Uncertainty principle

From http://en.m.wikipedia.org/wiki/Uncertainty_principle

 

In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously. For instance, in 1927, Werner Heisenberg stated that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.^[1] The formal inequality relating the standard deviation of position σ_x and the standard deviation of momentum σ_p was derived by Earle Hesse Kennard^[2] later that year and by Hermann Weyl^[3] in 1928:

(ħ is the reduced Planck constant).

The original heuristic argument that such a limit should exist was given by Heisenberg, after whom it is sometimes named the Heisenberg principle. This ascribes the uncertainty in the measurable quantities to the jolt-like disturbance triggered by the act of observation. Though widely repeated in textbooks, this physical argument is now known to be fundamentally misleading.^[4][5] While the act of measurement does lead to uncertainty, the loss of precision is less than that predicted by Heisenberg's argument; the formal mathematical result remains valid, however.

Historically, the uncertainty principle has been confused^[6][7] with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems. Heisenberg offered such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty.^[8] It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems,^[4] and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.^[9] It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer.^[10]

Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it. Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program. These include, for example, tests of number-phase uncertainty relations in superconducting^[11] or quantum optics^[12] systems. Applications dependent on the uncertainty principle for their operation include extremely low noise technology such as that required in gravitational-wave interferometers.^[13]

House Republicans Pass Bill to Lower Taxes on the Rich and Raise Taxes on the Poor

By Kevin Drum

Mon Jul. 28, 2014 2:12 PM EDT

 

So what are Republicans in the House of Representatives up to these days? According to Danny Vinik, they just passed a bill that would reduce taxes on the rich and raise them on the poor.
I know, I know: you're shocked. But in a way, I think this whole episode is even worse than Vinik makes it sound.

Here's the background: The child tax credit reduces your income tax by $1,000 for each child you have. It phases out for upper middle-income folks, but—and this is the key point—it phases out differently for singles and couples. The way the numbers sort out, it treats singles better than couples. This is the dreaded "marriage penalty," which is bad because we want to encourage people to get married, not discourage them.

So what did House Republicans do? Naturally, they raised the phase-out threshold for married couples so that well-off couples would get a higher benefit. They didn't have to do this, of course. They could have lowered the benefit for singles instead. Or they could have jiggled the numbers so that everyone got equal benefits but the overall result was revenue neutral.

But they didn't. They chose the path that would increase the benefit—and thus lower taxes—for married couples making high incomes. The bill also indexes the credit to inflation, which helps only those with incomes high enough to claim the full credit. And it does nothing to make permanent a reduction in the earnings threshold that benefits poor working families. Here's the net result:

If the House legislation became law, the Center for Budget and Policy Priorities estimated that a couple making $160,000 a year would receive a new tax cut of $2,200. On the other hand, the expiring provisions of the CTC would cause a single mother with two kids making $14,500 to lose her full CTC, worth $1,725.

So inflation indexing, which is verboten when the subject is the minimum wage, is A-OK when it comes to high-income taxpayers. And eliminating the marriage penalty is also a good idea—but again, only for high-income couples.
Which is crazy. I don't really have a firm opinion on whether the government should be in the business of encouraging marriage, but if it is, surely it should focus its attention on the people who need encouragement in the first place. And that is very decidedly not the upper middle class, which continues to get married at the same rate as ever.

So we have a deficit-busting tax cut. It's a cut only for the upper middle class. It's indexed for inflation, even though we're not allowed to index things like the minimum wage. And the poor are still scheduled for a tax increase in 2017 because this bill does nothing to stop it. It's a real quad-fecta. I wonder what Paul Ryan thinks of all this?

Third Siberian Crater “Doesn’t Look Like Natural Formation”

Is it possible that someone has been playing a big hoax on us?

Third Siberian Crater “Doesn’t Look Like Natural Formation”

 

OK, this hole definitely needs to be looked into. A third mysterious crater has been found in Siberia. This one was discovered in the Taymyr Peninsula by local reindeer herders who live in the northern village of Nosok.

Map showing locations of the three Siberian craters reported so far.

The area is east of Yamal, where the first crater was reported last week, and northeast of the Taz district where the second one was found. This hole is smaller than those two – about 4 feet in diameter – and observers say its perimeter is perfectly round and the 100-to-300-feet-deep hole is shaped like a cone. According to The Siberian Times, one described it this way:

It is not like this is the work of men, but also doesn’t look like natural formation.

News travels slowly in Siberia. Local residents say the hole was formed on September 27, 2013. Shortly after, Mikhail Lapsui, a deputy of the regional parliament, flew over the area by helicopter and gave this account:

“There is ground outside, as if it was thrown as a result of an underground explosion. Observers give several versions. According to the first, initially at the place was smoking, and then there was a bright flash. In the second version, a celestial body fell there.”

Geologists, ecologists and historians are unable to come to a consensus on the causes of the craters. The prevailing theory on the other two is methane gas releases caused by global warming melting the permafrost. However, the Taymyr crater is far from the gas fields of the Yamal and Taz areas and is smaller, cone-shaped and perfectly formed.

A view inside the Taymyr crater taken by herder who stayed far enough away to not fall in.

Could it have another cause? Marina Leibman, chief scientist of the Earth Cryosphere Institute, says more information is needed.

Undoubtedly, we need to study all such formations. It is necessary to be able to predict their occurrence.”

Especially if it “doesn’t look like natural formation.”

No, Earth Wasn’t Nearly Destroyed by a 2012 Solar Storm

By Clara Moskowitz | July 25, 2014 |  

The views expressed are those of the author and are not necessarily those of Scientific American.

  

---

Credit: NASA/SDO/AIA

 

Yes, a large glob of plasma and magnetic fields from the sun did just miss us two years ago, as news organizations have feverishly reported over the past few days, following a NASA press release. At the time, scientists were hugely relieved it flew by Earth and missed us entirely. If it had hit, the coronal mass ejection (CME) could have decimated power grids on the ground and sizzled satellite electronics in space, causing widespread communications and electricity blackouts. It would not, however, have destroyed the entire planet (unless you equate the loss of the internet with the end of existence).

Solar storms are a real threat, however, and we might not be lucky enough to dodge the next one.  Our sun is currently in the middle of its “solar maximum,” a period of especially high magnetic activity—the root cause of solar storms and CMEs. So far, we’ve avoided major trouble from our nearest star this year, and physicists are even pondering why this cycle appears to be unusually quiescent. But solar activity is hard to predict, and no one knows when the next tempest might erupt.

In the August 2008 issue of Scientific American, astrophysicists Sten F. Odenwald and James L. Green argued that better solar forecasting is a must. If another major CME hits Earth, similar in scale to the superstorm of 1859, the infrastructure damage could be catastrophic, they write, but an early warning would help mitigate damage. The authors lay out a plan for steeling Earth against future solar attacks by reinforcing power grids and shielding satellites, and by improving our ability to predict solar storms through improved sun monitoring. For more on what we should be doing to protect ourselves, check out the article (subscription required) here:

Bracing the Satellite Infrastructure for a Solar Superstorm

About the Author: Clara Moskowitz is Scientific American's associate editor covering space and physics. Follow on Twitter @ClaraMoskowitz.

The views expressed are those of the author and are not necessarily those of Scientific American.

RestoringHistory.US

Shared publicly  -  4:43 PM

 

Mosab Hassan Yousef (Son of Hamas Founder) tells the truth about Hamas

https://www.youtube.com/watch?feature=player_embedded&v=KakxXN5Z-XI

New theory says the Universe isn't expanding — it's just getting fat

George Dvorsky

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George Dvorsky

Filed to: Cosmology

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• astronomy
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• astrophysics
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• expansion of universe
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7/17/13 4:40pm 7/17/13 4:40pm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Conventional thinking says the Universe has been expanding ever since the Big Bang. But theoretical astrophysicist Christof Wetterich says it's not expanding at all. It’s just that the mass of all the particles within it is steadily increasing.

Top Image: T. Piner.

We think the Universe is expanding because all the galaxies within it are pushing away from one another. Scientists see this as the redshift — a kind of doppler effect that happens when atoms emit or absorb light. We see these frequencies as appearing in the red, an indication that mass is moving away from us. Galaxies exhibit this redshift, which is why scientists say the Universe is expanding.

But Wetterich, who works out of the University of Heidelberg in Germany, says the characteristic light emitted by atoms are also governed by the masses of the atoms’ elementary particles, particularly their electrons.

Writing in Nature News, Jon Cartwright explains:

If an atom were to grow in mass, the photons it emits would become more energetic. Because higher energies correspond to higher frequencies, the emission and absorption frequencies would move towards the blue part of the spectrum. Conversely, if the particles were to become lighter, the frequencies would become redshifted.

Because the speed of light is finite, when we look at distant galaxies we are looking backwards in time — seeing them as they would have been when they emitted the light that we observe. If all masses were once lower, and had been constantly increasing, the colours of old galaxies would look redshifted in comparison to current frequencies, and the amount of redshift would be proportionate to their distances from Earth. Thus, the redshift would make galaxies seem to be receding even if they were not.

Work through the maths in this alternative interpretation of redshift, and all of cosmology looks very different. The Universe still expands rapidly during a short-lived period known as inflation. But prior to inflation, according to Wetterich, the Big Bang no longer contains a 'singularity' where the density of the Universe would be infinite. Instead, the Big Bang stretches out in the past over an essentially infinite period of time. And the current cosmos could be static, or even beginning to contract.

Whoa. That is a radically different picture of the Universe than what we're used to.

Unfortunately, there’s no way for us to test this. Well, at least not yet.

But Wetterich says his theory is useful for thinking about different cosmological models. And indeed, it may offer some fresh insights into the spooky dark energy that's apparently pushing the Universe outwards at an accelerating rate.

The Big Rip Theory says the universe could end in tearsThe Big Rip Theory says the universe could end in tearsThe Big Rip Theory says the universe could end in

Some say the universe will end with a new Big Bang. Others say the cosmos will eventually succumb…Read moreRead on

Read the entire study — which has not yet been peer reviewed — at arXiv: “A Universe without expansion.” But as Cartwright notes in his article, other physicists are not hating the idea.

To AGW Doubters, Skeptics, "Deniers", and Anyone Interested in the Science Behind Global Warming

Almost all of what follows come from Wikipedia, but as it agrees with my own knowledge of chemistry and physics from many sources over the years, it makes a good if sometimes hard to follow summary of the science behind anthropogenic CO2 enhanced global warming.  It is theory however, so how much warming it has caused in the Earth's atmosphere over the last ~ 150 years, and the climatological consequences of that is left up to scientific debate.
___________________________________________________________

We start with Svante Arrhenius, in the latter 19'th century:

Greenhouse effect

Arrhenius developed a theory to explain the ice ages, and in 1896 he was the first scientist to attempt to calculate how changes in the levels of carbon dioxide in the atmosphere could alter the surface temperature through the greenhouse effect.^[8] He was influenced by the work of others, including Joseph Fourier and John Tyndall. Arrhenius used the infrared observations of the moon by Frank Washington Very and Samuel Pierpont Langley at the Allegheny Observatory in Pittsburgh to calculate the absorption of infrared radiation by atmospheric CO₂ and water vapour. Using 'Stefan's law' (better known as the Stefan-Boltzmann law), he formulated his greenhouse law. In its original form, Arrhenius' greenhouse law reads as follows:

if the quantity of carbonic acid [CO₂] increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression.

The following equivalent formulation of Arrhenius' greenhouse law is still used today:^[9]

ΔF = α Ln(/)

Here is carbon dioxide (CO₂) concentration measured in parts per million by volume (ppmv); denotes a baseline or unperturbed concentration of CO₂, and ΔF is the radiative forcing, measured in watts per square meter. The constant alpha (α) has been assigned a value between five and seven.^[9]

Arrhenius at the first Solvay conference on chemistry in 1922 in Brussels.

 

Based on information from his colleague Arvid Högbom (sv), Arrhenius was the first person to predict that emissions of carbon dioxide from the burning of fossil fuels and other combustion processes were large enough to cause global warming. In his calculation Arrhenius included the feedback from changes in water vapor as well as latitudinal effects, but he omitted clouds, convection of heat upward in the atmosphere, and other essential factors. His work is currently seen less as an accurate prediction of global warming than as the first demonstration that it should be taken as a serious possibility.

Arrhenius' absorption values for CO₂ and his conclusions met criticism by Knut Ångström in 1900, who published the first modern infrared spectrum of CO₂ with two absorption bands, and published experimental results that seemed to show that absorption of infrared radiation by the gas in the atmosphere was already "saturated" so that adding more could make no difference. Arrhenius replied strongly in 1901 (Annalen der Physik), dismissing the critique altogether. He touched the subject briefly in a technical book titled Lehrbuch der kosmischen Physik (1903). He later wrote Världarnas utveckling (1906) (German: Das Werden der Welten [1907], English: Worlds in the Making [1908]) directed at a general audience, where he suggested that the human emission of CO₂ would be strong enough to prevent the world from entering a new ice age, and that a warmer earth would be needed to feed the rapidly increasing population:

"To a certain extent the temperature of the earth's surface, as we shall presently see, is conditioned by the properties of the atmosphere surrounding it, and particularly by the permeability of the latter for the rays of heat." (p46)

"That the atmospheric envelopes limit the heat losses from the planets had been suggested about 1800 by the great French physicist Fourier. His ideas were further developed afterwards by Pouillet and Tyndall. Their theory has been styled the hot-house theory, because they thought that the atmosphere acted after the manner of the glass panes of hot-houses." (p51)

 

"If the quantity of carbonic acid [CO₂] in the air should sink to one-half its present percentage, the temperature would fall by about 4°; a diminution to one-quarter would reduce the temperature by 8°. On the other hand, any doubling of the percentage of carbon dioxide in the air would raise the temperature of the earth's surface by 4°; and if the carbon dioxide were increased fourfold, the temperature would rise by 8°." (p53)

 

"Although the sea, by absorbing carbonic acid, acts as a regulator of huge capacity, which takes up about five-sixths of the produced carbonic acid, we yet recognize that the slight percentage of carbonic acid in the atmosphere may by the advances of industry be changed to a noticeable degree in the course of a few centuries." (p54)

 

"Since, now, warm ages have alternated with glacial periods, even after man appeared on the earth, we have to ask ourselves: Is it probable that we shall in the coming geological ages be visited by a new ice period that will drive us from our temperate countries into the hotter climates of Africa? There does not appear to be much ground for such an apprehension. The enormous combustion of coal by our industrial establishments suffices to increase the percentage of carbon dioxide in the air to a perceptible degree." (p61)

 

"We often hear lamentations that the coal stored up in the earth is wasted by the present generation without any thought of the future, and we are terrified by the awful destruction of life and property which has followed the volcanic eruptions of our days. We may find a kind of consolation in the consideration that here, as in every other case, there is good mixed with the evil. By the influence of the increasing percentage of carbonic acid in the atmosphere, we may hope to enjoy ages with more equable and better climates, especially as regards the colder regions of the earth, ages when the earth will bring forth much more abundant crops than at present, for the benefit of rapidly propagating mankind." (p63)

Arrhenius clearly believed that a warmer world would be a positive change. His ideas remained in circulation, but until about 1960 most scientists doubted that global warming would occur (believing the oceans would absorb CO₂ faster than humanity emitted the gas).^{[citation needed]} Most scientists also dismissed the greenhouse effect as implausible for the cause of ice ages, as Milutin Milankovitch had presented a mechanism using orbital changes of the earth (Milankovitch cycles).^{[citation needed]}
Nowadays, the accepted explanation is that orbital forcing sets the timing for ice ages with CO₂ acting as an essential amplifying feedback.

Arrhenius estimated that halving of CO₂ would decrease temperatures by 4–5 °C (Celsius) and a doubling of CO₂ would cause a temperature rise of 5–6 °C.^[10] In his 1906 publication, Arrhenius adjusted the value downwards to 1.6 °C (including water vapor feedback: 2.1 °C). Recent (2014) estimates from IPCC say this value (the Climate sensitivity) is likely to be between 1.5 and 4.5 °C. Arrhenius expected CO₂ levels to rise at a rate given by emissions in his time. Since then, industrial carbon dioxide levels have risen at a much faster rate: Arrhenius expected CO₂ doubling to take about 3000 years; it is now estimated in most scenarios to take about a century.
___________________________________________________________

And now onto the 20'th century, and the quantum-mechanical explanation of why certain gasses exhibit the greenhouse effect, i.e., molecular vibrations and infrared radiation absorption:

Molecular vibration

Molecular vibration occurs when atoms in a molecule are in periodic motion while the molecule as a whole has constant translational and rotational motion. The frequency of the periodic motion is known as a vibration frequency, and the typical frequencies of molecular vibrations range from less than 1012 to approximately 1014 Hz.

In general, a molecule with N atoms has 3N – 6 normal modes of vibration, but a linear molecule has 3N – 5 such modes, as rotation about its molecular axis cannot be observed.^[1] A diatomic molecule has one normal mode of vibration. The normal modes of vibration of polyatomic molecules are independent of each other but each normal mode will involve simultaneous vibrations of different parts of the molecule such as different chemical bonds.

A molecular vibration is excited when the molecule absorbs a quantum of energy, E, corresponding to the vibration's frequency, ν, according to the relation E = hν (where h is Planck's constant). A fundamental vibration is excited when one such quantum of energy is absorbed by the molecule in its ground state. When two quanta are absorbed the first overtone is excited, and so on to higher overtones.

To a first approximation, the motion in a normal vibration can be described as a kind of simple harmonic motion. In this approximation, the vibrational energy is a quadratic function (parabola) with respect to the atomic displacements and the first overtone has twice the frequency of the fundamental. In reality, vibrations are anharmonic and the first overtone has a frequency that is slightly lower than twice that of the fundamental. Excitation of the higher overtones involves progressively less and less additional energy and eventually leads to dissociation of the molecule, as the potential energy of the molecule is more like a Morse potential.

The vibrational states of a molecule can be probed in a variety of ways. The most direct way is through infrared spectroscopy, as vibrational transitions typically require an amount of energy that corresponds to the infrared region of the spectrum. Raman spectroscopy, which typically uses visible light, can also be used to measure vibration frequencies directly. The two techniques are complementary and comparison between the two can provide useful structural information such as in the case of the rule of mutual exclusion for centrosymmetric molecules.

Vibrational excitation can occur in conjunction with electronic excitation (vibronic transition), giving vibrational fine structure to electronic transitions, particularly with molecules in the gas state.

In the harmonic approximation the potential energy is a quadratic function of the normal coordinates. Solving the Schrödinger wave equation, the energy states for each normal coordinate are given by

,

where n is a quantum number that can take values of 0, 1, 2 ... In molecular spectroscopy where several types of molecular energy are studied and several quantum numbers are used, this vibrational quantum number is often designated as v.^[7][8]

The difference in energy when n (or v) changes by 1 is therefore equal to , the product of the Planck constant and the vibration frequency derived using classical mechanics. For a transition from level n to level n+1 due to absorption of a photon, the frequency of the photon is equal to the classical vibration frequency (in the harmonic oscillator approximation).

See quantum harmonic oscillator for graphs of the first 5 wave functions, which allow certain selection rules to be formulated. For example, for a harmonic oscillator transitions are allowed only when the quantum number n changes by one,

but this does not apply to an anharmonic oscillator; the observation of overtones is only possible because vibrations are anharmonic. Another consequence of anharmonicity is that transitions such as between states n=2 and n=1 have slightly less energy than transitions between the ground state and first excited state. Such a transition gives rise to a hot band.

Intensities

In an infrared spectrum the intensity of an absorption band is proportional to the derivative of the molecular dipole moment with respect to the normal coordinate.^[9] The intensity of Raman bands depends on polarizability.

Symmetrical stretching	Asymmetrical stretching	Scissoring (Bending)
Rocking	Wagging	Twisting