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--------------------------------------- 2274 - String Theory
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- What is String Theory? It is composed of the smallest things we can think of. Well maybe not you and me , but, the smallest things scientists can think of. We think in 3 dimensions, that comprises our intuition and our perception.
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- However, Albert Einstein discovered his theory of gravity by thinking in 4 dimensions. He developed the 4 dimensional metric of space-time. Who knows what exists that we have not yet seen? Maybe there are more than 4 dimensions.
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- Slicing is one way to replace higher dimensions with lower ones. A 3 dimensional book has 2-dimensional slices, called pages. A second way is to us projections. Your 2 eyes can see in 3 dimensions, however, a single eye constructs a 2-dimensional projection of a 3 dimensional reality.
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- A boundary always has a lower dimension than the object it bounds. Picasso was a famous painter who used several projections simultaneously, each at a different angle. Holographs are a third way to record 3 dimensions on a 2 dimensional surface.
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- Still higher dimensions could exist if they were rolled up dimensions as small as 10^-35 meters. 10^-35 meters is called the Planck length and it is distance light would travel in the smallest interval of time, 10^-43 seconds.
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- This small dimension is 25 orders of magnitude smaller than an atom which is 10^-10 meters. It is 17 orders of magnitude smaller than a proton which is 10^-18 meters. With this invisibly tiny size the higher dimensional geometry could be present at every point in space and we would not see it.
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- A TV picture is composed of tiny dots , but our eye’s resolution sees the pictures as a smooth continuum. Physical objects around us appear to be continuous and uniform, but, in reality they are not. We live in a “quantum” world that we can not see and everything is quanta, even time and space.
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- The area of a sphere’s surface is proportional to its radius squared. This mathematical law only works in a 3 dimensional world. The Inverse Square with Distance law only works in 3D. Isaac Newton’s inverse square law for gravity fails at very high speeds and with very large mass or energies.
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- For those extremes in gravity and speed you have to use Albert Einstein’s gravity laws in the Theory of Relativity. Space and time are clearly different and their quantities you measure depend on the speed at which you are traveling. In the case of time, moving and stationary clocks must tick at different rates, moving clocks are slower.
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- The effects of acceleration can not be distinguished from those of gravity. An object’s inertial mass determines how it will respond to any force.
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------------------------- F = m*a.
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------------------------- Force = mass * acceleration.
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- The acceleration induced by gravity is entirely independent of the mass that gets accelerated. Acceleration therefore does not depend on mass. Heavy objects and light objects fall at the same rate. Free falling is acceleration that precisely cancels the evidence of gravity.
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- The photon always travels at the speed of light and it is massless. Because it is massless it “must always” travel that fast. If it is going through a changing gravitational potential a photon will lower its energy by decreasing its frequency, not its speed. This is also know as the gravitational redshift.
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- Light emitted from a large body becomes redder as it accelerates away from the surface. The travel of photons is also bent by gravity because gravity can attract energy as well as mass ( E=mc^2). Matter and energy warp spacetime. Bending light waves is how gravitational lensing works in astronomy. Large masses in space can act as a lens and magnify the objects directly behind them.
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- Free fall is the path of least resistance and is the motion along the space time geodisc. Gravity is a property of spacetime itself. Matter and energy tell spacetime how to curve and spacetime tells matter how to move. Warped spacetime is gravity. Before gravity can act space time must deform. The process does not happen instantaneously. It takes time. Gravity waves travel at the speed of light.
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- The wavelength of a photon is indirectly proportional to its momentum.
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------------------------(w = h/p).
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- Another way to say this is that a photon’s frequency is directly proportional to its momentum. “p” is momentum, and “h’ is Planck’s is Constant of Action
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------------------------ h = 6.625*10^-34 kilogram*meters2 / second
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----------------------- (f = c*p/h).
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----------------------- frequency = (3*10^8 / 6.625*10^-34 ) * momentum = 0.45 * 10^42 * momentum / kg* meter.
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- Or, the energy of a photon is directly proportional to its frequency.
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------------------------- (E = h*f).
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- Energy = 6.625 *10^-34 kilogram*meter^2 / second * frequency.
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- The only way to explore short distances is with high energies.
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------------------------------ (w = h/p).
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----------------------------- Wavelength = 6.625 kilogram*meter^2 / second * frequency / momentum.
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---------------------------- (E = h*c/w).
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------------------------- Energy = 6.625*10^-34 * 3*10^8 / wavelength = 20 * 10^-26 kg*m^3/sec^2 / wavelength
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- Energy is indirectly proportional to wavelength. The smaller the wavelength the large the energy. Ultraviolet sunlight burns your skin more than infrared.
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------------------------- rate = distance / time.
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-------------------------- c = d / t.
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-------------------------- 3*10^8 m/sec = 10^-35 meters / 10^-43 seconds.
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- That is the reason particle physicists have to build large, high energy particle accelerators. With these high energies particle accelerators can create, or convert energy into particle- antiparticle pairs, and study these subatomic particles.
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- Einstein’s equations for general relativity fail when applied to extremely short distances. Quantum mechanics equations must be used for dimensions below that of the atom. At the Planck scale length ( 10^-35 meters) gravity exerts a substantial force even for near massless particles. Any energy sufficient to probe into these distances would snap into a Black Hole.
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- String Theory is the mathematics used to probe these small distances. In order for this math to work it must use multiple dimensions. The formulas work well with 10 dimensions of space and one of time.
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- The math works but are the dimensions real? Could rolled up dimensions actually exist in space? String Theorists lack experimental evidence needed to answer that question. But, a lot of science is working on it and the particle accelerators being built are getting more and more energy needed to probe the quantum world of strings. We may soon learn the answer. How many dimensions is the world we live in?
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- “ Warped Passages - unraveling the mysteries of the Universe’s hidden dimensions” by Lisa Randall.
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- See also:
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- 1735 - Cosmic String Theory.
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- 1210 - String Theory is the new math.
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- February 13, 2019 794
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-------------------------- Friday, February 15, 2019 --------------------------
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