Answers for a statist moralist

In a blog entry on the New York Time website Amia Srinivasan asks some questions for “free market moralists”. She starts by summarising Rawls:

 In 1971 John Rawls published “A Theory of Justice,” the most significant articulation and defense of political liberalism of the 20th century. Rawls proposed that the structure of a just society was the one that a group of rational actors would come up with if they were operating behind a “veil of ignorance” — that is, provided they had no prior knowledge what their gender, age, wealth, talents, ethnicity and education would be in the imagined society. Since no one would know in advance where in society they would end up, rational agents would select a society in which everyone was guaranteed basic rights, including equality of opportunity. Since genuine (rather than “on paper”) equality of opportunity requires substantial access to resources — shelter, medical care, education — Rawls’s rational actors would also make their society a redistributive one, ensuring a decent standard of life for everyone.

There is a very large assumption in this first paragraph smuggled in under the term “equality of opportunity”. Srinivasan doesn’t explain what it consists of or why anybody should be interested in it. Rawls on p.63 of the book she refers to writes (you can get the book in pdf by searching “rawls theory of justice pdf” it’s the first hit):

More specifically, assuming that there is a distribution of natural assets, those who are at the same level of talent and ability, and have the same willingness to use them, should have the same prospects of success regardless of their initial place in the social system.

This is unclear and doesn’t make much sense. Let’s suppose that Jim is born into a poor family and he cleans toilets for a living but yearns to be a poet. Note that the mere fact that Jim wants to be a poet doesn’t imply he would be a good poet. So then Jim should make some effort to persuade people to pay him for poetry. And if he can’t persuade people and he is still unhappy with cleaning toilets then there is a problem. It’s not clear what the problem is exactly or how to solve it because if that was clear, Jim wouldn’t be unhappily cleaning toilets: the problem would have been solved. And if you’re going to force people to pay Jim to write poetry then you have no check on whether the poetry is any good.

What we need is to set up institutions to make it easy for people to change how they spend their time and money. That way, if you want people to spend their time and money on what you’re doing they can choose not to and give you some information about whether you’re doing stuff badly. If you don’t get time and money from people you’re doing something that’s not persuasive.

She then summarises Nozick:

In 1974, Robert Nozick countered with “Anarchy, State, and Utopia.” He argued that a just society was simply one that resulted from an unfettered free market — and that the only legitimate function of the state was to ensure the workings of the free market by enforcing contracts and protecting citizens against violence, theft and fraud. (The seemingly redistributive policy of making people pay for such a “night watchman” state, Nozick argued, was in fact non-redistributive, since such a state would arise naturally through free bargaining.) If one person — Nozick uses the example of Wilt Chamberlain, the great basketball player — is able to produce a good or service that is in high demand, and others freely pay him for that good or service, then he deserves to get rich. And, once rich, he doesn’t owe anyone anything, since his wealth was accumulated through voluntary exchange in return for the goods and services he produced. Any attempt to “redistribute” his wealth, so long as it is earned through free market exchange, is, Nozick says, “forced labor.”

I’m not going to defend Nozick specifically partly because I don’t remember much about him so he might suck.

Wilt Chamberlain “deserves” to get rich? “Deserve” is the moral equivalent of “justify”. That is if Wilt Chamberlain deserves the money that means he can show that it is true he should have it or he should probably have it or something like that. But justification is impossible, so it is impossible to show that somebody deserves something. So if that was the only free market position it would be wrong.

The real reason Wilt Chamberlain should get to keep his money is just that you haven’t offered an alternative other people consider better. A contract n a free market is a means of testing whether a person consents to be legally bound to the terms of a particular exchange. See Randy Barnett’s papers 1 and books on contract law for a detailed discussion. The enforceability of laws required for the operation of a free market has nothing to do with whether they arise through free bargaining. Rather, it has to do with whether the law in question is required to deal with other people consentually. See Randy Barnett’s The Structure of Liberty.

I’m going to skip a bit because there’s a lot of boring stuff and get on to the bit where she demands that free market people answer a load of questions:

 1. Is any exchange between two people in the absence of direct physical compulsion by one party against the other (or the threat thereof) necessarily free?

If you say yes, then you think that people can never be coerced into action by circumstances that do not involve the direct physical compulsion of another person. Suppose a woman and her children are starving, and the only way she can feed her family, apart from theft, is to prostitute herself or to sell her organs. Since she undertakes these acts of exchange not because of direct physical coercion by another, but only because she is compelled by hunger and a lack of alternatives, they are free.

We have a welfare state and people do engage in prostitution and sell organs. The welfare state doesn’t solve that problem. So why is Srinivasan brining up flaws in her own position?

If a person doesn’t want to fuck or sell her organs she can ask for charity. That charity should come with strings attached. That is, if you’re going to get a charity’s money they should require you to gain skills of some sort so that you’re not stuck on their roles permanently. And the charity should be free to turn people down who are a bad risk.

Let’s suppose that every charity decides a particular person is a bad risk. She has chosen to have children. That is her responsibility. If she can’t raise them she should offer them up for adoption. The knowledge already exists to get children adopted by people who have better options than selling sex unwillingly.

Would I prefer to see a world in which the only people who engage in the sex trade are people who want to do that? Yes. But that requires the creation of better knowledge to help people avoid that. The government hasn’t done that and I don’t think it can since taxation makes it difficult for people to stop supporting bad government institutions that help create such problems. Also, it’s not my responsibility to do that unless I take on that responsibility and I shouldn’t do that unless I have a really kickass idea about how to do it and can raise money for it voluntarily.

2. Is any free (not physically compelled) exchange morally permissible?

If you say yes, then you think that any free exchange can’t be exploitative and thus immoral. Suppose that I inherited from my rich parents a large plot of vacant land, and that you are my poor, landless neighbor. I offer you the following deal. You can work the land, doing all the hard labor of tilling, sowing, irrigating and harvesting. I’ll pay you $1 a day for a year. After that, I’ll sell the crop for $50,000. You decide this is your best available option, and so take the deal. Since you consent to this exchange, there’s nothing morally problematic about it.

If we’re talking about a free market you have other options and can point this out to get a better deal. “Give me more than $1 a day or your crops will rot in the field and you get nothing.”

3. Do people deserve all they are able, and only what they are able, to get through free exchange?

I’ve pointed out the flaw in the idea of desert above but let’s see what she has to say anyway.

If you say yes, you think that what people deserve is largely a matter of luck. Why? First, because only a tiny minority of the population is lucky enough to inherit wealth from their parents. (A fact lost on Mitt Romney, who famously advised America’s youth to “take a shot, go for it, take a risk … borrow money if you have to from your parents, start a business.”) Since giving money to your kids is just another example of free exchange, there’s nothing wrong with the accumulation of wealth and privilege in the hands of the few.

You don’t have to get money from your parents. If you have a good business idea you can persuade people to loan you the money.

Second, people’s capacities to produce goods and services in demand on the market is largely a function of the lottery of their birth: their genetic predispositions, their parents’ education, the amount of race- and sex-based discrimination to which they’re subjected, their access to health care and good education.

It’s also a function of what the market happens to value at a particular time. Van Gogh, William Blake, Edgar Allan Poe, Vermeer, Melville and Schubert all died broke. If you’re a good Nozickian, you think that’s what they deserved.

If somebody hasn’t produced a good or service in demand on the market all you know is that there is some unsolved problem that prevents them from doing this. Srinivasan hasn’t got anywhere near to producing an explanation of why a monopolistic institution that threatens to imprison people who don’t give it money is a good solution to these problems.

4. Are people under no obligation to do anything they don’t freely want to do or freely commit themselves to doing?

If you say yes, then you think the only moral requirements are the ones we freely bring on ourselves — say, by making promises or contracts. Suppose I’m walking to the library and see a man drowning in the river. I decide that the pleasure I would get from saving his life wouldn’t exceed the cost of getting wet and the delay. So I walk on by. Since I made no contract with the man, I am under no obligation to save him.

I’m not entirely sure what obligation means in this context. Does it mean that if I walk past a man drawing in a rive I might be prosecuted for not saving him? That would be a bad idea. Perhaps I don’t know how to swim. Or maybe I have done any swimming for a long time and I think I would drown trying to save him. Or maybe I’m really tired that morning and fear I would drown trying to save him as a result of exhaustion.

If it means people who knew about the drowning would think worse of me that might be fair enough if I could easily have raised the alarm and got somebody else to come save him. Both I and other people are better off having another creative problem-solving person in the world than letting his drown.

If it means that in the case where I couldn’t easily raise the alarm I should take a large risk of killing myself to save him, then you can fuck off. I don’t know much about him so taking a large risk of killing myself trying to save him would be a bad idea since I have no idea whether it’s worth the risk.

Most of us, I suspect, will find it difficult to say yes to all four of these questions.

The rest of us, who know the questions are ill-formed, think that this illustrates the peril of taking bad questions for granted.

Freedom and employment

Anarchopac who is an anarchist/socialist thinks that wage labour is incompatible with freedom. His argument is that workers must work to earn a living. And even if a worker wants to start his own business he must work for a wage to save up money to start the business and so has to work for a wage. Since he has no choice but to work for a wage he isn’t free since he has no alternative. I don’t think it does much good to argue about whether this or that action is compatible with freedom because it frames the debate in a misleading way. If you go along with discussing the issue in this way you’re going to end up talking about the definition of freedom.

Such discussions tend to go nowhere because of a general philosophical problem: discussing definitions is a bad idea. If somebody wants to argue about the definition of a word the best thing to do is just to concede the definition and move on to discussing a substantive issue. A word is just a label for an idea. If you disagree with me about an idea then we need to discuss the idea, not the label. For more criticisms of discussing definitions see Karl Popper’s The Open Society and its Enemies Volume 2, Chapter 11, Section II. Specifically when we want to discuss a pattern of behaviour, such as wage labour, we should discuss what problem it solves, whether the pattern is problematic. If it is problematic is there some variant that would be better? Or is the pattern in question so bad it should be abolished, like slavery?

Some people who work for a wage dislike their job and wish they didn’t have to do it. But a person can dislike doing something because he has bad ideas, so this doesn’t tell us much. Nor does disagreement tell us which party to the disagreement, if either, is correct.  So if an employer and employee disagree about what the employee should do we can’t say which of them is right without knowing more.

Socialists say that the way to solve this problem is for the employers to give up their property rights in the plant they own to the workers. The workers are better suited to run the plant because they actually use the machines and know how they perform in practise. Bu there is a problem with this argument. Why did the employer own the machines in the first place?

The employer had an idea about some good or service. He thought that people would want that good or service and he thought about the best way to provide it. He then got the money to buy the plant, the premises in which to install it and so on. And he makes decisions about how to use the plant for as long he owns it. If not enough people buy his product or service then his business will fail. He pays the employees money in advance of knowing whether their labour will make him a profit or not. Doing anything novel entails risk. The employer takes that risk and the employees don’t. If the employees genuinely have a better idea about what risk should be taken then they could try to raise the money to buy the employer out.

Some socialists might say there isn’t really that much risk. You can just produce stuff that people know they want. This idea is problematic: it presupposes that people know the best way of making stuff and just have to tell other people to go do it. But figuring out how to do stuff well is hard. It requires trial and the correction of error. This is equally true of producing new technology and continuing to produce stuff that was produced before under changing conditions. The way the market does this is that if the good is being supplied badly enough by the lights of the people who might buy it the people supplying it won’t make a profit and will have to stop.

Somebody has to take the risky decisions and those people should get the profit or take the hit. If they don’t then they will not be able to make decisions about whether to continue making a product or service or not. That is, they will not be able to decide whether they prefer to make the product under current conditions or not, nor will they have any guidance on whether other ways of making it might work.

What the socialists propose amounts to saying that nobody should want to make the tradeoff of getting money now and taking a lot less risk rather than taking a large risk and getting money later. But what about the worker who needs the money right now and has no choice but to make that tradeoff? If he has no idea how to produce goods and services better then there is no reason for anybody to give him stuff when he doesn’t know how to use it. If he does have a great idea then he should want to put in the time and effort needed to persuade other people to give him money to try it, or he should save the required money. To say anything else entails that people should give him stuff when they don’t think it’s a good idea. It requires people to act irrationally: that is, to ignore criticisms of their actions.

But the worker might be unhappy I hear you cry. If somebody can’t convince other people to give him stuff or money to try some great idea he should be interested in working out why they aren’t convinced. So he has an opportunity to learn. If he doesn’t have good ideas for a business but wants to have good ideas about that then he should be interested in learning about how to have such ideas. And if he wants neither of those things, that’s fine but he shouldn’t want people to give him stuff when he doesn’t know how to use it and has no intention of learning. And when I say it’s fine not to want those things I really mean it. Some people want to do philosophy or poetry or draw or whatever and don’t want to run a business. All I’m saying is that if that’s what you want to do and you’re not willing to persuade other people to sponsor you to do it you shouldn’t expect to get stuff for doing it.

The problems of induction socialist calculation and altruism

The problem of induction is a philosophical problem about how knowledge is created. The socialist calculation problem is a problem in economics: it is impossible to do economic calculation without a free market. They may sound very different but they are actually very closely related to one another.

The problem of induction

Philosophers like to think that scientific knowledge is created by a process called induction that involves doing observations, using them to come up with an idea about how the world works and then showing that idea is true or probable with more observations. The problem is that induction is impossible.

Observations don’t imply any particular idea about how the world works. Any such idea implies a lot about stuff we don’t observe. Our best idea about how the sun works implies stuff about the core of the sun, which we can’t observe. Nobody has ever observed a dinosaur, only a dinosaur skeleton, but those theories are not primarily about skeletons. As a result of this it is impossible to invent an idea or to prove it is true or probably true.

In addition, it is impossible to do an observation without having some explanation of what you want to observe and why. So ideas are required for observations and cannot be created by doing observations.

Rather, knowledge is created by a process that does not resemble induction in any important respect. First, you look for problems with your current ideas. A problem is just anything that seems worth changing. You then propose guesses about how to solve these problems. You look for criticisms of the proposed solutions and eliminate criticised solutions until only one is left. You then look for new problems with your new set of ideas.

Note that there is no step of trying to show your ideas are good or probable. This is just not possible because all of your ideas about how to solve your problems are guesses. And since all of your ideas about how to test stuff are solutions to problems, all of them are guesses too. So all of your knowledge is guesswork. It is not confirmed or shown to be true or anything like that. Rather, you try to get rid of bad ideas through criticism. This means, in particular, that all of your ideas may be flawed and you should be willing to reconsider any idea.

Another important issue is that it could hardly be the case that your proposals for how to solve problems could be anything other than guesses. If you knew in advance how to solve a problem, then you wouldn’t have that problem in the first place. Sometimes people make the right guess about a problem the first time they say something about it but that must be a result of them having tried and discarded ideas before they said anything about it.

There is nothing about this discussion that limits its conclusions to science. Any process that creates any kind of knowledge (useful or explanatory information) has to proceed by variation of current knowledge and selection among those variations.

The socialist calculation problem

Socialists like the idea that people who are able to produce should give stuff to people who are not able to produce. This idea is morally bad for reasons I will explain later, but let’s leave that aside for the moment and think about whether you could actually run the world like this.

Let’s consider the problem of whether we should make flour and if so how we should make it, and how we should distribute it. According to socialism we’re supposed to do this by considering need, so let’s try to do that.

Let’s start with somebody who is hungry: let’s call him Jack. If you give Jack a bag of flour he might eat it. How much flour should you give Jack? If you drive a dump truck up to his house with a ton of flour and dump it in his grade, then he might not like that too much. He might not be able to eat it before it starts going off and it might attract vermin. So you should give him less than a ton and he won’t want you to dump it in his garden. But exactly how much should you give him? And how should the flour be packaged?

And the problem is worse than that. Jack might want to use the flour to make bread. So then he needs to have the other ingredients of bread and without those ingredients he might not want the flour at all.

But there is more complexity to come. If you sent the flour to a baker who makes bread and the baker gave Jack the bread, Jack would also eat the bread. So should you give any flour to Jack? Maybe you should just give him bread.

Another problem: whether we give Jack flour directly or give it to the baker to make bread the flour has to be made somewhere. In the place where you make it you can’t make many other things. You can’t have a factory that makes computer chips and a flour factory in the same place.

Indeed, you might even want to start making a factory for a product that doesn’t exist yet. You might have an idea for something you could invent that lots of people would want and maybe you should get some space to make it now.

This is starting to look very complicated. It looks like you have to take into account lots of knowledge you can’t have. Is this starting to sound familiar? Doesn’t it sound a bit like trying to come up with a scientific idea that covers lots of stuff you haven’t seen? If you want to make stuff for other people then you need to have lots of knowledge about how those other people will respond to what you’re doing, which is an emergent consequence of the laws of physics, biology chemistry, epistemology and other stuff. The solution to this problem has to be created by variation and selection of current knowledge.

So let’s suppose you know how to make flour. To make the flour you need certain items, like corn, say. So if you’re going to keep making flour you have to get a new supply of the stuff required to make if you want to continue. Unless the person who wants the flour happens to have exactly what you need to make it then he has to give me something you can exchange for stuff you can use to make flour. Now you might imagine he could give you stuff that a particular person wants if that person could supply the stuff you need to make the flour. But all sorts of things could go wrong with that. The person who makes the stuff I need might decide to do something else instead. Or he might have a change of circumstances that means he needs slightly different stuff. So what is really needed is something that he can exchange with other people to get what he wants. What is needed, in short, is a good that can be exchanged for anything – a medium of exchange. We have a name for that good: it is called money.

If you get more money by selling your flour to a baker than to Jack you can make more flour. If you make more money by making the flour in a different way, or with a different variety of corn or whatever then you can make more flour. You can also do other stuff with the money, like buying yourself food or an iPhone or whatever. So if different ways of making flour seem equally attractive in other respects you can choose among them by how much money they make. So the free market solves economic problems, not socialism.

Just like when we’re creating scientific knowledge, economic knowledge has to be created by looking for problems, guessing solutions, selecting among those solutions and then looking for more problems.

A moral flaw of socialism

To create knowledge you have to find problems. Socialism recommends looking at problems other people have and then trying to solve those problems. This is a bad idea shared by many other ideologies: let’s call it altruism. To solve a problem you have to try to understand it. So if you are trying to solve Jack’s problems then who is going to work on the problems that you know more about than anyone else? Nobody. So those problems won’t be solved.

And since you have to spend all of your time catching up to the other person’s problems, you are going to be interfering in that other person’s life in a ham fisted way.

The problems you should try to solve are the problems you know about, the problems you are interested in. You shouldn’t be trying to solve another person’s problems. You can help other people when cooperating with them helps you to solve your problems but that is very different from making it your aim to solve their problems.

Similar problems arise with many other political and moral ideologies that aim at solving another person’s problems. Some conservatives like to think they can solve the problems of poor people by encouraging them to get married. Some libertarians like to claim they can solve everybody else’s problems. Walter Block claims that Nazis can be libertarians if only they are willing to use persuasion rather than force to get Jews into gas chambers. Walter Block ought to have realised that gross irrationality like wanting to murder Jews is incompatible with liberty but he was paying too much attention to their problems and not enough to problems with his own knowledge.

To create knowledge about science or how to live better or anything else you have to start with problems you know something about: problems you are interested in. You propose solutions to those problems, select among the solutions by looking for criticisms and then look for new problems with the surviving solution.

Further reading

On induction: Realism and the Aim of Science and Objective Knowledge by Karl Popper. The Beginning of Infinity and The Fabric of Reality by David Deutsch.

On the socialist calculation problem: Socialism and Human Action by Ludwig von Mises.

On the moral problems of altruism more generally: Atlas Shrugged and The Fountainhead by Ayn Rand.

Measurement is theory-laden part 3

In my two previous posts in this series I pointed out that measurement is theory laden: you need an explanation of what is happening to bring about the results. Without such an explanation you can’t work out what the results of a measurement mean.

One example where I think naive ideas about measurement have caused problems is in quantum mechanics. Many physicists seem to think that when you do a measurement the measurement has to reveal a complete picture of the state of the system being measured and otherwise it just doesn’t count. So if I see my toothbrush sitting in a plastic tumbler on my right then that measurement has the outcome it does because that’s where the toothbrush is and that’s all there is to it. In quantum mechanics measurement just doesn’t work that way.

According to quantum mechanics, there are multiple versions of the toothbrush and of everything else. Those multiple versions form layers that are approximately dynamically isolated from one another – they act like parallel universes. The whole of physical reality, which includes those parallel universes, but also has richer structure, is called the multiverse. A lot of physicists seem to think that they don’t actually see multiple versions of the brush, only one version exists and quantum mechanics must be modified to take account of this. However, quantum mechanics accounts for the fact that I only see one version of the brush without eliminating the other versions. What happens is that when I see the brush different versions of the brush produce different versions of me and those different versions of me can’t interact with one another directly. So there is no conflict between the existence of multiple versions of the brush and the fact that I only ever see one version of the brush.

The next thing physicists often say when they hear this explanation is that if I can only ever see one version of the toothbrush then the existence of the multiverse makes no difference to anything. One problem with this idea is single particle interference. That is, we can do experiments in which a single particle behaves as if there are multiple versions of it going along all of the possible paths through an experiment and those different versions interact with one another but we only ever see one of them at the end of the experiment. Are we supposed to think that all the versions we didn’t see just vanish at the end of the experiment, even when quantum mechanics implies that they don’t?

There are also experiments with macroscopic systems that can’t be explained without the multiverse, such as the EPR experiment. In one version of the EPR experiment, two photons are produced by the same source at the same time and head in different directions. Let’s call one of the photons photon A and the other photon B. A photon has a property called polarisation that has some similarities to angular momentum. In particular we can measure the polarisation along different directions. We measure the polarisation along a particular direction with a filter that only lets through photons polarised in that direction. For each photon, regardless of the direction in which we measure the polarisation the probability of it going through the filter is 50%. If we measure the polarisations of A and B along the same direction then we find that they match. If we measure the polarisations along different directions we find that they don’t match with a probability that depends on the angle between the directions in which we measure the polarisations. So whether the polarisations are later found to match or not depends on whether two detectors happen to have the same setting. We can put the detectors far enough apart so that no signal can travel at or below the speed of light from one to the other during the detection process. Some physicists have decided that this means the photons influence one another by some faster than light means during the detection process. Since the probability of any given measurement result on a single photon doesn’t depend on what happens to the other photon, there is no way to use this supposed link to send messages but nevertheless many physicists seem to think the link exists. This leads to a lot of confusion about how quantum mechanics can be consistent with relativity. This confusion is entirely unnecessary because the EPR experiment can be explained without any nonlocality.

The two photons are generated in the same process at the start of the experiment t = 1 and so the multiversal description of photon A at t=1 depends on the multiversal description of photon B at t=1. After they part the photons fly apart and evolve independently of one another. They then get measured. This, too, is an entirely local process with no funny business involving photons magically influencing one another. I’ll start by discussing photon A: everything I say about photon A applies to photon B with the photons labels switched around. What happens is this: the multiversal description of the measuring device for photon A comes to depend on the multiversal description of photon A. Since the multiversal description of photon A depends on that of photon B at t = 1, the multiversal description of the measuring device for photon A also depends on the multiversal description of photon B at t=1. Exactly what information about photon B is transmitted by photon A to the measuring device depends on what happens to photon A between the t=1 and when the measurement process is over. Now regardless of exactly what polarisation observable we choose to measure in 50% of the universes the photon goes through and in 50% it doesn’t. However, the multiverse doesn’t just consist of parallel universes and some of the multiversal information contained in photon A, including the information it contains about photon B, isn’t revealed by the measurement on photon A alone, i.e. – it isn’t reflected in the way the multiverse locally differentiates into non-interacting parallel universes. What happens instead is that hidden information is transmitted to the measuring device and then to other systems that interact with the measuring device and at some point in the future the information from photon A is transmitted to some system that contains information from measurements on photon B and the measuring results from photons A and B become correlated due to the hidden multiversal information the two photons contained about one another. The precise pattern of the correlation depends on what multiversal information was transmitted by each photon to the measuring devices and so depends on what happened to them between t=1 and when they were measured.

For more technical detail see Information Flow in Entangled Quantum Systems and Does Quantum Nonlocality Exist? Bell’s Theorem and the Many-Worlds Interpretation.

What is needed to understand measurement in quantum mechanics is a more subtle idea about the role measurement plays in our understanding of the world. A measurement is an interaction whose results are relevant to whether we should accept or reject a theory. This doesn’t require that there is only one version of me after the measurement. A theory should be judged by whether it is a good explanation and whether it successfully predicts the results of experiments, not by whether it matches a naive and parochial intuition about how measurement should work.

Nicholas Dykes has not replied to my criticism

Nicholas Dykes claims that  he has not replied to my criticism. I have criticised his non-reply reply.

Measurement is theory-laden part 2

In my previous post in this series I discussed the idea that all measurement is theory laden and gave an example of a bad explanation of a measurement. In this post, I will give a good example, from the special theory of relativity. The point is to illustrate  that a good explanation consists of taking an idea seriously and working out its consequences, not of sweeping apparently strange implications under the rug. Doing that is an error since either those new implications are false and your idea is a dud or they are true and you have discovered something new and important. You can’t find out which of those two possibilities is true without working out the consequences of the idea.

First, two definitions that will be relevant. An frame of reference is a set of physical systems used to measure the motion of other systems. An inertial reference frame (IRF) is a frame of reference in which objects that do not suffer some external force move in straight lines. Empty space far away from any masses is a good approximation to an inertial frame. If you measure everything relative to your car while it is accelerating that won’t be a good approximation to an inertial frame because you will see things accelerating when no forces act on them.

Special relativity uses two assumptions.

(1) All IRFs are the same with respect to the laws of physics. For example, if two people use different IRFs, they will both see that objects obey conservation of momentum.

(2) The speed of light in empty space has the same value in all IRFs, denoted by c.

The second assumption looks a bit strange. If you were to get in your car and drive down the road, the cars coming in the opposite direction would be moving at a different velocity relative to you if you speed up or slow down. If you’re driving at 30mph with respect to the pavement and the chap driving in the opposite direction is also travelling at 30mph then you will see him coming at you at 60mph. But you can consistently work out the consequences of these assumptions and that’s part of what matters when it comes to doing experimental tests. (It is not the only thing that matters since some consistent and well worked out ideas don’t have empirically testable consequences.)

I will illustrate two consequences of these assumptions to illustrate what I’m talking about. The consequences in question are that if an object is moving at constant velocity (moving at a constant speed and in a constant direction) with respect to an IRF will act as if it is shorter along the direction in which you are moving than in an IRF in which it isn’t moving and any clocks attached to that object will run slower. This happens in such a way as to make measurements of the speed of light come out the same in both IRFs.

Suppose that you have a clock X that is at rest in an IRF S. This clock consists of two mirrors A and B, a distance L apart with a pulse of light bouncing between them. Each time the light pulse bounces off one of the mirrors it causes a clock attached to mirror A to tick. In the frame S the time T between ticks is 2L/c.

Now suppose there is another IRF S‘ that is moving at a speed v with respect to S at a right angle to the pulse of light bouncing between the mirrors:clocks

The distance between the mirrors in S isn’t going to change because that distance is at right angles to the direction in which the clock is moving. The time it takes the clock to tick in S‘ is T‘. The light takes T‘/2 to hit the mirror B in S‘ and during that time the mirror has moved vT‘/2. The light then takes another T‘/2 to hit the first mirror again at position C. So using Pythagoras theorem the total distance the light travels in S‘ is

AB + BC = 2\sqrt{L^2+(vT'/2)^2}.

The total distance travelled by the light pulse must be cT‘ because the speed of light doesn’t change between the two frames, so

cT' = 2\sqrt{L^2+(vT'/2)^2}

and a bit of rearrangement gives:

T' = \frac{2L}{\sqrt{c^2-v^2}}.

Since L = cT/2 we can write

T' = \frac{T}{\sqrt{1-v^2/c^2}}

Now,

1 > \sqrt{1-v^2/c^2}

because v < c so the amount of time it takes for the clock to tick increases.

Now suppose that we consider another frame S” moving  at speed parallel to the direction in which the light travels in the clock:

clocks1

Since the far end of the clock is moving away from the light pulse it has to travel farther than the length of the clock in S” to get to the mirror at the far end of the clock:

L'' + vt'' = ct''.

When the light pulse is travelling back from the far end of the clock to where it started, it travels a shorter distance:

L'' - vu'' = cu''.

The total time is

T'' = u'' + v'' = \frac{2L''c}{c^2-v^2}=\frac{2L''/c}{1-v^2/c^2}.

The time measured in S‘ and S” will be the same so:

T'' = \frac{T}{\sqrt{1-v^2/c^2}}

L'' = L\sqrt{1-v^2/c^2}

and so moving objects will act as if they are shorter.

On the scales of speed and distance we use in everyday life these effects are very small, but they can be measured for particles travelling near the speed of light and they have been found.

For more information, see Special Relativity by A. P. French.

Measurement is theory-laden

Followers of Karl Popper say that measurement is theory-laden. This means that every time you do a measurement you are making assumptions about how the measurement works. This implies that the idea of our knowledge being derived from measurement makes no sense since knowledge is required for measurement.

However, this is often left a bit abstract, so I thought I would provide an example in which you can be led astray by bad ideas about measurement.

Isaac Newton, despite making great contributions to our understanding of how the world worked, also came up with some confused ideas about absolute space and time. I will illustrate these ideas with quotes from an English translation of Newton’s scholium on absolute space and time.

First, Newton states that he thinks motion can’t just be relative motion:

Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

Newton clarifies:

Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be continually changed…

Absolute motion is the translation of a body from one absolute place into another; and relative motion, the translation from one relative place into another. Thus in a ship under sail, the relative place of a body is that part of the ship which the body possesses; or that part of the cavity which the body fills, and which therefore moves together with the ship: and relative rest is the continuance of the body in the same part of the ship, or of its cavity. But real, absolute rest, is the continuance of the body in the same part of that immovable space, in which the ship itself, its cavity, and all that it contains, is moved. Wherefore, if the earth is really at rest, the body, which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on the earth. But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth, in immovable space, partly from the relative motion of the ship on the earth; and if the body moves also relatively in the ship, its true motion will arise, partly from the true motion of the earth, in immovable space, and partly from the relative motions as well of the ship on the earth, as of the body in the ship; and from these relative motions will arise the relative motion of the body on the earth. As if that part of the earth, where the ship is, was truly moved towards the east, with a velocity of 10010 parts; while the ship itself, with a fresh gale, and full sails, is carried towards the west, with a velocity expressed by 10 of those parts; but a sailor walks in the ship towards the east, with 1 part of the said velocity; then the sailor will be moved truly in immovable space towards the east, with a velocity of 10001 parts, and relatively on the earth towards the west, with a velocity of 9 of those parts.

Newton also thought that it was possible to measure this absolute motion:

It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the obser- vation of our senses. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common center of gravity, we might, from the tension of the cord, discover the endeavor of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. And then if any equal forces should be impressed at once on the alternate faces of the globes to augment or diminish their circular motions, from the increase or decrease of the tension of the cord, we might infer the increment or decrement of their motions; and thence would be found on what faces those forces ought to be impressed, that the motions of the globes might be most augmented; that is, we might discover their hindmost faces, or those which, in the circular motion, do follow. But the faces which follow being known, and consequently the opposite ones that precede, we should likewise know the determination of their motions. And thus we might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared. But now, if in that space some remote bodies were placed that kept always a given position one to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies, whether the motion did belong to the globes or to the bodies. But if we observed the cord, and found that its tension was that very tension which the motions of the globes required, we might conclude the motion to be in the globes, and the bodies to be at rest; and then, lastly, from the translation of the globes among the bodies, we should find the determination of their motions. But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it.

So Newton imagines an experiment involving two globes in empty space connected by a cord undergoing circular motion with respect to absolute space. The tension in the cord between the spheres increases if the globes move faster with respect to absolute space. So by measuring the tension in the cord you can tell how fast the globes are moving with respect to absolute space.

There a few problems with this proposal. First, the real universe isn’t like that, it actually has other stuff in it. Second, if there was such a universe, nobody would be able to measure the tension in the cord because there would be nobody around to measure it. Third, the globes are accelerating so at most this experiment would refute the idea that accelerated motion is motion relative to other bodies.

Newton also describes another experiment that he actually did and sounds a lot more plausible:

The effects which distinguish absolute from relative motion are, the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion, they are greater or less, according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; thereupon, by the sudden action of another force, it is whirled about the contrary way, and while the cord is untwisting itself, the vessel continues for some time in this motion; the surface of the water will at first be plain, as before the vessel began to move; but after that, the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little from the middle, and ascend to the sides of the vessel, forming itself into a concave figure (as I have experienced), and the swifter the motion becomes, the higher will the water rise, till at last, performing its revolutions in the same times with the vessel, it becomes relatively at rest in it. This ascent of the water shows its endeavor to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, becomes known, and may be measured by this endeavor. At first, when the relative motion of the water in the vessel was greatest, it produced no endeavor to recede from the axis; the water showed no tendency to the circumference, nor any ascent towards the sides of the vessel, but remained of a plain surface, and therefore its true circular motion had not yet begun. But afterwards, when the relative motion of the water had decreased, the ascent thereof to-wards the sides of the vessel proved its endeavor to recede from the axis; and this endeavor showed the real circular motion of the water continually increasing, till it had acquired its greatest quantity, when the water rested relatively in the vessel. And therefore this endeavor does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation.

But this experiment only refutes the idea that the force on the water is determined by its motion relative to the objects that immediately surround it.

The fact that the water rises up the side of the bucket has nothing to do with absolute space and time. Rather, the water rises up the bucket because it is accelerating with respect to the gravitational field. Newton didn’t find that explanation, Einstein did that. Newton wasn’t looking for a good explanation because he thought he had already found it and proved it by doing measurements.

One moral of this story is that you should be critical of the explanations behind measurements.