Ben C. Davis

Chapter 1

• Newton's conception was that space and time are absolute and immutable entities. They are invisible structures.

Chapter 3

• What is space?
• Newton reasoned that (to explain the bucket and what caused the concave nature of spinning water) that space represented the absolute benchmark to which all other motion is measured by. Any acceleration we feel is due to our movements relative to absolute space.
• Mach disagreed. He suggested than instead the effects of acceleration are relative the distribution of matter throughout the universe, thus in an entirely empty universe spinning uniformly and bring perfectly still are the same thing; there's so point of reference for movement so therefore no movement.
• In newtons empty universe, acceleration would still be felt.

Chapter 4

• Building on work by faraday and others maxwell discovered the interconnection between electric and magnetic fields: electromagnetic fields.

• He also discovered that the speed of these electromagnetic waves was exactly what had been measured for the speed of light. There they supposed that light is an electromagnetic wave.

• The speed was determined to be relative the medium of electromagnetic waves: the aether.

• If this were the case then it follows that moving relative to the movement of these waves would affect the measured speed of light, but it was found that regardless of the movement of the observer, the speed of light was constant.

• Therefore Einstein suggested that the speed of light is 670 millions miles per hour relative to everything and anything.

  • It follows that in order for this to happen, space and time must change depending on the observer so that the speed of light remains constant.

• The core of special relativity is that the speed with which something moves through space and time, is precisely equal to the speed of light.

  • Therefore if you observe a stationary car then all it's movement is though time.
  • If it begins to move through space, then it's movement through time slows down.
  • So to the observer, the car is moving through time slower than it is.

• Therefore light does not move through time.

• Spacetime is itself an absolute to which all other motion is relative.

• Imagine that Spacetime can be divided into time slices: each slice containing all the events that happened in a given region of space at a particular moment in time.

  • Observers of events will divide them up into differing but equally valid time slices.
  • **Observers in relative motion do not agree on simultaneity - they do not agree on what things happen at the same time. **

• Since gravity and acceleration are the same, if you feel gravity's influence then you are accelerating.

• Only those who feel no force whatsoever are justified in saying they are not accelerating.

• Accelerating observers don't just carve space time in different angles relative to others, but they carve slices that are warped by the presence of energy and matter.

• Gravity is nothing but a warping of Spacetime.

• Anything moving trough warped space will travel along the resulting curved trajectory.

• The mathematics that describe these warps and trajectories is called the Einstein Field Equations.

• The transmission of gravity is therefore though the warping of Spacetime, and is transmitted at exactly the speed of light.

• The gravitational field is the manifestation of Spacetime and is the benchmark with which motion can be relative.

• Pre-quantum scientists believed the world to be local: locality means that you can only affect in any way those local to you (in the sense that something has to pass between in you in order to transmit that influence).

• Experiments in the early part of the 20th century seemed to show that the universe was not local; that some happening in one part of it could instantaneously influence something happening on the opposite side of the universe.

• It suggested that particles can be entangled. The measurement of an entangled particle would instaneously cause the same measurement to be observed in its entangled twin, regardless of the spatial separation between them.

• The experiments were hard to prove though because as Einstein argued, why should it not be so that the particles were just endowed with the same properties when they were created so therefore caused the same measurements to be observed.

• Through heinsenbergs uncertainty principle, quantum mechanics calcined that there are certain features of the world that cannot simulataneous definite values.

• Particles hover in a state of quantum limbo, a probalistic mixture of all possible valued, only when observered do they take on a definite value.

• EPR argued that the uncertainty principle was a limitation of the quantum theory not a unknowable fact of the universe, instead they suggested that everything is preprogrammed with particular values

• John bell disproved them through a simple thought experiment: if truly predetermined, the results gathered from these experiments should agree with the entangled particle more than 50% of the time; they do not.

• The result is that particles are entangled. Things that happen here instaneously effect things over there.

• This is understood to not break relativity as the collapse of the wave function governing the two particles collapased when observed and as their entanglement means that they are essentially part of the same entity, no information is transferred between them, therefore relatively stays in tact.

• The reason that now information is transferred is because we cannot control or predict the results of these entangled measurements, therefore we cannot pass any information between them.

• The problem is that the collapse of a wave function (if it even exists) seems to happen at a particular point in time across the entire universe, which goes against relativity's frame of reference agnostic approach to the universe.

Chapter 5

• None of the laws of physics give time a direction; time has no arrow outside the human consciousness.
• Our conception if what is happening now is entirely dependent on our relative motion to the test of the universe. When we move relative to the universe at varying speeds, we carve up Spacetime at different angles and therefore change what we think of as happening now.
• If you take that space is infinite, then Spacetime can be carved up into every possible angle by any observer anywhere in the universe, so therefore Spacetime encompasses all that ever was or will be at every point in the universe. It just is. Your past, present, and future exist in exactly the same way as your now.

Chapter 6

• Entropy is the process of systems moving order into chaos. Systems that can be altered in many ways without affected overall structure have high entropy. Those with only a few ways of achieving such a structure have low entropy. Systems always tend towards high entropy.
• They do this as statistically it it more likely for something to have high entropy.
• This applies in exactly the same way for the future as for the past.
• This implies that entropy too has no preference for the arrow of time.
• However the universe started in an incredibly low entropy state: uniform gas spread throughout the universe. Slowly over time, gravity has been slowly collapsing gas into planets and things. A process which emits high entropy as a biproduct. So overall the universe is still tending towards high entropy.
• Therefore the initial low entropy state of he universe gives us an arrow of time.

Chapter 7

• Quantum theory suggests (by Feynman) that all possible histories of a quantum entity affect its present observed results.
• Experiments have shown that any knowledge of the life of an entity on the quantum world will remove its multi-history weirdness.
• Knowing the path of any particle in one of these experiments causes the interference pattern to disappear.
• How this happens, how the wave function collapses upon observation, is known as the quantum measurement problem.
• Decoherence is the idea that environments slowly remove any quantum weirdness from an entity at a large scale, which is akin to observing it.
• Therefore our observing is no different to any other environmental impact.

Chapter 8

• Symmetry underpins all the laws of physics.
• It gives an elegance and therefore a weighting of likeliness to potential theories.
• Newtons laws (as all laws) operate in exactly the same way in one part of the universe as another, which is known as translational symmetry.
• The uniformity of the cosmic background radiation is a symmetry. It implies the uniformity of time.
• Hubble discovered that space itself is expanding.
• Therefore there is no special place in the universe, all viewpoints are equal and would see the same expansion.
• As any observer moving only with expanding space are not moving relative to each other, they will carve up Spacetime in the same way. It is to this viewpoint that we can measure the age of the universe.
• The expansion of space doesn't expand the objects within space as they are held together by other forces.
• The symmetry of space allows us to consider only a few shapes of the universe.

** ** Chapter 9

• Phase transitions of matter cause abrupt changes in symmetry. Increased temperatures increase symmetry and decreased temperatures reduce symmetry.
• It is believed the universe went through such transitions at early states of the universe.
• The substance that condensed or froze when the universe cooled is the Higgs field.
• Fields underpin most of modern physics.
  • Electromagnetic: photons
  • Gravitonal: gravitons
  • Strong force: gluons
  • Weak force: W and Z particles.
• With high temperatures (high energy), fields undulate dramatically, and the reverse if true for low energy.
• The Higgs field is different though. With low energy, the Higgs field actually settles to a particular nonzero value. It would actually require the presence of energy to reach a zero value.
• This is due to the shape of the fields potential energy.
• So the Higgs field permeates all vacuum space.
• The creation of the nonzero is known as spontaneous symmetry breaking.
• The Higgs field provides the inertia of matter, but only for accelerating matter.
• Different fundamental particles are affected by the Higgs field in various strengths; they have different masses.
• At the early stages of the universe, when the temperatures were very high and the Higgs field hasn't formed (hadn't become it's nonzero state), all particles and force carriers had the same zero mass.
• This meant that electromagnetic ism and the work force actually a part of the same force: the electroweak force.
• The Higgs field is what differentiates the forces today.
• Grand unification would combine all these forces into a single force.
• One suggestion was that at even higher temps, the electroweak force would combine with the strong force. The Higgs field would then decrease in jumps, separating first into the electroweak and strong, and then the electromagnetic, weak, and strong.
• These have never been proven experimentally so have been discarded.
• The Higgs field, if discovered (it was!), would mean that our understanding of the fundamental nature of particles and forces is correct. It would also prove the power of symmetry in understanding the hidden nature of the universe.

** ** Chapter 10

• Einstein's general relativity was extremely successful in solving many of the experimental puzzles of his time, but there was one feature of the theory he disliked: that it allowed the change in size of the universe.
• Einstein, like everyone else, assumed the universe was static. So in order to make his theory work with this , he introduced a term called the cosmological constant.
• One of the feature of general relativity is not only does mass effect the Gravitonal field, but so too does energy and pressure.
• There is such a way that pressure can be negative, and when it is so, it causes negative of repulsive gravity. (Think about the curvature of the gravitational field in the presence of mass).
• Einstein introduced this dark energy or cosmological constant, that implied space is filled with this uniform energy that provides negative pressure. Einstein balanced this constant with the force of gravity to allow for a static universe.
• Einstein however was wrong. The universe is expanding, and when he realised this, he removed all traces of the cosmological constant from the theory.
• In the 80s Guth and Tye were studying the Higgs field in grand unification theories. They discovered that as the universe cooled the Higgs field may have actually trapped itself in a higher energy state (what effect this has on the fields value, I'm not sure). They realised that this higher energy Higgs field, as well as contributing energy to the universe, would actually exert a negative pressure, in exactly the same proportions as predicted by the cosmological constant.
• Guth discovered though that this negative pressure exerted by the Higgs field (dubbed the inflaton field when in this state), is changeable.
• They also realised that the shape of the fields potential energy was more smooth, meaning that the field would naturally fall back to its natural zero energy, nonzero value state after a very brief amount of time.
• They realised that the value of the field during this high energy state is huge. It caused the initial explosive inflation of the universe.
• Inflationary cosmology can explain the uniform temperature of the cmb sure to the speed and time taken to expand during the earliest moments of the universe.
  • The cosmic horizon is the limit of a point int space's perspective on the rest of the universe; it's the furthest point in space that could have affected it's point.
  • The standard big bang theory constructed this event horizon too much, meaning that two points in space that had this same temperature radiation could never have interacted.
  • But due to the rapid expansion of inflation, these two regions actually did interact, providing an explanation of the background radiation.
• The flatness problem is a problem with the standard Big Bang theory. It's to do wth the critical density of the universe and it's effect on the shape of the universe.
• We observe a very flat universe (implying infinite flatness) which meant that according to the Big Bang, the early stages of the universe would have to be extremely close the critical density as any deviation would be exacerbated over time causing a different value to what we observe.
• Inflationary theory suggests hat because of the size of the universe, our observable portion of it would always seem flat regardless of the actual shape of its entirety.
• The predicted 100% of critical density of inflationary theory isn't actually what's initially observed, only about 5%.
• A scientist looking at the gravitational effects of a galaxy cluster realised that the amount of visible matter would cause the outer galaxy to spin off from the main cluster. So he proposed that the cluster was also made up of invisible matter called dark matter.
• Observations of other galaxies seemed to suggest that dark matter makes up 25% of the universe, totally 30%.
• 70% is dark energy: akin to einsteins cosmological constant.
• During the initial phase of inflation, the force from the inflaton field far outweighed that of dark energy.
• As the universe grew, the gravitational forces slowed down the rate of expansion.
• But as the universe grew even more, this force became weaker than the force from dark energy causing the universe to start expanding again.

** ** Chapter 11

• One of other puzzles inflationary theory solved is how the universe came to have galaxy, planets, moons, and other matter.
  • Taking into account quantum fluctuations, the inflaton field underwent minor changes in its value across the universe; it was not entirely uniform.
  • Because of the rapid expansion during the inflationary period, these tiny fluctuations in the field were magnified enormously, causing inhomogenities that brought together pieces of matter.
• Similar quantum fluctuations also caused variations in the temperature of the cosmic background radiation (as regions of space that are slightly denser require slightly more energy to overcome and therefore cause a slightly higher temperature). These were predicted by inflationary theory and confirmed with extreme expirmental accuracy.
• As the universe expands matter and radiation lose energy to gravity (think about things moving and hitting the edges of a box). The inflaton field however gains energy from gravity. So as the universe expands the inflaton field grows in energy.
• It turns out that the inflaton fields energy is uniform during the inflationary period, meaning that it gained energy in proportion to the expansion of the universe. This was a lot of energy.
• It means that in order to account for the amount of matter in the universe now, the energy of the inflaton field only needed to be something in the region of 20 pounds in a couple of centimetres.
• Time:
  • Recall that in order for entropy to be the guiding hand of time, the universe had to start out in a very low-entropy state. (The uniform distribution of matter is low entropy as gravity would likely cause clumping to occur, meaning that a highly disordered state is more unlikely).
  • The initial inflationary period was caused by repulsive gravity. This has the effect of ironing out inhomogenities and irregular distributions of matter.
  • Therefore at the end of the inflationary period, the universe was left in a very low entropy state.
  • Boom.
    • Bear in mind that although gravitational effects on entropy went down, total entropy went up as the drop of the inflaton field caused the creation of a huge amount of matter, leading to an increase in entropy. Just nowhere what it would have been without inflation.
• Before inflation:
  • In a highly disordered state prior to inflation, the inflaton field was varying wildly.
  • When any of these fluctuations reached a certain point in a very small region of space, inflation occurred, creating our universe.
  • But it's possible that other statistical flukes happened in other regions causing other bubbles of inflation to occur, causing the birth of different universes.
• To recap:
  • In a high entropy primordial state, a tiny twenty-pound nugget of space achieved conditions that led to a brief burst of inflationary expansion.
  • The inflation stretched out the twenty pounds of space into a very large and smooth universe.
  • As the inflaton field dropped back down to it's lowered energy state, it relaxed this energy to the universe uniformly with matter.
  • As the repulsive gravity of the inflaton field diminished, regular attractive gravity took over.
  • This caused matter to clump together and form the universe we know today.
  • The universe is now forever moving towards a state of high entropy.

** ** Chapter 12

• Vacuum fluctuations appear in otherwise empty space due to quantum uncertainty. Fields can never stay at zero exactly for any more than a brief moment in time.
• Two metal plates placed close together will create a region of lower pressure in the quantum realm, causing the plates to move slowly toward each other.
• At distances smaller than the Planck length and shorter than the Planck time, quantum fluctuations cause space and time to behave erratically, breaking down theories of relativity.
• String theory was originally an attempt to explain the strong force.
  • The ability for an old Euler equation to explain some of the strong force data was what started it.
• Superstring theory was eventually applied to gravity. Some of the equations of the theory predicted a particle that behaved exactly like the graviton should.
• The community didn't buy it because of mathematical inconsistencies that arose due to quantum anomalies.
• Two physicists eventually realised that these anomalies, if considered in a particular way, would cancel each other. The string revolution had begun.
• String theory suggests that all of the fundamental particles we have are actually all manifestations of a a single fundamental string vibrating in different ways.
• This allows quantum mechanics and general relativity to be merged due to the fact that the string in string theory is the smallest fundamental component of the universe. But it's not a point particle, instead it has a one dimensional length equal to the Planck length, which is the length where previously general relativity breaks down. With this, going smaller than the Planck scale makes no sense, so with some modifications to the mathematics of general relativity to account for gravitational field fluctuations, the two theories can be combined.
• If string theory is to be correct, the various possible vibrations of strings would have to exactly produce the particles in the standard model.
  • They don't. Or at least don't seem to. According to strong theory, it will produce particles with mass equal to multiples of the Planck mass, which is a phenomenally large number. But all the particles in the standard model are near zero, so can be considered a multiple of the Planck mass.
• Another issue is that in order for the mathematics of string theory to work correctly, there needs to be 9 spatial dimensions.
• In 1919 Kuluza suggested that general relativity could be extended to include 4 special dimensions instead of just one. If done so, the extended equations he found described maxwells equations of electromagneticism.
• Klien went onto to suggest that the extra dimension is too small for us to see, somewhere near the Planck length.
• String theory, rather than Kuluza-klien's predicts the existence of extra dimensions, rather than arbitrarily inventing them.
• The extra dimensions are required because in order for the vibrating strings to produce the right particles, they need to be able to vibrate within 9 dimensions.
• The exact shape of these extra dimensions is difficult to know.

** ** Chapter 13

• A problem with string theory is the fact that there are 5 separate mathematical frameworks that deceives the strings and their vibrations. Each are as valid as one and other.
• M-Theory is the resulting unification of these 5 frameworks. It shows that each is essentially a different language describing the same thing.
• M-Theory suggests 10 spatial dimensions.
• M-Theory introduced the idea of branes, which are higher energy (than strings) shape in each of the 10 dimensions.
• They were unseen by the earlier mathematics due to the fact that the equations became increasingly inaccurate as the energy increased.
• Polchinski found in 1995 that open ended strings seemed to be restricted to certain planes of movement. With the discovery of branes, he realised that these string's movement was being constricted to the brane.
• This allows the study of one dimensional strings to give insight into the nature of branes.
• Four dimensional Spacetime might just be a three dimensional brane moving through time.
• Electromagneticism, strong, and weak force, as well as all particles of matter are formed from open ended strings. These strings are constricted to their brane, so in our case everything we see and feel is limited to the three dimensional brane in which we might live. Everything except gravity.
• If we are able to find any case were the inverse square law of gravity is violated, we'd find evidence for extra dimensions.
• The weakness of gravity might not be due to an intrinsic weakness in the force, but instead a result of its ability for its strings to move within multiple dimensions. The force would spill into each dimensions therefore meaning that our perceived measurement of the strength of gravity would be greatly reduced.
  • This is now possible because the extra dimensions can be large and still be undetected, not small as previously thought.
  • This means that the strings can now he comparatively large (in comparison to the Planck length) and therefore could be experimentally observed.