Strings and Extra Dimensions

Chapter #21 of the course “Dark Matter, Dark Energy: The Dark Side of the Universe” by Prof. Sean Carroll. An interesting chapter to talk about these topics:

  • String theory: according to Wikipedia’s entry, “String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything (TOE), a self-contained mathematical model that describes all fundamental forces and forms of matter”. I am pretty sure that if you are reading this blog from time to time, you must have heard of String theory (this could be another “coincidence scandal“, be reading this blog, I mean… or this expression is reserved for other stuff? 🙂
  • Quantized gravity: “Quantized Gravity or Quantum Gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity”. This model should be able to produce the same results that are currently known in the following two limits: a) when there is weak gravity (when we use QM and not GR), and b) when we use only GR at much larger distances than h bar (Planck’s reduced constant, i.e., when we do not take into consideration quantum phenomena). In addition to this, it should be able to explain physical situations in which both QM and GR are involved. The most famous quantum gravity theories are String Theory and Loop Quantum Gravity. I am pretty sure that I will be posting about them in future entries of this blog.
  • QED: relativistic QFT (quantum field theory) of electrodynamics. It describes how matter and light interact and involves both quantum mechanics and the special theory of relativity. The founder (one of the founders) of this theory was Richard FeynmanSurely You’re Joking, Mr. Feynman!
  • Planck length: length scale at which the structure of spacetime becomes dominated by quantum effects. In some theories, it is proposed that the structure of spacetime is discrete and its smallest distance is the Planck length.

    Planck length

    Planck length

  • M-theory: this refers to the theory proposed by Edward Witten who in 1995 said that the 5 viable string theories were nothing but different aspects of the same theory. Please, don’t ask me what the M stands for. We Physicists don’t know! (mother? magic? mistery? matrix? master?… the W in Witten’s surname but inverted? Choose the one that you like best).
  • QCD: quantum chromodynamics is the theory that explains the strong interaction that binds together quarks and gluons to form hadrons (i.e., protons and neutrons). One of the fathers of this theory was Murray Gell-Mann. If you want to see Gell-Mann in action, I strongly recommend you this TED Talk about “Beauty and Truth in Physics“. Gell-Mann, you are an incredible man, you know! 
  • Branes: mathematical concept that appears in string and related theories such as the M-theory. Enough for the moment…

Although I recommend purchasing the original videos from The Teaching Company, this chapter can be seen on YouTube here (part 1) and here (part 2) and here (part 3).


Continuing with chapter #20 of the course “Dark Matter, Dark Energy: The Dark Side of the Universe” by Prof. Sean Carroll, now it is time to talk about “Inflation“. I remember when I was studying General Relativity at University that we didn’t spend much time on this concept. I thought by that time that it was a bit odd and also and old-fashioned idea but it has turned out to be a crucial theory (as it is seems to be quite stablished among many cosmologists) for the understanding of the very first moments of evolution of space-time, of our Universe.

As always, some of the concepts/ideas/people… whatever that Prof. Carroll has mentioned in this chapter are collected here for further reference (at least for myself):

  • Inflation: already mentioned in this previous post. It refers to a extremely short phase of the evolution of the Universe, at the beginning of the Big Bang, in which the Universe could have expanded exponentially fast, rapidly transforming curved space into flat one.
  • Alan Guth (1947 – ): american physicist that proposed the inflationary hypothesis in 1980.
Spectacular realization

Guth’s logbook showing the original idea of Inflation. December 7, 1979.

  • Inflaton: scalar field postulated to be the responsible of the rapid expansion of the Universe, known as inflation.
  • Reheating: this is a poorly understood process by which the temperature of the Universe prior to the inflationary phase gets back to its previous values. It is also known as thermalization. The reheating consists on a decay of the inflaton field into particles and radiation, starting the radiation dominant phase.
  • Multiverse: the multiverse is the hypothetical set of multiple possible universes or bubble universes that are popping into and out of existence and colliding all the time, with the space between them rapidly expanding.
  • Monopole problem:  Grand Unified Theories propose that at high temperatures, such as the ones taking place in the early universe, stable magnetic monopoles would be produced. Nevertheless, this heavy particles, which ought to be present today, haven’t been observed in nature so this is an open question in these theories. Here comes inflation to solve it: if a period of inflation occurred below the temperature where magnetic monopoles could separate from each other as the universe expands, the density of these particles would be highly lowered by many orders of magnitude and this could be the reason why there’s no track of them at the moment.
  • Horizon Problem: this referes to the problem of determining why the Universe appears to be homogeneous and isotropic. In a Big Bang model without inflation we couldn’t explain why two widely separated regions of the observable universe have the same temperature.
  • Flatness Problem: this referes to the problem of determining why the density of matter in the universe is comparable to the critical density necessary for a flat universe (Euclidean),  as recent observations of the cosmic microwave background have demonstrated. Inflationary theory solves this problem as it forces the universe to be very flat (to a very high degree, I mean).
  • Polarization of the CMB (Cosmic Microwave Background): one of the predictions of the inflationary universe is that primordial gravitational waves were created during the inflation era. These waves can be accessed by measuring the CMB polarization. Experiments to detect these perturbations are ongoing.

Although I recommend purchasing the original videos from The Teaching Company, this chapter can be seen on YouTube here (part 1) and here (part 2) and here (part 3).

Was Einstein right?

This is the title of chapter #19 from the course “Dark Matter, Dark Energy: The Dark Side of the Universe”, already commented in previous posts. This time some of today’s notes have to do with to great physicists. Apart from equations or theories that try to explain our Universe, it is also important to know a little bit of History of Science and be aware of these names:

  • Urbain Le Verrier: Le Verrier is mentioned in this chapter as he was the guy that made a prediction about the existence of a planet, not known in the first half of the 19th century. That planet was Neptune. He was also the first to report that the slow precession of Mercury’s orbit around the Sun could not be completely explained by Newtonian mechanics and perturbations by the known planets. You know, the same precession that was explained later by Einstein`s General Theory of Relativity.
  • Mordehai Milgrom: Israelei physicist that proposed the MOND or Modified Newtonian Dynamics as an alternative explanation to Dark Matter. MOND is a hypothesis that proposes a modification of Newton’s law of gravity to explain the galaxy rotation problem.
  • Vera Rubinshe was the astronomer that pointed out the phenomenon known as the galaxy rotation problem (already mentioned): discrepancy between the predicted angular motion of galaxies and their observed motion.
  • Jacob Bekenstein: another Israeli physicist famous because he contributed to the foundation of black hole termodynamics. He was the first one to suggest that black holes should have an entropy.
  • The bullet cluster: two colliding clusters of galaxies into one, whose Gravitational lensing studies are supposed to provide the best evidence of Dark Matter.
  • The Friedmann Equation: it is a well-known relationship between the energy density of the Universe, the expansion rate (Hubble constant) and the curvature of space. It governs the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. That is:

(8πG/3 ) ρ = H2 + K

  • The Cassinni probe: spacecraft mission launched in 1997 to study Saturn and its moons.

Although I would recommend purchasing the original videos from The Teaching Company, this chapter can be seen on YouTube here (part 1) and here (part 2).

An additional comment/confession that I’m not sure if I’ve already done before: you may realize that some of these notes or definitions are in some parts copy-pasted directly from Wikipedia. This is because I’m just trying to have short notes to illustrate (mainly for myself) what I’ve been reading/watching/working on… And what a better definition (of course, not always) that the one that appears on the Wiki, validated many times before… 


Quintessence is the title of chapter #18 from the course “Dark Matter, Dark Energy: The Dark Side of the Universe” I just mentioned in the previous post. A course taught by Prof. Sean Carroll. According to that course’s page,

Another idea about dark energy is that it results from a new field in nature, analogous to the electromagnetic field but remaining persistent as the universe expands. This field is called quintessence. It would be observationally distinguishable from the cosmological constant.

That is, quintessence is a hypothetical form of dark energy postulated as an explanation of observations of an accelerating universe (Wikipedia’s definition). Real or not, it is a way of explaining one of the hottest open topics in Cosmology nowadays. A good article about the subject can be found here. According to Prof. Paul J. Steinhardt, from Princeton University,

Quintessence encompasses a wide class of possibilities. It is a dynamic, time-evolving and spatially dependent form of energy with negative pressure sufficient to drive the accelerating expansion.

Related concepts that appear in the aforementioned chapter are:

  • The “Coincidence Scandal”: it points out the coincidence between the observed vacuum energy and the current matter density. That is to say, we live in the era when vacuum and matter are comparable. Pretty strange.
  • The Phantom Field: scalar field with negative kinetic energy to realize the late time acceleration.
  • The “Big Rip”: The Big Rip is a cosmological hypothesis first published in 2003, about the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, is progressively torn apart by the expansion of the universe at a certain time in the future (from Wikipedia).
  • The Fifth Force of Nature: generally believed to have roughly the strength of gravity and to have a range of anywhere from less than a millimeter to cosmological scales.
  • Tangled Strings, Variable Mass Particles…: speculative ideas that try to explain dynamic dark energy.
  • The equation-of-state parameter (w): parameter that relates the energy density to the pressure, closely related to the thermodynamic equation of state and ideal gas law.

Although I would recommend purchasing the original videos from The Teaching Company, this chapter can be seen on YouTube here (part 1) and here (part 2).

Dark Matter, Dark Energy: The Dark Side of the Universe

Dark Matter, Dark Energy: The Dark Side of the Universe (image by The Teaching Company)

The Great Courses (so far)

I am a convinced follower of The Teaching Company video courses, known as “The Great Courses”. I have already visualized some of them, all related to Physics:

As I am in an advanced point in this last course, I’ll just leave here the contents of the course and in a later post I’ll write down the main concepts that have appeared in the later chapter I had seen (it’s a pity that I haven’t done this before), chapter #18 “Quintessence”, with some links to the explanation of those concepts. Here it is (extracted from Sean Carroll’s personal site):

  1. Fundamental Building Blocks
  2. The Smooth, Expanding Universe
  3. Space, Time, and Gravity
  4. Cosmology in Einstein’s Universe
  5. Galaxies and Clusters
  6. Gravitational Lensing
  7. Atoms and Particles
  8. The Standard Model of Particle Physics
  9. Relic Particles from the Big Bang
  10. Primordial Nucleosynthesis
  11. The Cosmic Microwave Background
  12. Dark Stars and Black Holes
  13. WIMPs and Supersymmetry
  14. The Accelerating Universe
  15. The Geometry of Space
  16. Smooth Tension and Acceleration
  17. Vacuum Energy
  18. Quintessence
  19. Was Einstein Right?
  20. Inflation
  21. Strings and Extra Dimensions
  22. Beyond the Observable Universe
  23. Future Experiments
  24. The Past and Future of the Dark Side