in attempt to make progress on these themes

(2) disseminate this research to an especially receptive public.

As project leader, John Martin Fischer, Distinguished Professor of Philosophy at the University of California at Riverside, seeks to foster such progress primarily by issuing requests for research proposals to fund scientific, philosophical, and theological projects that advance understanding of immortality and belief in immortality, and of how each of these is relevant to the way we live our lives at present.

In addition, the project will include public events and popular-level publications, including essay prizes, aimed at raising awareness of ways in which this topic can be understood and further investigated through careful empirical, philosophical, and theological means. A translation component is intended to provide German-language scholars with more resources for investigating some of the issues above.

The project has essay prizes and a page full of resources. Check it out.

Full Disclosure: The image is from Allegoria dell’immortalità by Giulio Romano and borrowed from a wiki page.

Hawking in Print


In addition to doing a great deal of work of fundamental interest in physics Stephen Hawking has managed to write a number of successful works in what might be called popular science. These include:

Check ’em out.