--------- #1478 - Messenger Spacecraft measures Mercury.
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- Today, May 26, 2012, the Messenger spacecraft is in orbit around the planet Mercury. the math to put it in orbit was developed in the 16th century. Tycho Brahe used the newly developed telescope to accurately measure the orbits of the planets. He died in 1601 and his assistant Johannes Kepler inherited his data that he had collected. Kepler spent 20 years analyzing the data. He concluded that to match the data planets had to be in elliptical orbits about the Sun and not the perfect circular orbits that the consensus at the time believed.
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- His mass analysis concluded that equal time intervals were swept by the radius vector from the Sun to the planet as the planet orbited the Sun.
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- Kepler’s third law in math was that the time it takes for a planet to make one full revolution around the Sun is proportional to Time^2 / Radius^3 = Constant. R is half the major axis of the Ellipse.
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- If factors are proportional they can be turned into an equality with the right Constant of Proportionality. Isaac Newton did the math to accomplish this for Kepler’s laws. He first assumed that the orbit were ellipses. He knew that a stable orbit was a balance of forces.
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- The force of gravity obeyed the inverse square law. The force varied inversely as the square of the distance between the masses.
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------------------------- Gravity Force = Constant / Radius^2
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-------------------------- F = Constant / R^2
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--------------------- Acceleration of object in circular orbit = velocity^2 / Radius
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------------------------- a = v^2 / R
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--------------------- Newton had is own law of motion = Force = mass * acceleration
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---------------------- F = m*a
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----- Substituting: F = m * v^2 / R
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----- Setting forces equal -------- Constant / R^2 = m* v^2 / R
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------ Solving for v^2 = Constant * R / m * R^2
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---- Calculating the period of an orbit = T = circumference / velocity
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------------------ T = 2 * pi * R / v
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------------------ T^2 = 4 * pi^2 * R^2 / v^2
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-------Substituting v^2 -------- T^2 = ( 4*pi^2 * m / Constant) * R^3
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- This was Kepler’s 3rd law of orbits because with a constant mass the factor , ( 4*pi^2 * m / Constant) , is simply another constant.
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---------------------- T^2 / R^3 = Constant
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- Newton defined the Constant of Proportionality with the Gravitational Constant , G.
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----------------------- T^2 / R^3 = 4 * pi^2 / G * m
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--------------------- G = 6.67*10^-11 meters^3 / (kilograms * seconds^2)
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-------------------- T^2 / R^3 = (5.91*10^11) * m
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- We will use this equation to solve for the mass of Mercury, but, first let’s try it out on the International Space Station that we know is orbiting at 6,738 kilometers radius. And we know the mass of the Earth is 5.9 *10^24 kilograms.
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------------------ T^2 = 5.91 ( 6.738*10^6)^3 / 5.9*20*10^24 = 30,640,000 seconds
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------------------- T = 92.3 minutes.
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- The International Space Station circles the Earth about every 90 minutes. You can see it. The scheduled pass over’s for your area are found on the web.
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- Now we have confidence to use this math on the planet Mercury On April 25, 2011 the Messenger spacecraft completed one orbit in 12 hours and 2 minutes. The radius of the orbit was 10,124 kilometers.
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--------------- T^2 / R^3 = 5.91*10^11 / m
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---------------- m = 5.91*10^11 * ( 10.124 * 10^6 meters )^3 / (43.32*10^3 seconds)^2
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---------------- m = 3.27*10^23 kilograms
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--------------- Another orbit on September 14, 2011
---------------- R - 10,085 kilometers
---------------- T = 11 hours , 58 minutes
---------------- m = 3.27 * 10^23 kilograms
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- A third orbit on May 25, 2012, yesterday
---------------- R - 7,715 kilometers
---------------- T = 28,800 seconds
---------------- m = 3.27 * 10^23 kilograms
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- The elliptical orbits around Mercury are changing but the mass remains constant. The radius, velocity, and period all adjust to keep the equation constant working according to the laws of physics.
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- My astronomy textbook had the mass of Mercury at 3.3 * 10^23 kilograms. Mercury is just 5.5% the mass of the Earth. The old guys had it right. An announcement will be made shortly, stay tuned.
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(1) To learn more : Request review # 1369, #1343, # 1165, #814, #44 five other reviews of things we have learned about this closest planet to the Sun
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
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707-536-3272, Sunday, May 27, 2012
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--------- #1477 - Hydrogen to fuel cars?
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- If our people technology could work like plant technology the world would be a nicer place. Plants soak up the sun to extract their fuel and expel pure oxygen which we like to breath. People technology disrupts the earth to collect fossil fuels and expels CO2 that causes Global Warming.
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- The Sun’s energy is enormous. More energy hit’s the Earth in one hour then the entire world consumes in one year.
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- Another great thing about plant technology is that plants have the ability to store energy when the Sun doesn’t shine. Plant technology has evolved and been perfected over 3,500,000,000 years. No wonder people technology is having great difficulty in duplicating it in the last several decades. Although we are trying; the desire is there.
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- Plant technology uses the Sun’s energy to split water, H2O, into its components hydrogen and oxygen. Plants then breath carbon dioxide and rearrange the chemistry to produce carbohydrates which store the energy. However, plants are not terribly efficient. Only about 2% of the Sun’s energy ends up stored in the carbohydrates. Also, plants are not especially robust. Too much Sun and they burn. Too little Sun and they wilt. To compensate robustness plant processes constantly reproduce and are renewed.
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- Carbohydrates are not a very efficient fuel either. Pure hydrogen would be much better fuel if it were used directly. Hydrogen produces 2.5 times more energy per pound than gasoline. A Fuel Cell can use hydrogen to produce electricity and expel drinking water. What is stopping Fuel Cells from being our ideal power source? They are 10 times more expensive then today’s alternatives. Fuel Cell development needs to create a cheap, efficient , robust technology that we have yet to achieve.
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- The problem starts with receiving the Sun’s energy. Silicon does a good job absorbing the Sun’s high energy photons. It can split out electrons with 1.1 electron volts of energy. To split water into hydrogen and oxygen it requires 1.23 electron volts of energy. So, why not stack silicon substrates together to get the higher electron volts. When silicon reacts with oxygen ( rusts) it creates an insulating layer of silica which stops the electron flow. Gallium Arsenide and Gallium Indium Phosphide semiconductors absorb the Sun’s energy at different wavelengths but they also oxidize. Metal - oxide semiconductors are another alternative being investigated.
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- The second part of the problem is that when you separate electrons and holes you have to keep them separated or they just recombine and become neutral in the atoms. When you split water into hydrogen and oxygen you have to suck away the electrons before they can recombine in the atoms. What we want to produce is free molecular oxygen and free protons. At a separate side of the process we want to produce molecular hydrogen.
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- To accomplish these chemical reactions two separate catalysts are required for hydrogen and for oxygen. Platinum works well but it is too expensive, it is like gold. Nickel and Molybdenum Sulphide are the other catalysts being studied for hydrogen.
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- For oxygen separation plants use Manganese atoms. People technology has found something more efficient in Indium Oxide. More efficient but again too expensive.
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- An “ artificial leaf ” has been developed that works in battery acid. Not good. Newer developments work in water and require Nickel, Molybdenum, and Zinc catalyst for the hydrogen and Cobalt-borate for the oxygen. But, the efficiency of the leaf is only 2.5% and it degrades with a couple weeks of use.
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- Using the triple-junction silicon is also too expensive. The hydrogen produced would cost $7 per kilogram. We can get hydrogen from methane for $2.50 per kilogram. The design goal for the “ artificial leaf” is to achieve $3 per kilogram at 5% efficiency.
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- An artificial leaf design is especially suited for regions where sunlight is abundant and access to clean water is a problem. A secondary benefit often in these regions is that they would replace paraffin lamps and diesel generators that are major polluters.
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- How soon will we be making hydrogen fuel as the sun shines? An announcement will be made shortly, stay tuned.
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(1) To learn more: Review #528 - The hydrogen economy will take awhile. Written in 2004
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
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707-536-3272, Saturday, May 26, 2012
--------- #1476 - 4 million years of “human” fossils:
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- Most of science is convinced the humans evolved in Africa some 2 to 3 million years ago. There are some dozen different lineages that go back 4 million years of ancestors.
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- Fossils suggest that humans left Africa some 120,000 years ago. There is even an ancient population in China, called Denisovans, that are dated 100,000 years ago. Neanderthals were found in Europe with ancestors that left Africa 400,000 to 600,000 years ago.
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- There as a species of hobbits found on the island Flores in southeastern Asia that lived 95,000 to 17,000 years ago.
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- Humans, and maybe I should call them “homos”, apparently migrated throughout the Earth taking refuge in ecological sanctuaries during recurring ice ages. These climate induced enclaves evolved restricted habitats and new species of homos. Many of these homo species have since gone extinct.
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- “Lucy” was a fossil found in East Africa that was the lineage “Homo Habilis“. 3,000,000 years ago Lucy and her relatives walked upright , on stubby legs, with tree-climbing hands, and small brains surviving in the African forests. One hallmark in their transition was more meat in their diets, a richer source of calories where fruits and nuts became scarce.
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- “ Australopitheus Sediba” is another lineage that was recently uncovered in the John Nash Nature Reserve 25 miles northeast of Johannesburg, South Africa, not East Africa where Lucy was found.
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- In East Africa homo fossils came from sediments sandwiched between layers of volcanic ash. The ashes were carbon dated at 1,977,000 years old + or - 2,000 years.
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- In South Africa 220 bones of A. Sediba were found. The skull brain size was 420 cubic centimeters. 1/3 the size of today’s human brains. The bones displayed the features of both apes and man at the same time. The arm alone suggest an ape, while the anklebone matches modern man. The juvenile male and the adult female skeletons are the most complete.
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- Fossilization decomposes organic components such as skin, hair, organs leaving behind only mineralized bones. However, there is some evidence that skin is on some of the bones. Currently the oldest homo DNA is dated 100,000 years old, a Neanderthal. There is a chance that the Al Sediba bones may contain the oldest genetic information found so far.
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- Another piece of evidence is the tarter stains on the teeth. this could provide the evidence of the diet. Silvia crystals , called hydroliths, embedded in the tarter may indicate what plants were eaten.
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- The cave were the skeletons were found was 30 to 50 meters deep . the homos were probably there to access fresh water that we hard to find in the area.
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- The dating of the bones was nearly coincident with the Earth’s magnetic polarity flip, magnetic north becomes magnetic south. The timing raises curiosity about possible environmental changes that occur when the Earth’s magnetic polarities flip.
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- Only surfaces fossils at the site have been collected to date. Excavation is planned once the site is turned into a state-of-the-art field laboratory which is to be completed later this year.
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An announcement will be made shortly, stay tuned.
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(1) To learn more: ScientificAmerican.com/apr2012/sediba
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
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707-536-3272, Friday, May 25, 2012
--------- #1475 - When will electric cars take over?
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- Oil production today is primarily serving the cars on the road. The U.S. uses 9,000,000 barrels of oil every day. The entire world uses 90,000,000 barrels a day so we are using 10% of the world’s output.
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- The first predictions for “peak oil” production, when the supply of oil in the ground would be exhausted and production would decline was for the 1950’s. More oil and more ways of getting it have been found and today the peak is predicted for 2020. But, this may surprise you, it will not be because we are running out of oil, it will because demand will decline due to electric cars and highly efficient gasoline engines.
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- By 2020 there will be 20,000,000 electric cars on the road. That is only 2% of the total. So, the real hero is the gains in efficiency and cost competitiveness of the gasoline engine. There are major improvements in fuel economy using internal combustion engines. I will just call them all engines or gas engines. But, before getting into this let’s summarize where we are in electric cars;
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- Today there are 130 models available worldwide. There are 6 basic designs today:
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- (1) One uses a conventional gas engine with a Stop-Start that kills the engine whenever it pauses in traffic. A larger battery is required to start the engine and run the car for a little way after restart. This brief run allows the gas engine to reach better efficiency before engaging the wheels. ( 9% improved efficiency)
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- (2) A hybrid electric adds regenerative breaking , a traction battery used with the electric motor. The electric motor only supplements the gas engine it never powers the wheels by itself. ( Honda Civic).
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- (3) A full hybrid like Toyota Prius uses gas plus electric, plus nickel-metal hybride traction battery. 100% pf electricity is generated by the gas engine and the battery. Both the electric motors and the gas engine can power the wheels. Electric power is used up to 25 miles per hour then the gas engine takes over. ( 53 miles per gallon).
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- (4) A plug-in hybrid like the Volvo V60 all batteries and uses an socket to charge the batteries at an electric outlet.
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- (5) A plug-in hybrid like the Chevy Volt. The gas engine only used to generate electricity to supply the batteries and the electric motors that power the wheels. The gas engine never powers the wheels. The batteries will go about 30 miles on a charge then the gas engine generates electricity until the next recharge occurs. ( 94 miles per gallon).
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- (6) All batter y electric like the Nissan Leaf can travel about 100 miles on a single charge.
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- Why are these models not selling like hotcakes. Because they are too expensive. Lithium-ion batteries add $12,000 to the cost of the car. 13 cents / mile is the average cost for the American gas driven car. The electric car cost is not easily justified even though the electric car cost per mile is about 3 cents per mile.
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- Batteries are expected to drop in price as production volume ramps up. The will still cost $7,000 by 2015. Saving 10 cents per mile needs to make up this price difference. Of course, government using tax payer subsidies are another way to make up the difference.
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- However, the internal combustion engines are not standing still during this time. To remain competitive they are expected to double in efficiency by 2035. Here are some of the major changes in the works:
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- The Start-Stop mechanism already discussed will produce 9% efficiency improvements. Smaller engines with turbochargers will gain a 6% efficiency. Fuel injection optimizations will add 5% efficiency. In total gas engines should improve 30% in efficiency by 2020. None of these are breakthroughs that are not already known.
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- Pollution is another driver for electric cars and gas efficiencies. Even including the coal fired electric prost plant the all electric car will be 40% cleaner in CO2 that the gas engines.
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- Government standards in fuel economy will be 54.5 miles per gallon by 2025. Standards in CO2 emissions are mostly used in Europe, but also in the U.S. With more miles per dollar a rebound effect may be that people will drive more. More driving would offset more efficiency.
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- Whatever, the next 10 years will see a major change in the transportation on the road. How we power cars and trucks is on the move and oil consumption is destined to turn around.
- An announcement will be made shortly, stay tuned.
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
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707-536-3272, Wednesday, May 23, 2012
--------- #1474 - Interesting numbers you should know:
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- Some things you should know about your world. Often our reality is expressed in numbers. Zero is a strange number. It means nothing, but, sometimes nothing is hard to obtain. Take a vacuum for example. A vacuum is just space. A vacuum is defined as the physical state with the lowest possible energy. However, in our real world the lowest possible energy is not zero energy. Even in a vacuum, even in empty space, there are particles and fields that exist and they carry energy.
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- The laws of Quantum Mechanics allow particles to pop in an out of existence as long as it happens in a small fraction of time. The more massive the “ virtual particle” the shorter the amount of time it can exist.
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- It is current belief in physics that a Higgs Field exists in a vacuum. The Higgs Field is an omnipresent field that is responsible of the different masses of all the fundamental particles.
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- The energy of a vacuum although tiny on worldly scales becomes considerable on astronomical scales. It is the energy of the vacuum in space that is collectively known as “ Dark Energy “. It is the energy that is responsible for the Universes expansion at an even accelerating rate. Space is expanding and all matter in the Universe is going away from us, if it is not overpowered by gravity in a localized area of space.
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- A great mystery in physics today is that Dark Energy is very small, some 20 orders of magnitude smaller that the calculations made using Quantum Mechanic equations for particles and fields for energy in a vacuum. Multiplying anything by 10 adds a zero to it. 20 orders of magnitude adds 20 zeros. The radius of the Earth is 6.4*10^9 meters. The wavelength of ultraviolet light is 10^10-9 meters. These 2 distances are 18 orders of magnitude differing in size. That gives you some indication how much 20 orders of magnitude would be.
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- The distance light travels in one year is 6 trillion miles 6*10^12 miles. In 1983 International Standards define the length of one meter to be the distance light travels in 1 / 299,792,458 seconds. Light only travels this fast in a vacuum. In all other media it travels slower than the 186,282 miles per second.
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- Baryons are “ ordinary matter” that we know and understand. However, baryonic matter and energy only comprise 4.6% of the matter-energy in the Universe. The other 95.4% is called Dark Matter and Dark Energy that we are trying to understand.
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- Dark Matter is 22.8%. It was first discovered when astronomers calculated the motion of galaxies. The calculations did not make sense unless there was 5 times more mass out there around the galaxy that was not accounted for in what we could see. It was not ordinary matter that makeup the stars and planets. Dark Matter was invisible and undetectable except by gravity. Dark matter is 83% of all matter and all matter is only 27.4 % of the total matter-energy in the Universe. 72.6% of the Universe is not matter it is energy, Dark Energy. Because space is expanding, the proportion of Dark Energy in the Universe is growing. When the Universe was ¼th its present size Dark Energy in space was only 5% of the total mass-energy. Mass and gravity were dominant in the beginning.
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---------------------- ¼ size ----------------- 5% Dark Energy
---------------------- ½ size ----------------- 20% Dark Energy
---------------------- 1 size ----------------- 73% Dark Energy
---------------------- 2 size ----------------- 90% Dark Energy
---------------------- 4 size ----------------- 98% Dark Energy
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- 72.6% makes Dark Energy the dominant mass-energy in today’s Universe. The Universe keeps getting less dense and more diluted, and cooler. Today it is only 3 degrees Kelvin. 3 degrees above absolute zero temperature. -270 degrees Centigrade. Today space is expanding at 73.8 kilometers per second per mega parsec. Translated to units we know this expansion is 47,000 miles per hour per million lightyears of space.
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- In some areas of this Universe gravity is still stronger than Dark Energy. Gravity is directly proportional to the masses and inversely proportional t the square of the distance between the masses. The gravitational constant that turns this proportionality into an equality is the Gravitational Constant ,G.
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---------------------- Force of Gravity = G * M * m / r^2
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--------------------- G = 6.673*10^-11
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--------------------- G = 0.000,000,000,066,73, which is a very small number.
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- There are several other numbers that you should know about your world:
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---------------------The age of the Universe = 13,725,000,000 years
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-------------------- The number of galaxies = 125,000,000,000
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-------------------- The number of planets = 125,000,000,000 of which about 1,000 have been discovered so far.
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--------------------- The diameter of the Milky Way Galaxy = 120,000 lightyears
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-------------------- The nearest other star from us = 4.22 lightyears.
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------------------------- The number of planets with life = 1
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- Maybe, an announcement will be made shortly, stay tuned.
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
or, use: “Jim Detrick” www.facebook.com, or , www.twitter.com.
707-536-3272, Monday, May 21, 2012
--------- #1473 - The math that makes an atom work.
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- This is a 100 year story of how physicists were able to figure out the mathematics that defines the behavior of an atom. They are still figuring, but, we have come a long way. One of the biggest issues was infinity, which is a very long way. It kept showing up in the equations. Physicists ignored it, hope it cancelled out, but, kept making discoveries to understand how infinites could be avoided.
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- Early attempts to calculate the strength of the electromagnetic interactions that hold electrons in orbits around the nucleus of atoms required the term 1/137. It was a dimensionless constant called ALPHA. The problem was 1/137 was in an infinite series of growing exponentials,( 1/137)^2 + ( 1/137)^3 + (1/137)^4 + ………. to infinity.
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- ( 1/137) became known as the Fine Structure Constant, called FSC or ALPHA. It is a constant in nature equal to 0.0072973531.… which is approximately 1/137. FSC is calculated from 4 basic physical constants:
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------------------------ electronic charge = e
------------------------ speed of light in a vacuum = c
------------------------ Planck’s Constant of action = h
------------------------ Permittivity of free space = Pe
------------------------ or, Permeability of a vacuum = Po , where Pe * Po = 1 / c
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- FSC measures the strength of an electromagnetic interaction.
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- FSC is the ratio of the velocity of the electron in orbit to the speed of light.
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-------------------------- FSC = v / c = 1 / 137 = 0.73%
-------------------------- v = 0.73% * c where c = 186,000 miles per second.
-------------------------- v = 4,888,080 miles per hour.
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- The electron is traveling almost 5 million mile per hour around the nucleus of the atom. But, the image needs to be a wave not just a single particle in orbit traveling at that speed.
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- FCS defines the interactions of all electrically charged particles, electrons, muons, and photons. The Fine Structure Constant that shows up in these equations is directly proportional to the velocity of light and the electric charge.
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-------------------- FSC = Po /2 ( velocity of light ) * ( electric charge squared ) / Plank’s Constant
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--------------------- FSC = Po * c * e^2 / 2 * h
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- FSC often showed up in math equations as a series of exponential sums to higher powers that proceeded to infinty : (0.00728)^2 + (0.00728^3 + ( 0.00728)^4 + ……………. off to infinity with smaller and smaller numbers. In the 1920”s the higher order factors were ignored , the infinities were ignored. Ignoring infinities is disturbing to pure mathematicians.
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- There are several other problems understanding the atom using classical theories. A hydrogen atom is composed of a proton nucleus and a single electron in orbit. The proton is a positive electric charge and the electron a negative electric charge. Opposite charges attract so that force pulls the electron inward. . Inside a hydrogen atom 10 electron volts separates the proton and the electron over a gap of 0.1 nanometers. Angular momentum in a circular orbit pushes the electron outward. The two forces are in balance for a neutral hydrogen atom. BUT, the electron is an accelerating charge constantly changing direction in orbit it should be radiating energy. It should spiral into the proton nucleus in 10^-10 seconds.
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- The next improvement in the math recognized the electron was not just a particle it was a wave. AND, only certain orbits were allowed for the wave to be is resonance in one complete orbit. Therefore, the electron could only exist at certain energy levels in the atom. When the electron jumped from one allowed level to another allowed level it emitted ( or absorbed) a photon of that exact difference in energy level. No two electrons can share the same energy level, called the Wolfgang Pauli Exclusion Principle.
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- The other problem was apparent for heavier atoms. Say, helium with 2 protons in the nucleus and 2 electrons in orbit. The 2 electrons can have opposite spins so they would not be sharing the same energy level. HOWEVER, The 2 protons in the nucleus have the same positive electric charge. Like charges repel. What could be holding the protons together in the nucleus.? They should be flying apart?
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- This next step required the discovery of the Strong Nuclear Force which was 100 times stronger than the Electromagnetic Force. Theories developed force carriers for the Strong Nuclear Force called “ Gluons”. The force carriers for the Electromagnetic Force were the photons.
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- An infinite sum can be a series that has a finite answer: 1 + ½ + ¼ + 1/8 + …… = 2
BUT, another infinite series can sun to INFINITY: 1 + ½ + 1/3 + ¼ + ……. infinity
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- The math used to explore the atom, particularly the nucleus, was called Quantum Electrodynamics, QED. This math gave physicists infinite series of 1 / FSC growing at an exponential rate .
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- The Strong Nuclear Force is the binding force that holds the atomic nucleus together. The Weak Nuclear Force destabilizes the nucleus causing radioactive decay. Math had the same problems with The Weak Force. The formulas all had infinity in the calculations.
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- Another mystery in studying the radioactive decay of atoms was that these subatomic particles seemed to have a left-handed screw. If you cup your left hand , point your thumb up and your fingers curl clockwise. If you point your thumb in the direction of motion the particles spins in the same direction as the fingers curl. Do the same with your right hand with the thumb pointing in the direction of motion and the fingers curl counter-clockwise. Photons can be polarized with left handed spin or right handed spin.
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- The energy of the photons is proportional to its frequency of oscillation. A photon at the high-frequency violet end of the rainbow has twice the energy of the photons at the low frequency red end of the rainbow, 350 nanometers versus 700 nanometers wavelengths.
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- Hot sodium and mercury vapor lamps glow yellow or turquoise hue because the heat is shaking photons lose from the atom’s electromagnetic force. They have characteristic colors because photons emerge with energies, or frequencies, unique to each element’s atom. The colors represent the pattern of energy levels available to the electrons within those atoms.
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- The hot Sun and all the stars emit electromagnetic radiation across the entire spectrum. There is a lot of hot gases in their outer atmospheres that contain a smorgasbord of elements. The result is white light. However, the elements can be individually identified because they also absorb photons at the same unique energy levels. Each element can be identified by these absorption lines, black lines, found in the spectrum.
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- Each atom has its own unique energy ladder for the electrons to orbit and electrons can only orbit in whole resonant wavelengths. In 1928 Paul Dirac came up with the equations to define these levels. Today the math is know as Quantum Electrodynamics, QED. In QED the electromagnetic force is transmitted by force carriers which are the photons. The scale of the force carrier interactions is controlled by the constant dimensionless number, the Fine Structure Constant, 0.00728.
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- FSC often shows up in QED equations as a series of exponential sums to higher powers that proceed off to infinity. (0.00728)^2 = 0.0000530, (0.00728)^3 = 0.000000386, off to infinity with each number being smaller and smaller. That is why in the early calculations in the 1920’s the infinities were ignored. However, ignoring infinities is disturbing to pure mathematicians.
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- In Quantum Mechanics individual particles have an infinite number of possible paths. However, a group of particles together at molecular size mutually cancel individual probability amplitudes for all the paths except those that are near the classical one’s we see. Particles will always take the path of least time. In Quantum Mechanics calculations allow particles to travel backwards and forwards in time.
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- In the 1930’s QED calculations worked as a first approximation but beyond that it got into a meaningless series of infinities. When dealing with electric and magnetic fields you need 4 numbers. The field force vectors have 3 directions and one direction of time ( put could be plus or minus). Drawing the axes horizontally and vertically in plotting a field vector is a measure of “ gauge”. Gauge invariance means the field symmetry is the same no matter how you orient the axes. The photon is known as a massless vector boson , or, a gauge boson. The photons carry energy and momentum from one electric charge to another transferring motion across space.
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- For the Strong Nuclear Force there are 3 massless gauge bosons. One is electrically neutral. One is charged positive and the third is charged negative. W+ and W- and Z bosons.
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- The electron and the neutrino are particles that do not feel the Strong Nuclear Force. They do feel the Weak Nuclear Force. These particles are called “ Leptons”.
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- The Weak Nuclear Force changes one form of matter into another form of matter through beta radioactivity. When radioactivity occurs a neutron converts into a proton and releases an electron and an anti-neutrino.
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- The Strong Nuclear Force can squeeze 4 protons into a tight clump but it is the Weak Nuclear Force the converts them into a nuclei of helium.
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- In 1964 the math was developed introducing quarks using Group Theory. The particular math groups was SU3. Each quark carries any of three varieties of a property known as “ Color”. Color has nothing to do with light rather it is similar to electric charge, where electric charge is the source of electromagnetic force , color is the source of the Strong Force interactions. The three fold nature of color allows up to 3 quarks to occupy the same quantum state in the nucleus as long as each carries a different color charge. This triplet property is the basis of Quantum Chromo dynamics which explains the behavior of Quarks and hadrons.
-
- Neutrinos are like electrons but without an electric charge Highly elusive, they pass through the Universe almost as if they were mere spectators, so shy it is remarkable that we even know they exist If the Z boson did not exist they would be unable to bounce off anything.
-
- Physicists in the 1970’s assumed that gravity behaved like the other 3 forces in nature and sought the theories that would bring gravity into the QED, QCD and the Standard Model. However, the theories in Quantum Mechanics produced nonsensical results when applied to gravity. Physicist tried super symmetry and string theory as new math to try to merge gravity into the Standard Model for the other particles
-
- What physicists were searching for were ”Gravitons” that could carry the force of gravity similar to how “ Gluons” are the force carriers for the Strong Nuclear Force. In the 1980”s a new method proposed that a Graviton would be two Gluons stitched together. When first developed the Feynman Diagrams used in Quantum Electrodynamics, QED, math described accurately the interactions between electrons and photons.
-
- In the 1990’ the Feynman diagram techniques were extended to the Gluons and the Strong Nuclear Force, the math became Quantum Chromo dynamics, QCD. But, the math got much more complex. When dealing with QCD physicists had to deal with “virtual particles” that pop in and out of existence in the space between other particles. The larger the mass of the virtual particle the shorter its lifetime. They defied the Conservation of Energy because they existed in such a short time. QCD started with Feynman diagrams for the first approximation and then added “perturbation” of virtual particle loops and virtual electron and anti-electron annihilations that produce photons. As more loops are added more precision in the calculations was attained.
-
- A new method of calculating in the 1990’s was called “unitarily” in which the math required the square roots of probabilities of all the possible outcomes of an interaction sum to 100%.
-
- If the Large Hadron Collider at CERN discovers the Higgs Particle it will be evidenced in the collision producing a single electron, a pair of jets, and a neutrino. The neutrino being detected as a particular energy gone missing. The math is still the method of defining the particles behavior and discovering new particles. The struggle to get rid of infinities as brought us a long way but many discoveries remain to be found. An announcement will be made shortly, stay tuned.
-
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(1) To learn more: The Infinity Puzzle by Frank Close, 2011.
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
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707-536-3272, Sunday, May 20, 2012
--------- #1471 - Our Strange Universe
-
- Our Strange Universe: A slight change to any one of the several laws of physics would cause some disaster that would disrupt the evolution of the Universe that got us here. Our mere existence would be impossible. It all starts with the slightest modification to the 4 forces of nature that came out of the Big Bang.
-
- The Strong Nuclear Force binds the atomic nucleus together. If it were slightly stronger or slightly weaker the element carbon and several other elements would never have formed.
-
- If a proton was just 0.2% heavier all hydrogen would have decayed into neutrons. Hydrogen is 75% of all the matter in the Universe and the building blocks for all the elements and for the nuclear fusion in stars.
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- Our Universe is very unique. What are the odds of that happening if only one Universe has formed? Maybe our Universe is just one among many. If many, many universes formed then the odds of ours being just right might become plausible. The existence of a superior God is the only other explanation I can think of.
-
- The Cosmological Constant is responsible for the rate of expansion of the Universe. The “ Dark Energy” , as it is now called, is just strong enough to resist the collapse of gravity and just weak enough not to expand so fast that the stars, planet, and galaxies have the time to form.
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- The Big Bang nucleosynthesis took place because the Strong Nuclear Force pulled the Quarks together to make protons and neutrons. The Electromagnetic Force allowed the positively charged protons to capture negatively charged electrons and neutrally charged hydrogen atoms formed. With 2 protons neutral helium and with 3 protons neutral lithium were formed. This happened within a few seconds after the Big Bang.
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- The expansion was just fast enough to not allow nuclear fusion to occur. Instead the hydrogen and helium got spread out in the Cosmos. Pockets of gravity brought them back together to allow nuclear fusion of hydrogen into helium and the stars were born. Our Sun is a 3rd or 4th generation star and it is still burning hydrogen into helium after 13,725,000,000 years of generations of recycled interstellar medium.
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- Our Universe contains overwhelmingly more matter than anti-matter. For the Universe to emerge from “nothing” there had to be equal amounts of both. We still do not understand why , but, we think that some small asymmetry occurring in nucleosynthesis is responsible for matter being slightly dominant in our Universe.
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- All of the heavier elements were created in the powerful explosions of supernovae, the death of stars. We think intelligent life requires some form of organic chemistry, which by definition is carbon based. The nucleus of carbon has 6 protons and the neutral atom has 6 electrons. The 6 electrons allow carbon to bind to an immense variety of complex molecules. In addition to carbon we need hydrogen 1 and oxygen 8 to get organic chemistry.
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- The neutron is 0.1% heavier that the proton If it were 2% heavier carbon could not form. If the protons were 1% heavier then hydrogen would not exist, it would all have collapsed into neutrons.
-
- Einstein’s Theory of General Relativity requires that all forms of energy exert gravity. Spacetime is expanding against this attractive force. There must exist a positive as well as a negative gravitational energy in space. This is needed to explain how the space is expanding at an accelerating rate today. The + and - balance is very delicate because a deviation of even the 100th decimal point would not allow the structure of the Universe to have expanded to what we have today.
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- We need a much deeper knowledge of our Universe in order to explain our own existence. The odds of all of these parameters being just right and not the least bit different is mind boggling.
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- It is thought that the Universe started out with one Big Force and the 4 forces we have today froze out of the expanding and cooling Bang. Gravity froze out first and it becomes the dominate force in the Universe because it is only an attractive force. The Electromagnetic Force froze out as both a positive and a negative force which tend to cancel out to neutral. The Strong and Weak Nuclear forces only operate inside the atomic nuclei. Gravity extends to infinity even though it is the weakest of the 4 forces.
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- Gravity is what makes the stars and planets into spheres and holds planets in orbit around stars and stars in orbit around the center of galaxies.
-
-------------------- Force of Gravity = G * m * M / d^2
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- The force of gravity is equal to the product of the masses and inversely to the square of the distance between them.
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- The force that governs chemistry and biology is the Electromagnetic Force. It is what hold electrons in orbit about nuclei creating neutral atoms. It creates molecules by interconnecting electrons with other element atoms. Molecules form proteins in the living cells and electrons send impulses to the brain.
-
-------------------- Force of Electromagnetism = k * q * Q / d^2
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- The electromagnetic force is equal to the product to the electric charges and inversely to the square of the distance between them.
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- Only the element hydrogen could exist if some other force could not overcome the positive to positive repelling electromagnetic force that exist in the nucleus of atoms. Two or more protons in a single nucleus should be flying apart. The Strong Nuclear Force is 100 times stronger than the Electromagnetic Force. It over powers and holds the nucleus together. the Strong Nuclear Force also causes fusion which is how all the elements heavier than hydrogen are created.
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- The Strong Nuclear Force is strongly attractive holding the protons together but it only operates over a very short distance. Neutrons and protons in the nucleus of atoms are separated by only 10^-15 meters. The atom itself with electron in orbit is only 10^-10 meters across.
-
- Lastly we have the Weak Nuclear Force. It operates on even a smaller scale than the Strong Nuclear Force. Its range is about 1% the size of the atomic nucleus. It operates in the realm of quarks and makes up the protons and neutrons.
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- The Weak Nuclear Force allows quarks to change flavor and transform protons into neutrons and neutrinos. It can also convert a neutron into a proton plus an electron and an anti-neutrino. This is what happens in radioactive decay and in fission reactors.
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- Together these 4 forces control everything in the Cosmos, well almost?
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- We still have Dark Energy and Dark Matter that represents 95% of the Cosmos. And, we do not know what forces are involved here. Dark Matter operates with gravity but not with the Electromagnetic Force. Dark Energy is the repulsive force that is a type of anti-gravity. These phenomena remain “ Dark” because science does not know what they are. An announcement will be made shortly, stay tuned
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(1) To learn more :
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
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707-536-3272, Tuesday, May 15, 2012www.physlink.com/education/essay/weinberg.cfm
--------- #1470 Are there atoms in space-time?
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- Our ancient ancestors believed there were atoms in matter long before anyone could discover atoms. It just made sense to them that there is a smallest bit of matter that can not be divided any further. The idea of the atom was that it was indivisible. Why not the same concept for space-time? Shouldn’t there be a distance so small it can not be sub-divided? Shouldn’t there be a small instant of time that can not be made any shorter?
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- Atoms were not physically characterized until 1905 when Einstein used them to explain Brownian Motion. Brownian Motion is observed with dust grains in a liquid. The dust is continually jittering in a random fashion. Einstein explained this as atoms bumping into the dust grains in a random statistical manner. He did the math to prove it.
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- It took 20 years later to get a deeper explanation of the working of atoms using Quantum Mechanics. And, another 30 years before the microscopic image of an atom was made by Erwin Muller.
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- Atoms became the building blocks in the explanation for matter and all the elements in the Periodic Table. Today physicists are trying to do the same thing with space-time. Does space-time itself have some fine-scale structure? Are there space-time atoms that are the smallest indivisible units of distance? The theories say there are and that distance is 10^-35 meters. The shortest distance we can measure using modern technology is 10^-18 meters . We are 17 orders of magnitude away from achieving such a feat.
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- Regardless of some empirical evidence theories are evolving to explain the existence of space-time atoms. One is called “ Loop Quantum Gravity” developed in the 1990’s. General Relativity is related to “loops” like electric and magnetic field lines are related to electromagnetic behavior. The math used on these field lines is treating them with “knot theory“. The math in turn is used to explain the behavior of gravity and relativity.
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- Another theory is “ string theory” applied to all particle interactions. When space-time is packed with energy as it was in the Big Bang, the fine structure of the space-time becomes dominant and the predictors of Loop Quantum Gravity diverge from those of General Relativity.
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- In this theory space-time is grainy, it is a breakup of the continuum into discrete intervals. A strange reversal occurs when gravity becomes so large it approaches a Big Bang or Blackhole Singularity. Loop Quantum Gravity suggests that the atomic structure of space-time changes the nature of gravity at very high energy densities, making it a repulsive force rather than an attractive force.
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- This is like a sponge that takes on some water, absorbing it until it is full, then, repulsing any more water. When energy densities become too large, repulsive forces come into play in the same way. The energy densities we are talking about are a trillion Solar Mass in the size of a proton.
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- When gravity becomes a repulsive force it causes space to expand. At some point densities thin out and gravity become the attractive force again. The inertia of this repulsive force is what kept the expansion of the Universe growing. When the acceleration of the expansion slowed down the excess energy was transferred into creating ordinary matter according to E = mc^2. That is how matter got created out of pure energy.
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- One scenario that comes out of Loop Quantum Gravity is that a previous Universe collapsed under the attractive force of gravity. The density grew so high that gravity switched to a repulsive force. And, the Universe started expanding again. In this way Universes are “ bouncing’ into existence from previous Universes.
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- Can the effects of Loop Quantum Gravity be measured to prove their existence?
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- Quantum fluctuations of space-time could affect the propagation of light over long distances. According to loop gravity, a light wave can not be continuous, it must fit on the lattice of the space that has a finite structure. The smaller the wavelength , the more the lattice structure distorts the light wave. As a consequence light at different wavelengths should travel at different speeds. Very tiny differences can add up over very long distances. Distant Gamma- Ray Bursts may be astronomers best hope of seeing these small effects.
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- When the ancient philosophers first proposed atoms to explain the composition of matter 25 centuries elapsed before atoms were experimentally established to exist. Space-time atoms may be discovered in a few decades. An announcement will be made shortly, stay tuned.
-
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(1) To learn more:
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
or, use: “Jim Detrick” www.facebook.com, or , www.twitter.com.
707-536-3272, Monday, May 14, 2012http://relativity.livingreviews.org/ and search for loop quantum gravity.
--------- #1469 - How we think the Universe began.
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- The Observable part of the Universe is inhabited by 100,000,000,000 galaxies. Each of these galaxies contains on average 100,000,000,000 stars and each of these galaxies contains 100,000,000,000 planets. All, as best we can estimate.
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- Galaxies themselves seem to be held together by the gravity of Dark Matter. These galaxies are accelerating away from each other on a wave of expanding space. This anti-gravity in space is called Dark Energy. We do not know what either Dark Matter or Dark Energy is. We just know the two combined occupy 96% of the total matter - energy that composes the Universe. The matter - energy that we are familiar with only occupies 4% of the expanding Universe.
-
- Space itself is expanding and galaxies , stars and planets are just being carried along for the ride. This expansion has been going on for 13,725,000,000 years. The rate of expansion today is measure to be 47,000 miles per hour per million light years distance. (called the Hubble Constant at 74 kilometers per second per mega parsec.)
-
- Expanding space also means that light traveling through the space is being stretched to longer wavelengths. The energy of light is a direct function of the frequency of the oscillation and indirectly a function of the wavelength. So, expanding wavelengths loose energy. The wavelengths are red-shifted . Consequently the Universe is cooling as it expands. It is today about 3 degrees Kelvin.
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- A light from a distant galaxy is redshifted, stretched out to a longer wavelength. The amount of redshift tells astronomers how much the Universe has grown over the intervening years. The greatest redshift astronomers have measured to date is a redshift of 8.0. At that time the Universe was a few hundred million years old and 1/9th its present size.
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- The measurements indicate that stars and galaxies first emerged in the Universe when it was 100,000,000 years old. At that time the Universe composition was 5 parts Dark Matter and 1 part hydrogen - helium.
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- The quantum fluctuations of particles created slightly uneven density in the plasma at the very beginning of the expansion. The quantum fluctuations come from the Heisenberg Uncertainty Principle which states that particles are also waves and their position is determined by a range of probabilities. The particle’s position and velocity as a product must be less than Planck’s Constant, a very small number, 10^-16. Being a product if one probability increase the other decreases, the better you know velocity the less you know about position.
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------------------ Probability of position * Probability of momentum = < 6.58 * 10^-16 electron volt - seconds. Momentum is mass * velocity.
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- These quantum fluctuations created regions of higher density which in turn created regions of higher gravity. Gravity acted to amplify these denser variations. Denser regions expanded more slowly and eventually the gravity in these clumps became large enough for the matter to collapse. Each region was about 1,000,000 Solar Mass of material. Dark Matter accounted for a bulk of this mass.
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- Because the Dark Matter could not emit or absorb light it remained in an extended cloud. However, hydrogen and helium particles emitted light , lost energy, and became concentrated at the center of the cloud. When the concentrations were great enough stars were born.
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- These first stars were massive, hundreds of Solar Mass. Big stars have short life spans. They go supernovae after a few million years. Supernovae explosion create all the heavier elements in the Periodic Table. So, the next stars that are born out of this new cloud of material will contain the full range of heavier elements. So, when planets form they have all the chemistry and biology needed for life.
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- If we go back as close to the Big Bang as we can get the redshift is 1,100. This light traveling through the expanding Universe has redshifted from visible light into the microwaves. We detect this light as Cosmic Microwave Background radiation, first discovered in 1964. It is light that left 380,000 years after the Big Bang. It is the period when the first atoms were formed and the particle plasma became neutrally charged. The temperature of the plasma had cooled to 3,000 Kelvin at this point in the expansion.
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- In 1992 studies of the Microwave Background Radiation discovered variations in temperature of 0.001%. This slight lumpiness represents the seeds for the formation of the galaxies billions of years later.
-
- These studies revealed that prior to 100,000 years after the Big Bang the energy density or radiation exceeded that of matter. This initial radiation kept the matter from clumping and collapsing in the beginning. Prior to 100,000 years the composition of the Universe was 25% helium and 75% hydrogen nuclei. There were very small amounts of lithium and isotopes of deuterium and helium 3. All the heavier elements formed billions of years later in the stars and supernovae explosions. All this “ ordinary matter” comprises only 4.5% of the total Universe matter - energy density.
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- If we take the evolution back to less than one microsecond not even protons and electrons could exist. The plasma was quarks, leptons, and force carriers photons, W and Z bosons and gluons.
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- We know that galaxies are held together by the Dark Matter that is 23% of the Universe. Science has not determined what “ Dark Matter” is. Theories include “ Neutralinos” and “axions” but the answer has yet to be discovered.
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- The theories also require there to be equal parts of matter and anti-matter. When matter and anti-matter meet they both evaporate into a burst of radiation. However, theories also hold that there was an imbalance of one extra quark out of every billion anti-quarks that survived to explain the existence of ordinary matter that exists today.
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- To explain the general uniformity of the overall Universe on the largest scale science uses the theory of Cosmic Inflation that occurred 10^-34 seconds after the Big Bang. When Inflation ceased the decaying energy formed the quarks, anti-quarks, leptons, and other particles. The inflation was faster that the speed of light. So, what we see today appears flat in its geometry, and uniform in all directions.
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- The pattern we see is in the Cosmic Microwave Background radiation is a giant image of this early subatomic world.
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- Going back earlier than 10^-34 seconds is beyond any physics that we understand today. Back to 10^-43 seconds is called Plank Time when space-time were first created. Theories persist that multiple Universes likely formed, not just the one we live in. If Cosmic Inflation happened once it could have happened any number of times. Really, these ideas reside beyond the realm of science. You have to use your imagination.
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- Today, the story above is what science can say about the Universe we live in. The most amazing part about this Universe is that we are here thinking about it. Happy Mother’s Day. An announcement will be made shortly, stay tuned.
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(1) To learn more: http//arixiv.org/abs/0803.0982
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
or, use: “Jim Detrick” www.facebook.com, or , www.twitter.com.
707-536-3272, Sunday, May 13, 2012
---------- #1468 - The decline in moral management
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- Management morals:
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Management in the broadest sense, anyone responsible for people or money. Morals in the narrowest sense. Do good to others as you would do for yourself.
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In my 40 years observing and being part of management I have witnessed a decay in moral management. You can substitute politics for management but I did not pay much attention to politics in my early years. I did see the cultural decay in business first hand.
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To make my point I will polarize my statements, call yesterday my first 20 years and call today my last 20 years.
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-- Yesterday trust and integrity were thought to be essential for business success.
-- Today trust and integrity are hard to find in Big Business, or politics.
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-- Yesterday managers said what they would do and did what they said.
-- Today managers say one thing and do another. They say what ever you want to hear. They are careful to say what is politically correct, regardless of true intentions.
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-- Yesterday managers always had 2 decisions, what to do, then how to do it. Both what and how were equally important.
-- Today managers think the end justifies the means.
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-- Yesterday managers were so conservative with money they chose accounting rules that were almost worst case.
-- Today managers choose anything within the stretch of rules to make things look good (often breaking the rules). It is better to look good than to do good.
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-- Yesterday managers were in it for the long term, generations.
-- Today managers are in it for their next pay check, the next quarter, the next bonus.
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-- Yesterday managers viewed employees, stockholders, and customers as their most important business assets.
-- Today managers view them and the voters as simpletons that are more easily manipulated than educated.
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Of course, things are not this black like I have written, but they are gray and American culture has decayed in moral management. Leaders like yourself, directors, teachers, and all managers need to police themselves and their fellow managers. Ultimately, people deserve the government they get. Policy makers, governors, need to regain trust and integrity. We must do better for a better America. Culture is hard to change but show me you are on the right road for change.
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
or, use: “Jim Detrick” www.facebook.com, or , www.twitter.com.
707-536-3272, Thursday, May 10, 2012
--------- #1467 The Growth and Decay of Money--------- #1467 The Growth and Decay of Money
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- Let’s study the growth of money. The math is very interesting and it applies to many situations in nature that experience growth or decay. It involves compound interest in the case of money. In nature it is any continuous rate of change, usually with time.
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- Interest is really the price of money. The higher the interest rate the more valuable the money is. The interest rate is the rate of growth with time. In stable economics the interest rate is normally a point or two above the inflation rate. The inflation rate is how fast prices are rising. Under ideal conditions the inflation rate is tied to the productivity which defines how efficiently the economy is growing. Productivity is the ratio of the value of the output to the cost of the inputs. It all fits together as a natural process, ideally.
- Let’s start with money and cover other natural processes later:
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- Starting with $100 and letting it grow at a 4% annual interest rate at the end of the first year you would have $104. - $100 is called the Principle and $4 is called the interest on that Principle. For our purposes we will call the $104 the Future Value of money.
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---------------------- Future Value = Present Value * ( 1 + interest rate) ^n
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------------------- where: “n” is the number of years at 4% per year.
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--------------------------- FV = PV ( 1+i)^n
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- If we let the money ride for another year, n = 2
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---------------------- FV = 100 ( 1.04)^2 = 100 ( 1.08)
---------------------- FV = $108
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- If we let it ride for 10 years:
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-------------------- FV = 100 ( 1.04)^10 = 100 ( 1.48)
--------------------- FV = $148
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- After 10 years the $100 has grown to $148. You have made $48 in interest on your money. If that principle were $100,000 you would have made $48,024.
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- When interest grows on top of interest we call that “compound interest”. Getting interest on your interest. The growth of compound interest is an exponential growth rate. It is the natural growth rate found in nature with most types of growth and decay.
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- In the money example we compounded yearly and got $148 after 10 years. What would you get if you compounded interest hourly instead of yearly? There are 8,760 hours in a year.
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------------------- FV = PV ( 1 + i /n)^n
-------------------FV = 100 ( 1+ 0.04/8760)^ 87,600
------------------ FV = $149.18
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- Compounding hourly only gained another $1.16. So, what would happen if you compounded continuously as normally happens in nature?
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- We introduce the natural constant “e” which is the base of natural logarithms. A logarithms is another name for “exponent“, and, we are working with “exponential growth” . e^x is the only function that has a rate of change that is the same e^x.
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-------------------- FV = PV * e^n*i
-------------------- FV = 100 * 3^10*(0.04) = 100 * ( 1.4918)
--------------------- FV = $149.18
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- Compounding interest continuously did not get us any more growth in interest over 10 years of compounding hourly. But, note that the exponential curve gave us the same answer, $149.18.
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- Imagine a x-y plot and y = e^x as the exponential curve, y is a function of 2.7 raised to the power of “x”. What is unique about the base “e”, which is a constant that has a value of 2.718, the value of the function is the same as the slope of the curve. The slope is rise over run, which is (delta y) / (delta x).
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----------------------------- y = e^x
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----------------------------- dy / dx = e^x
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- For an exponential curve the value of the function is the same as the change in y to a change in x as you travel up the curve. dy / dx is the tangential slope of the curve. e^x has some other unique properties. It can be expanded into an infinite series.
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---------------- y = e^x = 1 + x / 1 + x^2 / 2! + x^3 / 3! + x^4 / 4! + x^5 / 5! + x^6 / 6! + x^7 / 7! + ………
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- 3! is 3 factorial which is shorthand for 3 * 2 * 1, just as 5! is 5 * 4* 3 * 2 * 1
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- When x + 1 the function y = e which = 1 + 1 / 1 + 1^2 / 2 + 1^3 / 6 + 1^4 / 24 + 1^5 / 120 + 1^6 / 720 + 1^7 / 5040 + ………
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- y = e = 2 + 0.5 + 0.167 + 0.0417 + 0.008 + 0.001389 + 0.0001984 + ………
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- e = 2.718254
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- Note that the series for compound interest is the same type of exponential function:
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-------------- FV = PV ( 1+i) + PV ( 1+i)^2 + PV ( 1+i)^3 + PV ( 1+i)^4 + PV ( 1+i)^5 + ……… PV ( 1+i)^ n
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--------------- FV = PV e ^ n*i
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- This is the equation for all exponential functions. The equation appears everywhere in nature, not just in banking and mortgages. Any situation where the amount (A) of something varies with the time , such that the time rate of change of (A) is proportional to (A) itself.
-
----------------------dA / dt = k* A
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- Solving this differential equation gets us to the same formula with different symbols:
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--------------- A = Ao * e^k*t
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- This equation could be the growth of money, the decay of a voltage across a capacitor, the cooling of a voltage regulator in your car. The voltage across a capacitor decays at a rate proportional to the voltage. It the voltage is 20 volts and 2 seconds later is 10 volts it has a decay rate of - 10 volts / second. When will the voltage across the capacitor be 2 volts? ANSWER: 6.64 seconds:
-
---------------- A = FV = 10 volts
---------------- Ao = PV = 20 volts, the initial voltage at time equal zero.
--------------- k = i = the rate of decay. If it were linear it would be - 10 volts per second. But, it is exponential and we have to solve for it.
--------------- t = time = 2 seconds
-
--------------- FV = PV * e^i*t
---------------- 10 = 20 * e^ 2 i
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- The unknown “i” is in the exponent so we need to take the natural logarithm.
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----------------- 10 / 20 = e^2i
----------------- e^ 2i = 0.5
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- The natural logarithm to the base “e” of 0.5 = the exponent 2i
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-------------------- log e (0.5) = 2*i
------------------- -0.693 = 2 * i
-------------------- - 0.3465 = i
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- In the next interval of time the capacitor discharges from 10 volts to 2 volts at this constant decay rate of - 0.3465 volts per second
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-------------------- 2 = 10 * e^-0.3465 * t
------------------- log e 0.2 = -0.3465* t
------------------- - 1.605 = -0.3465 * t
-------------------- t = 4.64 seconds
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- The voltage across the capacitor decays at an exponential rate. It will decay from 20 volts to 10 volts in only 2 seconds , and, an additional 4.64 seconds for the capacitor to decay down to 2 volts. A total time of 6.64 seconds.
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- How long does it take an amount of money to double if the investment is growing at 10% compounding interest?
-
------------------- FV = 2
------------------- PV = 1
--------------------- n = ?
-------------------- i = 10%
-
--------------- FV = PV * e^n*i
--------------- 2 = e ^ n*(0.1)
--------------- log 2 = 0.1 * n
-------------- 0.693 = 0.1*n
--------------- n = 6.93 years
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- It takes 7 years for money to double growing at 10% per year. You will learn i * n = 70 later on:
-
--------------- FV = PV * e^n*i
---------------- FV = $100 * e ^0.7 = 100 * ( 201)
--------------- FV = $201
-
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-
- Objects cool at an exponential rate, temperature decreases at a rate proportional to the difference of the units temperature (u) and the temperature of the surrounding environment (T).
-
------------------- du / dT = k (u-T)
-
- Integrating to solve the differential equation:
-
---------------- (u - T) = (uo - T) * e^ k*t
-
- (u - T) = FV = the future temperature difference, then:
-
----------------- FV = PV * e^n*i
-
- The car’s regulator is at 90 decrees C and the garage is at 20C. Turn off the ignition and 10 minutes later the regulator cools to 60 C. At what temperature will it be after 20 minutes?
-
----------- PV = 90 - 20 = 70
---------- FV = 60 - 20 = 40
----------- i = rate of decay in degrees per minute. ( - 3 degrees / minute if the decay was linear.)
------------ n = is in 10 minute intervals and that doubles in time n = 1 for each interval.
-
------------ 40 = 70 * e^1* i
----------- 0.5714 = e^i
----------- log e (0.5714) = i
------------ ( - 0.56) = i
-
- The next interval drops the temperature from 60 degrees , which is a difference of 40 degrees above ambient to some temperature u = ?.
-
--------------- FV = u - T = 40 * e^-.56
--------------- u - T = 40 / 1.75 = 23
------------- u = 20 + 23 = 55 C
-
- After 20 minutes the regulator cooled 90 - 55 = 35 degrees to get to 55C.
-
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-
- “e” has many unique properties: “e” is a “transcendental” number, like pi, it is a series of decimals that goes to infinity and never repeats itself. It is an “irrational” number that can not be written as a ratio of two integers.
-
--------------- e^ square root of -1 . pi + 1 = 0 ( think about it )
-
----------------- e ^ix = cos x + i sin x
-
------------------ i * t = 70
-
- By dividing the interest rate into 70 you get how many years it will take for the investment to double. This simple equation has a multitude of every day uses:
-
- If we double our national debt in 10 years what is the rate of growth of spending?
------------------------ 70 / 10 years = 7% per year.
-
- If the population is growing at 2% per year when will it double?
---------------------- 70 / 2% = 35 years
-
- If you got a 5% mortgage for 30 years, when will you double the amount of your loan with interest?
------------- 70 / 5% = 14 years.
-
- Put one penny in a kitchen jar on December 1st and double it every day. How much will you have in time for Christmas?
------------------------ $117,772
-
- Google’s official revenue target was $2,718,281,828. ( get it? )
-
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Other reviews on math:
- #1329 - The most important math you will ever learn.
- # 1281 - Math was invented to solve problems.
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707-536-3272, Saturday, May 12, 2012
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Which is greater? The number of heartbeats during your lifetime , or the number of minutes since the birth of Christ
-
--------- #1454 - There was this old stone wall separating two farms. Each farmer had 600 feet of fence. One farmer wanted to have maximum rectangular area using his fence and the wall for one side. What was the length of each side of the fence he designed? The other farmer wanted to have only two sides of the fence and for them to be the same length and still have the maximum area in the triangle. What was the length of each side of his fence and what angle did the fence meet the wall?.
-
- Request e-mail to receive the answers?
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RSVP, please reply with a number to rate this review: #1- learned something new. #2 - Didn’t read it. #3- very interesting. #4- Send another review #___ from the index. #5- Keep em coming. #6- I forwarded copies to some friends. #7- Don‘t send me these anymore! #8- I am forwarding you some questions? Index is available with email and with requested reviews at http://jdetrick.blogspot.com/ Please send feedback, corrections, or recommended improvements to: jamesdetrick@comcast.net.
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707-536-3272, Tuesday, May 1, 2012
