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What is science for? (36 Views of Mount CritRat)

The critical rationalists have a specific view of what scientists should be trying to achieve. This means they will talk at cross-purposes with scientists who are trying to achieve different things.

At base, the point of science is the same as the point of philosophy: to express universal truths. It’s (usually) conceded absolute certainty is unattainable, but a truth-claim can be more or less well justified. Part of the work of philosophers is producing better justifications via better arguments (according to agreed-upon criteria). Another part is producing new universal truth-claims. Not everyone would agree with this definition of philosophy. For example Felix Guattari in What Is Philosophy? argues that the point of philosophy is to generate new concepts. I rather like that, but I want to describe philosophy in a way I think critical rationalists would agree with.

Science’s goals are narrower than philosophy’s. The search for truth is restricted to truths about the physical world. As opposed to more “metaphysical” questions like “what is the nature of knowledge? Is it justified true belief?” Moreover, no scientific truth-claim can be considered well justified without interaction with the physical world. No sort of pure argumentation is sufficient.

Physical interaction requires that theory (sets of universal truth-claims) be used to make predictions about what will be observed under specified conditions, thus narrowing the universal truth-claims to special cases. A theory that doesn’t make testable claims isn’t a scientific theory.

Matters like how scientists should handle predictions that don’t come true, etc., are about the nature of justification rather than the nature of science, so that’s it. Except…

Instrumental science

Here’s an interesting observation about the physical world. Abraham Lincoln and John Kennedy are two of the Presidents of the United States who’ve been assassinated. Lincoln had a secretary named Kennedy, and Kennedy had a secretary named Lincoln. Valerie Klein, “The Odd Parallels Between Kennedy and Lincoln,” 2002. From this observation of nature, I can produce a theory:

Any US President who has a secretary sharing a family name with a previous president will be assassinated during his or her term of office. That’s a testable prediction that will get a “natural experiment” every so often. (Just wait for a President to be elected who has a secretary named Taft or Fillmore or Roosevelt.)

The prediction might be refuted, in which case I could be a good Popperian and adjust the theory to add the requirement that the President also have a Vice President named Johnson (as both LIncoln and Kennedy did). This is critical rationalism: I responded to a refutation with an adjusted theory that both explains the refutation and creates a novel prediction.

Fine, but somehow this doesn’t seem like proper science. What’s missing is a causal mechanism: why does the choice of secretary lead to an assassination?

Science that leaves out causality is called (purely) instrumental science. Critical rationalists don’t like it. So add that requirement: scientists (theorists) must seek a cause, not just a reliable correlation. But what is meant by “cause”?

Enter quantum mechanics

The second quarter of the 20th century was an awkward time for theoretical physicists working on teensy entities. I’ll attempt to explain some of the issues, but I caution that I’m woefully unqualified to do so. I enrolled at CalTech intending to be a scientist, specifically: a physicist. I discovered I wasn’t smart enough, so I transferred to the University of Illinois, which had a much better computer science department at the time and was way cheaper.

First, some background.

Since at least Galileo, the assumption in physics has been that there is no action at a distance. An effect on something over there caused by something over here must have that causality carried from here to there by some other thing (or things). Consider heat. Per Galileo:

Those materials which produce heat in us and make us feel warmth, which we call by the general name fire, would be a multitude of minute particles having certain shapes and moving with certain velocities. Meeting with our bodies, they penetrate by means of their consummate subtlety, and their touch which we feel, made in their passage through our substance, is the sensation which we call heat.

Causality is contact, you might say. Kepler agreed. Quoting Wikipedia:

Kepler’s laws were developed based on a physical theory of planetary motion in which the Sun emitted magnetic fibrils which pulled the planets into orbits. The fibrils were somewhat elastic allowing non-circular motion driven by the inertia of the planets.

The Newton of the Principia agreed, though he left undescribed what specifically was moving the planets:

that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.

Newton also wrote a book on Opticks. He had to confront the question of why light can pass through a vacuum and have an effect on, say, mirrors. His solution was that light is formed of corpuscules (particles) – not dissimilar to Galileo’s minute particles of heat.

Newton’s approach fell out of favor in the early 1800s as experimental evidence came to favor the wave theory of light. But that doesn’t violate “causality is contact” because waves are waves in something (like an ocean). It’s the wave’s “medium” that does the pushing and pulling and contact.

The “something” light waves are in was called the luminiferous aether which is “an invisible and infinite material with no interaction with physical objects.“ Seems absurd, right? Snarky comment about dark matter or dark energy goes here.

It turns out that the experimental evidence pushed against the existence of a luminiferous aether. Frantic efforts to save the theory were put to bed by special relativity, whereupon you could respectably consider light a wave, a wave in… let’s talk about something else, shall we?

However in the same year, Einstein also explained the photoelectric effect using an assumption that light is tiny packets of energy (photons).

At this point, some experiments suggest light is particle-like in that it can have a definite position in space at a given time. Other experiments are more compatible with a wave-in-nothing hypothesis.

Particle or wave? The question arguably came to a head around 1926. In September 1925, Heisenberg published a framework theory for quantum mechanics. In January of the next year, Schödinger published a competing theory. Here’s the problem:

For the main contestants, Heisenberg and Schrödinger, the issue at stake was which view could claim to provide a single coherent and universal framework for the description of the observational data. The choice was, essentially between a description in terms of continuously evolving waves, or else one of particles undergoing discontinuous quantum jumps.

Great! We can see which theory goes unrefuted and thus resolve (at least for now) the particle-or-wave question. Unfortunately, in May Heisenberg published another paper showing that the two approaches were equivalent. If I understand that correctly, the two theories made all the same predictions, so no experiment could decide between them.

Meanwhile, other problems had been cropping up. One had to do with probabilities.

In “classical” physics, if you know the initial state of the system, you can predict its final state exactly. By that, I mean something like limits in calculus: the more precise your measurements of the initial state, the more precise your prediction will be. If a cue ball with a given mass and velocity (momentum) strikes the eight ball at a given angle, you know for sure whether the eight ball will go into the corner pocket (leaving aside friction, rips in the table’s fabric, how level the table is, yada yada yada).

However, the same is not true at the quantum scale. No matter what you know about how a photon hits an electron, the best you can do is predict probabilities about where the electron will be measured to have struck a target. What does it mean for a single cause to have in principle an infinite number of possible effects? (That is, measurement error isn’t the issue.)

To compound things, there are certain properties of the system that cannot be simultaneously known (complementarity). The most famous example is Heisenberg’s uncertainty principle: the more precisely you measure a particle’s position, the less you know about its momentum.

That seems tractable: just measure the position at one moment and the momentum at another, then work your way backward (using a billiard-ball style of reasoning) to the momentum the particle must have had at the moment its position was measured. Einstein proposed ingenious thought experiments for how that could be done, but they never worked. Frescura and Hiley:

By using one particular piece of apparatus only certain features could be made manifest at the expense of others, while with a different piece of apparatus another complementary aspect could be made manifest in such a way that the original set became non-manifest, that is, the original attributes were no longer well defined.

I think “non-manifest” might mean that, once you’ve measured the momentum, the earlier measurement of position is useless in further calculations/predictions. But I don’t know, because I don’t have the math, and I think the upshot of the “quantum revolution” is that trying to use analogies to macroscope entities – even at the level of “objects have at all times both a position and momentum” – to “picture” the quantum world is a mug’s game. Frescura and Hiley again:

In the traditional view, it is assumed that there exists a reality in space-time and that this reality is a given thing, all of whose aspects can be viewed or articulated at any given moment.

That view is wrong at the quantum level. One experimental apparatus is intended to measure position, and another is intended to measure momentum. They will, independently, produce results – but that doesn’t mean there’s an entity like a billiard ball, down there at the quantum level. Similarly, it’s meaningless to speak of a photon as being either a particle or a wave. Some apparatus will produce results compatible with a particle, some with a wave, but it’s meaningless to say a photon is either one or the other.

Einstein came to accept the results of quantum mechanics, but he still wanted causality:

[…] quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the “old one”. I, at any rate, am convinced that He [God] is not playing at dice.

I have the greatest consideration for the goals which are pursued by the physicists of the latest generation which go under the name of quantum mechanics, and I believe that this theory represents a profound level of truth, but I also believe that the restriction to laws of a statistical nature will turn out to be transitory….Without doubt quantum mechanics has grasped an important fragment of the truth and will be a paragon for all future fundamental theories, for the fact that it must be deducible as a limiting case from such foundations, just as electrostatics is deducible from Maxwell’s equations of the electromagnetic field or as thermodynamics is deducible from statistical mechanics.

He spent the rest of his life trying to find some “underlying” causal theory from which quantum mechanics could be derived. He did not succeed. Since then, no one has.

Causality has gone out the window. The equations work, but there’s no causal or mechanistic (this-then-that) explanation of them. They are merely instrumental. That’s the Copenhagen inter

Today, we call such statements part of the

All this

The upshot of “the quantum revolution”

When I learned about the uncertainty principle, the justification was something like this: to measure the position of an electron, you have to bounce a photon off of it. (“Causality is contact.") But the photon changes the momentum of the electron. Which seems like something you could work around. However, things seem more perverse. If I understand correctly, a later

This raises questions:

  • What does it mean to say that a particle “has” both a position and a momentum if, whenever you measure one of them, the other one

USE ROBBIN VS NORTHERN CARDINAL example of people just wanting to know.

Consider balls on a pool table. If the cue ball hits the eight ball at a given angle and momentum (mass times velocity), you can predict where the eight ball will go.

You know exactly where the ball is. It’s hit by the 3 ball, at an angle and velocity you also know. You can predict, two seconds after the collision, what where it will be, the direction it’ll be heading in, and how fast it’ll be going.

Alas](https://plato.stanford.edu/entries/qt-uncertainty/#WavePartDualComp):

For the main contestants, Heisenberg and Schrödinger, the issue at stake was which view could claim to provide a single coherent and universal framework for the description of the observational data. The choice was, essentially between a description in terms of continuously evolving waves, or else one of particles undergoing discontinuous quantum jumps.

Various similar problems came up in the early 1900s things arguably came to a head around 1925. In addition to “particle or wave? well, which is it?”, other problems were cropping up.

Such predictions don’t work when the objects in question are the size of atoms or less. The undisputed experimental results meant theory had to accept:

  • Hitting an electron with a photon is not the same as hitting one pool ball with another. You can’t choose a point in time and predict both the position and momentum of an object at that time. (Momentum gathers together the mass of the object, its direction, and its speed.)

– When some disruptive thing has happened to an innocent particle, experiments and theory agree that its later measured position is neither absolute nor random. Instead, you can predict how often the particle will be measured to be in a given place. That is, an exact result has been replaced by a probability distribution of measured results.

The number of apparently unanswerable questions kept piling up:

  • Particle or wave?
  • If there’s no way to know two properties of a thing at the same time, what does it mean to say it “has” them at that time?
  • About the probability distribution of position: are we saying the particle has an exact position even if we didn’t know it? Or is the position in some sense indistinguishable from the probability distribution? How could we tell?
  • Are we comfortable giving up that idea that there are specific causes that produce exact, predictable results. (At the micro scale – you might have to aggregate them at the macro scale. brownian motion)

  1. particle or wave? Different experiments predict different Two theories, one based on particles one on waves. They make the same predictions. So the question cannot be answered by QM theory.

  2. In conventional physics, if you know (relevant) initial conditions exactly, you can predict final conditions exactly. But not in QM: you inevitably get a distribution. What does it mean for a single cause to have an infinite number of possible effects?

  3. And you can’t know the initial conditions exactly (complementarity). Most famously, can’t know simultaneously the velocity and momentum (effectively, velocity). What does it mean to say a particle has mass x and momentum y at point t if there’s no way to ever measure them?

Wittgenstein whereove one cannot speak, one must remain silent. shut up and calculate. Mu, jaina… This is a radical break. It makes QM a purely instrumental theory, like predicting assassinations based on names without knowing why it works.

OR. there is an underlying theory that preserves locality from which QM can be derived. Einstein died trying.

Two approaches: einstein principle of locality, Bohr: mu, jaina

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Various experiments show that the position of a particle is unpredictable.

It used “things” above because it wasn’t just raw matter that could provide causal forces: it was also waves, such as light waves.

A problem for Popper is that the dominant interpretation

Here are some controversies:

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Light on the macroscopic scale acts like a wave, and I think everyone just assumed that was the reality until Einstein in 1905 proposed that it was composed of tiny packets of energy (particles of light) to explain the photoelectric effect.

Saying light is a particle (which has a position) is incompatible with it being a wave (which is stretched out in space and time). Well, which is it?

In 1926-7, Heisenberg and Schrödinger produced two competing quantum frameworks. Alas:

For the main contestants, Heisenberg and Schrödinger, the issue at stake was which view could claim to provide a single coherent and universal framework for the description of the observational data. The choice was, essentially between a description in terms of continuously evolving waves, or else one of particles undergoing discontinuous quantum jumps.

Bohr proposed to resolve the issue by saying the question is meaningless. I can’t help but think of the Zen Buddhist idea of “mu” in the koan: “A monk asked Master Chao-chou, ‘Has a dog the Buddha Nature or not?’ Chao-chou said, ‘Mu’” The interpretation I (not a Zen Buddhist) have heard is that Mu is an attempt to unask the question. I’m also reminded of Jaina seven-value logic, where one answer to a question is “From a certain standpoint, there’s nothing you can say about the truth or falsity of P.” There’s no way to talk sensibly about whether light (or matter) is a particle or a wave, so we should talk about something else. This became known as (part of) the [Copenhagen Interpretation] of quantum mechanics, which is likely the one most favored by people in the field. It’s fitting that “there is no definitive historical statement of what the [Copenhagen] interpretation entails.”

There are related issues:

  1. Given a particle, it is impossible to determine both its position and momentum at a given moment. Does it have both those properties at that moment?

  2. In classical physics, when one billiard ball collides into another, you can predict exactly

When you make measurements, you get values, but that tells you nothing about whether those values existed before you made the experiment. In the words of Asher Peres “unperformed experiments have no results.”

A related question is: where is a particle just before you measure its position? The answer to the question “where will the particle be when you measure it?” can be answered probabilistically: “the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system’s wavefunction at that position.” But does the particle have a position before the measurement? Bohr doesn’t think it’s a meaningful question.

Consider the Heisenberg Uncertainty Principle. It turns out that the more exactly you measure the position of a particle, the less exactly can you know its momentum.

Things to consider

  • Principle of locality
  • Copenhagen interpretation
  • Do unmeasurable quantities represent entities?
  • Galileo merged mathematics and science
  • Philosophical questions around quantum mechanics
  • Galilean science
  • Causality was an issue in quantum mechanics
  • Einstein-Podolsky-Rosen argument
  • The “lap” example for the uncertainty principle
  • Uncertainty principle
  • What is science for?

to create more justified beliefs in what is true. While truth is not necessarily attainable