The Epistemology Of Grand Unification

A dеtailed aссount of the subtlеtiеs and teсhniсalities that highlight the problеm, is a rеsеarch topiс by itself!

An attempt is made hеre to provide some brief discussion on epistemological arguments, without mathematical jargon or detailed phenomenology, which I am sure some would wish to complement or improve. I would welcome it.

There are a number of reasons which, when combined, can help us understand why we don’t see how to proceed in the endeavour of finding a good theory of quantum gravity and hence unify it with the other forces of nature. The main reason is the physically different structures of the gravitational force and the other forces of nature. When it comes to gravity, even the notion of quantum fluctuations of the fields is already problematic. While for the other forces of nature quantum fluctuations have meaningful interpretation and are relatively “easy” to calculate.

Another possible reason is, the tools we are using and the philosophy we hold on the notion of quantisation of fields, and that we try to push this philosophy to include gravity. This has been realised in the “old” approaches, in which attempts were made to construct perturbatively renormalizable theories of quantum gravity. They have all suffered from one or another shortcoming.

A successful quantum field theory allows us to do calculations, and extract sensible results which then can be tested against experiments. In the two main approaches to quantum gravity, string theory and loop quantum gravity, such testable calculations have not been possible to access experimentally, due to the large amount of energies required. So the results of these theories remain at best, at the present time, just theoretical speculations. But both these theories are still being developed and by no means they are, at this stage, completed theories of nature.

Fermat’s Story And Theorem

Fermat, in mathematical circles, was a bit of an jerk. He was a member of a circle of thinkers (centered around Marin Mersenne) who exchanged letters on mathematics and other topics which, along with a few others, would form today’s modern mathematics and science.

Did I mention he was an jerk? Yes, about that. When you’re talking about mathematics, it’s not cool just to spout out random facts. You have to prove them. The beauty isn’t just some cool fact about numbers, but why numbers behave this way. Fermat, however, was prone to simply spouting off about what he was thinking about. Fermat didn’t prove his thoughts, he just skipped to stating them as facts, so he gave off the impression of being a know-it-all asshole. His approach was smug, and condescending, saying “I know something, but I’m not going to tell you, because it should be obvious, and you’d just agree with me if you were smart.” I recall that Mersenne actually threatened to cut him off from the group unless he shaped up. I get the picture that he was smart, and said amazing things that were correct, so people put up with his crap anyways.

A diversion, with a bit of math. We know that squares of whole numbers can add up to other squares. For example, the areas of squares of 3 and 4 (with areas of 9 and 16) add up to 25, which is the area of a square of 5. Fermat is playing with concepts that flow from this, and is thinking about cubes, and beyond. He has a thought, and writes in the margin of his book…”I have a marvelous proof” that sums of cubes (and higher powers of numbers) don’t add up evenly. But he’s a lazy asshole, and doesn’t write it out, using the crappy excuse that the margin of the book is too small. This is like borrowing $5 for a burger because “All I have is a $100 bill”. Scumbag Steve Fermat.

So a guy who’s known for unproven crazy accusations and know-it-all statements out of left field, but is frustratingly correct, makes another crazy statement, hiding behind a lame excuse, after his death. On one hand, it makes us want to find his answer. It’s caused mathematicians incredible efforts and countless hours over the years. It started with a curiosity, and an attempt to confirm or deny a bloviating jerk. And given the length of time it took all of us, Fermat’s original ‘proof’ was probably incorrect.

But, curse his rotten soul, it turns out the bastard was still right. Again. What a schmuck. His ghost is probably sitting back, drinking over-priced scotch, right now. And he’s thinking to himself “You imbeciles. My horse could have figured that out!”

In addition to the fact that dozens have tried in vain to prove it since the 1630s (until Wiles proved it in 1994), it shows that the Pythagorean Theorem has no generalizations for higher dimensions (i.e. higher n values). The significance is not the individual result confirming the truth of this particular theorem, but the path that Wiles took to get his result. His work in pursuit of the proof led to significant developments in algebraic geometry and number theory, which are very important fields.

The Great Stallion (Pt 1) 

 

Mouth full of hay , Soul ready to ponder 

He sits in the stable , has some moments to squander.

Hair brown as berry , his mind has become a transponder. 

As he is to his master , nothing more than a responder.

As he blinks restlessly, knowing he cant do anything but concur.

To this world he is a slave , to his parents no less than alexandre.

He is trapped being free , in a dungeon of desires.

He is free being trapped , in a heaven promised by friars.

His thoughts dictated by history , his actions dictated by liars.

Sits there and wonders , yes , its his own freedom that he inquires

Free to believe that i am trapped?

Free to think that i ain’t mapped?

Free but still waiting for an apt?

Free but still enslaved and not ready to adapt?

The sky now becomes a cage

The floor becomes a stage

The universe screams , as it recognizes a sage

The sun dies , as his soul is ready to disengage

A voice proclaims :

 “His knowledge was redundant,

  His soul was discontent,

  All of this had forced him to dement,

  We have to end this , he can not be      allowed to further ascent,

  And as i raise this axe my heart is forced  to lament.”

The axe swings, his head falls on the burning ground.

And a universe of thoughts , with his head have drowned.

The drops of blood stained like a medallion , 

And he is remembered as the great stallion.

  

Quantum Electrodynamics And Quantum Chromodynamics

Quantum Electrodynamics :

  • the combination of light and charged particles understood through quantum electrodynamics
  • central to QED is the idea that virtual photons carry electromagnetic force
    • however, virtual means they cannot be seen or detected because their existence violates conservation laws

    The subfield of physics that explains the interaction of charged particles and light is called quantum electrodynamics. Quantum electrodynamics (QED) extends quantum theory to fields of force, starting with electromagnetic fields.Quantum electrodynamics, or QED, is a quantum theory of the interactions of charged particles with the electromagnetic field. It describes mathematically not only all interactions of light with matter but also those of charged particles with one another. QED is a relativistic theory in that Albert Einstein’s theory of special relativity is built into each of its equations. Because the behavior of atoms and molecules is primarily electromagnetic in nature, all of atomic physics can be considered a test laboratory for the theory. Agreement of such high accuracy makes QED one of the most successful physical theories so far devised.

    In 1926 the British physicist P.A.M. Dirac laid the foundations for QED with his discovery of an equation describing the motion and spin of electrons that incorporated both the quantum theory and the theory of special relativity. The QED theory was refined and fully developed in the late 1940s by Richard P. Feynman, Julian S. Schwinger, and Shin’ichiro Tomonaga, independently of one another. QED rests on the idea that charged particles (e.g., electrons and positrons) interact by emitting and absorbing photons, the particles of light that transmit electromagnetic forces. These photons are virtual; that is, they cannot be seen or detected in any way because their existence violates the conservation of energy and momentum. The particle exchange is merely the “force” of the interaction, because the interacting particles change their speed and direction of travel as they release or absorb the energy of a photon. Photons also can be emitted in a free state, in which case they may be observed. The interaction of two charged particles occurs in a series of processes of increasing complexity. In the simplest, only one virtual photon is involved; in a second-order process, there are two; and so forth. The processes correspond to all the possible ways in which the particles can interact by the exchange of virtual photons, and each of them can be represented graphically by means of the diagrams developed by Feynman. Besides furnishing an intuitive picture of the process being considered, this type of diagram prescribes precisely how to calculate the variable involved.

    Under QED, charged particles interact by the exchange of virtual photons, photons that do not exist outside of the interaction and only serve as carriers of momentum/force.

    • QED led to the unification of electromagnetic and weak forces, implying that all forces are one force under extreme conditions of temperature and energy (like with the Universe formed)

    Notice the elimination of action at a distance, the interaction is due to direct contact of the photons.In the 1960’s, a formulation of QED led to the unification of the theories of weak and electromagnetic interactions. This new force, called electroweak, occurs at extremely high temperatures such as those found in the early Universe and reproduced in particle accelerators. Unification means that the weak and electromagnetic forces become symmetric at this point, they behave as if they were one force.

    Electroweak unification gave rise to the belief that the weak, electromagnetic and strong forces can be unified into what is called the Standard Model of matter.


    Quantum Chromodynamics:

  • similar to QED, QCD describes the forces that bind quarks
  • instead of virtual photons, the strong force is transfered by gluons
    • each gluon can carry one of three color charges, red, blue or green so that particle built of quarks must be color neutral

    Quantum chromodynamics is the subfield of physics that describes the strong or “color” force that binds quarks together to form baryons and mesons, and results in the complicated the force that binds atomic nuclei together.Quantum chromodynamics, or QCD, is the theory that describes the action of the strong nuclear force. QCD was constructed on analogy to quantum electrodynamics (QED), the quantum theory of the electromagnetic force. In QED, the electromagnetic interactions of charged particles are described through the emission and subsequent absorption of massless photons, best known as the “particles” of light; such interactions are not possible between uncharged, electrically neutral particles. The strong force is observed to behave in a similar way, acting only upon certain particles, principally quarks that are bound together in the protons and neutrons of the atomic nucleus, as well as in less stable, more exotic forms of matter. So by analogy with QED, quantum chromodynamics has been built upon the concept that quarks interact via the strong force because they carry a form of “strong charge,” which has been given the name of color; other particles, such as the electron, which do not carry the color charge, do not interact in this way.

    In QED there are only two values for electric charge, positive and negative, or charge and anticharge. To explain the behavior of quarks in QCD, by contrast, there need to be three different types of color charge, each of which can occur as color or anticolor. The three types of charge are called red, green, and blue in analogy to the primary colors of light, although there is no connection whatsoever with color in the usual sense.

    Color-neutral particles occur in one of two ways. In baryons (i.e., particles built from three quarks, as, for example, protons and neutrons), the three quarks are each of a different color, and a mixture of the three colors produces a particle that is neutral. Mesons, on the other hand, are built from pairs of quarks and antiquarks, and in these the anticolor of the antiquark neutralizes the color of the quark, much as positive and negative electric charges cancel each other to produce an electrically neutral object.

  • note that the strong force overcomes the electromagnetic or gravitational forces only on very short range. Outside the nucleus the effect of the strong force is non-existent
  • Quarks interact via the strong force by exchanging particles called gluons. In contrast to QED, where the photons exchanged are electrically neutral, the gluons of QCD also carry color charges. To allow all the possible interactions between the three colors of quarks, there must be eight gluons, each of which generally carries a mixture of a color and an anticolor of a different kind.Because gluons carry color, they can interact among themselves, and this makes the behavior of the strong force subtly different from the electromagnetic force. QED describes a force that becomes weaker as the distance between two charges increases (obeying an inverse square law), but in QCD the interactions between gluons emitted by color charges prevent those charges from being pulled apart. Instead, if sufficient energy is invested in the attempt to knock a quark out of a proton, for example, the result is the creation of a quark-antiquark pair–in other words a meson. 


     

    The Fundamental Forces : Force Carriers

    Fundamental Forces :

    • Matter is effected by forces or interactions (the terms are interchangeable)
    • there are four fundamental forces in the Universe:
      • gravitation (between particles with mass)
      • electromagnetic (between particles with charge/magnetism)
      • strong nuclear force (between quarks)
      • weak nuclear force (that changes quark types)
    The first two you are familiar with, gravity is the attractive force between all matter, electromagnetic force describes the interaction of charged particles and magnetics. Light (photons) is explained by the interaction of electric and magnetic fields.The strong force binds quarks into protons, neutrons and mesons, and holds the nucleus of the atom together despite the repulsive electromagnetic force between protons. The weak force controls the radioactive decay of atomic nuclei and the reactions between leptons (electrons and neutrinos).

    Current physics (called quantum field theory) explains the exchange of energy in interactions by the use of force carriers, called bosons. The long range forces have zero mass force carriers, the graviton and the photon. These operate on scales larger than the solar system. Short range forces have very massive force carriers, the W+, W- and Z for the weak force, the gluon for the strong force. These operate on scales the size of atomic nuclei.

    So, although the strong force has the greatest strength, it also has the shortest range.


    Bosons (Force Carriers):

    • certain particles play and important role in the transfer of force, the bosons or force carriers
    • the use of virtual particles to carry force resolves the action at a distance problem
    Bosons are the particles which transmits the different forces between the matter particles, they normally have a whole number spin, 0, 1 or 2. And Fermions which are matter particles they often have spin 1/2. Real particles are the ones you are familiar with, all Fermions are real particles. The Bosons can sometimes be virtual and sometimes real. Virtual particles are the particles which transmits the force between the particles, e.g. virtual photon carries the electromagnetic force between e.g. electrons. They are called virtual particles because they can’t be directly detected, you can’t ‘see’ them so to speak. But their effect can be noticed, by e.g. the actual forces between particles.


    Baryons and Mesons:

    • the large number of new particles discovered in the 1950’s is resolved by quark model
    • quarks are fundamental building blocks to baryons and mesons, coming together as triplets or pairs
    Quarks combine to form the basic building blocks of matter, baryons and mesons. Baryons are made of three quarks to form the protons and neutrons of atomic nuclei (and also anti-protons and anti-neutrons). Mesons, made of quark pairs, are usually found in cosmic rays. Notice that the quarks all combine to make charges of -1, 0, or +1.

    • quarks have 1/3 charge and bind through the exchange of gluons of the strong force
    Thus, our current understanding of the structure of the atom is shown below, the atom contains a nucleus surrounded by a cloud of negatively charged electrons. The nucleus is composed of neutral neutrons and positively charged protons. The opposite charge of the electron and proton binds the atom together with electromagnetic forces.

    • the many particles of atomic nuclei become a simple combination of quarks
    • unlike electric charge, quarks bind by exchanging color charge of three colors, blue, red and green
    • gluons carry color to convert quarks
    • due to their fractional charge nature, quarks cannot exist in isolation
    • the strong force binds quarks like a rubber band force
    The protons and neutrons are composed of up and down quarks whose fractional charges (2/3 and -1/3) combine to produce the 0 or +1 charge of the proton and neutron. The nucleus is bound together by the nuclear strong force (that overcomes the electromagnetic repulsion of like-charged protons)Quarks in baryons and mesons are bound together by the strong force in the form of the exchange of gluons. Much like how the electromagnetic force strength is determined by the amount of electric charge, the strong force strength is determined by a new quantity called color charge.

    Quarks come in three colors, red, blue and green (they are not actually colored, we just describe their color charge in these terms). So, unlike electromagnetic charges which come in two flavors (positive and negative or north and south poles), color charge in quarks comes in three types. And, just to be more confusing, color charge also has its anti-particle nature. So there is anti-red, anti-blue and anti-green.

    Gluons serve the function of carrying color when they interact with quarks. Baryons and mesons must have a mix of colors such that the result is white. For example, red, blue and green make white. Also red and anti-red make white.

    There can exist no free quarks, i.e. quarks by themselves. All quarks must be bound to another quark or antiquark by the exchange of gluons. This is called quark confinement. The exchange of gluons produces a color force field, referring to the assignment of color charge to quarks, similar to electric charge.

    The color force field is unusual in that separating the quarks makes the force field stronger (unlike electromagnetic or gravity forces which weaken with distance). Energy is needed to overcome the color force field. That energy increases until a new quark or antiquark is formed (energy equals mass, E=mc2).

    • if energy is used to split a quark pair, new quarks are produced, this is how matter was produced when the Universe formed
    Two new quarks form and bind to the old quarks to make two new mesons. Thus, none of the quarks were at anytime in isolation. Quarks always travel in pairs or triplets.

    Wave Function And Holism : A Million Dices

    • the origin of new, original concepts from nothing is a property of emergence
    • classical physics can have few emerge properties, but quantum physics is dominated by emergent scenarios
    Does anything really new ever come about in physics? Are properties or characteristics of things ever created or evoked “from nothing”? Emergence is a view that holds the answer to these questions to be, in some very important sense, yes. Emergence is the rise of a system that cannot be predicted or explained from antecedent conditions. George Henry Lewes, the 19th-century English philosopher of science, distinguished between resultants and emergents–phenomena that are predictable from their constituent parts and those that are not (e.g., a physical mixture of sand and talcum powder as contrasted with a chemical compound such as salt, which looks nothing like sodium or chlorine). The evolutionary account of life is a continuous history marked by stages at which fundamentally new forms have appeared: (1) the origin of life; (2) the origin of nucleus-bearing protozoa; (3) the origin of sexually reproducing forms, with an individual destiny lacking in cells that reproduce by fission; (4) the rise of sentient animals, with nervous systems and protobrains; and (5) the appearance of cogitative animals, namely humans. Each of these new modes of life, though grounded in the physicochemical and biochemical conditions of the previous and simpler stage, is intelligible only in terms of its own ordering principle. These are thus cases of emergence.A property is said to be emergent if it cannot be defined or explained in terms of the properties of its parts or if it is not reducible to these properties and relations. Classical physics is reductionist. But, quantum entities have emergent properties. Things like position and energy simply do not exist until they are measured or observed (i.e. until the wave function collapses). They exist as potentialities, but can not explain the properties of the actualities.

     

     

    • the wave function contains a whole that is greater than the sum of the parts
    In this sense, quantum entities have a whole that is greater than the sum of its parts. And the reverse is true, that nothing can ever be wholly reduced to the sum of its constituent parts.

    Holism:

    • holism is a philosophy that the whole is primary and often greater than the sum of the parts
    • a holist is concerned with relationships not the pieces
    • quantum physics is difficult to reconcile with reductionism, requires a holistic view of Nature
    • the particle or wave aspect of a quantum entity requires a dialogue with the environment
    This is the holistic nature of the quantum world, with the behavior of individual particles being shaped into a pattern by something that cannot be explained in terms of the Newtonian reductionist paradigm. Newtonian physics is reductionist, quantum physics is holistic. Holism as an idea or philosophical concept is diametrically opposed to atomism. Where the atomist believes that any whole can be broken down or analyzed into its separate parts and the relationships between them, the holist maintains that the whole is primary and often greater than the sum of its parts. The atomist divides things up in order to know them better; the holist looks at things or systems in aggregate and argues that we can know more about them viewed as such, and better understand their nature and their purpose.The early Greek atomism of Leucippus and Democritus (fifth century B.C.) was a forerunner of classical physics. According to their view, everything in the universe consists of indivisible, indestructible atoms of various kinds. Change is a rearrangement of these atoms. This kind of thinking was a reaction to the still earlier holism of Parmenides, who argued that at some primary level the world is a changeless unity. According to him, “All is One. Nor is it divisible, wherefore it is wholly continuous…. It is complete on every side like the mass of a rounded sphere.”

    In the seventeenth century, at the same time that classical physics gave renewed emphasis to atomism and reductionism, Spinoza developed a holistic philosophy reminiscent of Parmenides. According to Spinoza, all the differences and apparent divisions we see in the world are really only aspects of an underlying single substance, which he called God or nature. Based on pantheistic religious experience, this emphasis on an underlying unity is reflected in the mystical thinking of most major spiritual traditions. It also reflects developments in modern quantum field theory, which describes all existence as an excitation of the underlying quantum vacuum, as though all existing things were like ripples on a universal pond.

    Where atomism was apparently legitimized by the sweeping successes of classical physics, holism found no such foundation in the hard sciences. It remained a change of emphasis rather than a new philosophical position. There were attempts to found it on the idea of organism in biology – the emergence of biological form and the cooperative relation between biological and ecological systems – but these, too, were ultimately reducible to simpler parts, their properties, and the relation between them. Even systems theory, although it emphasizes the complexity of aggregates, does so in terms of causal feedback loops between various constituent parts. It is only with quantum theory and the dependence of the very being or identity of quantum entities upon their contexts and relationships that a genuinely new, “deep” holism emerges.

    Every quantum entity has both a wavelike and a particlelike aspect. The wavelike aspect is indeterminate, spread out all over space and time and the realm of possibility. The particlelike aspect is determinate, located at one place in space and time and limited to the domain of actuality. The particlelike aspect is fixed, but the wavelike aspect becomes fixed only in dialogue with its surroundings – in dialogue with an experimental context or in relationship to another entity in measurement or observation. It is the indeterminate, wavelike aspect – the set of potentialities associated with the entity – that unites quantum things or systems in a truly emergent, relational holism that cannot be reduced to any previously existing parts or their properties.

     

    • numerous experiments have shown that quantum interactions produce results that are not predictable by analysis of components
    If two or more quantum entities are “introduced” – that is, issue from the same source – their potentialities are entangled. Their indeterminate wave aspects are literally interwoven, to the extent that a change in potentiality in one brings about a correlated change in the same potentiality of the other. In the nonlocality experiments, measuring the previously indeterminate polarization of a photon on one side of a room effects an instantaneous fixing of the polarization of a paired photon shot off to the other side of the room. The polarizations are said to be correlated; they are always determined simultaneously and always found to be opposite. This paired-though-opposite polarization is described as an emergent property of the photons’ “relational holism” – a property that comes into being only through the entanglement of their potentialities. It is not based on individual polarizations, which are not present until the photons are observed. They literally do not previously exist, although their oppositeness was a fixed characteristic of their combined system when it was formed.In the coming together or simultaneous measurement of any two entangled quantum entities, their relationship brings about a “further fact.” Quantum relationship evokes a new reality that could not have been predicted by breaking down the two relational entities into their individual properties.

    The emergence of a quantum entity’s previously indeterminate properties in the context of a given experimental situation is another example of relational holism. We cannot say that a photon is a wave or a particle until it is measured, and how we measure it determines what we will see. The quantum entity acquires a certain new property – position, momentum, polarization – only in relation to its measuring apparatus. The property did not exist prior to this relationship. It was indeterminate.

    Quantum relational holism, resting on the nonlocal entanglement of potentialities, is a kind of holism not previously defined. Because each related entity has some characteristics – mass, charge, spin – before its emergent properties are evoked, each can be reduced to some extent to atomistic parts, as in classical physics. The holism is not the extreme holism of Parmenides or Spinoza, where everything is an aspect of the One. Yet because some of their properties emerge only through relationship, quantum entities are not wholly subject to reduction either. The truth is somewhere between Newton and Spinoza. A quantum system may also vary between being more atomistic at some times and more holistic at others; the degree of entanglement vary. Where a reductionist believes that any whole can be broken down or analyzed into its separate parts and the relationships between them, the holist maintains that the whole is primary and often greater than the sum of its parts. Nothing can be wholly reduced to the sum of its parts.

     

    • the rules of the quantum world follow logic, but a logic of both/and rather than the logic of either/or of the macroscopic world
    The highest development of quantum theory returns to the philosophy of Parmenides by describing all of existence as an excitation of the underlying quantum vacuum, like ripples on a universal pond. The substratum of all is the quantum vacuum, similar to Buddhist idea of permanent identity.Quantum reality is a bizarre world of both/and, whereas macroscopic world is ruled by either/or. The most outstanding problem in modern physics is to explain how the both/and is converted to either/or during the act of observation.

    Note that since there are most probable positions and energy associated with the wave function, then there is some reductionism available for the observer. The truth is somewhere between Newton and Parmenides.

    The Cosmological Constant And Einstien’s Real Blunder

    If Las Vegas were taking bets on dark energy, the odds would favor a concept known as vacuum energy or the cosmological constant. In essence, it suggests that space itself produces energy, which is “pushing” the universe outward.

    Albert Einstein invented the cosmological constant as part of his theory of gravity, known as General Relativity.

    Particle Collisions

     1. Empty space. 2. Two particles suddenly appear. 3. Particles ram together and annihilate each other. 4. They leave ripples of energy through space.

    Einstein’s equations showed that the gravity of all the matter in the universe would exert a strong pull, pulling all the stars and galaxies toward each other and eventually causing the universe to collapse. At the time, though, astronomers believed that the universe was static – that it was neither expanding nor contracting. To counteract this problem, Einstein added another term to his equations, called the cosmological constant, to balance the inward pull of gravity.

    Within about a decade, though, astronomer Edwin Hubble discovered that the universe is expanding. Einstein discarded the cosmological constant, calling it his greatest scientific blunder.

    When dark energy was discovered, though, many physicists began to think that Einstein’s only blunder was in removing the constant. This “repulsive” force could begin to explain the acceleration of the universe. In other words, it might be the dark energy.

    Today, physicists explain the cosmological constant as the vacuum energy of space.

    In essence, this says that pairs of particles are constantly popping into existence throughout the universe. These “virtual pairs” consist of one particle with a negative charge and one with a positive charge. They exist for only a tiny fraction of a second before they collide and annihilate each other in a tiny burst of energy. This energy may be pushing outward on space itself, causing the universe to accelerate faster.

    One of the appealing elements of vacuum energy is that it could explain why the acceleration has only started fairly recently on the cosmic timescale.

    In the early universe, all the matter was packed much more densely today. In other words, there was less space between galaxies. With everything so close together, gravity was the dominant force, slowing down the acceleration of the universe that was imparted in the Big Bang. In addition, since there was less space in the universe, and the vacuum energy comes from space itself, it played a much smaller role in the early universe.

    Today – 13.7 billion years after the Big Bang – the universe has grown much larger, so the galaxies are not packed so close together. Their gravitational pull on each other is weakened, allowing the vacuum energy to play a more dominant role.

    Vacuum energy has its own set of problems, though. It should be far too weak to account for the acceleration seen in the present-day universe, for example — by a factor of at least 1057 (a one followed by 57 zeroes), and perhaps as much as 10120 (a one followed by 120 zeroes). Yet it is the most complete scenario to date, so it leads the pack of dark-energy contenders.

    Orbits

    Planetary Configurations:

    The planets outside of the Earth’s orbit (Mars, Jupiter, Saturn, Uranus, Neptune) are called superior planets

    Likewise, the planets inside of the Earth’s orbit (Mercury, Venus) are called inferior planets.

    Other configurations are:

    • Object at greatest western elongation = “morning star”
    • Object at greatest eastern elongation = “evening star”
    • only inferior planets have phases
    • transit = passage of an inferior planet across the Sun

    Galileo’s laws of Motion:

    Aside from his numerous inventions, Galileo also laid down the first accurate laws of motion for masses. Galileo realized that all bodies accelerate at the same rate regardless of their size or mass. Everyday experience tells you differently because a feather falls slower than a cannonball. Galileo’s genius lay in spotting that the differences that occur in the everyday world are in incidental complication (in this case, air friction) and are irrelevant to the real underlying properties (that is, gravity). He was able to abstract from the complexity of real-life situations the simplicity of an idealized law of gravity.

    Key among his investigations are:

    • developed the concept of motion in terms of velocity (speed and direction) through the use of inclined planes.
    • developed the idea of force, as a cause for motion.
    • determined that the natural state of an object is rest or uniform motion, i.e. objects always have a velocity, sometimes that velocity has a magnitude of zero = rest.
    • objects resist change in motion, which is called inertia.

    Galileo also showed that objects fall with the same speed regardless of their mass. The fact that a feather falls slowly than a steel ball is due to amount of air resistence that a feather experiences (alot) versus the steel ball (very little).

    Hammer and Feather on Moon


    Kepler’s laws of Planetary Motion:

    Kepler developed, using Tycho Brahe’s observations, the first kinematic description of orbits, Newton will develop a dynamic description that involves the underlying influence (gravity)

    • 1st law (law of elliptic orbits): Each planet moves in an elliptical orbit with the Sun at one focus.

    Ellipses

        that are highly flattened have high eccentricity. Ellipses that are close to a circle have low eccentricity.
    • 2nd law (law of equal areas): a line connection the Sun and a planet (called the radius vector) sweeps out equal areas in equal timesObjects travel fastest at the low point of their orbit, and travel slowest at the high point of their orbit.
    • 3rd law (law of harmonics): The square of a planet’s orbital period is proportional to its mean distance from the Sun cubed.The mathematical way to describe Kepler’s 3rd law is:P2 α R3where the α symbol means `proportional to’. Proportions are expressions that imply there exists some constant, k, that relates the period, P, and the radius, R, such thatP2 = kR3We can determine k by expressing the formula in units of the Earth and its orbit around the Sun, such that

      (1 yr)2 = k (1 A.U.)3so k is equal to one, as long as we use units of years and A.U.’s (the Astronomical Unit, i.e. the distance from the Earth from the Sun). With k=1, then kepler’s 3rd law becomes

      P2 = RThe 3rd law is used to develop a “yardstick” for the Solar System, expressing the distance to all the planets relative to Earth’s orbit by just knowing their period (timing how long it takes for them to go around the Sun).


    Orbits:

    Many years after Kepler, it was shown that orbits actually come in many flavors, ellipses, circles, parabolas and hyperbolas; a family of curves called conic sections. There are five basic types of simple orbits: radial, ballistic, stable, polar and geosynchronous.

    For an escape orbit, the velocity sufficient to escape gravitation pull of the planet, i.e. the major axis is infinite, such as the Voyager spacecraft

    The direction a body travels in orbit can be direct, or prograde, in which the spacecraft moves in the same direction as the planet rotates, or retrograde, going in a direction opposite the planet’s rotation.

    The semi-major axis of an orbit is determined by the kinetic energy acquired by the rocket at burnout. This is equilvent to the burnout velocity. For low burnout velocities (below 25,000 ft/sec) the orbit is ballistic, meaning it does not escape the surface of the Earth. Burnout velocities above 25,000 ft/sec achieve stable orbit. At 35,000 ft/sec, the orbit reaches the distance of the Moon.

    The amount of burnout velocity also determines the orbit type, an ellipse, a parabola or a hyperbolic path.

    Satellites use a wide variety of orbits to fullfil their missions. The orbit chosen for a satellite is a comprimise between the mission requirements, the capabilities of the rocket used to launch the satellite and orbital mechanics.

    • The orbital period. This increases with the mean altitude of the orbit, so a satellite in a low earth orbit moves faster than a satellite in a geostationary orbit. Also the velocity of a satellite in an eccentric orbit varies along the orbit, being fastest at perigee & slowest at apogee (Keplers second law of equal areas).
    • Inclination. The angle between the plane (major axis) of the satellite orbit and the equator
    • Eccentricity: A perfectly circular orbit has an eccentricity of zero, an elliptical orbit an eccentricity of 0< to <1, a parabolic orbit an eccentricity of 1 and a hyperbolic orbit of >1. The low point of an orbit is known as perigee, whilst the high point is apogee. The major axis is the vector connecting the perigee to the apogee.
    • The ascending node is where the orbit crosses the equator in a northbound direction (ie. the direction of the satellite motion). Likewise, the descending node is where the orbit crosses the equator in a southbound direction.

    Low Earth Orbit:

    Weather and spy satellites use over pole orbits so that Earth turns under them once per day, i.e. total coverage of the Earth’s surface

    Landsat 7 is an earth resources spacecraft which images the earth’s surface in visible and infrared light. Therefore this satellite orbit is optimised for earth observation. For this reason a near polar orbit of 700km, 98.8 inclination, 98 minute period is used which ensures that the satellite can (at least in theory) observe the entire globe. Several other features of this orbit make it especially useful for remote sensing satellites.

    • Circle of visibility = yellow circle around satellite indicating the region of the earth visible from the satellite.
    • Part of orbit in sunlight = yellow.
    • Part of orbit in shadow = red.
    • Dayside of earth = light blue.
    • Nightside of earth = dark blue, after the terminator three lines indicate the boundaries of civil, nautical & astronomical twilight.

    General view of Landsat 7 orbit.

    Left: View perpendicular to plane of orbit
    Right: View of orbit from ascending node

    In theory an orbit should remain fixed in space whilst the earth rotates beneath the satellite. In reality the earth is slightly bulged and the effect of this bulge is to shift the point of perigee and the ascending node for any orbit which has an inclination other than 90. This effect is known as nodal regression, the result of which is that the plane of the orbit rotates or precesses.

    Ground tracks. Red dots along the ground track show the position of the satellite at regular intervals. Closely spaced dots indicate slow speed, widely spaced dots high speed.

    However, this effect is used to advantage here to shift the orbit at exactly the same rate as the daily change in position of the sun over any point of the earth. So the satellite always passes over the earth on the sunlit part of its orbit at the same local time of day (for example at 9 am local time). This ensures that lighting conditions are similar (ignoring seasonal differences) for images taken of the same spot on the earth at different times. Additionally the orbit is resonant with the rotation period of the earth, meaning that the satellite passes over the same point on the earth at the same time of day at regular intervals (which may be daily or every 2 or more days depending on the resonance). In the case of Landsat there are 14.5 orbits per day or 29 orbits every 2 days.


    Geosynchronous Orbits (GEO):

    Communication satellites use geosynchronous orbits for continuous coverage of one region of the globe, i.e. the orbital period is exactly one day. This turns out to be approximately 24,000 miles up.

    A geosynchronous orbit is an orbit which has an orbital period close to that of the earths rotation. A geostationary orbit is a special case of the geosynchronous orbit where inclination = 0 and the period is equal to the rotation period of the earth (approx 1436 minutes), corresponding to a cricular orbit of approx. 35,700km altitude. A satellite in this orbit appears essentially stationary in the sky, which is why this orbit is used extensively for telecommunications & weather satellites. In reality lunar & solar gravitational influences perturb the satellites orbit, so that through the day the satellites position shifts slightly.

    Below is shown the orbit of the TDRS-7 satellite, one of a series of NASA satellites which used to provide a near continous communications link with the Space Shuttle, International Space Station & other spacecraft such as the Hubble Space Telescope.

    General view of TDRS-7 orbit

    View of orbit from ascending node

    Compared with the LEO orbit of Mir a much larger portion of the earth’s surface is visible from the TDRS-7 spacecraft. The zone of visibility of the spacecraft has been highlighted by a cone. Approximately 40% of the earths surface can be viewed at any one time from geostationary altitude. Additionally, the spacecraft orbit is sunlight apart from a small zone which passes into the earths shadow. Actually, geostationary satellites only experience eclipses at two periods of the year – for a few weeks at a time at the spring and autumn equinoxes. The reason for this is simple. The earths rotation axis is inclined with respect to the ecliptic, hence the earth’s shadow cone misses the plane of a zero inclination geostationary orbit apart from the times when the suns declination is close to zero. This occurs twice a year, once at the spring equinox and once at the autumn equinox.

    Ground tracks. Red dots along the ground track show the position of the satellite at regular intervals. Closely spaced dots indicate slow speed, widely spaced dots high speed.

    As can be seen from this graphic a perfectly geostationary satellite stays over the same spot on the equator all day. However, if we were to look closely we would see that the satellite does appear to change position, generally describing a small figure of 8 or an arc due to the effect of lunar / solar pertubations dragging the satellite into a slightly elliptical, slightly inclined orbit. There are many non operational satellites in “graveyard” orbits slightly above or below a true geostationary orbit. Since the orbital period is slightly more or less than the earths rotation period these satellites appear to drift slowly around the earth.


    Anti-de Sitter/Conformal Field Theory

    The AdS/CFT correspondence is one of the largest areas of research in string theory. AdS/CFT stands for Anti-de Sitter/Conformal Field Theory, an expression that’s not particularly elucidating.

    AdS/CFT is a particular, and deeply surprising, example of a duality. It relates two very different theories and at first sight seems obviously wrong. It states that there is a duality between theories of gravity in five dimensions and quantum field theories (QFTs) in four dimensions. This correspondence was first formulated by Juan Maldacena in 1997, and is generally thought to be the single most important result in string theory in the last twenty years.

    The original example of AdS/CFT linked two very special theories. The gravitational side involved a particular extension of gravity (type IIB supergravity) on a particular geometry (5-dimensional Anti-de-Sitter space). The QFT was the unique theory with the largest possible amount of supersymmetry. There’s a specific dictionary that translates between the theories.

    This relationship has no formal mathematical proof. However a very large number of checks have been performed. These checks involve two calculations, using different techniques and methods, of quantities related by the dictionary. Continual agreement of these calculations constitutes strong evidence for the correspondence.

    The first example has by now been extended to many other cases, and AdS/CFT is more generally referred to as the gauge-gravity correspondence. Formally this is the statement that gravitational theories in (N+1) dimensions can be entirely and completely equivalent to non-gravitational quantum field theories in N dimensions.

    The AdS/CFT correspondence has a very useful property. When the gravitational theory is hard to solve, the QFT is easy to solve, and vice-versa! This opens the door to previously intractable problems in QFT through simple calculations in gravity theories.

    Moreover AdS/CFT allows a conceptual reworking of the classic problems of general relativity. Indeed if general relativity can be equivalent to a QFT, then neither one is deeper than the other. Finally physicists can use it to develop new intuitions for both QFT and general relativity.

    Nuclear Fission/Fusion And Anti-Matter

    Fission/Fusion:

    • since quantum events do not have a “cause”, this also means that all possible quantum events must and will happen
    • without cause and effect, conservation laws can be violated, although only on very short timescales (things have to add up in the end)
    • violation of mass/energy allowed for the understanding of the source of nuclear power in the Universe, fission and fusion
    One of the surprising results of quantum physics is that if a physical event is not specifically forbidden by a quantum rule, than it can and will happen. While this may strange, it is a direct result of the uncertainty principle. Things that are strict laws in the macroscopic world, such as the conversation of mass and energy, can be broken in the quantum world with the caveat that they can only broken for very small intervals of time (less than a Planck time). The violation of conservation laws led to the one of the greatest breakthroughs of the early 20th century, the understanding of radioactivity decay (fission) and the source of the power in stars (fusion).Nuclear fission is the breakdown of large atomic nuclei into smaller elements. This can happen spontaneously (radioactive decay) or induced by the collision with a free neutron. Spontaneously fission is due to the fact that the wave function of a large nuclei is ‘fuzzier’ than the wave function of a small particle like the alpha particle. The uncertainty principle states that, sometimes, an alpha particle (2 protons and 2 neutrons) can tunnel outside the nucleus and escape.

    • fission is the splitting of atomic nuclei, either spontaneously or by collision (induced)
    • fusion is the merger of atomic particles to form new particles
    Induced fission occurs when a free neutron strikes a nucleus and deforms it. Under classical physics, the nucleus would just reform. However, under quantum physics there is a finite probability that the deformed nucleus will tunnel into two new nuclei and release some neutrons in the process, to produce a chain reaction.Fusion is the production of heavier elements by the fusing of lighter elements. The process requires high temperatures in order to produce sufficiently high velocities for the two light elements to overcome each others electrostatic barriers.

    • quantum tunneling and uncertainty are required for these processes
    • and quantum physics, even though centered on probabilities, is our most accurate science in its predictions
    Even for the high temperatures in the center of a star, fusion requires the quantum tunneling of a neutron or proton to overcome the repulsive electrostatic forces of an atomic nuclei. Notice that both fission and fusion release energy by converting some of the nuclear mass into gamma-rays, this is the famous formulation by Einstein that E=mc2.Although it deals with probabilities and uncertainties, the quantum mechanics has been spectacularly successful in explaining otherwise inaccessible atomic phenomena and in meeting every experimental test. Its predictions are the most precise and the best checked of any in physics; some of them have been tested and found accurate to better than one part per billion.

    Antimatter:

    • symmetry in quantum physics lead to the prediction of opposite matter, or antimatter
    • matter and antimatter can combine to form pure energy, and the opposite is true, energy can combine to form matter/antimatter pairs
    A combination of quantum mechanics and relativity allows us to examine subatomic processes in a new light. Symmetry is very important to physical theories. Thus, the existence of a type of `opposite’ matter was hypothesized soon after the development of quantum physics. `Opposite’ matter is called antimatter. Particles of antimatter has the same mass and characteristics of regular matter, but opposite in charge. When matter and antimatter come in contact they are both instantaneously converted into pure energy, in the form of photons.Antimatter is produced all the time by the collision of high energy photons, a process called pair production, where an electron and its antimatter twin (the positron) are created from energy (E=mc2). A typical spacetime diagram of pair production looks like the following:

    • spacetime diagrams provide a backwards time interpretation for antimatter, symmetry in space and time
    Positrons only survive for a short time since they are attracted to other electrons and disintegrate. Since quantum mechanics states that energy, time and space can be violated, another way of looking at pair production is to state that the positron does not exist, but rather it is an electron traveling backwards in time. Since it is going backwards in time, its charge would be reversed and its spacetime diagram would look like the following:

    • the quantum world leads to new ways of looking at existence and reality
    In this interpretation, the collision of an electron and two photons causes the electron to go backward in time till it meets another pair of photons, then reverses itself again. The world of quantum physics allows for many such strange views of subatomic interactions.