Author: Daniel Castellano

How Vaccines Help the Immune System

Much of vaccine hesitancy is grounded in the supposition that one is better off relying on one’s “natural immunity.” This in turn supposes that there is some dichotomy or antithesis between “natural” and “artificial” immunization. In fact, vaccines operate by introducing an inert virus or protein into the bloodstream, so that the immune system can respond and learn to create antibodies. It is actually the immune system doing the “work” of immunization. The role of the vaccine is to introduce a harmless version of the pathogen, so that immunity can develop in this safe environment, and the immune system will be better prepared if the real thing comes. The alternatives would be to (1) hope that one is never exposed to the pathogen or (2) get exposed to the new pathogen and hope that the immune system can deal with it effectively on the first try. The choice is not between “artificial” or “natural” immunity, but between a prepared and unprepared immune system.

COVID-19 is now endemic, so it is a statistical near-certainty that everyone will be exposed to it at some point in their lives. Since it is a novel pathogen, our immune systems are not prepared for it with any specificity. For the unvaccinated, the risk of hospitalization and death varies greatly by age and existing health conditions. Even those who are not hospitalized, however, may suffer lasting “long COVID” effects. These include neurological disorders, respiratory damage, and increased risk of blood clots. Thus COVID-19 presents a substantial health risk to most unvaccinated adults.

You could say that you are willing to assume this substantial risk, or that, in your particular case (e.g., due to young age), the risk is objectively small. It makes no sense, however, to be sanguine about the risk associated with COVID exposure while at the same time being fearful of the risk associated with the vaccine, which does nothing but introduce an inert spike protein into the bloodstream, albeit indirectly. It makes no sense to be fearful of the inert spike protein while having no fear of exposure to the real thing. In fact, all the side effects of vaccines, including the serious effect of blood clotting, are effects associated with COVID-19. This only makes sense, because the inactive ingredients of the vaccine are harmless in their minute quantities, so whatever side effects result would be from the spike protein and the immune response to the same.

The mRNA vaccines (Pfizer and Moderna) work by introducing mRNA into muscle cells, instructing the body to create the spike protein. The mRNA itself, being quite fragile, disintegrates within a few days. The spike protein can remain for a few weeks, as the immune system takes time to develop a response. The Johnson & Johnson (Janssen) vaccine uses a piece of virus DNA (incapable of replicating) with instructions to create the spike protein. This adenovirus method has been in use since the 1970s. The mRNA method, though newly implemented, has been studied for decades. It has not been used previously not because it is unsafe (the mRNA does nothing but code for the inert protein), but because there has been no practical need. The difficulty and cost of storing mRNA is offset by the need to produce vaccines in unprecedented large quantities in a short time.

The COVID vaccines are different from most vaccines only in that they introduce the protein indirectly by genetic instructions, though even this is not truly novel, since DNA has long been used in adenovirus vaccines. Most vaccines operate by introducing the inert pathogen directly. They are not “medicines” or “artificial chemicals,” but pseudo-pathogens introduced to stimulate the immune system to prepare a defense. This is why the side effects of all vaccines are generally similar to the symptoms of the disease to be prevented.

The only lasting products of the COVID vaccines are the antibodies produced by the immune system. The mRNA/DNA disintegrates in days, and the spike protein is gone in a few weeks. These are all “natural” substances that operate according to well-understood biochemistry that regularly occurs in the body.

There is some evidence from Israel suggesting that the immunity (measured in antibody levels) resulting from exposure to COVID in the unvaccinated is greater than that provided by vaccination. Even if this is true, it is not a worthy comparison, for this ignores the substantial health risk involved in being exposed to COVID while unvaccinated. The greater immunity achieved is only subsequent to going through COVID, and it is not possible to know in advance if one will get a severe case or long-term symptoms. It would not be surprising if exposure to the real thing indeed provides better immunity than exposure to a pseudo-pathogen, but this is achieved only after a failure to prevent the disease. The same Israeli study notes that immunity is further enhanced by vaccination following exposure. This finding shows that “natural” and “vaccine” immunity are not antithetical, but complementary.

Early claims about the efficacy of the mRNA vaccines proved to have been overstated, at least with regard to preventing infection. Some of this has to do with the more infectious delta variant, and some has to do with the degradation of immunity levels over time, becoming substantial at six months. A regimen of once or twice annual boosters seems likely. Nonetheless, the vaccines do remain highly effective at reducing severe cases and the long-term health effects associated with these. It would obviously be more prudent to obtain this immunity before one enters the high-risk age group.

In short, without getting into the propriety of legal mandates and the rights of the individual versus those of society, we can see a unilateral prudential benefit to vaccination, at least for adults. All of the risks associated with vaccines are objectively small, and even if they were not, they are necessarily no worse than the risk assumed by not being vaccinated, once it is understood that COVID is endemic and that the vaccines operate solely by introducing inert pathogens, letting the immune system do the work of developing a defense.

By now, practically all of us know someone who has had COVID, perhaps including an unvaccinated person with a severe case and an elderly vaccinated person with a mild case. Some of us may have noted how immunity to infections drops after six months, and those with boosters fare better when exposed in large unmasked gatherings. We cannot reasonably pretend that the health risk is negligible, nor that outcomes are not materially affected by vaccination. Hopefully, a demystified understanding of the quite ordinary processes by which vaccines operate will help remove hesitancy in more people.

The muon g-2 experiment: Physics beyond the Standard Model?

This past Wednesday, I attended the webinar that presented the first results of the muon g-2 experiment since it was transferred to Fermilab in Illinois. I had worked on this experiment when it was at Brookhaven National Laboratory on Long Island. The collective results of the Brookhaven experiments contradicted the theoretically predicted value for the muon’s magnetic moment or g-factor, suggesting that physics beyond the Standard Model may be needed to explain this phenomenon. Experiment deviated from theory by over 3 standard errors, enough to suggest a new phenomenon, but not enough to meet the accepted threshold of 5 sigma (standard errors) for a new discovery. The team at Fermilab hope to meet this threshold by reducing the systematic error (e.g., by improving the uniformity of the magnetic field by a factor of 3) and by having large statistics, using the lab’s accelerator as high-intensity source of muons (decaying from pions).

In the 15 years since the last published results from Brookhaven, the computed theoretical value had been fine-tuned, only amplifying the discrepancy with experiment. Dirac’s relativistic quantum mechanics predicts that the dimensionless magnetic moment of all charged leptons (electrons, muons, tau particles) should be exactly 2. Under quantum field theory, however, there should be small effects by self-interaction mediated by virtual particles. These virtual interactions should span all possible combinations within the Standard Model. The largest of these corrections, discovered by Schwinger, is a virtual photon interaction resulting in a deviation of  alpha/2pi, where alpha is the fine structure constant, approximately equal to 1/137, so this modifies g  to 2.00116. There are other, smaller scale corrections by other types of interactions. When we consider all of these, the consensus theoretical value for the muon’s anomalous magnetic moment, i.e., its deviation from 2, or g – 2, published in 2020 is:

116,591,810(43) x 10-11

where the parenthetic figure is the error in the value. The reason this theoretical computation has an error is that some of the contributions, notably those of quantum chromodynamics (QCD), cannot be computed exactly, due to the analytic unsolvability of the integrals. Instead, numerical approaches must be used. The largest source of error is the leading-order hadronic vacuum polarization (LO-HVP) contribution. There are two major approaches to modeling this hadronic contribution. The more purely computational approach is lattice QCD, where we approximate space-time as a discrete lattice with finite volume, and use Monte Carlo sampling to select points for computation. (We must sample points randomly so that the error is not proportionate to the large number of variables.) The other approach is to use dispersive methods, combined with experimental data on electron-positron cross-sections. The latter approach, though it is more data-driven and less purely computational, has the advantage of a smaller error. Dispersive techniques tend to have lower values for the hadronic contribution, and thus more strongly deviate from the experimentally measured muon g-2, which at Brookhaven was:

116,592,089(63)x 10-11

The theoretical consensus value differs from the Brookhaven results by 279 x 10-11, or 3.7 sigma, where the standard error sigma is the theoretical and experimental errors added in quadrature.

On April 7, 2021, the Fermilab team announced the results of its first run. This was not expected to meet the 5-sigma threshold, since there are not yet enough statistics. That problem should be surmounted when the next runs are analyzed, which will take at least another two years. Even with the smaller statistics, the reductions in systematic error already resulted in a smaller total error than Brookhaven. The investigators were blinded to their high-precision clock’s time scale, and they agreed in their by-laws to publish the results no matter what, once unblinded (to eliminate bias by cherry-picking results). The dramatic unblinding took place at the webinar, as two non-investigators revealed the handwritten clock scale in a sealed envelope: 39997844. This allowed the instant computation of the anomalous magnetic moment:

116,592,040(54)x 10-11

This was slightly lower than Brookhaven’s result, though within the error of both experiments. It was still different from theory by 230 x 10-11, or 3.3 sigma. When the Fermilab results are combined with those of Brookhaven, reducing the statistical error, we get an experimental result of:

116,592,061(41)x 10-11

This is a difference of 251 x 10-11, or 4.2 sigma, from the 2020 consensus value. The probability of this discrepancy being due to chance sampling choice is 1/40,000. (The 5-sigma threshold would be 1 in 3.5 million.) This result is already strongly indicative of the likelihood of physics beyond the Standard Model.

Or is it? Recall we have the unusual situation where a theoretical value has significant error. The contributions to the 2020 value, as identified by Aida al-Khadra at the Fermilab webinar, are:

  • 116,584,718.9(1) x 10-11 quantum electrodynamic (QED) contribution
  • 153.6 (1.0) x 10-11 weak interaction contribution
  • 6845(40) x 10-11 hadronic vacuum polarization (HVP) contribution
  • 92(18) x 10-11 hadronic light-by-light (HLbL) contribution

The hadronic contribution has the largest error and the second-largest value, so improving this calculation has the most importance for confirming if the muon g-2 result really does contradict the standard model. Over the last 15 years, theoreticians reduced the error in the computed muon g-2, yet its value remained within the range of previous calculations.

On the same day as the result announcement, Chao et al. published an improved value of the hadronic light-by-light scattering contribution: 106.8(14.7) x 10-11. They used lattice QCD. Although this slightly increases the HLbL contribution, it is not enough to account for the discrepancy between theory and experiment.

More notably, Borsanyi, Fodor et al. published in Nature (again on April 7) a significant result on the leading hadronic contribution to the muon magnetic moment. While its error is larger than that of dispersive techniques, it is by far the smallest error yet achieved by ab initio QCD. Their value for the LO-HVP contribution is 7075(55) x 10-11. If their value is used instead of the consensus, we get a muon g-2 that is close to the Brookhaven result, and in near-perfect agreement with the combined Brookhaven-Fermilab result! Factoring in the HLbL by Chao et al., I get a revised theoretical value of:

116,592,055(57) x 10-11

which is within 0.1 sigma of the experimental value (BNL-Fermilab).

This would seem almost too good to be true, were it not for the fact that Borsanyi, Fodor et al. certainly could not have known the Fermilab value in advance, as this was not known even to the investigators themselves! Nonetheless, we must be wary of arbitrarily selecting computations that agree with experiment, even though these particular computations (Borsanyi; Chao) happen to be the best in their respective classes (Lattice QCD for HVP; HLbL). We would need grounds for preferring the improved lattice QCD models over the dispersion techniques, before deciding this issue. While Borsanyi et al. agree with experiment, they now have a 2-sigma discrepancy with other theoretical calculations, so this disagreement must be resolved.

If the Borsanyi, Fodor et al. (2021) result is confirmed, then there would indeed be no new physics indicated by the muon g-2 experiment, and the Standard Model would have withstood its most ultra-precise test yet. This would strongly suggest that our inventory of the fundamental particle and interaction types in nature is in fact complete.

Conspiracy Theories Can Kill

There have always been conspiracy theories, with greater or lesser degrees of plausibility, that are believed by at least a substantial minority of the population. These are generally harmless except when someone with perceived authority gives sanction to such a theory, emboldening people to act upon them. This is exactly what happened on January 6.

The mob that stormed the Capitol consisted of diverse groups, including survivalists, QAnon conspiracy theorists, militias, white supremacists, and anti-Semites. Some of the better prepared groups had murderous or otherwise terroristic intentions, while others were violent only in their unlawful entry and destruction of property. Many more, unaffiliated with any group, were simple thrill-seekers caught up in crowd euphoria, entering the Capitol because everyone else was doing it. (See Elle Reeve’s immersion reporting, CNN, January 7, 2021, 1:00 ET) What they all had in common was anger at a perceived injustice, motivated by a strong belief that the 2020 presidential election had been stolen.

It is not unprecedented for so many to believe a presidential election was stolen. Many still believe this was the case for the 2000 election, though Gore would have still lost under the recount rules its legal team accepted, if these had been implemented. (Chicago Tribune) Some historians hold that the 1960 election was swung to Kennedy by mob votes in Chicago and Texas, though this is unprovable. Nixon, believing this, nonetheless thought it prudent not to contest the election openly, both for his own political future and the good of the country, though he allowed his surrogates to pursue legal challenges that corrected the vote count slightly. There is nothing untoward about aggressive legal challenges to perceived electoral fraud or error. What is unprecedented is for the losing candidate to proclaim publicly that he was defrauded even after all legal challenges have failed.

Trump did not stop even there. He actually advocated blocking constitutional processes by extra-legal means. First, he encouraged state legislatures to refuse to certify the electors’ votes, or even to replace the electors outright. When that failed, he waged a weeks-long pressure campaign on Congress and his own vice president to contest or even reject the electoral votes received, remanding them to the states, that they might choose new electors. (Reportedly, he even considered invoking martial law, and he seems to still be getting advice on this as of yesterday.) Moreover, he urged his followers to rally at the Capitol that day to demand that this be carried out. When the vice president failed to “do the right thing,” many in the crowd naturally believed they had no recourse but storming the Capitol in order to reverse the “stolen” election.

Some of the better organized groups had come to this conclusion weeks earlier, as evidenced by their planning. This is why the role of Trump as an inciter was much more obvious in the preceding weeks than in the content of his January 6 speech. It was in the preceding weeks that he asserted unequivocally that the election was fraudulent, and that he would never concede. On January 4 in Georgia, he gave the most incendiary speech yet, calling the opposition Communists and Marxists who hate this country. By doing this, he was putting them beyond the pale, outside of the polity. This is the rhetoric that lays the groundwork for civil war. Between this and what was discussed on fora such as thedonald.win, it was obvious to me then that a civil war would be attempted. I believed it would fail immediately, based on the usual levels of security at the Capitol for such events.

What was shocking is not that the crowd attempted to storm the Capitol, but that they succeeded. Many past protesters would have loved to do the same if it were possible. Exactly how this security failure occurred remains to be fully investigated. Trump was unfortunate in this momentary success by the crowd, of which he was an avid spectator. By invading the Capitol and threatening the lives of the entire Congress and vice president, the riot rose to the level of insurrection. Trump did not denounce it until it was clear that it would end. Only in the aftermath did he acknowledge there would be a peaceful transition of power. The leader of a failed coup should not complain if the worst penalty he faces is being debarred from office.

If Trump did not exactly “lie” about the election being stolen, since he sincerely believes the falsehood, he is nonetheless guilty of a consistent disregard for truth, clinging to falsified claims that he wishes were true. An example is his repetition of the claim that 139% of people voted in Detroit, which is easily refuted by publicly available data. To believe the election fraudulent, we should have to believe that the notoriously mendacious Trump and his allies are the only truth-tellers, against a conspiracy including:

  • Judges in state and federal courts, including some Trump appointees
  • Election officials of both parties in various states
  • Most major news organizations
  • Numerous poll workers paid near minimum wage
  • Volunteer poll watchers
  • Federal intelligence agencies
  • The U.S. Postal Service

Anyone so conspiracy-minded is impervious to facts, since one can always add the source of any unfavorable facts to the list of conspirators. Such vast conspiracies are credible only to those lacking familiarity with how the election and result canvassing processes work.

All of Trump’s fraud claims are without factual foundation, which is why his lawyers had the good sense not to present most of them in court. There were some state practices that may have been erroneous in law, but misapplication of the law is not generally grounds for disenfranchising voters who followed the published rules. More importantly, no individual or state has standing to sue for such errors unless they can show actual, not speculative, harm.

The one Trump claim that had legal merit was the challenge of the Pennsylvania rule allowing late-arriving ballots, contrary to the legislative will. There were only 10,000 such ballots, not nearly enough to change the electoral outcome, nor did the late ballots break more favorably for Biden than the timely mail-in ballots. The conservative-leaning 3rd Circuit Court of Appeals correctly found the plaintiffs had no standing, and even if they did, they would not be granted relief, due to the lateness of the petition so close to the election. The late ballots were excluded anyway.

Since Trump’s strategy has simply been to conjecture that every conceivable mode of electoral fraud or error actually did occur, space does not permit the refutation of every single claim. That which is freely asserted may be freely denied with equal force. As for those claims which have at least some equivocal factual support, here are some fact checks:

In every election, there are minor instances of error and fraud, but quantity matters. There are no error-free elections, but the errors are generally much too small to affect the outcome with rare exceptions (e.g. Florida in 2000). Sometimes larger errors occur (in the thousands) on election night counts, but those are just first drafts for the purpose of notifying the public, not the official certified count. The initial count is followed by a thorough results canvassing process, during which the more substantive omissions can be identified. This happens in every election, and there was nothing unusual about this one. More importantly, the original records (ballots and machines) are kept available for inspection, so the data isn’t lost.

Enhanced voter ID and better signature verification would only guard against voter impersonation, which is known to be a statistically rare form of fraud. For fraud to occur on the scale Trump claims (hundreds of thousands of votes in a single state), there would need to be the complicity of election officials. Yet even states with Republican election officials have contradicted his claims.

Notably, Trump still repeated crackpot Dominion theories about removal or replacement of machines in his infamous call to the Georgia secretary of the state, along with other factless claims that had been already debunked publicly. In this call, Trump demonstrates himself to be an uninformed, uncritical thinker who only accepts “facts” in accordance with his preconceived conclusion that he could not have lost the election. Yet we are to accept his highly partial testimony over that of the election officials with access to primary data (all of which is monitored by observers of both parties).

More broadly, an examination of the county-by-county results in key areas is consistent with statewide and nationwide trends, adjusted for the known political demographics of each county. There are no stunning outliers in any major city. In fact, Trump did slightly better than expected in some cities, and fared better than expected with higher turnout, but had slightly weaker support than in 2016 in the suburbs, consistent with trends in recent years. That a president with approval ratings consistently below 50% should lose a tight election is hardly an indicator of fraud. Much less should we expect any Democratic conspirators to be kind enough to permit down-ballot Republicans to win their elections even in areas where Trump lost the presidential race.

Anyone still unpersuaded is likely impervious to argument, because they make the cognitive error of starting with a desired conclusion, and then accepting or rejecting data based on conformity with that conclusion. Such errors are common and generally harmless, except when they are actively and avidly reinforced by someone of the President’s stature and public influence. If a John Bircher or Lyndon LaRouche became President, the result would be comparably noxious to public discourse. The problem is more acute when the conspiracy in question is the purported crime of fraudulent government takeover. Thus we have the crazed spectacle of rioters engaging in an actual insurrection while believing themselves to be resisting an imagined one.

Our uncritical, deluded president undoubtedly provided much amusement at times, but foolishness stops being funny when people die, even if that consequence was not directly intended by the fool. There is something to be said for boring, policy wonky, slick-talking politicians. Perhaps the older, more genteel form of mendacity will have to suffice for now, if truth is too optimistic an ideal for democratic discourse. Ironically, the Trumpistas’ “attack on democracy” may itself have been symptomatic of a deep flaw in secular democracy itself, insofar as it makes the will of the people the arbiter of truth.