apk xtreme

Three weeks ago, the ACME collaboration (Jacob Baron et al.) improved (i.e. reduced) the previous, 2012 best limit on the electron's electric dipole moment by a factor of \(12\) (and by 3 orders of magnitude relatively to TRF 2011) in the article

Order of Magnitude Smaller Limit on the Electric Dipole Moment of the Electron

The experiment looks like this (click to zoom in):



OK, some exotic thorium monoxide molecules (which have the strongest known "internal" electric fields) with optical pumping via lasers in electric and magnetic fields are changing and the (produced) photons are (or could be, if they were produced) measured. Readers interested in the clever experimental setup will have to find a better source. Physics World, The Register, HuffPo, SciAm, and other semipopular media that covered it didn't discuss the method too much, either.

First, let us ask: What is the dipole moment that is being measured and how large is it?




Generally, at the high school level, an electric dipole is a pair consisting of a negative charge \(-Q\) at \(\vec r = 0\) and a positive charge \(+Q\) at \(\vec r=\vec r\), if you forgive me a tautology (the meaning of the two \(\vec r\) symbols is different). In that case, the magnitude of the electric dipole is\[

\vec p = Q\cdot \vec r.

\] Its magnitude is \(Q|\vec r|\); its direction agrees with the separation of the two charges (from minus to plus). For more general charge distributions, the dipole is\[

\vec p = \int \rho(\vec r) \vec r \,\dd^3 r.

\] You may notice that this depends on the choice of the origin of coordinates (it changes when we shift the coordinates by a constant) unless the total charge \(\int \rho \,d^3 r=0\). If the total charge is nonzero, the electric dipole moment defined above may be changed to "anything" (any vector) after an appropriate shift of the coordinates.




That's bizarre because the total electric charge of the electron is nonzero. So what can we possibly mean by "the" electric dipole moment of the electron? The answer is that we use the definition above and require that the origin of the coordinates agrees with the center of mass of the electron. In effect, the "center of the charge distribution" is shifted relatively to the "center of mass" of the electron. And this distance (vector) multiplied by the electron charge is the electric dipole moment of the electron.

It is linked to the spin and small

But the dipole moment is a vector; what is the direction of the vector? Is it some preferred direction in the Universe? Does the vector point to Mecca? Well, no. Mecca doesn't define any preferred direction and a billion of people who believe otherwise can't change this fact. There is no preferred direction in the Universe.

The direction of the dipole moment \(\vec p\) has to be correlated with a preexisting direction in our situation. The situation only contains the electron and the only vector-like, directionful information that the electron has is its spin. So \[

\vec p_e = C\cdot \vec S.

\] In particle physics, we like to derive all the equations of motion and dynamics from the Hamiltonian (a fancy name for the total energy) or the Lagrangian. What is the energy of an electric dipole? Well, you just sum the electrostatic potential energy \(Q\phi\) from the charges contained in the dipole (imagine the simple dipole composed of \(-Q\) and \(+Q\)) to see that\[

U = - \vec d_e\cdot \vec E = - d_e \vec S_e \cdot \vec E.

\] The electric dipole moment may be defined as "whatever multiplies \(\vec E\) by the inner product" to get an interaction term in the total energy. The expression (including the minus sign) is analogous to the magnetic dipole moment \(\vec m\) that adds \(-\vec m\cdot \vec B\) to the energy.

So far, we were thinking of the world as if it were non-relativistic and classical. If we switch to quantum field theory which is relativistic and quantum mechanical, the expression for the potential energy above is replaced by an interaction term in the Hamiltonian or, in our case, the Lagrangian\[

\LL_{\rm EDM} = -i d_e \cdot \bar\psi_e \sigma^{\mu\nu}\gamma_5 \psi_e \cdot \partial_\mu A_\nu

\] You see that it is similar to the usual interaction term \(\bar\psi\psi\cdot A\) which would have a dimensionless constant \(e\). However, in the dipole case, there is an extra derivative \(\partial_\mu\) in front of the gauge potential which makes the interaction "non-renormalizable" and the coefficient \(d_e\) has the units of length (like the electric dipole: the electric charge is treated as a dimensionless quantity).

If you substitute the non-relativistic (low-speed) form of the spinor \(\psi_e\) and the gauge field and calculate the expectation value of the operator above in a one-electron state of quantum field theory, the Lagrangian reduces to the expression for the potential energy \(U\) above.

Great. So is this electric dipole nonzero? And if it is, how large is it?

The first thing you should notice is that the spin \(\vec S\) is an axial vector while the electric dipole moment is an ordinary, polar vector. So if one is proportional to the other, the theory will fail or refuse (depending on your ethical preferences) to be symmetric under P, the parity. Imagine that the electron is spinning like a wheel of your bike while you are riding; imagine that the electron is the wheel. By the right hand rule, the spin (angular momentum) vector goes to the left side from the wheel's axis. But it's really just a (right hand) convention: Why should the charge of the electron be concentrated on the left side away from the bike? The left side and the right side were equally good to start with. This "unintuitive" asymmetry arises when the parity P is violated.

A bigger problem or audacity is that it violates CP (and therefore the time reversal T) as well (these microscopic violations of T have nothing whatsoever to do with the "cause" of the thermodynamic or logical arrow of time!).

So the underlying theory has to violate P and CP for the coefficient \(d_e\) to be nonzero. In a CP-invariant theory, we would derive \(d_e=0\). Fortunately, the Standard Model is violating CP, a little bit, because of the complex phase in the CKM matrix, the unitary matrix transforming the upper quark mass eigenstates to the upper \(SU(2)\) partners of the lower quark mass eigenstates.

However, this CP-violation only materializes if the quarks of all three generations "show up" in some way. How can it affect the electron? Well, it affects the electron because the quarks of all three generations may emerge as "virtual particles". When you draw the "simplest" Feynman diagram which is not too simple, you will find out that the Standard Model implies that the electron has an electric dipole moment comparable to\[

d_e \approx 10^{-40} e\cdot {\rm m}

\] or slightly smaller. If you divide it by the charge \(e\), you will see that the separation between the electron's "center of mass" and electron's "center of charge" is nonzero but extremely tiny: \(10^{-40}\) meters. That's approximately \(10^{30}\) times shorter than the atomic radius and... \(100,000\) times shorter than the Planck length. (In spite of the misconceptions held by defenders of loop quantum gravity and similar childish "paradigms" about the quantum spacetime constructed out of a Planckian LEGO, there is absolutely nothing wrong if similar quantities with the units of length are shorter than the Planck length. This coefficient is just a universal constant that may have any value and that may manifest itself in experiments with any precision.)

Clearly, you probably can't measure it in your kitchen. Even the world's best experimenters are very far from being able to measure the electric dipole moments that are this tiny.

The new 2013 upper bound on the electric dipole moment assures us that\[

|d_e|\leq 0.87\times 10^{-32}e \cdot {\rm m}.

\] It's a small number but it's \(10^{8}\) i.e. 100 million times greater than the Standard Model value. Once again, the experimenters are telling us that the dipole moment is smaller than 100 million times the Standard Model value. That's not shocking at all for those who believe that the Standard Model is the "whole" story: one is indeed smaller than 100 million so what's the big deal?

There is a lot of room in the middle. The dipole moment may be smaller than 100 million times the Standard Model prediction but it may still be larger than the Standard Model prediction. For example, it may be 10,000 times larger than the Standard Model prediction (due to new physics) which is still 10,000 times smaller than the experimental upper bound (the maximum value allowed by the restrictions-loving experimenters).

Garden variety new physics

However, the experimental bounds are not quite useless because new physics "around the corner" could be able to produce much stronger sources of CP violation that is larger than 100 million times the Standard Model value! How large is the dipole moment according to a "garden variety" mode of new physics? Well, it may be estimated as\[

d_e\approx c\frac{m_e}{16\pi^2 M^2}

\] where the constant \(c\) is comparable to \(1\) if we adopt the type of "true garden variety" popular among many phenomenologists. However, there may be very good reasons why a model implies that \(c\ll 1\).

Why did we include all the factors? The factor \(1/16\pi^2\) (it is \(0.00633\) but many of us would still agree that it is a "number of order one"!) is a "one-loop factor" that always appears in one-loop diagrams and a Feynman diagram contributing to the dipole has to have at least one loop.

The expression is proportional to the electron mass \(m_e\) because almost any leading correction to the dipole moment depends on "both 2-component spinors" that are included in the electron's Dirac field and their leading interaction is proportional to \(m_e\).

Finally, \(1/M^2\) is a power of the "scale where new physics appears" and it must be there for dimensional reasons, to return the units of length (i.e. inverse mass if we use \(c=\hbar=1\) and we do) to the dipole moment. One may justify this \(1/M^2\) in various ways – optimally, from the general arguments of the "Renormalization Group"; or from direct integrals over momentum volumes scaling like powers of \(M\) and propagators going like \(1/M\) or \(1/M^2\) (fermions/bosons) in the loop diagrams, and so on.

At any rate, the estimate is OK for a large class of "garden variety" models of new physics. How large the dipole is? I have already mentioned that \(1/16\pi^2\approx 0.00633\) so including \(c\) slightly smaller than one, we get \(10^{-3}\). The new physics may (but doesn't have to) emerge at \(M\sim 100\GeV\) or \(M\sim 1\TeV\).

For the extreme \(100\GeV\) case – being excluded (or discovered) while you're reading these lines (well, when the LHC starts again) – the ratio \(m_e/M\) is of order \(1/100,000\); recall that the electron mass is half an \(\MeV\). When multiplied by \(10^{-3}\) encountered earlier, we get \(10^{-8}\). And in the units of meters, \(100\GeV\) is inverse to \(10^{-18}\) meters or so; that's the distance scale that the current colliders are already safely probing. So when this distance is multiplied by \(10^{-8}\), we get about \(10^{-26}\) meters.

That's about the maximum value you may get from "maximally CP-violating" physics that is only "starting" to be excluded by the LHC. The ACME upper bound is \(10^{-32}\) meters so it is almost 1 million times stricter and more nontrivial. The new electron electric dipole moment upper bound surely excludes "maximally CP-violating, utterly generic new physics" not only at the scale \(100\GeV\) but even at scales \(10\TeV\) and perhaps a bit higher. If a god told us that the new physics has to be generic and maximally CP-violating (offering no tricks to suppress the CP-violation relatively to the simple estimate above), the ACME result would tell us much more about the non-existence or "huge distance" of new physics than the LHC.



Check the post by Jester who is among those who think that they have already heard this particular god speaking. His blog post ends with an estimate of an "unrefined" garden variety supersymmetric model. The Feynman diagram above which contributes to the electric dipole of a quark (or lepton) and exploits a one-loop process with virtual charginos and a virtual slepton (or squark) is taken from Jester's blog.

Prof Matt Strassler has only written one sentence about the ACME experiment.

SUSY, new physics has no reason to be "garden variety"

Well, I don't really trust this estimate. I don't think that the ACME result really implies that the LHC isn't allowed to discover new physics in the 2015- run (and the chances at the Very Large Hadron Collider would be even higher, of course). The reason is that there may be very natural cancellations that make the constant above \(c\lll 1\). This is also – or particular – true for SUSY.

In fact, the people who have known me for a decade or so know that I have always considered moderately small dimensionless constants of order \(1/1,000\) etc. to be just fine. In fact, I have always believed that we ultimately have lots of experimental evidence for some hierarchies and large or small dimensionless ratios – so their origin has to be "somewhere" (and whether the largeness or smallness is "explained" anthropically doesn't really matter here; what matters is that they exist). A more refined understanding may always render an estimate by dimensional analysis naive.

In fact, I have never considered the "purpose" of SUSY to be to provide us with a "totally generic garden variety model of new physics". SUSY is very constrained. It is actually giving us many cancellations and that's one of the main reasons of its importance. The cancellations don't seem to directly apply to the constant \(c\) above but there are other cancellations and other patterns and mechanisms that, in combination with supersymmetry, may make \(c\) very small, too.

For a (slightly randomly chosen) discussion of the status of naturalness in SUSY and ways by which SUSY models solve the CP-problems like the dangerous overgrown dipole moment as well as flavor problems (transformations of fermions from one generation to another that are also predicted to be much faster by "garden variety new physics" than the experimental bounds allow), I recommend you this 2 months old paper by Arvanitaki et al.

The Last Vestiges of Naturalness

They conclude that even if superpartners are discovered at the LHC in 2015, "naturalness will not emerge triumphant". Well, I think it has been non-triumphant for some years and I have never seen any reasons why it should "triumph". For me, naturalness is just a vague guide, a non-rigorous or Bayesian way to direct us. Due to its probabilistic and ignorance-dependent character, it is not an unbreakable principle of physics. So it's just fine if naturalness fails to emerge triumphant or if it will be shown to be pretty much a loser.

On the other hand, I do care about SUSY, I am sure it's there in Nature, and I find it sufficiently important to know whether or not it's close enough to be discovered by the LHC (or other experiments). The key point is that the positive motivation for SUSY is still with us and some classes of models are naturally compatible with the small CP-violating parameters (like the dipole moment discussed here) and the small flavor-violating parameters as well as with a tolerable degree of residual fine-tuning for the Higgs mass.

Arvanitaki et al. summarize the literature on "viable SUSY models" (in the sense of the previous sentence) as a composite of three classes of models or ideas:

1. split families (unfortunately and confusingly called "natural SUSY" by many physicists)
2. baryonic R-parity violation
3. Dirac gauginos

These scenarios have been discussed on this blog repeatedly, especially the last two and mostly for theoretical reasons, not so much because of the purely phenomenological upper bounds or obsession with naturalness. But again: What do these possibilities mean and why they're viable?

Split families

The split families are often called "natural SUSY". I don't like this phrase because while this scenario is motivated by some general ideas about naturalness (in a modern technical sense), the adjective reveals some hype because the name is meant to make you believe that it's the only way how naturalness may be incorporated (it's not, see e.g. the other two options in the list) and it doesn't really respect the long-term meaning of the word "natural" that keeps on evolving as our relation to Nature's own naturalness is becoming increasingly intimate (we are refining our knowledge of Nature's "discrete rules" and improving our "rough estimates").

At any rate, the split family models were actually introduced long before the LHC began its collisions. They want to make the cancellations of the Higgs mass etc. "natural" and it's good to have light superpartners for that but the proponents of these models noticed that not all superpartners are equally important to achieve this goal. In particular, it's only the third generation and gluinos (and electroweakinos) whose lightness is important for the lightness of the Higgs boson.

The first two generations may be much heavier. Because their interaction with the Higgs boson is much weaker (that's reflected by the much lower mass of the light generations of fermions – after the Higgs takes on a nonzero vev) – they don't influence the Higgs mass (and its lightness and the related Higgs fine-tuning) too much. So the first two generations of leptons and quarks (selectron, smuon, two sneutrinos, sup, sdown, sstrange, and scharm) may be allowed to be heavy; physicists like to say that these two generations "decouple" (they're not "localized" at the same energy scale).

This discriminatory treatment of the first two generations is also good because of the recent LHC constraints. The LHC has shown that too light superpartners don't exist. However, the first two generations are much more constrained than the third generation. It's because it's much easier (or "it would be much easier" if they existed) to produce the first (and, to just slightly lesser extent, second) generation of quarks and leptons (because the protons are composed of the first generation and the conversion to the second generation is relatively easy).

Quantitatively, we know that the first two generations of squarks are heavier than something comparable to several or \(10\TeV\). The third-generation leptons and/or quarks (stop, sbottom, stau, and one sneutrino) may still be lighter than \(1\TeV\) (the bounds on the gluino are something like \(1.2\TeV\) now). This segregated attribution of mass to the quarks and leptons is good because it allows particles "maximum freedom to be heavy" while not spoiling the Higgs' lightness; it is a generic way to agree with the current, "non-uniform" upper bounds; but we get some extra advantages, too.

Because of the gap, the flavor-changing processes are automatically suppressed i.e. the counterpart of the constant \(c\ll 1\). We may imagine that the grouped generations allow us to define a new \(U(1)\) group under which the third generation has a different charge than the first two – this construction may be made literal and visualized as different locations of the generations on different branes in a (stringy) braneworld. So we get some new (approximate) conservation laws, so to say, and the flavor-changing processes are discouraged.

For similar reasons, the split families also reduce all the CP-violating parameters such as \(c,d_e\) relevant for the dipole moment we discuss here. You know from the CKM matrix that the CP-violating phases depend on the mixing of many fields (three generations in the case of quarks) and if two generations are "qualitatively segregated" from the third one (in the case of squarks), the mixing between the first two and the third one is reduced which may also reduce the CP-violating phase.

Baryonic RPV

In most of the model building, it's still being assumed that the R-parity which is equal to\[

P_R = (-1)^{2J+B-L}

\] for the MSSM particles (it's \(+1\) for all the Standard Model particles and \(-1\) for their superpartners: check it, it is easy) is exactly conserved. Such a conservation has a virtue – the lightest \(P_R=-1\) particle, the LSP (lightest superpartner), is exactly stable and may be assumed to be the particle of dark matter.

However, the R-parity may also be violated in which case Nature allows the \(P_R=-1\) particles to decay to \(P_R=+1\) particles only. If that's so, the LSP isn't stable but the gravitino may play the role of the dark matter instead because its decay is very slow, mostly due to the weakness of gravity (which dictates the strength of gravitino's interactions, too).

This improves the naturalness simply because the LHC events with a large "missing energy" (=ultimately LSP) are erased because the LSP decays to well-known particles. Consequently, RPV (R-parity violating) models become compatible with the LHC data even if the superpartners are much lighter than allowed in R-parity-conserving models. See a 2011 text on some RPV models; there have been several others.

Because of the formula for \(P_R\) above and because of the "unbreakable" conservation of the spin (which follows from the rotational symmetry; but the conservation of the spin modulo one, i.e. the conservation of the statistics, is an even more unbreakable law), the R-parity violation requires to violate either the conservation of the baryon number \(B\) or the lepton number \(L\) or both, too. If both are violated, we're in trouble because it becomes easy for the proton to decay to a positron and some neutral junk. We know from the "futile" searches for decaying protons that this decay is either non-existent or (more likely) so slow that the relevant term in the Lagrangian is so tiny that it can't matter for the LHC physics.

So in viable models, the R-parity violation may occur through lepton-number-violating terms only; or through baryon-number-violating terms only. The experimental tests seem to be much more tolerant to baryon-number-violating, R-parity-violating terms like the superpotential\[

{\mathcal W}_{bRPV} = \frac{\lambda''_{ijk}}{2} U^c_i D^c_j D^c_k.

\] Such an operator may destroy up, down, down (s)quarks in some combination. In some sense, it's able to destroy a "sneutron" and convert it to pure energy. The electric charge and overall color (none) is conserved but the baryon number jumps by \(\pm 1\). There are some other reasons why the baryon RPV (bRPV) models seem more attractive than lepton-number-violating RPV models and why they became popular in the very fresh literature.

At any rate, they allow the superpartners to be much lighter – these lighters superpartners become largely invisible at the LHC because they don't produce missing energy (stable LSP) in the decays. This improves the situation of the Higgs lightness fine-tuning. The CP (e.g. electron electric dipole moment) and flavor problems aren't solved too well, as far as I know, and the baryon violation may also cripple baryogenesis. This puts a pressure on the gravitino mass from both sides (a few \(\GeV\) is marginally OK) and none of the values seems really great, despite some improvements that hidden sectors may bring.

But when one focuses on the degree of "unexplained fine-tuning" needed to avoid a contradiction with the empirical bounds (if it can be avoided at all), this class of models seems less contrived than garden-variety models of new physics, too.

Dirac gauginos

I have discussed Dirac gauginos in many articles. If the gauginos (superpartners of the gauge bosons) are Dirac fermions, they contain not just one two-component Majorana (or Weyl) spinor but two. Because of the \(\NNN=1\) SUSY, the second one must be paired with a boson and it can't be a \(j=1\) vector boson anymore because a gauge group may only support one vector field; instead, it must be a \(j=0\) scalar.

Consequently, such gauginos belong to a pair of multiplets (chiral supermultiplet and vector supermultiplet) which may be combined into the \(\NNN=2\) vector multiplet. That sounds great because the gauge fields and their pals could actually show us more supersymmetry than the minimal amount, some extended supersymmetry. I have argued that such extended supersymmetry (eight conserved supercharges) could follow from a braneworld description of gauge fields in string theory. Extended supersymmetry is surely cool and stringy; after all, it's the (even more extended) \(\NNN=4\) supersymmetry that the Yang-Mills fields are given if people study the most popular example of the AdS/CFT (even if they use it as a model for QCD).

The Dirac gluinos also improve the situation in many purely phenomenological questions. They may be much heavier than the usual Majorana gluinos – and still allow the Higgs lightness to be pretty natural. Flavor-changing dangerous processes are slowed down because they depend on the Majorana mass and this parameter may be made much smaller (basically zero) now. The gluino exchange in the \(t\)-channel decreases more quickly at higher energies so that the production of squarks is predicted to be less frequent. This reduces the potential contradictions with the LHC constraints, too. I don't know what new sources of CP-violation are doing; I don't really expect them to be too suppressed because we're switching to more "complex/Weyl" fields and those like to produce CP-violating phases.

To summarize this section, there are several proposed "pretty structures" on top of supersymmetry that may make many if not all of the potential "problems of garden-variety new physics" or at least "problems of general SUSY models" go away. These extra ideas are not as profound as the idea of supersymmetry itself but they're still pretty cute and they could finally turn out to be the right explanations why some naive estimates of new effects by dimensional analysis are (very) inaccurate.

New physics may be relatively close and it may be far. We don't really know. We may exclude some particular models of "nearby new physics" while others remain viable. There are vague arguments that may support each possible answer. Because the option "no new physics almost anywhere" is pretty much understood (it's been studied as "the Standard Model" for 40 years), it's logical that both experimenters and (pheno-oriented) theorists focus on the other option that assumes some new physics. The ACME experiment is telling us something – under some assumptions, it is telling us "more" about new physics than the whole LHC; with some other assumptions, it's telling us about some "qualitative properties" of the new physics that aren't so terribly new or surprising.

Many of the contemporary theoretical arguments, ideas, and mechanisms are neat and clever and Nature may very well be exploiting one of them or several of them – or some other insights that may be found by the theorists in the near or far future. Some of these "extra structures" have the potential to tell us about the way by which string theory is realized in the Universe, e.g. about the shape and our (and different particles') location within the extra dimensions.

Stay tuned.

Bubbles will arrive before inflation

When I was six or so, I had an idea that many other kids – and many of you – probably have also arrived to. If one may buy anything for the money and someone is able to print the money, why doesn't he print an unlimited amount of money in order to make everyone happy and solve all the world's problems?

The Keynesians and similar folks believe that this is a great idea even when they are adults. But many of us have managed to figure out – or were told – why this isn't such a great idea. After all, the nominal information expressed in the units of currency means nothing. A dollar or a crown or a deutschmark is just a lame unit of wealth. If everyone owns 10 times greater an amount of money, everyone will also demand a higher price for his goods and services.

So I quickly realized that the fact that a dollar was 30 times greater than the Czechoslovak crown was just an inconsequential choice of the units, just like the difference between meters and feet. One may design physically and socially equivalent situations by simply multiplying all the prices by \(C = \exp(\lambda)\) – by reducing the money by the factor of \(C\).

This "financial gauge invariance" may be used even for a single currency which evolves in time. You may rescale all the prices and related quantities expressed in the units of currency, \(P_i\), by a function of time \(t\),\[

P_i\to P'_i= C(t)\cdot P_i = \exp[\lambda(t)] P_i

\] and it's quite possible that nothing really changes. There are things like "rates" – interest rates, inflation rates, and so on. They're defined as the time derivatives of some quantity \(P_i\) divided by the quantity itself. So if you switch from the numerical value \(P_i\) to \(P'_i\), the new rate will be\[

\eq{
\frac{1}{P'_i}\cdot\ddfrac{P'_i}{t} &= \ddfrac{\ln(P'_i)}{t} =\\
&=\frac{1}{P'_i}\ddfrac{\zav{\exp[\lambda(t)] P_i}}{t} = \\
&= \frac{1}{P_i} \zav{\ddfrac{P_i}{t} + P_i \ddfrac{\lambda(t)}{t} }
}

\] by the Leibniz rule (for the derivative of a product).




The first term on the right hand side is nothing else than \(\dd \ln( P_i)/\dd t\), the old "rate", but there is one more term, \(\dd \lambda(t)/\dd t\): old rates are additively shifted by this universal quantity.

This shift is mathematically analogous to the transformation of charged fields and the gauge fields under the \(U(1)\) gauge symmetry in physics. All the charged fields get multiplied by \(\exp[i\lambda(x,y,z,t)Q]\) while the gauge field, analogous to rates, is shifted by \(e\partial_\mu \lambda(t)\).

The only different feature of the "financial gauge invariance" is that the argument of the exponential contains no imaginary unit \(i\). This difference means that the gauge group isn't really \(U(1)\) but its noncompact version, \(\RR^+\), the multiplicative group rescaling all the prices at time \(t\) by a positive factor. In fact, Hermann Weyl has introduced this \(\RR^+\) gauge symmetry (rescaling the distances, not prices) to the physics of general relativity, too. String theorists doing perturbative calculations use the Weyl symmetry (on the world sheet, in their case) all the time.




I am not saying that the "financial gauge invariance" implies that any procedure whose goal is to change the inflation rate will create a physically equivalent situation and that it will be inconsequential. I am saying that it's possible to have physically equivalent situations with (arbitrarily, vastly) different inflation rates. All the prices will get rescaled; all the rates (including all the interest rates) will get an extra additive universal contribution of the "enhanced inflation".

It's my feeling that many people, especially the Ron Paul types, don't quite get this gauge invariance – the point that the numerical value of the prices and even its change in time doesn't really matter.

That's a good initial insight but for some years, I as a kid didn't make much progress in understanding the world of the finance. For quite some time, I was assuming that there was only one interesting "rate". It was the inflation rate mixed up with the interest rate, and so on. The discount rate was probably the same thing, I would be thinking if I were told something about the discount rate. There may also be some "real GDP growth rate" but I wasn't thinking about its impact on the logic of the finance much. It took a long time for me to appreciate that these rates are different in general and the differences are extremely important. In particular, banks are increasing the interest rates if they want to lower the inflation rate and (much more likely these days) vice versa.

A closely related basic example: the interest rate on your saving account isn't the same thing as the inflation rate. In some "ideal world", you could be promised that they are equal – a vanishing real interest rates. But the real world is not an ideal one; these two rates may differ. A central bank may be legally obliged to target the inflation rate (the interest rates may only be specified after the inflation is calculated – unless we use a predicted inflation – so there may be a delay). But the central bank may also creatively change the interest rate so that the "real interest rate" is nonzero. The real interest rate (nominal interest rate minus inflation rate) has been negative in most Western countries for many years.

At the beginning, I wanted to convince you that the "nominal rates" don't really mean anything – physically equivalent situations related by the "financial gauge invariance" may have rates differing by an arbitrary function of time. But now we see that the difference between two rates is physical. The real interest rate is an example. If it is positive, the savers are getting "really richer"; if it is negative, it's the other way around.

This opens many basic yet important questions: Can the central banks really influence the real interest rates? If they can, isn't it always a counterproductive market intervention that makes the economy less efficient? In principle, can the free market determine the real interest rates by itself (in an idealized world that is naturally identified as a "world without government interventions")? What are the drivers that determine its value?

The answer to the first question is Yes, a central bank may influence the real interest rates. The central banks define the interest rates paid on the commercial banks' reserves. For banks, it may be a better idea to lend the money to real-world people and companies, at a higher interest rate, so you could think that the interest rate on the reserves is irrelevant. However, a fraction of the bank's holdings must be in cash – the actual reserves, banknotes – so the interest rate paid on these reserves does influence what the bank may pay to the savers.

In most countries, laws define "reserve requirements" that guarantee that a bank doesn't go bust well before someone notices that something is wrong. Between 3 and 30 percent of the banks' holdings are required to be in the form of actual banknotes or the reserves. So the rate on the reserves determined by a central bank does determine what you get on your saving account, too, although the expected influence is smaller than the change of the central interest rate (essentially by the fraction that says what part of the banks' holdings are kept as safe reserves).

The second question was whether the central banks should try to "engineer" the "right" real interest rates. Keynesians surely answer "Yes". They view the central banks as a miraculous part of the government that can make everyone happy. I, as a free-market advocate, realize that the engineering of real interest rates is de facto a form of wealth redistribution. If you lower real interest rates by an intervention, you de facto make the savers poorer and you defend this step by helping someone else. That's the reason why I agree with the Tea Party types that a central bank shouldn't be active in this way.

But it's important that I am talking about real interest rates, not the nominal ones. Nominal ones don't really matter for the real world. They are not gauge-invariant.

For these reasons, I find the inflation targeting to be among the most neutral monetary policies. Along with some similar policies, it involves the least amount of redistribution of the "real wealth". This anti-socialist virtue is almost equivalent to another virtue: it makes the currency unit as predictable as possible and in average, it's good for everyone. The amplitude of oscillations is minimized. The amount of "lottery" in your financial results is reduced. In other words, the correlation between "good work" and "income" is maximized. Whatever the detailed policy is, I think it is healthy if the central banks have as little influence as possible, if the policies are "automatized". As a bonus, this condition automatically reduces the room for inside trading and speculations (those that are unproductive for the society), too.

Drivers affecting the real interest rates

Can the market determine the real interest rates by itself? What do they mean if we imagine that the government interventions are eliminated (in particular, you can't borrow from the government and you don't lend to the government, or at least the government is treated just like "another company" trying to maximize its well-being rather than an omnipresent institution intervening into the markets)? Well, borrowers offer low real interest rates if it is easy for them to borrow the money elsewhere – if the lenders have a lot of competition. And vice versa: Lenders may achieve high returns if many people want to borrow, and if they badly want to borrow. In other words, the real interest rates are high if there is a competition between borrowers, if too many people want to borrow. And vice versa: they are low if no one wants to be in debt.

(Their being near zero today is a sign that people and companies are (relatively) afraid of creating new debt. Savers have a special, sensible reason for that: they feel that they are poor and will be poorer. They can't afford to spend too much. At least when it comes to savers, policies trying to hurt them and discourage saving actually reduce consumption. The chronic borrowers are encouraged to borrow by low interest rates but it comes with a price – an increased risk of insolvency.)

The paragraph starting with "Can" explains how a healthy economy should decide about the real interest rates. Real interest rates should be determined by the balance between the supply and demand, too. If people want to save (and lend) too much, the market automatically discourages them because with too many fellow savers (and lenders), the real interest rates go down due to the competition and the saving (and lending) becomes less attractive. And on the contrary, if too many people get mad and start to borrow too much, there is a competition between them which allows the lenders to increase the real interest rates. This ultimately discourages the borrowers from borrowing.

Because of this simple mechanism – one that is fully analogous to the invisible hand's ability to dictate the right prices of everything and anything – the market knows best whether it's right for the savers to lose the money in the real terms or not. It seems to me that the world's economy is so brutally distorted by the Keynesians that most people don't even realize what I wrote in the previous paragraphs of this section – i.e. how the markets should decide about the real interest rates in an ideal world (and that they have a solid, "automatic" mechanism to do so at all). In fact, I think that even central bankers who are typically drowning in the ocean of the Keynesian feces fail to understand the right mechanisms that should decide about the real interest rates – and that normally protect the economy from oversaving as well as overborrowing. We clearly live in an overregulated world in which Keynesian and other ad hoc superstitions largely overshadowed something that I would consider the textbook knowledge about economics – e.g. that the market determines relative prices and rates most efficiently and most safely.

Particular distortion by the central banks in the recent years

The central banks kept on inventing all sort of Keynesian and quasi-Keynesian excuses for various random distortions of the market. Because the free market is the best tool to decide about the optimal allocation of the capital and all prices and (real) interest rates, any intervention that distorts the prices and interest rates reduces the efficiency of the economy.

This comment would apply regardless of the "sign". However, we live in a particular era and in recent years, the economies were distorted in a particular direction. I think that everyone knows what the direction was. The central banks were printing tons of money, pumping them into the economy. They were pushing banknotes to the people's throats (assuming that this will make the people more hungry), intervening, and trying to "punish the savers" by steps artificially lowering the real interest rates as much as possible. The interventions took the form of keeping the interest rates near zero or at zero and other non-standard procedures. Some of the non-standard procedures (like QE) don't really matter. Others, like the interventions against the Czech crown, surely matter but only locally – distorting the Czech economy exactly in the opposite way than what is their (more diluted) impact on the eurozone (euro reserves were being piled by the Czech Central Bank for a few weeks: about EUR 8 billion were bought for freshly printed Czech banknotes).

The motivation for this artificial loosening is a (partly irrational) fear of a recession and the obsession with the positiveness of the GDP growth rate, regardless of the fact that much of the added GDP results from an increased debt (a thing that one should really be worried about much more than about a smaller GDP growth) and from various tricks that imply that much of the activity in the GDP is really "fake".

At any rate, these interventions have had no severe consequences yet – like hyperinflation. Everything looked like a relatively smooth sailing. But something has been changing about the underlying numbers. Look at these scary graphs from Harvard's PolicyMic:



Between early 1980s and now, the currency in circulation increased 7-fold or so, to $1.2 trillion. Clearly, this growth by the factor of 7 vastly exceeds the increase of the GDP, even the nominal one. At least, the graph above looks uniform and sustainable. But there are more shocking graphs.



This is the St Louis adjusted monetary base that contains not only the banknotes and coins in circulation but also the commercial banks' cash reserves, roughly speaking. Since 2009, just in four years, it grew by a factor of 4 or so. That more or less means that the commercial banks' cash reserves have grown dramatically.

This huge, four-fold relative increase of the monetary base in 4 years certainly hasn't led to a quadrupling of prices. The prices in the U.S. have barely changed and the GDP growth has been minor, too. If you just print lots of banknotes and lock them in the basement, they will not influence anything. And that's really what was more or less happening so far. The dramatic increase of the monetary base above didn't mean much because it's mostly spurious. Banks' balance sheets were increasing, much of their assets are kept as reserves, these reserves are included into the monetary base graphed above, but the increased debt of the banks isn't counted even though it really "cancels" the increased reserves.

The monetary policies have largely affected the flows of loans between the arms of the government and banks only – the real-world loans of the real-world people are determined by other things than the government apparatchiks' proclamations.

Those procedures behind the quantitative easing are the ultimate prototype of the interventions that shows why these interventions are slightly counterproductive but more clearly, futile. The goal of all these interventions, the printing and pumping of the money, is to accelerate the real economy. However, much of the extra money that is being printed and pumped remains locked in basements and they influence nothing. They only influence mostly unphysical (thank God, so far) graphs like the St Louis monetary base graph above.

The real economy isn't affected much (or detectably) for a simple reason: The desire of the actual people to lend and borrow isn't actually affected by extra banknotes that appear in the basements. It's determined by the free market, by the balance of the supply and demand – i.e. ultimately by the people's desire (or need) to save and lend or, on the contrary, borrow. As I have argued at the beginning, most of the real interest rate is dictated by the people's own situation and psychology, by the balance of the supply and demand (real-world lenders and real-world borrowers and how they evaluate the importance of the debt and the risks). The "activist", Keynesian manipulation with the interest rates only influences a small part of the interest paid on savings (the percentage equal to the percentage of banks' assets that are or have to be kept as reserves). The rest – the majority – is unaffected by the central banks' interventions.

Similarly, operations such as QE only distort some relative prices, relative interest rates i.e. the detailed shape of the yield curve and they redistribute the wealth in some way, creating some losers and some winners (according to what they were holding and what they are going to buy). But they don't really change anything about the "total activity" in the economy and any redistribution reduces the efficiency and fairness of the economy which ultimately reduces the GDP (by terms of second order in the magnitude of the intervention).

So thankfully, much of the misguided activity of the central banks has only affected "mostly spurious" graphs such as the monetary base in the graph above. So far. But the purpose of all this loosening and interventions has always been that the money will eventually be flushed out of the basements and they will get to real economy. Will they? There are trillions of dollars waiting in various basements that haven't really begun to circulate in the real economy but they were printed with the purpose to circulate ($4 trillion in the semi-locked basements is like 3 average monthly salaries waiting to be donated to each American including infants). Lots of things could change – and a huge inflation could start – if the original goals started to materialize.

I think, surprisingly, that the answer to the question "Will they?" above will depend on the collective thinking of the people which isn't quite predictable. If the people were thinking in a particular way, they just wouldn't care about the extra trillions in banknotes that are waiting in the basements. In effect, the Federal Reserve and other central banks may keep on printing obscene amounts of money but they will remain locked in the basements because people's "hunger" isn't really affected by the amount of food that they may buy and that is waiting in a basement. Balance sheets may be increased by balance sheets mean nothing – it's some equity that is immediately subtracted from itself to yield zero.

However, at some moment, inflation expectations are probably bound to emerge. A sufficient, critical amount of people will start to realize that due to the interventions, it's just a question of "when", not "whether", for the money to get out of the basements. Once a person who is effectively deciding about some reserves – even cash that he has borrowed – realizes that the banknotes will lose their value sometimes in the (foreseeable) future, he will start to get rid of them and convert them to something.

Once this motion starts, people will notice and an increasing number of people will bet that this trend is inevitable and it's time to get rid of the money. So I would say that we may have been in an equilibrium in which the continuing printing didn't matter but it's an unstable equilibrium because the banknotes are not hermetically locked in the basements and there is a risk that due to a perturbation, trillions of dollars will be flushed out in an unstoppable avalanche. (A future avalanche is the only possible ultimate result of some policies that hugely change some underlying graphs like those above but have virtually no effects on the real economy for a few years. That's why dangerous imbalances and instabilities are the only possible result of similar interventions – an explanation why the government should always better f*ck off, to put it very mildly.)

Because of this risk, some people are bound to think that this risk is a reality which means that they will effectively start the avalanche themselves. The apparent equilibrium we have been seeing for years – the Keynesian distortions of the financial markets by the activist central bankers – is an unstable one. It will start to collapse at some point and the instability will be only stoppable by a dramatic increase of the interest rates that the central bankers – who have been insanely dovish – won't have enough courage to set. Because of the limited influence of the central interest rates on the real-world interest rates, they could very well need 20% central interest rates to help to achieve 10% real-world interest rates that may be needed. Such a spike would produce an inverted yield curve that would lead to negative yields for some timescales in the future. All these things are problematic.

So if you agree that the money is not quite "hermetically" isolated and there's a risk that it will be flushed out due to a perturbation, you should agree that the process by which they will be flushed out is inevitable at some point and the only remaining question is where they will flow from the basements at the beginning.

I think that inflation – quickly increasing prices of common products and services – is likely if not guaranteed to arise. But I think that this won't be the first manifestation of the "semi-locked" money in the basements. Why? Because people's desire to spend the money for common goods and services is not directly affected or determined by the central banks' distortion of the financial markets.

Instead, they have a pretty much intrinsically, psychologically dictated level of desire to save and ensure themselves for the future, or to borrow. Because the "real spending" won't be affected, the risk of a deteriorating value of the money will mean that they will convert their cash to some other investment which is not "obviously" threatened by the flood that will flush out the cash from the basements.

So I tend to think that various bubbles in equities – stocks and perhaps real estate – will emerge before the inflation. People will first realize that it's safer to convert the cash holdings into a different form of investments. The flood from the basement will go into these other investments which will increase their value but not to "real spending", i.e. to everyday products and services which will continue to be unaffected.

In other words, bubbles will grow before the inflation will kick in. You might argue – especially if you look at Dow Jones above 16,000 etc. – that the bubbles have already begun to grow.

However, the word "bubble" implicitly means that we expect it to pop. My bonus point is that it doesn't have to be necessarily the case. Because of this flood of printed money, we may enter a long era in which the price-to-earnings ratio, P/E, will be much greater than the values we have been used to. If that long-term change materializes, people will effectively be gradually switching to stocks (and equivalent investments) as the money. An increasing number of people will hold their wealth (even borrowed cash) in the form of stocks which may continue to grow for quite some time.

Only once many of these people will find out that they're really richer, they may start to "really spend" and inflation will kick in.

So I am suggesting that P/E may be higher than the usual values of order 10 for many years. We must ask the question: What market forces dictate P/E?

Well, if a company is expected to grow and/or the recent earnings are seen as downward flukes, P/E may be much higher than 10. On the contrary, if a company is apparently declining or at risk to go bust, P/E may be much smaller than 10. Companies that are "guaranteed" to exist for many more years tend to have a higher P/E and vice versa. And of course, an unjustified bubble may inflate P/E, too. You might also think about antibubbles if you wish.

The basic logic that determines that some companies have a higher P/E than others is pretty clear. But what about the overall or average P/E? I used the number 10 in the previous paragraph which was mostly random but why is it 10? Can't it be a completely different number like 2 or 50? What is a company really worth?

Well, a company is a tool to produce profit. It has an expected lifetime. If you own stocks, you will get all the dividends from this expected lifetime. So P/E is "comparable" to the number of years over which the company will produce the dividends "comparable" to the last ones. If the company's profit will be halved every year, it will only generate a finite amount of profit in the whole future (equal to 2 years of the initial profit rate). A company that will last for "centuries" may be programmed to produce an infinite (total) amount of money in the future. But it's not a good idea to be too certain about the very far future, like 30 years from now, and a particular person whose lifetime is finite will be getting the income for a limited amount of time, anyway.

These are some of the hand-waving arguments why it is strange for P/E to exceed values like 30 or at least 50. But are these arguments waterproof? Can't the numbers be changed to totally different values because of the flood of trillions of dollars that will be flushed out of the basements?

I think that they can change, even in a (semi-)sustainable way.

The average or typical P/E may very well grow arbitrarily high, at least in principle. (In that case, the P/E ratios should increase globally – otherwise there would be clever transactions that would tend to make the P/E more uniform, anyway.) What would it mean and why would it be sustainable?

Well, if the people will start to decide that the cash is doomed, they will have an increasing fraction of their wealth, even "cash", in the form of stocks. To understand the idea, we may imagine that people will keep 90% of their salaries and all the savings in stocks and everyone will try to buy a "fair basket" or an "index fund" of stocks for most of his money. If that's so, the short-term fluctuations of the stock prices will be reduced. People will be effectively using the stocks or (approximately speaking) index funds as currency.

Once this trend reaches the people buying the everyday products and services are used to calculate the inflation rate, the inflation (growth of prices in the original currencies) will kick in. But there won't be any significant inflation if the prices are expressed in the "new currency" or "new currencies", the index funds.

If the average P/E reaches 100, it will still mean – in some careful interpretation – that the accumulated expected income from the company is equal to 100 years of recent dividends. But the reason why it's 100 won't be that something has fundamentally changed about the resilience of the companies etc. Instead, it will mean that the income is generated in the inflating old currencies such as dollars and this income is expected to grow.

If you knew that the inflation will be high (100%) but the interest rates will be kept at zero, and company's "real profit" is constant, to assume a simple situation, the company will produce something like 31 times recent dividends in the next 5 years (exponential growth etc.) So this is a justification for the P/E of the company to be vastly higher than just the number of years for which it is going to produce the same profit. Note that the condition needed for this increase of the "natural P/E" is the expectation of very low real interest rates for several years. Such conditions may justify higher stock prices (higher P/E). These sentences and this paragraph are therefore the most relevant ones for the claim promised in the title of this blog post. (In the real world, the real interest rates will not be of order –50 percent like here but closer to zero – but we may extrapolate companies to more than 5 years and the inflation [more precisely, loss of real wealth in savings] over the expected lifetime of the company may still be substantial.)

It's also sensible to expect a higher P/E in the environment of very low interest rates on savings because the dividends are successfully competing with the low interests even if these dividends are low.

So I do expect some rather dramatic changes in the years to come – changes that will result from the insanely loosened policies of the recent decade and something, especially the last 5 years. But I also do think that this will lead the people to de facto switch to different units of wealth that don't inflate that much so it won't be the end of the world. In fact, it's possible that nothing will change legally and the U.S. dollars etc. will continue to exist. Just the people's habits about how they store their holdings at various timescales may be vastly different than today and this will also mean that the numerical values of prices and even P/E may be very different than today.

Note that people rationally abandon units of currency whose value is decreasing too quickly (due to inflation) because it's dangerous to hold such "money". But when the value of some "coins" increases too much (deflation), it stops circulating as well because it's stupid to get rid of such a permanently growing miracle object (and it's better to keep it in the mattress than to lend it for zero or negative interest rates). In effect, only units of wealth whose inflation rate is "sufficiently" close to zero (which may perhaps include 10%) are picked by rational market players as something that is good to be used for payments for extended periods of time.

To summarize practical implications of the ideas above: I don't think that 16,000 is the end of the growth for Dow Jones, among related forecasts. The inflation will ultimately arrive to much of the world but equities should grow earlier and in the extended process of this growth, we may see a quasi-sustainably elevated P/E. This new, unusual regime isn't "quite" sustainable because at the end, the inflation will be tamed and there will be some ordinary real growth again.

The invisible hand spanks the government and restores some justice

You might interpret my point as a claim about the "long-term justice" that the invisible hand of the free markets is able to impose despite the distortions by the government. The observations can't guarantee that an investor will find the right timing for all transactions; he may be lucky or unlucky. But if the government or the central bank manages to artificially reduce the real interest rates – and especially their expectation – (well) below zero, it automatically means that the justifiable P/E ratio becomes (much) higher and stocks should be growing exactly when the expectation about the real interest rates in the future (comparable to the companies' lifetime) deteriorates. Once the expectation about the real interest rates improves again, the justifiable P/E decreases again and the bubble may pop. But it was not really an irrational bubble; there was a rational reason why the P/E was higher. As a result, the investor with an appropriately "averaged" portfolio cannot be punished by the government's interventions designed to punish investors, at least not in the long run. The government may only achieve a redistribution, a (more or less random) transfer of wealth from some people to others.

Today, it's been 50 years since the assassination of JFK.

The murder took place on Friday, just like today. For generic two years, the probability is 1/7 that a given day occurs on the same day of the week. However, for a 50-year gap, the probability is approximately 1/3 because each of the 50 years shifts the day of the week by 1 plus 11-13 (mostly 12) from leap years (it may be just 11 because about 3/8 of the 50-year intervals include a non-leap year like 1900).



A historical movie from that day, 15 minutes. Death at 6:01.

The shift is therefore 60, 61 (most likely), or 62 days which is 5,6 or 7 modulo 7. For 1963-2013, the case 62 i.e. 7 occurred. So even the same day of the week isn't too shocking – the day of the week is almost as likely to agree as it is to disagree after 50 years. These two paragraphs were preemptively included to fight another conspiracy theory about the day of the week. ;-)

I wrote about JFK 5 days ago but now I want to avoid particle physics.




About 2/3 of the Americans, including John Kerry and Oliver Stone, believe that there is some deeper story behind the murder than a lone gunman named Lee Harvey Oswald. Holy crap. Why are they doing it? I have already mentioned that they probably want to "restore some order", to save their (incorrect) assumption that famous men may only be killed by other famous men or their collectives.




In The Guardian, it is argued that people believe in conspiracy theories because conspiracies actually sometimes happen. This differentiates the believers from believers in telepathy and so on.

I agree that conspiracies do sometimes happen but I disagree that this fact prevents us from concluding that most people believing similar conspiracies are morons. One may estimate the probability \(P\) that there is some big conspiracy behind a collection of similar enough events and compare this probability with the percentage \(Q\) of people-event combinations in which the people believe that there was a conspiracy. If the people's opinions were sensibly reflecting some underlying reality (which isn't quite known), we would have \(P\approx Q\). However, in the real world, \(P\ll Q\). Assuming that you buy my arguments that \(P\) is actually small enough in the absolute sense, it proves that most people who believe the conspiracies must be systematically deluded.

First, the actual story seems so straightforward that I wouldn't normally spend much time with it. The best movie of the incident was captured by the amateur Abraham Zapruder. There were probably exactly 3 shots and The Zapruder film shows everything you need:



The camcorder was running at 18.3 frames per second. It's being said that in the frame 160, there was the first shot that missed everything. After 220, there was the second shot (magic bullet) that hit the governor in front as well as JFK (non-fatally). They react in some way. The third shot at 313 was used to make JFK's head explode which turned out to be lethal. The time between the first and third shot was probably over 8 seconds.

One may reconstruct the trajectory of the second bullet from the holes in the bodies. The Texas governor John Connally was closer to the center of the car and at a lower height and his chest was just turned to the right side. One may still trace the holes in their bodies and they agree with a straight single shot whose origin (from the back) is moreover compatible with the 6th floor of the building where Lee Harvey Oswald is located. The direction where the brain fragments appeared (front) and the direction of the momentum transfer to the body agree with the predictions of physics, too, although the momentum transfer is a bit subtle issue.

You may clearly see these things in the movie. They couldn't really fake movies well at that time. Why would you doubt it? Some people want to protest against a bullet that goes through both bodies. But what's so shocking about it? When one body is behind another, and it clearly was from that angle (it is not too unlikely in a car, anyway), a shot simply gets through both bodies.

Now, take the claims that there was a different shooter, like the driver. Well, the driver theory just disagrees with all the evidence I could see. An even more popular theory is the Grassy Knoll Badge Man. I watched this conspiracy video defending this meme and I just had to laugh out loud. They take a random place in the noise of a picture and argue not only that it contains a man. They can say that he had a particular haircut or hat and a uniform and some of them say that he wore glasses. Holy cow, I don't see a damn thing. It's as noisy a piece of the picture as almost any other in the area.

So some people analyzed this theory in some more detail, using the state-of-the-art computer techniques. No clear signs of a human – or glasses or anything like that – were found. More devastatingly, the person had to be one meter tall if he were exactly there; or he was several meters tall and flying 5 meters above the Earth's surface at a much more distant place.

Great. Even if a really tall human had a ladder over there, one that no one had noticed in 1963, what do you exactly want to achieve with this extra contrived assumption? There was no shot through the bodies that would be going in that direction. So what else than the complete stupidity – or a form of religion that may be classified as a type of complete stupidity – could be the reason that someone still believes the Badge Man Grass Knoll theory?

Quite generally, the very idea that there should be more people involved in this shooting is bizarre. A vast majority of similar incidents involves a single shooter. Think about Breivik and lots of others. Why would someone think that it's more convincing to create a theory with numerous shooters?

There are exceptions. When the Czechoslovak government in London needed to execute a blonde beast called Reinhardt Heydrich, perhaps the main father of the Holocaust and a gangster who acted as if he were a leader of 2/3 of Czechoslovakia for almost a year (1941-1942) just because a nutcase with one testicle told him that he was one, they sent several parachutists including two shooters. This "backup" is what governments or companies do when they want to be "insured" that the maneuver will work. And indeed, the first executer's gun got jammed which is why the second one was ready and useful because he could throw the hand grenade that killed the beast after some delay in the hospital. It worked fine. Thousands of Czech lives (including two whole villages) were terminated in the hysteria afterwards but it was needed for the Czechs not to be a nation of complete cowards and collaborators.

But in the case of the JFK assassination, there is simply no evidence that there were numerous shooters and/or that there was any organization or group of people who would want to increase the probability of the success by a backup plan or a spare shooter. In fact, it's very likely that if there had been several shooters, we would almost certainly learn about some traces the others have left. There aren't any.

So why the hell would someone switch from the minimal, effective theory to the contrived one – one which needs several shooters and perhaps even some synchronization of their shooting? A contrived hypothesis that is not only less plausible a priori but one that also seems to almost directly contradict the empirical data about the shots and their trajectories? I think that the stupidity is the only conceivable explanation.

It's just far more effective for gunmen to act individually if they want to achieve a similar "goal". Without backups, some of them may fail but indeed, they sometimes do. But if someone wants to have a decent enough chance to kill the president of the U.S., the best strategy is simply to try. Individually. It may even be better not to inform or ask anyone else because that could reduce the probability of the success. That's what happened according to all the evidence I see: a lone gunman. People who find it natural to believe that there should be several shooters and backups think like communists and would be lousy managers if they adopted the same philosophy in their management. Some jobs may simply be done by one person. Shooting a man – and whether he's a president doesn't really matter – is an example.

A related issue is the question whether the shooters or the originators of the plots must be famous people. The conspiracy theorists generally believe that the answer has to be Yes. But it's another fact that there are many more ordinary people – even ordinary people with some access to guns – who might want to kill a politician. If it is possible to get to a reasonable floor of a building, they may just give a try.

So by pure counting, it is simply much more likely that the shooter is someone who isn't famous at all. Famous people are just too rare. Moreover, they are more visible. So I would think that a famous man probably has a smaller chance to organize something that remains completely secret than an ordinary man.



A computer reconstruction etc., 4 minutes. See 10 minutes.

On the contrary, famous people like politicians are probably much more likely to be shot simply because many more people know them and either hate them or consider them to be symbols of something they hate. The Earth is a large place and it's often difficult even for the best agent to perfectly protect such a politician. You don't need a very contrived theory to explain such data.

Even though it is "academically plausible" that there is something beneath the obvious and mundane events we have seen, one should understand that there isn't any real evidence and it is just a sign of irrationality to be attracted to unjustified contrived hypotheses and to (loudly) dismiss simple, effective theories that agree with the evidence, especially if one does so repeatedly.

(Of course, Kerry is less of a nutcase. He "just" believes that Oswald was directed by the Soviets or Cubans. Well, I would say that a marine who defects to the Soviet Union is probably extreme enough to think of similar acts himself. Even if Kerry were right, I don't think it is an important change to the story. There were surely people in the USSR who would rather openly say that the U.S. president should have been killed – along with many other "imperialists". And what? They couldn't do it. Oswald could. So even if he had met with some people who told him he should have, why does it matter? He was almost certainly a more unhinged commie than an average member of the Central Committee of the Soviet Communist Party so he was still likely to be the key guy behind the murder. Unlike Oswald, the top Soviet officials were sane enough to realize that a murder of JFK wouldn't end capitalism in America etc. so they were less motivated than him, too.)

There are just so many illogical steps and contradictions with the empirical data from that day as well as with some historical data on similar events and with the knowledge about the human nature that these conspiracy theorists commit so that I can't avoid thinking that they're just stupid. But there must be more to it – it's some stupidity that is more likely to spread through the society. It may be the case that most of the JFK conspiracy believers haven't really tried to think about the sad day rationally and independently. They are just absorbing a mass delusion from their environment.

The misconception that famous men may only be "challenged" by famous challengers helps. Let me articulate a related, more religious point: Many people probably feel that death and sacrifice should always have a meaning and it must always be possible to find a fair, comparably large "revenge" for any crime (Oswald's death isn't a good enough revenge). But it's unfortunately not the case. The laws of physics guarantee neither afterlife nor the meaning for our lives nor universal justice.

While Oliver Stone shot another pro-conspiracy JFK movie, Bill O'Reilly was the executive producer of a movie whose main point was that there was no conspiracy. So much for the idea that conservatives are the conspiracy theorists. He points out that FBI wanted a conspiracy to exist at some point but they couldn't find it.