## sharp_young_ladyFrankly, it's not gonna happen

I’m exhausted with physics. And with something so complex I could never actually claim to understand it. Marvel at it, perhaps. 7 years ago

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I’m exhausted with physics. And with something so complex I could never actually claim to understand it. Marvel at it, perhaps. 7 years ago

Quantum events obey the laws of quantum theory, which governs the behavior of minute objects like atoms and subatomic particles, including photons of light. By contrast with the laws of **classical physics** (which apply to the relatively large objects of the everyday world), **quantum physics** often exhibits behavior that seems impossible.

One of the weird aspects of **quantum mechanics** is that something can simultaneously exist and not exist; if a particle is capable of moving along several different paths, or existing in several different states, the **uncertainty principle** of quantum mechanics allows it to travel along all paths and exist in all possible states simultaneously. However, if the particle happens to be measured by some means, its path or state is no longer uncertain. The simple act of measurement instantly forces it into just one path or state.

*Physicists call this a “collapse of the wave function.”*

Among several proposed explanations of all this is the **many worlds hypothesis**: the notion that for every possible pathway or state open to a particle, there is a separate universe. For each of 10 possible pathways a quantum particle might follow, for example, there would exist a separate universe.

**Entangled particles** are identical entities that share common origins and properties, and remain in instantaneous touch with each other, no matter how wide the gap between them.

The amazing thing is that if just one particle in an entangled pair is measured, the wave function of both particles collapses into a definite state that is the same for both partners, even separated by great distances.

The special quality of such pairs, as shown both by theory and experiment, is that they are entangled quantum mechanically. This means that if any aspect such as the polarization or energy or timing of one of the particles is measured, its indefinite state is destroyed and it falls into a definite state.

If the timing between the photons is exactly adjusted, each twin seems to know what the other is doing and matches its choice of pathway to coincide with that of its distant partner.

The astonishing consequence of this is that the particle’s distant twin experiences exactly the same metamorphosis at the same moment, even though there is no physical link or signal between the two twins.

In 1935 a famous paper by **Albert Einstein**, **Boris Podolsky** and **Nathan Rosen** challenged the **Quantum Theory** prediction that entangled particles could remain instantly in touch with each other. One of their objections was based on the speed limit imposed by Einstein’s **Special Theory of Relativity**: *nothing can travel faster than the speed of light.*

But again and again in recent years, increasingly sensitive experiments have decisively proved that Einstein’s explanation was wrong and quantum theory is correct. 7 years ago

**Maxwell’s equations**

From *Wikipedia*, the free encyclopedia

Maxwell’s equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter.

Maxwell’s four equations express, respectively, how electric charges produce electric fields (Gauss’ law), the experimental absence of magnetic monopoles, how currents and changing electric fields produce magnetic fields (the Ampere-Maxwell law), and how changing magnetic fields produce electric fields (Faraday’s law of induction).

**Historical development of Maxwell’s equations**

Maxwell, in 1864, was the first to put all four equations together and to notice that a correction was required to Ampere’s law: changing electric fields act like currents, likewise producing magnetic fields. (This additional term is called the displacement current.) The most common modern notation for these equations was developed by Oliver Heaviside.

Furthermore, Maxwell showed that waves of oscillating electric and magnetic fields travel through empty space at a speed that could be predicted from simple electrical experiments—using the data available at the time, Maxwell obtained a velocity of 310,740,000 m/s. Maxwell (1865) wrote:

**“This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.”**

Maxwell was correct in this conjecture, though he did not live to see the first experimental confirmation by Heinrich Hertz in 1888. Maxwell’s quantitative explanation of light as an electromagnetic wave is considered one of the great triumphs of 19th-century physics. (Actually, Michael Faraday had postulated a similar picture of light in 1846, but had not been able to give a quantitative description or predict the velocity.) Moreover, it laid the foundation for many future developments in physics, such as special relativity and its unification of electric and magnetic fields as a single tensor quantity, and Kaluza and Klein’s unification of electromagnetism with gravity and general relativity.

Maxwell’s 1865 formulation was in terms of 20 equations in 20 variables, which included several equations now considered to be auxiliary to what are now called “Maxwell’s equations” — the corrected Ampere’s law (three component equations), Gauss’ law for charge (one equation), the relationship between total and displacement current densities (three component equations), the relationship between magnetic field and the vector potential (three component equations, which imply the absence of magnetic charge), the relationship between electric field and the scalar and vector potentials (three component equations, which imply Faraday’s law), the relationship between the electric and displacement fields (three component equations), Ohm’s law relating current density and electric field (three component equations), and the continuity equation relating current density and charge density (one equation).

The modern mathematical formulation of Maxwell’s equations is due to Oliver Heaviside and Willard Gibbs, who in 1884 reformulated Maxwell’s original system of equations to a far simpler representation using vector calculus. (In 1873 Maxwell also published a quaternion-based notation that ultimately proved unpopular.) The change to the vector notation produced a symmetric mathematical representation that reinforced the perception of physical symmetries between the various fields. This highly symmetrical formulation would directly inspire later developments in fundamental physics.

**Links to relativity**

In the late 19th century, because of the appearance of a velocity,

c= 1 / sqrt{ε_0\ μ_0}

in the equations, Maxwell’s equations were only thought to express electromagnetism in the rest frame of the luminiferous aether (the postulated medium for light, whose interpretation was considerably debated). The symbols represent the permittivity and permeability of free space. When the Michelson-Morley experiment, conducted by Edward Morley and Albert Abraham Michelson, produced a null result for the change of the velocity of light due to the Earth’s motion through the hypothesized aether, however, alternative explanations were sought by George FitzGerald, Joseph Larmor and Hendrik Lorentz. Both Larmor (1897) and Lorentz (1899, 1904) derived the Lorentz transformation (so named by Henri Poincaré) as one under which Maxwell’s equations were invariant. Poincaré (1900) analysed the coordination of moving clocks by exchanging light signals. He also established the group property of the Lorentz transformation (Poincaré 1905). This culminated in Einstein’s theory of special relativity, which postulated the absence of any absolute rest frame, dismissed the aether as unnecessary, and established the invariance of Maxwell’s equations in all inertial frames of reference.

The electromagnetic field equations have an intimate link with special relativity: the magnetic field equations can be derived from consideration of the transformation of the electric field equations under relativistic transformations at low velocities. (In relativity, the equations are written in an even more compact, “manifestly covariant” form, in terms of the rank-2 antisymmetric field-strength 4-tensor that unifies the electric and magnetic fields into a single object.)

Kaluza and Klein showed in the 1920s that Maxwell’s equations can be derived by extending general relativity into five dimensions. This strategy of using higher dimensions to unify different forces is an active area of research in particle physics. 7 years ago

I just stumbled upon this site and the group. Though I am not sure about Pseudoscience or quackery, one thing I have in mind is to start brushing up and come upto speed on the latest happenings in the world of physics including mathematics. I know it is a daunting goal, but if there is anyone who can guide or interested in the same path, that would be great ! 8 years ago

Check out Brian Greene’s book The Elegant Universe. He does a great job of explaining general relativity, special relativity and quantum mechanics which form the basis of modern physics. His discussion on string/M theory doesn’t seem as strong though my suspicion is an 11 dimensional universe is too unintuitive for most people to grasp. There is also a PBS special based on the book out on DVD. Check it out too I’ve heard good things about it. 8 years ago

A new stack of books arrived today. Since I started on “Feynman’s Lectures on Computation”, I’ve been wanting to know more physics. The math isn’t as bad as I thought it would be. If I take it slow, I can follow along. As long as I don’t have to take midterms or finals on the material, I think I’m going to enjoy it just fine. 9 years ago

I think I’ll start with these 3 lectures given by Hans Bethe. 9 years ago

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