This past week the Computer Science, Math, Physics, and Philosophy Clubs invited Dr. Scott Aaronson to speak at YU. He spoke mostly about the theoretical uses for quantum computing, which was cool. Then he spent some time talking about the philosophical implications of quantum mechanics. Right up the CS-Math-Physics-Philosophy alley. He also threw in a couple “bagels,” like “Hashem is a fan of complex numbers” and a line comparing quantum decoherence to “baking a sponge cake for Pesach.”
Most of his philosophy talk was on the nature of measurement in QM. He mentioned the position of von Neumann and Wigner that the intention of a conscious mind collapses the wave function. As appealing as this position is to a religious crowd, it’s not much in vogue today, though Google leads me to discover that some thinkers are still pursuing it.
Aaronson explained the modern view in terms of decoherence. A measurement is simply the outside world interfering with a quantum system. If you are the one doing the interfering, you become entangled with the system. The many-worlds interpretation would then say that you yourself become part of the superposition of the system; one version of you sees one possible result of the measurement and the parallel version of you sees the other.
Aaronson went on to discuss the back-and-forth between the supporters and critics of the many-worlds interpretation. It seems to me that the many-worlds interpretation is just a semantic way to explain the strange math so our practical minds can understand, and that to the extent that the other worlds are disconnected from the one followed by my own consciousness, I can cut them from reality. Either way, the idea of measurement as joining the entanglement sounds like a compelling way to understand the bridge between the quantum and classical world.
One comment I almost made during the questions and answers at the end regards the philosophical significance of indeterminacy. Aaronson mentioned the view that indeterminacy opens the door for free will, but argued himself that indeterminacy isn’t enough.
Richard Feynman understood more than most people about mechanics. He argued that classical mechanics is already practically indeterminate, and that free will was already possible in that regard before quantum theory was known. The full passage, from The Feynman Lectures on Physics, Vol. 1, 38–9 ff., is worth quoting in full:
We have already made a few remarks about the indeterminacy of quantum mechanics. That is, that we are unable now to predict what will happen in physics in a given physical circumstance which is arranged as carefully as possible. If we have an atom that is in an excited state and so is going to emit a photon, we cannot say when it will emit the photon. It has a certain amplitude to emit the photon at any time, and we can predict only a probability for emission; we cannot predict the future exactly. This has given rise to all kinds of nonsense and questions on the meaning of freedom of will, and of the idea that the world is uncertain.
Of course we must emphasize that classical physics is also indeterminate, in a sense. It is usually thought that this indeterminacy, that we cannot predict the future, is an important quantum-mechanical thing, and this is said to explain the behavior of the mind, feelings of free will, etc. But if the world were classical—if the laws of mechanics were classical—it is not quite obvious that the mind would not feel more or less the same. It is true classically that if we knew the position and the velocity of every particle in the world, or in a box of gas, we could predict exactly what would happen. And therefore the classical world is deterministic. Suppose, however, that we have a finite accuracy and do not know exactly where just one atom is, say to one part in a billion. Then as it goes along it hits another atom, and because we did not know the position better than to one part in a billion, we find an even larger error in the position after the collision. And that is amplified, of course, in the next collision, so that if we start with only a tiny error it rapidly magnifies to a very great uncertainty. To give an example: if water falls over a dam, it splashes. If we stand nearby, every now and then a drop will land on our nose. This appears to be completely random, yet such a behavior would be predicted by purely classical laws. The exact position of all the drops depends upon the precise wigglings of the water before it goes over the dam. How? The tiniest irregularities are magnified in falling, so that we get complete randomness. Obviously, we cannot really predict the position of the drops unless we know the motion of the water absolutely exactly.
Speaking more precisely, given an arbitrary accuracy, no matter how precise, one can find a time long enough that we cannot make predictions valid for that long a time. Now the point is that this length of time is not very large. It is not that the time is millions of years if the accuracy is one part in a billion. The time goes, in fact, only logarithmically with the error, and it turns out that in only a very, very tiny time we lose all our information. If the accuracy is taken to be one part in billions and billions and billions—no matter how many billions we wish, provided we do stop somewhere—then we can find a time less than the time it took to state the accuracy—after which we can no longer predict what is going to happen! It is therefore not fair to say that from the apparent freedom and indeterminacy of the human mind, we should have realized that classical “deterministic” physics could not ever hope to understand it, and to welcome quantum mechanics as a release from a “completely mechanistic” universe. For already in classical mechanics there was indeterminability from a practical point of view.
There is a fundamental difference, though, between classical indeterminacy and quantum indeterminacy. In principle, you can get a arbitrarily accurate description of the world’s state in classical mechanics. You can’t in quantum mechanics. If, then, a theologian was looking for a mechanism by which a metaphysical entity, such as God or a mind, could manipulate the classical world, quantum indeterminacy could be a back door where that could happen.
Aaronson also argued out that indeterminacy is not sufficient for free will. Radioactivity is also indeterminstic. Does a nucleus have free will about when it breaks into pieces? Well, maybe, I’d say—each nucleus might have an angel speaking to it, like every blade of grass in that song. Indeterminacy builds an inherent “behind the scenes” for nature where science can’t peek. But Aaronson pointed out that indeterminate phenomena still obey statistical laws. The problem free will must overcome hasn’t changed since the days of Laplace: what does it mean to make choices in a mechanistic universe?
One way that indeterminism could help here is with the fact that laws become statistical. On the aggregate, people are relatively predictable. Insurance companies predict how many of us will run into this or that calamity, God forbid. But individuals are relatively unpredictable, and it is the individual who has the free will. Just like the radioactive nucleus.
Reuven Rand pointed out during the discussion that part of the problem is that free will isn’t rigorously defined. Aaronson liked the point, and so do I. Other issues also need fleshing out: at what point am I considered morally responsible for my actions? Who exactly am “I”? Etc. There’s been plenty of talk about this stuff, as you can imagine.
I turn then to the Rambam, who makes a forcefull argument for free will in MT Hilkhot Teshuva, chapter 5:
א. רשות לכל אדם נתונה אם רצה להטות עצמו לדרך טובה ולהיות צדיק הרשות בידו. ואם רצה להטות עצמו לדרך רעה ולהיות רשע הרשות בידו. הוא שכתוב בתורה הן האדם היה כאחד ממנו לדעת טוב ורע. כלומר הן מין זה של אדם היה יחיד בעולם ואין מין שני דומה לו בזה הענין שיהא הוא מעצמו בדעתו ובמחשבתו יודע הטוב והרע ועושה כל מה שהוא חפץ ואין מי שיעכב בידו מלעשות הטוב או הרע וכיון שכן הוא פן ישלח ידו:Translation from Chabad.org:
ב. אל יעבור במחשבתך דבר זה שאומרים טפשי אומה"ע ורוב גולמי בני ישראל שהקב"ה גוזר על האדם מתחלת ברייתו להיות צדיק או רשע. אין הדבר כן אלא כל אדם ראוי לו להיות צדיק כמשה רבינו או רשע כירבעם או חכם או סכל או רחמן או אכזרי או כילי או שוע וכן שאר כל הדעות. ואין לו מי שיכפהו ולא גוזר עליו ולא מי שמושכו לאחד משני הדרכים אלא הוא מעצמו ומדעתו נוטה לאי זו דרך שירצה. הוא שירמיהו אמר מפי עליון לא תצא הרעות והטוב. כלומר אין הבורא גוזר על האדם להיות טוב ולא להיות רע וכיון שכן הוא נמצא זה החוטא הוא הפסיד את עצמו. ולפיכך ראוי לו לבכות ולקונן על חטאיו ועל מה שעשה לנפשו וגמלה רעה. הוא שכתוב אחריו מה יתאונן אדם חי וגו'. וחזר ואמר הואיל ורשותנו בידינו ומדעתנו עשינו כל הרעות ראוי לנו לחזור בתשובה ולעזוב רשענו שהרשות עתה בידינו הוא שכתוב אחריו נחפשה דרכינו ונחקורה ונשובה וגו':
ג. ודבר זה עיקר גדול הוא והוא עמוד התורה והמצוה שנאמר ראה נתתי לפניך היום את החיים. וכתיב ראה אנכי נותן לפניכם היום. כלומר שהרשות בידכם וכל שיחפוץ האדם לעשות ממעשה בני האדם עושה בין טובים בין רעים. ומפני זה הענין נאמר מי יתן והיה לבבם זה להם. כלומר שאין הבורא כופה בני האדם ולא גוזר עליהן לעשות טובה או רעה אלא הכל מסור להם:
ד. אילו האל היה גוזר על האדם להיות צדיק או רשע או אילו היה שם דבר שמושך את האדם בעיקר תולדתו לדרך מן הדרכים או למדע מן המדעות או לדעה מן הדעות או למעשה מן המעשים כמו שבודים מלבם הטפשים הוברי שמים היאך היה מצוה לנו על ידי הנביאים עשה כך ואל תעשה כך הטיבו דרכיכם ואל תלכו אחרי רשעכם והוא מתחלת ברייתו כבר נגזר עליו או תולדתו תמשוך אותו לדבר שאי אפשר לזוז ממנו. ומה מקום היה לכל התורה כולה ובאי זה דין ואיזה משפט נפרע מן הרשע או משלם שכר לצדיק. השופט כל הארץ לא יעשה משפט. ואל תתמה ותאמר היאך יהיה האדם עושה כל מה שיחפוץ ויהיו מעשיו מסורים לו וכי יעשה בעולם דבר שלא ברשות קונו ולא חפצו והכתוב אומר כל אשר חפץ ה' עשה בשמים ובארץ. דע שהכל כחפצו יעשה ואף על פי שמעשינו מסורין לנו. כיצד כשם שהיוצר חפץ להיות האש והרוח עולים למעלה והמים והארץ יורדים למטה והגלגל סובב בעיגול וכן שאר בריות העולם להיות כמנהגן שחפץ בו. ככה חפץ להיות האדם רשותו בידו וכל מעשיו מסורין לו ולא יהיה לו לא כופה ולא מושך אלא הוא מעצמו ובדעתו שנתן לו האל עושה כל שהאדם יכול לעשות. לפיכך דנין אותו לפי מעשיו אם עשה טובה מטיבין לו ואם עשה רעה מריעין לו. הוא שהנביא אומר מידכם היתה זאת לכם. גם המה בחרו בדרכיהם. ובענין זה אמר שלמה שמח בחור בילדותך ודע כי על כל אלה יביאך האלהים במשפט. כלומר דע שיש בידך כח לעשות ועתיד אתה ליתן את הדין:
ה. שמא תאמר והלא הקב"ה יודע כל מה שיהיה וקודם שיהיה ידע שזה יהיה צדיק או רשע או לא ידע. אם ידע שהוא יהיה צדיק אי אפשר שלא יהיה צדיק ואם תאמר שידע שיהיה צדיק ואפשר שיהיה רשע הרי לא ידע הדבר על בוריו. דע שתשובת שאלה זו ארוכה מארץ מדה ורחבה מני ים וכמה עיקרים גדולים והררים רמים תלויים בה אבל צריך אתה לידע ולהבין בדבר זה שאני אומר. כבר בארנו בפ' שני מהלכות יסודי התורה שהקב"ה אינו יודע מדיעה שהיא חוץ ממנו כבני אדם שהם ודעתם שנים. אלא הוא יתעלה שמו ודעתו אחד ואין דעתו של אדם יכולה להשיג דבר זה על בוריו וכשם שאין כח באדם להשיג ולמצוא אמתת הבורא שנאמר כי לא יראני האדם וחי כך אין כח באדם להשיג ולמצוא דעתו של בורא. הוא שהנביא אמר כי לא מחשבותי מחשבותיכם ולא דרכיכם דרכי. וכיון שכן הוא אין בנו כח לידע היאך ידע הקב"ה כל הברואים והמעשים אבל נדע בלא ספק שמעשה האדם ביד האדם ואין הקב"ה מושכו ולא גוזר עליו לעשות כך. ולא מפני קבלת הדת בלבד נודע דבר זה אלא בראיות ברורות מדברי החכמה. ומפני זה נאמר בנבואה שדנין את האדם על מעשיו כפי מעשיו אם טוב ואם רע וזה הוא העיקר שכל דברי הנבואה תלויין בו:
1. Free will is granted to all men. If one desires to turn himself to the path of good and be righteous, the choice is his. Should he desire to turn to the path of evil and be wicked, the choice is his.
This is [the intent of] the Torah's statement (Genesis 3:22): “Behold, man has become unique as ourselves, knowing good and evil,” i.e., the human species became singular in the world with no other species resembling it in the following quality: that man can, on his own initiative, with his knowledge and thought, know good and evil, and do what he desires. There is no one who can prevent him from doing good or bad. Accordingly, [there was a need to drive him from the Garden of Eden,] “lest he stretch out his hand [and take from the tree of life].”
2. A person should not entertain the thesis held by the fools among the gentiles and the majority of the undeveloped among Israel that, at the time of a man's creation, The Holy One, blessed be He, decrees whether he will be righteous or wicked.
This is untrue. Each person is fit to be righteous like Moses, our teacher, or wicked, like Jeroboam. [Similarly,] he may be wise or foolish, merciful or cruel, miserly or generous, or [acquire] any other character traits. There is no one who compels him, sentences him, or leads him towards either of these two paths. Rather, he, on his own initiative and decision, tends to the path he chooses.
This was [implied by the prophet,] Jeremiah who stated [Eichah 3:381: “From the mouth of the Most High, neither evil or good come forth.” Accordingly, it is the sinner, himself, who causes his own loss.
Therefore, it is proper for a person to cry and mourn for his sins and for what he has done to his soul, the evil consequences, he brought upon it. This is implied by the following verse [ibid.:39]: “Of what should a living man be aggrieved? [A man of his sins.]”
[The prophet] continues explaining, since free choice is in our hands and our own decision [is what prompts us to] commit all these wrongs, it is proper for us to repent and abandon our wickedness, for this choice is presently in our hand. This is implied by the following verse [ibid.:40]: “Let us search and examine our ways and return [to God].”
3. This principle is a fundamental concept and a pillar [on which rests the totality] of the Torah and mitzvot as [Deuteronomy 30:15] states: “Behold, I have set before you today life [and good, death and evil].” Similarly, [Deuteronomy 11:26] states, “Behold, I have set before you today [the blessing and the curse],” implying that the choice is in your hands.
Any one of the deeds of men which a person desires to do, he may, whether good or evil. Therefore, [Deuteronomy 5:26] states:
“If only their hearts would always remain this way.” From this, we can infer that the Creator does not compel or decree that people should do either good or bad. Rather, everything is left to their [own choice].
4. Were God to decree that an individual would be righteous or wicked or that there would be a quality which draws a person by his essential nature to any particular path [of behavior], way of thinking, attributes, or deeds, as imagined by many of the fools [who believe] in astrology - how could He command us through [the words of] the prophets: “Do this,” “Do not do this,” “Improve your behavior,” or “Do not follow after your wickedness?”
[According to their mistaken conception,] from the beginning of man's creation, it would be decreed upon him, or his nature would draw him, to a particular quality and he could not depart from it.
What place would there be for the entire Torah? According to which judgement or sense of justice would retribution be administered to the wicked or reward to the righteous? Shall the whole world's Judge not act justly!
A person should not wonder: How is it possible for one to do whatever he wants and be responsible for his own deeds? - Is it possible for anything to happen in this world without the permission and desire of its Creator as [Psalms 135:6] states: “Whatever God wishes, He has done in the heavens and in the earth?”
One must know that everything is done in accord with His will and, nevertheless, we are responsible for our deeds.
How is this [apparent contradiction] resolved? Just as the Creator desired that [the elements of] fire and wind rise upward and [those of] water and earth descend downward, that the heavenly spheres revolve in a circular orbit, and all the other creations of the world follow the nature which He desired for them, so too, He desired that man have free choice and be responsible for his deeds, without being pulled or forced. Rather, he, on his own initiative, with the knowledge which God has granted him, will do anything that man is able to do.
Therefore, he is judged according to his deeds. If he does good, he is treated with beneficence. If he does bad, he is treated harshly. This is implied by the prophets' statements: “This has been the doing of your hands” [Malachi 1:9]; “They also have chosen their own paths” [Isaiah 66:3].
This concept was also implied by Solomon in his statement [Ecclesiastes 11:9]: “Young man, rejoice in your youth... but, know that for all these things God will bring you to judgment,” i.e., know that you have the potential to do, but in the future, you will have to account for your deeds.
5. One might ask: Since The Holy One, blessed be He, knows everything that will occur before it comes to pass, does He or does He not know whether a person will be righteous or wicked?
If He knows that he will be righteous, [it appears] impossible for him not to be righteous. However, if one would say that despite His knowledge that he would be righteous, it is possible for him to be wicked, then His knowledge would be incomplete.
Know that the resolution to this question [can be described as]: “Its measure is longer than the earth and broader than the sea.” Many great and fundamental principles and lofty concepts are dependent upon it. However, the statements that I will make must be known and understood [as a basis for the comprehension of this matter].
As explained in the second chapter of Hilchot Yesodei HaTorah, The Holy One, blessed be He, does not know with a knowledge that is external from Him as do men, whose knowledge and selves are two [different entities]. Rather, He, may His name be praised, and His knowledge are one.
Human knowledge cannot comprehend this concept in its entirety for just as it is beyond the potential of man to comprehend and conceive the essential nature of the Creator, as [Exodus 33:20] states: “No man will perceive, Me and live,” so, too, it is beyond man's potential to comprehend and conceive the Creator's knowledge. This was the intent of the prophet's [Isaiah 55:8] statements: “For My thoughts are not your thoughts, nor your ways, My ways.”
Accordingly, we do not have the potential to conceive how The Holy One, blessed be He, knows all the creations and their deeds. However, this is known without any doubt: That man's actions are in his [own] hands and The Holy One, blessed be He, does not lead him [in a particular direction] or decree that he do anything.
This matter is known, not only as a tradition of faith, but also, through clear proofs from the words of wisdom. Consequently, the prophets taught that a person is judged for his deeds, according to his deeds - whether good or bad. This is a fundamental principle on which is dependent all the words of prophecy.
I should break all that down, look up parallel Rambams, research other views, secondary sources, etc., but Shabbat is in a couple hours. So in a nutshell, the Rambam says that free will is really important, but its mechanism is beyond the limits of human inquiry. It sounds like there’s nothing new under the sun. And as I heard Dr. Moshe Bernstein put it this week, quoting a student, it's good to have “epistemological humility.”
This is all still fun to think about, and rather satisfying to quote both Feynman and Rambam at length in the same note.
