Tutorial

Discussion in 'Pseudoscience Archive' started by Reiku, Oct 19, 2008.

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    Part One

    Movement in One Dimension

    First of all, let us cover what a dimension is, and what we mean by moving in a dimension.

    A dimension is a ‘’degree of freedom.’’ If something has a degree of freedom, it is said to be within a dimension which it can move freely in. In the study of the motion of objects, from atoms to cars, we assume the use of initial starting points, and final velocities; these notions involve ‘’changes in velocities,’’ over some ‘’change in time,’’ and ultimately, ‘’a change in position.’’ The change in position is usually called the ‘’displacement.’’

    The two quantities used to describe the motion of something (whether in one or more dimensions), are focused on the speed and direction. The speed of something, is usually explained as simply the rate of a change in an objects position, and the direction coupled within the equations that describe velocity, give rise to a very important area of physics called ‘’the velocity vector.’’

    The direction can be seen as being very important, because it will ultimately explain where something will end up, in a certain location: It would be a big difference going 100 miles West to that of 100 miles East. So the direction is pivotal in describing the vector of velocity.

    What’s a Vector?

    The term vector should not worry you. It’s quite easy to explain and understand.

    A Vector is a quantity which has both a ‘’size’’ and a ‘’direction’’. Notice how when we added the quantities of speed and direction together, we arrived with velocity? This is what we mean by saying velocity is a vector, because it has a size and a direction to that size in question.

    Velocity

    Velocity is the movement of a thing: usually described as the average velocity of a change in some position: so if you are standing at the end of a corridor, and you move east until you come to the end, the initial position would be where you had started (west of your final position), and the final position is where you ended up.

    But that had a speed, and it also had been done in some time. To calculate these quantities, we use equations, which are short hand notation to help us calculate the values we are searching for.

    The velocity of something can be calculated through dividing the displacement by time . The arrows at the top of the letters (one for both the vector symbols of displacement and velocity), are the direction of velocity in question. (We end up with a vector quantity because we are dividing a scalar by a vector).

    \(\Delta \vec{v}=\frac{\Delta d_{i}}{\Delta t}\)

    A scalar is a quantity in physics which has only a size. It’s good practice to get to know your scalars and vectors.

    Changes in Velocity

    The following equations will require a little algebraic knowledge. When we deal with equations, we use symbols in terms of cutting the language down. In fact, in many respects, physics is a language of math and concepts.

    \(x_{0}\) – initial position
    \(x_{f}\) – final position
    \(t_{0}\) – initial time
    \(t_f\) – final time recorded
    \(v_0\) – initial velocity
    \(v_f\) – final velocity
    \(\Delta\) – the symbol ‘’delta’’ used to represent a change in the quantity*

    *so for instance, \(\Delta t\) would read a ‘’change in the value of t.’’ Also note, that the lower script of \(0\) and \(f\) help us to keep track of our positions in time and space.

    If we are dealing with changing positions, where something is displaced from one point \(x_0\) to another \(x_f\), we can represent this as:

    \(\Delta x=x_f – x_0\)

    This action will take some time as well, so it is logical to assume:

    \(\Delta t=t_f – t_0\)

    And that must also mean that there is a change in a velocity assumed, so;

    \(\Delta v=v_f – v_1\)

    Pretty simple so far eh? Easily understood, we can come to talk about the average velocity \(v*\), which we measure as a change in position by a change in time, so;

    \(v*=\frac{\Delta x}{\Delta t}\), which can also be written as:

    \(v*=\frac{x_f – x_0}{t_f – t_1}=\frac{x – 0}{t - 0}= \frac{x}{t}\)

    To calculate how far an object has traveled \(x\) after some time \(t\) , traveling with a ‘’constant velocity’’ (which means it travels at a velocity that is constant and does not change), you can now use the following formula which is derived from the equations above used in most standard physics textbooks:

    \(x=x_0+vt\)

    If you plug in the correct values, you can calculate the equation:

    \(x_0\) – 400mi
    \(v\) – 80 mi/h
    \(t\) – 9 h

    *the m/h is a fraction that represents ‘’miles per hour.’’

    So the way to solve the equation is by thus:

    \(x=(400)+(80)(9)\)

    *when you come across numbers expressed in brackets side by side (y)(x) for example, it means simply that (y) and (x) are multiplied together.

    So the answer is:

    \(x=(400)+(80)(9) = 1,120miles\)

    Acceleration

    Acceleration is not much more difficult to understand when compared so far with what we have covered. So far, we have been talking about a change in velocity, but this velocity has been homogenous. The reason why this is unrealistic, is because usually velocity are constantly changing.

    Acceleration is the varying velocity of something, so it is called ‘’the rate of change.’’ Acceleration is given as:

    \(a=\frac{\Delta v}{\Delta t}\)

    In physics, you might come across terms like ‘’instantaneous speed’’ and ‘’uniformly accelerated motion.’’ The instantaneous speed is a measurement made at a precise moment. Everyday, you might go to work, and make sure you don’t go over the speed limit because it will be recorded on a speed detector. These detectors use what is called a ‘’Light Gate,’’ and they use a device that uses a timer to calculate a card to pass through a beam of light. The equation used to calculate this is given as:

    \(v*=\frac{L_c}{t}\)

    Which reads, ‘’average velocity equals the length of the card over time.’’

    Uniform accelerated motion, is when something has a constant acceleration. These following two equations for now, should also be revised:

    A)
    \(v=\frac{v_f +v_0}{2}\)

    and

    B)
    \(a=\frac{v_f – v_0}{t}\)

    (hopefully, you are beginning to read these equations yourself.)

    If you have the equation \(d=vt\), which reads, distance equals velocity times time, we can use the definition of v (in the equation A) above) to find;

    \(x=\frac{v_f+v_0}{2}\). To find the general solution to this equation, we can solve by using algebra:

    \(x=\frac{v_f+v_0}{2}\frac{v_f-v_0}{a}=\frac{v_{f}^{2} – v_{0}^{2}}{2a}\)

    Simply, we can find that \(x=v_{f}^{2}\) .

    Part Two

    Why Do Things Move At All?

    We learn from fundamental physics, that everything moves. Your playing dice on the table might seem very solid, stable and stationary, but on much smaller levels (the level of atoms and subatomic particles), even the most stable non-moving macroscopic object is in constant motion.

    Nothing is ever still, and even objects are thought of being made of compact particles all buzzing around each other, vibrating to some quantum tune. At this level, ‘’classical mechanics’’ cannot fully describe why things move; we need the new physics.

    It turns out, that even if you could freeze the vacuum down to absolute temperature or zero-point temperature which an ideal gas would exert no pressure, where the Kelvin scale of temperatures is defined in terms of the triple point of water,\(T3=273.16\)° where the solid, liquid, and vapor phases coexist, you would imagine to be the point where even movement ceases to exist.

    However, it turns out that even at zero-temperatures there is still a lot of movement. This movement is called the zero-point energy field, and is an important aspect of quantum physics, and particle physics in general.

    But this all applies to particle physics. Before we had most of the knowledge we have on the world of protino’s and neutrino’s, (the world of the infinitesimally small), we had a smart man, and arguably the most intelligent man who had ever lived (even better than Einstein himself), was Sir Isaac Newton.

    He developed his Principia or laws of motion defining inertia, mass and forces in the 1600’s and they where published in the year of 1687 AD. They where revolutionary at the time, as they explained the forces at work in objects and explained Kepler’s laws of planetary motion (though we shall not divulge into Kepler’s work).

    He was able to derive new concepts on a force of gravity, where the world itself kept us to its surface by a force of gravity, and showed that every physical objects had a push and pull quality to them. It turned out that when talking about a force , it needed not be one force acting on an object, but in fact the vector sum of all the forces on the object, called the Net Force. So the acceleration of an object could be described in terms of the total force acting on an object.

    His forces came in ‘’balanced forces’’ and ‘’unbalanced forces’’. A balanced force, was when you had a force acting on something that exerted a force that was perfectly equal, and would therefore cancel the force out.

    A simple way to understand a balanced force, is by simply observing a box sitting on a table. The table exerts a force on the box, as much as the box exerts a force on the table, and both forces are cancelled out for they are equal.

    If we are dealing with an unbalanced force, then you might imagine yourself leaning on a wall, with your palm spread out upon it. If you exert a force that is too strong, the wall will collapse (that is if you are strong enough). This force is unbalanced.

    His laws came in three, and for the rest of this part, we shall explore each one of these laws.

    1st Law

    ’’A particle will remain at rest or in constant motion, unless acted upon by some external force.’’

    This is Newton’s first law of motion. The law itself, is really called the ‘’law of inertia,’’ and it is the tendency, or better said yet, the ‘’resistance,’’ of an object to accelerate or decelerate when stationary or in motion, unless some external force issues it to move. Interestingly enough, with what is known about inertia; it still hasn’t been given a proper origin. Einstein, a very smart physicist who developed theories that extended Newton’s idea’s called the Theories of Relativity, only equated an equivalence between matter, inertia and gravity, but never gave any real reason as to why inertia would be some fundamental property of matter.

    2nd Law

    ’’The force on an object is equal to the mass of the object multiplied by the acceleration.’’

    This is Newton’s second law of motion. It differs only very slightly from his first law.

    When Newton referred to motion, he did not refer to velocity only. He referred to mass as well, and this derives the notion of ‘’momentum’’ – the movement of some body with mass (though the term momentum can also be used for massless bodies). Momentum is found as simply then, the product of mass and velocity .

    Stated as an equation, the second law can be expressed as:

    \(F=\frac{d}{dt}(mv)\)

    The \(\frac{d}{dt}\) part simply means, ‘’the instantaneous rate of change.’’ So all in all, it would read as, ‘’force is equal to the change of momentum in a system of mass.’’

    When we take into consideration that the body in question has a mass that is constant, then with a little calculus of differentiation, we can arrive at:

    \(\frac{d(mv)}{dt}=m \frac{dv}{dt}\)

    (Don’t worry about differentiation. We just want to quickly arrive at the final premise) – which is, basically that Newtons final idea was that force equalled the mass multiplied by acceleration:

    \(F=ma\)

    This equation is practically universal on its scale of use in colleges and universities.

    3rd Law

    ’’To every action, there is an equal and opposite reaction.’’

    Newton had a final rule for his work. This was that forces always come in pairs. If one force A exerts a force on B, then B will exert a force on A, that is always the same. One way to imagine this, is when you shoot a bullet from a shotgun.

    Usually, the weedy kids, too young to take grip of the shotgun, will fall back on themselves, because the bullet that leaves the gun also exerts a force on the gun. Simple enough to understand eh? Or imagine being on a boat in the water. If you stood up and attempted to jump off the boat and onto the grass beside you, the boat might submerge a bit as you jump off. This is also a ‘’pair-force.’’

    So these are Newton’s laws of motion.

    Part Three

    Free Fall

    In the 1680’s, a very famous man called Galileo Galilei was one of the first physicists and mathematicians to bring physics and observational physics together into one framework. His many contributions to physics and astronomy where vast, from noting down celestial movement of bodies, to realization of Kepler’s planetary motion laws, but what he is most remembered for today, was the discovery that all objects fall at the same speed despite the mass content.

    This became to be called ‘’free-fall,’’ and its when gravity itself (which is a field of force that permeates the universe and keeps us on the face of this planet), pulls on the atoms of a system at the same rate.

    To test this, according to a biography on Galileo written by Vincenzo Viviani, Galileo dropped different weights from the top of the Leaning Tower of Pisa. He also dropped objects he assumed would drag due to the resistance of air. However, it has been in some dispute as to whether these experiments actually took place, but nevertheless, it’s an interesting story.

    His idea’s, of course, where revolutionary, since they absolutely went against the popular belief that all objects fell at different speeds due to their weight, an idea that was proposed by Aristotle.

    Galileo did propose however, and to add incorrectly, that objects fell with a uniform acceleration so long as the resistance was negligible. That just means, that the air resistance a bowling ball would have, is negligible due to its small quantity, whilst a feather’s drag cannot be negligible.

    According to myth, he created ramps in which he rolled things down, and came to the kinematical calculation of \(D \alpha T^{2}\), which basically means, the velocity at which a thing moved down a plane was proportional to the amount of time that passed by. More precisely, the distance accomplished would increase with the square of time that would pass.

    He came to understand, almost everything there was to know about a falling body (with the equipment of the time), and found that objects fell with a constant acceleration towards the earth. The value of this acceleration was \(g=9.8\frac{m}{s^{2}}\) , where \(g\) represents the acceleration due to the gravity of the earth.

    This would mean that the acceleration due to gravity near the surface of the earth would be given a value of \(1g\). Larger acceleration would obviously increase, such as \(2g\) and \(3g\) . This is why we say, an object falling towards the earth due to gravity is in a state of ‘’free fall.’’

    There are in fact two main forces acting on an object when it falls toward the earth. We have covered both already: These are drag (or air resistance) and gravity. These two forces can sum up (also called the net force, covered in last part), the active forces on an object. To calculate the net force, we can illustrate in an equation that;

    \(\vec{f}_{net}=\vec{F}_d+\vec{F}_g\)

    Where \(\vec{F_d}\) refers to the force of drag and \(\vec{F_g}\) is the force due to acceleration. It’s always recognized as a vector sum of forces.

    This brings us to the equation that describes the motion of an object that is falling. To understand the following equation, we must assume that the drag is negligible, so we are referring to an object very close to the surface of the earth, so that represents the position of the object in question, is for time, is for acceleration, is the initial position and is the initial velocity.

    \(x=x_0+v_0t+\frac{1}{2}at^{2}\)

    If one ever uses this equation to calculate the motion of a falling object, and it is assumed that the object must be dropped, then always note that the initial velocity must equal zero. If you ever do solve for this equation, you can give it in meters per second times time squared or \((m/s)t^{2}\).

    Gravity

    When Newton derived the first ideas of gravity being a force that kept us to the face of the planet, he did not ascribe it any fundamental property. Newton instead, described the field of gravity as a force under the power of God that kept us stuck to the earth.

    One of Newton’s major contributions to the force of gravity was the inverse-square law, a mathematical concept we will cover later, but in short, it explains how gravitational radiation coming from some source, if you double the distance from the source, the intensity of illumination is 1/4.

    If we tripled the distance, the luminous intensity becomes 1/9 of the intensity found from the source. So it is said that the intensity of illumination is proportional to the square of the distance. All types of radiation are therefore said to obey the inverse-square law.

    What is meant by the term ‘’fundamental’’, is the very simplest elements of existence; the very basis of what and how everything comes about. The fundamental particle of gravity is the graviton, which yet has not been observed. The graviton is said to mediate the force of gravity between two masses (more on particles and their roles much later in the guide.) Gravity is also a type of radiation, like the kind of radiative properties of sunlight.

    However impressive Newton’s ideas where concerning the role of gravity, he still had it greatly wrong, as it wasn’t till 1926 Einstein’s relativity papers toppled Newtonian ideas (though not by much), and gave matter, inertia, energy, curvature, acceleration, distortions and gravity all new terms as somehow being the same thing, (and more on relativity in the final part).

    The force of gravity is said to be an attractive force, and when talking about celestial bodies, we ascribe the idea of gravitation. Gravitation and gravity are said to be interchangeable words, as gravitation keeps planets in their orbits and star systems in their galactic orbits, whilst the term ‘’gravity’’ is commonly used to describe the force of gravity on planets themselves.

    With all that we know today about gravity, it still remains one of the most bizarre forces we have had to contemplate in physics. The major reason why, is that the gravitational force is the weakest force in the standard model – and this baffles quantum physicists.

    *The standard model is the model physics has used for the last 30 years to describe particles and the forces they mediate, in hope that it will lead to some unified theory of why everything is even here.

    To gain some idea how weak it truly is, the electromagnetic interaction between two particles, is \(10^{44}\) times weaker than the gravitational interaction! This is very, very weak, and so far, only theories like ‘’Supergravity’’ and ‘’String Theory’’ have been proposed as likely candidates to answering this strange paradoxical situation we are left with. These theories attempt to give answers to why gravity may be so weak, but even one of these theories make very little observational predictions, if any at all.

    So the quest to answer gravity completely still seems far away yet.

    What is meant by gravity being a field?

    Gravity is described as being ‘’field of force’’ that permeates every corner of the universe, generated by the mass contained inside the universe. We speak of forces in our equations, because \(1kg\) of mass has a force of about \(9.80N\) of acceleration due to gravity pulling it to the earth.

    We know \(9.80N\) is about correct, because the ‘’weight’’ of a \(1kg\) mass at the North Pole is nearly 9.83N and it weighs about 9.78N at the equator, and even though it might differ slightly depending on where you are on this curved planet, the direction remains radially inward towards the core of the earth.

    To calculate this gravity, you can use Newton’s equation:

    \(\vec{F}_{g}=m_{g}\vec{g}\)

    Where the gravitational force \(\vec{F}_{g}\) is equal to the gravitational mass \(m_{g}\) multiplied by gravity \(\vec{g}\). Now if we divide both sides by \(m\), we get;

    \(\vec{g}= \frac{\vec{F}_{g}}{m_{g}}\)

    which would allow us to calculate the magnitude of the gravitational force on any unit of mass.

    Gravity and Weight

    So far, we have looked at free fall, and how a thing falls to the earth due to an accelerated constant motion due to gravity. Now let’s discover the relationships between gravity and weight.

    Weight is equivalent to the product of gravitational mass and the acceleration due to gravity. So simply put, the equation to derive the weight of something is;

    \(\vec{w}=m \vec{g}\)

    Here we must remember that the weight \(\vec{w}\) is a vector component, because it is a quantity due to force measured in Newton’s. With matter, we usually calculate it in either kilograms \(kg\) or grams \(g\).

    If we deal with a 10 kilogram object on earth, how do we calculate its weight?

    Remember, the gravitational acceleration of the earth is given as 9.8N so if you want to calculate the weight, you need to multiply the acceleration due to gravity by its mass:

    \(mg=w\)
    \(10 x 9.8=98N\)

    So the weight is 98N. Simple eh? If you wanted to find the mass, you can use a little algebra, and work it out… for simplicity, look at the following with the same numerical values, and you will see they will always work out.

    \(w/g=m\)
    \(98/10=9.8kg\)

    And viola! We’ve solved for the mass in kilograms.

    Force and Distance

    When describing force and distance, we often consider projectiles. A projectile is either a fired, thrown or otherwise a propelled motion of an object travelling some path through space and time. The two equations used in physics to describe the motion of a projectile are:

    \(x=v_{OH}\tau\)

    and

    \(y=v_{OH}\tau -\frac{1}{2}gt^{2}\)

    These two equations are called parametric equations, and the symbol \(\tau\) here is the Greek letter Tau, and is used to define the parameter. If we solve for the parameter in either equation and then substitute the results in the other equation, we can totally eliminate the parameter. If we solve for the first equation, we have:

    \(\tau =\frac{x}{v_{OH}}. Using a little algebra, if we now substitute for the [tex]\tau\) in the final equation, we get a long equation:

    \(y=v_{0v} \frac{x}{v_{0H}} -\frac{1}{2}g \frac{x}{v_{0H}}^{2}=\frac{v_{0v}}{v_{0H}}x -\frac{1}{2}g \frac{x}{v_{0H}}^{2}=\frac{v_{0v}}{v_{0H}}x-\frac{g}{2v_0H^{2}}x^{2}\)

    This equation, is called a parabola; and generally while it is a useful equation to use to calculate the trajectory of a projectile, there are other ways usually explained to you in any standard course of physics.

    The idea is, is that gravity affects the motion of a projectile along some path. The gravitation in question that effects the path is perpendicular to the instantaneous velocity and is usually expressed as \(\vec{F}_{g}\)⊥ where the symbol ‘’ ⊥’’means perpendicular, and the components of the force of gravity is parallel to the instantaneous velocity, given by \(\vec{F}_{g||}\), where the sign ‘’||’’ means parallel, as you might have guessed.

    We can easily deduct that a projectile will certainly continue to move along a given trajectory in a straight line, unless acted upon by some external force; we covered this principle in part two, but so long as it did not have \(\vec{F}_{g}\)⊥ acting on it. The expression of \(\vec{F}_{g||}\) however means that the projectile will continue to move along that path and speeding up along its way.

    So ultimately we learn that the gravitational force on the projectile has one component deflecting it into a curved path, while the other entices it to speed up. This, in any standard textbook on physics used in colleges or universities, will be expressed as a smooth parabolic trajectory.

    Part Four

    The Universal Law of Gravitation

    It was an astrologer called Brahe who replaced Copernicus’ own geometric star system, where the sun went round the Earth; he did this by carefully measuring the moving celestial systems, documenting his work as he painstakingly went along.

    Johannes Kepler who lived (1571-1630) was a great fan of Brahe’s work, and with a strong mathematical background, helped to develop a mathematical model. After analyzing his astrological work, he discovered that they followed three simple mathematical laws: They are;

    1) All planets follow an elliptical path with the sun in center of motion.
    2) A line joining the Sun and the planet sweeps out equal area’s
    3) The ratio of the cube of the mean radius to the square of the period of revolution is the same for all planets. He gives the equation \(k=\frac{R^{3}}{T^{2}}\) for his calculations.

    Now, that smart guy, Newton, (the guy we covered detaling the laws of motion), used Keplers insights to create what we call, ‘’Newtons Gravitational Law,’’ or ‘’Newtons Universal Law of Gravitation.’’ He calculated that the paths of planets where not so much elliptical, but rather more circular. He gave:

    \(F=ma=m \frac{4 \pi^{2}R}{T^{2}}\)

    This says that the force of attraction of the sun for a planet is equal to the product of mass of a planet and centripetal acceleration. He used Keplers third law to calculate the force in terms of\(R\) and \(m\) only, \(R\) for radius and \(m\) for mass. He notes the force in the following fasion;

    \(F_{sp}=m_{p}\frac{4\pi^{2}R}{R^{3}{k}}=m_{p}\frac{4\pi^{2}Rk}{R^{2}}\)

    Along the same lines, Newton could calculate the attraction of the earth, for the moon and came along similar expressions. \(k\) is a constant associated with the earth – and that was;

    \(m_{m}\frac{4\pi^{2}k}{R^{3}}\)

    … and he knew instinctively there was some factor of the Earth this applied to. He came to the conclusion that this property was referring to the mass. He arrived at his universal law of gravitation, and no one to this day knows exactly how he arrived at it;

    \(F=\frac{mGM}{R^{2}}\)

    The \(G\) in this equation is for Newtons Gravitational Constant. It has a value of \((6.67)(10^{-11}\frac{N.m^{2}}{kg^{2}}\). And because of glorious math, with the right calculation, you can measure the acceleration due to gravity. For instance, if you wanted to calculate the acceleration of a satellite up at a certain altitude,

    \(W_{sh}=f_{gsh}\)
    \(=m_{s}g_{sh}=\frac{mGM}{R^{2}}\)
    \(g_{sh}=\frac{GM}{R^{2}}\)

    The solution itself says that the accleration due to gravity at any altitude is equal to the universal constant of gravitation times the mass of the earth divided by the square of the distance. This distance is between the centre of the earth and the satallite.

    Let us now do a calculation on the natural satellite of the earth, we call the moon. The moon is about \(3.8 x 10^{8}m\) from the earth, so:

    \(g=\frac{ \frac{((6.67)(10^{-11})}{N.m^2)}(5.98)(10^{24}kg)}{(3.8)(10^{8}m)^{2}}=(2.8)(10^{-3}m/s^{2})\)

    This calculates the centripetal acceleration of the satellite we call the moon. Any time you need to calculate the gravitational acceleration of a thing like a satellite, you can use this equation.

    The Inverse-Square Law of Radiation

    This now brings us to the nature of radiation. Gravity is a type of radiation. Gravity, just like the light that takes 8.3 minutes to reach us from the sun, follow an inverse square law. It’s not too difficult to understand.

    At any point source, which spreads its radiation equally outwards in all directions, will obey an inverse-square law; which only works if the emitted radiation has no limits to its range.

    When we describe the inverse-square law, we usually state that the intensity from the source is given as \(4 \pi GM\), and the value of \(4 \pi r^{2}\) calculates the area of a sphere in question: We deal with sphere’s in these equations, because we often associate the square law with stars that emit radiation, or planets which emit a gravitational radiation.

    The value of intensity \(I\) for a gravitational body, is defined simply as the acceleration due to gravity is an expression of intensity of the gravitational field. The so-called intensity of a sphere at the surface is given as:

    \(I= \frac{4 \pi GM}{4\pi r^{2}}=\frac{GM}{r^2}=g\)

    If we follow the inverse-square law, we find that as \(r_2\), twice the distance from the source, is in fact spread out over four times the area, which would invoke 1/4th of the intensity.

    Of course, this applies to all types of radiation, so even electric force has a inverse-square law \(E=\frac{Q}{4\pi \epsilon_{0}r^{2}\) and even light \(I=\frac{S}{4\pi r^{2}}\). In short all you need to know about the inverse-square law, is that the number of particles (the stuff all matter is made of) per unit of time remains constant, then we can calculate the intensity of illumination of each distance doubled from the source of intensity:

    \(\frac{I_{1}}{I_{2}}=\frac{N}{A_1}{N}{A_2}=\frac{A_2}{A_1}=\frac{4\pi r^{2}_{2}}{4\pi r^{2}_{1}}\)

    Part Five

    Atomic Makeup

    ……..relative mass relative charge
    proton……...1………..+1
    neutron…….1…………0
    electron…1/1836……-1

    And now in part five, we are going to explore the realm of materialistic science. It is very important that anyone should know the basics about the matter they are made of, if they want to pursue a career in physics.

    All of matter consists of tiny subatomic particles, and these particles exist in the hearts of what are called atoms. Atoms themselves make up about 1% of the entire system. The Nucleus, which consists of Nucleons, which are themselves made up of smaller particles called Quarks, make up the nucleus, which takes the lion’s share of 99% of the matter of the atom.

    The atom itself is imagined as sphere, or a shell which is about 10,000 times larger than the nucleus and is uncharged. Electrons do orbit the nucleus in a cloud of probability, however, their mass is usually neglectable. In fact, so neglectable, we don’t actually no how big it really is. All attempts to measure its radius have failed!

    The man who found the existence of the electrons charge, was British physicist J.J. Thomson, who was working on identifying different particles of a ray tube, and found that you can bend the trajectory of the electrons in a magnetic field, which suggested they had electrical charge.

    Despite its immeasurable size, we do have an approximation of about \(\frac{1}{1836}\) of that of a proton. Very small indeed. If we assumed a motionless electron, its rest mass (which is a measure of its inertial mass) is something like \((9.11)(10^{-30})\). These negative signs in this design, are using scientific notation. It’s pretty simple to learn. I’ll leave an introduction to using scientific notation at the end of this part.

    Today, we use Neil’s Bohr’s, who lived (1885-1962), atomic model. He tended to study the periodic table to see if he saw any correspondence between the structure of the atom and the periodically ascending periodic elements. He found that electrons structure themselves as orbitals round nuclei, and also derived the maximal amount of electrons that could orbit a particular nucleus.

    The Nucleons of an atom, are consistently the protons and neutrons. These are tiny subatomic particles, pivotal in the make-up of the nucleus.

    Neutrons, which are a slight give-away of their particular given name, are neutrally-charged. Charge itself, is a fundamental and intrinsic property of all particles. There are various charge entities in quantum mechanics, such as colour charge, which is carried by quarks, which are the tiny particles that make up protons and neutrons. Then there is electric charge, which is usually associated to electrically-charged particles, like electrons and positrons (the antiparticle of the electron). Then there is more complicated types of charge, such as the weak isospin charges of \(SU(2)\) Theory, but let us not get into that.

    The neutron has a neutral charge, whilst the proton has a positive charge. The neutrons mass is only very slightly larger than the protons mass at \(940MeV/c^{2}\). The protons mass is \(938MeV/c^2\). It is said that the proton has one unit of positive electrical charge, \(1.602 176 53(14)(10^{-19})\), and this positive charge is what ‘’attracts’’ the negative electron to the nucleus. So negative and positive charges attract, whilst like charges repel.

    The neutrons arrange themselves in specific way next to protons and electrons. In fact, there needs to be an exact balanced amount of protons and electrons, but an extra count of neutrons is allowed. In the popularly mentioned isotopes, Carbon-12 has 6 protons and 6 neutrons, but its isotope Carbon-14 has 6 protons and 8 neutrons.

    The proton is classed as a 'Baryon', which are always made up of three quarks. The proton has what are called 'two up quarks' and 'one down quark'. The 'neutron' has one up quark and two down quarks - thus it is also a Baryon, and both the neutron and proton are in the family of Hadrons.

    The proton is very strange indeed, because it has a lifetime of \(10^{31}\) years, and this is such a strange lifetime. Some physicists have adopted the idea that the proton is infinitely stable. By ‘’lifetime,’’ we usually mean how long it takes for a particle to decay into another particle. For us to notice a proton decay, it is assumed we would need to wait a very long time.

    In some extreme cases, there can be what is called, ‘’Exotic Nuclei.’’ This is when a certain threshold of neutrons cannot sustain stability in the core of atoms no longer and instead of breaking off the atom entirely, stray neutrons can orbit the nuclei of atoms.

    The nature of neutrons can be seen in even stranger light. Taking into account that the nucleus is about 99% times the mass of the whole atom, could you imagine a star being made of nearly 100% neutron matter? This is where neutron stars come into the picture. These collapsed stars are made up mostly of neutrons and thus extremely heavy in weight.

    The more space a neutron has between another neutron as you can guess measures their density. Density as a mathematical equation is derived as \(D=\frac{m}{v}\). Because the density of neutron star is amazing, that the size of a star would weigh thousands upon thousands of times heavier than earth - a spoonful of neutron pulp would weigh as much as a mountain! This has led physicists to contemplate new and exciting ideas, like entire 'quark stars.'

    Quarks

    All protons and neutrons, including other subatomic particles, are themselves made up of elementary particles, called 'quarks'. There can only ever be, according to theory, a maximum of three quarks to any proton or neutron - this is because quarks themselves are made up of 'colours.' Individual quarks have specific colours, called 'strange,' 'charmed', 'up', 'down', 'top' and 'bottom' - but when three quarks come together, they are colourless. These are paradoxically the colourless objects that make up all of nature. Quarks are quite large subatomic particles - it even has more mass than the nucleus it makes up, and the missing mass is turned into gluon energy, to hold it all together. A little more on gluons next.

    However, there was an experiment conducted a few years ago in Russia 1997, by Maxim Polyakov and Victor Petrov at Petersburg Nuclear Physics Institute, that seemed to indicate the existence of a particle that was made up of five quarks. The hypothetical particle came to be called the 'Pentaquark,' for obvious reasons. For reasons of experimentation, the results are conspicuous and under heavy controversy.

    Gluon Energy

    It was believed for a while that gravitational forces between particles where extremely weak. In fact, gravitational interactions between particles are at least thirty orders of magnitude (that is \(1/1,000,000,000,000,000,000,000,000,000,000\)) smaller than the weak interaction. It was then considered that gravitational effects can be ignored in particle physics processes involving small numbers of particles, but a large collection of particles, something as large as \(10^27\) particles cannot be ignored, which is about the same amount of particles that make up the brain.

    So you can imagine, that gravity is not strong enough to hold a very small collection of particles together, so something else must be holding the quarks together, those fundamental pieces of matter that make up the nucleons…

    Well, quarks are considerably heavier than the atomic nucleus, and when they come together, like the three quarks that make up Baryons, they give up a small amount of mass (this is due to the equation \(E=Mc^{2}\), which will be talked about in the last part). The ‘’missing mass’’ is actually turned into a type of energy particle called ‘’gluons.’’

    Gluons help to bind quarks together, which ultimately are responsible for the creation of binding the nucleus together. This elementary force holds all quarks together, and help to create a stable atom, and atoms, and molecules, so that everything you see about you today is possible to nature.

    Spin

    Talking about intrinsic properties, like the one we just covered (charge), what exactly is an intrinsic property?

    My definition of an intrinsic property, is something part of a particle that cannot be removed, and is a fundamental attribute of the constituents they make up. And in many cases, an intrinsic property like ‘’spin’’ has no explanation, and is just taken for granted most of the time.

    Spin, no longer in physics can be envisioned as something spinning on an axis. Spin cannot be seen like the spin of a planet, which is what classical physics defines it as. The reason why, comes about because of a fundamental flaw in understanding.

    The electron exists in a family called ‘’Fermions’’. But in effect, the electron cannot have a radius that can be measured – so far, all we can tell about the electron is that it is a point particle (zero dimensions to its body).

    Now suppose we take the spin of the electron, manipulate it, so that it will rotate \(360\) degrees and brought finally back to orientation. Now, you would think that the \(360\) degree spin forward, would be the same as the common unrotated electron, because \(360\) degrees means a full circle. But it turned out that only atoms with a multiple integer of \(\frac{h}{2 \pi}\) (h is for Plancks Constant \(6.626 x 10^-33\) Joule sec) will be able to arrive at the same location. This is quantized angular momentum. However, the results for all 1/2-spin particles ''fermions,'' would need to move another \(360^2\) degrees just to arrive at the same location. This obviously goes for all fermions... protons... neutrons ect.

    This means there is an obvious problem in how we used to define spin. For an electron to have a classical spin, it is then said, the electron would need to spin faster than light.

    So now, spin is simply defined as an angular momentum, without the problems of any classical physics getting in the way.

    Pauli’s Exclusionary Principle

    Then there is Pauli's exclusion principle - a cornerstone of physics. The principle of exclusion was in fact a way to explain fundamental interactions between real and virtual electrons whilst constrained within the atom, and explained why the positive matter simply doesn't just sink back into the Dirac vacuum. The principle is quite true, if let's say, two electrons are close to each other. In that case, the particles must cancel each other out, and to achieve this, they must have unique characteristics. For instance, electron 1 cannot fall into a lower state of energy, if electron 2 also has the same state, unless both particles have opposite spins. All matter cuts everything down in this strange manner.

    Note however, that Pauli's Exclusion Principle, or also known as 'Fermi-Dirac Statistics' only abide to Fermions. However, if we are dealing with Boson particles, like a photon, a photon tend to fall into the same quantum states. This is also called the 'Bose-Einstein Statistics'. It is because of such equations, lasers work the way they do, and predicts photon behaviour quite admirably. Thus, photons can settle quite easily among each other, not worried about each others positions, though, electrons, as a Fermion particle example, must all cancel each other out due to Exclusion.

    Now, the principle of exclusion can be looked upon as being very important in fundamental coherence between other fundamental objects. And, of course, there is Heisenberg’s principle of indeterminism, or uncertainty. Not only do the fundamental particles need to cancel each other out, but they must do so in complete uncertainty about each other, and about themselves. Thus, good relationships can be made out of the uncertain. Pauli's exclusion principle and Heisenberg’s uncertainty principle govern fundamental interactions, and makes it possible for everything to have a bit of order.

    All the particles called Fermions, such as the nucleons (neutrons and protons) and even the point like electrons, must obey to Wolfgang Pauli’s Exclusion Principle. This means that the Fermions inside the atom cannot be in the same quantum energy states. To exclude this property, they must cancel each other out.

    An electron unless disturbed in some subtle way (more on this soon) will have both a spin up \((s,z=1/2)\) and a spin down \((s,z=-1/2)\) simultaneously because it is governed by the wave of probabilities. But when two electrons come together, one must have either an up spin or a down spin. They can have the same spin, but they must have a different energy level.

    Observables

    Inside the atom, we have the protons, neutrons and electrons. The basic building blocks of all matter, have what are called ‘’observables’’. Observables turn out to the Eigenstate that remains after some observation quality can be drawn from it.

    An Eigenstate is one of the many possible states that a system can be found in, upon a phenomena called the collapse of the wave function (more on this later). Without going into the collapse with great detail, all that need to be known right now, is that individual systems, like particles, have all their states (such as spin, location and size) all smeared together. Is someone was to come along and disturb these smear of Eigenstates, then a certain observables will literally ‘’pop’’ into reality as the only properties of that system; they are properties called observables. Spin is an observable, and so is its mass, location.

    Atoms and Isotopes

    And so, we find that the quarks that make up protons and neutrons, the protons and neutrons themselves make up individual atoms. These atoms are described as being like a shell. They can absorb and emit energy, through angular momentum (which we have covered), but from time to time, you might hear about isotopes of atoms.

    So what is an isotope?

    It is relatively easy to understand. In an atom, you will always find the same amount of protons as you will electrons. This is why they are said to have a neutral net charge (‘’net charge’’ just means all the charges in question). We call this the atomic number.

    On the periodic table, you will notice that each and every element has its own unique atomic number; with hydrogen being the first. Usually we class hydrogen as a unique element on its own, and treat it as its own family. So hydrogen has one proton, and if it had two protons, it would be helium, a natural gas that is produced by the Sun, and the same gas you find in children’s balloons.

    But, as you might remember from earlier, neutrons can vary. If the neutron varies, but the chemical properties remains, then all that has changed is the mass, and this is the meaning of isotopes: Atoms of the same chemical properties which have only changed in mass content.

    There are actually three natural types of hydrogen isotopes. Hydrogen \(H^{1}\), Deuterium \(H^2\) and Tritium \(H^3\). \(H^1\) is the most abundant element in the universe at about 99%. Because Hydrogen has only one proton, is has been called by physicists, ‘’protium.’’

    Deuterium is a stable isotope which consists of one proton and one neutron, whilst Tritium consists of one proton and two neutrons, and is radioactive. Chemical properties are determined by the electrons. Electrons remember, are those particles with such a tiny mass we can ignore their mass altogether.

    Covalent Bonds

    Some people find it interesting to see the implications of physics jargon in topics covered by chemistry. Covalent bonds are the sharing of electrons, simply put, between two atoms. But there’s more to it.

    An atom shares energy through what is called ‘’Angular Momentum.’’

    Covalent bonding includes many types of interactions, such as gas bonding, metallic bonding, and strong gas bonding. Covalent bonding comes in two main types. The type that can bind with same element, or not. They form diatomic molecules, such as \(H_{2}\), \(O_2\) and \(NO\). The last being nitrogen monoxide. Their ability to be diverse in interaction is named by having electronegativity.

    The energy (namely electrons) of atoms are thus shared due to their angular momentum, is given as \(L=rXp\), where \(L\) is the angular momentum, \(X\) is the cross product, and \(r\) is the position and finally \(p\) is for linear momentum.

    Considering an atom, going from \(t_1\) to \(t_2\), in a time of \(0<t<r<c\), energy can be exchanged with the angular momentum of the object. The ability to do so, allows electrons to be shared, and sometimes lost to another atom, and this creates the complex systems of molecules.

    If you try and speed an electron up, there is an electromagnetic inertia. It turns out that an electron will emit particles of light, and accelerating an electron would permit it to radiate more energy. It was Richard Feynman who first called it ‘’electromagnetic inertia.’’

    Types of Matter

    Today, we know something like 410 particles. These particles can make up four types of known matter forms: They are gas, liquid, solid and plasma*. Though plasma is never really considered in college chemistry, it is a form of matter considered quite different to other forms of matter. It is an ionized gas, and is therefore considered by some as the fourth state of matter.

    In fact, we are often taught to think of gas, when the universe began. Either as a gas of photons, or a gas of quarks, everything began from a gas of particles one way or another. In a sense, you could say that fluids and solids are created from dense gas clouds.

    * This is traditionally speaking. It could be argued that there is some other forms.

    Wave-Particle Duality of Matter

    Subatomic matter behaves very differently to larger masses. One example of this estranged behaviour is called the 'double slit experiment' introduced by physicist Thomas Young in 1805. This experiment consists of a machine that shoots a beam of photons, electrons or even atoms towards film screen - but before the particles reach the screen and leaves tiny marks, it needs to pass through either an upper slit, or a lower slit that are closely separated. Each slit can be closed, or both can be left opened by the choice of the observer.

    Now, when the beam of particles hit the screen, you would suppose the particles had to pass through either the upper slit or the lower slit, yes? However, the strange thing is, is that if you close down one of slits, more particles reach the screen than if you left both slits open! How can this be? You would imagine more particles reaching the screen if both slits were opened - but this is not the case.

    One strange answer came about. The particle wasn't a pointlike particle at all. It acted as though it were a wave! If one uses the wave description, the problem seemed to go away. We know how waves act in the sea, and this also means that the particle will take these attributes on board.

    A wave could reach both slits at the same time - and just like a wave coming into contact with two openings, the wave can split into two smaller waves, one, as i am sure you can guess, in each slit. If the two waves travel different paths, they can be made to interfere with themselves after passing the slits; in doing so, less waves reach the screen. If one slit is only open, the wave will travel through the slit, and, just like a wave hitting the shore, it will hit many places simultaneously on the screen - thus hitting more places with one slit open, than having both slits open.

    However, the particle wasn't only just a wave - after all, when it hit the screen, it left a tiny 'pointlike' mark. Somehow when the wave hit the screen, it hit many places on the screen as dots. Thus, a new description had to made for a particle that travelled through space as a wave, and finishes its journey as a single object - this description has been come to be called the 'wave-particle duality.' The particle therego was in fact a wave and a particle simultaneously.

    Why did the particle act as a wave?

    Well, at first, physicists thought that the wave was a product of the human mind - it wasn't real, and it was just a means for us to keep track of experiments. The wave became to be called the 'quantum wave function.' This was a wave of possibilities. The wave probability enables us to calculate the possibility for a particle and its path, location, spin, orbital reference, ect. The wave spreads out over space, and resembles likelihoods, not actualities... However, another theory came about called Parallel Universe Theory, which did treat them as actualities, but let’s not delve into this.

    It seemed that all of matter existed in some kind of ghostly superpositioning (more on superposition theory later), where one potential attribute was no more probable than another. It held that the spin states of Fermions where simultaneous before any resolution was made on a particle, so that even a single electron could have both a spin up and a spin down at the same time.

    The electron, with a position, momentum and energy is totally described by the state vector, given as |Ø>. Although, the rule of complimentarity (see reference guide) ruled itself by the uncertainty principle (see reference guide) forbids us ever knowing everything about the mathematics behind |Ø>. Though, potentially, anything you want to know is behind that variable. The state/wave vector spreads out over spacetime. It can potentially and theoretically calculate the wave vector of entire galaxies and even the universe itself.

    So, a particle or a wave?

    Asking whether a particle is pointlike or a wave, is in itself an inconsistency, because with all knowledge on particle nature today, we cannot say it is absolutely one and not the other. Somehow, we must deal with the wave-particle duality, and not just a wave or a particle.

    You might think that when one speaks of a wave function of a system, it applies to subatomic particles only; but this is not the case. It turns out that quantum mechanics does deal with a wave property of macroscopic objects as well, but we can’t observe these wavelengths, because they are far too small.

    In the nineteenth century Thomas Young showed that light acted like waves, by passing them through the double slit experiment; but the steady nature of light was about to take a turn around.

    It was Albert Einstein’s analysis of the photoelectric effect that showed that photons also contained particle-like properties. In the photoelectric effect if you shoot a wave of particles at the surface of a metal plate, particles of electrons would be emitted from the source of contact.

    Einstein showed that the electrons are receiving energy from the electromagnetic field, but could only do so if it was in discrete packets of light, he called them quanta. Because \(E=hf\), only photons of a high wave length could knock one of these electrons out of the plate.

    Of course, not just light had a wavelike property, as a famous French physicist called Louis-Victor de Broglie showed. Now called the de Broglie hypothesis, he related the wavelength \(\lambda\) with momentum \(p\) and Planck’s constant \(h\), claiming that all matter had a wavelike property:

    \(\lambda = \frac{h}{p}\)

    To settle this, it is very safe to say particles have pointlike properties as well as wavelike properties. When the wavelike nature of matter diminishes, it is called the collapse of the wave function. This can happen a number of ways.

    A simple observation from the scientist can collapse the wave function in all matter. This is called the observer effect of quantum mechanics, and is a real thing. There is also a natural collapse, called quantum decoherence which was witnessed for the first time in 1996 by a French physicist called Alain Aspect. One way to explain decoherence is by saying that the environment does in fact alter the wave states of matter and can collapse them into a single state.

    Superpositioning

    Remember when I was explaining how observables ‘’those tiny observable attributes of particles’’ where all smeared together into a messy state of possibilities? Well, a thing can be in a dizzy state called ‘’superpositioning’’.

    Because the wave function of matter spreads the particles throughout space and time, certain particles can exist in more than one place at one time! It can also have two spin states simultaneously and even more than one path through spacetime!! This is because, before any resolution is made, such as a collapse in the wave function, quantum states, or observables are said to be in a state of quantum superpositioning.

    If we could imagine for a second, the electron as a quantum coin, it would have a spin up or a spin down, analogous to any coin with face up and face down. A quantum coin will have both a spin up and a spin down before any measurement can pull it out of its superpositioned state.

    Take the gluon charge again. If the gluon is not disturbed in any way, as to break it out of its superpositioning, its superpositioning between two colours can be expressed mathematically;

    \(\frac{r \bar{b}+\bar{b}r}{\sqrt{2}}\)

    This is read as "red-antiblue plus blue-antired." (The factor of the square root of two is required for renormalization.

    In order to bring about the collapse of the wave function, we find that the probability density of finding the particle in either a state red-antiblue or blue-antired, is found by the absolute square of the wave function;

    \(\int_{\Omega} |\psi \psi|^2= 1\)

    And upon a collapse, a thing as phantom-like as the wave function, can condense to become ‘’real’’ in every sense. In fact, it is generally considered that the wave function represents a state of potential reality, whilst the collapse indicates that a real reality has been born.

    Let’s take another example. Let’s say to find a particle in either position A or B, we can state:

    \(|\psi>=0.50i|A>+0.50|B>\)

    Where it is \(0.50%\) to find the particle in either position A or position B. To find its superpositioned path along the same lines, we can say;

    \(|\psi>_{1,2}=|\theta>_{1}|\Phi>_{2}=\alpha|\theta>_{1}+\beta|\Phi>_{2}\)

    Both these equations can describe path and position, but an interesting situation can arise in quantum mechanics, if one tried to know both the path and location of a subatomic particle.

    There is a variable amount of uncertainty in the subatomic world. Without getting into it too deeply, it says that we can never know two observables of a quantum particle at simultaneous times. So a strange thing occurs if you try to locate the path and position of a particle.

    Since both the path and location are observables, what would happen if we knew one of them with total certainty? Well, it turns out, that if we knew with total certainty let’s say it path, then a superpositioning of an infinite amount of positions are then given to the system. If you want to know the position of the particle, with the added knowledge you now have of its path, then you have to be willing to observe an infinite amount of positions.
     
    Last edited: Oct 19, 2008
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  3. Reiku Banned Banned

    Messages:
    11,238
    Oh the tex is wrong. I'll sort that out. There's also more, put i'm only posting this for now.
     
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  5. camilus the villain with x-ray glasses Registered Senior Member

    Messages:
    895
    I'll take care of the bold part.

    Momentum is:

    \(p = mv\)

    differentiate:

    \(\frac{d(p)}{dt}=m \frac{dv}{dt}\)

    now recall that \(v = \frac{ds}{dt}\), where s is position, or x. So if you differentiate s again, you get \(a = {d \over dt}[\frac{dv}{dt}]=\frac{d^2v}{dt^2}\)

    So

    \( \frac{dp}{dt}=m {d \over dt}[\frac{dv}{dt}]=m\frac{d^2v}{dt^2} = ma\)

    then

    \(F=\frac{d}{dt}(p)\)

    -=-=-=-=-==-=-=-=-=-=-=-=-=-=-=-

    Now a side note:

    Within Newton's Second Law can be derived the Conservation of Linear Momentum.

    Just imagine two particles with masses \(m_1\) and \(m_2\), and velocities \(u_1\) and \(u_2\), where u is the initial velocity and v the final velocity.

    Since \(p_{1i} = m_1u_1\) and \(p_{2f} = m_2v_2\), and \(p_{2i} = m_2u_2\) and \(p_{2f} = m_2v_2\)

    Conservation of Linear Momentum:

    \(P = p_1 + p_2\)

    Differentiate both sides and:

    \(\frac{dP}{dt} = {d \over dt}(p_1 + p_2)\) which equals \({d \over dt}(p_1 + p_2) = {dp_1 \over dt} + {dp_2 \over dt}\)

    \( = {dp_1 \over dt} + {dp_2 \over dt} = {d \over dt}(m_1v_1) + {d \over dt}(m_2v_2)\)

    \(\frac{dP}{dt} = F_1 + F_2\)

    The internal forces cancel out and Newton's Second Law takes the form:

    \(F_{ext} = \frac{dP}{dt}\)

    So if \(F_{ext} = 0\), then \(P = \Sigma p = \text {constant}\) and can be generalized to as many particles as you want so that \(P_n = p_1 + p_2 + p_3 + \dots\)

    So in conclusion:

    So if \(F_{ext} = 0\), then \(P = \Sigma p_n = \text {constant}\)
     
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  7. AlphaNumeric Fully ionized Registered Senior Member

    Messages:
    6,702
    Going from explaining to someone how to use F=ma to get the motion of an accelerating object through to trying to explain the mathematics of quantum mechanics is pointless. You skip so much, in terms of qualitative and quantitative, material that to someone whose never seen F=ma it's pointless talking about complex rigged Hilbert spaces.

    Not only that, but your expressions for the quantum mechanical results are partly incorrect (learn the difference between amplitude and probability!) and don't think I don't recognise \(\int_{\Omega}|\psi|^{2}=1\) from the many times I've explained to you that normalisation is not that \(|\psi|^{2}=1\) but \(\int_{\Omega}|\psi|^{2}=1\) where \(\Omega\) is ..... go on, tell me

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    So just how much of all this stuff is from 'college' then? Given you don't learn Dirac notation till 2nd or 3rd year of a physics degree, you're lying about it being something you've covered. The fact you don't realise that the colour charge of the strong nuclear force is actually more complicated than the charge of the weak nuclear force shows you've studied neither. This harkens back to those pesky things 'gauge groups', which you many a time on PhysOrg tried to pretend you knew about.

    Electromagnetic charge arises from a u(1) values gauge potential. Electroweak from su(2). Colour from su(3). Then there's things like so(3,1) for spin connections in space-time.

    And your equation for the distance a particle under acceleration with an initial velocity is valid in any units. It's just that homeworks are usually in SI units now. You can work in units of velocity of feet per fortnight, provided you're consistent.

    A tutorial is about picking a subject and explaining it in depth. You've just skimmed through a long list of topics, hardly explained them, sometimes getting concepts and even equations wrong and so it seems to have achieved little.

    Why not let someone nominate a particular topic from the many topics in your first post and then write a proper tutorial for it? For instance, explaining to people how to go about solving projectile motion problems or how to take into account air resistance for falling objects? Rather than starting with an explaination of what 'velocity' is and within a single post gotten to colour indices on gluons and Hilbert spaces. Doing so just means you miss out so much the 'tutorial' is of little value. A read of Wikipedia on a particular topic is more illuminating and more likely to be correct.
     
  8. Vkothii Banned Banned

    Messages:
    3,674
    A "helpful hint":

    Substitute the idea of 'calculating' the square of the amplitude, with 'measuring' it, and there we are.
     
  9. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

    Messages:
    8,967
    Reiku---why are you doing this? Are you trying to prove something?

    Either way:

    This equation is incorrect. The left hand side is a vector, the right hand side is a scalar quantity.

    Again, you should keep clear the difference between vectors and scalars. Acceleration is a vector.

    No. You can find that \(v_f^2-v_o^2 = 2a\Delta x\)

    I don't quite know what you're trying to achieve here...this is a huge leap from velocities and such. You might want to take a smaller leap here. As it stands, this "tutorial" is not very much of a tutorial---that is, someone who could learn something from part one has no chance of learning anything from part two.

    No. This is wrong. There is no movement at zero temperature, as this is one of the ways temperature is defined. It is not possible, however, to reach zero temperature.

    Source? This is wrong, I think.

    I'm not an editor, so I won't bother correcting the (bad) grammar, but what the fuck is a protino?

    Grammar, again. Were mass, inertia, and forces different in the 1600's?

    And, for the record, Principia was a book.

    Now you're on to calculus? You should really pick an audience and stick to it. You're not tutoring me, or anyone else who visits this forum, I think.

    So I have to ask again---what are you trying to prove?

    Galileo died in 1642.

    I won't bother listing a long line of physicists who came before Galileo, but here are a few:
    Copernicus
    Prolemy
    Ibn al-Haytham
    I'm sure I can find more.
    I don't understand---"larger acceleration would obviously increase"? Does this mean that larger accelerations are larger numbers?

    Wrong. Newton had no idea about gravitational radiation.

    Umm...relevance? Newton had no idea about gravitons.

    No, he had it incomplete---there is a difference.

    No. This is completely wrong.

    No. This is wrong. Gravity is misunderstood not because it is the weakest force, but for entirely different reasons.

    Non-sequitir? This makes absolutely no sense.

    This must be qualified. This is only correct on Earth.

    This probably should have been at the top of your tutorial.
    Shouldn't you put this in the section where you discuss projectile motion?

    \(y=v_{0v} \frac{x}{v_{0H}} -\frac{1}{2}g \frac{x}{v_{0H}}^{2}=\frac{v_{0v}}{v_{0H}}x -\frac{1}{2}g \frac{x}{v_{0H}}^{2}=\frac{v_{0v}}{v_{0H}}x-\frac{g}{2v_0H^{2}}x^{2}\)

    Is this correct? I don't think so. What's H?

    Speaking from experience?

    No. This is wrong.

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    uke: :roflmao:

    Now we're on to gravitational radiation?

    I think you need to re-evaluate your outline here.
    What if we're dealing with electromagnetic radiation?

    How can a sphere have intensity? Do you mean the intensity of the radiation across the surface of the sphere?

    What??? Now you're claiming that matter is made of gravitons?

    The logical next step...

    What system? Atoms make up 1% of...atoms?

    You may want to explain what this means...

    Again, this doesn't follow. What are we measuring the radius of, the atom? The electron? How does the fact that the electron's mass is negligible, when doing atomic calculations, have anything to do with the fact that it's radius hasn't been measured?

    In fact, the mass of the electron is one of the best measured numbers in all of physics.

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    uke:

    You just mentioned the electron's mass in kg, but now you're using amu? You might want to pick a unit and stick with it.

    This is wrong.

    Source? I was under the impression that the proton's lifetime was not known.

    I've never met a physicist who thinks this. The proton can decay via graviton emission, at the least.

    Or just look at

    I'm pretty sure that this is wrong. A free neutron decays in like 10 minutes. Do you have a reference for this?

    What about electrons?

    Why is this paradoxical?

    No. They are point-like.

    How is this possible? You just told me that a proton weighs about 980 MeV, but
    looking up the mass of an up quark, I see 5 MeV. Last time I checked, 5 < 980. Right?

    Care to explain?

    No. This is about the number of particles that make up the human body.

    Again, this is wrong.

    Do you want me to explain spin to you?

    I just can't do it anymore. I don't even think I'm half way though.

    But I will say that this cannot stay in this forum. You've done a lot of work, but there are many conceptual errors and many things that are just outright wrong.

    Sorry Reiku. This can't stay here.
     
    Last edited: Oct 19, 2008
  10. Vkothii Banned Banned

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    3,674
    The model needs a few tweaks?
    The odd mathematical detail.
     
  11. funkstar ratsknuf Valued Senior Member

    Messages:
    1,390
    Without going into all the other rubbish here, this is so very telling. That's the sort of explanation you would give a high school student or a layman.

    Oh, and "The arrows at the top of the letters (one for both the vector symbols of displacement and velocity), are the direction of velocity in question."?

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    Surely you aren't being serious?
     
  12. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

    Messages:
    8,967
    It is very confusing---it's almost as if he has no idea of his audience.
     
  13. Stryder Keeper of "good" ideas. Valued Senior Member

    Messages:
    13,105
    There is also the very small point that it lacks Citations or References. In honesty if a person writes a paper that is suppose to be even remotely Academically related they will look at perhaps using the Harvard Citation method. You can find numerous versions of this out there on University websites, i.e. Leeds Metropolitan University

    Citation and Reference is very handy because for one it proves the person writing has read some literature, it provides a clue to their sources so should they get a date wrong or something else fundamentally messed up, others can look to see where and how the error occurred.

    Without Citation and Referencing there is no telling the amount of Plagiarism that can occur and obviously that is a major sin in regards to Academia.
     
  14. camilus the villain with x-ray glasses Registered Senior Member

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    895
    ,

    Damn, shit Reiku, you wasted thse fuck out of my time. Thanks a fuckin lot. Like Ben said, go back to community college...

     
  15. AlphaNumeric Fully ionized Registered Senior Member

    Messages:
    6,702
    I'm reminded, in the most tenuous of ways, of 'Road to Reality'. Penrose bills it as a book which is accessible to people who have only basic knowledge of fractions and he'll do the rest for you. By page 200 he's on multivariable calculus and fibre bundles and by page 500 it's spin connections on spinors in curved space-time and g-valued gauge potentials! At least Penrose writes a coherent, indepth, mathematically correct door stop (which for £10 is/was worth buying even if it's practically unfinishable), Reiku has tried to cover much of the spectrum of discussion you'll find on physics forums, from introduction to Newtonian mechanics through to the discussion a few of us have about gauge potentials in QFT. Unfortunately, he's tried to be a jack of all trades and has mastered none, in neither his own understanding or his ability to explain these concepts to others. After all, the test of your understanding of a topic is precisely your ability to explain them to others. My understanding of particular section of QFT and GR has improved since posting on PhysOrg or here, because I've been forced to think about questions I have otherwised passed by. Unfortunately Reiku hasn't covered many of the topics he tries to talk about and so his understanding comes from pop science books, posts people like Ben and myself have made and his imagination.

    If he wants to pick a specific topic, I still nominate 'curvature'.
     
  16. Reiku Banned Banned

    Messages:
    11,238
    I will fix the mistakes. I am not going to get into an arguement about where this has been placed. It's absolutely pointless. Arguing won't get it anywhere.

    Alphanumeric, i'll get to you soon.

    Vkothii... a few mistakes mind you. But yes, i would have thought could have been tweaked up, but hardly psuedoscience of the natural degree.

    Ben, get to you soon.

    Camilus, then don't involve yourself. Don't blame me for your own actions of joining in.
     
  17. Reiku Banned Banned

    Messages:
    11,238


    ''why are you doing this? Are you trying to prove something?''

    No not at all. I told you, i had already created it, and i found it a shame for it to be waisted.

    ''This equation is incorrect. The left hand side is a vector, the right hand side is a scalar quantity.''

    No its not. \(d_i\) is for displacement. Both coexist.

    ''Again, you should keep clear the difference between vectors and scalars. Acceleration is a vector.''

    The equation is correct though.

    No. You can find that \(v_f^2-v_o^2 = 2a\Delta x\)

    Why not?

    ''I don't quite know what you're trying to achieve here...this is a huge leap from velocities and such. You might want to take a smaller leap here. As it stands, this "tutorial" is not very much of a tutorial---that is, someone who could learn something from part one has no chance of learning anything from part two.''

    I did not design this particularily so that parts coincided. I did a bit, trying to clump gravitation and gravitational laws, but in effect, i wanted each part unique in its own sense.

    I am the creator of it, i should be allowed to see how its presentation is fit no? To a degree at least?

    ''No. This is wrong. There is no movement at zero temperature, as this is one of the ways temperature is defined. It is not possible, however, to reach zero temperature.''

    Communication perhaps? A bit of semantics? When we talk about freezing something down to a zero temperature, most layman imagine something to be completely frozen, totally immobile. I am saying here that its not.

    ''I'm not an editor, so I won't bother correcting the (bad) grammar, but what the fuck is a protino?''

    That's my silly terminology coming out describing protons. I've done it for years, and i've said it without realizing. Sorry.

    ''Wrong. Newton had no idea about gravitational radiation.''

    I thought he did introduce the square law of gravity?

    ''Umm...relevance? Newton had no idea about gravitons.''

    True. Newton did not have a physical carrier of the gravitational force. But i never say in the tutorial he did?

    ''No, he had it incomplete---there is a difference.''

    He did have it wrong. He attributed the force of gravity to the work of God. We now believe their is some mediator of the force. So yes, he was wrong.

    ''No. This is wrong. Gravity is misunderstood not because it is the weakest force, but for entirely different reasons.''

    I disagree. I would say that gravity is misunderstood because it is weak. The fact it is so weak, is a hint of breakdown in our fundamental understandings.

    Hold on.
     
  18. Reiku Banned Banned

    Messages:
    11,238
    Right so far, in my opinion, the only mistakes i have made are purely what is called historical knowledge. You've said two equations where wrong, but i know it was down to what you where reading the symbols as.

    Anyway, let's go on.

    ''Grammar, again. Were mass, inertia, and forces different in the 1600's?

    And, for the record, Principia was a book.''

    I know principia is a book. And i don't understand your question.

    ''What system? Atoms make up 1% of...atoms?''

    Atoms make up (the shell), 1% of the mass of the entire entity.

    ''Again, this doesn't follow. What are we measuring the radius of, the atom? The electron? How does the fact that the electron's mass is negligible, when doing atomic calculations, have anything to do with the fact that it's radius hasn't been measured?''

    In quantum chemistry, we are told to ignore the mass of the electron in a model of the atom, because it is so small. Surely you knew this?

    ''In fact, the mass of the electron is one of the best measured numbers in all of physics.''

    No its not. Do you remember the papers Vern directed you to, showing that all attempts to even measure a radius has failed? If we can't measure the radius, we cannot make a completely accurate number of its mass. In fact, I don't even think all scientists agree whether it truely is a poinlike entity.

    ''Galileo died in 1642.''

    I apologize. Real mistake. And so what if i use a tiny ounce of calculus? It was just to quickly show how Newton derived his idea's.

    ''This must be qualified. This is only correct on Earth.''

    And its Earth i am talking about. You really did just nit-pick at little things for an excuse.

    '' Shouldn't you put this in the section where you discuss projectile motion? ''

    I hadn't properly decided.

    ''No. This is wrong. ''

    Show me. Because i am positive it is right.

    ''You just mentioned the electron's mass in kg, but now you're using amu? You might want to pick a unit and stick with it.''

    Point taken.

    ''What if we're dealing with electromagnetic radiation?''

    I've explained this in the tutorial.

    ''What??? Now you're claiming that matter is made of gravitons?''

    I never said this. Gravitons are exchanged between particles, and they are a form of radiation. I never said what you said. I'm seriously going to James about this evaluation, because i know fine right what i said is true, and you are putting words into my mouth.

    ''Source? I was under the impression that the proton's lifetime was not known.''

    It truely isn't known, but Hawking as well as other scientists have put a limit of 10^31 years on it.

    ''I'm pretty sure that this is wrong. A free neutron decays in like 10 minutes. Do you have a reference for this?''

    I'll find one... i haven't looked through them, but here is some that look like possible links.

    Exotic Nuclei - the Key to Our Universe
    Warning: Unsolicited Emails
    Webpage of the Gesellschaft für Schwerionenforschung mbH, GSI ... nucleus also form filled shells that lead to particularly stable nuclei - the magic nuclei. ...
    www.gsi.de/portrait/Broschueren/Wunderland/04_e.html - Cached
    Structure of Exotic Nuclei - Forschungszentrum Dresden-Rossendorf, FZD
    ... Radiation Physics > Divisions > Nuclear Physics > Structure of Exotic Nuclei ... excitation of Exotic Nuclei in the field of a heavy target nucleus or transfer ...
    www.fzd.de/pls/rois/Cms?pNid=313 - Cached
    Exotic nuclei
    Scientists take giant step forward in understanding exotic nuclei ... Exotic oxygen nucleus. Definition for the kilogram. Quantum physics and computers ...
    www.theallineed.com/math/07091302.htm - Cached
    EXOTIC NUCLEI
    EXOTIC NUCLEI. EXON-2001. Proceedings of the International Symposium ... The talks were given by the leading scientists in the physics of exotic nuclei. ...
    www.worldscibooks.com/physics/4989.html - Cached
    Exotic nuclei: why and how to make them?
    Fig 5 To produce exotic nuclei and to make beams of them, two ... the selection, so that only the exotic nucleus of interest is sent to the experiment room. ...
    www.europhysicsnews.com/full/28/article3/article3.html - Cached

    ''What about electrons?''

    That is why i said;

    '' All protons and neutrons, including other subatomic particles, are themselves made up of elementary particles, called 'quarks'. ”

    Ben you are just at it aren't you?

    I'm going to leave it there. About the quarks, i've been taught different. That's how gluon energy is created; the superfluous mass of the quarks is turned into energy to bind them together.
     
    Last edited: Oct 20, 2008
  19. Reiku Banned Banned

    Messages:
    11,238

    I was going to provide references at the end.

    Funkstar

    If its like any of the so-called mistakes Ben pointed out, then don't bother.
     
  20. Oli Heute der Enteteich... Registered Senior Member

    Messages:
    11,888
    Shotguns don't fire bullets.

    No he didn't.

    Viola? Or cello?

    Geometric star system? GEOMETRIC??!!

    The essence of clear writing is concision, precision and unambiguity.
    So far you've failed to master any one of these.
    As usual.
     
  21. Stryder Keeper of "good" ideas. Valued Senior Member

    Messages:
    13,105
    I'm sure most writers (I can't of course be sure of those that do write dissertations) tend to start with a "Skeleton". When they write a book they don't just start clicking away on a keyboard or typewriter not knowing the destination they intend to arrive, instead they will draw up a very simplified plan of where they are going. Perhaps they will have a Chapter title and a brief paragraph attempting to explain what they intend to do in that chapter.

    They will then go about filling out their book, chapter by chapter. Again if they amend the storyline, they will change that skeleton to show where they are going. Some more indepth writers will even go as far as to write entity tables for the players in their story, in your case that's the Citation and Referencing.

    Since the story when being bolstered with additional thoughts means those entities increase with information to generate a "real" character as opposed to something two dimensional. Those Entity tables are in a location where they are constantly updated, to mark those facts that change about the character.

    In the instance of Citation and Referencing I would suggest doing something similar, so: you have the section for referencing already as you being and as you update you add to it. This way you aren't leaving it to last, it doesn't get left out.
     
  22. Reiku Banned Banned

    Messages:
    11,238
    What does a shotgun shoot then? Pellets?

    And yes, it is of some debate as to whether he did drop balls off the Eifell tower. Did i not make that point?

    Also, a geometric star system is opposed to non-geometric star system: one that follows geometrical paths.

    ''The essence of clear writing is concision, precision and unambiguity.
    So far you've failed to master any one of these.''

    Piss off.
     
  23. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

    Messages:
    8,967
    Yes.

    I thought Europeans were supposed to be cultured and proud of their history? At least, that's what every European I've ever met has claimed, sometimes while pointing out how ignorant us poor American bastards are

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    I only point this out to show how humorous I found the fact that Galileo, who died in 1642, was dropping balls off of the Eiffel Tower, which was biuld in 1890.
     

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