Quantum Mechanics III: Wavefunctions

[Fixed typo in Schrodinger's equation below—AW]

Previously I talked about interference, the chief weird thing about QM that makes it different from Classical Mechanics.  You have to think about complex-valued "amplitudes", from which you derive (real-valued) probabilities.  From this you can also derive the notion of a Hilbert Space of states.  We discussed the space of states for the polarization of a photon (a 2 state system), and how there are many different choices of "basis", representing different ways of identifying a mutually exclusive set of two possibilities.

Now let's consider a more complicated system: a single particle moving around in empty space.  There are infinitely many states, because space is a continuum.  Hence we need to use an infinite dimensional Hilbert space.  This is harder to visualize than a two-dimensional one, but it will still be true that, in any given basis, each state can be regarded as a quantum superposition of a bunch of possibilities.

There are many possible choices of basis, but two of them are particularly nice.  You can choose to either express the system as superposition of position states, or as a superposition of momentum states, but you can't specify both at the same time, because they are two different bases of the Hilbert Space!  This is the origin of the Heisenberg Uncertainty Principle.

Of course, since the position and momentum are continuous variables, the probability of having any particular exact value of position or momentum is always 0.  So we have to generalize the framework slightly and talk about amplitude densities.  (However, there are other choices of basis where you don't have to do that).

An amplitude density is an amplitude per unit square-root-of-volume.  I know these units sound a bit strange, but that way when you square it, you get a probability per unit volume, which is as things should be for purposes of doing measurements.  The amplitude density is more commonly called the wavefunction of the particle.  So the wavefunction can be written as a function of position: \Psi(x,\,y,\,z), or as a function of momentum: \Psi(p_x,\,p_y,\,p_z), but not both at the same time.  However, if you know one of them, you can calculate the other one by a Fourier transform (should you be lucky enough to know what that is).

If you have multiple particles, you shouldn't think that each particle has a separate wavefunction.  Instead, you use a single wavefunction which depends on the positions (or momenta) of all of the particles.  For example, if there are two different particles which we'll call #1 and #2, then you'd write:

\Psi(\vec{r}_1, \vec{r}_2),

where I'm now using vector notation as a shorthand; but each vector still has x, y, and z components.  Hence the wavefunction for 2 particles actually is a function living in a 6 dimensional space!  (More generally, the wavefunction of N particles will live in 3N-dimensions, assuming that space is 3 dimensional.)

(Given these two particles, it might be that the wavefunction factorizes, so that

\Psi(\vec{r}_1, \vec{r}_2) = \Psi_1(\vec{r}_1)\Psi_2(\vec{r}_2).

That's what would happen if you independently prepare each particle in a state, and don't let them interact with each other.  But in general, there's lots of wavefunctions you could write down which do not factorize in this way.  This allows the particles to be correlated in strange ways not allowed by classical physics.  We call this phenomenon entanglement.)

Now the two particles might be either different type, or the same type.  One of the principles of particle physics is that apart from a limited number of attributes such as position/momentum, "spin", and a few other things, all particles of a given type are identical.  (E.g. all electrons have identical properties, and all photons also have identical properties.)

If the two particles are identical, then it shouldn't make any difference which particle we choose to label as "1" and which we choose to label as "2".  So there should be a symmetry of the wavefunction if we switch the two particles.  (Remember, in QM we have interference whenever two histories end up in the same place, so to get things right we have to obsess about exactly when two situations count as exactly the same, and when they don't.)  There are two different ways to implement this symmetry.  The obvious thing to do is to say that:

\Psi(\vec{r}_1, \vec{r}_2) = \Psi(\vec{r}_2, \vec{r}_1),

so that the amplitude is the same in both cases.  This sensible approach is taken by identical bosons, which includes particles such as photons, gluons, gravitons, mesons, He-4 nuclei, and so on.

Another, more perverse way to implement the symmetry is to insert a minus sign:

\Psi(\vec{r}_1, \vec{r}_2) = -\Psi(\vec{r}_2, \vec{r}_1).

This bizarre form of identicalness is used by fermions such as electrons, quarks, neutrinos, protons, neutrons, and He-3 nuclei.  (In general, something made out of an odd number of fermions is also a fermion, since if you switch two copies, you'll get an odd number of minus signs.)

So photons are strictly identical, while electrons are almost identical, but you get a minus sign if you switch them.  But remember, the overall phase of a QM system doesn't matter.  So you won't actually notice anything weird if you definitely switch two fermions.  The minus sign only matters in situations where they might-or-might-not have gotten switched, because then the interference between the two histories will be different.

A somewhat more straightforward implication is that no two identical fermions are ever in exactly the same position, because then the weird antisymmetry tells us that \Psi(x_1, x_1) = - \Psi(x_1, x_1) = 0.  This is a special case of the Pauli Exclusion Principle, which is the reason for the Periodic Table.  Since electrons can be either "spin up" or "spin down", you can only put 2 distinct electrons in each energy level of an atom.  Then the energy levels get full, and you have to put the electrons into higher energy shells.

Bosons, on the other hand, are gregarious and love to be in the same place.  Or rather, to speak less anthropomorphically, their probability to be in the same place is greater than you would expect from classical probability theory.  This is what makes lasers (a bunch of photons all in the same state) practically possible.

I've mentioned "spin" several times, but I haven't actually said what it is.  In QM, some particles also have an intrinsic angular momentum or polarization, which gives them a certain sort of directionality in space (even though they are point particles).  Unlike a lot of the cute terms used in particle physics such as "color" or "charm", the term "spin" really does refer to actual literal angular momentum.  But it works in a weird way.  The angular momentum along any axis is quantized, meaning it has to be either an integer or an integer + 1/2 (times the Planck constant \hbar).  The maximum possible angular momentum along any axis is called the "spin" of the particle.

In Nature, there is a rule called spin-statistics which says that particles with integer spin are always bosons, and particles with half-integer spin are always fermions.  (You can prove this rule mathematically in QFT, but it requires Special Relativity and some additional physical assumptions.)

Every known fundamental fermion is spin 1/2, which means that along any given axis it is either spinning clockwise (a.k.a. "up" or +1/2) or counterclockwise (a.k.a. "down" or -1/2).  You only get to specify the spin along one axis, say the vertical one.  This is not to say that an electron can't spin "left", "right", "in", or "out", but these states are quantum superpositions of the "up" and "down" states.  By rotational symmetry, we could pick a different basis (e.g. right / left) and instead think of up and down as superpositions of right and left.  The (2 complex dimensions = 4 real dimensions) space of possible electron spins is called a spinor.

A spinor needs to be rotated by 720º (2 full circles) to get back to its original state.  Yes, you read that right.  If you only rotate it by 360º (1 full circle) then it comes back to itself with an extra minus sign in the amplitude.  Just like when you switch two electrons.  They're just perverse that way.

Most of the fundamental bosons are spin 1, so their polarization is given by a vector, as in the case of the photon which we discussed last time.  Vectors get a minus sign when you rotate them by 180º, and return back to the way they were after 360º, just like you were taught in school.

However, the Higgs boson (which gives mass to most of the other fundamental particles) is a spin-0 or scalar field.  That means it doesn't change at all when you rotate it. On the other hand, the graviton is a spin-2 particle, which means it gets a minus sign when you rotate it 90º, and goes to itself under 180º.  Its polarization is described by a matrix, but let's not get into that here.

The bottom line is that for anything more complicated than a scalar field, in addition to the position or momentum variables you also need to include the spin degrees of freedom.  So if we have one electron and one photon, the wavefunction will look like e.g.

\Psi(\vec{p}_e, s_e,\vec{p}_\gamma, s_\gamma),

where s represents the spin of the electron or photon along e.g. the z-axis.  This is still a 6 dimensional space since s_e can only take the values (+1/2, -1/2), and s_\gamma can only take the values (+1,0,-1).  (Incidentally, since the photon is massless, its spin is always required to be perpendicular to its momentum, so there are really only 2 polarization states, not 3.  But the explanation of this involves relativity and gauge symmetry and a bunch of other things from QFT...)

There is also a third kind of basis, distinct in general from both the position and the momentum basis, in which time evolution is particularly simple.  This is the basis where the energy of the system takes on a definite value.  In this basis, the only thing that changes is the phase of each energy state.  The phase changes with time at a speed proportional to the energy.

So one way to specify the dynamics of a QM system is simply to say what the formula for the energy H is, as a function of all the positions and momenta of all the particles in the problem.  (You think of this an operator, a gadget which acts on the wavefunction to get another wavefunction.  So if you are in the position basis, the "momentum operator" is given by \vec{p} \Psi = (i / \hbar) \vec{\nabla} \Psi, which is equivalent to switching from the position to the momentum basis, multiplying by p, and then switching back.)  Then you can figure out how the wavefunction changes with time by using the Schrodinger equation:

\frac{d\Psi}{dt} = -\frac{i}{\hbar} H \Psi.

Thus, if you know what the formula for the energy is, you can predict the dynamics of the wavefunction as time passes.  This is related to the Hamiltonian approach in Classical Mechanics.  As you take the \hbar \to 0 limit, you recover classical mechanics.

There is also a "path integral" picture due to Feynman, related to the Lagrangian or "Least Action" approach to physics mentioned at the same link, where you assign to each history an amplitude proportional to e^{iS/\hbar}, where S is the action.  This approach is actually more closely related to the picture I started with in part I!

In this sense, Quantum Mechanics is a fulfillment of Classical Mechanics, just as (in Christian doctrine) the New Covenant fulfills the Old Covenant.  That is, the new model justifies the quirky, previously-inexplicable features of the old model, in terms of a more basic (yet also more mysterious) set of ideas.  Concepts such as action, energy, momentum, the associated conservation laws, and so on, all follow naturally from the interference of wavefunctions over space and time.

Incidentally, there's a very important flaw in what I've told you so far.  Generally speaking, in modern physics it's better to think of the universe as being made of fields, not particles!  This is the subject of Quantum Field Theory.  The idea is that we should really think of the universe as being made of some finite number of types of fields (e.g. the electron field, the photon/EM field, the quark field, etc.).  Consider a scalar field \Phi(t,x,y,z), which is basically a function of the spacetime points.  If we want to keep track of the amplitude for any possible configuration of the field, then we really need our wavefunction to be a function of all possible configurations of \Phi at one moment of time.  Morally speaking (i.e. I am about to make certain dreadful oversimplifications) this means that the state of the universe at one time is something more like:


in other words the wavefunction is a function of functions!  The "particles" are then quantized excitations associated with different modes of this field.  (The relationship between QFT and the QM of multiple particles should not be obvious from what I've said so far...)

QFT gets kind of complicated, but the advantages are that 1) it is easier to make it compatible with Special Relativity, and 2) it allows one to consider situations where particles are created and destroyed, e.g. an electron can emit or absorb a photon.  Since this happens all the time in the real world, that's kind of important!

But as long as you're dealing with situations where the particles are all going much slower than the speed of light, and none of them decay into other particles, you can use QM as described above.  (Perhaps I shouldn't have given the photon as an example, because it always travels at the speed of light and is never nonrelativistic.)

Posted in Physics | 37 Comments

Why the Senate should confirm Garland

I didn't want to say anything in my tribute to Justice Scalia about the politics of filling the vacancy he left behind.  However, for what it is worth, I believe that the Senate should hold hearings and confirm Judge Merrick Garland to the Supreme Court.

Mind you, the Senate has NO constitutional obligation to consider any presidential nominee.  The Constitution says only that "The President shall nominate, and, by and with the advice and consent of the Senate, shall appoint..." judges.

The phrase "advise and consent" cannot possibly be regarded as mandatory, since that would imply that the Senate must consent, which is absurd since nobody questions their power to reject a candidate by voting them down.  Journalists and politicians who claim that the Constitution requires the Senate to "advise and consent" are abusing the meaning of these words.  The word "consent" cannot possibly mean "decide whether to consent".  And if the "consent" part is optional for the Senate, then the "advise" part must also optional for the Senate.  Nor can "advise" mean "hold hearings", since the Senate didn't regularly hold hearings on Supreme Court nominees until recently.  The phrase means only that IF the Senate provides its advice and consent, THEN the President may go ahead and appoint the nominee.

At best, the word "shall" imposes a duty on the President to nominate candidates.  However, the Supreme Court has rejected this interpretation, saying that filling vacancies is also optional for the President (Marbury vs. Madison)!

Nevertheless, just because there is no constitutional obligation to confirm the nominee, doesn't mean the Senate is justified in its obstruction.  There are other norms and conventions in politics besides constitutional norms.  Without them, the system could not function.

Until very recently there has been an expectation that the Senate will confirm any reasonable and moderate Supreme Court nominee proposed by the President.  Voting down, and even filibusters, have been discussed only in cases where (it has been claimed that) the candidate is unqualified, extreme or unacceptable in some other specific way.  And nobody has suggested that Garland is particularly extreme.  This is not to say he is a conservative, but he does seem to believe in some sort of policy of judicial restraint, which is as good as Republicans can expect from a Democratic president.

At the "object level" (as opposed to the "meta level" of the politics of filling vacancies) I would very much prefer for Scalia to be replaced by someone with a similar judicial philosophy.  However, the short term gain that comes from subverting the process for one nominee, will simply make it harder for Republicans to confirm nominees in the future.  No one gains from increasingly bitter "no holds barred" confirmation fights.  It's a game of interated Prisoner's dilemma, and both sides keep defecting!

Although pre-emptively announcing that one will not fill a vacancy is unprecedented obstruction in the modern era, one-up-manship in confirmation fights isn't at all unprecedented.  It is rather nauseating the way both parties routinely and hypocritically switch sides about whether obstructing nominees is good or evil, every time the Presidency changes sides.  (At least the current hijinks aren't blatantly illegal, the way the nuclear option was!)

In the long run, it's best to allow the President to fill any vacancies which arise during his term with reasonable candidates.  The alternative equilibrium, in which a party division between the Senate and Presidency leads to no appointment, will just make life harder for everyone in the long run.  The Republicans can't seriously believe that the Democrats won't retaliate once they retake control of the Senate.

Also, this seems like very bad timing for Senate Republicans to take this particular stand, seeing as the two people most likely to be President next care even less about the Constitution than the current one.  St. Hillary Clinton seems to believe that Congressional acts can and should change the meaning of the Constitution.  And I don't think Donald Trump (who would discriminate against Muslims, and already has abused the power of eminent domain) has any more genuine concern for the Constitution than he does for the teaching of Jesus!  (Maybe Republican pressure would keep him on the straight and narrow when it comes to appointments, but then again maybe not.)  Most likely it will be Clinton, in which case the Republicans will have eroded faith in the process without actually getting anything to show for it.

(Unless their previous posturing has caused St. Obama to nominate somebody more moderate than he otherwise would have, which actually seems fairly likely now that I think of it.  But this is only relevant if the Senate actually confirms Garland!)

Waiting to confirm based on who the next President is, also seems like a unwholesome habit for the Senate to acquire.  An 8 member court is not the end of the world, but 4-4 tie votes are a bit annoying.  Also, since the next Supreme Court term begins in October, delaying the confirmation until after the elections in November is awkward, since then Garland (if confirmed) would have to rehear any important cases.

So I think that the Senate should confirm Garland, who seems to be an all around decent person unlikely to try to shift court precedent extraordinarily far to the left.  At least, no more than one would expect from Scalia being replaced by a moderate.  (In fact I am a little concerned he believes in judicial restraint so much that he won't protect civil liberties quite as much as the current liberals do.)  But it is hard to determine his true opinions based on his current record as an appellate judge, bound to follow Supreme Court precedent.  In the even that he is appointed, we shall just have to see.

Posted in Politics | 34 Comments

My Whiteboard

I've been SUPER busy this month what with:

i) faculty job interviews at a couple places,
ii) a bad cold, thankfully now over,
iii) a minicourse I'm currently teaching at the University of Maryland.

In the absence of a more substantive post, you can console yourself by pondering the following snapshot of my whiteboard.

Note: the cartoon has nothing to do with the equation above (or the sentence partially displayed below).  But feel free to try to figure out what the equation means, if you can!

Posted in Blog | 9 Comments

German translations

I am honored that St. Patrick Zimmerman has chosen to translate some of my blog posts into the German language.  His translation website, now included in my sidebar, includes the following posts so far:

Bei der Liebe Gottes!

Ist die Sühnung ethisch nachvollziehbar?

Wenn Gott die Unschuldigen tötet

Fragen zu Adam

Die Einheit der Kirche suchen

This is now the second language into which my blog posts have been translated; the first being Portuguese.  As Patrick finishes more translations, I will update the list on this post (without making any other announcement).  I'm grateful for his efforts.

Posted in Blog | 6 Comments

St. Antonin Scalia

As Charles de Gaulle is reputed to have remarked when his aides told him he could not resign as president of France because he was the indispensable man:
"Mon ami, the cemeteries are full of indispensable men."
Justice St. Antonin Scalia, "God's Justice and Ours".

I was deeply saddened this weekend to hear of the death of Justice Scalia, the most engaging, provocative, and brilliant of all of the justices on the Supreme Court.  As someone who reads Supreme Court decisions for fun, I will definitely miss his wit and humor and crankiness, and the way he made the job fun.  However, I also feel quite strongly that his loss is a significant blow to the Court and to my country.

There are countries in which the fundamental principle is rule by some human being or set of human beings.  The United States is not such a country; we are a constitutional republic.  In our country the fundamental legal principle is a document, the Constitution, which outlines the divisions of power between different branches of government, limits the powers of government, and provides for certain fundamental rights which cannot be abridged.

Of course no document interprets itself, and therefore there is a need for human beings to read the Constitution and decide what it means.  Sometimes the meaning is clear; other times there is an ambiguity which must be settled somehow or another.

It would be lovely if Congress and the Executive Branch could be trusted to police the boundaries of their own limited powers.  In principle, there is no inherent logical reason why this could not work.  In practice, politicians are too venal to be trusted with this; the general tendency is for people to interpret things in their own favor, expanding their role in the system until there are no restrictions at all.  There were only 9 years between the time that Congress proposed the First Amendment (1789) and the time when Congress passed the manifestly unconstitutional Alien and Sedition Acts (1798).  Hence the importance of judicial review from an outside body designed to be as neutral as possible.  In our system, that role is played by the Supreme Court.

When settling a dispute between two parties requires resolving an ambiguity in a statute or the Constitution, the Court is supposed to resolve the ambiguity with the most reasonable interpretation that is consistent with previous judicial precedents.  These decisions are binding on lower courts.  (On rare occasions the Supreme Court may reverse their previous decisions, if they are clearly wrong or prove to be unworkable.)  In cases where a statute is inconsistent with the Constitution, the Court has not only the power but also the obligation to strike down or modify the statute to make it conform to the higher law.

There is obviously a danger here, that the judges might substitute their own political will instead of trying to find the most reasonable interpretation.  This is a form of corruption, because they are there as judges, not politicians.  If we had wanted a tribunal with the power to strike down Congressional acts for political reasons (and sometimes to invent new pseudo-legislation), it is unclear why a democracy would want nine unelected Ivy League lawyers with lifetime tenure get to decide for the whole country, based on the arguments of two other lawyers hired by the two parties who lobby for their preferred position—our own American version of the "House of Lords"!  The only possible legitimacy the Court has, comes from the idea that generally speaking (aside from the inevitable but regrettable exceptions), the Court is engaged in acts of interpretation, not naked partisan will.

I am prepared to be quite generous here.  I do not require that all constitutional rules be explicitly spelled out, so long as there is some fair and reasonable argument that they are implied by structure or context.  But there are limits to this.  Many judicial decisions exist which can hardly be called textual interpretation by the most generous stretch of the imagination.

The danger of misinterpretation becomes greater when one remembers that our legal system is based on precedent.  A single wrong precedent can become a launching pad for even greater departures, and when you stack them together the final result can be the complete and total erosion of some provision or right spelled out in the Constitution, or  the generation of some completely new provision or right almost out of whole cloth.  Like a rough stone becoming smooth after lying under a riverbed, it is easy for a system of laws to lose its distinctive features over a couple centuries.

For the past few decades the most dominant school of legal interpretation in the legal academy has been that this is not a bug but a feature.  (I have even found this view endorsed by textbooks written for Middle School students.)  The idea is that there is a "living constitution" which grows and adapts to the needs and ideals of each new generation.

To which I would reply: one may as well not have a Constitution at all, as to have one which is flexible enough to adapt itself to each new generation at the mere whim of judges.  If the duly elected representatives of the people pass a piece of legislation, then clearly the mores of the current generation are consistent with that law existing.  If, nonetheless, a bunch of unelected politicians decide to strike it down because it is incompatible with the current social mores of legal scholars, well that is merely a minority of the people exercising will-to-power over the majority.  Unless, of course, the legal scholars were actually using their legal expertise to interpret the text of the Constitution, which is of course the reason why we select them for the role in the first place.  I don't care whether you call it Originalism or Textualism or something else.  There are multiple reasonable ideas about how to do interpretation but Living Constitutionalism is not one of them.

In fact, it is only what these scholars might call a "dead constitution" which could actually exert a meaningful influence on the body politic.  It is the Constitution with definite meaning that should be called "alive", while the one whose flavor conforms to its surroundings like tofu is "dead".  As St. Chesterton said in another context:

A dead thing can go with the stream, but only a living thing can go against it.  A dead dog can be lifted on the leaping water with all the swiftness of a leaping hound; but only a live dog can swim backwards.

The rule of law is, simply speaking, the idea that there are certain written ideals which the government is permanently responsible to.  The idea of a "living constitution" is pernicious because it subverts our ability to have such permanent ideals.  A living constitution is an erasable Constitution.  If you value your rights to criticize the government or to have a fair trial, then this can continue to exist only if the government believes in the ideal of upholding the Constitution even when it is inconvenient .

You may ask, why should a few people who lived in 1787 or 1866 (when the 14th Amendment radically changed the balance of power between the federal government and the states) have more power than the rest of us to decide what should be the fundamental rules of society?  Haven't we developed morally since then?  The people in 1787 even allowed slavery!  (Although admittedly this has since been fixed.)  Well I should hope we have improved, but this objection is not to the point.  The Constitution is not perfect, but it is the one we have.  Therefore, until the next political revolution, it defines what is legal and illegal.  Furthermore it contains a number of very important principles about due process and so on, which I would rather not have forgotten.

And if there is a powerfully strong consensus that the Constitution should be changed, it contains procedures allowing the people to do so.  But it needs to be a stable bipartisan consensus, not the blowing of fickle political winds.

Nothing prevents Congress and the Presidency from acting based on the most up-to-date and progressive understanding of morality.  These are progressive, forward-looking institutions.  But the Supreme Court is backwards-looking: to make sure we are obeying the ground rules for American politics as traditionally defined by text and precedent.  Brown v. Board revolutionized American society, not by inventing a new racial ideal, but by holding the people to the ideal of racial equality which had already been incorporated into the Constitution a hundred years before.

Lawlessness has a general tendency to breed more lawlessness.  A given activist court may vote to increase your rights in some particular area, but if those rights are not based on sound legal construction, then at the same time it erodes the rule of law, which is a necessary to protect the existence of legal rights in the first place.  It's a shortsighted trade.  As St. Thomas More says in the brilliant play "A Man for All Seasons":

William Roper: So, now you give the Devil the benefit of law!

Sir Thomas More: Yes! What would you do? Cut a great road through the law to get after the Devil?

William Roper: Yes, I'd cut down every law in England to do that!

Sir Thomas More: Oh? And when the last law was down, and the Devil turned 'round on you, where would you hide, Roper, the laws all being flat? This country is planted thick with laws, from coast to coast, Man's laws, not God's! And if you cut them down, and you're just the man to do it, do you really think you could stand upright in the winds that would blow then? Yes, I'd give the Devil benefit of law, for my own safety's sake!

Let me give some specific examples of legal BS.  There are many historical examples such as Dred ScotPlessy, Cruikshank, Korematsu and Lochner, which have since been repudiated.

The most infamous currently valid precedent is of course Roe v. Wade, which reads more like a rambling college essay than anything resembling legal analysis.  Leaving aside your moral views on abortion (mine is that it is deeply evil, but that has nothing whatsoever to do with my current point), no reasonable person reading the actual text of the Constitution would ever guess that this is a protected constitutional right, implicit in "nor shall any State deprive any person of life, liberty, or property, without due process of law".  Even many liberal scholars agree that Roe is indefensible from a legal standpoint.  Wikipedia's article on Roe has a nice collection of quotes:

In a highly cited 1973 article in the Yale Law Journal,[81] Professor John Hart Ely criticized Roe as a decision that "is not constitutional law and gives almost no sense of an obligation to try to be."[82] Ely added: "What is frightening about Roe is that this super-protected right is not inferable from the language of the Constitution, the framers’ thinking respecting the specific problem in issue, any general value derivable from the provisions they included, or the nation’s governmental structure." Professor Laurence Tribe had similar thoughts: "One of the most curious things about Roe is that, behind its own verbal smokescreen, the substantive judgment on which it rests is nowhere to be found."[83] Liberal law professors Alan Dershowitz,[84]Cass Sunstein,[85] and Kermit Roosevelt[86] have also expressed disappointment with Roe.

Jeffrey Rosen[87] and Michael Kinsley[88] echo Ginsburg, arguing that a legislative movement would have been the correct way to build a more durable consensus in support of abortion rights. William Saletan wrote, "Blackmun’s [Supreme Court] papers vindicate every indictment of Roe: invention, overreach, arbitrariness, textual indifference."[89] Benjamin Wittes has written that Roe "disenfranchised millions of conservatives on an issue about which they care deeply."[90] And Edward Lazarus, a former Blackmun clerk who "loved Roe’s author like a grandfather," wrote: "As a matter of constitutional interpretation and judicial method, Roe borders on the indefensible.... Justice Blackmun’s opinion provides essentially no reasoning in support of its holding. And in the almost 30 years since Roe’s announcement, no one has produced a convincing defense of Roe on its own terms."[91]

If you support legal abortion as a policy matter, imagine how you would feel if the Supreme Court had decided that the state allowing abortions was a violation of the 14th Amendment right to "life" and "equal protection of the laws".  This is not about who is right as a policy matter, this is about not resorting to BS interpretations to short-circuit the political process.

Or consider the Congressional power to "regulate commerce....among the several states" has now become so broad that it includes the power to regulate literally almost anything.  One time, Congress passed a law that forbade anyone to bring a gun within 1,000 feet of a school.  The point has nothing to do with whether you like guns or hate them, the question is whether this was within the powers of Congress (as opposed to the relevant State Legislature).  Their justification was that guns cause violence, violence causes students to feel scared and disrupts education, which leads to a worse-trained workforce, negatively impacting interstate commerce.  Clearly, if that counts as interstate commerce, then everything counts as interstate commerce, and there are actually no limits on Congress' legislative powers, aside from the handful of explicit prohibitions in the Bill of Rights and other places.  The other sections of the Constitution need not have been written.

In United States v. Lopez, the majority (including Justice Scalia) ruled that this was a bridge too far.  This was the first time since FDR stacked the Court that they had ever struck down a law for this reason.  Yet it was only a 5-4 decision.  4 Justices were willing to buy the absurd argument, in order to obtain their preferred policy result.  The decision was considered a legal revolution for drawing any lines at all, even though in practice it led to very few consequences or future decisions placing limits on what Congress can do.  Congress simply re-passed the law to apply to any firearm "that has moved in or that otherwise affects interstate or foreign commerce", and the courts looked the other way.

It is very strange that the Framers would have enumerated 18 different powers of Congress in Article I section 8, if one of them turns out to give them the power to do anything at all.  The original idea proposed by the Federalists, was that these 18 powers would be so limited that there would be no need for a Bill of Rights.  The rights would simply be everything not covered by one of the limited powers.  (Of course, this would still leave you in the soup if a State tried to violate one of your rights, but I guess the idea was that the States would have constitutions of their own.)  We can see how that idea worked out.  So I'm glad the Anti-Federalists gave us the Bill of Rights.  (Nowadays the 14th Amendment has been interpreted—correctly in my opinion, although to be honest I wouldn't want it overrule this now even if it had been bullshit—to mean that the States to also obey most of the provisions the Bill of Rights.)

For some more recent examples, consider Kelo v. City of New London, which ruled by a 5-4 decision that the government to use its power of eminent domain, which is supposed to be for "public use" only, to repossess "economically blighted" property in order to turn it over to private developers.  In other words, the government is allowed to give property from one private owner to another, but only when it steals from the poor and gives to the rich.   Amazingly the five more "liberal" justices were in favor of this approach, while the conservatives (including of course Justice Scalia) were against it.

Or United States v. Comstock, which ruled that the "necessary and proper" clause allows the federal government to keep people in prison indefinitely, after they have completed their prison sentence.  Under a federal law which incidentally applies retroactively to people who were jailed beforehand.  There are few laws which are more obviously unconstitutional than this—it is a more interesting game to try to count the number of different constitutional norms which it violates—and yet it was a 7-2 decision, with only Sts. Scalia and Thomas dissenting!  Oh, I forgot to mention that the law in question only applies to child molesters.  So far.  Remember that line about knocking down all the laws in order to get the Devil?

(To be fair, the justices were considering only whether this law was within the Article I powers of Congress, completely separating out the question of whether it violated the Bill of Rights, trial by jury, or the ex post facto clause.  But in this case, separating the two analyses is completely absurd.  How can an extension of Congressional power possibly be considered "proper" if every imaginable application of that power would violate other provisions of the Constitution?)

I admit I have aesthetic objections to this kind of bullshit as well as moral objections.  I remember being in the 5th grade, reading through the Constitution after finishing the in-class assignments.  I would like to believe that the words I read then have some relevance to what actually happens.  There is a limit to my populism: if some word had a different meaning in 1787 than it does today, or if I was unaware of its traditional legal context, then I don't insist that the courts defer to any accidental misconceptions I may have had.  But I would like to think that a citizen who reads the Constitution even today, would have a pretty decent idea of what it means, and would only need to consult a lawyer for the hard cases.

I really don't want to paint too bleak of a picture here.  I am deliberately focussing on the bad examples here.  There are many examples of Supreme Court decisions which were correctly decided, and there are many constitutional rights (including the all-important First Amendment) which are alive and well.  Taken as a whole, the country is far better off with judicial review, than it would have been without it.  That is exactly my point—the rule of law is a good thing, more important than the outcome of the individual cases, and we need to protect it.

Believe it or not, it is actually possible to be too cynical about politics.  In fact, excessive cynicism is actually the cause of our current political dysfunction; if everyone assumes the worst about a class of individuals, then they have no incentive to be better than that.  (Even Members of Congress have to have mostly started out with some real ideals buried under all their dissembling and compromises, or they wouldn't have entered politics in the first place.  I can't believe they did it for the pay or the job security!)

Lots of people would say that all judicial decisions are just politics, and any pretense of jurists to be principled and neutral are just hypocrisy.  But this is patently untrue.  Even if all of life were just "shades of grey", you can still usually tell which greys are whiter and which are blacker, when you hold them up right next to each other in the same light.  And right now—historically it has sometimes been the other way around—it is the "conservatives" on the Court who are clearly much more principled in their reading of the texts, and the "liberals" who are just trying to get their preferred policy outcomes.

(Here I am speaking only about the judicial philosophies labeled "conservative" and "liberal", and not about the merits of the Republican and Democratic political platforms in general.  It would be perfectly possible for someone with Democratic policy beliefs to be a judicial "conservative", it just tends not to happen in the current political environment.)

There are many examples where conservative judges say things like "I would prefer a different result if I were a legislator, but I think this is the law".  Liberal justices are much less likely to say things like that, and much more likely to appeal to vague or nebulous standards in order to get outcomes they obviously prefer personally.  In other words they are cheating.

I say this as somebody who has read most of the Supreme Court decisions written in the last decade, and several of the more notable ones before that.  Nor am I a knee-jerk conservative; when the court splits 5-4 I agree with the liberals about a quarter of the time.  For example, I strongly support habeas corpus rights even for suspected terrorists.  There are some constitutional principles I like, which might get less protection if the Court got more Republican appointees.

I do not doubt that there have been several times when conservative judges have, hypocritically, ruled in accordance with their conservative political principles (which they have no right to do) instead of in accordance with their claimed principle of interpreting the text fairly.  But it is better to sometimes fall short of a claimed standard of goodness, than not to have any standard at all.  "Living constitutionalism" is just a name for anything goes, it is not actually a coherent standard that one can fall short of.

I am not one of those partisan hacks who believes that somehow one of the two parties has an monopoly on dirty tricks and shoddy reasoning.  But I do believe that it makes a difference what our stated ideals are, and that a nebulous gas of constititual flexibility cannot act as a solid foundation for freedom, but principled reasoning from a black-and-white text can.

Now in the last 30 years, nobody has done a better job of promoting the rule of law than Justice Scalia, who has continually fought against all manner of sophistry, and given it the mocking it so richly deserves.  More than anything else his opinions, often his dissents, have made Originalism a viable interpretation in the academy.  He was not a "rebel without cause"; his cynicism was that of a wounded idealist, who stood for something quite definite.  His goal was not to revert decades of precedent back to some imaginary time when the Constitution was followed perfectly (although there are a few specific howlers he would have liked to kill).  Instead his goal was to contain the unprincipled exceptions, and to leave the law clearer than he found it.

Scalia was also a tremendously insightful person.  Hard as it is to imagine, given the current political environment, he was confirmed 98-0 by the Senate back in 1986.  Even jurists with radically different takes on the law recognized that he had some valid and interesting points to make about the law.  For example, his warnings on the dangers of relying too much on legislative history to decide what laws mean (if you do that, Congress will notice, and people will try to influence future legal decisions by means of their speeches before the house, subverting majority rule.)

True, his acid tongue made him some enemies.  In light of his professed Roman Catholic faith, some might wonder whether his bitter (and sometimes unfair) sarcasm was really compatible with a meek Christian spirit.  On the other hand, if we define Christianity by the behavior of Jesus in the Gospels, one could argue that it is actually very Christlike to react with hyperbolic outrage when you see people trying to legalistically distort the rules, in a way that subverts their actual meaning!

Yet Justice Scalia would be the first to admit that there is a distinction between the Kingdom of God and the kingdoms of this world.  In comparison with his faith, his life's work to to help improve the American system of law was of minor importance.  It would be wrong to reduce him as a person to his role as a judge.  His famous friendship with Justice Ginsburg (see elephant below) shows him to have been broad enough to like those who disagreed with his judicial philosophy.

Goodbye, St. Antonin Scalia, and God rest your soul.  I will miss you.

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