Why should you learn physics?

In a comment, Elliot Temple asked questions about when and why people should learn physics:

what’s the point of learning about physics? who should learn about it and why? should everyone learn about physics? how should someone decide if they should learn some physics, and which physics, and how to learn it?

There are several reasons people might want to learn about physics.

(1) Learning physics involves figuring out stuff, which can be fun. It’s like trying to figure out a very complicated puzzle. One difference from trying to solve a puzzle invented by a person is that  for lots of physics problems nobody knows the answer. There are some puzzles invented by people for which nobody knows the answer. You can have computer games in which a program generates a puzzle. But even in cases like that the rules for generating the puzzle are known and written down in the text of the program. The laws of physics are not known or written down in many cases.

(2) You can want to learn physics for technological reasons. The laws of physics rule out some ways of solving problems. For example, you can’t travel faster than light so technology that requires faster than light travel won’t work.

(3) You can want to learn some physics for philosophical reasons. There are philosophical disputes about stuff like whether it is possible to understand the world and physics is relevant to those disputes. A person is a physical object, so a person can’t know X if learning X requires breaking the laws of physics. In The Beginning of Infinity, David Deutsch argues that all problems that are worth solving can be solved. This rules out some bad ideas people have about people being unable to understand how the world works cuz our brains evolved by natural selection only to solve some problems, see BoI Chapter 3 starting at about p. 53.

You can comment on the above or explain reasons I left out in the comments below.

The Right Kind of Light

The physicist Seth Lloyd said that “Almost anything becomes a quantum computer if you shine the right kind of light on it.”

This is related to computational gates. A computational gate is an operation performed on some fixed finite number of bits as input and gives a fixed finite number of bits as output after a fixed finite amount of time. The not gate takes one bit as input and changes its value from 1 to 0 or 0 to 1. A controlled not gate takes two bits as input and flips the second bit if the first bit is 1 and leaves it alone otherwise so it would change the bits as follows

(0,0) \to (0,0),

(0,1) \to (0,1),

(1,0) \to (1,1),

(1,1) \to (1,0).

Classical computers like the laptop I am using to write this post can do any classical computation. A classical computation takes bits with some definite set of values as input and changes them to produce some bits as output.

A quantum computer uses qubits – the closest quantum mechanical equivalent of a classical bit. A qubit need not have only a single value, it can have multiple values at the same time: the qubit exists in different versions that have different values. Those different values can undergo a process called interference that pushes both versions into the same state in a way that depends on what happened to both of them while they were different. If you have a set of qubits you can prepare them in all of the possible values of the bits at the same time. You can then do computations on all of the possible states of the qubits and combine those values to get solutions to problems that would be solved far more slowly with a single computation on a single set of values.

It is possible to construct a quantum computer that can do any computation another quantum computer can do – a universal quantum computer. A universal quantum computer would be able to simulate any finite physical system if you give it enough qubits and enough time.

And it is possible to do any computation the universal quantum computer could do by combining computational gates that act on qubits instead of bits. This might not sound too impressive since you might need really huge gates to do big computations. But in reality you can do all possible computations to any accuracy you like by composing gates out of a particular set of gates. Any possible gate for a single single qubit can be described by a set of three numbers all in the range [0,2\pi]. The set of single qubit gates and the controlled not gate form a universal set of gates.

An atom can be isolated in various ways, e.g. – putting the atom in a specially chosen magnetic field.  The atom’s outer electron can be moved between its lowest possible state and the next highest energy state by shining light of the right energy on it. The energy of each photon has to match the energy of the difference between the states. By shining the light at a controlled intensity for a controlled amount of time you can control the electron’s state by giving it a controlled probability of moving from one level to another. You can also control the interference properties of the different versions of the electron. This allows you to do any single qubit gate on the electron by treating what energy level it is on as a qubit. You can also get the atoms to interact by sending light signals between them and in particular you can do a controlled not gate. So by shining the right kind of light on atoms you can make a universal quantum computer. The property of having two or more possible states for an electron in an atom is common. “Almost anything becomes a quantum computer if you shine the right kind of light on it.”

This sounds very complicated. Perhaps all of the work and information is stored in the apparatus for manipulating the qubits. This is the wrong way of looking at the issue. That equipment is needed to set up the atoms to do a computation but it won’t do any computation without the atoms. A large part of your ordinary desktop or laptop computer is not doing computation. Rather, some of the equipment provides ways to put information into the computer, e.g. – the keyboard. Other parts of the equipment supply power to the computer or cool parts that get hot. But without the chips that do the computation, this equipment can’t do much for you. The same is true for the quantum computer. You can shift some of the storage of information out of the qubits into the surrounding apparatus, but you can’t do any quantum computation without the atoms.

Bad Spectator article saying Brexit is better than Trump

The Spectator published a bad editorial called Why Trump’s victory isn’t like Brexit. The article claims that:

[Brexit] was an argument about encouraging more trade, lowering tariffs, restoring sovereignty, reducing net immigration — all ideas which voters proved very capable of understanding.

The author continues:

Donald Trump has no similar agenda. He offers emotion, but not much beyond that. He dislikes trade, and global capitalism in general. His immigration policy has amounted to a bizarre threat to ban Muslims from entering the country and build a wall between the United States and Mexico. At any other time, these policies would have disqualified him from the office — but this year Americans were not looking for solutions. Trumpism was about stopping Hillary Clinton from becoming president and sticking two fingers up to the machine. And beyond that, it is not about very much.

Trump has a website full of policies. The Spectator doesn’t mention these let alone criticise them. This is very bad journalism and very bad writing. Trump’s presidential campaign website is on the first page of Google hits when you search “Donald Trump”. If you read the website then you find he has substantive policies on a lot of issues.

The immigration part of Trump’s platform includes stuff like deporting criminal illegal aliens, detaining anybody caught entering illegally until they can be deported, reforming legal immigration to serve American interests and lots of other stuff including building a wall on the Mexican border. The website also lists problems that these changes are supposed to address.

The healthcare part of his platform is also substantive. He wants to repeal Obamacare and replace it with health savings accounts. He wants to allow competition between insurers across state lines. Again, the site lists problems that these changes will address.

The trade part of Trump’s platform is also substantive. It lists policies and the problems that Trump thinks they will solve. A direct quote:

Use every lawful presidential power to remedy trade disputes if China does not stop its illegal activities, including its theft of American trade secrets – including the application of tariffs consistent with Section 201 and 301 of the Trade Act of 1974 and Section 232 of the Trade Expansion Act of 1962.

This looks like a policy he has thought about. There are lots of people who object to trade and lots of economists who can’t answer their objections. For an example see Vox Day’s discussion with such an economist. Whether Vox Day is right or wrong in the light of a performance like this by an economist it is not surprising that a lot of people don’t agree with free trade.

Trump has also proposed a tax planrepeal anti-fossil-fuel policies and has proposed many other policies.

To the extent that Trump is wrong, the Spectator’s editorial won’t convince anybody to reject his bad policies because it doesn’t explain any substantive points of disagreement. The article doesn’t even refer to another article or a book with arguments against Trump’s policies. Whoever wrote this article needs to learn how to argue.

Notes on “Superintelligence” by Nick Bostrom

Some notes on “Superintelligence” by Nick Bostrom, which is a bad book.

Summary: Bostrom sez that we might make superintelligences that are better than us. He doesn’t realise that saying there could be a qualitatively different kind of intelligence means that science and critical discussion are not universal methods of finding truth. If that’s true, then his whole discussion is pointless since it uses tools he claims are trash: critical discussion and science. Superintelligences might have motivations very different from us and make us all into paperclips, or use us to construct defences for it or something. He doesn’t seem to have any understanding at all of critical discussion or moral philosophy or how they might help us cooperate with AIs. Superintelligences might make us all unemployed by being super productive he sez. Or we might waste all the resources the superintelligences give us. He doesn’t discuss or refer to economics. It’s as if he doesn’t realise there are institutions for dealing with resources. And he also doesn’t seem to understand that more stuff increases economic opportunity, so if AIs make lots of cheap stuff people will have more opportunities to be productive. His proposed solution to these alleged problems is government control of science and technology. Scientists and AIs would be slaves of the govt.

I go through the book chapter by chapter, summarising and criticising.

Chapter 1 Bostrom sez vague stuff about the singularity. This is a prophecy of accelerating progress in something or other. Prophecy is impossible because what will happen in in the future depends on what we do in the future. What we will do depends on what knowledge we will have in the future. And we can’t know what knowledge we will have in the future, or how we would act on it without having the knowledge now. See The Beginning of Infinity by David Deutsch chapter 9 and The Poverty of Historicism by Karl Popper. Anyway, he gives an account of various technologies people have tried to use for AI. He eventually starts describing a Bayesian agent. The agent has a utility function and can update probabilities in that function. He sez nothing about how the function is created. He sez some stuff about AI programs people have written. He then starts quoting surveys of AI researchers (i.e. – people who have failed to make AI) about when AI will be developed as if such surveys have some kind of significance.

Chapter 2 Bostrom sez an AI would have be able to learn. He discusses various ways we might make AI without coming to a conclusion.

Chapter 3 Bostrom discusses ways a computer might be super intelligent. An AI might run on faster hardware then the brain. So it might think a lot of thoughts in the time it takes a human to think one thought. Thinking faster isn’t necessarily much use. People thought for thousands of years at the speed we think now without making much progress. He sez stuff about collective super intelligence: people can do smarter stuff by cooperating according to rules than they can individually. This is not very interesting since all the thinking is done by the people cooperating using those rules, so it’s not an extra level of thinking or intelligence. He sez a super intelligence might be qualitatively better than human intelligence. Qualitative super intelligence would imply that the scientific and rational worldview is false since it could understand stuff we couldn’t understand by rational and scientific methods. The stuff that can’t be understood by scientific and rational methods would interact directly or indirectly with all of the stuff we could understand  by rational methods. We would not be able to understand those interactions or their results, so we couldn’t really understand anything properly.

Chapter 4 vague prophecy stuff about the rate at which super intelligence might develop.

Chapter 5 includes a lot more vague prophecy. He sez govts might want to control super intelligence projects if they look like they might succeed other stuff like that. He sez AIs might maximise utility without taking into account the ways govts restrain themselves from doing stuff that maximises utility. He writes about deontological side constraints: I think this means principles like “don’t murder people” but he doesn’t explain. He doesn’t explain how utility is measured or anything like that. He doesn’t explain how you can know an option has more utility for somebody without giving him a choice between that option and others. He sez AI might be less uncertain and so act more boldly but he doesn’t explain any way of counting uncertainty. He doesn’t explain epistemology, which is dumb since the book is supposed to be about agents who create knowledge. He sez an AI wouldn’t have problems of internal coordination like a group of people. This is dumb since people have lots of internal conflicts.

Chapter 6 Bostrom sez our brains have a slightly increased set of capacities compared to other animals. He doesn’t realise that we’re qualitatively different from other animals. Humans can guess and criticise explanations, animals can’t. He sez a super intelligence might be able to do lots of stuff better than people and then take over the world. They might use nanotechnology or von Neumann probes or something. This is super vague and kinda dumb. If that sort of technology is available then it may be improved and made cheaper by capitalism till everyone can use it, so why wouldn’t everyone use it? So then the supposed super intelligence wouldn’t have a great advantage.

Chapter 7 Bostrom sez a super intelligence might have very different motivations than humans. It might want to maximise the production of paperclips. But we might design a super intelligence to have particular goals. Or it might be made by scanning a human brain or something so it has similar ideas to us. Or the super intelligence might do whatever is necessary to realise some particular goal, including making the whole Earth into defences to protect itself or something. He talks a lot about predicting the super intelligence’s behaviour. This is just prophecy, which is impossible. He also doesn’t mention objective moral standards or critical discussion as things that might help AIs and humans get along.

Chapter 8 Bostrom worries that an AI might act nice to lull us into a false sense of security before making us all into paperclips or whatever. Or the AI might try to do nice stuff by a bad means, like make u happy by putting electrodes in parts of the brain that produce pleasure. This is just more of the same crap as in chapter 7.

Chapter 9 Bostrom talks about controlling AIs so they won’t kill us or whatever. He considers limiting what the AI can do and dictating its motivations. He doesn’t consider critical discussion or moral explanations.

Chapter 10 discusses ways in which a super intelligence might be useful. It might be able to answer any question in a particular domain. As David Deutsch points out in The Fabric of Reality chapter 1, we already have an oracle that can tell us what will happen if we do thing X: it’s called the universe. This isn’t very useful. Being able to explain stuff is more important than prediction. Also, any particular oracle will be fallible and have some limitations. So again we’re back Bostrom ignoring the importance of critical discussion and explanation. A super intelligence might also act as a genie he sez. He sez we would have to design it so it would do what we intended rather than act in some way that formally does what we asked but is actually dumb. Again, critical discussions and explanations just don’t exist in Bostrom’s world.

Chapter 11 Bostrom talks about superintelligences making everyone unemployed. He doesn’t explain why people would be unemployed when cheap stuff made by AIs would open up more economic opportunities. He also sez AIs might produce lots of wealth that people would squander for some unexplained reason. He also sez that people might create lots of AIs on demand for particular kinds of work then get rid of them when the work is done. And people might make AIs work very hard so they are unhappy. He sez this might be avoided by lots of treaties limiting what people can do. This is all kinda dumb. He’s just arbitrarily saying stuff might happen without thinking about it. Like if you create AIs that can create knowledge, you should be interested in their objections to some proposed course of action since they might point a problem you didn’t notice.

Chapter 12 Bostrom discusses deciding what values AIs will have and how to impose them. He seems to think that values work by deciding on some goal and then pursuing it without any reconsideration. But even if AIs wanted to maximise the production of paperclips it wouldn’t make people into paperclips. Rather, the AI would have to work out all of the best stuff we know about how to make stuff, such as critical discussion and free markets. See Elliot Temple’s essay on squirrels and morality for more discussion of this point.

Chapter 13 More of the same. He finally has a discussion of epistemology. He is assuming Bayesian epistemology is true since he writes about priors. But Bayesian epistemology is wrong. Ideas are either true or false so they can’t be assigned probabilities. And the only way to create knowledge is through guessing and criticism, as explained by Karl Popper, see Realism and the Aim of Science, Chapter I and The Beginning of Infinity by David Deutsch chapter 4. The acknowledgements to the book say he consulted David Deutsch.

Chapter 14 sez the govt should control science to make superintelligences serve the common good. So scientists and superintelligences should be slaves to the govt.

Chapter 15 More of the same sort of trash as chapter 14.

Why are atoms stable in quantum mechanics?

In a previous post I explained why atoms are unable in classical physics. The post is about why atoms are stable in quantum mechanics.

Summary Atoms in quantum mechanics don’t suffer from the same radiation problem as atoms in classical mechanics. A quantum system exists in many instances that can interfere with one another on a small scale. As a result, on an atomic scale an electron doesn’t have a trajectory and so it can’t be said to accelerate and it doesn’t radiate. In addition, when the probability of finding an electron is highly peaked at a particular location, quantum mechanics makes the instances spread out. The potential produced by the nucleus pulls the electron instances toward the nucleus. Atoms can be stable because the spreading out produced by quantum mechanics and the attraction produced by the potential balance out.

In classical mechanics, an electron’s orbit around an atom is unstable because it emits the energy it would need to stay in orbit as light. And the electron does this because it is accelerating. To be able to say the electron is accelerating, it has to have a trajectory – a line it travels along. Then if the line changes direction or the electron speeds up along the line you can say it is accelerating. In quantum mechanics, systems sometimes don’t have trajectories.

Absence of microscopic trajectories in quantum mechanics

In quantum mechanics, particles are described very differently from how they are described in classical mechanics. Particles are more complicated than they look. Each particle exists as multiple instances. these instances are copies in the sense that they all obey the same rules. They are instances of a specific particle in the sense that they only interact with other instances of that particle. Sometimes two instances of a particle are different: they have different locations or different momentum or different values of some other measurable quantity.  Sometimes these instances are all fungible – there is literally no detectable physical difference between them. Two instances of the same particle can become different and then become fungible again in a way that depends on what happened to the different versions of the particle: this process is called quantum interference.

Now suppose you have an electron in empty space near some point Pstart. Consider a point Pfinal that some instances of the electron will reach later. How does those instances get there? First instances of the electron spread out from Pstart in all directions. Some instances go to points intermediate between Pstart and Pfinal: P1 and P2. Then some instances of the electron spread out from P1 and P2 in all directions. Some of those instances end up at Pfinal. Figure 1 shows this process with the little domes over the intermediate points indicating the instances moving in all possible directions. There is no explanation of how the electron moves that refers to just one trajectory. And none of the instances individually change direction either. At each point there is some instance coming in from any given direction and another instance leaving in the same direction. And all of the instances of the electron at a given point are fungible so you can’t tell whether the one that left in a given direction came in from that direction or not. So there is no trajectory and no acceleration.


Figure 1 Instances of the electron become different and then come back together.

Now to deal with some objections you might have.

You may be thinking that people can measure where things are and this seems incompatible with there being lots of instances of the electron in different places. Quantum mechanics deals with this problem in the following way. When you do a measurement, the instances of the electron are divided up into sets. When you see some particular outcome of the measurement, the result means something like ‘this electron is within 5mm and 7mm of the corner of your desk.’ There are multiple sets of instances of the electron that give different measurement results like ‘this electron is within 0mm and 5mm of the corner of your desk’ or whatever. When you do the measurement, your instances and the instances of the measuring instrument are also divided into sets. Each of those sets acts as a record of some particular measurement result. For example, if you are detecting the electron with an instrument with a dial, there is a set of instances for each distinguishable position of the dial.

Why don’t you see multiple instances of yourself interfering in everyday life? Multiple instances of you do interfere in everyday life. They just interfere on a very small scale because it is difficult to arrange interference on a large scale. The reason it is difficult to arrange interference on a large scale is that large differences between instances can be recorded by measuring instruments and other interactions, e.g. – air molecules and light bouncing off your body. That measurement process changes the recorded instances. The only way to undo the change so the instances can become fungible again is to undo the transfer of information about the differences. You would have to track down all the light and air molecules and so on and arrange to exactly undo their interaction with you. This cannot be done with current technology so you don’t undergo quantum interference. As a result, the different instances of you don’t interfere with one another. The different instances of the objects you see around you don’t interfere with each other either. Rather, the instances form independent layers where each layer approximately obeys the laws of classical physics: parallel universes. For more explanation of quantum mechanics see The Fabric of Reality by David Deutsch, especially chapter 2, for more on quantum mechanics and fungibility see The Beginning of Infinity by David Deutsch, Chapter 11 and my post on fungibility.

The electron can have something that looks a bit like a trajectory. The electron can have more instances in some places than in others. The number of instances at different positions can be represented by a curve, like this (Figure 2):


Figure 2 A graph of number of instances with distance along some line for an electron.

If you look at a section of the curve, and find the area of the curve under that section, that tells you the probability of finding the electron in that region. In Figure 3, there is a higher probability of finding the electron in the red region since it has a higher area, so the probability of finding the electron between the two red lines is larger than the probability of finding it between the two green lines:


Figure 3 A graph of the area under the curve in two different regions of the curve.

I said that there is a number of instances, but that number is continuous and the only way to know anything about it is by calculating or measuring probabilities.

If you look at the electron on a wide enough section of the curve, then the probability of finding the electron there will be close to 1. The curve changes continuously over time so the curve could move so the peak is in different places and that could look a bit like a trajectory:


Figure 4 The curve for the electron moves around, and so the region where there is a large probability of finding the electron moves around. This is the closest thing to a trajectory in quantum mechanics.

For electrons on a large enough scale, and for large objects like a person or car, the trajectory approximation is very accurate. Things move by lumps of high probability moving from one place to another. But the scale of a single atom is small enough that the trajectory approximation doesn’t work.

Stability of atoms

The absence of trajectories by itself doesn’t explain the stability of atoms. It just explains why the problem of radiating accelerating charges doesn’t occur. To understand why atoms are are stable, let’s go back to the electron. To understand the next bit we have to know a little about how the number of instances curve changes over time. The simple version goes a bit like this:

the rate of change of the curve over time = -(curvature of the curve + the potential the electron is in).

The rate of change of the curve near a point is its slope. If the curve is very curvy, then the slope changes a lot. So the curvature is the rate of change of the rate of change of the curve. Figure 5 illustrates this with some lines near the curvy bit illustrating large change of slope, and in less curvy bit representing less change of slope.


Figure 5 The blue lines change gradient a lot over a small region, so that region has high curvature. The green lines don’t change gradient much and so the region with the green lines doesn’t have much curvature.

The rate of change of the curve over time = -curvature, so near a high peak the curvature is high and the curve gets flatter over time because it decreases at that point. Away from the peak the curvature is smaller and so the curve tends to get flatter more slowly over time. So the curvature term tends to flatten out the curve.

What about the potential? The potential is negative, as explained in the comments on the previous post. So the curve tends to get larger where the potential is large: near the nucleus. The electron can be a stable state that doesn’t change much over time if the flattening caused by the curvature term and the peaking cause by the potential match one another. In this interaction, the electron and proton are recording one another’s position, so their instances are divided up so that the electron and proton stick together.

That’s why atoms are stable in quantum physics.

Why atoms are unstable in classical physics

Why are atoms unstable in classical physics?

Summary: The nucleus of an atom is a positive charge, an electron is a negative charge. Positive charges attract negative charges as a result of electric forces between them. This attraction causes electrons to orbit nuclei according to classical physics. But electron orbits are unstable in classical physics. Charges exert forces on other charges and those forces are described by fields. The field tells you what the force on a charge would be if the charge was at a particular position. An electric field describes the forces on a static charge from another static charge. A magnetic field is basically the electric field produced by a charge moving at constant speed. Electric and magnetic fields are so closely related that they are often described in terms of a single field called the electromagnetic field. An accelerating charge produces waves in the electromagnetic field since the field has to transition between its electric and magnetic components and vice versa. Those waves carry away energy from the accelerating charge. An orbiting electron is an accelerating charge, so this mechanism causes it to lose energy and spiral into the nucleus. This happens in a very short time, around 10^{-11}s.

An electron accelerates when it is orbiting

The nucleus of an atom is a positive charge, an electron is a negative charge. Positive charges attract negative charges as a result of electric forces between them. This attraction causes electrons to orbit nuclei according to classical physics.

An electron is An electron orbiting a nucleus is changing direction at every point on its orbit, as illustrated in Figure 1:


Figure 1 – An object in a circular orbit is accelerating at every point on the orbit. The same would be true for an elliptical orbit.

As a result, its velocity is changing: it is accelerating. An accelerating charge radiates, so the electron loses energy by radiating. Since the electron is losing energy it falls into the nucleus. You might think that the electron could lose energy without falling into the nucleus. A car loses energy in the form of stored fuel when you drive it, but it doesn’t just fall into a ditch as a result. But an electron doesn’t store fuel. All of its energy is tied up in its motion since it has nowhere else to store the energy. So when the electron loses energy it loses speed and it falls toward the nucleus as a result.

Why does an accelerating charge radiate? To understand that, we have to know some stuff about charges in motion, fields and forces.

Forces and fields

A force is any influence on a physical system that can cause it to accelerate or decelerate: Newton’s first law of motion. The size of the force on an object is the mass of the object times the acceleration produced by the force: Newton’s second law of motion. If physical system 1 exerts a force on system 2, then system 2 exerts the same amount of force on system 1: Newton’s third law of motion.

The nucleus exerts a force on the electron before it comes in contact with the electron. As a result, at each point in space there is a vector that describes the forces an electron would experience if it was at that point. A particle with a different charge would experience a different force. The electric force depends linearly on charge. So it is useful to define a vector at each point in space that doesn’t depend on the size of the charge of the electron that can be used to help describe the forces on a particle without  giving a charge in advance. The electric field is a vector valued quantity defined at every point that gives the force applied on a charged particle at that point due to other static charges.

If you had a charged object much larger than an electron, the field might be different at different parts of the object. As a result different parts of the object would experience different amounts of force. So larger objects introduce additional complications to trying to understand what’s going on. It’s more useful for this discussion to consider objects that are so small that the change in the field over those objects is so small it produces negligible internal forces: such objects are called point charges.

You can think of the electric field of a particle in terms of field lines. Field lines are a picture representation of the field. The field lines have arrows on them. The arrows point in the direction a positive charge would move in that field. More lines per unit area means more force.

A point charge will have field lines going out evenly in every direction. So a point positive charge would look like this (figure 2):


Figure 2 – Electric field lines of a stationary charge.

A positive charge would move toward a negative charge. So a point negative charge would have a similar diagram with the lines pointing toward it.

Moving charges

What about a moving charge? The field lines in the direction of the charge’s motion would shrink in that direction. Why objects shrink in the direction of their motion is explained by special relativity. As a result, the field lines get shorter parallel to the charge’s motion, but not at right angles to it. So all the field lines that are not perfectly parallel to the particle’s direction of motion change their slope so they are pointing at a steeper angle to the direction of motion (figure 3):


Figure 3 – Field lines of a charge moving at a constant velocity.

So it’s like there is more charge at right angles to the charge’s direction of motion. So the field at right angles to the charge gets larger.

There is one more issue to understand before I can explain why accelerating charges radiate: the relationship between electricity and magnetism. Magnets exert a force on charged particles like electrons. This effect was used in televisions until about 5-10 years ago. The inside of the television screen was coated with pixels that included materials that would glow different colours when bombarded with electrons. The TV would produce a beam of electrons and move it back and forth across that screen to produce images in quick succession. The path of the electrons was controlled by a magnet that deflected the beam to the appropriate place on the screen. Magnetic forces on a particle depend on the particle’s velocity and charge. At any given point in space, there is a vector that could be combined with the charge and velocity of a point charge at that point to give the magnetic force on that point charge: this vector is called the magnetic field.

Changing electric fields give rise to magnetic fields and vice versa. You can see this effect in action in some scrapyards where people use cranes with electromagnets. These cranes have a lump of iron with wires wrapped around it in a circular pattern, like so:


This arrangement produces a magnetic field running through the curves of the coil. How do the moving charges in the wire produce a magnetic field?

Consider a wire with current flowing through it. The electrons in the wire are moving and the nuclei of the atoms in the wire are not. As noted with the moving charge in the picture above this gives the electrons a larger field at right angles to their motion. That field looks like a magnetic field to a charge outside the wire. The magnetic field lines are at right angles to the line between the wire and the point where the field is being calculated. As a result, there is a field inside the coil pointing through the coil. So magnetic fields are a result of moving charges.

Whether a charge is moving is just a matter of your velocity relative to the charge. So an electric field is also the same as a moving magnetic field. Since electric and magnetic fields are so closely related they are usually considered to be aspects of a single field called the electromagnetic field.

You might be thinking that permanent magnets don’t need to have electricity running through them to work. In permanent magnets, the magnetic field is produced by spinning electrons whose spins are aligned with one another. So the magnetic field in such magnets is produced by the motion of charges.

Accelerating charges

We can now get back to explaining why accelerating charges radiate. An electromagnetic wave is a pattern of changes in electric and magnetic fields that can move. So if an accelerating charge generates  changing electric and magnetic fields, then it radiates.

The laws of physics don’t change at different speeds: an increase from 0 speed to 5, or 5000 speed to 5100 follow the same laws. So you can understand what’s going on by considering the situation where the charge starts stationary and then starts moving.

The charge starts out with field lines like those in figure 1, then the lines change to resemble the field lines in figure 2. This happens at a finite speed so the field lines further from the charge look like those in figure 1. The lines closer to the charge look like those in figure 2. Between those two sets of lines there has to be a transition in which the lines change, as illustrated in figure 4:



Figure 4 – An illustration of the transition in field lines in an accelerating charge.

The circle is just there to illustrate the spherical symmetry of the field lines further out from the charge. This transition produces changing electromagnetic fields that spread out over time, i.e. – radiation. More generally, an accelerating charge makes components of the field transition from being electric to being magnetic and vice versa. These changes produce patterns in the electromagnetic field that move away from the accelerating charge: the charge radiates.

Since an electron is an accelerating charge, it radiates. This radiation leads to the electron losing energy and falling into the nucleus of an atom in classical physics. As a result, atoms are unstable in classical physics. Since electromagnetic fields are strong, the electron’s orbit would decay quickly in a time of the order 10^{-11}s.

Fake Constitutional Scruples

The British High Court recently decided that the government could not leave the European Union without a vote in Parliament. The politicians who brought this case claimed they had constitutional concerns. Their alleged scruples make no sense.

The government has the power to use force against those who disagree with it. If you think a law is wrong, the government can use violence to force you to follow it or lock you up for breaking it. You also have no choice about paying for the policies of the current government. If you like the government’s policy on harsher sentences for burglars and dislike the welfare state, you can’t fund one policy and not the other. If you tried to withhold some of the taxes imposed by the government, the government will ultimately lock you up for refusing to pay. This makes the government extremely dangerous. A constitution is a set of rules that constrains how the government can use force. Part of that constraint is that the constitution should specify some means by which the government can be held accountable and dismissed for incompetence or malice. So you can’t plead a constitutional scruple to stop the government from taking an action that will help restore accountability.

The European Union is an organisation that gives EU officials power without accountability. The EU also damages the accountability of British MPs since they have to pass laws to implement EU directives. Since politicians can’t control what the EU does they have excuses for failing to carry out promises to their constituents. So leaving the EU will make the government more accountable. As such, claiming constitutional scruples about leaving the EU makes no sense.

The excuse given for this ruling is that leaving the EU will take rights away from British people. This is rubbish. The EU takes rights away by passing laws that stop people from dealing with one another voluntarily. For example, if an employer wishes to hire you only on condition that you work more than 48 hours per week, he is not allowed to do that according to the EU’s working time directive. His right to choose the terms on which he deals with people has been taken by the EU. This is not an increase in rights for him. Nor is it an increase in rights for people who want to work those hours. Given the legal issues involved, employers will be less willing to offer such people what they want since they can’t make your employment conditional on working more than 48 hours per week. So the stated reason for the ruling makes no sense.