Let's Break the Law--Newton's that is.

In classical mechanics, Newton's Three Laws are considered inviolate. Well, OK, his first law is really just a special case of his second. No matter, the topic today is the third law, known and loved by all as:

For every action there is an equal and opposite reaction.

In introductory physics, this is made real and quantitative when constructing free body diagrams. If I want to use Newton’s Second Law, F = ma, applied, say, to a person, you make a diagram that includes all the forces on the person. If the problem states that the person is pushing on a wall to the right with a force of 10 units, that force does not appear on the free body diagram because you want forces on the person and not by the person. So you reason that from Newton’s Third Law the wall exerts a force 10 units to the left, that is, equal and opposite. That force, from the wall, is the one that gets put on your diagram.

Ask any number of physics students, and many physics professors: is Newton's Third Law always valid? The answer they will likely give is yes.

But it is not. Consider the picture shown, of two charged particles travelling along perpendicular axes. Take both charges as positive. The Coulomb force between the charges, which acts along the line joining them, will be equal and opposite. But what about the magnetic forces?

The detailed magnetic fields are complicated, but the directions are easy—it just requires application of various forms of the right hand rule. And we will only need directions—because to show a violation of Newton’s third we need only show the direction of the magnetic force from q₁ on q₂ is not opposite to the direction of the magnetic force from q₂ on q₁. In fact, it is equal but not opposite.

The charge q₁, moving along the x axis as shown, is effectively a current flowing along the x axis. Such a current produces loops of magnetic field, and the direction of the magnetic field comes from (a) placing the thumb of your right hand in the direction of the current (the positive x axis) and letting your fingers curl—they will curl as the magnetic field curls. Thus B anywhere on the xy plane with y > 0 will be coming up and out of the xy plane in the positive z direction, as shown by B (of q₁) in the diagram.

Now the moving q₂ is effectively a current along the positive y direction. From basic physics there will an IL×B force on q₂, where L is a vector in the direction of the current I, i.e., the plus y direction. Here we use the other form of the right hand rule: align your fingers with L (+y direction) curl them in the direction of B (+z) and your thumb will point in the direction of the force, in this case, +x, as indicated by F₂₁.

That is, the magnetic force from q₁ on q₂ is in the +x direction.

The same analysis, to get the force of q₂ on q₁ yields not the opposite direction, but the +y direction as indicated by F₁₂.

F₁₂ and F₂₁, as you see, are not opposite.

What is happening here?

Well, Newton's Third Law is actually a "usually" correct statement of a truly inviolate law (under the conditions we are discussing) which is conservation of momentum. That says that the change in q₁'s momentum is equal and opposite to the change in q₂'s. That is:

dp₁ = - dp₂ (where dp₁ means the change in p₁)

If we divide by dt, the time of the interaction, we get dp₁/dt = -dp₂/dt. Students will recognize dp/dt as the force. (Newton’s Second Law is not really F = ma, but F = dp/dt, but dp/dt is the same as ma for the usual case where the mass is constant.) Thus we have, if you will, derived Newton's Third Law from conservation of momentum.

Thus Newton's Third law is really a statement of conservation of momentum—but we have made an assumption that all the momentum is found in the two particles. If something else can absorb some momentum, then conservation of momentum really reads that dp₁ + dp₂ + dp_{something-else} is zero, and when we divide by dt we do not get that the magnetic forces are necessarily equal and opposite, because the dp_{something-else} is ruining the equation.

What is this "something else?" It is the electromagnetic field. The field can carry momentum. Careful analysis, taking the momentum of the field into account, shows that the momentum is indeed conserved.

In most classical physics problems there is no field, and the particles themselves have to bear the burden of conserving momentum—and that in turns leads to slavish obedience of Newton’s third law.

NOTE: The picture was taken from here, which has a similar discussion.

Kenneth Miller's CNU Talk

Kenneth Miller of Brown University spoke on our campus yesterday. The topic was more-or-less the compatibility of science and faith and evolution vs. ID. I would say he talked mostly about evolution. He did speak some about his faith (he is a Christian—a practicing Catholic.)

First of all, I must say I was really impressed with the CNU students. They asked great questions.

Miller first presented a “workshop” which was really nothing more than a Q/A session. I asked him several questions, including what he thought of the Neville Chamberlain “appeaser” charges coming from people like PZ Myers. He laughed and said that he actually really likes PZ—but (his body language and expression suggested to me) found it mysterious and odd that PZ would call him so many things—he enumerated a few; it included the dreaded “creationist” tag. He then, for reasons unknown, asked how many people in the room had never heard of PZ Myers—and everyone except a couple of us professor types raised their hand.

Which does make a point—this cesspool of militant atheist science blogs is more or less preaching to a micro-choir. The students, the bulk of whom I discerned were very pro-evolution, had all heard of Dover, and Intelligent Design, and were aware of the evolution-creation controversy, and even very aware of the Flying Spaghetti Monster—but they didn’t know about PZ or his blog. That says something.

During Miller's talk I was struck, no doubt because of my frequent forays into ugly blog wars, by how civilized and accommodating educated people are when they meet face to face even if the topic is this controversial. Here is Miller—quite an accomplished scientist, speaking about faith and stating, point blank, “I am a Christian.” He spoke favorably—if not glowingly—about Francis Collins, mentioning that he was a committed evangelical Christian, had written a fantastic book, as that he was probably on some short lists for a Nobel Prize. (He also mentioned where he has friendly disagreements with Collins, especially about Collins’s testimony.) There was no acrimony from the audience—nobody stood up and said what some will say on the nastier science blogs, that you [Miller] and Collins are not real scientists. I think in person, when a man of such substantive scientific achievement is right there standing in front of you—well, not many are brazen enough to say: “you are not a real scientist” or “how do you deal with such levels cognitive dissonance?” No—it requires the mob mentality of the blogosphere to bring out such asinine behavior. In real life—at a minimum it would take an supremely arrogant person whose scientific achievements were at least comparable (if not better) to make such a claim. On the science blogs, the arrogance coupled with even scientific illiteracy is sufficient.

At one point Miller was asked about interpreting Genesis. He argued that he is surprised that he has to remind Protestants so often that the Reformation was fought over the right of having the scripture in the vernacular and the right of private interpretation. What he meant was: don’t criticize me for not taking a literal view—after all it was you guys who opened up the door. Well, I don’t criticize him for taking a non-literal view. Like some prominent church fathers (including Augustine,) I don’t take a literal view either. But his characterization of the Reformation was wrong on two fronts: one, the primary cause was not the right of private interpretation, but the Solas, i.e., Sola Fide and Sola Scriptura. And two, the doctrine of private interpretation never meant that you are free, willy-nilly, to create your own interpretation. It meant you were free to examine the scriptures and reach conclusions—but that was to be done responsibly and not in a vacuum.

The most effective part of his presentation was arguing against the irreducible complexity of the bacterial flagellum. Showing how the parts of the flagellum have other functions is a strong rebuttal. He followed that with a demonstration that Behe’s mousetrap was not irreducibly complex. I didn’t find that compelling—because it felt a bit contrived—and Behe used the mousetrap as an analogy; for his purposes it doesn’t have to be perfect, just reasonably illustrative. Miller’s examples of fish-amphibian transitional fossils, some of which were discovered after the Dover trial, were also quite fascinating.

In terms of his theology, he insists that he is not a theistic evolutionist, although he lamented that even his friends call him that. I would agree—the usual notion of theistic evolution is that God continues or at least could continue to intervene—as the Great Genetic Engineer. Also, a garden-variety theistic evolutionist would still insist that our species, as part of God’s plan, was inevitable. But Miller does not concede that—he concedes only that some big brain species was inevitable and that God could have used, say, big-brained dinosaurs instead of “hairless, bipedal primates.” I asked about this—something I have always argued concerning the NCSE is that they are too cavalier when they say the Catholic Church is OK with evolution. In particular, I asked him if it weren’t true that the Catholic Church is actually fine with classic theistic evolution—with man as the inevitable pinnacle thereof, and I think it is fair to say that he conceded that point (about Rome approving "classic" TE, not about the NCSE, which was not mentioned by either of us)—while also pointing out that he hasn’t been charged with heresy yet.

I would characterize his theology-science intersection, in as much as he presented it, close to benevolent deism. He has a nice, loving God—but not one that interacts with creation. His typical argument is “but that doesn’t mean God didn’t do it that way.” For example, when asked about the evolutionary explanation for universal morality, he said (I think I have this more or less correct) that the evolutionary explanation sounded plausible but was by no means demonstrated. And then he added—but that doesn’t mean that God didn’t intend for that to happen that way.

This theology, it seems to me, preserves God’s sovereignty to only the flimsiest of degrees. But I have the feeling that in his non-scientific life his view of God is much more traditional—and that, most importantly, he does indeed view Christ as the redeemer of lost men.

Miller said something that I have been saying for years: that as a theist he is, like all other theists, a believer in a small i, small d intelligent designer. I was impressed that he didn’t go on and on about how this doesn’t mean he is an IDer—he assumed that the students would grasp the distinction, and they did.

I must mention that I talked to Miller after the workshop, and the subject of blogs came up. He had mentioned that he gets it from “both sides.” I puffed up my chest and said: “me too.” I have been skewered on PZ’s blog (though not banned) and outright banned from Dembski’s blog. This led to a discussion about Dembski, where we both admitted that we can’t believe those infamous Dembski antics—the Jones animation, the Vice Strategy, publishing the names, addresses and phone numbers of the Baylor board, the Oklahoma lecture video incident, etc. Miller told the story of how they were waiting for Dembski to show up to be deposed for the Dover trial—and how only Dembski’s lawyer showed up—and said something along the lines of “Dr. Dembski has withdrawn. Good day gentlemen.” And that was that.


In his general presentation, Miller used Philip Johnson’s (he, the godfather of the ID movement) relatively recent quote:

"I also don’t think that there is really a theory of intelligent design at the present time to propose as a comparable alternative to the Darwinian theory, which is, whatever errors it might contain, a fully worked out scheme. There is no intelligent design theory that’s comparable. Working out a positive theory is the job of the scientific people that we have affiliated with the movement. Some of them are quite convinced that it’s doable, but that’s for them to prove…No product is ready for competition in the educational world" (Phillip Johnson, interview quoted in Berkeley Science Review)

The gasp and murmuring that the quote produced in the audience convinced me that this is a killer anti-ID PR bullet. The ID guys must wish that they could surgically remove that quote from the inter-webs the way they periodically cleanse UD of embarrassing posts.

All in all a great time was had by all. No matter what your opinion is of Miller or his views, it is undeniable that his intelligence, charm, breadth of knowledge, and humor make him a very entertaining lecturer.

How many books belong in the bible?

I don’t know, and it doesn’t matter.

I had this discussion recently on an atheist blog. It started out with a commenter, a guy with a one-song repertoire. All over the relevant subblogosphere he is very proud to drop this nugget:

Is it wrong to goad the local Christian fundamentalists into proving that they are really believers via Jesus' litmus test: Drinking deadly poison and surviving (Mark 16:18)?

Now on at least two other occasions I have pointed out to him that many people believe that the so-called Marcan Appendix (Mark 16:9-20) from which he is taking his slam-dunk criticism is likely a redaction.

The responses were predictable, and along the lines of how convenient that such an inconvenient passage turns out to be an addition. The implication being that it is just as good as any other scripture, and we have no basis for excluding it. It does not matter that a great deal of legitimate scholarship has gone into justifying the suspicion on the basis of the facts that the passage bears no connection to what precedes it, contains more unique vocabulary that one would expect from statistics, uses a different style, and, most importantly, isn't found in the earliest extant manuscripts. According to this logic, Christians never noticed that the passage implies that believers can drink poison with no ill effects—not until millennia later when someone was finally born clever enough to call upon us to demonstrate our faith by drinking Draino and so we slink away muttering “redaction.”

To this I pointed out that there are a few other likely redactions in scripture, including the potential proof text for the Trinity in 1 John 5:7-8 (in the KJV). Also, the beloved story of the women caught in adultery in John 8. These passages, which we could certainly use to our advantage, have been identified as suspect. Why? Well according to the logic I recently encountered on the atheist site, the only possible reason that I can see is that we are Machiavellian enough to sacrifice some “good” passages so that we have credibility when we boot unfortunate text, such as the Marcan Appendix.

Not to mention:

And Philip said, "If you believe with all your heart, you may." And he answered and said, "I believe that Jesus Christ is the Son of God." (Acts 8:37, NASB)

This passage is left out of some translations, because, again, it is absent from the earliest manuscripts. I commented, sarcastically, that

So you can see why we are embarrassed and arbitrarily leave it out, and without merit attribute its absence to some unnamed scholars,--it is so damaging to Christian theology and it leaves us at the mercy of our critics. We just had to dump it, before [people] used it against us.

The argument shifted to a general consensus that it was absurd to claim that scripture was inerrant, and simultaneously claim that bibles contain errors. I suppose I can see from the viewpoint of an atheist it appears that we want to have our cake and eat it too. But the truth is that there is trivially no contradiction here. The chain of events is manifestly logical:

1) The original manuscripts as penned by the apostles (or their secretary, as you will, e.g. Luke for Paul or Mark for Peter) are assumed to be inspired.

2) Others (such as Clement) wrote perfectly fine books that can be used for our advantage, but as they lacked apostolic authority they cannot lay claim to inspiration.

3) These books have been fallibly transcribed and fallibly translated.

4) Misguided scribes have had opportunity to make redactions.

5) Men, having to decide which of these books should be in the canon, could not agree on some of them. The Catholic Church argues that they were infallibly guided by the Holy Spirit. Protestants, who profess Sola Scriptura, have no basis other than hope/faith to assert that no mistakes were made.

Point 5 opens up a whole new can of worms, one which I’ve discussed here, and one which not only left the atheists feeling as if they were firing at a moving target, but one which not all Protestants have considered. That is:

The table of contents of your bible was not inspired.

You may believe, as a Protestant, that the 27 books of the New Testament are exactly the 27 books that belong there, but you have to admit that for at least that one little instance you are abandoning the reformers cry of Sola Scriptura and adopting the Catholic position of sacred tradition. You are arguing that the Holy Spirit guided the process of canon selection—which is not an outrageous thing to believe—but in doing so you are making exactly the same argument that the Catholic church makes for, say, her Marion doctrines.

Apart from adopting a form of sacred tradition, you must say what may be hard to say: It is possible that there is an error not just in certain passages, but in the canon itself. It is possible that, say, Jude does not belong in the canon. Jude being one of the books about which there was debate—the entire list of debated books being Hebrews, James, 2 Peter, 2 John, 3 John, Jude, and Revelation (they made it in) as well as 1 Clement, The Shepherd of Hermas, The Epistle of Barnabas, and the Didache (they didn’t make it).

Personally of these books the one that would break my heart, should it be found to have been included in error, is Hebrews—but we must admit that Hebrews was admitted in spite of the fact that it does not really meet the requirement that it is indisputably of apostolic origin, or endorsed by an apostle. (Revelation—is this awful to say?—I could do without—I can’t really use a book that is impenetrable to any advantage.)

Now if, to continue picking on Jude, Jude does not belong in the canon, does that mean Jude is somehow a bad book? Absolutely not—it would just mean Jude is a useful commentary rather than inspired scripture.

And how bad would it be if all the books in question were admitted or omitted in error? It would be of no substantive consequence. The gospel message is accurately contained, presented, and preserved in the books for which there was no debate, those books whose apostolic seal of approval is certain.

My friends on the atheist blog, who argue mostly against crude fundamentalist caricatures, do not like this at all—somewhat counter intuitively.

I think the reason is this: the Catholic dogmatic position (that the canon was, infallibly, delivered to the Church) is reasonable—that is to say it is self consistent. What they would like is for the Protestant position to be inconsistent.

I see this all the time. Most commonly I see it this way: the atheists think the YECs are dumb as door nails. But they also argue that YECs are, at one and only one instance, exegetical savants. The one instance is Genesis One. Here they say that the in-all-other-instances mocked and ridiculed YECs have the only possible correct interpretation of Genesis. (And the often unspoken but always understood next point is that since science so soundly disproves that interpretation, the whole bible is therefore nonsense.) That is, they use the YECs as, in their minds, useful idiots to make it easy to dismiss the bible.

Same thing here, but slightly more subtle. They hated my arguments that the canon might be wrong. Why? Because from Sola Scriptura alone it is the only logical conclusion—and the last thing they want us to be is logical. They would rather hear irrational arguments, because that would fit their stereotype of conservative Protestants.