All Physics in One Medium Post, for Alice & Julien
An amateur summary of all physics for my kids.
Objects and forces.
Physics used to be about four fundamental things: objects and forces interacting in space over time. Special relativity showed that space and time were linked and had no fixed coordinates, while general relativity showed that forces could be a result of objects falling into dents in curved spacetime, caused by other objects, at large scales.
At the small scale forces can be the exchange of objects (particles) too, so this leaves two things: force exchanging objects interacting in spacetime at the small scale and objects interacting in force creating spacetime at the large. The objects and the spacetime may come from the same stuff, as objects can be created from spacetime itself.
For a grand unified theory of physics there may just be relationships between different aspects of one type of thing if we can resolve what happens with very large masses (general relativity) which are simultaneously small in size (quantum mechanics).
Unfortunately, these conditions only exist in extreme circumstances such as black holes, very high energy particle collisions or shortly after the big bang. So this will be hard.
If we are able to do this, and the relationships between aspects of one kind of universal stuff are in very specific amounts (lots of unknown constants), then maybe there is some meta-law that allows these constants to self-configure for the universe to work as it does, i.e. the laws of physics themselves evolve.
At the small scale, everything is made up of atoms (which was meant to mean they are indivisible, except they aren’t). Atoms are made of a nucleus and electrons. The nucleus is made of particles called protons and neutrons and these in turn are made of quarks. Particles can have 4 main attributes: charge; color charge; mass energy and spin.
All particles can also behave like waves (propagating undulations of a spacetime field), rather than droplets (fluctuations) rolling about in it.
Particles do not sit in a physical, fixed background, spacetime medium (ether), they are part of it. Spacetime is a curved 4 dimensional field of point vectors (representing state, a bit like the arrows at each point in the picture below) which constitute ‘events’ (things that happen at a particular time and place relative to an observer).
The creation of stuff from nothing is possibly due to something like the vortex (left) and anti-vortex (right) in the image below, which represent a particle and antiparticle pair and where arrows represent the spacetime vector field (2 dimensions here, 4 in reality). Pairs of disturbances to a field like this (fermionic field) require less energy than a vortex on its own but the energy required to stress the field like this is equivalent to the rest mass energy (from Einstein, mass is a form of energy, not something that ‘converts’ into energy) of the particle.
In our part of the universe there seem to be more vortex particles than antivortex particles (or everything would self destruct). Where all the anti-vortex ones are is a mystery.
There used to be three known forces: electricity, magnetism and gravity.
Maxwell combined electricity and magnetism and later two new forces were discovered: weak nuclear and strong nuclear, to give four fundamental forces of nature: electromagnetism; weak nuclear; strong nuclear and gravity.
The electroweak theory combined electromagnetism and weak nuclear and QCD added the strong nuclear to the explanation, to effectively leave two fundamental forces: particle forces and gravity.
Forces (at the small, quantum, scale) can be considered as particles, however the particle antiparticle pairs in the animated image from the previous section (particles) are the kind of ripples that typically constitute matter particles (fermions), they don’t overlap each other, because they have hard ‘cores’ and are that’s why they are good at creating matter. Usually, force particles (bosons) are single ripple types (in a bosonic field) and they can overlap each other and spread out, so that you don’t know how many particles there are in a field.
Forces (at the large, general relativistic, scale) are a result of curled up geometry of spacetime, where the space is continuous, rather than a field of discrete points.
Forces are particles which are the result of curled up dents and balls of spacetime but one is a field of points, the other is continuous. This needs to be resolved.
By extending the idea of General Relativity (that the gravitational force can be shown to be a geometric effect resulting from adding time to 3 spatial dimensions) to a fourth dimension, Kaluza showed this could mathematically account for another force (electromagnetism). Klein showed that this dimension might look like imperceptibly small loops at points in spacetime and this formed the basis of modern string theory, which until recently has been a leading candidate for this resolution of big (relativistic) and small (quantum) physics.
Pre 20th Century Physics
1. Classical (Newtonian) Mechanics — forces acting on objects.
2. Electricity and Magnetism (gravity already under Newtonian mechanics) — fundamental forces.
3. Classical Thermodynamics & Statistical Mechanics — energy exchange.
1. Classical (Newtonian) Mechanics — forces acting on objects.
Newton’s Laws (laws are now called theories, but that doesn’t make them less true i.e. less able to reliably predict things).
Three laws of motion
He said that objects change speed if a force acts (first law: effectively, force is proportional to acceleration), and that this change is less if they are more massive (second law: force=mass x acceleration), and that all forces have an equal push-back— occur in equal pairs in opposite directions (third law).
Newton also showed that two really big objects attract each other (gravity) based on how massive they are and how far apart. The specific relationship, was that gravitational force is proportional to their masses multiplied together (not added) and inversely proportional to the square of the distance apart. F = GMM/R², where G is the gravitational constant which shows exactly how they are proportional. It explains how planets move.
Newton’s laws of motion and gravity show mass has 2 forms:
(a) Inertial mass (an object’s resistance to being accelerated by a force).
(b) Gravitational mass (mass that is evident from the force either produced in a gravitational field on an object from a gravitational field=“passive” or by an object which creates one=”active”).
Both are equivalent according to conservation of momentum (passive =active) + general relativity (gravitational=inertial)).
In the Newtonian model, forces propagate instantly (Maxwell later showed that this is not true and it led to relativity).
2. Electricity and Magnetism (gravity already under Newtonian mechanics) — fundamental forces.
Before Maxwell we had this to understand magnets and electricity:
Maxwell: Electricity + Magnetism leads to: understanding of light (electromagnetism)
Maxwell’s Equations complete the laws of electromagnetism via a thought experiment which added a new term to the existing ones derived experimentally which showed that an oscillating electric field dD/dt produces a magnetic field (just as the opposite was already known from Faraday):
This meant that you got a wave like disturbance as an electric field produced a magnetic field which in turn produced an electric field which produced a magnetic one and so on, creating an oscillating disturbance in the field, a wave.
These waves were calculated to propagate at the speed of light, so light was a property of both electricity and magnetism which are parts of the same thing: electromagnetism.
It also meant that forces propagate through space at the speed of light rather than instantly, which paved the way for relativity. Maxwell thought the field consisted of something fixed in space (ether). Relativity showed this fixed background medium did not need to exist.
3. Classical thermodynamics & statistical mechanics — energy exchange
Classical thermodynamics (here ‘classical’ means to do with macro features directly measurable in lab in 19th C. — vs statistical interactions of collections of microscopic, particles in aggregate) looks at: temperature, pressure and volume of gases and energy exchange as heat, where temperature and pressure are caused by jiggling atoms (e.g. gas particles banging on a container wall being what creates heat, as suggested by Bernoulli in 1738).
Classical Thermodynamics Timeline:
Boyle’s Law (c. 1660): pressure and volume are inversely proportional.
Carnot, 1824, start of proper science of heat engines.
Laws of thermodynamics:
1st and 2nd are product of work by Rankine, Clausius, and Thomson (Kelvin) in 1850s.
0th: If (a) is in thermal equilibrium with [no heat exchange] (b) and © is also in thermal equilibrium with (b), (a) is in thermal equilibrium with © — so temperature is a fixed measure independent of observer/measurer, and thermometers always read the same temperature (unlike later, and Einstein’s clocks).
1st: Total energy of isolated system is constant (no perpetual motion machines).
2nd: Entropy (measure of non usable energy) increases over time, heat flows from hot to cold.
3rd: Entropy approaches a minimum value as temperature approaches absolute zero (NB: this means that as temperature approaches zero and all physical processes stop, usable energy maximises. What this means is that the energy is in a very simple form that any system can process, not that the quantity of useful energy is high).
Statistical mechanics (Maxwell, Boltzmann, Planck, Clausius and Gibbs) is to do with the microscopic interactions of particles or quantum states.
Statistical Mechanics Timeline:
1859, Maxwell distribution of molecular velocities (gives proportion of molecules having a certain velocity in a specific range). First-ever statistical law in physics.
Boltzmann extends Maxwell’s ideas to a full statistical theory of thermodynamics, where entropy is related to:
The probability of occurrence of a macrostate.
More precisely: the number of possible microstates corresponding to the macroscopic state of a system [this is easiest thought of in terms of digits (macrostates) and the numbers they represent (e.g. 100 microstates and 3 macrostates, digits) which are used in information entropy, see later section on information theory].
Still more precisely: number of (unobservable) “ways” the (observable) thermodynamic state of a system can be realized by assigning different positions and momenta to the various atoms.
This relationship was summed up as the following formula which appears on Boltzmann’s tomb:
S=k log W (S=entropy, W because Wahrscheinlichkeit is the German for probability)
Later, Gibb’s classic 1902 book became the standard for statistical mechanics, it was derived directly from classical mechanics and was general enough to be adaptable to quantum mechanics.
20th C. Physics:
1. Special relativity: important for very fast objects
2. General relativity: important for very massive objects
3. Quantum Mechanics: important for very small objects
4. Information Theory.*
*Information Theory isn’t technically a branch of physics, but I’m including it as I think it is unquestionably critical to a full understanding of the physical world. As John Archibald Wheeler put it: it from bit.
Measurements of the speed of light in different directions, by Michelson and Morley in 1887, all gave the same result, how could the speed be the same in all directions if we are moving through space? Relativity solved this paradox by saying that the speed was right, but the clocks and the space were weren’t (at least how we understood them). That took guts.
If the measure of something’s speed (light) is always the same in any direction even if you are moving and you accept that its speed really is the same then either speed of the hands on the speed dial change (time slows) or the distance measured (space contracts), or both, depending on your own movement relative to the light source.
Lorentz had the idea that objects might change size in direction of movement, Einstein changed this to be the space itself to resolve the speed of light paradox. Space and time distances interacted in conjunction, unlike the Newtonian world view where changes to one couldn;t affect the other.
With stretchy space and time, there is no fixed background or preferred static point in space as an origin, you can take any starting point for a relative frame of reference with its own coordinate system.
In fact space and time are the same type of thing, but because we can’t see more than one bit of time at once (unlike space where we can view a landscape) we must be looking at the 4th dimension edge on.
Spacetime is a field of point events (things that happen in a particular place and time). The ‘flat’ spacetime of special relativity with four coordinates (x, y, z, t) is called a Minkowski space.
NB the energy mass equivalence that is a result of the special theory is often described wrongly as if mass can be converted into energy — NO, mass IS energy, they are equivalent. When a nuclear explosion happens mass energy is converted into heat energy.
2. General Relativity
Mass distorts spacetime, distortions in spacetime result in movement of masses. (The idea that mass distorts spacetime actually predates Einstein by decades, being suggested by William Clifford in 1878).
This made the geometry of spacetime much more complicated as it is curved. Curved geometries in three dimensions are straightforward (e.g. we can visualise that the angles of a triangle on a globe add up to less than 180 degrees) but in four dimensions they are hard to imagine or calculate. The mathematics required to calculate the geometry of four dimensional curved space use the Riemann tensor (which allows for any dimensions of curved space).
It was Riemann, not Einstein, who, by looking at curved multi dimensional spaces, introduced the idea that forces could be understood as being effects of geometry i.e. curved spacetime.
In general relativity, space is presumed to be smooth and continuous but particles can be at specific points, unlike in quantum mechanics, where particles are spread out and not at specific points until measured, but space isn’t. So there is an obvious disconnect at the conceptual level that carries through into the mathematics, making them incompatible.
3. Quantum Mechanics
In classical physics the intensity (energy) of a light beam of given frequency can be arbitrarily weak (frequency and wavelength are independent of energy). But in quantum mechanics it cannot be less than 1 photon. This implies the uncertainty principle since there is a limit to how ‘gently’ you can measure a system.
Both Classical and Quantum Mechanics look at systems in two ways:
- A snapshot in time of the whole system, mathematically encoded as a phase point (classical mechanics) or a pure quantum state vector (quantum mechanics).
- An equation of motion which carries the state forward in time: Hamilton’s equations (classical mechanics) or the time-dependent Schrödinger equation (quantum mechanics)
Quantum mechanics describes sets of particles/waves as point state-vectors (fancy coordinates) in a multidimensional space where each coordinate is a complex number (Hilbert space). The ordinary use of the term vector as a pointer, an arrow with a length is merely a specific use of the much more general and abstract term vector that we use in quantum mechanics, called ket vectors where the equiv of a point ‘a’ is denoted by ‘|a>’.
If we want to measure the quantum state as we travel from point A to point B in a quantum field, we have to take into account that there is no fixed point B in space, so our measurement of its state may not be possible using the same measuring ‘gauge’, where the gauge itself is made of the same stuff as the field, so is a gauge field. Mathematically, a gauge is just a coordinate system that varies depending on one’s location with respect to a base “parameter space”. Luckily there are only a handful of these gauges to be able to compare fields at different places in spacetime.
Quantum Mechanics Timeline (has lots of people and separate discoveries involved):
In 1859, Kirchhoff suggested a body which absorbs all radiation (which wouldn’t reflect therefore would look black — a blackbody) would also be perfect re-emitter of energy which would be a function (J) of the temperature of the body and the frequency of radiation emitted.
The electron discovered by (JJ Thomson), 1897.
In 1900 Planck produced the formula for J, by assuming that the energy was ‘quantized’.
1901, Ricci and Levi-Civita create mathematics which happened to be needed for quantum theory (tensor analysis for Riemannian (curved) spaces of any dimension. Particle spin states later required different tensor mathematics ‘spinors’).
1905, Einstein proposes quantum of light — (named photon by Lewis in 1926) by looking at photoelectric effect (electrons emitted by shining light on metals ro semiconductors).
1911, Rutherford shows atoms have nucleus (with a proton 1919).
1913, Niels Bohr creates quantum theory of atomic structure (showing laws of spectral lines of atoms).
1921 Chadwick & Bieler discover strong force (holds nucleus together). Up to this stage quantum mechanics was set up in Euclidean (flat) space and used cartesian tensors of linear and angular momentum.
1924, de Broglie shows all particles (not just photons) have dual particle/wave properties.
1926, Schrodinger wave mechanics (describes boson behavior in quantum terms).
1926, Born gives probability interpretation of quantum mechanics.
1927, Heisenberg uncertainty principle.
1928, Dirac combines special relativity and quantum mechanics to describe electron.
At this point, 1930, there are 3 particles, protons, electrons and photons (although Dirac’s result has suggested anti-particles for these).
This same year, Pauli suggests the neutrino.
The neutron was discovered in 1931 by Chadwick, and the proton/neutron model of the atomic nucleus was developed.
In 1932, von Neumann formulated quantum mechanics in rigorous mathematical terms (using operator algebra).
1933–4, Fermi proposes weak nuclear force (to explain Beta decay).
1937, muon discovered in cosmic rays.
1954, Yang and Mills create a new class of theories called gauge theories, which form basis of standard model.
1957–59, Schwinger, Bludman, Glashow propose W+ and W- bosons.
1961 Mathematical system to organise particles SU(3), developed.
1962, the two distinct types (electron and muon) of neutrino confirmed experimentally.
Phew! Despite the unbelievable sophistication and predictive power of Quantum Mechanics, unlike, say, special relativity, it has a complex history and has lots of components. The hunch is that although general relativity will have to be expressed in terms of the quantum view of the world rather than the other way around, it might eventually result in a more elegant (less moving parts) grand unified theory.
4. Information Theory
In 1948 Claude Shannon produced a very simple but profound, mathematical theory of information exchange (communication), which happens to have very similar mathematics to statistical thermodynamics. Potential information (which Shannon calls information — i.e. information here does not = ‘meaning’, as it sometimes does colloquially) in a message is proportional to the number (log) of digits (macrostates) representing the total number of bits (arrangements of digits — microstates), just as thermodynamic entropy is the number of arrangement of macrostates. Shannon extended the maths to work for a general case of message, where the bits could be not just ‘ones’ and ‘zeros’ of equal probability, but any letter of an alphabet, with different frequency probabilities for each letter.
Many people argue that information entropy and thermodynamic entropy are completely different, however these people are often merely pointing out that the mathematical similarity is trivial and therefore not particularly coincidental. However, the idea that any quantitative measure such as energy can be represented as information is fairly natural, and thermodynamic entropy is often referred to in terms of information when looking at things like the black hole information paradox. A resolution of the two requires examining what we mean by ‘energy’ and ‘meaning’.
Entropy is confusing for two reasons:
1. The word refers to the wrong way we think of things — our brains naturally think in term of negentropy (useable energy) decreasing (things running down) rather than disorder ‘increasing’.
2. In everyday usage we talk about things like reduction in energy use to stop climate change, however, the energy we use is zero, we use ‘negentropy’, which is much less than the measure of (entropy units aren’t same as energy) energy we don’t use — entropy. In fact we are low entropy living machines that use negentropy to increase the overall rate of waste heat — entropy, that is dumped out into space. Maximum entropy is the maximum energy (heat), but minimum useful energy, in everyday usage we don’t call that energy. The more advanced we (or any organism) are the more usable energy we can extract from any unit amount of energy.
Similarly the maximum information in a message is the highest entropy version of it — i.e. most jumbled up letters (which tend to have no meaning), however, the more advanced our knowledge, the higher the potential meaning that can be extracted from a high entropy message. Just as we colloquially call negentropy ‘energy’, we colloquially call negative information entropy, which technically = less than maximum bits of information — ‘information’ or meaning.
In summary, maximum entropy = maximum information, but minimum useable energy or meaning. The key here is usable. Energy cannot be created or destroyed so maximum entropy =maximum information = maximum unusable energy (dissipated heat). Useable energy (negentropy) or useable information (meaning) will always be less and will not be a fixed amount but a relative quality dependent on the characteristics of the system which wants to use or process it.
Resolving Quantum Mechanics and (Special) Relativity
Quantum mechanics does not deal with relativistic physics. A resolution started with Dirac who took Schrodinger’s equation and made it apply to fast moving (relativistic) particles, making it work with Lorentz transformations. His new equation had twice as many solutions as he expected — and these corresponded to new partners for particles, called anti-matter.
Reconciliation of quantum theory and special relativity continued post Dirac by extending it to deal with fields rather than particles: Quantum Field Theory.
Two quantum fields theories exist describing three of the four fundamental forces (electromagnetism, weak nuclear, strong nuclear, gravity). [There is no quantum field theory of gravity, yet]:
- The electroweak theory which combines Quantum Electrodynamics (QED) describing electromagnetism, and a quantum field theory of the weak nuclear force.
2. Quantum Chromodynamics (QCD) which describes the strong nuclear force.
The fundamental forces became: (a) those described by QCD and (b) gravity.
Then, the Standard Model (c. 1971) predicted more particles:
Gluon (discovered 1979)
W & Z Bosons (discovered 1983)
Top quark (discovered 1995)
Higgs boson (discovered 2012)
Which takes us to the image below (which is a ‘standard diagram’ of the Standard Model, I helped develop at a CERN Webfest).
A Grand Unified Theory of Physics
To resolve general relativity and quantum mechanics requires looking at things that are simultaneously very massive (general relativity) and very small (quantum mechanics), and often trying to describe spacetime as quantized.
This could be: (a) very high energy particle collisions; (b) big bang; (c) black holes.
There are places where there are hints that the general relativity and quantum mechanics stories fit. For example the answer as to why at the very large scale, the universe isn’t uniform gas with no galaxies or why there are patterns in the noise of the Cosmic Background Radiation map is because of quantum fluctuations in early, very small scale, universe.
Many current theories to resolve QM and General Relativity involve thought experiments around black holes and what they show fits, and seeing what clues can be gotten from where they don’t.
Two where they don’t are:
- The Bekenstein/Hawking black hole entropy puzzle (black holes seem to have an ‘atomic’ structure — be made of bits) (1972–4)
Bekenstein: a black hole of radius R (center to the event horizon) can store x bits, based on total energy of a black hole derived from relativity and energy per bit added, derived from quantum mechanics.
Hawking: black holes radiate heat and therefore have a temperature proportional to radius, therefore have some kind of ‘atomic’ structure (are made of bits), where number of bits = energy/temperature, where hawking calculated the number of bits as being same as Bekenstein:[c³R²/h(bar)G]
Because the number of bits is proportional to R² and not R³, it means that its information (and therefore the information in a gravitating system) is proportional to its event horizon surface area rather than volume, hence ‘holographic principle’, which would be a different nature for space (i.e. different relativity).
- The Hawking black hole information paradox (they seem to destroy information) (1976)
Quantum mechanics says space is full of particle/anti-particle pairs that pop into existence and annihilate each other (precise measurements of energy levels of atoms confirm this). As his happens, on a black hole event horizon one particle can fall inside and the other escape (taking energy away with it) so black holes can evaporate and information is lost. Information being lost means we can’t rewind and see what the past state was, and so the physical laws that govern black holes are not reversible. Since quantum mechanics is reversible, it means there is a different nature of quantum mechanics happening in black holes.
Information being lost from a body which is so dense that not even light can escape means that the bits would have to travel faster than light, so there is a conflict here between quantum mechanics and relativity. i.e. information lost violates quantum mechanics, information escaping violates relativity.
There is no current resolution of QM and General Relativity, but discrepancies in the above thought experiments around black holes are partly solved by theory proposed by Maldacena.
The Majority of the Universe is Suddenly Unexplained
In the late 1990s, the discovery that the universe was pushing apart faster and faster meant there could be a new repulsive force: dark energy (or something more fundamental was wrong with our world view, such as the speed of light not being constant). Mass and energy being equivalent, dark energy constitutes most of what makes up the universe.
This added to the fact that since the 1930s, study of the spin of galaxies showed that there must be a type of matter that didn’t interact with light: dark matter. This constitutes the majority of all matter.
The situation today is that special relativity and quantum mechanics fit, but general relativity doesn’t, most of our universe consists of matter which is unidentified and we have no idea at all about what most of the energy in the universe could be. It’s possible that solving these new mysteries might actually help with a grand unified theory of physics.
A Meta-theory of Physics— Physical Theory of Natural Selection
Even if a grand unified theory of physics resolved the relationship between gravity and the standard model, this relationship would perhaps have certain constants, which would indicate that the universe was not just relationships but specific quantities of relationships with no explanation for them. The existence of these specific rather than continuous relationships result in phase changes which in turn form the basis of the boundaries between different things to produce a universe that has features in it such as particles and galaxies.
Perhaps, and this is pure speculation, these specific relationships could have an underlying principal such as maximising rate of flow of energy or increase in entropy, while still maintaining the existence of difference through universal constants.
This would possibly mean that universal constants were a result of the entropy distribution among different parts of the universe and even that these would change over time as the patterns of entropy distribution of the universe changed, too. It’s possible that this underlying principal would lead to self selection of environments where fundamental constants were tuned for maximum rate of entropy production.
This would seem paradoxical — ie the constants defining specific relationships that give rise to difference would be at the service of an underlying principal which was the elimination of difference (which is one way of looking at entropy increase). The paradox is resolved by looking at how real word features and complexity (such as living things) are like local areas of low entropy that increase the overall entropy of the the environment.
One of the interesting things about natural selection is that it can be considered in the abstract to be the variable (because of noise) inheritance (some become more prevalent, due to finite environment) of rules which lead to maximum energy or information flow. i.e. it is a method for maximising the rate of production of entropy.
Newer theories combine insights from cosmology, information theory and natural selection to suggest that perhaps the laws of physics themselves are selected for and that the one part of science that shows how things can self evolve is not limited to biology but may underpin everything.