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------------------ 2002 - Physics the Way I Learned It
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- Physics is the science of nature. It is the study of the Universe’s matter, energy, motion and force. Matter and Energy are the same thing , Energy = 90,000,000,000,000,000 * mass. ( E=mc^2). Motion and Force are related as: Force = mass * acceleration. (F=m*a). Acceleration is a change in a change in distance with time. ( In calculus it is called the 2nd derivative) . Distance can be called space, it can also be called length. Physics boils down to:
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-------------- velocity = length / time
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-------------- acceleration = length / time^2
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-------------- momentum = mass * length / time, Momentum = mass* velocity
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------------- Energy = mass * length^2 / time^2, Energy = Force * length
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------------- Force = mass * length / time^2 , Force = Momentum / time
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------------- Power = mass * length^2 / time^3, Power = Energy / time
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------------ Action = mass * length^2 / time, Action = Energy * time
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------------- Frequency = 1 / time Frequency = (time)^-1
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------------- Pressure = mass / length * time^2, Mass = Pressure * acceleration
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------------- Work = Torque = Energy = Heat Flow = mass * length^2 / time^2
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- If we replace these fundamental physic’s concepts with units of measurement it all boils down to kilograms, meters and seconds.. ----------------------------------------
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------------- Velocity = meters / second
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------------- Acceleration = meters / second / second
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-------------- Momentum = kilograms * meters / second
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------------- Energy = kilograms * meters^2 / second ^2, called joules
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------------- Force = kilograms * meters / second^2, called Newton’s
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------------- Power = kilograms * meters^2 / time^3 , called watts = joules / second
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------------ Action = kilograms * meters^2 / second
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------------ Frequency = 1 / seconds, called hertz
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------------ Pressure = kilograms / meters * seconds^2
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------------ Work = Torque = Energy = Heat Flow = kilograms * meters^2 / second ^2 = joules = electron volts = kilowatt hours
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- So, you can see that physics is simply kilograms, meters and seconds. Mass, space and time. Or, Energy, and Space-time. That is pretty simple. You only have 2 things to remember. It gets even simpler. There are only 20 or so particles that make up all mass and all the forces that affect mass. In our everyday lives this boils down to 3 particles: Quarks , electrons, and photons ( called Fermions, Leptons, and Boson , if you are a physicists). Up and Down Quarks and electrons make up ordinary matter, or mass. Photons are the carriers of the forces that carry light and all electric and magnetic energy. Chemistry and Biological are really only electric forces, so physics has live covered as well as the stars and planets.
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- If we list all the particles that make up the Universe we can see only 4.5% of the total Universe. Hydrogen gas throughout space and the intergalactic medium is 4% so that leaves only 0.5% that is the Ordinary Matter for all the stars, planets, and life that we know of. We see and know only 1 part in 200 of what is out there.
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---------------------- 0.5 % stars, planets, and all the elements in the Periodic Table
--------------------- 4 % hydrogen gas
--------------------- 22% Dark Matter
--------------------- 71.5 % Dark Energy.
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- 95% of the Universe is outside the physics that we understand. We are dealing with only 5 % . Are there many more particles that are unknown? Or, are there more fundamental particles that these particles are made? Maybe all the fundamental particles are made up of vibrating strings. Then there would be only one fundamental particle.
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- When we study Particle Physics we use two branches of mathematics, Quantum Mechanics and Relativity. These two maths do not get the same answers, the math is not consistent. There must be another theory out there that needs to bring these two together because Quantum Mechanics works perfectly on small things and Relatively works perfectly on big things, but not vice versa.
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- There are four particles that exchange or carry all four forces (called Bosons). Photons carry the electromagnetic forces. Gluons carry the Strong Nuclear forces that hold protons and neutrons inside the nucleus of atoms. Bosons carry the Weak Force that causes radioactivity and atomic decay. Gravitons carry the force of gravity, although no one has discovered this particle to date. Quantum Mechanics says Gravitons exist, yet Relativity says that gravity is not a force at all but a bending of space-time. The pull of gravity is the path of least resistance through warped space-time. Like centripetal force is not a force at all it is just an object resisting its normal motion to go in a straight line at a constant speed. Some physicists believe these three forces can be combined into one fundamental force. Gravity, Electro weak, and Strong Nuclear force would combine together at 10^25 electron volts.
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- In the 1860s the electric force and the magnetic force were thought to be two separate forces. Now, we know it is carried by photons and only one electromagnetic force. This force carried by photons and the Weak Nuclear force carried by Bosons may also be a single force. The “Electro weak” force.
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- Because space has 3 dimensions forces radiate as a sphere with a surface are of 4*pi*r^2. Therefore the forces decay is proportional to 1/ (radius)^2 , or, (radius)^-2. Gravitons and photons act over infinite distances. Gluons and Weak Bosons only act over less than the diameter of the atom, 10^-10 meters. The range of the Boson’s Weak Nuclear Force is only 10^-18 meters. ( See note 1 for small numbers)
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- Gravity is extremely weak compared to the other forces. 2 electrons repel each other with like negative polarities with a force 10^42 times greater than the force of gravity pulling them together. Gravity is always an attractive force. There is no negative gravity as far as we know. However, electric and magnetic forces come in opposite polarities to cancel each other out. Quarks carry positive charges and electrons carry negative charges. Add all the charges up in the Universe and it sums to zero. Magnetic forces come with north and south polarities. The same is true, these magnetic forces sum to zero.
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- The energy of any particle is a function of its mass and its motion. E=mc^2 and K.E. = 1/2*m*v^2. Kinetic Energy is the energy of motion. It is equal to 1/2 times mass * (velocity)^2. Energy can be expresses in joules or electron volts, or kilowatt-hours. One electron volt is the energy change of one electron moving across the electric potential of 1 volt. 1 eV = 1.602*10^-19 joules. Since mass and energy are the same thing, mass too can be expressed as electron volts. m = E/c^2 . However, the c^2 , speed of light squared is always assumed for mass, expressed in electron volts. It is never shown, but it is there. The mass of an electron is 511,000 eV / c^2, but the c^2 is always assumed. The mass of a proton is 938,000,000 eV.
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- Particles are often described as waves. The wave is nothing more than description of the way in which particles convey energy. Remember, mass and energy are the same thing. Waves are not characterized by positions. Waves are characterized as having wavelength, frequency, amplitude and phase.
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- The frequency of visible light is a range from 400,000,000,000,000 wavelengths/ second to 800,000,000,000,000 wavelengths / second. Frequency is sometimes referred to as cycles / second. The wavelengths of visible light ranges from 750 nanometers for red light to 375 nanometers for blue light. The velocity of light is always constant, the same, 299,792,458 meters / second (3*10^8 m/sec). Sometimes light appears slower in another medium but the speed is actually slower because light is being absorbed and remitted by atoms of the medium. Between atoms it is still light speed. The product of frequency and wavelength is 3*10^8 (f*w = c)
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- The energy of an electromagnetic wave is proportional to the frequency of the wave and inversely proportional to the wavelength of the wave. The higher the frequency the higher the energy. The smaller the wavelength the higher the energy. X-Rays have higher energy than radio waves. Gamma Rays have smaller wavelengths than visible light waves.
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-------------------- E = proportional --- f
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- Any time one variable is proportional to another variable the expression can be turned into an equality if the appropriate Constant of Proportionality is a multiplier. “h” is Planck’s Constant of Action which is equal to 10^-34 ( See note 2 for details)
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--------------------- E = h * f
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--------------------- E = 10^-34 * f
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- Momentum is inversely proportional to wavelength. Frequency* Wavelength = Speed of light, f * w = c, f * w = 3*10^8
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------------------ Momentum = 10^-34 / w
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------------------ Energy = 10^-34 * c / w = 10^-26 / w
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- These energy and momentum numbers seem awfully small. But, it is not small to an electron. If the wavelength of an electron is accelerated through an electric potential of 50 volts, that is 50 eV, its wavelength is 2 * 10^-10 meters, which is roughly the spacing between atoms in a crystal. (20 nanometers). A wave is simply the way a particle distributes its energy. Normally a particle has a mass, but, a photon is massless, yet, it still has wavelength, energy, and momentum. An electron has a little mass and a wave of energy the length of which is the diameter of an atom, 10^-10 meters. A proton has a mass 1,800 times that of an electron and a much smaller wavelength for distribution of its energy.
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- To observe a sub-atomic particle it must interact with something from the system of the observer. Some physical quantities are waves with positions expressed as uncertainties (or, probabilities, or statistics). Some quantity uncertainties are linked together as “conjugates“. The product of their uncertainties is always less than 10^-34. If one uncertainty is very high than the other uncertainty is very low. Energy and time are conjugate quantities. The certainty you can determine the energy the less certainty you can measure the time it takes to measure the energy. Position and momentum are two other conjugate quantities. Momentum is mass * velocity.
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---------- probability of position * probability of velocity < 10^-34
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---------------- dx * dv < 10^-34 ( See Note 1)
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- If you measure the position of an electron with greater certainty,( a larger probability for delta x) than you can not know its velocity with certainty ( a smaller probability for delta v) because the product of the two probabilities must be less than 10^-34. If you measure the velocity with greater certainty you can know its position with less certainty. The same trade off happens with Energy and time.
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---------------- dE * dt < 10^-34
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- Mass is a gravitational charge. It generates a gravitational field. Much the same as an electrical charge generates an electric field, or a magnetic charge generates a magnetic field.
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------------- Force of Gravity = G *M * m / r^2
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------------- Force of Gravity = 10^-11 *M * m / r^2
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------------- where: “M” and “m” are the masses, “r” is the distance between them and “G” is the Constant of Proportionality. ( See note 3)
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------------- Force of Electric Charge = K * Q * q / r^2
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---------------Force of Electric Charge = 10^9 * Q * q / r^2
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------------ where: “Q” and “q” is the two electric charges, “r” is the distance between them and “K” is the Constant of Proportionality. (See Note 3) Note that the electric force is much larger than the force of gravity.
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- Symmetry requires there be laws of Conservation for Energy and Charges. The conservations laws came from the fact that there is Symmetry in the Universe where things remain unchanged regardless of the frame of reference. If something stays constant with changes in space and time it is “invariant“. Emmy Noether (1882-1935) developed the theory that for every global invariant there is a physical quantity that is conserved. Energy is conserved, Charge is conserved. Momentum is conserved. Neither can be created or destroyed, they can only change from one form to another. From space-time Symmetry we can conclude the Conservation of Energy. Energy can have many forms, however, all can be boiled down to Kinetic Energy, the energy of motion, or Potential Energy, the potential energy of mass and fields. Energy is the product of Force and distance. A theory is that all 3 forces can be combined into one unified force. Gravity, electro weak, and the Strong Nuclear forces unify at 10^16 billion electron volts. The 4 forces come from Gauge Symmetry. Relativity comes from the Symmetry of space and time. Rotational Symmetry is the Conservation of Angular Momentum. Parity is mirror Symmetry.
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- Angular Momentum, or spin, is always an integer or half integer of “h”, Planck’s Constant, 10^-34.
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-------------------------- 0, h/2, h, 3h/2, 2h, 5h/2, 3h............ etc.
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-------------------------- Fermions are the 1/2 integer spins and Bosons are the integer spins.
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- Matter is made from Fermions, Light is made from Bosons. Quarks and electrons are Fermions and photons are Bosons. Fermions can not occupy the same space. Bosons can. Two flashlight beams can face each other and overlap easily. Two electrons can not occupy the same space inside an atom. However, if the light beams were made more powerful sending Gamma Rays at each other the photons energy can change into matter.(E=mc^2). Photons can collide and electron and anti-electrons are produced. Anti-electrons and all anti-matter are negative energy particles traveling backwards in time.
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- As you add more energy to matter new generations of particles are created. Most decay rapidly as all particles seek the lowest energy level. Ordinary matter is at the lower energy level. That is what makes it stable:
---------------------- Quark Up --------- 3,000,000 eV
--------------------- Down ------------- 7,000,000 eV
---------------------- Electrons --------- 511,000 eV
--------------------- Neutrino --------- 0.13 eV
- Now add more energy and the next generation of 4 particles are formed:
---------------------- Quark Charm --------- 1,200,000,000 eV
--------------------- Strange ------------------ 120,000,000 eV
---------------------- Muon ---------------------- 200,000 eV
--------------------- Muon Neutrino ------------------ 0.13 eV
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- Add even more energy and the 3rd generation of 4 particles are created:
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---------------------- Quark Top --------- 175,000,000,000 eV
--------------------- Bottom ---------------- 4,200,000,000 eV
---------------------- Tau ------------------ 1,800,000,000 eV
--------------------- Tau Neutrino -------------------- 0.14 eV
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- For the force carriers the mass-energy of photons, gluons and gravitons is zero. However, the mass of bosons that carry the Weak Nuclear force range from 80,420,000,000 eV to 91,190,000,000 eV. You can see why particle physicists need to use high energy cyclotrons and beam colliders to study these particles. But, the amazing thing is that there are only 12 particles of matter and 4 force carriers. That is the whole Universe that we know of. The other 95% we are still working on. Physics just got started. There is a lot more to learn:
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- Relativity comes from symmetry in space-time. Physics is the laws of nature and the laws remain the same regardless of where you are, which direction you are going, or how fast you are moving. That is space-time symmetry. Light is the communicator of motion. Communication can only move at 3*10^8 meters / second. Holding this speed constant in all frames of reference requires that as a object approaches the speed of light, v = d /t , time must slow down, distance must shorten, mass must increase. The equation for Relativity where “o” stands for the observer, where T, Time, L, length, and c+ 3*10^8. ( 1 / ( 1-v^2 / c^2) is called “ Gamma” or the Lorentz Factor.)
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------------------- To^2 - Lo / c = T^2 - (L / c)^2
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------------------- To^2 = T^2 / ( 1 - v^2 / c^2)
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--------------------- Lo = [ 1 / (1 - v^2 /c^2)] ( L - v * T)
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- If an observer is traveling at 87% the speed of light than in 1 second we would observe 2 seconds, because time has slowed down. If the spaceship was 100 feet long we would observe it at 50 long and flattened like a pancake. Mass approaches infinity and it would take an infinite amount of energy to accelerate it further.
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- Relativity’s equation for Energy. Energy is proportional to Time. Momentum is proportional to Space, where E, energy, p, momentum, p=m*v = mass * velocity.
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------------- E o^2 - p * c^2 = E - p * c^2
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- If a particle is at rest than momentum, p, = zero. And the equations are reduced to:
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---------------- E^2 = m^2 c^4
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- To get the famous equation E = mc^2 we have to take the square root of E^2 = m^2 * c^4. When you take a square root you always get two answers because a square of a negative is a positive. Therefore, mathematically a negative energy does exist.( E=mc^2)
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- Maybe Dark Energy has something to do with negative energy. The vacuum of space may be filled with particles in the Negative Energy state. Anti-matter may be negative energy going backwards in time.
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- E = mc^2 is for particles at rest. If a particle is moving we have to add Kinetic Energy in order to get Total Energy.
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--------------------- E = mc^2 + p^2 / 2m
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-------------------- p = m * v
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--------------------- E = mc^2 + m*v^2 / 2
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(1) Getting used to big and small numbers. 2.2 pounds, or one mole of material has 602,000,000,000,000,000,000,000 molecules. The mass of an electron = 0.000000000000000000000000000000911 kilograms There numbers are more easily expressed as 6.02*10^23 molecules and 9.11*10^-31 kilograms.
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(2) Whenever things are proportional the expression can be turned into an equality by multiplying by a Constant of Proportional. E = h * f. 10^-34 is Planck’s Constant of Action actually equal to 6.6260755*10^-34 joule * seconds, or, 4.1356692*10^-15 electron volt * seconds, or, h/2*pi, the wavelength of one 2*pi cycle, 1.0545727*10^-34 joule* seconds. We will just use 10^-34 for our constant of proportionality and keep the units in kilogram*meters^2/ second.
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(3) G is the Gravitational Constant = 6.67259 * 10^-11 meters^3 / (kilogram * second^2) “K” is the Coulomb Constant = 8.987552*10^9 kilogram* Meters^3 / (seconds^2 * coulombs^2)
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