Philosophy

The Path to Gun Control in America Goes through Political Philosophy Thomas R. Wells Volume 2, Number 1 Spring 2019 DOI: 10.25335/PPJ.2.1-4 This essay argues that gun control in America is a philosophical as well as a policy debate. This explains the depth of acrimony it causes. It also explains why the technocratic public health argument favored by the gun control movement has been so unsuccessful in persuading opponents and motivating supporters. My analysis also yields some positive advice for advocates of gun control: take the political philosophy of the gun rights movement seriously and take up the challenge of showing that a society without guns is a better society, not merely a safer one. Abstract 1. Introduction Every time there is a mass killing in America-at a school, a place of worship, an open air-concert-a familiar ritual plays out. Gun control and gun rights advocates spring to the airwaves to present their cases, fail miserably to persuade anyone who didn't already agree with them, and leave everybody on both sides fuming with even more indignation than before. It is a sad picture of democratic failure, especially when set beside successful national conversations-such as over civil rights or gay marriage-in which large majorities changed their minds because of the arguments they heard. It is easy enough to connect this failure to America's general turn to a partisan politics more concerned with which political tribe you identify with than the exchange of ideas and arguments about the public good, or to cite the pernicious influence of the National Rifle Association's (NRA's) election spending on Republican primaries. However, such explanations are both too easy and rather unhelpful. I think I have something better to offer-better both because it embodies a more idealistic view of democracy and because it is more likely to be politically successful. Of course it is up to Americans to decide what kind of society they should have-not philosophers, and certainly not foreign ones like me. Indeed, part of my argument is that the place of guns in America has to be decided politically-by the people-and not by appeal to the special authority of sacred constitutional principles, or social science, or even philosophy. Philosophers' pronouncements of truth and rightness have no special authority over politics, nor should they. What philosophical analysis can offer are new perspectives and argumentative resources by which a political debate such as this one might be freed from its toxic stalemate. So what does my philosophical perspective come down to? First, a diagnosis: America's decades long national argument about guns is so pernicious and acrimonious because it is not just a policy debate about what the government should do to best fix some problem (like an opioid epidemic or car accident fatalities). It is also about what kind of politics to have: how citizens should relate to each other and the state. Politics with a capital P. This ideological dimension is explicit in the arguments of the gun rights movement but has been largely neglected by the other side. Second, some positive advice for the advocates of gun control: Talk about civic values is not a squishy second best to the objective statistical facts of gun violence. It is an essential ingredient for building a committed political majority. Winning this debate requires showing that a society without guns is a better society, not merely a safer one. Wells PPJ 2.1 (2019) 2 2. Why the Public Health Argument Is Not Enough America's gun control movement relies extensively on a public health argument for saving lives that has so far failed to achieve political results. First, because it doesn't connect to the values arguments of the gun rights movement, it doesn't persuade opponents to change their minds. In fact, it appears to increase the ardency of their opposition by adding the insult of being ignored to the original disagreement. Second, its technocratic character doesn't much engage the values of even those voters who are persuaded by it. Thus, the public health argument has so far failed to make gun control a political priority for its supporters; for example, by motivating them to turn out in primaries to vote candidates up or down on that single issue.1 The combined result is to allow a political minority of ardent, values-motivated gun rights supporters to keep winning legislative victories. What makes guns special is that they are an excellent killing technology. They are extremely good at transforming an intention to kill into its achievement. This is what makes them dangerous according to the public health argument. But it is also exactly what makes them empowering according to the gun rights movement. Thus, right from the start the public health case seems unlikely to win over principled opponents of gun control: those who see other-civic-values at stake besides lives. However, even for those who see negligible virtue in gun ownership, the fact that guns kill lots of people does not seem very politically compelling. It turns out that this is a general problem with public health arguments, which face the challenge of translating statistical facts about society into reasons for action by individuals who have many other calls on our attention. 1. As in the case of state senators who lost their Democratic majority seats for supporting gun control after the Aurora movie theatre shooting, see Firmin DeBrabander, Do Guns Make Us Free?: Democracy and the Armed Society (New Haven, CT : London: Yale University Press, 2015), xii; Sean Trende, "What Colorado's Recall Results Mean for Dems," RealClearPolitics, September 11, 2013, http://www.realclearpolitics.com/articles/2013/09/11/what_colorados_recall_results_mean_for_dems_119913.html. In 2015, around 36,000 people were killed by guns in America (of which 13,000 were homicides, 1,000 were accidental deaths and the rest were suicides).2 That looks like a big number, but then America is a big country in which 2.7 million people die every year. The 36,000 gun deaths represent a little over 1 percent of deaths (0.5 percent if we limit the statistics to gun homicides). To most Americans that level of risk just isn't that big a deal. If this attitude seems blasé, it is at least consistent. More than twice as many Americans die from diabetes as from guns, yet that fact has failed to prove the political case for regulating major contributors to that illness like sugary soft drinks. Even successful public health arguments can take decades to gain political traction (as in the case of seat-belts and other automobile safety features), and some remain decades from full implementation (as in the case of tobacco). The basic problem is that these risks are only some of the many things that people have to worry about as we go about our lives. Therefore, they do not stand out as a political priority and government action to reduce them can be successfully opposed by more motivated political minorities or vested interests. The political significance problem is compounded by the role of other factors in causing gun violence. Social scientists have shown pretty convincingly that a higher prevalence of guns correlates with higher homicide rates, other things being equal. Yet this fact is underwhelming in the larger context of a historic decline in violence. The rollback of gun control laws by judges and Republican legislators began in the 1980s, but the murder rate in America has actually fallen by half since then, back to what it was in 1950.3 The reason is not that the statisticians are wrong but that access to guns is only one piece of the problem of gun violence. Rates of violence have a lot more to do with social conditions and political institutions than with particular technologies.4 Ready 2. CDC, "Deaths: Final Data for 2015," National Vital Statistics Reports, 66, no. 6 (2017): 75. In addition, many survivors of gun violence suffer lifelong debilitating injuries. 3. CDC, "Table 32: Death Rates for Homicide, by Sex, Race, Hispanic Origin, and Age: United States, Selected Years 1950–2013," Health, United States, 2014 – Individual Charts and Tables, 32, accessed August 3, 2018, https://www.cdc. gov/nchs/hus/contents2014.htm. 4. Richard G. Wilkinson and Kate Pickett, The Spirit Level: Why More Equal Societies Almost Always Do Better (Allen Lane, 2009); Rachel Kleinfeld, A Savage Order: How the Wells PPJ 2.1 (2019) 3 access to illegal handguns makes this violence more lethal, but its main drivers are failures of social justice that America, among rich democracies, seems particularly bad at addressing. This is reflected in the geographic and demographic concentration of America's gun violence. Most of middle-class (white) America is nearly as safe as Western Europe, but some areas of concentrated poverty and hopelessness within particular cities like Chicago, Detroit, and Baltimore, have the murder rates of Central America.5 This poses a challenge to the public health argument insofar as it is structured as an appeal to people's self-concern to protect their own lives (and those of their loved ones), since it is really only a minority of voters whose life-expectancy would be much improved by expanded gun control. To ask voters to care about reducing the suffering that gun violence brings to far away fellow citizens requires appealing to broader civic values. It means engaging the ideological debate about what a just society should look like. A similar point can be made about suicides, which make up the great majority of deaths by gun. The public health argument is that impulsivity is a major factor in suicide, and that guns, like the Golden Gate Bridge, greatly facilitate the transformation of suicidal impulses into death. If fewer people kept guns at home, fewer suicide attempts would succeed and this would mean many lives saved because many suicide survivors do not repeat the attempt. Again, though statistically sound, it is not surprising that such arguments fail to generate political traction. First, suicide is not a source of fear in the way that murder is, because it seems like something in our control rather than a risk to which we are involuntarily subjected. Second, the issue of gun suicides seems irrelevant to the central political debate about gun control. Preventing suicide by gun would seem to require either more or less invasive- but anyway quite different-government interventions than those designed to prevent mass killings or to reduce the gun murder rate. World's Deadliest Countries Can Forge a Path to Security (New York: Pantheon, 2018). 5. FBI, "Table 6: Crime in the United States by Metropolitan Statistical Area, 2017," Crime in the United States 2017 (Federal Bureau of Investigation, 2018), https://ucr.fbi.gov/ crime-in-the-u.s/2017/crime-in-the-u.s.-2017/tables/table-6. Either Americans shouldn't be allowed to keep guns in their own houses (which goes much further than any constitutionally plausible gun control measure), or they should be encouraged to reduce this risk for themselves via a public information campaign (which is not most people's understanding of gun control). The political failure of the public health argument can also be shown the other way around. The main driver of America's stop-start national debate about guns are the mass killings that dominate the news cycle every few weeks. These events do have political significance (as I will explain below), but not because they support the public health case for gun control. The media attention makes it seem like there are a lot of them, but actually there have only been 105 mass killings since 1982.6 Perhaps they are becoming more frequent (it is hard to extrapolate trends from such small numbers) and perhaps they are more deadly thanks to the availability of militaristic weapons like the AR-15. But, even so, a few dozen deaths per year spread among a population of 330 million are statistically irrelevant to public health. In conclusion, it is true that guns kill (and maim) lots of people in America, and that many of those people would not have died if access to guns were more controlled (with practical measures like a universal registry to track guns used in crimes back to those who bought them). But truth is not the same thing as political significance. Gun control advocates have put their faith in the special power of facts to convince (from the Latin to overcome/ conquer) at the expense of making a broader values case for gun control. This has left their supporters undermotivated and their opponents free to frame the debate around their own ideological vision of what kind of society America should be. 3. The Gun Debate Is About What Kind of Politics to Have My criticism of the public health argument may have some readers worrying that I am just another NRA stooge claiming that facts don't 6. Deanna Pan, "US Mass Shootings, 1982-2018: Data from Mother Jones' Investigation," Mother Jones (blog), accessed November 7, 2018, https://www.motherjones.com/ politics/2012/12/mass-shootings-mother-jones-full-data/. Wells PPJ 2.1 (2019) 4 matter. But I intend it in another way. By showing the political limitations of the public health case, I hope to persuade the proponents of gun control to give more attention to the values case for gun control. That means getting clearer about your own vision of citizenship and government-a political philosophy of peace, not mere safety-and recognizing and responding to the philosophical arguments made by gun rights advocates. Specifically, I believe that an underlying motivation on both sides of this debate is a subjective feeling of vulnerability as citizens, which is something quite different from objective actuarial risk to life and cannot be adequately expressed in its technocratic language. Americans worry about what their armed fellow citizens might do: about arguments over parking spaces turning into gunfights; about their son getting shot by a racist fool for wearing a "threatening" hoodie; about maniacs with military grade weapons appearing on their subway car, or in shopping malls, or at their workplaces. This subjective feeling deserves to be taken seriously. In this light, mass killings matter not because they present a significant public health risk to our lifespans to be analyzed like car accidents or cigarettes but because they are deliberate attacks on our society to be analyzed like terrorism. Mass killers are nearly always loners lacking the political organization and agenda of regular terrorists. But they nevertheless engage in symbolic violence against civic institutions, such as schools, that is particularly terrifying exactly because it is so impersonal-the victims of their violence are merely interchangeable extras in the screenplay they are trying to produce.7 Mass killings are not interpersonal squabbles but deliberate attacks on the peace itself, and this is something for which citizens have the right to hold their government responsible. It is a truism of political philosophy that a necessary (though not sufficient) condition for the legitimacy of any state is its ability to provide its citizens with freedom from fear. But there are different routes to this. Some believe that 7. Randall Collins, "Micro-Sociology of Mass Rampage Killings," Revue de Synthèse 135, no. 4 (December 1, 2014): 405– 20, https://doi.org/10.1007/s11873-014-0250-2. they can only overcome this feeling of vulnerability with the right to carry a gun of their own (hence the spike in gun sales after every mass shooting). Others want the freedom to live as civilians rather than in a state of militaristic hypervigilance always ready and alert to respond to deadly attack. There are thus two views of government and citizenship in play. In one political philosophy, the job of government is to enable good citizens to solve their own security problems, to defend their rights and liberties for themselves.8 In the other, government is expected to solve such problems for us, to guarantee security directly by preventing or containing threats. There is a reason most gun control advocates are on what passes for the Left in American politics and are often mocked as "European." This is fundamentally a dispute about how citizens should relate to the state, and especially a dispute between the state as a guarantor of security or as a guarantor of liberty. 4. The Political Philosophy of the Gun Rights Movement Banning guns would certainly save some American lives. But so would banning cars. Of course, no one proposes that because it is generally agreed that cars provide benefits that outweigh their dangerousness. (Even environmentalists who refuse to drive a car for moral reasons aren't motivated by road deaths.) It is a symptom of their political blindness that gun control advocates refuse to admit the obvious political fact that guns have benefits as well as costs. This brings me to what guns do for people. Of course they do various things. They are beautifully made objects that also, as the Democrat voting gun-lover Dan Baum puts it, like sky-diving give off "a little contact high from the Grim Reaper."9 But they also make people feel more powerful and thus, indirectly, more in possession of their political rights as citizens: less willing to put up with being over-managed 8. Jeffrey Snyder, "A Nation of Cowards," The Public Interest, Fall 1993, https://www.nationalaffairs.com/public_interest/detail/a-nation-of-cowards. 9. Dan Baum, "Happiness Is a Worn Gun," Harper's Magazine, 2010, https://harpers.org/archive/2010/08/happiness-is-a-worn-gun/?single=1. Wells PPJ 2.1 (2019) 5 and under-respected by the state. Dan Baum again: Going armed has connected me with an entire range of values I didn't use to think much about-self-reliance, vigilance, muscular citizenship-and some impulses I'd rather avoid, like social pessimism and irrational fear. It has militarized my life; all that locking and loading and watching over my shoulder makes me feel like a bit player in the perpetual global war in which we find ourselves. There's no denying that carrying a gun has made my days a lot more dramatic. Suddenly, I'm dangerous. I'm an action figure. I bear a lethal secret into every social encounter.10 The gun rights movement seems to me to reflect a heroic vision of citizenship, and hence of society, that taps into an enduring strain of rugged individualism in America's political psychology. Most Western polities are characterized by an overwhelming emotional and institutional dependence on a beneficent, all seeing, all powerful government. This plays a significant role in American politics too. (Just look at how Americans from all points on the political spectrum responded to 9/11 by demanding the Federal government do whatever it took to make them feel safe again). However, America also has a long tradition inspired by the rebellious individualism of a seventeenth-century English political philosopher named John Locke.11 This emphasizes the enduring independence of the individuals who make up a political society, including their right to revolution if the state fails to respect their "self-evident" natural rights to life, liberty, and property. John Locke may not be a household name, but his ideas are part of America's DNA. His natural rights arguments and assumptions permeate America's founding documents and the logic of the Second Amendment itself, and these values have been resurgent on the Right since the Reagan revolution. I want to emphasize 10. Dan Baum, "Happiness Is a Worn Gun," Harper's Magazine, 2010, https://harpers.org/archive/2010/08/happiness-is-a-worn-gun/?single=1. 11. Alex Tuckness, "Locke's Political Philosophy," in The Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta (Stanford University, 2018), https://plato.stanford.edu/archives/sum2018/entries/locke-political/. here that this is an interesting and even attractive political philosophy. It deserves to be considered seriously and respectfully. In the Lockean vision of society as a social contract, government is seen as a convenience rather than a necessity; an institution created by and dependent upon the people's consent rather than the other way around. Government is worth having because it allows some collective action problems to be overcome, thereby enhancing the provision of law and order and other public goods that make everyone better off. But otherwise it should get out of the way so that people can get on with their own business. It is a device for securing and extending the liberties of citizens rather than advancing aggregate social welfare (or social justice). Even when limited to its proper domain, faith in government is distinctly limited. Government is analyzed as any other institution, a vested interest whose powers can be dangerous as well as useful to society. The wide distribution of political power throughout American society- including the power of violence conferred by civilian gun ownership-may be socially inefficient, but it is supposed to reduce the danger of tyranny. If guns are sometimes used against society, that may be a price worth paying to maintain a free society. So, what is the role of guns in this political philosophy? Contra certain Second Amendment fantasists, armed citizens do not deter government tyranny by putting a real power behind the people's theoretical right to revolution. Nevertheless, gun rights do reflect and support a different vision of the relationship between citizens and the state. Having in one's pocket a device capable of a miniature whirlwind of mayhem makes people feel more like a force with which to be reckoned. Unlike the "sheeple" who have reduced themselves to pathetically pleading for the government to save them from bad guys, these citizen heroes willingly take up their share of responsibility to protect themselves and others in society. Such faith in their own powers and abilities spills over into political citizenship. By making citizens feel less dependent on the institutions of the state to guarantee their freedom and security, guns allow them to believe that they are in a position to bargain with the state rather than to submit, Wells PPJ 2.1 (2019) 6 like frightened sheep, to its authority to decide what is best for them. The gun rights movement is entwined with a philosophical view of the soul of America. Defeating it will require more than the recitation of actuarial statistics. In the remainder of this essay I outline two complementary paths that may be more successful. 5. Engaging with the Philosophical Debate Gun rights activists talk constantly about their political philosophy. I suggest doing the same. I do not suppose that all gun rights supporters are open to such philosophical debate, or even that they recognize John Locke as the original source of many of their views. But assuming the least and the worst of gun owners has become troublingly common in this debate. However hard it is to persuade people with whom one fundamentally disagrees, it becomes even harder if they feel that what they say isn't being taken seriously. Making the philosophical values case for gun control has three potential pay offs. First, some opponents may be persuaded by superior arguments, or at least recognize weaknesses and limits to their own previously unchallenged beliefs. Second, it is the respectful, democratic thing to do and that in itself may draw some of the poison from the debate and lower the vehemence of opposition. (In the face of widespread denigration, a kind of solidarity is emerging among civilian gun owners united by a feeling of membership of a misrecognized and endangered tribe.12) Third, those who already accept that guns are more dangerous than they are worth, but who aren't much motivated by wonkish public health arguments, may be more motivated to vote for a vision of a better society. Gun control advocates should articulate and defend their own vision of political society and citizenship. What do they believe in besides slightly increased life-expectancy? Until now their opponents have been free to portray both sides of the debate: a truly American (Lockean) 12. Dan Baum, Gun Guys: A Road Trip (New York: Vintage, 2013). society of free people versus an un-American tyranny of frightened sheeple.13 They might-to take up one example-explain that progressivism is a respectable form of liberalism-a home-grown pragmatic form developed by the American philosopher John Dewey-and a more effective partner for advancing the freedoms of individuals than a seventeenth-century Englishman like Locke. The pragmatic view I have in mind embodies a healthy and heartily American skepticism of the state without lapsing into the paranoid cynicism of some contemporary followers of Locke. For example, while progressives see the state as a partner in society's projects of self-improvement, this is because of its special powers to make laws and raise money; not because it has some special faculty of judgement that supersedes that of the citizenry. Government is a partner not an overlord; valued for what it can help achieve in terms of problem-solving, not because it deserves awe and respect as the constitutional sovereign, representative of the true will of the people, Hobbesian savior, or what have you. Pragmatism requires an experimentalist seewhat-works attitude rather than merely applying one's preferred theory of society to every problem, giving the same answer to every question. The law and order approach that began in the 1980s and is now finally being rolled back was predicated on such a theory, a foolish one that divided the world into bad guys and good guys and assumed bad guys could only be controlled by deterrence. It abjectly failed to address the circumstances of violence and the right of citizens to be free of it. A pragmatic politics would have demanded more evidence that it was working before expanding such draconian powers of the state against its people, and it would have looked continuously at how individual policies, from the overarching war on drugs to minimum sentencing and racial profiling, might be reformed and improved. Moreover, while a pragmatic politics respects what works, and thus the known quantity of inherited institutions, it has no particular respect for tradition in itself. Even institutions and laws that successfully solved or prevented problems 13. As in this classic example of gun rights literature: Snyder, "A Nation of Cowards." Wells PPJ 2.1 (2019) 7 in the past-such as the Second Amendment defense against tyranny and the return of the English-may end up causing new problems if they do not evolve to fit changing conditions and needs. Properly explained, progressivism seems to satisfy many of the concerns that draw Americans to Locke's philosophy of defending individual rights against the state. The unpopularity of such pragmatism on the Right seems to relate mainly to disagreement about what counts as a problem in the first place (for example, is the gender pay gap really something that society needs to solve?). But that is a normal political disagreement between those more or less satisfied with the status quo, not a disagreement about how politics itself should go. However, this is not the end of the argument. For it seems to me that despite Locke's central place in the theory of America, his ideas have not actually done much service. Recall that Locke's account is most associated with individuals hanging on to their personal rights (to life, liberty, and property) even while agreeing to live under a government. Critics of progressive liberalism complain that a government dedicated to solving social problems will often trample over the rights of individuals that stand in the way of increasing aggregate welfare. We need individual rights to prevent such excesses, and therefore we need Lockean constraints and a muscular citizenry that will insist on them. The first problem with this claim is that, however inspirational Locke may have been for its founding fathers, the actual history of American government doesn't hew very closely to Lockean values and constraints. The American social contract was apparently compatible with the genocides of Native Americans, economic dependence on racial slavery, the suppression of women, mass conscription in wars of choice, moralistic laws against contraception and homosexuality, and so on. A more immediate problem is that a muscular citizenry has become a goal in its own right rather than merely a means to restrain government. And that is a mistake incompatible with a civilized society. Where every citizen must retain responsibility for upholding the law and judging the use of deadly force, every individual must be a hero or else a victim (or else a villain) in a pre-political Homeric world in which society is no more than a band of heroes. Hence the strange belief-which appears central to the gun rights movement; see for example the popularity of stand your ground laws-that the world is divided into good guys and bad guys, and the government has no right to interfere in what the good guys get up to. This is neither attractive nor feasible nor Lockean. A society fit only for heroes is not a fit society to live in, but rather resembles a nostalgic fantasy of movies of the Wild West.14 Still, a society of sheeple uninterested in anything but getting on with their own small lives is an appalling prospect. There should be heroes, citizens willing to stand up for more than themselves. Fortunately, the choice is not binary. The second path to advancing gun control is to disentangle guns from the ideal of strong citizenship. 6. Strong and Healthy Citizenship Let's start by uprooting the myth. Neither handguns nor even those military grade AR-15s are going to stop the US army from crushing you if that's what it has a mind to do. (Fatuous comparisons with terrorist insurgencies like ISIS or the Taliban will not do; unless your idea of strong citizenship is extorting concessions from the US government by threatening a terrorist campaign against fellow Americans.) Gun rights may induce a feeling of political significance and that feeling may be of significant power. Yet, the first thing to note is that this feeling is founded on a delusion as great as that of the sports enthusiast who looks up from his bowl of Buffalo wings to shout instructions at the football players on the TV screen. And, second, gun rights, like Buffalo wings, introduce new health problems of their own into society. This is because, besides fostering political assertiveness in defense of classical liberal views of the state, extensive gun ownership also undermines the very society it is supposed to defend against tyrannical government. Gun rights introduce a new fear and distance 14. For an extended analysis of the failure of the "Lockean" justification of gun rights on its own terms, see DeBrabander, Do Guns Make Us Free? Wells PPJ 2.1 (2019) 8 between fellow citizens, whether they choose to arm themselves or not. As the philosopher Firmin DeBrabander argues, an armed society is a polite society not because everyone in it recognizes that others deserve respect, but only because everyone is afraid to say or do anything that might be considered threatening: Our gun culture promotes a fatal slide into extreme individualism. It fosters a society of atomistic individuals, isolated before power-and one another-and in the aftermath of shootings such as at Newtown, paralyzed with fear. That is not freedom, but quite its opposite.15 Here the feeling of vulnerability to guns comes back into political significance. Guns were supposed to protect society from threats, including from its own government. But instead they undermine its health from within, weakening civil society and leaving us unable to relate to each other except via the legalistic forms controlled by the state or else down the barrel of mutual suspicion, as in a spaghetti Western. The great irony of gun rights is that they actually make citizens more dependent on the state and less able to resist it because we lose the sense of solidarity that a civilian society so readily supports. This is a different conception of public health than the aggregation of statistics about individuals' risk of death. It directly concerns the political power of citizens that gun rights activists claim to be defending, the very benefit they claim makes guns worth having. But there is one more line of positive argument to make. For, fortunately, gun rights are not the only path to strong citizenship. If heroic citizenship is about taking up one's share of responsibility to protect self and others from tyrannical lawlessness or legalized tyranny, then America's own history shows that gun rights are not necessary for it. The civil rights movement is probably the most impressive demonstration of the power that citizens can mobilize against tyrannical government, but there are plenty of other more recent models of strong citizenship, from the progressive 15. Firmin DeBrabander, "The Freedom of an Armed Society," New York Times, December 16, 2012, sec. Opinion: The Stone, https://opinionator.blogs.nytimes.com/2012/12/16/ the-freedom-of-an-armed-society/. liberalism of #blacklivesmatter to the classical liberalism of Edward Snowden. These movements succeed, when they do, by relying on the social relations that gun rights undermine. They do not shout up at the government demanding to get their way or else. Instead they bypass the government and address the people themselves. "Here's a problem," they say, "and this what we think should be done. If you agree let's go tell the government what to do together." 7. Conclusion I share the intuition of many Americans that there is something very wrong with a society in which peace is supposed to be achieved by each individual's fear of their fellow citizens' capability for deadly force. I understand their appall at the gun rights pundits lining up on mainstream media after every atrocity to somberly declare that the only solution to bad guys with guns is more good guys with concealed carry permits. This is not the kind of society I would want to live in either. But I do not think that what is wrong about an armed society is really captured by the actuarial risks it imposes on individuals. And I worry that the narrowness of the public health framing crowds out powerful values arguments; for example, about the damage that widespread civilian gun ownership inflicts on the civic virtues of a free society. This is a harm that at least a large proportion of believers in gun rights might be persuaded to take seriously, since it undermines the very integrity and resilience of society-and thus its independence of government-that is central to their political philosophy. Some gun control advocates may still be skeptical. Science already tells us the objective truth about the dangers of guns. Why give up that advantage to talk about differences of philosophical opinion on an equal footing with gun rights enthusiasts? I have argued that having science on our side may not be such a great political advantage if it narrows the kind of arguments we make and their appeal. It would do no harm and probably much good if at least some proponents of gun control added to the public health case by explaining why an Wells PPJ 2.1 (2019) 9 unarmed America would be a better as well as a safer society. ACKNOWLEDGMENTS I am indebted to my two PPJ reviewers, Firmin DeBrabander and Ted Alcorn, and to my colleague Nathan Wildman, for their criticism and helpful suggestions. BIBLIOGRAPHY Baum, Dan. Gun Guys: A Road Trip. New York: Vintage, 2013. ---. "Happiness Is a Worn Gun." Harper's Magazine, 2010. https://harpe r s . o r g / a r c h i v e / 2 0 1 0 / 0 8 / h a p p i ness-is-a-worn-gun/?single=1. CDC. "Table 32. Death Rates for Homicide, by Sex, Race, Hispanic Origin, and Age: United States, Selected Years 1950-2013." Health, United States, 2014 – Individual Charts and Tables. Centers for Disease Control and Prevention: National Center for Health Statistics, 2014. https://www.cdc.gov/nchs/data/ hus/2014/032.pdf. CDC. "Deaths: Final Data for 2015." National Vital Statistics Reports 66, no. 6, (2017): 75. Collins, Randall. "Micro-Sociology of Mass Rampage Killings." Revue de Synthèse 135, no. 4 (December 1, 2014): 405–20. https://doi. org/10.1007/s11873-014-0250-2. DeBrabander, Firmin. Do Guns Make Us Free?: Democracy and the Armed Society. New Haven, CT: Yale UP, 2015. ---. "The Freedom of an Armed Society." New York Times, Dec. 16, 2012, sec. Opinion: The Stone. https://opinionator.blogs.nytimes.com/2012/12/16/the-freedom-of-anarmed-society/. FBI. "Table 6: Crime in the United States by Metropolitan Statistical Area, 2017." Crime in the United States 2017, 2017. https://ucr. fbi.gov/crime-in-the-u.s/2017/crime-in-theu.s.-2017/tables/table-6/table-6. Kleinfeld, Rachel. A Savage Order: How the World's Deadliest Countries Can Forge a Path to Security. New York: Pantheon, 2018. Pan, Deanna. "US Mass Shootings, 1982-2018: Data from Mother Jones' Investigation." Mother Jones (blog), Feb. 15, 2019. https:// www.motherjones.com/politics/2012/12/ mass-shootings-mother-jones-full-data/. Snyder, Jeffrey. "A Nation of Cowards." The Public Interest, Fall 1993. https://www.nationalaffairs.com/public_interest/detail/anation-of-cowards. Trende, Sean. "What Colorado's Recall Results Mean for Dems." RealClearPolitics, Sept. 11, 2013. http://www.realclearpolitics.com/articles/2013/09/11/what_colorados_recall_results_mean_for_dems_119913.html. Tuckness, Alex. "Locke's Political Philosophy." In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. Stanford University, 2018. https://plato.stanford.edu/ archives/sum2018/entries/locke-political/. Wilkinson, Richard G., and Kate Pickett. The Spirit Level: Why More Equal Societies Almost Always Do Better. Bristol: Allen Lane, 2009. CONTRIBUTOR INFORMATION Thomas R. Wells teaches philosophy at Tilburg University in the Netherlands. His research focuses on practical ethics, on using the resources of academic philosophy to solve real world problems. The Path to Gun Control in America Goes through Political Philosophy Ted Alcorn Volume 2, Number 1 Spring 2019 DOI: 10.25335/M5/PPJ.1.1 A Public Holistic Response America's great gun debate is about more than guns, and Thomas Wells sets out to examine its philosophical dimensions. As someone who worked at the debate's white-hot core for years, I greatly appreciate his contribution. His focus on the ideas underpinning the debate, necessarily a critique of the messaging and positions adopted by the gun violence prevention movement, is refreshing, though at times I think slightly misplaced. For example, in drawing a contrast between what he sees as the dominant "public health argument" for gun violence prevention and a "values" argument that makes the case in philosophical terms, he goes too far in minimizing how consequential gun violence is for the American public and the power inherent in acknowledging it. "Truth is not the same thing as political significance," he writes-but preserving and protecting life is moral high-ground, and many committed advocates draw their sense of righteousness from the knowledge they are standing on it. Likewise, I think many observers fail to appreciate the advances being made by today's gun violence prevention advocates. In my observation, the relative power of the gun violence prevention movement has grown according to the resources available and the institutions for effectively employing them (which does not corroborate-though need not contradict-Wells's thesis about the centrality of values). There has been a sea-change in these two factors over the last decade, as private and public funders have poured resources into a once-starved movement, fueling durable organizations that are fostering activity in university laboratories, legislative chambers, and communities. And sweeping changes in state law and a new tenor in the halls of Congress are the undeniable results. That the process is slow-perhaps too slow, disastrously slow-is not enough to declare this a "democratic failure," or today's activists "undermotivated." Nevertheless, I do not dispute Wells's main assertion that the gun violence prevention movement could-and should-do a better job explaining how its recommendations will yield "a better society, not merely ... a safer one." Marc Solomon, who helped lead the marriage equality movement, wrote that they won by convincing people that, "in order for them to live up to their own value system," they needed to adopt a new position on marriage.1 Gun violence prevention advocates would be wise to engage in similar thinking. Wells's proposals of how to do so are a good place to start. BIBLIOGRAPHY Becker, Amanda. "U.S. House Approves Expanded Background Checks for Gun Sales." Reuters, 27 Feb. 2019. https://www.reuters. com/article/us-usa-guns-congress/u-shouse-approves-expanded-backgroundchecks-for-gun-sales-idUSKCN1QG2VD. Moms Demand Action. "Gun Politics in 2018 and What's Ahead in 2019." Everytown.org, 12 Dec. 2018. https://everytown.org/documents/2018/12/gun-politics-in-2018.pdf/. 1.Marc Solomon, Winning Marriage: The Inside Story of How Same-Sex Couples Took On the Politicians and the Pundits and Won (Lebanon, NH: UP of New England, 2014), 232. Alcorn PPJ 2.1 (2019) 11 Solomon, Marc. Winning Marriage: The Inside Story of How Same-Sex Couples Took on the Politicians and the Pundits and Won. Lebanon, NH: UP of New England, 2014. Ted Alcorn is a researcher, journalist, and educator with expertise in gun violence prevention policies and programs.


A Case for Lorentzian Relativity

Philosophy

Foundations of Physics manuscript No. (will be inserted by the editor) A case for Lorentzian relativity Daniel Shanahan 18 Sommersea Drive, Raby Bay, Queensland, Australia, 4163 email: email@example.com The date of receipt and acceptance will be inserted by the editor Abstract The Lorentz transformation (the LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de Broglie, regarding the underlying unity of matter and radiation. To show the nature of these changes, a massive particle is modelled as a standing wave in three dimensions. As the particle moves, the standing wave becomes a travelling wave having two factors. One is a carrier wave displaying the dilated frequency and contracted ellipsoidal form described by the LT, while the other (identified as the de Broglie wave) is a modulation defining the dephasing of the carrier wave (and thus the failure of simultaneity) in the direction of travel. The superluminality of the de Broglie wave is thus explained, as are several other mysterious features of the optical behaviour of matter, including the physical meaning of the Schrödinger Eqn. and the relevance to scattering processes of the de Broglie wave number. Consideration is given to what this Lorentzian approach to relativity might mean for the possible existence of a preferred frame and the origin of the observed Minkowski metric. Key words Special relativity * Covariance * de Broglie wave * Dirac equation * Schrödinger equation 1 Introduction For the student of physics, there comes a moment of intellectual pleasure as he or she realizes for the first time how changes of length, time and simultaneity conspire to preserve the observed speed of light. Yet Einstein's theory [1] provides little understanding of how Nature has contrived this apparent intermingling of space and time. 2 Daniel Shanahan The language of special relativity (SR) may leave the impression that the Lorentz transformation (the LT) describes actual physical changes of space and time. Thus we have Minkowski's confident prediction that, Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows and only a kind of union of the two will preserve an independent reality [2]. The impression that the LT involves some physical transmutation of "spacetime" might seem consistent with the change of that nature contemplated in general relativity (GR). But in GR a change in the metric affects in like manner all that occupies the region of space in question. In SR it is necessary to distinguish what actually changes from what is merely "observed"1 to change. Consider two explorers, who we will call Buzz and Mary. They had been travelling, in separate space ships, side by side, in the same direction. But Buzz has veered away to explore a distant asteroid. Mary concludes from her knowledge of the LT that time must now be running more slowly for Buzz and that he and his ship have become foreshortened in the direction that Buzz is travelling relative to her. Buzz observes no such changes either in himself or in his ship. To Buzz, it is in Mary and her ship that these changes have occurred. Buzz is also aware that events that he might previously have regarded as simultaneous are no longer so. No relevant physical change has occurred in Mary or her spacecraft. She has not accelerated. She is in the same inertial frame as before. Nor (ignoring gravitational effects, in this case negligible) has any actual, as distinct from observed, change occurred in the space through which the travellers are moving. To suggest otherwise would be to suppose that space is able to contract in one way for one particle and in a different way for another moving relatively to the first, albeit that the two (or at least their correspondingly contracted fields) could be occupying the very same piece of space. Even Buzz will have realized, as he observed the contraction of the constellations, that the stars were not in fact closing ranks around him. A change of inertial frame has occurred for Buzz and his spacecraft. It must be this change that is the source of the changes that the two explorers are observing. It is not diffi cult to understand that Buzz's change of velocity may have caused a change in him that has affected how he is perceived by Mary. But it must also be the case, since nothing else has changed, that it is this same change in Buzz that has caused him to consider the (in fact unchanged) Mary in a different light. Buzz will not sense that he has changed. After all everything in his inertial frame will have changed in like manner. Unlike the carousel rider 1 "Observed" is used here, in the sense conventional in SR, to denote not what is "seen" at a particular instant, but what the observer considers to have occurred at that instant. What is seen includes light from events that occurred progressively earlier the further they were away, an effect here irrelevant. A case for Lorentzian relativity 3 who sees the fairground whirling about her, but is under no illusion as to what is really happening, Buzz has suffered relativistic changes in his vital processes, and lost the means of discernment. For Buzz the LT will describe very well his altered perspective. But it would be as inappropriate to explain length contraction, time dilation and loss of simultaneity as resulting from a physical transformation of space or spacetime as it would be to describe the rotation of an object in 3-space as a rotation of space rather than a rotation in space. While one might wish to elevate the discussion by reference to differential manifolds, the spacetime continuum, or the Minkowski metric, the curious effects described by the LT must be explained by a change that occurs in matter as it suffers a "boost" from one inertial frame to another. Indeed the Minkowski metric should itself be seen as a kind of illusion, and as a consequence rather than the cause of this change in matter. But to entertain these thoughts is to embark upon a process of reasoning, associated primarily with Lorentz, that became unfashionable2 following Einstein's famous paper of 1905 [1]. Lorentz had sought to explain the transformation that bears his name on the basis of changes that occur in matter as it changes velocity. This was, it is suggested, an idea before its time. We will consider in this paper how Lorentz's program might have proceeded if informed by later insights as to the underlying wave nature of matter, including ironically those of Einstein himself, but in particular that of de Broglie [9]. 2 Lorentz and Einstein Briefly first some history. The problem addressed by Lorentz and subsequently Einstein was the speed of light. This emerged as a constant in Maxwell's equations, but if as was generally supposed, light is wave-like, it seemed reasonable to assume that it must be carried by some medium (the "luminiferous aether") at a velocity characteristic of that medium. Thus its velocity relative to an observer should have varied with the motion of the observer through the medium. Experiments of increasing sophistication failed to reveal any trace of that variation. Several explanations were put forward. It was proposed that the Earth must carry the local aether with it, but a more fruitful suggestion made independently by Fitzgerald [10] and Lorentz [11] was that objects moving through the aether must be somehow shortened along their direction of travel, thereby disguising relative changes in the velocity of light. It was supposed that intermolecular forces must be transmitted at the same velocity as electromagnetic waves, so that movement through the aether would 2 Described as "best forgotten except by historians" by Rindler [3], p 11. For views more consonant with those offered here, see Bell [4], Brown and Pooley [5], and in particular, Brown [6]. The pedagogical merits of this "constructive" approach to SR are also discussed in Miller [7], and Nelson [8]. 4 Daniel Shanahan influence the degree of attraction between molecules and thus the separation of those molecules. To effect a reconciliation with Maxwell's equations, it was necessary to assume changes not only of length, but also of time, and thus the LT, x′ = γ (x− vt) , y ′ = y, z ′ = z, t′ = γ ( t− vx c2 ) , where c is the speed of light, γ is the Lorentz factor,( 1− v 2 c2 )− 12 , (1) and the unprimed coordinates are for an event in the observer's rest frame, while the primed are for those in a frame moving in the x direction at the velocity v. The LT was already reasonably well known by 1905. There had been significant contributions to its development, not only from Lorentz and Fitzgerald, but also by (among others) Heaviside, Larmor and Poincaré. It was Heaviside's analysis of the disposition of fields accompanying a charged particle (the "Heaviside ellipsoid") that had suggested to FitzGerald the idea of length contraction [12]. Larmor had described an early form of the LT and discussed the necessity of time dilation [13]. Poincaré had recognized the relativity of simultaneity and had studied the group theoretic properties that form the basis for the covariance of the transformation [14]. But these "trailblazers" (Brown [6], Ch. 4 ) appear to have missed in varying degrees the full significance of the transformation3 . It is not only particular phenomena, but all of Nature that changes for the accelerated observer. Lorentz struggled to explain how all aspects of matter could became transformed in equal measure, being discouraged by experimental reports that seemed to show that particles do not contract in the direction of travel (see Brown [6], p 86). A wider view seems to have been noticed by Poincaré [14], who has been regarded by some as codiscoverer of SR (see, for instance, Zahar [15], and Reignier [16]). But it is not apparent that these earlier investigators saw the changes described by the LT as anything more than mathematical constructs. In his paper of 1905 [1], Einstein simply asserted that the velocity of light, and other properties of Nature, must appear the same for all uniformly moving observers, thereby effecting an immediate reconciliation between Maxwell's equations and classical mechanics. 3 There are differing opinions as to who knew what in 1905. For an interesting sampling of conflicting views on priority (Einstein, Lorentz or Poincaré?) see the preamble to Reignier [16]. A case for Lorentzian relativity 5 In 1905, Einstein's approach may have been the only way forward. It was not until 1924, only a few years before the death of Lorentz, and well after that of Poincaré, that de Broglie proposed that matter is also wavelike [9], an idea that might have suggested to Lorentz why molecules become transformed in the same degree as intermolecular forces. But as inadequate and ad hoc as Lorentz's suggestions may have seemed at the time, he at least had sought an underlying physical basis for the transformation. Lorentz commented, presumably with some chagrin, that, Einstein simply postulates what we have deduced, with some difficulty, and not altogether satisfactorily, from the fundamental equations of the electromagnetic field [17]. In what follows, the distinction drawn will be between Einstein's SR (ESR) and what we will call Lorentzian SR (LSR). This is not to diminish the contributions of others, but it was Lorentz in particular who sought to explain SR from underlying physical processes, as will be the objective below. Once the form of the LT was known, all else in SR then followed, including the composition of velocities, the group theoretic properties of the transformation, and the invariance of Maxwell's equations. It may be argued that with these refinements (largely due to Einstein and Poincaré), ESR and LSR are essentially equivalent. They cannot be distinguished, mathematically or empirically, through the privileged frame that was supposed by Lorentz, but declared "superfluous" by Einstein [1]. It would seem that any such frame is rendered undetectable by the covariance of the LT. Nor can ESR and LSR be distinguished by supposing that in ESR, though not in LSR, the LT describes a transformation of spacetime. As we have seen, the LT must be explained in either case by changes occurring in matter as it is accelerated from one inertial frame to another. Historically, the two approaches are distinguished by the assumptions made by Einstein in justifying the LT. His confident assertion of these "postulates" gave impetus to the recognition and development of SR. But by raising "to the status of a postulate", the conjecture that Nature displays "no properties corresponding to the idea of absolute rest", and introducing the further postulate that the speed of light must be the same for all observers [1], Einstein avoided all necessity of explaining how Nature has arranged these matters. He left the impression that there was nothing more that needed explaining. Einstein's postulates presuppose that everything in Nature transforms in the same degree. Accepting that this is so, we should suspect the existence of some unifying feature common to matter and radiation that ensures that it is so. If it had been possible to see the LT as a transformation of space carrying with it all within space, this would have explained very nicely the all-encompassing generality of the transformation. Having dismissed that possibility, we will proceed now on a different tack. 6 Daniel Shanahan 3 The scheme of the paper It will be supposed (taking our cue from de Broglie [9]) that radiation and matter transform in like manner because they are constituted in like manner from similar wave-like influences. By modelling a massive particle as a standing wave in three dimensions, it will be shown in the next section (Sect. 4) that the changes in length, time and simultaneity described by the LT are the immediate consequences of changes in the wave structure of the particle as it changes inertial frame. As discussed in Sect. 5, a compelling advantage of this treatment will be the emergence of the otherwise mysterious de Broglie wave, not as the independent wave generally supposed, but as a modulation defining the dephasing of the underlying wave structure in the direction of travel. This conception of the de Broglie wave is not itself new. Such a modulation may be discerned in a toy model described by de Broglie himself in his famous doctoral thesis of 1924 [9]. It has been discussed in various contexts on several occasions since [18] [19] [20] [21] [22]. However, it will be shown here that this interpretation of the wave explains several curious features of the wave-like behaviour of matter. It avoids the anomalous nature of the superluminality of the wave, it makes sense of the role of the wave in quantization and in the Schrödinger Equation; and it explains the relevance of the de Broglie wave number to the optical properties of massive particles. Its primary significance to this paper is that the dephasing defined by the modulation is the measure of the failure of simultaneity that is perhaps the most counter-intuitive aspect of SR. In Sect. 6, we will consider the suffi ciency of the model particle introduced in Sect. 4. It will be shown that this test particle exhibits, not so much the properties of all matter, but more relevantly, those implicitly assumed by ESR. In Sect. 7, consideration will be given to the possible existence of a preferred frame, that is to say, a frame in which the speed of light is not simply observed to be, but in fact is, the same in all directions. The position will be taken that the fixed rate at which photons are observed to propagate through space suggests very strongly, if not a light-carrying medium, then at least the preferred frame favoured by Lorentz. In Sect. 8, it will be argued that "Lorentz invariance" the invariance of the laws of physics to all inertial observers is itself a consequence of the wave-like characteristics of matter. A brief summary in Sect 9 will conclude the paper. 4 A model particle In 1905, Einstein took as his yardstick, the rigid rod, avoiding consideration of underlying structure [1]. However a massive particle has, from the PlanckEinstein relation, E = ~ωE = ~γωo, (2) A case for Lorentzian relativity 7 an associated frequency ωE , and from the de Broglie relation, p = ~κdB = ~γωo v c , (3) a wave number κdB (the de Broglie wave number), where E and p are respectively the energy and momentum of the particle, ~ is the reduced Planck's constant, and ωo is the natural or characteristic frequency of the particle at rest. Wave number κdB and frequency ωE define the wave that de Broglie referred to as a pilot wave, and that we now know as the de Broglie or matter wave. Considered as an independent wave it is anomalous. It has in free space the form of a transverse plane wave, ei~(ωEt−κdBz), of superluminal velocity c2/v. What is also curious (though a pointer to the true nature of this wave) is that its speed increases as the particle slows, becoming infinite as the particle comes to rest. In its rest frame, the particle retains nonetheless the frequency ωo, which we will assume is not a fictitious or merely internal frequency, but the measure of some oscillatory disturbance communicated through space at velocity c. From this assumption we model a massive particle in its rest frame by the simple symmetrical waveform, Ψ (r, t) = |r|−1 [ei(ωot−κo*r) − ei(ωot+κo*r)]/2, (4) or, taking real parts, Ψ (r, t) = |r|−1 sinκo * r cosωot, which is a spherical standing wave centred at r = 0 and comprising incoming and outgoing waves of velocity c, where, ωo κo = c, so that κo is not here the de Broglie wave number but the wave number that must be associated with a wave of frequency ωo and velocity c4 . Model particle (4) is depicted (in two dimensions) in Fig. 1(a). This particular structure is evidently unphysical because of the singularity at r = 0. It is nonetheless the simplest expression of the assumption, essential to ESR, that influences moving to and from (and indeed through) a particle do so at the speed of light. We will consider this model further in Sect. 6. We now investigate how this particle must change if it is to acquire a velocity v in the frame of the laboratory, when subject to the constraint that its constituent influences (rays) must retain the velocity c with respect to that frame. (We are thus assuming for the moment that the inertial frame in which this particle has the form (4), which we have called the laboratory 4 κo also has significance as the reduced Compton wave number. 8 Daniel Shanahan frame, is at the same time the preferred or privileged frame supposed by Lorentz. To simplify matters further the amplitude |r|−1 is omitted in what follows). What we require now is not a standing wave but a travelling wave. Its form can be established in either of two ways, and it will be instructive to consider both. The first is by construction, and we begin by considering rays, directed forward and rearward along the direction of travel, which we will take to be the positive x-direction. At rest in the preferred (laboratory) frame, the composition of these rays results in the one-dimensional standing wave Ψ(x, t) = [ei(ωot−κox) − ei(ωot+κox)]/2, = sinκox cosωot. (5) This standing wave becomes a travelling wave of velocity v if the wave characteristics of the rays directed forward and rearward (which we now label 1 and 2 respectively) become, ω1 = γω0(1 + v c ), ω2 = γω0(1− v c ), κ1 = γκ0(1 + v c ), κ2 = γκ0(1− v c ), (6) where γ is again the Lorentz factor (1), and since, ω1 κ1 = ω2 κ2 = ω0 κ0 = c, (7) both rays retain as required the velocity c with respect to the preferred frame. We then have by composition, Ψ (x, t) = [ei(ω1t−κ1x) − ei(ω2t+κ2x)]/2, (8) = sin( ω1 − ω2) 2 t− κ1 + κ2) 2 x) cos( ω1 + ω2) 2 t− κ1 − κ2) 2 x), (9) which from relations (6) may also be written, Ψ (x, t) = sin γ(βω0t− κ0x) cos γ(ω0t− βκ0x), (10) and is a travelling wave of the kind illustrated in Fig. 2(b). This onedimensional travelling wave already displays features that will become more apparent when we consider the full three-dimensional travelling wave, namely a carrier wave of velocity v (the first factor in Eqn. (10) ) and a superluminal modulation (or beating) of velocity c2/v (the second factor). The structure of the full model wave at velocity v is now obtained by noticing that (as shown in Fig. 3) the amplitude of this wave at any point P at time t, when the centre of the wave has reached B, results from the interference of the outgoing ray that left the particle centre when it was A case for Lorentzian relativity 9 at A at the earlier time t − t1, with the incoming ray that will reach the particle centre when it is at C at the later time t + t2. (To an observer in the frame of the moving particle, the paths of these rays will appear to coincide, but they do not coincide in the laboratory frame). In a more realistic model, phase might be expected to vary with angular displacement about the particle centre, but in this simple model we have supposed that all rays passing through the centre are of the same phase. Thus, from Eqn. (9) for the one dimensional case, ΨA(t− t1) = exp i [ ω1 + ω2 2 (1− v 2 c2 )(t− t1) ] , and (11) ΨC(t+ t2) = exp i [ ω1 + ω2 2 (1− v 2 c2 )(t+ t2) ] , (12) (where the arguments of ΨA and ΨC are the phases at A and C respectively). We now need t1 and t2. From Fig. 3, c2t21 = [(x− v(t− t1)]2 + y2 + z2, from which, t1 = v c2 (x− vt) + 1 c √ (x− vt)2 + ( 1− v2c2 ) (y2 + z2) 1− v2c2 , (13) and similarly, t2 = − vc2 (x− vt) + 1 c √ (x− vt)2 + ( 1− v2c2 ) (y2 + z2) 1− v2c2 . (14) Composing Eqns. (11) and (12), and substituting for t1 and t2 from Eqns. (13) and (14) respectively, we obtain after some algebra the full travelling wave, Ψ (x, y, z, t) = sinκo √ γ2(x− vt)2 + y2 + z2 cos γωo(t− βx/c), (15) which is sketched for a particle of relativistic velocity in Fig. 1(b). The corresponding amplitudes of such a wave (in the x-direction) are of the general form suggested by Fig. 2. Travelling wave (15) could have been obtained by simply Lorentz transforming model wave (4). In following the longer route we have not derived the LT, for we have assumed the Lorentz factor γ (an assumption that will be examined in Sect. 8), but we have demonstrated the physical effect of the LT, not as Einstein did with reference to rigid rods and synchronous clocks, but as Lorentz might have done, from the underlying oscillatory nature of matter. In doing so we have of course had the advantage of a unified view of matter and radiation that was not available to Lorentz. 10 Daniel Shanahan It is important to notice the composite form of the transformed wave (15). It has two factors. The first, sinκo √ γ2(x− vt)2 + y2 + z2, (16) is a form of carrier wave. It moves with velocity v, the classical velocity of the particle and, as suggested by the ellipses in Fig. 1(b), describes the relativistically contracted ellipsoidal form of the moving particle as considered from the standpoint of an observer in the laboratory frame. It has the dilated frequency ωo/γ. The second factor, cos γωo(t− βx/c), (17) is a plane wave of superluminal velocity c2/v, the wave fronts of which are suggested by the vertical lines in Fig. 1(b). This plane wave has the wave number and frequency of the de Broglie wave, and is indeed the de Broglie wave. But it is not here an independent wave but a modulation of the carrier wave (16), describing the dephasing of that wave (and thus the failure of simultaneity) in the direction of travel of the particle. Travelling wave (15) displays all the effects predicted by SR length contraction, time dilation and failure of simultaneity. If all matter changed between inertial frames in the same manner as our model particle, this would explain why Mary considered Buzz to have changed in accordance with the LT. But the transformation is here a change of wave structure, not of space, nor even yet of reference frame. There has been no opportunity, let alone necessity, for some additional transformation of "spacetime". What, then, of Buzz's belief that it was Mary who changed. In its altered state, the model particle has become a somewhat untidy affair. But to an observer moving with the particle (such as Buzz), and transformed in like manner, the particle will seem to have its original form (4). Being composed of influences developing at the speed of light, this observer will also lack the means of discerning differences in his or her velocity relative to that of light. In whatever inertial frame the observer occupies, the covariance and group theoretic properties of the LT will guarantee the constancy of the observed speed of light and the laws of physics. It is these properties that ensure that if a preferred frame does exist (of which more will be said in Sect. 7) it is likely to remain undetected. When considered as the composition of wave influences moving with the speed of light, it also becomes apparent why that speed must be a limiting velocity for the movement of matter (see also Nelson [8]). 5 The de Broglie wave Once the de Broglie wave is seen as a modulation rather than an independent wave, several mysteries become resolved. As a modulation, its superluminal velocity is no longer that of energy transport and need not be explained away by the usual but awkward device of equating the velocity of the particle A case for Lorentzian relativity 11 with the group velocity of a packet of such de Broglie waves. It is also only natural that the velocity of this modulation should increase as the particle slows, and become infinite as the particle comes to rest. At rest, the crests of the composite wave are no longer peaking in sequence, but in unison. Simultaneity has been restored, alignment of phase has become instantaneous, and the velocity of the modulation describing the progress of that alignment has thus become infinite. In effect the de Broglie wave now disappears. Other diffi culties are explained. It can be seen why the de Broglie wave cannot be fitted to electron orbits. It is not the superluminal modulation but the full composite wave that follows the orbital path. Yet it is the modulation that defines the phase lost by the electron in following that path, and it is thus the de Broglie wave number κdB of Eqn. (3) that appears in Bohr quantization conditions for stable orbits, which are of general form,∮ κdB ds = 2nπ (n = 1, 2, 3...), (18) a requirement that evidently ensures continuity in the wave structure generated by the orbit in question. The Schrödinger equation (the SE) is also based on the modulation rather than the full wave, thus explaining the diffi culties that have been experienced in according physical significance to solutions of this equation5 . In constructing a wave equation that would have solutions consistent with the Planck-Einstein and de Broglie relations (Eqns. (2) and (3) above), Schrödinger made the substitutions, p→ i~ ∂ ∂x , and E → i~ ∂ ∂t , in the non-relativistic equation of motion, E2 = p2 2 + V (r, t), to obtain the non-relativistic SE, i~ ∂ψ ∂t = − ~ 2 2m ∇2ψ + V (r, t)ψ, and likewise in the relativistic equation of motion to obtain the corresponding wave equation (now called the Klein-Gordon equation). But as we have seen, Eqns. (2) and (3) define the wave characteristics, not of the full waveform, but of the de Broglie wave. Thus solutions to the SE, whether in its relativistic or non-relativistic form are not actual waves 5 Of Schrödinger's own diffi culties in interpreting those solutions, see Dorling [23]. 12 Daniel Shanahan but distorted mappings of a modulation. These solutions are able to identify allowed energy levels only because each such solution is homologous to a set of quantization conditions, the continuity implied by those conditions being at the same time the continuity required for physically realistic solutions of the SE. This criticism does not apply to the bispinor solutions of the Dirac equation. The Dirac bispinor combines two null (light-like) first rank spinors occupying opposite sides of the light cone. It thus contemplates (as in Sect. 4) the interference of counter-propagating waves of velocity c. By composing the null four-vectors that correspond to the two null first rank spinors (as, described, for example, in Steane [24], Chap. 17.3) it can be seen that this interference generates the four-momentum of the fermion, and thus the four-vector of its associated de Broglie wave. The de Broglie wave thus emerges from the Dirac equation as the modulation of an underlying wave structure in essentially the manner contemplated in the preceding section (Sect. 4). One further curiosity is also explained. Once considered as a modulation, it becomes understandable, not only that the superluminal wave does not outrun the subluminal particle, but why the wave vector κdB of this wave has a controlling influence on the optical properties of the particle. Any change in the trajectory of the particle will be accompanied by a rotation throughout space of the wave fronts of the de Broglie wave and, as the immediate consequence of that rotation, a rearrangement of phase (and simultaneity) throughout the entire composite wave structure. It is only necessary to assume that a scattered particle (for instance a diffracted particle) will prefer a trajectory that preserves its characteristic transverse wave form to see why the particle tends to adopt a path through the scattering medium in which the de Broglie wave recombines coherently, that is to say, by which its recombining parts interfere constructively rather than destructively. 6 The suffi ciency of the model It might be objected that without knowing all there is to know about the constituent particles and fundamental forces of Nature, we are no better equipped than was Lorentz to base the LT on the properties of matter. It might also be argued that what we have been assuming are waves are not waves at all but particles that display oscillatory characteristics, or if waves, not real waves, but the probabilistic waves of standard quantum mechanics (SQM). The model assumes that a massive particle comprises influences of frequency ωo moving to and from the particle centre at velocity c. That the interaction of a particle with its fellows can be expressed in terms of incoming A case for Lorentzian relativity 13 and outgoing influences is obvious and well recognized6 . It is also apparent that, as assumed in Sect. 4, the natural frequency ωo, which becomes γωo for the moving particle, is not the measure of some merely internal property of the particle. This is suffi ciently evidenced by the de Broglie wave, which is itself of frequency γωo, and reveals its presence externally in diffraction, interference and quantization. Conservation then demands that energies passing to and from the particle be commensurate, and thus the standing wave (4). ESR assumes that all influences in Nature propagate at velocity c. If some particle or force were shown to respond at a velocity differing from c, this would constitute as much an exception to ESR as it would to LSR7 . Massive particles do not move at that velocity, but it is implicit in ESR that the influences by which these particles interact do develop between and through the particles at velocity c. There is an analogy here with refraction. From interference between the incident (free space) wave, and reradiation from moments induced by that wave, the transmitted wave acquires a phase velocity that may be greater or smaller than c. Nonetheless, any change in the wave develops through the medium at the velocity c. Let us suppose that some particle, let us say a meson mediating the strong force, or perhaps we should say, a string linking quarks, were to respond at velocity C (differing from c) to some change in the relationship between one nucleon and another. The composition of incoming and outgoing influences could then be expressed in the form of Eqn. (8), that is as, Ψ (r, t) = [ei(ω1t−κ1*r) − ei(ω2t+κ2*r)]/2, (or if not in that form then in some superposition of waves of that form), where contrary to relations (7) above, ω1 κ1 = ω2 κ2 = C 6= c. From the discussion of the LT in Sect. 4, it is thus apparent that on a change of inertial frame, this supposed meson or string would suffer contraction, dilation and a changed simultaneity to a degree differing from that experienced by other matter, so that contrary to ESR (and as will be discussed in Sect. 8), the laws of physics would not then be the same in all inertial frames. 6 See, for example, the discussions of advanced and retarded influences by Wheeler and Feynman [25] [26]. Those papers concerned action at a distance but such incoming and outgoing influences are explicit in field theories. 7 We do not ignore the nonlocality implied by the formalism of SQM or the apparent confirmation of that nonlocality in dynamic Bell's experiments, notably those of Aspect et al [27] and Weihs et al [28]. We are content to rely (here at least) on the "peaceful coexistence" between SR and SQM declared by Shimony [29] from the circumstance that the nonlocality claimed does not permit superluminal signalling. 14 Daniel Shanahan Once it is accepted that in its rest frame a particle comprises, or is at the focus of, influences oscillating at the natural frequency ω0 and moving inwardly and outwardly at velocity c, the exact nature of those influences becomes of no consequence to the demonstration in Sect. 4. These influences could be waves or fields, real, virtual or probabilistic, continuous or particulate. They might be concentrated upon some additional central body, but if having spatial extension, the material of that body would be of such a nature that influences propagating through the material did so at velocity c. Whatever the case, the moving "wave" will display the contraction and dilation described by the LT, and be subject to a modulation consistent with the predicted loss of simultaneity. The plausibility of this model is evidenced by the physically consistent provenance it provides for the de Broglie wave. As to the infinity at the core of the model, it must be supposed that any viable wave form would exhibit some asymmetry avoiding such a singularity. 7 A preferred frame? We have supposed, with Lorentz, a preferred frame of reference the frame in which the speed of light is not only observed to be, but in fact is, the same in all directions. If, as seems the case, this frame is undetectable, it might be argued from considerations of economy that it should play no part in the description of SR. Einstein stated: The introduction of a luminiferous aether will prove to be superfluous inasmuch as the view here to be developed will not require an "absolutely stationary space" provided with special properties [1]. Yet space does have at least one "special property" essential to ESR and assumed implicitly by Einstein. Unlike projectiles and massive particles, one photon never overtakes another. Photons pass through space at a common rate of progress, and their passage is thus similar in this respect to the propagation of a wave through an elastic medium, where the velocity of the disturbance is determined only by the nature of the wave and the properties of the medium. Einstein suggested that the photon must be an "autonomous entity" requiring no supporting medium (see Kostro [30], pp. 37 and 94), but it might be asked why such an unconstrained object should confine itself to a particular rate of progress. Moreover, photons not only propagate as waves, they have the oscillatory characteristics of waves. So too does matter. In the absence of some more plausible explanation, there would seem ample grounds for suspecting the light-carrying medium supposed by Lorentz. Following the completion of GR, Einstein relaxed his stance against the aether, but not to the extent of admitting that such a medium could constitute a preferred frame (see Kostro [30]). Yet the argument for a preferred frame seems even stronger than that for an aether. It may be A case for Lorentzian relativity 15 possible to imagine some reason other than a light-carrying medium for the photon's fixed rate of progress, perhaps the involvement in some way of the surrounding Universe. But it is the fixed rate of progress, not how it is enforced, that implies the existence of a frame of reference. The argument becomes particularly insistent once the LT is explained from the wave characteristics of matter. There are practical and conceptual diffi culties in presenting a wave based explanation of the LT without supposing such a frame. Consider, for instance, the frequencies ω1 and ω2 of Eqn. (7). No matter how asymmetrical the Universe might be, it must be possible at least in principle to attain a velocity in any direction we choose for which one of these frequencies, (ω1 or ω2) is the greater, and in the opposite direction for which the other is the greater, so that between these velocities, there must exist an inertial frame in which ω1 = ω2 = ω0. There must therefore exist, at least locally, a preferred frame. In GR the speed of light is metric-dependent, but subject to that qualification, the arguments above appear as applicable in GR as in SR. However, in GR, the distribution of matter and radiation now hints at the location of such a frame. It would be the frame of the galaxies and of the cosmic microwave background the frame from which spacetime itself is spatially isotropic as is nearly so from the frame of our own local system. Nor is the covariance of GR (general covariance) as convincingly agnostic of the existence and location of this frame as the LT of the special theory. It was objected by Kretschmann in the first days of GR that by the suffi cient exercise of mathematical ingenuity any equation of physics might be expressed in covariant form [34]. Kretschmann thus argued that neither a relativity principle nor the primacy of Einstein's theory could be established by covariance per se8 . Einstein conceded the point, but argued for the superiority of his equation on the basis of simplicity [35]. And of course, he could have also cited the compelling utility and elegance of manifest covariance. Yet any inference from general covariance that there is no preferred frame is weakened in practice by the existence of a gauge freedom allowing a choice of coordinates adapted to the symmetries of the problem, which is to say, the curvature of the metric. The very notion of curvature implies a centre of curvature, and it thus becomes possible to see the curvature tensor of the Universe at large as suggesting, mysterious though that concept may be, a preferred basis for the consideration of the curvature of the Universe itself. Further arguments for a preferred frame may be mentioned. It has been argued that such a frame is implied by the assumption, now orthodox, that the vacuum (the modern aether) is the seat of the zero point energies of the modes of the fields. This has suggested in turn the possibility of frame-dependent effects in the extreme and perhaps pathological situation at the event horizon of a black hole (see Winterberg [36]). And there is 8 Kretschmann's objection has been much discussed, see for instance Norton [31], Dieks [32], and Giovanelli [33]. 16 Daniel Shanahan the hypothesized (and, it has been argued, detectable) Unruh-Davies effect, according to which an observer, who is accelerating with respect to the vacuum, experiences a thermal bath and consequent temperature rise from radiative effects (see, for example, Crispino et al [37]). But it is not essential to the case for Lorentzian relativity presented here that this preferred frame have any particular location or that it be capable of detection. There is reason to believe, as the next section may show, that this frame lies beyond all possibility of detection. But once the LT is explained, not from a change in the properties of space, but from changes in the wave-constituted material occupying that space, there must be in consequence one particular frame in which the underlying waves develop at the same speed in every direction. If undetectable, this frame can play no essential role in the mathematical description of SR or GR. But with due respect to the friar of Occam, the dismissal of this frame as "superfluous" has had the effect of discouraging, if not entirely suppressing, lines of enquiry that imply its existence. 8 Lorentz invariance While there would seem little doubt that the laws of physics are the same for all observers, one might ask why this should be so. In the context of ESR this satisfying situation would seem fortuitous. However, a consideration of the wave nature of matter may suggest at least a partial explanation for this invariance. Notice firstly the unusual effects that would result if the LT were not exactly as it is, for instance if the Lorentz factor γ was not (1− v2/c2)−1/2 but had some other value γa (a being a real number other than unity). Consistently with relations (7), a wave travelling at any desired velocity v could still be constructed, but as in the case of a = 0, which is the Galilean transformation, the preferred frame would then be detectable. In the Galilean case, longitudinal contraction is replaced by transverse contraction that increases with acceleration away from the preferred frame. For other values of a, contraction or expansion (both longitudinal and transverse), time dilation and simultaneity would be observed to differ according to whether velocity were increased or decreased with respect to the preferred frame. The laws of physics would not then be invariant, and the Universe would be rather more curious and less elegant than it is. But that alone does not explain why it is not so. Consider now, however, the stability of matter. The elementary particles exist in a limited variety of precisely defined characteristic forms. Why that should be so is not apparent, but what is apparent is that they are constrained by those forms and by their wave-like nature to combine in a limited number of ways, as is well illustrated by the Bohr conditions (18). Even in matter that we would think of as stationary, underlying microprocesses are occurring at relativistic speeds, as illustrated well enough A case for Lorentzian relativity 17 again by the Bohr orbits. For these processes to remain undisturbed by a change of inertial frame, dynamic relationships between particles must be preserved, including for instance relative velocities, accelerations, masses and polarizations. In other words, the laws of physics must be the same for all inertial observers, and this is so only at a = 1. Considered in this way, Lorentz invariance is not the fortuitous cause, but rather the inevitable effect, of the manner in which the constituent elements of matter must persist and combine. It is not then the metric that determines how matter transforms, but the stability of matter that determines the LT and the observed (Minkowski) metric. Of any pre-existing or primordial metric little can be said, except that the simplest possible metric, the Euclidean, was that assumed by Lorentz. 9 Summary The effects described by the LT can be explained in their entirety by changes occurring in matter as it changes inertial frame. This is not to suggest that the LT does not describe a transformation of space and time. But what the LT describes are changes in what is observed, and in the Lorentzian approach offered here, what is observed by an accelerated observer is essentially an illusion induced by changes in that observer. This view relies crucially on the conclusion reached in Sect. 1 that the LT does not involve actual physical change in the properties of space. But once that conclusion is reached, it becomes apparent that there is something elusive in Einstein's theory, and that it is the Lorentzian approach that better explains the origin of the contraction, dilation and loss of simultaneity described by the LT. Once the LT is explained from the wave characteristic of matter a good deal else becomes apparent. The de Broglie wave is seen to be a modulation rather than an independent wave, thus explaining the superluminality of this wave, its significance in the Schrödinger equation, and its roles in determining the optical properties of matter and the dephasing that underlies the relativity of simultaneity. Einstein's bold assertion that the laws of physics must be the same for all observers revealed the elegance of SR and something indeed of the elegance of the universe itself. It is suggested nonetheless that it is a Lorentzian approach that will provide the deeper understanding of the physical meaning of SR. Acknowledgements Thanks are due to Will Nelson and Larry Hoffman for encouragement and helpful suggestions, and to the anonymous reviewers for drawing attention to a number of relevant and interesting issues arising in the context of general relativity. CAPTIONS TO DRAWINGS 18 Daniel Shanahan FIG. 1. A model particle is represented: (a) as a spherical standing wave; and (b) as a relativistically contracted carrier wave of velocity v, subject to a modulation (the de Broglie wave) of superluminal velocity c2/v. The ellipses in (b) represent the wave fronts of the carrier wave and the vertical lines those of the de Broglie modulation. FIG. 2. Amplitudes (indicative only) at times t1 < t2 < t3 for a wave of the kind shown in FIG 1(b). As shown by the arrows, the modulation (the de Broglie wave) develops through the carrier wave. It moves at the superluminal velocity c2/v, while the carrier wave moves at velocity v, the classical velocity of the particle. FIG. 3. 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