- 3301 - GRAVITY - understanding Dark Matter? The mystery of dark matter doesn't have an obvious solution. Astronomers continue to design experiments to search for these elusive particles. When they do figure out what they are and how they are distributed throughout the universe, they will have unlocked another chapter in our understanding of the universe.
--------------------- 3301 - GRAVITY - understanding Dark Matter?
- The earliest scientists try to understand why objects fall toward the ground. The Greek philosopher Aristotle gave one of the most comprehensive attempts at a scientific explanation of this behavior by putting forth the idea that objects moved toward their "natural place."
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- This natural place for the element of Earth was in the center of the Earth which was the center of the universe in Aristotle's geocentric model of the universe. Surrounding the Earth was a concentric sphere that was the natural realm of water, surrounded by the natural realm of air, and then the natural realm of fire above that.
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- Thus, Earth sinks in water, water sinks in the air, and flames rise above air. Everything gravitates toward its natural place in Aristotle's model, and it comes across as fairly consistent with our intuitive understanding and basic observations about how the world works.
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- Aristotle further believed that objects fall at a speed that is proportional to their weight. In other words, if you took a wooden object and a metal object of the same size and dropped them both, the heavier metal object would fall at a proportionally faster speed.
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- Aristotle's philosophy about motion toward a substance's natural place held sway for about 2,000 years, until the time of Galileo Galilei. Galileo conducted experiments rolling objects of different weights down inclined planes (not dropping them off the Tower of Pisa, despite the popular apocryphal stories to this effect), and found that they fell with the same acceleration rate regardless of their weight.
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- In addition to the empirical evidence, Galileo also constructed a theoretical thought experiment to support this conclusion.
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- The major contribution developed by Sir Isaac Newton was to recognize that this falling motion observed on Earth was the same behavior of motion that the Moon and other objects experience, which holds them in place within relation to each other.
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- This insight from Newton was built upon the work of Galileo, but also by embracing the heliocentric model and Copernican principle, which had been developed by Nicholas Copernicus prior to Galileo's work.
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- Newton's development of the law of gravity, brought these two concepts together in the form of a mathematical formula that seemed to apply to determine the force of attraction between any two objects with mass. Together with Newton's laws of motion, it created a formal system of gravity and motion that would guide scientific understanding unchallenged for over two centuries.
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- Then in 1903 Einstein redefines “gravity“. His “general theory of relativity“ describes the relationship between matter and motion through the basic explanation that objects with mass actually bend the very fabric of space and time.
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- This changes the path of objects in a way that is in accord with our understanding of gravity. Therefore, the current understanding of gravity is that it is a result of objects following the shortest path through spacetime, modified by the warping of nearby massive objects. Mass warps spacetime.
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- In the majority of cases that we run into, this is in complete agreement with Newton's classical law of gravity. There are some cases which require the more refined understanding of general relativity to fit the data to the required level of precision.
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- There are also some cases where not even general relativity can quite give us meaningful results. Specifically, there are cases where “general relativity” is incompatible with the understanding of “quantum physics“.
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- One of the best known of these examples is along the boundary of a blackhole, where the smooth fabric of spacetime is incompatible with the granularity of energy required by quantum physics. This was theoretically resolved by the physicist Stephen Hawking, in an explanation that predicted blackholes radiate energy in the form of Hawking radiation.
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- We still need a “comprehensive theory of gravity” that can fully incorporate quantum physics. Physicists have many candidates for such a theory, the most popular of which is “string theory“, but none which yield sufficient experimental evidence (or even sufficient experimental predictions) to be verified and broadly accepted as a correct description of physical reality.
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- In addition to the need for a quantum theory of gravity, there are two experimentally-driven mysteries related to gravity that still need to be resolved:
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- Scientists have found that for our current understanding of gravity to apply to the universe, there must be an unseen attractive force (called dark matter) that helps hold galaxies together and an unseen repulsive force (called dark energy) that pushes distant galaxies apart at faster rates.
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- Understanding the law of gravity, one of the fundamental forces of physics, offers profound insights into the way our universe functions. This goes along with Newton’s “Three Laws of Motion“, outlined his law of gravity in the 1687 book “Philosophiae naturalis principia mathematica” (Mathematical Principles of Natural Philosophy).
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- Johannes Kepler (German physicist, 1571-1630) tried using these three laws governing the motion of the five then-known planets. He did not have a theoretical model for the principles governing this movement, but rather achieved them through trial and error over the course of his studies.
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- Newton's work, nearly a century later, was to take these laws of motion he had developed and applied them to planetary motion to develop a rigorous mathematical framework.
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- Newton named that force gravitation (or gravity) after the Latin word gravitas which literally translates into "heaviness" or "weight."
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- Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.
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-------------------- Force of Gravity, Fg = G * m1 * m2 / r^2
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-------------------- Fg = The force of gravity ( newtons)
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-------------------- G = The gravitational constant, which adds the proper level of proportionality to the equation. The value of G is 6.67259 x 10V-11 N * m^2 / kg^2,
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-------------------- m1 & m1 = The masses of the two particles ( kilograms)
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-------------------- r = The straight-line distance between the two particles
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- This equation gives us the magnitude of the force, which is an attractive force and therefore always directed toward the other particle. As per Newton's Third Law of Motion, this force is always equal and opposite.
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- Newton's Three Laws of Motion give us the tools to interpret the motion caused by the force and we see that the particle with less mass will accelerate more than the other particle.
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- This is why light objects fall to the Earth considerably faster than the Earth falls toward them. Still, the force acting on the light object and the Earth is of identical magnitude, even though it doesn't look that way.
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- The force is inversely proportional to the square of the distance between the objects. As objects get further apart, the force of gravity drops very quickly. At most distances, only objects with very high masses such as planets, stars, galaxies, and blackholes have any “significant’ gravity effects.
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- In an object composed of many particles, every particle interacts with every particle of the other object. Since we know that forces (including gravity) are vector quantities, we can view these forces as having components in the parallel and perpendicular directions of the two objects.
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- In some objects, such as spheres of uniform density, the perpendicular components of force will cancel each other out, so we can treat the objects as if they were point particles, concerning ourselves with only the net force between them.
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- The center of gravity of an object is generally identical to its center of mass.
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- Instead of calculating the forces between two objects every time, we instead say that an object with mass creates a “gravitational field” around it. The gravitational field is defined as the force of gravity at a given point divided by the mass of an object at that point.
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- When an object moves in a gravitational field, work must be done to get it from one place to another. Using calculus, we take the integral of the force from the starting position to the end position. Since the gravitational constants and the masses remain constant, the integral turns out to be just the integral of “1 / r^2” multiplied by the constants.
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- We define the gravitational potential energy, “U“, such that “W = U1 - U2“. This yields the equation for the Earth with mass mE.
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- On the Earth, since we know the quantities involved, the gravitational potential energy “U” can be reduced to an equation in terms of the mass “m” of an object, the acceleration of gravity (g = 9.8 m/s). This simplified equation yields “gravitational potential energy” of:
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--------------------------- U = m * g * y
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- There are some other details of applying gravity on the Earth, but this is the relevant fact with regards to gravitational potential energy.
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- Notice that if “r” gets bigger (an object goes higher), the gravitational potential energy increases (or becomes less negative). If the object moves lower, it gets closer to the Earth, so the gravitational potential energy decreases (becomes more negative). At an infinite difference, the gravitational potential energy goes to zero.
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- As a form of energy, “gravitational potential energy” is subject to the law of conservation of energy.
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- Albert Einstein explained gravitation as the curvature of spacetime around any mass. Objects with greater mass caused greater curvature, and thus exhibited greater gravitational pull.
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- This has been supported by research that has shown light actually curves around massive objects such as the sun, which would be predicted by the theory since space itself curves at that point and light will follow the simplest path through space.
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- Current efforts in quantum physics are attempting to unify all of the fundamental forces of physics into one unified force which manifests in different ways. So far, gravity is proving the greatest hurdle to incorporate into the “unified theory“.
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- Such a universal theory of quantum gravity would finally unify general relativity with quantum mechanics into a single, seamless and elegant view that all of nature functions under one fundamental type of particle interaction.
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- In the field of “quantum gravity“, it is theorized that there exists a virtual particle called a “graviton” that mediates the gravitational force because that is how the other three fundamental forces operate.
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- The graviton has not been experimentally observed, however!
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- The universe is made up of at least two kinds of matter. Primarily, there's the material we can detect, which astronomers call "baryonic" matter. It's thought of as "ordinary" matter because it's made of protons and neutrons, which can be measured. Baryonic matter includes stars and galaxies, plus all the objects they contain.
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- Second, there is also "stuff" out there in the universe that can't be detected through normal observational means. Yet, it does exist because astronomers can measure its gravitational effect on baryonic matter.
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- Astronomers call this material "dark matter". It doesn't reflect or emit light. This mysterious form of matter presents some major challenges to understanding a great many things about the universe, going right back to the beginning, some 13.7 billion years ago.
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- There is not enough mass in the universe to explain things like the rotation of stars in galaxies and the movements of star clusters. Mass affects an object's motion through space, whether it's a galaxy or a star or a planet.
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- Judging by the way some galaxies rotated, it appeared that there was more mass out there somewhere. It wasn't being detected. It was somehow "missing" from the mass inventory that assembled using stars and nebulae to assign a galaxy a given mass.
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- Dr. Vera Rubin was observing galaxies when they first noticed a difference between expected rotation rates (based on estimated masses of those galaxies) and the actual rates observed. This was the first discovery of dark matter.
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- There's observational evidence for dark matter around galaxies. Theories and models point to the involvement of dark matter early in the universe's formation. So, astronomers and cosmologists know it's out there, but haven't yet figured out what it is yet.
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- What could dark matter be? As of yet, there are only theories and models. They can actually be slotted into three general groups: hot dark matter , warm dark matter , and cold dark matter (CDM).
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- Of the three, CDM has long been the leading candidate for what this missing mass in the universe is. Some researchers still favor a combination theory, where aspects of all three types of dark matter exist together to make up the total missing mass.
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- CDM is a kind of dark matter that, if it exists, moves slowly compared to the speed of light. It is thought to have been present in the universe since the very beginning and has very likely influenced the growth and evolution of galaxies. as well as the formation of the first stars. Astronomers and physicists think that it's most likely some exotic particle that hasn't yet been detected. It very likely has some very specific properties:
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- Dark matter would have to lack interaction with the electromagnetic force. This is fairly obvious since dark matter is dark. Therefore it doesn't interact with, reflect, or radiate any type of energy in the electromagnetic spectrum.
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- Any candidate particle that makes up cold dark matter would have to take into account that it has to interact with a gravitational field. For proof of this, astronomers have noticed that dark matter accumulations in galaxy clusters wield a gravitational influence on light from more distant objects that happen to be passing by. This "gravitational lensing effect" has been observed many times.
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- While no known matter meets all of the criteria for cold dark matter, at least three theories have been advanced to explain CDM .
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- Weakly Interacting Massive Particles: Also known as WIMPs, these particles, by definition, meet all the needs of CDM. However, no such particle has ever been found to exist. WIMPs have become the catch-all term for all cold dark matter candidates, regardless of why the particle is thought to arise.
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- Axions are particles that possess the necessary properties of dark matter, but for various reasons are probably not the answer to the question of cold dark matter.
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- MACHOs, Massive Compact Halo Objects, are objects like blackholes, ancient neutron stars, brown dwarfs and planetary objects. These are all non-luminous and massive. But, because of their large sizes, both in terms of volume and mass, they would be relatively easy to detect by monitoring localized gravitational interactions.
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- There are other problems with the MACHO hypothesis. The observed motion of galaxies is uniform in a way that would be hard to explain if MACHOs supplied the missing mass.
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- Star clusters would require a very uniform distribution of such objects within their boundaries. That seems very unlikely. Also, the sheer number of MACHOs that would have to be fairly large in order to explain the missing mass.
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- Right now, the mystery of dark matter doesn't have an obvious solution. Astronomers continue to design experiments to search for these elusive particles. When they do figure out what they are and how they are distributed throughout the universe, they will have unlocked another chapter in our understanding of the universe.
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- I’m still working on that! We are right back to where we started.
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- October 12, 2021 GRAVITY - understanding Dark Matter? 3301
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--------------------- --- Tuesday, October 12, 2021 ---------------------------
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