The Right Kind of Light

December 13, 2016 23 Comments

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.

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Why atoms are unstable in classical physics

November 24, 2016 24 Comments

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

circorbit

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):

pointcharge

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):

velocityatom

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:

electromagnet

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:

acceleratingcharge

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.

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Pusey and all that jazz

December 7, 2013 3 Comments

In this post I’m going to present some philosophical dialogues to help explain what’s wrong with some current debates about quantum mechanics.

Philosophical Dialogue 1: The Right Argument

Scene: the living room of John’s house, where John is sitting at his computer. Jane enters.

Jane: This house does not exist.

John looks around, he seems appropriately puzzled.

John: Why do you say that?

Jane: I admit that the idea that this house exists can be used to do calculations of things like air currents, but it doesn’t actually exist, it’s just a rule for computing temperature and air currents.

John: That’s dumb. All you’re doing is taking the idea that the house does exist relabelling part of it as not existing. What you’re saying just makes the explanation of the air currents and temperature more complicated and less clear.

Jane: Oh, this metaphysical fantasy that the house actually exists is just complete hogwash, it’s not the sort of thing with which I, as a practical person, can possibly be expected to believe.

John: Your incredulity is not an argument. Kindly go away you silly person.

Philosophical Dialogue 2: The Wrong Argument

Scene: the living room of John’s house, where John is sitting at his computer. Jane enters.

Jane: This house does not exist.

John looks around, he seems appropriately puzzled.

John: Why do you say that?

Jane: I admit that the idea that this house exists can be used to do calculations of things like air currents, but it doesn’t actually exist, it’s just a rule for computing temperature and air currents.

John: But when I do experiments I find that the house does exist.

Jane: No you don’t. You just find that the air currents and temperature can be predicted with the house formulae, which are just tools for calculation.

John: Oh yeah. Well, I’ll prove it by coming up with a great experiment to test your idea. An experiment that will trash your idea forever.

Jane: So what?

Commentary

The statistical interpretation of quantum mechanics is the idea that quantum mechanics is just a set of formulae for calculating probability. The appropriate response to this is to say something similar to what John said in the first dialogue. A few years ago, Pusey et al proposed an experiment that they claimed would test the statistical interpretation of quantum mechanics. This is analogous to what John said in the second dialogue. Pusey et al are wrong, not because the statistical interpretation is right but because they give it too much credit. The statistical interpretation is complete garbage and cannot be tested by any conceivable experiment because it says nothing about anything. The statistical interpretation may or may not lead people into making some mistakes when doing calculations, but it is mistaken about physics and epistemology.

Physics is about what exists in reality. It is not about formulae for calculating stuff. The formulae are useful for testing ideas about what exists in reality and they may also have technological applications. But in both applications it is important to keep your eye on the underlying physical reality so you understand what you’re doing with the formulae. If you don’t keep your eyes on the prize you will end up making epistemological and technological mistakes.

To understand better what quantum mechanics says about reality read the structure of the multiverse, The Fabric of Reality and The Beginning of Infinity by David Deutsch.

Filed under epistemology, everett, multiverse, physics, quantum mechanics

Measurement is theory-laden part 3

August 26, 2013 Leave a comment

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.

Filed under epistemology, everett, multiverse, physics, quantum mechanics

Measurement is theory-laden part 2

August 13, 2013 10 Comments

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 v 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.

Filed under epistemology, physics Tagged with , ,

Measurement is theory-laden

August 10, 2013 Leave a comment

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.

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