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-------------------- 2526 - MEASUREMENTS - mass and spacetime?
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- Mass is the same as Energy according to E=mc^2. Energy equals the product of mass in kilograms and the speed of light times the speed of light. So, Energy is measured as the product of kilograms and meters per second times meters per second.
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- The speed of light is a constant number, 300,000,000 meters/second, so the speed of light squared is a constant number, 9*10^16 meters^2/second^2. Energy and mass are the same thing with this constant number as the multiplier for mass.
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----------------------- Energy = mass in kilograms * (9*10^16 meters^2/second^2)
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----------------------- Energy is measured in kilograms * (meters/second)^2
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----------------------- Energy = kg*m^2 / sec^2
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----------------------- E = mass * 10^16
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- Force is the product of mass and acceleration. Acceleration is the rate of change of velocity , or velocity per second.
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----------------------- F = m * a.
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----------------------- Force is measured in kilograms * meters / second^2
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----------------------- Force = kg* m / sec^2
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----------------------- Force is about the same as Energy. Energy is simply a force operating over a distance.
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----------------------- Energy = Force * distance.
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- Action is Energy expended of some time. Action is therefore Force used over a distance over some time.
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----------------------- Action = Force * distance * time
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----------------------- Action = kg * m^2 / sec
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- Gravity is a force unless you get into the theory of relativity where it becomes a curvature of spacetime. But, that is getting ahead of ourselves. Let’s deal with gravity as a force first. Weight is often mistaken for mass. Weight is actually the force of gravity. Force = mass * acceleration and on the surface of Earth the constant acceleration of gravity is 9.81 meters / second^2. The force of gravity = mass * 9.81 m / sec^2
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----------------------- Gravity = kg* meters / second^2
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- Pressure is the same as a force and it is measured in the same units:
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----------------------- Pressure = kg* m / sec^2
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- Torque is also a force over distance, distance of rotation. So, torque is a form of energy, the energy of angular momentum.
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----------------------- Torque = kg*m^2 / sec^2
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- Heat Flow is another form of energy and it too is measured in kilograms*meters^2 / second^2
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----------------------- Heat Flow = kg*m^2 / sec^2
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- Entropy is heat flow per degree Kelvin temperature. Entropy is also measured in kilograms*meters^2 / second^2 * Kelvin. Entropy is Energy / degree Kelvin. Entropy in a total system always increases. Entropy always increases because the Universe is always moving towards greater “randomness“.
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----------------------- Entropy = kg*m^2 / sec^2 / Kelvin
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- Of course we have other names for these units to make them easier to say, but I do not believe the new names make them easier to understand:
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----------------------- kilograms*meters / second^2 = Newtons, the unit of force
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----------------------- kilograms*meters2 / second^2 = Joules, the unit of energy
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- Power is energy used over a period of time. Power = Energy / second.
Power is measured in kilograms * meters^2 / seconds^3. The more common unit for kg*m^2 / sec^3 is watts. One Horsepower is 745.7 watts.
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- Space per unit time is called velocity. Velocity = meters / second. Both space and time are relative because they always need a reference point to measure against. To measure distance you must have a starting point and an ending point. To measure time you need a start and stop time. The measurement of space and time is always made relative to the reference.
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- To measure total time in the Universe we need to start with the Big Bang and go out as far as light has traveled at the constant velocity of 300,000,000 meters per second. (186,000 miles per second).
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- To measure total space we also need to start with the Big Bang and go out as far as light has traveled. This we call the Observable Universe because that is as far as light has gone for us to see. The Observable Universe is 1.3 *10^26 meters in its radius.
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- The total time therefore is 1.3 * 10^26 meters divided by 3 * 10^8 meters / second. (time = distance / velocity ) There are 3.16 seconds in a year. The calculation works out to the Universe being 13.7 billion years old.
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- The scale of the size man is right in the middle. In round numbers the scale of the Universe is 10^26 big. And the scale of the smallest fundamental particles if 10^-26 meters small. We stand are right in the middle.
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- So if you zoom out by a factor of 10 and you do it 26 times you reach the edge of the Observable Universe. If you zoom in by a factor of 10 and you do it 26 times you reach the smallest fundamental particles that the Universe is made of. We humans are about 2*10^0 meters. ( Any number raised to the zero power is 1). So, 2*1 = 2 meters. We are 10^0 meters tall.
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- Some strange things happen at both these extremes of the space scale. Recent discoveries at the edge of the Universe is that the rate of expansion of space is accelerating at an ever faster rate. The further distance the galaxies are the faster they are receding.
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- In fact, at the edges of the Observable Universe the galaxies are receding faster than the speed of light. It is not their local velocity is greater than the speed of light. It is that the space between us and the distant galaxy is expanding faster than the speed of light.
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- Space expansion does not contradict the theory of relativity which says no object exceeds the speed of light in a vacuum. The effect of this discovery is that all the galaxies are receding out of sight. The Universe is becoming a giant void. In a few billion years we will not be able to see any other galaxies. The Milky Way will appear to be all alone in the Universe.
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- On the other extreme, as we zoom down by a factor of ten to the -26 times we find that the fundamental particles of the Universe are actually waves, not just particles. But, they are waves that come in packets, that might be called particles, or quantum’s. At the smallest extreme we enter the world of Quantum Mechanics where particles and waves are interchangeable concepts.
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---------------------------- The diameter of the atom is 10^-10 meters.
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----------------------------- The diameter of the atomic nucleus is 10^-15 meters.
- The diameters of the electron, photon, neutrino, and the other smallest fundamental particles gets down below 10^-26 meters. We enter the Heisenberg Uncertainty Principle which directs that we can not know both position and motion of a particle at the same time. Space at the quantum level becomes measurements of uncertainty and probabilities. Waves and particles have a dual identity that can only be understood statistically.
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- The smallest Quantum Length is 1.616*10^-35 meters. That is the smallest dimension of space, theoretically.
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---------------------------- The smallest Quantum Mass is 2.18*10^-8 kilograms
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---------------------------- The smallest Quantum Time is 1.71*10^-43 seconds.
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- All of these quantum units are defined by the quantum unit of action known as Planck’s Constant which is 6.63*10^-34 joule* seconds. The symbol for Planck’s Constant is “h”.
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----------------------- “h” = 6.63*10^-34 kg*m^2 / sec
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----------------------- “h” = 10^-34
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----------------------- A unit of action = Force * distance* time.
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----------------------- A unit of action = Energy * time.
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- Each of these Planck Units can be defined as ratios of Planck’s Constant, the Gravitational Constant , and the Constant Speed of Light. I will not go into the formulas but the Gravitational Constant is the only one not introduced and it has the symbol “G”.
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----------------------- G = 6.67*10^-11 m^3/kg*sec^2
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----------------------- G = 10^-11
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- Note that all of these measurements can be reduced down to kilograms, meters and seconds. Mass, Space and Time. If you had more endurance as a reader we could get into electricity and magnetism and gravity. These two would contain the basic units of kilograms, meters and seconds. Amazing!
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---------------------------- Planck Length = square root G*h / 2*pi*c^3
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---------------------------- Planck Mass = square root h*c / 2*pi*G
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---------------------------- Planck Time = square root G*h / 2*pi*c^5
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- 96% of the Universe is made of Dark Matter ( 26%) and Dark Energy (70%). Only 4% of the Universe is made of the stuff we understand, Ordinary Matter. Only 4% of the Universe we can see with electromagnetic radiation.
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- We “see “ Dark Matter only because of its effect on gravity. We see Dark Energy only because of its effect on accelerating the expansion of the Universe. We call them “Dark” because today they are beyond our understanding to explain what they are. However, the search is leading us to the smallest fundamental particles that make up the Universe.
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- When particles become very small they behave as waves. We believe the entire Universe is made of these waves but we just can not see them until we look at dimensions smaller than the atom. An atom is 10^-10 meters.
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- When you get down to these dimensions everything becomes lumpy. We no longer have a “continuous” Universe. Light is radiation that is lumpy. We call each lump a photon. We have learned that all forms of energy is lumpy, not just light. And, even space and time are lumpy. The waves are lumps that come in distinct packets called quantum. It is the world of Quantum Mechanics and it is very weird.
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- The packets all have a constant unit of Action, called Planck’s Constant. Action is Energy expended over time.
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----------------------- Planck’s constant uses the symbol “h”
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----------------------- h = 6.625 *10^-34 kilograms * meters^2 / second.
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----------------------- “h” = E * t
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----------------------- “h” = 10^-34
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- I will remove the numbers and the units and just use the magnitudes in this review. The constant wave packet of Action is 10^-34. In order to understand biology at the fundamental level he will have to use physics. In astronomy, in order to understand the stars, galaxies, the Big Bang, gravity, Dark Matter, Dark Energy, etc. we have to understand the physics and the behavior of fundamental particles.
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- The wave packet for Energy is 10^-34 times the frequency of the wave, ”f“. This is the energy of a single photon. The formula says that the higher the frequency the greater the energy. This should make sense to you because X-rays and Gamma rays have a lot greater energy than radio waves. But, also blue light has more energy than redlight. Red light fells warm but blue, ultra-blue light will burn the skin.
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----------------------- E = h * f.
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- Since “h” is a unit of Action which is Energy times Time, and, Frequency is cycles per second, then Action times Frequency = Energy. But, the Action is a constant quantity, just like the speed of light is a constant quantity.
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----------------------- E = 10^-34 * f
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- Frequency times Wavelength = Velocity. In the case of electromagnetic radiation, Frequency * Wavelength = the velocity of light. So, Frequency * Wavelength = 3*10^8 meters per second. Following the convention that we agreed to Frequency * Wavelength = 10^8. So, a wave packet of Energy is also equal to 10^-34 * 10^8 / Wavelength =
10^-26 / Wavelength.
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----------------------- E = 10^-26 / w
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----------------------- f * w = c
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----------------------- f * w = 10^8
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- Frequency * Wavelength = speed of light. Frequency is the number of cycles per second and wavelength is the distance per cycle so the product of the two equals velocity.
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----------------------- E = h * f
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----------------------- E = h * c / w
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----------------------- E = m*c^2 , This is Einstein’s formula for the conversion of mass to Energy.
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----------------------- m * c^2 = h * c / w
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----------------------- Wavelength = h / m*c
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---------------------- Wavelength is equal to 10^-34 / mass * 10^8
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----------------------- Wavelength = 10^-42 / mass
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- Where in this case “c” is the velocity of light = 3 * 10^8 meters per second. At lower velocities we substitute “v” for “c”.
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----------------------- Wavelength = h / m * v
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- “m * v” is mass times velocity which is momentum, or inertia of a moving object.
“m *c” can be considered the momentum of a light beam.
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- Wavelength = 10^-34 / momentum. Everything is a wave. Your body is a wave. A baseball is a wave. Let’s try this formula out for a 0.1 kilogram baseball thrown at a slow pitch of 10 meters per second. The Wavelength for the baseball is 10^-34 / 10^-1*10^1 = 10^-34 meters. The uncertainty of the baseball’s wave at 10^-34 meters would hardly cause you to miss it in a called STRIKE.
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- Baseballs are too big to see the effect of the duality of particles becoming waves. Let’s do the calculation for an electron orbiting a nucleus of an atom. The mass of the electron is 10^-30 kilograms. The velocity of the electron is 99% the speed of light, or 10^6 meters per second. Wavelength = 10^-34 / momentum of the electron. Wavelength = 10^-34 / mass times velocity of the electron. Wavelength = 10^-34 / 10^-30 * 10^6.
Wavelength = 10^-10 meters.
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- The uncertainty of the electron’s position inside an atom is about the diameter of the atom. This gets us into another property of small wave particles in our Small World,
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- The Small World is that it is not only lumpy it is not deterministic. It is governed by uncertainties and probabilities. Using the electron as our illustration, although the same applies to any fundamental particle, the electron’s position in space and its motion in space can “not” be known exactly.
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- There is always a trade off being position and velocity. The uncertainty of position times the uncertainty of velocity must always be less than h/4*pi, which is 1.1*10^-34. So, there is always a trade-off. The better you measure the position the more uncertain the velocity will be in your measurement. And, vise versa.
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- If you know the velocity with some high probability than the knowledge of the position is a low probability. The same uncertainty trade-off exists between the measurements of energy and time. It is as though these paired wave packets were complementary. The product of the uncertainties must always be greater than 10^-34. Let’s go back to E = h * f :
------------------------ E = h * c / w
- ----------------------- Energy = 10^-26 / Wavelength.
- This formula tells us that the smaller the wavelength ( or the higher the frequency) the greater the energy. However, there is a limit. When the wavelength gets so small and the energy gets so extremely concentrated it collapses into a black hole. This happens at the wavelength of 10^-35 meters.
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- Light takes 10^-35 seconds to traverse this distance. That is where physics breaks down because nobody knows what goes on inside a blackhole. A proton is 10^-15 meters diameter. This wavelength is 10^19 times smaller than a proton.
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- The quantum of energy within this tiny wavelength each carry as much energy as the rest-mass of 10^19 protons. E = 10^9. This energy is in joules, in electron-volts, it is equivalent to 10^28 eV. Our best particle accelerators are Terra-electron-volts, TeV. That is 10^12 eV so the energy needed to create these baby black holes has to grow by 10^16, which is 10 times a quadrillion fold.
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- These distance scales that we are working with are smaller than atoms by just as much as atoms are smaller than stars.
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- Within orders of magnitude we can get to these numbers using Newton’s formulas and not bother with the accuracies we get from more complex Einstein relativistic formulas. A Black Hole has so much mass and therefore so much gravity that the escape velocity needed to leave it exceeds the speed of light. It is the point where the Kinetic Energy of the velocity of light equals the Potential Energy of mass being pulled by gravity at radius, “r”
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----------------------- Kinetic Energy = Potential Energy
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----------------------- KE = PE
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----------------------- ½ *m*v^2 = G * m * M / r , where the velocity, v , of the speed of light is “c”.
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----------------------- “r” = 2 * G* M / c^2
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----------------------- “G” = the gravitational constant = 6.7*10^-11
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----------------------- “M” = mass of 10^19 protons, 1.17*10^-27 kilograms each.
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----------------------- “r” = 10^-11 * 10^-8 / 10^16
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----------------------- “r” = 10^-35 meters.
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- This radius is the smallest dimension. 10^-35 is the smallest unit of length. You can not get any smaller than that because it turns into a black hole.
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- So, In conclusion, we have defined all the lumps, the smallest quantities we can have in our Small World:
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----------------------- , in space, 10^-35 meters.
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----------------------- , in time, 10^-43 seconds,
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----------------------- , in mass, 10^-8 kilograms with a radius of 10^-35 meters,
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----------------------- , in energy, 10^9 joules, which is 10^28 electron-volts,
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----------------------- , in action, 10^-34 kilograms / meters^2 / second, which is Max Planck’s Constant.
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- It does not get any smaller than that. And, that is the end of my physics lesson. Amen.
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--------------------- Other Reviews available:
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- 2184 - Redefine the kilogram
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- 2120 - Measurements in Quantum Mechanics.
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- 1412 - Measurement accuracy is as good as your standards.
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- 784 - Spacetime, energy and calculus
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- 630 - Neutrinos - The Little Neutral Ones
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- 631 - Mass, Momentum, and Inertia. What is mass?
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- 632 - Muons and Taus - The Heavy Electrons
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- 633 - The Force Carriers - Gluons, Bosons, and Photons
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- December 6, 2019 2526 723 724 725
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----- Comments appreciated and Pass it on to whomever is interested. ----
--- Some reviews are at: -------------- http://jdetrick.blogspot.com -----
-- email feedback, corrections, request for copies or Index of all reviews
--- to: ------ jamesdetrick@comcast.net ------ “Jim Detrick” -----------
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--------------------- Monday, December 16, 2019 --------------------
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