The Identity of Elementary Particles and Einstein’s Discovery of Quantum Statistics

In 1924, Albert Einstein received an amazing very short paper from India by Satyendra Nath Bose. Einstein must have been pleased to read the title, “Planck’s Law and the Hypothesis of Light Quanta.” It was more attention to Einstein’s 1905 work than anyone had paid in nearly twenty years. The paper began by claiming that the “phase space” (a combination of 3-dimensional coordinate space and 3-dimensional momentum space) should be divided into small volumes of h3, the cube of Planck’s constant. By counting the number of possible distributions of light quanta over these cells, Bose claimed he could calculate the entropy and all other thermodynamic properties of the radiation.

Bose easily derived the inverse exponential function. Einstein too had derived this. Maxwell and Boltzmann derived it, without the additional -1, by analogy from the Gaussian exponential tail of probability and the theory of errors.

1 / (e – hν / kT -1)

(Planck had simply guessed this expression from Wien’s law by adding the term – 1 in the denominator of Wien’s a / e – bν / T).

All previous derivations of the Planck law, including Einstein’s of 1916-17 (which Bose called “remarkably elegant”), used classical electromagnetic theory to derive the density of radiation, the number of “modes” or “degrees of freedom” of the radiation field,

ρνdν = (8πν2dν / c3) E

But now Bose showed he could get this quantity with a simple statistical mechanical argument remarkably like that Maxwell used to derive his distribution of molecular velocities. Where Maxwell said that the three directions of velocities for particles are independent of one another, but of course equal to the total momentum,

px2 + py2 + pz2 = p2 ,

Bose just used Einstein’s relation for the momentum of a photon,

p = hν / c,

and he wrote

px2 + py2 + pz2 = h2ν2 / c2 .

This led him to calculate a frequency interval in phase space as

 dx dy dz dpx dpy dpz = 4πV ( hν / c )3 ( h dν / c ) = 4π ( h3 ν2 / c3 ) V dν,

which he simply divided by h3, multiplied by 2 to account for two polarization degrees of freedom, and he had derived the number of cells belonging to dν,

ρνdν = (8πν2dν / c3) E ,

without using classical radiation laws, a correspondence principle, or even Wien’s law. His derivation was purely statistical mechanical, based only on the number of cells in phase space and the number of ways N photons can be distributed among them.

Einstein immediately translated the Bose paper into German and had it published in Zeitschrift für Physik, without even telling Bose. More importantly, Einstein then went on to discuss a new quantum statistics that predicted low-temperature condensation of any particles with integer values of the spin. So called Bose-Einstein statistics were quickly shown by Dirac to lead to the quantum statistics of half-integer spin particles now called Fermi-Dirac statistics. Fermions are half-integer spin particles that obey Pauli’s exclusion principle so a maximum of two particles, with opposite spins, can be found in the fundamental h3 volume of phase space identified by Bose.

Einstein’s 1916 work on transition probabilities predicted the stimulated emission of radiation that brought us lasers (light amplification by the stimulated emission of radiation). Now his work on quantum statistics brought us the Bose-Einstein condensation. Either work would have made their discoverer a giant in physics, but these are more often attributed to Bose, just as Einstein’s quantum discoveries before the Copenhagen Interpretation are mostly forgotten by historians and today’s textbooks, or attributed to others.

This may have been Einstein’s last positive contribution to quantum physics. Some judge his next efforts as purely negative attempts to discredit quantum mechanics, by graphically illustrating quantum phenomena that seem logically impossible or at least in violation of fundamental theories like his relativity. But information philosophy hopes to provide explanations for Einstein’s paradoxes that depend on the immaterial nature of information.

The phenomena of nonlocalitynonseparability, and entanglement may not be made intuitive by our explanations, but they can be made understandable. And they can be visualized in a way that Einstein and Schrödinger might have liked, even if they would still find the phenomena impossible to believe. We hope even the layperson will see our animations as providing them an understanding of what quantum mechanics is doing in the microscopic world. The animations present standard quantum physics as Einstein saw it, though Schrödinger never accepted the “collapse” of the wave function and the existence of particles.

Frege’s Puzzle and the New Theory of Reference – Quine, Marcus, and Kripke

Most of the metaphysical problems of identity, and especially recent claims about the necessity of identity, can be traced back to the great rationalist philosopher Gottfried Leibniz, who argued for the replacement of ordinary language with a lingua characterica, an ambiguity-free set of terms that would eliminate philosophical puzzles and paradoxes. Bertrand Russell, Ludwig Wittgenstein, and Rudolf Carnap all believed in this Leibnizian dream of ambiguity-free, logically true, facts about the world that may be true in all possible worlds. Unfortunately, fundamental limits on logic and language such as the Gödel and Russell paradoxes have prevented Leibniz’s ideal ambiguity-free language, but many modern paradoxes, including questions about identity and necessity, are resolvable in terms of information, as we shall see

More than any other philosopher, Leibniz enunciated clear principles about identity, including his Identity of Indiscernibles. If we can see no differences between things, they may be identical. This is an empirical fact, and must be tested empirically, as Leibniz knew. But once again, whenever we are talking about two things, that there is a difference between them, a discernible difference, is transparently obvious. Two things are numerically distinct even if they have identical internal information. Leibniz also described a corollary or converse, the Indiscernibility of Identicals.  But this idea is necessarily true, if such things as numerically distinct identical objects exist. We shall show that such things have only a relative identity, identity in some respects

Gottlob Frege implemented Leibniz’s program of a purely logical language in which statements or sentences with subjects and predicates are replaced with propositional functions, in which a term can be replaced by a variable. In modern terminology, the sentence Socrates is mortal can be replaced, setting the subject Socrates = x, and the predicate “is mortal” with F. “x is F” is replaced by the propositional function Fx, which is read “x is F,” or “x F’s.”

Names and Reference

Although Frege was very clear, generations of philosophers have obscured his clarity by puzzling over different names and/or descriptions referring to the same thing that may lead to logical contradictions – starting with Frege’s original example of the Morning Star and Evening Star as names that refer to the planet Venus. Do these names have differing cognitive value? Yes. Can they be defined qua references to uniquely pick out Venus. Yes. Is identity a relation? No. But the names are relations, words that are references to the objects. And words put us back into the ambiguous realm of language.

Over a hundred years of confusion in logic and language have consisted of finding two expressions that can be claimed in some sense to be identical, but upon substitution in another statement, they do not preserve the truth value of the statement. Besides Frege, and a few examples from Bertrand Russell (“Scott” and “the author of Waverly.” “bachelor” and “unmarried man”), Willard Van Orman Quine was the most prolific generator of substitution paradoxes (“9” and “the number of planets,” “Giorgione” and “Barbarelli,” “Cicero” and “Tully,” and others).

Just as information philosophy shows how to pick out information in an object or concept that constitutes the “peculiar qualifications” that individuate it, so we can pick out the information in two designating references that provide what Quine called “purely designative references.” Where Quine picks out information that leads to contradictions and paradoxes (he calls this “referential opacity”), we can “qualify” the information, the “sense” or meaning needed to make them referentially transparent when treated “intensionally.”

Ruth Barcan Marcus

In 1947, Ruth C. Barcan (later Ruth Barcan Marcus) wrote an article on “The Identity of Individuals.” It was the first assertion of the so-called “necessity of identity.” Five years later, Marcus’s thesis adviser, Frederic B. Fitch, published his book, Symbolic Logic, which contained the simplest proof ever of the necessity of identity, by the simple mathematical substitution of b for a in the necessity of self-identity statement:

(1) a = b, (2) ☐[a = a], then (3) ☐[a = b], by identity elimination.

Saul Kripke

The indiscernibility of identicals claims that if x = y, then x and y must share all their properties, otherwise there would be a discernible difference. Saul Kripke argues that one of the properties of x is that x = x, so if y shares the property of ‘= x,” we can say that y = x. Then, necessarily, x = y. But this is nonsense for distinct objects. Two distinct things, x and y, cannot be identical, because there is some difference in extrinsic external information between them. Instead of claiming that y has x’s property of being identical to x (“= x”), we can say only that y has x’s property of being self-identical, thus y = y. Wiggins called this result “impotent.” Then x and y remain distinct in at least this intrinsic property as well as in extrinsic properties like their distinct positions in space.

Information philosophy shows that the indiscernibles x and y have only relative identity.


Robert Kane’s Self-Forming Actions and Ultimate Responsibility

Since his earliest book, Free Will and Values (1985), Kane has focused on free choices that have moral or prudential significance, as as well as those with merely practical significance. He accepts two-stage models of free will as relevant to practical choices, but thinks “something more” is needed for moral choices, which are the grounds for his character-developing “Self-Forming Willings” or “Self-Forming Actions.”

Like most philosophers, Kane does not separate free will from moral responsibility. Indeed , he conflates these two, which he describes as “the traditional definition of free will.” He describes what he calls “ultimate responsibility” as his basis for free will.

But whether or not we are predetermined by the laws of nature can not be shown by any verbal definition. Freedom of the will is a question for science.

Kane follows ideas that he traces back through Daniel DennettKarl PopperArthur Holly Compton, and David Wiggins. (They can be traced even earlier to Bertrand RussellArthur Stanley Eddington, all the way to Epicurus, whom Kane mentions briefly.)

Kane’s most original contribution to the free-will debates may be his account of decisions that involves some indeterminism, but for which the agent can properly claim responsibilityCompatibilists believe that any chance involved in the cause of an action compromises agent control and therefore responsibility. But in the case of what Kane calls a “torn decision” or “self-forming action” (SFA) the agent may have excellent reasons for choosing “either way.” In such a case, indeterminism may be involved (Kane defends the possibility of irreducible quantum indeterminism), yet the agent may properly take responsibility for either option, as long as the final choice is a result of the agent’s “efforts.” Kane calls this “plural (or dual) rational control.”

Kane’s most careful articulation of his position was given in response to the Luck Objection, raised by several critics of Kane’s inclusion of indeterminism in his Self-Forming Actions. Kane’s critics who found indeterminism unhelpful in all cases included Galen StrawsonAlfred MeleBernard BerofskyRichard Double, and Ishtiyaque Haji. Earlier works on Moral Luck by Thomas Nagel and Bernard Williams had similar implications.

Separating Free from Will and Responsibility from Punishment, Whether Retributive or Consequential

The Separability of Free Will and Moral Responsibility

We propose four Degrees of Separation:

  1. The Separation of “Free” from “Will”
  2. The Separation of “Responsibility” from “Moral Responsibility”
  3. The Separation of “Free Will” from “Moral Responsibility”
  4. The Separation of “Free Will and Moral Responsibility” from “Punishment” – both Retributive and Consequentialist

We must separate the concept “free” from the concept of “will” in order to better understand “free will,” as John Locke recommended we do to avoid verbal confusion. He said, “I think the question is not proper, whether the will be free, but whether a man be free.” 
(Essay Concerning Human Understanding, Book II, Chapter XXI, Of Power, s.21)

We must also separate “moral responsibility” from ordinary “responsibility” or simple accountability. If our intentions and decisions caused an action, we are responsible for it, but moral responsibility requires that the action has moral consequences. Immanuel Kant and the modern free willist Robert Kane think that only moral decisions can be free decisions. We think that is an “ethical fallacy.” Most free decisions and consequent actions do not involve moral responsibility.

Free will is a scientific question. Moral responsibility is a social and cultural question.

Compatibilists have blurred and confused this important distinction in order to give their moral beliefs a more substantial foundation than they deserve.

We must go even further to clarify the relationship between free will and moral responsibility. Some philosophers, e.g., John Martin Fischer, deflect direct discussion of free will and study it only as the “control condition for moral responsibility.” Others, e.g., Daniel Dennett, argue that free will IS moral responsibility, and it is the only “free will worth wanting.” Fischer and Dennett at least agree that moral responsibility exists.

By contrast, many other thinkers, e.g., Galen Strawson, Derek Pereboom, and Saul Smilansky, argue that moral responsibility does not exist. It is just an illusion, along with free will and consciousness.

Finally, we explore the connection between moral responsibility and punishment,  both backward-looking retributive punishment (revenge or restitution) and forward-looking consequentialism (re-education and rehabilitation).

Liberal and humanitarian thinkers who see that retributive punishment is sometimes cruel and unproductive should not try to argue that punishment is not “deserved” because free will does not exist.

They have excellent reasons for preferring rehabilitation and education to vengeance.

Naturalists argue that humans are just a form of animal and that we lack free will because animals do. The idea that there is no free will in animals, that they are completely determined, was the old religious argument that God had given man the gift of free will. The new version is that animals lack moral responsibility, which is now being questioned in many sociobiological studies.

Whether man – and higher animals too – have free will is an empirical scientific question. Whether they have moral responsibility is a social and cultural question.

To make it depend on arguments against vengeance and retributive punishment is to get the cart before the horse.

Equating free will with moral responsibility, then to use spurious arguments to deny free will, and thus to deny moral responsibility – in order to oppose punishment – is fine humanism but poor philosophy, and terrible science.

We must separate both free will and moral responsibility from “punishment,” whether retributive or consequentialist.

God and Immortality Are Human Inventions to Defy Death and Control Behaviors

Most of the world’s religions have some concept of gods or a God, with some notable exceptions such as Buddhism.

Theologians claim to have discerned the essential attributes of a monotheistic God, such as omniscience (perfect foreknowledge), omnipotence (unlimited power), omnipresence (present everywhere), omnibenevolence (perfect goodness), and a necessary and eternal existence.

Information philosophy offers a simple test of the “revealed truth” of these attributes, specifically the visions by inspired thinkers that have no empirical evidence. Although these visions are in the realm of “pure ideas,” we can say that if every world religion agreed completely on the attributes of God, it would increase their believability. As it is, the comparative study of religions with the incredible diversity of their claims, renders the idea of God as implausible as Santa Claus.

At the present time, arguments like these will carry little weight with the believers in a religion, most of whom have little exchange of knowledge with those of other faiths. This can be expected to change with the reach of the Internet via smartphones to most of the world’s population by 2020.

In theism, God is the creator and sustainer of the universe. In deism, God is the creator, but not the sustainer of the universe, which is now assumed to be running itself following deterministic laws of motion. Open theism denies that God’s foreknowledge has already determined the future. Monotheism is the belief in the existence of one God or in the oneness of God. In pantheism, God is the universe itself. Polytheists hold that there are many gods. For atheists, no gods exist.

God is sometimes conceived as an immaterial being (without a body), which information philosophy accepts, since God is quintessentially an idea, pure information. Some religions think an avatar of God has come to earth in the past. Some religions see God as a personal being, answering human supplications and prayers. A God intervening in human affairs is often thought to be the source of all moral norms. Logical “proofs” of God’s existence are based on various of these assumed attributes. Now that information philosophy and physics has identified the essential attributes and properties of the cosmic creation process, the problem for theologians is to reconcile their views of their gods with these new discoveries.

Creation Without A Creator?

Modern cosmology confirms that the universe came into existence at a definite time in the past, some 13.8 billion years ago. Although this does not imply the Creator some religions want, it does confirm a creation process. Because this process continues today (indeed human beings are co-creators of the world), deists are wrong about a creative act at the beginning followed by a mechanical clockwork universe tending to itself ever since. So “creationism” is wrong.

Evolution Without A Designer?

What about “intelligent design?” This is the ancient teleological notion that the “essence” or idea of something was there before the thing itself came into existence. Since all information structures, first cosmological and then biological, were “emergent,” at least some of their peculiar specific information did not pre-exist them. The “existentialists,’ from Nietzsche to Sartre, were correct in this respect, but their idea that “God is dead” was absurd.

Mind Without A Soul?

Actually information philosophy explains the human soul, but it is a mortal soul. And it explains the mind, but it is an immaterial mind, embodied in the material brain. Mind and soul are key components of the Self, the seat of our “spiritual” character. Self also corresponds to the Ego, which positivists, empiricists, materialists, reductionists, and naturalists have denied since the early nineteenth century. It is Gilbert Ryle’s famous “ghost in the machine.”

An Experience Recorder and Reproducer

Mental information is stored and recalled in an experience recorder and reproducer that also recalls the emotions, the passions, the feelings, the drives that accompanied past experiences. The ERR is beyond any computational reasoning system, beyond mere cognition, beyond logic and language. It is the basis for sentiments, for values, for agency, and ultimately, for free will and moral responsibility.

Man is not a machine and the mind is not a computer.

Freedom Without Values Is Absurd.

Compare Continental Rational Existentialism

Values Without Freedom Are Useless.

Compare British Empirical Utilitarianism


Quantum Probabilities Are a Function of Space and Its Boundary Conditions

For my Einstein lecture today, I review the slow progress on my fourth book, My God, He Plays Dice! How Albert Einstein Invented Most of Quantum Mechanics.

I must admit that lecturing five times a week has taken a toll on my writing. A large part of the delay has been solving a number of technical problems in my iTV-Studio. My streaming equipment failed on some occasions and I had to manually upload backup files from those saved at CCTV, my local cable channel in Cambridge. I have now connected two video recorders in my studio, so I will have backups here for future failures.

I now have an earphone monitor that let’s me hear the levels when I play music or YouTube videos (and apologize for my early videos with distorted sound that was too loud).

Another impact on my time has been learning to manage the user interfaces for YouTube and Facebook, arranging my lectures in “playlists,” etc. I am trying to put my lectures on Apple Podcasts (and perhaps the new Google Play) but am only partly along that learning curve.

The good news is that improving my arguments for viewers, and especially my animations of quantum mysteries like entanglement, the two-slit experiment, and wave-function collapse, will help the arguments in my book.

But sadly, a printed book is really inadequate for explaining these difficult but critically important ideas. My web page on Einstein is my best tool. 

Today I will continue to struggle with the probabilistic and statistical nature of quantum mechanics revealed by the two-slit experiment.

The quantum possibility field, calculated from the deterministically evolving Schrödinger equation, is a property of space. Like all fields, it exists whether or not there is a particle present. It only depends on the particle through the particle’s wavelength.

Experiments with one-slit and two-slits open, showing the possibilities field calculated from | ψ |2. The possibilities field for two slits open applies whichever slit the particle enters. It is a property of the boundary conditions for the space.

Following Einstein’s objective reality view that particles have paths even if they cannot be measured, we can now animate the above cases of one slit open or two. Note that with two slits open, the paths start from one slit or the other, distributing themselves randomly between the interference fringes.

See for more.



The Ships of Theseus and Otto Neurath

The Ship of Theseus was a famous vessel

The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrus Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question as to things that grow; one side holding that the ship remained the same, and the other contending it was not the same.

In his De CorporeThomas Hobbes followed up an ancient suggestion that the ship’s original planks might have been hoarded by a collector on land and reassembled, once every part had been replaced. Hobbes offered the reassembled ship as the true original. But he may have had his tongue in his cheek about the ambiguous use of language in truth claims. It is the true original, qua material, but not qua a functioning ship.

Information philosophy resolves the paradox

From an information philosophy perspective, the Ship of Theseus is just a quibble about naming. But the full facts of the matter provide the information to name a ship uniquely.

We have perfect information about the constituting planks, especially if they are carefully distinguished and stored for reassembly of the original planks as a museum copy (presumably the ship reassembled from old planks will not be seaworthy).

We have perfectly understandable and meaningful names for all the parts in this problem. We have the original ship. We have for example original plank 224, replacement plank 175, etc. We have the repaired ship with specific replacement planks in position. We can keep a diagram showing where all the planks fit. Finally we have the reassembled ship. We can see two numerically distinct ships (or at least collections of ship parts) at all times

The comparable problem of identifying parts of an organism, – specific cells, even atoms, is extremely difficult if not impossible. The exact boundaries of organs and limbs are vague, etc.

So apart from denials that composite inanimate objects exist at all, where is the deep metaphysical problem?

If it is the problem of identity through time, the information philosophy solution is straightforward.

Otto Neurath was an founding member of the Vienna Circle. Starting in the 1920’s, he developed what he called the Vienna Method of Pictorial Statistics (Wiener Methode der Bildstatistik) in which simple and attractive icons were used to communicate knowledge.

After emigrating from Nazi Germany, while working in London, he renamed the method Isotype (International System Of TYpographic Picture Education) 

The idea of communicating ideas with pictures is a part of the Tractatus Logico-Philosophicus, the early Ludwig Wittgenstein‘s work for Bertrand Russell inspired by logical positivism. And it is the foundation of information philosophy, which analyzes the physical arrangement of material particles in any information structure.

Neurath’s image of knowledge (our SUM) as a ship that must be built while out at sea is his most lasting metaphor.

There is no way to establish fully secured, neat protocol statements as starting points of the sciences. There is no tabula rasa. We are like sailors who have to rebuild their ship on the open sea, without ever being able to dismantle it in dry-dock and reconstruct it from its best components.