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title: Ask a Mathematician / Ask a Physicist | Your Math and Physics Questions Answered

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on3
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M_1
M_2
\vec{P}_1
\vec{P}_2
M_1 \ddot{\vec{P}}_1 = -\frac{GM_1M_2}{|\vec{P}_1-\vec{P}_2|^3}\left( \vec{P}_1-\vec{P}_2\right)
\vec{P}_1-\vec{P}_2
M_1 \left| \ddot{\vec{P}}_1 \right| = \frac{GM_1M_2}{|\vec{P}_1-\vec{P}_2|^3}\left| \vec{P}_1-\vec{P}_2\right|= \frac{GM_1M_2}{|\vec{P}_1-\vec{P}_2|^2}
M_2 \ddot{\vec{P}}_2 = -M_1 \ddot{\vec{P}}_1
\begin{array}{ll}\ddot{\vec{P}}_1-\ddot{\vec{P}}_2\\=\ddot{\vec{P}}_1-\frac{M_2}{M_2}\ddot{\vec{P}}_2\\=\ddot{\vec{P}}_1 +\frac{M_1}{M_2} \ddot{\vec{P}}_1 & \left(because\quad M_2 \ddot{\vec{P}}_2 = -M_1 \ddot{\vec{P}}_1\right)\\=\left(1 +\frac{M_1}{M_2}\right) \ddot{\vec{P}}_1 \\=\left(1 +\frac{M_1}{M_2}\right) \frac{M_1}{M_1} \ddot{\vec{P}}_1 \\= -\left(1 +\frac{M_1}{M_2}\right) \frac{1}{M_1} \frac{GM_1M_2}{|\vec{P}_1-\vec{P}_2|^3}\left( \vec{P}_1-\vec{P}_2\right) & \left(because\quad M_1 \ddot{\vec{P}}_1 = -\frac{GM_1M_2}{|\vec{P}_1-\vec{P}_2|^3}\left( \vec{P}_1-\vec{P}_2\right) \right)\\= -\left(1 +\frac{M_1}{M_2}\right) \frac{GM_2}{|\vec{P}_1-\vec{P}_2|^3}\left( \vec{P}_1-\vec{P}_2\right)\\= -\left(M_2 +M_1\right) \frac{G}{|\vec{P}_1-\vec{P}_2|^3}\left( \vec{P}_1-\vec{P}_2\right)\\= -\frac{G(M_1 +M_2)}{|\vec{P}_1-\vec{P}_2|^3}\left( \vec{P}_1-\vec{P}_2\right)\\\end{array}
\vec{x}
M_1 +M_2
M
\ddot{\vec{x}} = -\frac{GM\vec{x}}{|\vec{x}|^3}
\frac{N(N-1)}{2}
\begin{array}{ll}M_1 \ddot{\vec{P_1}} = -\frac{GM_1M_2}{|\vec{P}_1-\vec{P}_2|^3}\left( \vec{P}_1-\vec{P}_2\right) -\frac{GM_1M_3}{|\vec{P}_1-\vec{P}_3|^3}\left( \vec{P}_1-\vec{P}_3\right)\\M_2 \ddot{\vec{P_2}} = -\frac{GM_2M_1}{|\vec{P}_2-\vec{P}_1|^3}\left( \vec{P}_2-\vec{P}_1\right) -\frac{GM_2M_3}{|\vec{P}_2-\vec{P}_3|^3}\left( \vec{P}_2-\vec{P}_3\right)\\M_3 \ddot{\vec{P_3}} = -\frac{GM_3M_1}{|\vec{P}_3-\vec{P}_1|^3}\left( \vec{P}_3-\vec{P}_1\right) -\frac{GM_3M_2}{|\vec{P}_3-\vec{P}_2|^3}\left( \vec{P}_3-\vec{P}_2\right)\end{array}
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Q: Is there an equation that determines whether a question gets answered on ask a mathematician/physicist?

Q: If you could hear through space as though it were filled with air, what would you hear?

Q: What is the three body problem?

Q: How are fractals made?

Q: CERN’s faster than light neutrino thing: WTF?

Q: What’s the point of purely theoretical research?

H3

Q: Is there an equation that determines whether a question gets answered on ask a mathematician/physicist?

Q: If you could hear through space as though it were filled with air, what would you hear?

Q: What is the three body problem?

Q: How are fractals made?

Q: CERN’s faster than light neutrino thing: WTF?

Q: What’s the point of purely theoretical research?

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Q: Is there an equation that determines whether a question gets answered on ask a mathematician/physicist?
October 13, 2011
The Mathematician
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Q: If you could hear through space as though it were filled with air, what would you hear?
October 9, 2011
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Q: What is the three body problem?
October 3, 2011
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September 29, 2011
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Q: CERN’s faster than light neutrino thing: WTF?
September 23, 2011
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Q: What’s the point of purely theoretical research?
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Q: Is there an equation that determines whether a question gets answered on ask a mathematician/physicist?
Q: If you could hear through space as though it were filled with air, what would you hear?
Q: What is the three body problem?
Q: How are fractals made?
Q: CERN’s faster than light neutrino thing: WTF?
Q: What’s the point of purely theoretical research?
Q: Why does lightning flash, but thunder rolls?
Q: Hyperspace, warp drives, and faster than light travel: why not?
Burning Man 2011
Q: If light slows down in different materials, then how can it be a universal speed?
Q: What is mass?
Q: How much of physics can be deduced from previous equations/axioms?
Q: If God were all-seeing and all-knowing, the double-slit experiment wouldn’t work, would it? Wouldn’t God’s observation of the location of the photon collapse its probability wave function?
Q: How do those “executive ball clicker” things work?
Q: Why is cold fusion so difficult?
Q: Why does light choose the “path of least time”?
Q: Does light experience time?
Q: Would it be possible for humans to terraform mars?
Q: Can light be used to transfer energy instead of power lines?
Particle physics, neutrinos, and chirality too!
Q: What are integral transforms and how do they work?
Q: How does reflection work?
Q: What does a measurement in quantum mechanics do?
Q: If you stood in the beam of a particle accelerator, what would happen?
Q: What exactly is the vacuum catastrophe and what effects does this have upon our understanding of the universe?
Q: What is a “measurement” in quantum mechanics?
Q: How close is Jupiter to being a star? What would happen to us if it were?
Q: Can you fix the “1/0 problem” by defining 1/0 as a new number?
Q: How can we have any idea what a 4D hypercube or any n-D object “looks like”? What is the process of developing a picture of a higher dimensional object?
Q: Is it possible to destroy a black hole?
Q: Why does the Earth orbit the Sun?
Q: If you suddenly replaced all the water drops in a rainbow with same-sized spheres of polished diamond, what would happen to the rainbow? How do you calculate the size of a rainbow?
Q: If we meet aliens, will they have the same math and physics that we do?
Q: Is 0.9999… repeating really equal to 1?
Q: What would Earth be like to us if it were a cube instead of spherical? Is this even possible?
Q: How do velocities add? If I’m riding a beam of light and I throw a ball, why doesn’t the ball go faster than light?
Q: What is the universe expanding into? What’s outside the universe?
Cheap experiments and demonstrations for kids.
Q: How do I estimate the probability that God exists?
Q: How do you calculate 6/2(1+2) or 48/2(9+3)? What’s the deal with this orders of operation business?
Q: Is there a single equation that proves black holes are real?
Q: Is the edge of a circle with an infinite radius curved or straight?
Q: As a consequence of relativity, objects becomes more massive when they’re moving fast. What is it about matter that causes that to happen?
Q: What is the evidence for the Big Bang?
Q: Is there a formula to find the Nth term in the Fibonacci sequence?
Q: Why is the integral/antiderivative the area under a function?
Thank you!
Mathematical proof of the existence of God.
Video: Getting Computers to Learn
Q: What is going on in a nuclear reactor, and what happens during a meltdown?
Q: How do I find the love of my life? (a Mathematician’s perspective)
Q: Are all atoms radioactive?
Q: How do you talk about the size of infinity? How can one infinity be bigger than another?
Q: Why does E=MC2 ?
Q: What are the equations of electromagnetism? What all do they describe to us?
Q: What is the entropy of nothing?
Q: How can quantum computers break encryption?
Q: How does quantum computing work?
Q: What causes buoyancy?
My bad: If atoms are mostly made up of empty space, why do things feel solid?
Q: How many mathematicians/physicists does it take to screw in a light bulb?
Q: Why is it that (if you exclude 2 & 3) the difference between the squares of any two prime numbers is divisible by 12?
Q: Why does relativistic length contraction (Lorentz contraction) happen?
Q: Why does Lorentz contraction only act in the direction of motion?
Q: If atoms are mostly made up of empty space, why do things feel solid?
Q: Can we build a planet?
Q: π = 4?
Q: How does a scientist turn ideas into math?
Q: Is Santa real?
Q: Why isn’t the shortest day of the year also the day with the earliest sunset?
Q: Why does “curved space-time” cause gravity?: A better answer.
Q: According to relativity, two moving observers always see the other moving through time slower. Isn’t that a contradiction? Doesn’t one have to be faster?
Q: What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree?
Q: Can you do the double slit experiment with a cat cannon?
Q: How is the “Weak nuclear force” a force? What does it do?
Q: Does Gödel’s Incompleteness Theorem imply that it’s impossible to be logical?
Q: If accelerating charges radiate, and everything is full of charges, then why don’t I radiate every time I move?
Q: If you zoom in far enough, what do particles look like?
Q: What would you experience if you were going the speed of light?
Q: Why is pi not a definite number?
Q: What came before the big bang?
Q: How do “Numerology Math Tricks” work? (adding digits and tricks with nines)
Q: What is a magnetic field?
Q: What is the probability that two randomly chosen people will have been born on the same day?
Q: Which is a better approach to quantum mechanics: Copenhagen or Many Worlds?
Q: Why is our vision blurred underwater?
Q: In the NEC “faster than light” experiment, did they really make something go faster than light?
Q: How does a Tesla coil work?
Q: What are Feynman diagrams, how are they used (theoretically & practically), and are there alternative/competing diagrams to Feynman’s?
Q: Does the 2nd law of thermodynamics imply that everything must eventually die, regardless of the ultimate fate of the universe?
Q: What is The Golden Ratio? How is it used in Mathematics?
Q: Why can’t you have an atom made entirely out of neutrons?
Q: What is the physical meaning of “symmetries”? Why is there one-to-one correspondence between laws of conservation and symmetries? Why is it important that there is such correspondence?
Q: Why does energy have to be positive (and real)?
Q: How does the Twin Paradox work?
Q: How can photons have energy and momentum, but no mass?
Q: If you were on the inside of the Sun falling in, the matter closer to the surface doesn’t affect your acceleration, but the matter closer to the core does. Why is that?
Q: How do surge protectors work?
Relativity and Quantum Mechanics: the elevator pitch
Q: Why are orbits elliptical? Why is the Sun in one focus, and what’s in the other?
Q: What would happen if everyone in the world jumped at the same time?
Q: How can electrons “jump” between places without covering the intervening distance?
Q: Why do we only see one rainbow at a time?
Q: Why does putting spin on a ball change how it moves through the air?
Quantum mech, choices, and time travel too!
Q: Why is the speed of light finite?
Q: Why is the speed of light the fastest speed? Why is light so special?
Q: Will we ever overcome the Heisenberg uncertainty principle?
Q: If gravity is the reaction matter has on space, in that it warps space, why do physicist’s look for a gravity particle? Wouldn’t gravity be just a bi-product of what matter does to space?
Q: Is it possible to beat the laws of physics?
Q: What’s the chance of getting a run of K or more successes (heads) in a row in N Bernoulli trials (coin flips)? Why use approximations when the exact answer is known?
Q: Aren’t physicists just doing experiments to confirm their theories? Couldn’t they “prove” anything they want?
Q: What’s up with that “bowling ball creates a dip in a sheet” analogy of spacetime? Isn’t it gravity that makes the dip in the first place?
Q: If we find a “Theory of Everything” will we be done?
Q: Is it possible to say if the Earth is moving or sitting still without going into space?
Q: Will there always be things that will not or cannot be known?
Q: If you could see through the Earth, how big would Australia look from the other side?
Q: How is it that Bell’s Theorem proves that there are no “hidden variables” in quantum mechanics? How do we know that God really does play dice with the universe?
Q: Does an electric field have mass? Does it take energy to move an electric field?
Q: What would the consequenses for our universe be if the speed of light was only about one hundred miles per hour?
Q: Do virtual particles violate the laws that energy can be created or destroyed? Have virtual particles ever been observed? In any other instance can energy ever be destroyed or created?
Video: How do we know that 1+1=2? A journey into the foundations of math.
Q: Would it be possible to generate power from artificial lightning?
Q: What is the optimum spectrum to visualize things with? Theoretically, which type of vision would be the best to see things with?
Q: What causes iron, nickel, and cobalt to be attracted to magnets, but not other metals?
Q: Is it possible to fill a black hole? If you were to continuously throw galaxies worth of matter into a black hole, would it ever fill up? And what would theoretically happen if all the matter in the universe was thrown into a single black hole?
Q: Can math and science make you better at gambling?
Q: Spectroscopy?
Q: Is it possible to breach the center of a nebula?
Q: How does a gravitational sling shot actually speed things up?
Q: If energy is quantized, what is the least amount of energy possible? And how did they measure it?
Q: How did Lord Kelvin come up with the absolute temperature? I mean, how could he say surely that it was 273.15 C below zero?
Q: What do complex numbers really mean or represent?
Q: Is it odd that the universe’s constants are all so perfectly conducive to life?
Q: How/when will the world end?
Q: What would happen if an unstoppable force met with an unmovable, impenetrable object?
My bad: Have aliens ever visited Earth?
Q: How do Bell pairs (entangled particles) behave experimentally?
Video: What your Spiritual Guru Never Told you about Quantum Mechanics
Q: How big does an object have to be to gravitationally attract a Human or have a molten core?
Video: The Scientific Investigation of Aliens – Evidence Examined
Q: How do I count the number of ways of picking/choosing/taking k items from a list/group/set of n items when order does/doesn’t matter?
Q: Who would win in a fight: Gödel or Feynman?
Q: How hard would it be to make a list of products of primes that could beat public key encryption?
Q: What are complex numbers used for?
Q: Can one truly create something from nothing? If matter formed from energy (as in the Big Bang expansion), where did the energy come from?
Q: Why does wind make you colder, but re-entry makes you hotter?
Q: Are explosions more or less powerful in space?
Q: What is infinity? (A brief introduction to infinite sets, infinite limits, and infinite numbers)
Q: Are there physical limits in the universe other than the speed of light?
Q: Is it of any coincidence that mathematics is able to describe physical reality – given that both are inventions of the human mind?
Q: If you were to break down an average human body into its individual atoms, and then laid the atoms out in a single straight line, how far would it stretch?
Q: What’s it like when you travel at the speed of light?
Q: Is there a real life example where two negatives make a positive?
Q: Do the “laws” of physics and math exist? If so, where? Are they discovered or invented/created by humans?
Q: Do we have free will?
Q: How did mathematicians calculate trig functions and numbers like pi before calculators?
Q: How can planes fly upside-down?
Q: A flurry of blackhole questions!
Q: Why does going fast or being lower make time slow down?
Q: What’s so special about the Gaussian distribution (i.e. the normal distribution / bell curve)??
Q: Is the universe infinitely old?
Q: Have aliens ever visited Earth?
Q: Why is the sky blue?
Q: Is there a formula for how much water will splash, most importantly how high, and in what direction from the toilet bowl when you *ehem* take a dump in it ?
Q: What is the meaning of the term “random”? Can thinking affect the future?
Q: Is it possible to choose an item from an infinite set of items such that each one has an equal chance of being selected?
Q: Do aliens exist?
Q: Is it true that all matter is simply condensed energy?
Q: Which is better: Math or Physics?
Q: Why is the number 1 not considered a prime number?
Q: If the universe is expanding and all the galaxies are moving away from one another, how is it possible for galaxies to collide?
Q: What happens when you fall into a blackhole?
Q: Is the total complexity of the universe growing, shrinking or staying the same?
Q: If two trains move towards each other at certain velocities, and a fly flies between them at a certain constant speed, how much distance will the fly cover before they crash?
Q: Why does oxygen necessarily indicate the presence of life?
Q: What’s the relationship between entropy in the information-theory sense and the thermodynamics sense?
Q: Would it be possible to kill ALL of Earth’s life with nuclear bombs?
Q: Will black holes ever release their energy and will we be able to tell what had gone into them?
Q: What are the Intersecting Chord and Power of a Point Theorems?
Q: How far away is the edge of the universe?
Q: Why do superconductors have to be cold?
Q: Why does the leading digit 1 appear more often than other digits in all sorts of numbers? What’s the deal with Benford’s Law?
Q: How does the Monty Hall Problem work?
Q: How/Why are Quantum Mechanics and Relativity incompatible?
Q: What the heck are imaginary numbers, how are they useful, and do they really exist?
Q: What’s that third hole in electrical outlets for?
Q: Do physicists really believe in true randomness?
Q: Could a simple cup of coffee be heated by a hand held device designed to not only mix but heat the water through friction, and is that more efficient than heating on a stove and then mixing?
Q: What did Einstein mean by: “Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”
Q: Why does saliva boil in the vacuum of space?
Q: Can things really be in two places at the same time?
Q: Why do weird things happen so much?
Q: Why?
Q: Will CERN create a black hole?
Q: What’s the highest population growth rate that the Earth can support?
Q: What is time?
Q: What is “Dark Matter”?
Q: Why do heavy objects bend space and what is it they are bending?
Q: Why does math work so well at modeling the world around us?
Q: Why is it that when you multiply a positive number with a negative number you get a negative number?
Q: What is the best way to understand relativity theory? Why is it so counter intuitive?
Q: Will we ever go faster than light?
Q: If you were on a space station, would you be able to tell the difference between centrifugal force and normal gravity?
Q: Is teleportation possible?
Q: If black holes are “rips” in the fabric of our universe, does it mean they lead to other universes? If so, then did time begin in that universe at the inception of the black hole? Could we be in a black hole?
Q: Since pi is infinite, do its digits contain all finite sequences of numbers?
Q: What is the connection between quantum physics and consciousness?
Q: What is the probability that in a group of 31 people, none of them have birthdays in February or August?
Q: What is the meaning of life?
Q: Why is e to the i pi equal to -1?
Q: How does a refrigerator work?
Q: How do I find the love of my life?
Q: Why does “curved space-time” cause gravity?
Q: What is monotony?
Q: How do we know if science is right?
Q: How plausible is it that the laws of physics may actually function differently in other parts of the universe?
Q: Are there an infinite number of prime numbers?
Q: How can we prove that 2+2 always equals 4?
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