Stability of matter

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https://en.wikipedia.org/wiki/Stability_of_matter 

In physics, the stability of matter refers to the ability of a large number of charged particles, such as electrons and protons, to form macroscopic objects without collapsing or blowing apart due to electromagnetic interactions. Classical physics predicts that such systems should be inherently unstable due to attractive and repulsive electrostatic forces between charges, and thus the stability of matter was a theoretical problem that required a quantum mechanical explanation.

The first solution to this problem was provided by Freeman Dyson and Andrew Lenard in 1967–1968, but a shorter and more conceptual proof was found later by Elliott Lieb and Walter Thirring in 1975 using the Lieb–Thirring inequality. The stability of matter is partly due to the uncertainty principle and the Pauli exclusion principle.^[4]

Description of the problem

In statistical mechanics, the existence of macroscopic objects is usually explained in terms of the behavior of the energy or the free energy with respect to the total number ${\displaystyle N}$ of particles. More precisely, the ground-state energy should be a linear function of ${\displaystyle N}$ for large values of ${\displaystyle N}$.  In fact, if the ground-state energy behaves proportional to ${\displaystyle N^a}$ for some ${\displaystyle a\ne 1}$, then pouring two glasses of water would provide an energy proportional to ${\displaystyle (2N{)}^a-2N^a=(2^a-2)N^a}$, which is enormous for large ${\displaystyle N}$. A system is called stable of the second kind or thermodynamically stable when the free energy is bounded from below by a linear function of ${\displaystyle N}$. Upper bounds are usually easy to show in applications, and this is why scientists have worked more on proving lower bounds.

Neglecting other forces, it is reasonable to assume that ordinary matter is composed of negative and positive non-relativistic charges (electrons and ions), interacting solely via the Coulomb's interaction. A finite number of such particles always collapses in classical mechanics, due to the infinite depth of the electron-nucleus attraction, but it can exist in quantum mechanics thanks to Heisenberg's uncertainty principle. Proving that such a system is thermodynamically stable is called the stability of matter problem and it is very difficult due to the long range of the Coulomb potential. Stability should be a consequence of screening effects, but those are hard to quantify.

Let us denote by

${\displaystyle H_{N,K}=-\sum _{i=1}^N\frac{{\mathrm{\Delta }}_{x_i}}{2}-\sum _{k=1}^K\frac{{\mathrm{\Delta }}_{R_k}}{2M_k}-\sum _{i=1}^N\sum _{k=1}^K\frac{z_k}{|x_i-R_k|}+\sum _{1\le i<j\le N}\frac{1}{|x_i-x_j|}+\sum _{1\le k<m\le K}\frac{z_k{z}_m}{|R_k-R_m|}}$

the quantum Hamiltonian of ${\displaystyle N}$ electrons and ${\displaystyle K}$ nuclei of charges ${\displaystyle z_1,...,z_K}$ and masses ${\displaystyle M_1,...,M_K}$ in atomic units. Here ${\displaystyle \mathrm{\Delta }={\mathrm{\nabla }}^2=\sum _{j=1}^3{\mathrm{\partial }}_{jj}}$ denotes the Laplacian, which is the quantum kinetic energy operator. At zero temperature, the question is whether the ground state energy (the minimum of the spectrum of ${\displaystyle H_{N,K}}$) is bounded from below by a constant times the total number of particles:

${\displaystyle E_{N,K}=min\sigma (H_{N,K})\ge -C(N+K).}$

1

The constant ${\displaystyle C}$ can depend on the largest number of spin states for each particle as well as the largest value of the charges ${\displaystyle z_k}$. It should ideally not depend on the masses ${\displaystyle M_1,...,M_K}$ so as to be able to consider the infinite mass limit, that is, classical nuclei.

History

19th century physics

At the end of the 19th century it was understood that electromagnetic forces held matter together. However two problems co-existed. Earnshaw's theorem from 1842, proved that no charged body can be in a stable equilibrium under the influence of electrostatic forces alone. The second problem was that James Clerk Maxwell had shown that accelerated charge produces electromagnetic radiation, which in turn reduces its motion. In 1900, Joseph Larmor suggested the possibility of an electromagnetic system with electrons in orbits inside matter. He showed that if such system existed, it could be scaled down by scaling distances and vibrations times, however this suggested a modification to Coulomb's law at the level of molecules. Classical physics was thus unable to explain the stability of matter and could only be explained with quantum mechanics which was developed at the beginning of the 20th century.

Dyson–Lenard solution

Freeman Dyson showed in 1967 that if all the particles are bosons, then the inequality (1) cannot be true and the system is thermodynamically unstable. It was in fact later proved that in this case the energy goes like ${\displaystyle N^{7/5}}$ instead of being linear in ${\displaystyle N}$. It is therefore important that either the positive or negative charges are fermions. In other words, stability of matter is a consequence of the Pauli exclusion principle. In real life electrons are indeed fermions, but finding the right way to use Pauli's principle and prove stability turned out to be remarkably difficult. Michael Fisher and David Ruelle formalized the conjecture in 1966 According to Dyson, Fisher and Ruelle offered a bottle of Champagne to anybody who could prove it. Dyson and Lenard found the proof of (1) a year later and therefore got the bottle.

Lieb–Thirring inequality

As was mentioned before, stability is a necessary condition for the existence of macroscopic objects, but it does not immediately imply the existence of thermodynamic functions. One should really show that the energy really behaves linearly in the number of particles. Based on the Dyson–Lenard result, this was solved in an ingenious way by Elliott Lieb and Joel Lebowitz in 1972.^[12]

According to Dyson himself, the Dyson–Lenard proof is "extraordinarily complicated and difficult" and relies on deep and tedious analytical bounds. The obtained constant ${\displaystyle C}$ in (1) was also very large. In 1975, Elliott Lieb and Walter Thirring found a simpler and more conceptual proof, based on a spectral inequality, now called the Lieb–Thirring inequality. They got a constant ${\displaystyle C}$ which was by several orders of magnitude smaller than the Dyson–Lenard constant and had a realistic value. They arrived at the final inequality

${\displaystyle E_{N,K}\ge -0.231q^{\frac{2}{3}}N{\left(1+2.16Z(K/N{)}^{\frac{1}{3}}\right)}^2}$

2

where ${\displaystyle Z=max(z_k)}$ is the largest nuclear charge and ${\displaystyle q}$ is the number of electronic spin states which is 2. Since ${\displaystyle N^{1/3}{K}^{2/3}\le N+K}$, this yields the desired linear lower bound (1). The Lieb–Thirring idea was to bound the quantum energy from below in terms of the Thomas–Fermi energy. The latter is always stable due to a theorem of Edward Teller which states that atoms can never bind in Thomas–Fermi model. The Lieb–Thirring inequality was used to bound the quantum kinetic energy of the electrons in terms of the Thomas–Fermi kinetic energy ${\displaystyle {\int }_{{\mathbb{R}}^3}\rho (x{)}^{\frac{5}{3}}{d}^{3}x}$. Teller's no-binding theorem was in fact also used to bound from below the total Coulomb interaction in terms of the simpler Hartree energy appearing in Thomas–Fermi theory. Speaking about the Lieb–Thirring proof, Dyson wrote later

Lenard and I found a proof of the stability of matter in 1967. Our proof was so complicated and so unilluminating that it stimulated Lieb and Thirring to find the first decent proof. (...) Why was our proof so bad and why was theirs so good? The reason is simple. Lenard and I began with mathematical tricks and hacked our way through a forest of inequalities without any physical understanding. Lieb and Thirring began with physical understanding and went on to find the appropriate mathematical language to make their understanding rigorous. Our proof was a dead end. Theirs was a gateway to the new world of ideas.

Further work

The Lieb–Thirring approach has generated many subsequent works and extensions. (Pseudo-)Relativistic systems, magnetic fields, quantized fields and two-dimensional fractional statistics (anyons) have for instance been studied since the Lieb–Thirring paper. The form of the bound (1) has also been improved over the years. For example, one can obtain a constant independent of the number ${\displaystyle K}$ of nuclei.

Indeterminism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Indeterminism

Indeterminism is the idea that events (or certain events, or events of certain types) are not caused, or are not caused deterministically.

It is the opposite of determinism and related to chance. It is highly relevant to the philosophical problem of free will, particularly in the form of metaphysical libertarianism. In science, most specifically quantum theory in physics, indeterminism is the belief that no event is certain and the entire outcome of anything is probabilistic. Heisenberg's uncertainty principle and the "Born rule", proposed by Max Born, are often starting points in support of the indeterministic nature of the universe. Indeterminism is also asserted by Sir Arthur Eddington, and Murray Gell-Mann. Indeterminism has been promoted by the French biologist Jacques Monod's essay "Chance and Necessity". The physicist-chemist Ilya Prigogine argued for indeterminism in complex systems.

Necessary but insufficient causation

Further information: Necessary and sufficient conditions

Indeterminists do not have to deny that causes exist. Instead, they can maintain that the only causes that exist are of a type that do not constrain the future to a single course; for instance, they can maintain that only necessary and not sufficient causes exist. The necessary/sufficient distinction works as follows:

If x is a necessary cause of y; then the presence of y implies that x definitely preceded it. The presence of x, however, does not imply that y will occur.

If x is a sufficient cause of y, then the presence of y implies that x may have preceded it. (However, another cause z may alternatively cause y. Thus the presence of y does not imply the presence of x, or z, or any other suspect.)

It is possible for everything to have a necessary cause, even while indeterminism holds and the future is open, because a necessary condition does not lead to a single inevitable effect. Indeterministic (or probabilistic) causation is a proposed possibility, such that "everything has a cause" is not a clear statement of indeterminism.

Probabilistic causation

Main article: Probabilistic causation

Interpreting causation as a deterministic relation means that if A causes B, then A must always be followed by B. In this sense, however, war does not always cause deaths (see Cyberwarfare), nor does a singular moment of smoking always cause cancer. As a result, many turn to a notion of probabilistic causation. Informally, A probabilistically causes B if A's occurrence increases the probability of B. This is sometimes interpreted to reflect the imperfect knowledge of a deterministic system but other times interpreted to mean that the causal system under study has an inherently indeterministic nature. (Propensity probability is an analogous idea, according to which probabilities have an objective existence and are not just limitations in a subject's knowledge).

It can be proved that realizations of any probability distribution other than the uniform one are mathematically equal to applying a (deterministic) function (namely, an inverse distribution function) on a random variable following the latter (i.e. an "absolutely random" one); the probabilities are contained in the deterministic element. A simple form of demonstrating it would be shooting randomly within a square and then (deterministically) interpreting a relatively large subsquare as the more probable outcome.

Intrinsic indeterminism versus unpredictability

A distinction is generally made between indeterminism and the mere inability to measure the variables (limits of precision). This is especially the case for physical indeterminism (as proposed by various interpretations of quantum mechanics). Yet some philosophers have argued that indeterminism and unpredictability are synonymous.

Philosophy

Ancient Greek philosophy

Leucippus

The oldest mention of the concept of chance is by the earliest philosopher of atomism, Leucippus, who said:

"The cosmos, then, became like a spherical form in this way: the atoms being submitted to a casual and unpredictable movement, quickly and incessantly".

Aristotle

Main article: Four causes

Aristotle described four possible causes (material, efficient, formal, and final). Aristotle's word for these causes was αἰτίαι (aitiai, as in aetiology), which translates as causes in the sense of the multiple factors responsible for an event. Aristotle did not subscribe to the simplistic "every event has a (single) cause" idea that was to come later.

In his Physics and Metaphysics, Aristotle said there were accidents (συμβεβηκός, sumbebekos) caused by nothing but chance (τύχη, tukhe). He noted that he and the early physicists found no place for chance among their causes.

We have seen how far Aristotle distances himself from any view which makes chance a crucial factor in the general explanation of things. And he does so on conceptual grounds: chance events are, he thinks, by definition unusual and lacking certain explanatory features: as such they form the complement class to those things which can be given full natural explanations.

— R.J. Hankinson, "Causes" in Blackwell Companion to Aristotle

Aristotle opposed his accidental chance to necessity:

Nor is there any definite cause for an accident, but only chance (τυχόν), namely an indefinite (ἀόριστον) cause.

It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destruction; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will this be, or not? Yes, if this happens; otherwise not.

Pyrrhonism

The philosopher Sextus Empiricus described the Pyrrhonist position on causes as follows:

...we show the existence of causes are plausible, and if those, too, are plausible which prove that it is incorrect to assert the existence of a cause, and if there is no way to give preference to any of these over others – since we have no agreed-upon sign, criterion, or proof, as has been pointed out earlier – then, if we go by the statements of the Dogmatists, it is necessary to suspend judgment about the existence of causes, too, saying that they are no more existent than non-existent

Epicureanism

Epicurus argued that as atoms moved through the void, there were occasions when they would "swerve" (clinamen) from their otherwise determined paths, thus initiating new causal chains. Epicurus argued that these swerves would allow us to be more responsible for our actions, something impossible if every action was deterministically caused. For Epicureanism, the occasional interventions of arbitrary gods would be preferable to strict determinism.

Early modern philosophy

In 1729 theTestament of Jean Meslier states:

"The matter, by virtue of its own active force, moves and acts in blind manner".

Soon after Julien Offroy de la Mettrie in his L'Homme Machine. (1748, anon.) wrote:

"Perhaps, the cause of man's existence is just in existence itself? Perhaps he is by chance thrown in some point of this terrestrial surface without any how and why".

In his Anti-Sénèque [Traité de la vie heureuse, par Sénèque, avec un Discours du traducteur sur le même sujet, 1750] we read:

"Then, the chance has thrown us in life".

In the 19th century the French Philosopher Antoine-Augustin Cournot theorized chance in a new way, as series of not-linear causes. He wrote in Essai sur les fondements de nos connaissances (1851):

"It is not because of rarity that the chance is actual. On the contrary, it is because of chance they produce many possible others."

Modern philosophy

Charles Peirce

Tychism (Greek: τύχη "chance") is a thesis proposed by the American philosopher Charles Sanders Peirce in the 1890s. It holds that absolute chance, also called spontaneity, is a real factor operative in the universe. It may be considered both the direct opposite of Albert Einstein's oft quoted dictum that: "God does not play dice with the universe" and an early philosophical anticipation of Werner Heisenberg's uncertainty principle.

Peirce does not, of course, assert that there is no law in the universe. On the contrary, he maintains that an absolutely chance world would be a contradiction and thus impossible. Complete lack of order is itself a sort of order. The position he advocates is rather that there are in the universe both regularities and irregularities.

Karl Popper comments that Peirce's theory received little contemporary attention, and that other philosophers did not adopt indeterminism until the rise of quantum mechanics.

Arthur Holly Compton

In 1931, Arthur Holly Compton championed the idea of human freedom based on quantum indeterminacy and invented the notion of amplification of microscopic quantum events to bring chance into the macroscopic world. In his somewhat bizarre mechanism, he imagined sticks of dynamite attached to his amplifier, anticipating the Schrödinger's cat paradox.

Reacting to criticisms that his ideas made chance the direct cause of our actions, Compton clarified the two-stage nature of his idea in an Atlantic Monthly article in 1955. First there is a range of random possible events, then one adds a determining factor in the act of choice.

A set of known physical conditions is not adequate to specify precisely what a forthcoming event will be. These conditions, insofar as they can be known, define instead a range of possible events from among which some particular event will occur. When one exercises freedom, by his act of choice he is himself adding a factor not supplied by the physical conditions and is thus himself determining what will occur. That he does so is known only to the person himself. From the outside one can see in his act only the working of physical law. It is the inner knowledge that he is in fact doing what he intends to do that tells the actor himself that he is free.

Compton welcomed the rise of indeterminism in 20th century science, writing:

In my own thinking on this vital subject I am in a much more satisfied state of mind than I could have been at any earlier stage of science. If the statements of the laws of physics were assumed correct, one would have had to suppose (as did most philosophers) that the feeling of freedom is illusory, or if [free] choice were considered effective, that the laws of physics ... [were] unreliable. The dilemma has been an uncomfortable one.

Together with Arthur Eddington in Britain, Compton was one of those rare distinguished physicists in the English speaking world of the late 1920s and throughout the 1930s arguing for the “liberation of free will” with the help of Heisenberg’s indeterminacy principle, but their efforts had been met not only with physical and philosophical criticism but most primarily with fierce political and ideological campaigns.

Karl Popper

In his essay Of Clouds and Clocks, included in his book Objective Knowledge, Popper contrasted "clouds", his metaphor for indeterministic systems, with "clocks", meaning deterministic ones. He sided with indeterminism, writing

I believe Peirce was right in holding that all clocks are clouds to some considerable degree — even the most precise of clocks. This, I think, is the most important inversion of the mistaken determinist view that all clouds are clocks

Popper was also a promoter of propensity probability.

Robert Kane

Kane was one of the leading contemporary philosophers on free will. Advocating what is termed within philosophical circles "libertarian freedom", Kane argues that "(1) the existence of alternative possibilities (or the agent's power to do otherwise) is a necessary condition for acting freely, and (2) determinism is not compatible with alternative possibilities (it precludes the power to do otherwise)". The crux of Kane's position is grounded not in a defense of alternative possibilities (AP) but in the notion of what Kane refers to as ultimate responsibility (UR). Thus, AP is a necessary but insufficient criterion for free will. It is necessary that there be (metaphysically) real alternatives for our actions, but that is not enough; our actions could be random without being in our control. The control is found in "ultimate responsibility".

What allows for ultimate responsibility of creation in Kane's picture are what he refers to as "self-forming actions" or SFAs — those moments of indecision during which people experience conflicting wills. These SFAs are the undetermined, regress-stopping voluntary actions or refrainings in the life histories of agents that are required for UR. UR does not require that every act done of our own free will be undetermined and thus that, for every act or choice, we could have done otherwise; it requires only that certain of our choices and actions be undetermined (and thus that we could have done otherwise), namely SFAs. These form our character or nature; they inform our future choices, reasons and motivations in action. If a person has had the opportunity to make a character-forming decision (SFA), he is responsible for the actions that are a result of his character.

Mark Balaguer

Mark Balaguer, in his book Free Will as an Open Scientific Problem argues similarly to Kane. He believes that, conceptually, free will requires indeterminism, and the question of whether the brain behaves indeterministically is open to further empirical research. He has also written on this matter "A Scientifically Reputable Version of Indeterministic Libertarian Free Will".

Science

See also: Philosophy of physics and indeterminism

Mathematics

In probability theory, a stochastic process, or sometimes random process, is the counterpart to a deterministic process (or deterministic system). Instead of dealing with only one possible reality of how the process might evolve over time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths may be more probable and others less so.

Classical and relativistic physics

The idea that Newtonian physics proved causal determinism was highly influential in the early modern period. "Thus physical determinism [..] became the ruling faith among enlightened men; and everybody who did not embrace this new faith was held to be an obscurantist and a reactionary". However: "Newton himself may be counted among the few dissenters, for he regarded the solar system as imperfect, and consequently as likely to perish".

Classical chaos is not usually considered an example of indeterminism, as it can occur in deterministic systems such as the three-body problem.

John Earman has argued that most physical theories are indeterministic. For instance, Newtonian physics admits solutions where particles accelerate continuously, heading out towards infinity. By the time reversibility of the laws in question, particles could also head inwards, unprompted by any pre-existing state. He calls such hypothetical particles "space invaders".

John D. Norton has suggested another indeterministic scenario, known as Norton's Dome, where a particle is initially situated on the exact apex of a dome.

Branching space-time is a theory uniting indeterminism and the special theory of relativity. The idea was originated by Nuel Belnap. The equations of general relativity admit of both indeterministic and deterministic solutions.

Boltzmann

Ludwig Boltzmann was one of the founders of statistical mechanics and the modern atomic theory of matter. He is remembered for his discovery that the second law of thermodynamics is a statistical law stemming from disorder. He also speculated that the ordered universe is only a small bubble in a larger sea of chaos. The Boltzmann brain is a similar idea.

Evolution and biology

Darwinian evolution has an enhanced reliance on the chance element of random mutation compared to the earlier evolutionary theory of Herbert Spencer. However, the question of whether evolution requires genuine ontological indeterminism is open to debate

In the essay Chance and Necessity (1970) Jacques Monod rejected the role of final causation in biology, instead arguing that a mixture of efficient causation and "pure chance" lead to teleonomy, or merely apparent purposefulness.

The Japanese theoretical population geneticist Motoo Kimura emphasises the role of indeterminism in evolution. According to neutral theory of molecular evolution: "at the molecular level most evolutionary change is caused by random drift of gene mutants that are equivalent in the face of selection.

Prigogine

In his 1997 book, The End of Certainty, Prigogine contends that determinism is no longer a viable scientific belief. "The more we know about our universe, the more difficult it becomes to believe in determinism." This is a major departure from the approach of Newton, Einstein and Schrödinger, all of whom expressed their theories in terms of deterministic equations. According to Prigogine, determinism loses its explanatory power in the face of irreversibility and instability.

Prigogine traces the dispute over determinism back to Darwin, whose attempt to explain individual variability according to evolving populations inspired Ludwig Boltzmann to explain the behavior of gases in terms of populations of particles rather than individual particles. This led to the field of statistical mechanics and the realization that gases undergo irreversible processes. In deterministic physics, all processes are time-reversible, meaning that they can proceed backward as well as forward through time. As Prigogine explains, determinism is fundamentally a denial of the arrow of time. With no arrow of time, there is no longer a privileged moment known as the "present," which follows a determined "past" and precedes an undetermined "future." All of time is simply given, with the future as determined or undetermined as the past. With irreversibility, the arrow of time is reintroduced to physics. Prigogine notes numerous examples of irreversibility, including diffusion, radioactive decay, solar radiation, weather and the emergence and evolution of life. Like weather systems, organisms are unstable systems existing far from thermodynamic equilibrium. Instability resists standard deterministic explanation. Instead, due to sensitivity to initial conditions, unstable systems can only be explained statistically, that is, in terms of probability.

Prigogine asserts that Newtonian physics has now been "extended" three times, first with the use of the wave function in quantum mechanics, then with the introduction of spacetime in general relativity and finally with the recognition of indeterminism in the study of unstable systems.

Quantum mechanics

Main article: Quantum indeterminacy

At one time, it was assumed in the physical sciences that if the behavior observed in a system cannot be predicted, the problem is due to lack of fine-grained information, so that a sufficiently detailed investigation would eventually result in a deterministic theory ("If you knew exactly all the forces acting on the dice, you would be able to predict which number comes up").

However, the advent of quantum mechanics removed the underpinning from that approach, with the claim that (at least according to the Copenhagen interpretation) the most basic constituents of matter at times behave indeterministically. This comes from the collapse of the wave function, in which the state of a system upon measurement cannot in general be predicted. Quantum mechanics only predicts the probabilities of possible outcomes, which are given by the Born rule. Non-deterministic behavior in wave function collapse is not only a feature of the Copenhagen interpretation, with its observer-dependence, but also of objective collapse and other theories.

Opponents of quantum indeterminism suggested that determinism could be restored by formulating a new theory in which additional information, so-called hidden variables, would allow definite outcomes to be determined. For instance, in 1935, Einstein, Podolsky and Rosen wrote a paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" arguing that such a theory was in fact necessary to preserve the principle of locality. In 1964, John S. Bell was able to define a theoretical test for these local hidden variable theories, which was reformulated as a workable experimental test through the work of Clauser, Horne, Shimony and Holt. The negative result of the 1980s tests by Alain Aspect ruled such theories out, provided certain assumptions about the experiment hold. Thus any interpretation of quantum mechanics, including deterministic reformulations, must either reject locality or reject counterfactual definiteness altogether. David Bohm's theory is the main example of a non-local deterministic quantum theory.

The many-worlds interpretation is said to be deterministic, but experimental results still cannot be predicted: experimenters do not know which 'world' they will end up in. Technically, counterfactual definiteness is lacking.

A notable consequence of quantum indeterminism is the Heisenberg uncertainty principle, which prevents the simultaneous accurate measurement of all a particle's properties.

Cosmology

Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. Currently, the most widely accepted explanation for their origin is in the context of cosmic inflation. According to the inflationary paradigm, the exponential growth of the scale factor during inflation caused quantum fluctuations of the inflaton field to be stretched to macroscopic scales, and, upon leaving the horizon, to "freeze in". At the later stages of radiation- and matter-domination, these fluctuations re-entered the horizon, and thus set the initial conditions for structure formation.

Neuroscience

Neuroscientists such as Björn Brembs and Christof Koch believe thermodynamically stochastic processes in the brain are the basis of free will, and that even very simple organisms such as flies have a form of free will. Similar ideas are put forward by some philosophers such as Robert Kane.

Despite recognizing indeterminism to be a very low-level, necessary prerequisite, Björn Brembs says that it's not even close to being sufficient for addressing things like morality and responsibility.

Other views

Against Einstein and others who advocated determinism, indeterminism—as championed by the English astronomer Sir Arthur Eddington—says that a physical object has an ontologically undetermined component that is not due to the epistemological limitations of physicists' understanding. The uncertainty principle, then, would not necessarily be due to hidden variables but to an indeterminism in nature itself.

Determinism and indeterminism are examined in Causality and Chance in Modern Physics by David Bohm. He speculates that, since determinism can emerge from underlying indeterminism (via the law of large numbers), and that indeterminism can emerge from determinism (for instance, from classical chaos), the universe could be conceived of as having alternating layers of causality and chaos.

Incompatibilism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Incompatibilism 

Classical incompatibilists hold that determinism leaves no room for free will.

Incompatibilism is the view that the thesis of determinism is logically incompatible with the classical thesis of free will. The term was coined in the 1960s, most likely by philosopher Keith Lehrer. The term compatibilism was coined (also by Lehrer) to name the view that the classical free will thesis is logically compatible with determinism, i.e. it is possible for an ordinary human to exercise free will (the freedom-relevant ability to do otherwise), even in a universe where determinism is true.

These terms were originally coined for use within a research paradigm that was dominant among academics during the so-called "classical period" from the 1960s to 1980s, or what has been called the "classical analytic paradigm". Within the classical analytic paradigm, the problem of free will and determinism was understood as a compatibility question: "Is it possible for an ordinary human to exercise free will (classically defined as an ability to do otherwise) when determinism is true?" Those working in the classical analytic paradigm who answered "no" were incompatibilists in the original, classical-analytic sense of the term, now commonly called classical incompatibilists; they proposed that determinism precludes free will because it precludes the ability to do otherwise. Those who answered "yes" were compatibilists in the original sense of the term, now commonly called classical compatibilists. Given that classical free will theorists (i.e. those working in the classical analytic paradigm) agreed that it is at least metaphysically possible for an ordinary human to exercise free will, all classical compatibilists accepted a compossibilist account of free will (i.e. a compossibilist interpretation of the ability to do otherwise) and all classical incompatibilists accepted a libertarian account of free will (i.e. a libertarian interpretation of the ability to do otherwise).

The classical analytic paradigm has fallen out of favor over the last few decades, largely because philosophers no longer agree that free will is equivalent to some kind of ability to do otherwise; many hold that it is, instead, a type of sourcehood that does not require an ability to do otherwise. The number of philosophers who reject the classical assumption of anthropocentric possibilism, i.e. the view that it is at least metaphysically possible for a human to exercise free will, has also risen in recent years. As philosophers adjusted Lehrer's original (classical) definitions of the terms incompatibilism and compatibilism to reflect their own perspectives on the location of the purported "fundamental divide" among free will theorists, the terms incompatibilism and compatibilism have been given a variety of new meanings. At present, then, there is no standard meaning of the term incompatibilism (or its complement compatibilism).

Definition

On one recent taxonomy, there are now at least three substantively different, non-classical uses of the term incompatibilism, namely: neo-classical incompatibilism, post-classical incompatibilism (a.k.a. incompossibilism), and anti-classical incompatibilism. Correspondingly, there are neo-classical, post-classical (compossibilist), and anti-classical versions of compatibilism as well. Neo-classical incompatibilism is a two-tenet view: incompossibilism is true (i.e. it is metaphysically impossible for an ordinary human to act freely when determinism is true), and determinism-related causal/nomological factors preclude free will (which explains why incompossibilism is true). Correspondingly, neo-classical compatibilism is the two-tenet view that: the negative, non-explanatory tenet of neo-classical incompatibilism is false (i.e. compossibilism is true), and that the positive, explanatory tenet of neo-classical incompatibilism is false. Anti-classical incompatibilism is the explanatory thesis of neo-classical incompatibilism; anti-classical incompatibilism is neutral on the truth-value of incompossibilism. Correspondingly, anti-classical compatibilism is the negation of neo-classical incompatibilism's positive tenet, i.e. anti-classical compatibilism is the contradictory of anti-classical incompatibilism. Post-classical incompatibilism is just the negative, non-explanatory thesis of neo-classical incompatibilism; this view is neutral on whether the positive, explanatory thesis of neo-classical incompatibilism is true. (Put another way, on the post-classical redefinition of incompatibilism, it is just an alternative name for incompossibilism, a view which is completely silent on whether determinism-related causal factors are relevant to free will or are a total "red herring" in discussions of free will.) Correspondingly, post-classical compatibilism is identical to compossibilism (i.e. on the post-classical redefinition of compatibilism, it denotes mere compossibilism).

The ambiguity of incompatibilism can be a source of confusion because arguments with very different (even inconsistent) conclusions are currently lumped together under the umbrella phrase "arguments for incompatibilism". For example, it is easy for the casual reader to overlook that some arguments for post-classical incompatibilism (a.k.a. incompossibilism) are not arguments for neo-classical incompatibilism on the grounds that the argument does not aim to support the latter's explanatory tenet (a.k.a. anti-classical incompatibilism). Other arguments support post-classical incompatibilism (a.k.a. incompossibilism) but conclude that neo-classical incompatibilism is false on the grounds that its explanatory tenet (a.k.a. anti-classical incompatibilism) is false. Arguments in the last category conclude that people lack free will when determinism is true but not at all because determinism is true (i.e. not at all because certain causal/nomological factors obtain); most propose that the real threat to free will is that people lack adequate control over their own constitutive properties, or what is often called their "constitutive luck" (as opposed to causal luck).

Libertarianism

Main article: Libertarianism (metaphysics)

Free-will libertarianism is the view that the free-will thesis (that we, ordinary humans, have free will) is true and that determinism is false; in first-order language, it is the view that we (ordinary humans) have free will and the world does not behave in the way described by determinism. Libertarianism is one of the popular solutions to the problem of free will, roughly the problem of settling the question of whether we have free will and the logically prior question of what free will amounts to. The main rivals to libertarianism are soft determinism and hard determinism.

Libertarian Robert Kane (editor of the Oxford Handbook of Free Will) is a leading incompatibilist philosopher in favour of free will. Kane seeks to hold persons morally responsible for decisions that involved indeterminism in their process. Critics maintain that Kane fails to overcome the greatest challenge to such an endeavor: "the argument from luck". Namely, if a critical moral choice is a matter of luck (indeterminate quantum fluctuations), then the question of holding a person responsible for their final action arises. Moreover, even if we imagine that a person can make an act of will ahead of time, to make the moral action more probable in the upcoming critical moment, this act of 'willing' was itself a matter of luck. Kane objects to the validity of the argument from luck because the latter misrepresents the chance as if it is external to the act of choosing. The free will theorem of John H. Conway and Simon B. Kochen further establishes that if we have free will, then quantum particles also possess free will. This means that starting from the assumption that humans have free will, it is possible to pinpoint the origin of their free will in the quantum particles that constitute their brain.

Such philosophical stance risks an infinite regress, however; if any such mind is real, an objection can be raised that free will would be impossible if the choosing is shaped merely by luck or chance.

Libertarianism in the philosophy of mind is unrelated to the like-named political philosophy. It suggests that we actually do have free will, that it is incompatible with determinism, and that therefore the future is not determined.

One famous proponent of this view was Lucretius, who asserted that the free will arises out of the random, chaotic movements of atoms, called "clinamen". One major objection to this view is that science has gradually shown that more and more of the physical world obeys completely deterministic laws, and seems to suggest that our minds are just as much part of the physical world as anything else. If these assumptions are correct, incompatibilist libertarianism can only be maintained as the claim that free will is a supernatural phenomenon, which does not obey the laws of nature (as, for instance, maintained by some religious traditions).

However, many libertarian view points now rely upon an indeterministic view of the physical universe, under the assumption that the idea of a deterministic, clockwork universe has become outdated since the advent of quantum mechanics. By assuming an indeterministic universe, libertarian philosophical constructs can be proposed under the assumption of physicalism.

There are libertarian view points based upon indeterminism and physicalism, which is closely related to naturalism. A major problem for naturalistic libertarianism is to explain how indeterminism can be compatible with rationality and with appropriate connections between an individual's beliefs, desires, general character and actions. A variety of naturalistic libertarianism is promoted by Robert Kane, who emphasizes that if our character is formed indeterministically (in "self-forming actions"), then our actions can still flow from our character, and yet still be incompatibilistically free.

Alternatively, libertarian view points based upon indeterminism have been proposed without the assumption of naturalism. At the time C. S. Lewis wrote Miracles, quantum mechanics (and physical indeterminism) was only in the initial stages of acceptance, but still Lewis stated the logical possibility that, if the physical world was proved to be indeterministic, this would provide an entry (interaction) point into the traditionally viewed closed system, where a scientifically described physically probable/improbable event could be philosophically described as an action of a non-physical entity on physical reality (noting that, under a physicalist point of view, the non-physical entity must be independent of the self-identity or mental processing of the sentient being). Lewis mentions this only in passing, making clear that his thesis does not depend on it in any way.

Others may use some form of Donald Davidson's anomalous monism to suggest that although the mind is in fact part of the physical world, it involves a different level of description of the same facts, so that although there are deterministic laws under the physical description, there are no such laws under the mental description, and thus our actions are free and not determined.

Consequence argument

Main article: Consequence argument

Peter van Inwagen proposed his consequence argument to argue that free will is not compatible with determinism. He assumes the truth of determinism to argue that a person could not have acted differently from how they actually did. from this, he rejects that determinism is true to preserve free will, but concludes that they are mutually exclusive. His argument is formally valid as follows:

(1) If determinism is true, then the conjunction of P0 and L entail P (2) It is not possible that J have raised his hands at T and P be true (3) If (2) is true, then if J could have raised his hand at T, J could have rendered P false (4) If J could have rendered P false, and if the conjunction of P0 and L entails P, then J could have rendered the conjunction of P0 and L false (5) If J could have rendered the conjunction of P0 and L false, then J could have rendered L false (6) J could not have rendered L false (7) If determinism is true, J could not have raised his hand at T

Where J is a judge who did not raise their hand at time T, P is the entire physical state of the world at T, P0 is the entire physical state of the world in the remote past, and L is the conjunction of all the laws of nature, which by definition cannot actually be rendered false.

Van Inwagen then presents a dilemma, we can either:

• Deny determinism and accept incompatibilism
• Accept that contradictions could be true in the actual world
• Accept that we can change the remote past
• Accept that we can render false the laws of nature
• Deny Free will and accept incompatibilism

The compatibilist is committed to rejecting the former and the latter, so they choose option 2, 3, or 4 to maintain their position. David Lewis objected by denying that laws of nature are never violated with counterpart theory, although counterpart theory is very controversial, and this leaves us with a significantly diluted version of free will.

Kadri Vihvelin rejected the argument by dismissing the conclusion, but refused to choose a premise to deny, arguing that the conclusion is false; therefore, one of the premises must be too. She later accepted Lewis's position, which is known as "local miracle compatibilism."

Semicompatibilism

Main article: Semicompatibilism

Semicompatibilism is unaffected by the consequent argument, as it is indifferent as to whether or not free will is compatible with determinism. It had previously been assumed that free will is required for moral responsibility, meaning that if determinism threatened free will, it would threaten moral responsibility as well. Semi-compatibilists deny this entailment, arguing that, regardless of free will's compatibility, moral responsibility is compatible with determinism. However, Van Inwagen's Direct Argument argues in a similar manner for the incompatibility of determinism with moral responsibility. A semicompatibilist would have to engage with this argument, although its validity is questioned over modal logic.

Hard determinism

Main article: Hard determinism

Schopenhauer said "Man is free to do what he wills, but he cannot will what he wills." The hard determinist says then, there is no "free will".

Those who reject free will and accept determinism are variously known as "hard determinists", hard incompatibilists, free will skeptics, free will illusionists, or impossibilists. They believe that there is no free will and that any sense of the contrary is an illusion. Hard determinists do not deny that one has desires, but say that these desires are causally determined by an unbroken chain of prior occurrences. According to this philosophy, no wholly random, spontaneous, mysterious, or miraculous events occur. Determinists sometimes assert that it is stubborn to resist scientifically motivated determinism on purely intuitive grounds about one's own sense of freedom. They reason that the history of the development of science suggests that determinism is the logical method in which reality works.

William James said that philosophers (and scientists) have an "antipathy to chance". Absolute chance, a possible implication of quantum mechanics and the indeterminacy principle, supports the existence of indefinite causal structures.

Moral implications

Since many believe that free will is necessary for moral responsibility, hard determinism may imply disastrous consequences for their theory of ethics, resulting in a domino theory of moral nonresponsibility.

As something of a solution to this predicament, one might embrace the so-called illusion of free will. This thesis argues in favor of maintaining the prevailing belief in free will for the sake of preserving moral responsibility and the concept of ethics. However, critics argue that this move renders morality merely another "illusion", or else that this move is simply hypocritical.

The determinist will add that, even if denying free will does mean morality is incoherent, such a result has no effect on the truth. However, hard determinists often have some sort of moral system that relies explicitly on determinism. A determinist's moral system simply bears in mind that every person's actions in a given situation are, in theory, predicted by the interplay of environment and upbringing.

Hard incompatibilism

Hard incompatibilism, like hard determinism, is a type of skepticism about free will. Hard incompatibilism is a term coined by Derk Pereboom to designate the view that both determinism and indeterminism are incompatible with having free will and moral responsibility. Like the hard determinist, the hard incompatibilist holds that if determinism were true, people would not have free will. But Pereboom argues in addition that if decisions were indeterministic events, free will would also be precluded. In his view, free will is the control in action required for the desert aspect of moral responsibility—for people to deserve to be blamed or punished for immoral actions, and to be praised or rewarded for morally exemplary actions. He contends that if people's decisions were indeterministic events, their occurrence would not be in the control of the agent in the way required for such attributions of desert. The possibility for free will that remains is libertarian agent causation, according to which agents as substances (thus not merely as having a role in events) can cause actions without being causally determined to do so. Pereboom argues that for empirical reasons it is unlikely that people are agent causes of this sort, and that as a result, it is likely that they lack free will.

Experimental research

In recent years researchers in the field of experimental philosophy have been working on determining whether ordinary people, who are not experts in this field, naturally have compatibilist or incompatibilist intuitions about determinism and moral responsibility. Some experimental work has even conducted cross-cultural studies. The debate about whether people naturally have compatibilist or incompatibilist intuitions has not come out overwhelmingly in favor of one view or the other. Still, there has been some evidence that people can naturally hold both views. For instance, when people are presented with abstract cases which ask if a person could be morally responsible for an immoral act when they could not have done otherwise, people tend to say no, or give incompatibilist answers, but when presented with a specific immoral act that a specific person committed, people tend to say that that person is morally responsible for their actions, even if they were determined (that is, people also give compatibilist answers).