More on Quantum things

English: Schrödinger equation of quantum mecha...
English: Schrödinger equation of quantum mechanics (1927). (Photo credit: Wikipedia)

Schrodinger’s wave equation describes how the quantum state of a quantum system changes with time. Everett’s insight was that the observer of a quantum state was as much part of the system as the observed part of the system. Therefore they were “entangled” in the quantum sense and would be covered by a single quantum state equation.

If the observer and the observed are thus entangled, then so must be an observer who observes the quantum state of the observer and the observed. One can then extend this to the whole universe, which leads to the concept of a wave equation or function which describes the whole Universe.

English: Quantum mechanics travelling wavefunc...
English: Quantum mechanics travelling wavefunctions (Photo credit: Wikipedia)

That there is an equation for the universe is not really surprising and indeed, it is not surprising that it could be a quantum wave equation as the quantum world seems to form the basis of the physical, apparently classically described, world that we see.

I base this idea on the fact that everything that we sees appears to be describable in terms of a deterministic equation. It has been argued that such things as “psi phenomena“, but such claims are yet to be conclusively verified, with many putative examples having been discredited.


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Some people argue for a soul or mind as an example of a non-physical entity, but any such concept leaves a lot of questions to be asked. A non-physical entity cannot, by definition almost, be measured in any way, and there is difficulty in showing how such a non-physical entity can interact with physical ones, and therefore be noticed or detected.

By definition almost, a physical entity, such a body, is only influenced by physical things. If this were not the case we would see physical entities not following the laws of physics. For example, if it is possible to move an object by mind power or telekinesis, one would see the object disobeying fundamental scientific laws, like Newton’s First Law of Motion.

English: Isaac Newton Dansk: Sir Isaac Newton ...
English: Isaac Newton Dansk: Sir Isaac Newton Français : Newton (1642-1727) Bahasa Indonesia: Issac Newton saat berusia 46 tahun pada lukisan karya Godfrey Kneller tahun 1689 Lietuvių: Seras Izaokas Niutonas 1689-aisiais Македонски: Сер Исак Њутн на возраст од 46 години (1689) Nederlands: Newton geboren 4 januari 1643 Türkçe: Sir Isaac Newton. (ö. 20 Mart 1727) (Photo credit: Wikipedia)

The mind is a curious example of a physical entity which is often thought of as being non-physical. After all, a mind does not have a physical location, apart from the skull of the person whose mind it is, and it can’t be weighed as such.

The mind however is a pattern, on the brain, made up of the state of trillions of neurones. It is made up of information, and is much like a computer program which is made up of the state of a few billion physical logic circuits in the guts of the computer.

Vista de la Motherboard
Vista de la Motherboard (Photo credit: Wikipedia)

Open a computer and you won’t see “an image” anywhere. You will see patterns of bits of data in the memory, or on the hard disk, or maybe in transit, being sent to a computer screen. Similarly if you open someone’s skull you will not see an image there either. Just a bunch of neurones in particular states.

The one glaring exception to all the above, is, perhaps, consciousness. It’s hard to describe consciousness in terms of a pattern or patterns of the states of our neurones, but I believe that that is fundamentally what it is.

Schéma d'un neurone , commenté en francais
Schéma d’un neurone , commenté en francais (Photo credit: Wikipedia)

Some people argue that we are conscious beings, (true), and that we consciously make choices (false, in my opinion). When we look closely at any choice that we make, it appears to be that choice is in fact illusory, and that our actions are determined by prior factors.

People seem to realise this, although they don’t acknowledge it. When questioned, there is always some reason that they “choose” in a particular way. Perhaps they don’t have enough cash to choose the luxury option when out shopping, or their desire outweighs their financial state. When pushed people can always think of a reason.

English: A choice of which way to go The choic...
English: A choice of which way to go The choices are a path to Greengore or Intack or the Old Clitheroe Road (Photo credit: Wikipedia)

To be sure, many “reasons” are actually post choice rationalisations, and choices may be based more on emotions than valid rational reasons, but whatever the emotions (such as the desire for an object), the emotions precede decision.

If, as sometimes happens, a person has to make a choice between two alternatives, that person can be almost paralysed with indecision. Even then, when a decision is finally made, it can be either a random choice, or maybe the person may say that they made a particular choice because they had decided a different way in another situation, or similar (e.g. they like the colour blue!).

English: Choose your leaders and place your trust
English: Choose your leaders and place your trust (Photo credit: Wikipedia)

If there is no non-physical component to the Universe, as appears very likely, and psi phenomenon do not exist, then everything has a cause. I don’t mean this in the sense that event A causes event B which causes C, but more in the sense that the slope that a marble is on causes it to move in a particular direction.

Causality seems to be a continuum thing, rather than the discrete A causes B case. We can only get an approximation of the discrete case if we exclude all other options. There is a latin term for this : ceteris paribus – all other things being kept the same. “Ceteris paribus” would exclude the case where a wind blowing up or across the slope changes the path of the marble.

English: Picture of marbles from my collection
English: Picture of marbles from my collection (Photo credit: Wikipedia)

For this reason I dislike the Many Worlds Interpretation of Quantum Physics, as it is usually stated. The usual metaphor is a splitting movie film, which results in two distinct tracks in the future. I feel that a better picture would be a marble on a slope with a saddle.

The marble may go left, or it may go right, or it may even follow the line of the saddle. We still require “ceteris paribus” to exclude crosswinds, but there is no split as such. In a quantum model, the marble goes both left and right (and traverses the peak of the saddle with vanishing probability).

Monkey saddle
Monkey saddle (Photo credit: Wikipedia)

The probability that it goes left or right is determined by the wave equation for the system, and has a real physical meaning, which it doesn’t (so far as my knowledge goes) in the splitting metaphor.

I don’t know how my speculations stack up against the realities of quantum mechanics, but I like my interpretation, purely on aesthetic grounds, even if it is far from the mark!


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Many worlds or only one?

English: Position and momentum of a particle p...
English: Position and momentum of a particle presented in the phase space. (Photo credit: Wikipedia)

Scientists often use the concept of a “phase space“, which is basically a representation of all the possible states that a system may be in. For the trajectory of a thrown stone for instance, the phase space would be a four-dimensional space, comprising the three dimensions of space, which define where the stone is, and one of time, which defines when the stone is in a particular position.

The trajectory of the stone is a line in this 4-d space, as the location and time information about the stone is known exactly. However, the stone is not a point and maybe be spinning at the same time that the whole object is flying through the air. This means that the trajectory would actually be a complex four-dimensional worm in phase space.

An animated GIF of a tesseract
An animated GIF of a tesseract (Photo credit: Wikipedia)

What if we were to introduce a probability factor into the experiment? Maybe we would set up the projectile to be triggered by an atomic decay or something similar. We would get a different worm depending on how long the atom takes to decay.

Clearly, if we want to show the all of the possible versions of the worm, the worm now becomes a sort of 4 dimensional sheet. Well, more like a 4-d duvet really, as the stone is not a point object.

Bedding comforter or duvet. Français : Couette...
Bedding comforter or duvet. Français : Couette (literie). Deutsch: Daunendecke, umgangssprachlich Federbett. (Photo credit: Wikipedia)

Within the 4-d duvet, each worm represents a case where the atom has decayed, and each of these cases has a probability associated with it. The probability can be expressed as the probability that the atom has decayed by that time or not, and can run from one to zero.

Actually the probability starts from zero and approaches one but doesn’t quite reach it. In practise in a group of atoms some will decay quickly and others will take longer. If there are a finite number of them, then the chances of any one lasting a long, long time are quite small, and all of the atoms are likely to decay in a moderately short time, a few multiples of the half-life anyway. However there will be a finite but microscopic in the extreme possibility, that an atom will survive for as long as you may consider.


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We can add another dimension to the phase space, one of probability. This gives us a five dimensional phase space, and the duvet becomes five dimensional. However, an atom decays at a certain time, and there is a single five dimensional worm in the phase space going forward. The space is no longer a phase space though, as a phase space, by definition, describes all possible states of the rock/launcher/atomic trigger, and doesn’t change.

According to the Copenhagen interpretation of quantum physics the state of a quantum system is described by a set of probabilities. When a measurement of the system is made the state becomes certain, and it is said that the waveform described by the probability function has “collapsed”.

Copenhagen
Copenhagen (Photo credit: Wikipedia)

The famous thought experiment of Schrodinger’s Cat is a description of the difficulties of such a case. The cat is enclosed in a box equipped with a mechanism which will release a poison and kill the cat if triggered by the decay of an atom. At some time after the experiment starts the atom may or may not have decayed so the quantum states “decayed” and “not decayed” are superimposed, and therefore so are the states “dead” and “not dead” of the cat.

How do we know if the stone has been fired yet? Well, we go and look to see, and we either see the stone in its launcher or we don’t. Quantum physics says that the stone exists in a superposition of states – launcher and not launched. The question this raises is, if this is so, how does looking at the stone “collapse” the superposition when we look?

Three wavefunction solutions to the Time-Depen...
Three wavefunction solutions to the Time-Dependent Schrödinger equation for a harmonic oscillator. Left: The real part (blue) and imaginary part (red) of the wavefunction. Right: The probability of finding the particle at a certain position. The top two rows are the lowest two energy eigenstates, and the bottom is the superposition state \psi_N = (\psi_0+\psi_1)/\sqrt{2} , which is not an energy eigenstate. The right column illustrates why energy eigenstates are also called “stationary states”. (Photo credit: Wikipedia)

That quantum superposition is real is indicated by any number of experiments, even though many physicists working in the field (including Schrodinger himself) have expressed discomfort at the idea.

In quantum physics the evolution of everything is defined by the Universal Wave Function. This can be used to predict the future of any quantum physical system (and all physical systems are fundamentally quantum physical systems). Unfortunately for easy understanding, interpretation leads to the superposition problem mentioned above.

Many people have tried to resolve this issue, and the best success has been achieved by the exponents of the Many Worlds Interpretation (MWI), as described by Everett and championed by Bryce DeWitt and David Deutsch. The view of the MWI exponents is that the Universal Wave Function is fundamental and expresses a true picture of all reality. All of it, that is. Not just a physical system and its observer.

Everett’s view, as described in his thesis, is that an observer, as well as the object that he is observing is a subsystem of the system described by the Universal Wave Function. The wave function of these two subsystems does not describe a single state for each of these subsystems, but the states of the two subsystems are superposed, or in Everett’s term, correlated.

en:Many-worlds interpretation
en:Many-worlds interpretation (Photo credit: Wikipedia)

When a particle is observed it may appear to be in state A 70% of the time (correlated with a state A for the observer). Similarly it may appear to be in state B 30% of the time (correlated with a state B for the observer). This led Everett to postulate a ‘split’ of the universe into a state A and a state B.  (The term ‘split’ appears to come from DeWitt’s interpretation of Everett’s work).

The probabilities don’t seem to have a function in this model, and this is odd. The probability that the cat is dead when you open the depends on how long you wait until you open the box. If you wait a long time the cat will more likely be dead than if you opened it earlier.

English: Diagram of Schrodinger's cat theory. ...
English: Diagram of Schrodinger’s cat theory. Roughly based on Image:Schroedingerscat3.jpg (Photo credit: Wikipedia)

This means that the world splits when the cat is put in the box, as from any moment it can be alive or dead, but you do not find out which branch you are in until you open the box sometime later.

I’m ambivalent about the MWI. On the one hand it is a good explanation of what happens when a measurement is made or the cat’s box is opened, and it does away with the need for a waveform collapse, which Everett argued against in his paper. However it is profligate in terms of world creation.

English: Schrödinger's Cat, many worlds interp...
English: Schrödinger’s Cat, many worlds interpretation, with universe branching (Photo credit: Wikipedia)

Another issue is that the split is decidedly binary. The cat is alive in this world and dead in that one. However most other physical processes are, at the macro level anyway, continuous. When a scientist takes a measurement he writes down, for example, 2.5, but this is only inaccurate value as it is impossible to measure something exactly and it may be wrong by up to 0.05 on either side of 2.5 (given the one decimal point value shown).

Consequently, I’d prefer an interpretation where there is no split, but instead a continuum of possibilities as part of a single world. Maybe the single path that we tread through life is an illusion and across the Universe, by virtue of the Universal Wave Function, we experience all possibilities, though to us it feels like we are only experiencing the one.


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Philosophy and Science


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Philosophy can be described, not altogether accurately, as the things that science can’t address. With the modern urge to compartmentalise things, we designate some problems as philosophy and science, and conveniently ignore the fuzzy boundary between the two disciplines.

The ancient Greek philosophers didn’t appear to distinguish much between philosophy and science as such, and the term “Natural Philosophy” described the whole field before the advent of science. The Scientific Revolution of Newton, Leibniz and the rest had the effect of splitting natural philosophy into science and philosophy.

Statue of Isaac Newton at the Oxford Universit...
Statue of Isaac Newton at the Oxford University Museum of Natural History. Note apple. (Photo credit: Wikipedia)

Science is (theoretically at least) build on observations. You can’t seriously believe a theory that contradicts the facts, although there is a get-out clause. You can believe such a theory if you have an explanation as to why it doesn’t fit the facts, which amounts to having an extended theory that includes a bit that contains the explanation for the discrepancy.

Philosophy however, is intended to go beyond the facts. Way beyond the facts. Philosophy asks question for example about the scientific method and why it works, and why it works so well. It asks why things are the way they are and other so called “deep” questions.


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One of the questions that Greek philosopher/scientists considered was what everything is made of. Some of them thought that it was made up four elements and some people still do. Democritus had a theory that everything was made up of small indivisible particles, and this atomic theory is a very good explanation of the way things work at a chemical level.

Democritus and his fellow philosopher/scientists had, it is true, some evidence to go and to be fair so did those who preferred the four elements theory, but the idea was more philosophical in nature rather than scientific, I feel. While it was evident that while many substances could be broken down into their components by chemical method, some could not.

Antoine Lavoisier developed the theory of comb...
Antoine Lavoisier developed the theory of combustion as a chemical reaction with oxygen (Photo credit: Wikipedia)

So Democritus would have looked at a lump of sulphur, for example, and considered it to be made up of many atoms of sulphur. The competing theory of the four elements however can’t easily explain the irreducible nature of sulphur.

My point here is that while these theories explained some of the properties of matter, the early philosopher/scientists were not too interested in experimentation, so these theories remained philosophical theories. It was not until the Scientific Revolution arrived that these theories were actually tested, albeit indirectly and the science of chemistry took off.

Model for the Three Superior Planets and Venus...
Model for the Three Superior Planets and Venus from Georg von Peuerbach, Theoricae novae planetarum. Image enhanced for legibility. The abbreviations in the center of the diagram read: C[entrum] æquantis (Center of the equant) C[entrum] deferentis (Center of the deferent) C[entrum] mundi (Center of the world) (Photo credit: Wikipedia)
Before that, chemical knowledge was very run by recipes and instructions. Once scientists realised the implications of atomic theory, they could predict chemical reactions and even weigh atoms, or at least assign masses to atoms, and atomic theory moved from philosophy to science.

That’s not such a big change as you might think. Philosophy says “I’ve got some vague ideas about atoms”. Science says “Based on observations, your theory seems good and I can express your vague ideas more concretely in these equations. Things behave as if real atoms exist and that they behave that way”. Science cannot say that things really are that way, or that atoms really exist as such.

English: Adenine_chemical_structure + atoms nu...
English: Adenine_chemical_structure + atoms numbers (Photo credit: Wikipedia)

Indeed, when scientists took a closer look at these atom things they found some issues. For instance the (relative) masses of the atoms are mostly pretty close to integers. Hydrogen’s mass is about 1, Helium’s is about 4, and Lithium’s is about 7. So far so tidy. But Chlorine’s mass is measured as not being far from 35.5.

This can be resolved if atoms contain constituent particles which cannot be added or removed by chemical reactions. A Chlorine atom behaves as if it were made up of 17 positive particles and 18 or 19 uncharged particles of more or less the same mass. If you measure the average mass of a bunch of Chlorine atoms, it will come out at 35.5 (ish). Problem solved.

English: Chlorine gas
English: Chlorine gas (Photo credit: Wikipedia)

Except that it has not been solved. Democritus’s atoms (it means “indivisibles”) are made up of something else. The philosophical problem is still there. If atoms are not indivisible, what are their component particles made of? The current answer seems to be that they are made of little twists of energy and probability. I wouldn’t put money on that being the absolute last word on it though. Some people think that they are made up of vibrating strings.

All through history philosophy has been raising issues without any regard for whether or not the issues can be solved, or even put to the test. Science has been taking issues at the edges of philosophy and bringing some light to them. Philosophy has been taking issues at the edge of science and conjecturing on them. Often such conjectures are taken back by science and moulded into theory again. Very often the philosophers who conjecture are the scientists who theorise, as in famous scientists like Einstein, Schroedinger and Hawking.

:The Black Hole, Los Alamos
:The Black Hole, Los Alamos (Photo credit: Wikipedia)

The end result is that the realm of philosophy is reduced somewhat in some places and the realm of science is expanded to cover those areas. But the expansion of science suggests new areas for philosophy. To explain some of the features of quantum mechanics some people suggest that there are many “worlds” or universes rather than just the one familiar to us.

This is really in the realm of philosophy as it is, as yet, unsupported by any evidence (that I know of, anyway). There are philosophers/scientists on both sides of the argument so the issue is nowhere near settled and the “many worlds interpretation” of quantum mechanics is only one of many interpretations. The problem is that quantum mechanics is not intuitively understandable.

Diagram of one interpretation of the Nine Worl...
Diagram of one interpretation of the Nine Worlds of Norse Mythology. (Photo credit: Wikipedia)

The “many worlds interpretation” at least so far the Wikipedia article goes, views reality as a many branched tree. This seems unlikely as probabilities are rarely as binary as a branched tree. Probability is a continuum, like space or time, and it is likely that any event is represented on a dimension of space, time, and probability.

I don’t know if such a possibility makes sense in terms of the equations, so that means that I am practising philosophy and not science! Nevertheless, I like the idea.

Displacement of a continuum body, from a refer...
Displacement of a continuum body, from a reference configuration to the current configuration. Continuum mechanics. (Photo credit: Wikipedia)

 

The number of the universe.

English: Measurement unit

Anything that can be measured can be encoded in a single number. Take for instance the trajectory of a stone thrown into the air. Its position in relation to the point of launch and the time it has taken to reach that point can be encoded into a set of numbers, three for the spacial dimensions and one for the time dimension. This can be done for all the points that it passes through. These individual numbers can then be encoded into a single number that uniquely identifies the trajectory of the stone.

Or, a physicist can describe the motion of the thrown stone by using generic equations and plug in the starting position and starting velocity of the stone, which can then be encoded, probably in a simpler fashion than the above point by point encoding.

Throwing Stones

If we can imagine a set of equations that describe all the possible physical processes (the “laws of nature”?) and we can imagine that we can measure the positions of all the particles (including photons,’dark matter’ and any more esoteric things that might be out these), then we could encode all this in a huge number which we could call the ‘number of the universe’. Such a number would be literally astronomical and I do mean ‘literally’ here.

The most concise expression of the state of the universe over all time is probably the universe itself and the laws that govern it. Each individual particle has its own attribute, like charge, mass, position and so on as well as things like spin, charm and color. Some of these change over time and some are fundamental to the particle itself – if they change so does the nature of the particle. The rest of the universe consists of other particles which have a lesser or greater effect on the particle, all of which sum together to describe the forces which affect the particle.

English: Position and momentum of a particle p...

There are a couple of things which might derail the concept of the number of the universe. Firstly there is Heisenberg’s Uncertainty Principle and secondly there is the apparent probabilistic nature of some physical processes.

What follows is my take on these two issues. It may make a physicist laugh, or maybe grimace, but, hey, I’m trying to make sense of the universe to the best on my abilities.

uncertainty principle

People may have heard of the Uncertainty Principle, which states that there are pairs of physical properties which cannot both be accurately known at the same time. You may be able to know the position of a particle accurately, but you would not then be able to tell its momentum, for example.

It is usually explained in terms of how one measures the position of something, which boils down to hitting it with something else, such as a photon or other particle. The trouble here is that if you hit the particle with something else, you change its momentum. This is, at best, only a metaphor, as the uncertainty principle is more fundamental to quantum physics than this.

Staccato aerophagia waveform. Its characterise...

Wikipedia talks about waveforms and Fourier analysis and an aspect of waves that I’ve noticed myself over the years. If you send a sound wave to a frequency analyser you will see a number of peaks at various frequencies but you cannot tell how the amplitude of the wave changes with time. However, if you display the signal on an oscilloscope you can get a picture of the shape of the wave, that is the amplitude at any point in time, but not the frequencies of the wave and its side bands. Err. I know what I mean, but I don’t know if I can communicate what I mean!

The picture above shows a spectrum analysis of a waveform. I don’t have the oscilloscope version of the above, but below is a time-based view of a waveform.

English: sinusoidal waveform

In any case, the uncertainty doesn’t imply any indeterminacy. A particle doesn’t know its position and momentum, and these values are the result of its properties and the state of the rest of the universe and the history of both. This means that the uncertainty principle doesn’t introduce any possible indeterminacy into the number of the universe.

On the second point, some physical processes are probabilistic, such as the decay of a radioactive atom. I don’t believe that this has any effect on the number of the universe. The number incorporates the probabilistic nature of the decay, including all the possibilities.

There is an interpretation of quantum physics called the “Many Worlds Interpretation“, where each possible outcome of a probabilistic process splits off into a separate world, resulting in an infinity of separate worlds. I don’t believe that this tree of probabilistic worlds is a useful view of the situation.

English: Schrödinger's Cat, many worlds interp...

No, I think that there is a probabilistic dimension, just like time or space. All the things that can happen, ‘happen’ in some sense. The probability of you throwing 100 tails in a row with a fair coin is very small, but it is possible. As I see it the main objection to this view is the fact that we only see one view of the universe and we don’t appear to experience any other possible views of the universe, but this is exactly the same with the dimensions of space and time. We only experience one view of space at a time as we can’t be in two places at the same time. While we could be in the same place at two times they are two distinct views of the universe.

In any case the number of the universe encompasses all probabilities so if you still adhere to the single probability model of the universe, our universe and all possible universes are encoded by it. The question then becomes how you can extract the smaller number that encoded the single universe that we experience. I believe that that is not a question that needs to be answered.

The question that does remain open is – why is that number the number of our universe? Why not some other number?

English: Level II Multiverse: every disk is a ...