Wavelength

In case you look at the checklist of the Forbes 40 richest folks in Singapore, you will notice many who made their fortunes growing and investing in real estate. Or simply look around you – the average Singaporean's wealth in all probability comes more from the appreciation of his HDB flat or non-public property than from another asset.

As my husband and I are also Singapore PR, we plan to take our criticism to our MP as properly, hopefully the government will turn into conscious of this drawback or perhaps they knew about it already, but it is time to take some action to right this lengthy standing grievance among patrons, and even amongst brokers who acquired shunned out from offers like my poor agent. She misplaced a sale for certain and unbeknownst to her, she in all probability never had an opportunity with that property proper from the start! I feel sorry for her, and appreciated her effort in alerting us about this unit and attempting to get us the property; but I'm a bit of aggravated or perhaps a bit resentful that we lost that condo basically as a result of we had been attached to her or any co-broke agent?

A very powerful part of the process of finding and securing housing is finding a superb estate agent, which is greatest achieved by word of mouth. As soon as expats have managed this feat, what follows is significantly less complicated and less annoying. Steps to renting property in Singapore We've got collected a cross-section of the most effective property resources and repair providers, multi function simple-to-use location, to additional streamline your property purchase or sale. Whether or not you are a first time home buyer or a seasoned seller, you will discover SingaporePropertyExchange.com the essential resource to strengthen your property transaction. iii) for such different period as the Registrar might enable, and had been resident in Singapore throughout that period. ECG Property Pte. Ltd.

Have passed an industry examination i.e Common Examination for House Agents (CEHA) or Actual Estate Company (REA) exam, or equal; Exclusive agents are extra willing to share listing data thus guaranteeing the widest doable coverage inside the actual property group thru Multiple Listings and Networking. Accepting a critical provide is easier since your agent is fully aware of all marketing exercise related together with your property. This reduces your having to verify with a number of agents for another affords. Price control is well achieved. Paint work in good restore-discuss along with your Property Advisor if main works are nonetheless to be accomplished. Softening in residential property costs continue, led by 2.eight per cent decline in the index for Remainder of Central Area

With the steam of an overheated property market dying down, the excitement has now shifted to builders playing discount video games to push new ec launch singapore [that guy] initiatives or clear outdated stock. With so many ‘great offers', patrons are spoiled for choices. In case you overprice your house, buyers shall be delay by the worth. Because of this your own home may take longer to sell, and end up being sold at a lower cost. Patrons may think that you are desperate in promoting (so that you have interaction multiple brokers to sell it off quick). Since they think you might be determined, they may not offer you a great value. Additionally, estate agents are responsibility-certain to avoid another potential conflicts of interest (equivalent to if a celebration to the transaction is related to the agent) until the client's waiver is obtained.

Like anywhere else, cash goes farther when you're exterior the prime districts. In case you plan to stay in a central location, you will have to settle for much less space or fewer onsite services. While rental prices are nonetheless high, 2013 has seen costs adjusting downwards in the higher brackets above $10,000 and the central districts flat-lining. Nevertheless, good value properties in the outer regions and decrease priced items have retained and even seen will increase as individuals typically have been downsizing

It's also usually free to tenants. However tenants paying lower than $three,500 monthly in rental typically pay a half month commission for annually of rental. For rentals above $3,500, tenants don't pay any commission. Does the acquisition process differ for residential, retail, office and industrial properties? Our Guide will assist you to have a head begin within the SEARCH ENGINE OPTIMIZATION bandwagon by performing the right WEBSITE POSITIONING implementation with our custom-made WEBSITE POSITIONING ranking tatics. Basic Search Engine Optimization Capacity to add / edit or delete Challenge Change Ordering of Venture Unpublish or Publish a Undertaking Capability to add / edit or delete a banner of the Undertaking I feel what amazes us firstly is that each owner and agent have to be there with us! Month-to-month rent is $3,888

Wave–particle duality is a theory that proposes that all matter exhibits the properties of not only particles, which have mass, but also waves, which transfer energy. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects. Standard interpretations of quantum mechanics explain this paradox as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer. This treatment focuses on explaining the behavior from the perspective of the widely used Copenhagen interpretation, in which wave–particle duality serves as one aspect of the concept of complementarity, that one can view phenomena in one way or in another, but not both simultaneously.Primarily based on the most recent URA personal property value index (PPPI) flash estimates, we know that the PPPI, which represents the overall real property price development, has dipped in 2013Q4. That is the first dip the market has seen within the final 2 years.

To give you some perspective, the entire number of personal properties in Singapore (together with govt condominiums) is 297,689 in 2013Q3. Primarily based on the projection that there will be 19,302 units accomplished in 2014, the rise in residential models works out to be more than 6%. With a lot New Ec Launch Singapore provide, buyers might be spoilt for alternative and this in flip will lead to their reluctance to pay a premium for potential models. The complete textual content of the Copyright Act (Cap sixty three) and different statutes regarding IPR might be found on the Singapore Statutes Online Website online The Group's income jumped forty.1 p.c to $324.5 million from $231.6 million in FY 2013, lifted by increased development income and sales of growth properties in Singapore and China. Actual Estate Shopping for

One factor we've on this nation is a big group of "economists," and "market analysts." What's interesting about this group of real property market-watchers is that there are two very other ways wherein they predict Boomers will affect housing markets over the subsequent decade. Let's check out those two opposites and see how every can change the best way real property investors strategy their markets. The good news is that actual property buyers are prepared for either state of affairs, and there's profit in being ready. I'm excited and searching ahead to the alternatives both or each of these conditions will supply; thank you Boomers! Mapletree to further broaden past Asia Why fortune will favour the brave in Asia's closing real property frontier

The story of the 23.2 home begins with a stack of Douglas fir beams salvaged from varied demolished warehouses owned by the consumer's household for a number of generations. Design and structure innovator Omer Arbel, configured them to type a triangulated roof, which makes up one of the placing features of the home. The transient from the entrepreneur-proprietor was not solely to design a house that integrates antique wood beams, however one which erases the excellence between inside and exterior. Built on a gentle slope on a large rural acreage surrounded by two masses of previous-development forests, the indoors movement seamlessly to the outdoors and, from the within looking, one enjoys unobstructed views of the existing natural panorama which is preserved

First, there are typically extra rental transactions than gross sales transactions, to permit AV to be decided for each property primarily based on comparable properties. Second, movements in sale costs are more unstable than leases. Hence, utilizing rental transactions to derive the AV helps to maintain property tax more steady for property homeowners. If you're buying or trying to lease a property. It's tiring to call up individual property agent, organize appointments, coordinate timing and to go for particular person property viewing. What most individuals do is to have a property agent representing them who will arrange and coordinate the viewings for all the properties out there based mostly on your necessities & most well-liked timing. Rent Property District 12 Rent Property District thirteen

The Annual Worth of a property is mostly derived based mostly on the estimated annual hire that it may well fetch if it have been rented out. In determining the Annual Worth of a property, IRAS will think about the leases of similar properties within the vicinity, dimension and condition of the property, and different relevant components. The Annual Worth of a property is determined in the identical method regardless of whether the property is let-out, proprietor-occupied or vacant. The Annual Worth of land is determined at 5% of the market price of the land. When a constructing is demolished, the Annual Worth of the land is assessed by this method. Property Tax on Residential Properties Buyer Stamp Responsibility on Buy of Properties – Business and residential properties Rent House District 01

Within the event the Bank's valuation is decrease than the acquisition price, the purchaser has to pay the distinction between the purchase value and the Bank's valuation utilizing money. As such, the money required up-front might be increased so it's at all times essential to know the valuation of the property before making any offer. Appoint Lawyer The Bank will prepare for a proper valuation of the property by way of physical inspection The completion statement will present you the balance of the acquisition price that you must pay after deducting any deposit, pro-rated property tax and utility costs, upkeep prices, and different relevant expenses in addition to any fees payable to the agent and the lawyer. Stamp Responsibility Primarily based on the Purchase Price or Market Value, whichever is larger

Origin of theory

The idea of duality originated in a debate over the nature of light and matter that dates back to the 17th century, when Christiaan Huygens and Isaac Newton proposed competing theories of light: light was thought either to consist of waves (Huygens) or of particles (Newton). Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles also have a wave nature (and vice versa). This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected.

Brief history of wave and particle viewpoints

Aristotle was one of the first to publicly hypothesize about the nature of light, proposing that light is a disturbance in the element air (that is, it is a wave-like phenomenon). On the other hand, Democritus—the original atomist—argued that all things in the universe, including light, are composed of indivisible sub-components (light being some form of solar atom). At the beginning of the 11th Century, the Arabic scientist Alhazen wrote the first comprehensive treatise on optics; describing refraction, reflection, and the operation of a pinhole lens via rays of light traveling from the point of emission to the eye. He asserted that these rays were composed of particles of light. In 1630, René Descartes popularized and accredited the opposing wave description in his treatise on light, showing that the behavior of light could be re-created by modeling wave-like disturbances in a universal medium ("plenum"). Beginning in 1670 and progressing over three decades, Isaac Newton developed and championed his corpuscular hypothesis, arguing that the perfectly straight lines of reflection demonstrated light's particle nature; only particles could travel in such straight lines. He explained refraction by positing that particles of light accelerated laterally upon entering a denser medium. Around the same time, Newton's contemporaries Robert Hooke and Christiaan Huygens—and later Augustin-Jean Fresnel—mathematically refined the wave viewpoint, showing that if light traveled at different speeds in different media (such as water and air), refraction could be easily explained as the medium-dependent propagation of light waves. The resulting Huygens–Fresnel principle was extremely successful at reproducing light's behavior and, subsequently supported by Thomas Young's discovery of double-slit interference, was the beginning of the end for the particle light camp.

Thomas Young's sketch of two-slit diffraction of waves, 1803

The final blow against corpuscular theory came when James Clerk Maxwell discovered that he could combine four simple equations, which had been previously discovered, along with a slight modification to describe self-propagating waves of oscillating electric and magnetic fields. When the propagation speed of these electromagnetic waves was calculated, the speed of light fell out. It quickly became apparent that visible light, ultraviolet light, and infrared light (phenomena thought previously to be unrelated) were all electromagnetic waves of differing frequency. The wave theory had prevailed—or at least it seemed to.

While the 19th century had seen the success of the wave theory at describing light, it had also witnessed the rise of the atomic theory at describing matter. In 1789, Antoine Lavoisier securely differentiated chemistry from alchemy by introducing rigor and precision into his laboratory techniques; allowing him to deduce the conservation of mass and categorize many new chemical elements and compounds. However, the nature of these essential chemical elements remained unknown. In 1799, Joseph Louis Proust advanced chemistry towards the atom by showing that elements combined in definite proportions. This led John Dalton to resurrect Democritus' atom in 1803, when he proposed that elements were invisible sub components; which explained why the varying oxides of metals (e.g. stannous oxide and cassiterite, SnO and SnO₂ respectively) possess a 1:2 ratio of oxygen to one another. But Dalton and other chemists of the time had not considered that some elements occur in monatomic form (like Helium) and others in diatomic form (like Hydrogen), or that water was H₂O, not the simpler and more intuitive HO—thus the atomic weights presented at the time were varied and often incorrect. Additionally, the formation of HO by two parts of hydrogen gas and one part of oxygen gas would require an atom of oxygen to split in half (or two half-atoms of hydrogen to come together). This problem was solved by Amedeo Avogadro, who studied the reacting volumes of gases as they formed liquids and solids. By postulating that equal volumes of elemental gas contain an equal number of atoms, he was able to show that H₂O was formed from two parts H₂ and one part O₂. By discovering diatomic gases, Avogadro completed the basic atomic theory, allowing the correct molecular formulae of most known compounds—as well as the correct weights of atoms—to be deduced and categorized in a consistent manner. The final stroke in classical atomic theory came when Dimitri Mendeleev saw an order in recurring chemical properties, and created a table presenting the elements in unprecedented order and symmetry. But there were holes in Mendeleev's table, with no element to fill them in. His critics initially cited this as a fatal flaw, but were silenced when new elements were discovered that perfectly fit into these holes. The success of the periodic table effectively converted any remaining opposition to atomic theory; even though no single atom had ever been observed in the laboratory, chemistry was now an atomic science.

File:Wave-particle duality.ogv

People are nonetheless rushing to buy properties in Singapore. A new residential condominium mission in Bedok had a long queue three days before its official launch and bought more than 350 units on the very first day. Nonetheless, there is a ‘development' that had emerged in 2011 that the majority have possibly overlooked.

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for a borrower with one or more excellent residential property loans3; and No SSD will be payable by the seller if the property is bought more than three years after it was bought. Non-extension of the Jan 2009 Funds assistance measures for the property market when the measures expire. Permitting up to 2 years of property tax deferral for land accepted for improvement. Lively secondary marketplace for easy exit of property investments. Curiosity on mortgage fee is tax deductible when the property is rented out. We've progressive property tax rates for residential properties- the higher the value of the residential property, the upper the tax charge. Why do I've to pay property tax on my house when I'm an onwer-occupier and not deriving rental earnings? Palacio Cluster Landed

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Skilled property brokers in Singapore will assist the client and defend their interests throughout the acquisition, and will help safe the provide at the best possible price. The agents may even be sure that all paperwork are in order and that the vendor is the rightful proprietor of the property. Most of the property brokers share their databases with each other. Tuesday's measures come after the Monetary Authority of Singapore in June tightened rules on property loans, and closed loopholes that allowed some householders to circumvent loan restrictions and avoid paying levies when buying extra property. Contact us for a FREE housing loan analysis and to study concerning the newest mortgage to worth on Singapore housing loans. J Gateway Condominium (Bought Out) Oct, 2013

6. Completion of automotive park, roads and drains serving the housing project 5% 7. Notice of Vacant Possession (Upon obtaining Temporary Occupation Permit) The estimates given by SingaporeHousingLoan.SG's calculator are not quotations and are usually not binding in any way on SingaporeHousingLoan.sg or the consumer. The method of calculation does not exactly mirror that of which is being used by the individual monetary establishment and the data provided should be used as a information only. SingaporeHousingLoan.SG's calculator does not pre-qualify you for any housing loan from any monetary institution. Undercover Report Finds Unlawful Rat Meat Sold In London Market Unpasteurized Tempeh Linked To Salmonella Outbreak That Sickens 60 Hottest EC Launch in Sengkang!

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Turn of the 20th century and the paradigm shift

Particles of electricity

At the close of the 19th century, the reductionism of atomic theory began to advance into the atom itself; determining, through physics, the nature of the atom and the operation of chemical reactions. Electricity, first thought to be a fluid, was now understood to consist of particles called electrons. This was first demonstrated by J. J. Thomson in 1897 when, using a cathode ray tube, he found that an electrical charge would travel across a vacuum (which would possess infinite resistance in classical theory). Since the vacuum offered no medium for an electric fluid to travel, this discovery could only be explained via a particle carrying a negative charge and moving through the vacuum. This electron flew in the face of classical electrodynamics, which had successfully treated electricity as a fluid for many years (leading to the invention of batteries, electric motors, dynamos, and arc lamps). More importantly, the intimate relation between electric charge and electromagnetism had been well documented following the discoveries of Michael Faraday and James Clerk Maxwell. Since electromagnetism was known to be a wave generated by a changing electric or magnetic field (a continuous, wave-like entity itself) an atomic/particle description of electricity and charge was a non sequitur. Furthermore, classical electrodynamics was not the only classical theory rendered incomplete.

Radiation quantization

Black-body radiation, the emission of electromagnetic energy due to an object's heat, could not be explained from classical arguments alone. The equipartition theorem of classical mechanics, the basis of all classical thermodynamic theories, stated that an object's energy is partitioned equally among the object's vibrational modes. This worked well when describing thermal objects, whose vibrational modes were defined as the speeds of their constituent atoms, and the speed distribution derived from egalitarian partitioning of these vibrational modes closely matched experimental results. Speeds much higher than the average speed were suppressed by the fact that kinetic energy is quadratic—doubling the speed requires four times the energy—thus the number of atoms occupying high energy modes (high speeds) quickly drops off because the constant, equal partition can excite successively fewer atoms. Low speed modes would ostensibly dominate the distribution, since low speed modes would require ever less energy, and prima facie a zero-speed mode would require zero energy and its energy partition would contain an infinite number of atoms. But this would only occur in the absence of atomic interaction; when collisions are allowed, the low speed modes are immediately suppressed by jostling from the higher energy atoms, exciting them to higher energy modes. An equilibrium is swiftly reached where most atoms occupy a speed proportional to the temperature of the object (thus defining temperature as the average kinetic energy of the object).

But applying the same reasoning to the electromagnetic emission of such a thermal object was not so successful. It had been long known that thermal objects emit light. Hot metal glows red, and upon further heating, white (this is the underlying principle of the incandescent bulb). Since light was known to be waves of electromagnetism, physicists hoped to describe this emission via classical laws. This became known as the black body problem. Since the equipartition theorem worked so well in describing the vibrational modes of the thermal object itself, it was trivial to assume that it would perform equally well in describing the radiative emission of such objects. But a problem quickly arose when determining the vibrational modes of light. To simplify the problem (by limiting the vibrational modes) a longest allowable wavelength was defined by placing the thermal object in a cavity. Any electromagnetic mode at equilibrium (i.e. any standing wave) could only exist if it used the walls of the cavities as nodes. Thus there were no waves/modes with a wavelength larger than twice the length (L) of the cavity.

Standing waves in a cavity

The first few allowable modes would therefore have wavelengths of : 2L, L, 2L/3, L/2, etc. (each successive wavelength adding one node to the wave). However, while the wavelength could never exceed 2L, there was no such limit on decreasing the wavelength, and adding nodes to reduce the wavelength could proceed ad infinitum. Suddenly it became apparent that the short wavelength modes completely dominated the distribution, since ever shorter wavelength modes could be crammed into the cavity. If each mode received an equal partition of energy, the short wavelength modes would consume all the energy. This became clear when plotting the Rayleigh–Jeans law which, while correctly predicting the intensity of long wavelength emissions, predicted infinite total energy as the intensity diverges to infinity for short wavelengths. This became known as the ultraviolet catastrophe.

The solution arrived in 1900 when Max Planck hypothesized that the frequency of light emitted by the black body depended on the frequency of the oscillator that emitted it, and the energy of these oscillators increased linearly with frequency (according to his constant h, where E = hν). This was not an unsound proposal considering that macroscopic oscillators operate similarly: when studying five simple harmonic oscillators of equal amplitude but different frequency, the oscillator with the highest frequency possesses the highest energy (though this relationship is not linear like Planck's). By demanding that high-frequency light must be emitted by an oscillator of equal frequency, and further requiring that this oscillator occupy higher energy than one of a lesser frequency, Planck avoided any catastrophe; giving an equal partition to high-frequency oscillators produced successively fewer oscillators and less emitted light. And as in the Maxwell–Boltzmann distribution, the low-frequency, low-energy oscillators were suppressed by the onslaught of thermal jiggling from higher energy oscillators, which necessarily increased their energy and frequency.

The most revolutionary aspect of Planck's treatment of the black body is that it inherently relies on an integer number of oscillators in thermal equilibrium with the electromagnetic field. These oscillators give their entire energy to the electromagnetic field, creating a quantum of light, as often as they are excited by the electromagnetic field, absorbing a quantum of light and beginning to oscillate at the corresponding frequency. Planck had intentionally created an atomic theory of the black body, but had unintentionally generated an atomic theory of light, where the black body never generates quanta of light at a given frequency with an energy less than hν. However, once realizing that he had quantized the electromagnetic field, he denounced particles of light as a limitation of his approximation, not a property of reality.

Photoelectric effect illuminated

Yet while Planck had solved the ultraviolet catastrophe by using atoms and a quantized electromagnetic field, most physicists immediately agreed that Planck's "light quanta" were unavoidable flaws in his model. A more complete derivation of black body radiation would produce a fully continuous, fully wave-like electromagnetic field with no quantization. However, in 1905 Albert Einstein took Planck's black body model in itself and saw a wonderful solution to another outstanding problem of the day: the photoelectric effect, the phenomenon where electrons are emitted from atoms when they absorb energy from light. Ever since the discovery of electrons eight years previously, electrons had been the thing to study in physics laboratories worldwide.

In 1902 Philipp Lenard discovered that (within the range of the experimental parameters he was using) the energy of these ejected electrons did not depend on the intensity of the incoming light, but on its frequency. So if one shines a little low-frequency light upon a metal, a few low energy electrons are ejected. If one now shines a very intense beam of low-frequency light upon the same metal, a whole slew of electrons are ejected; however they possess the same low energy, there are merely more of them. In order to get high energy electrons, one must illuminate the metal with high-frequency light. The more light there is, the more electrons are ejected. Like blackbody radiation, this was at odds with a theory invoking continuous transfer of energy between radiation and matter. However, it can still be explained using a fully classical description of light, as long as matter is quantum mechanical in nature.

If one used Planck's energy quanta, and demanded that electromagnetic radiation at a given frequency could only transfer energy to matter in integer multiples of an energy quantum hν, then the photoelectric effect could be explained very simply. Low-frequency light only ejects low-energy electrons because each electron is excited by the absorption of a single photon. Increasing the intensity of the low-frequency light (increasing the number of photons) only increases the number of excited electrons, not their energy, because the energy of each photon remains low. Only by increasing the frequency of the light, and thus increasing the energy of the photons, can one eject electrons with higher energy. Thus, using Planck's constant h to determine the energy of the photons based upon their frequency, the energy of ejected electrons should also increase linearly with frequency; the gradient of the line being Planck's constant. These results were not confirmed until 1915, when Robert Andrews Millikan, who had previously determined the charge of the electron, produced experimental results in perfect accord with Einstein's predictions. While the energy of ejected electrons reflected Planck's constant, the existence of photons was not explicitly proven until the discovery of the photon antibunching effect, of which a modern experiment can be performed in undergraduate-level labs. This phenomenon could only be explained via photons, and not through any semi-classical theory (which could alternatively explain the photoelectric effect). When Einstein received his Nobel Prize in 1921, it was not for his more difficult and mathematically laborious special and general relativity, but for the simple, yet totally revolutionary, suggestion of quantized light. Einstein's "light quanta" would not be called photons until 1925, but even in 1905 they represented the quintessential example of wave–particle duality. Electromagnetic radiation propagates following linear wave equations, but can only be emitted or absorbed as discrete elements, thus acting as a wave and a particle simultaneously.

Developmental milestones

Huygens and Newton

The earliest comprehensive theory of light was advanced by Christiaan Huygens, who proposed a wave theory of light, and in particular demonstrated how waves might interfere to form a wavefront, propagating in a straight line. However, the theory had difficulties in other matters, and was soon overshadowed by Isaac Newton's corpuscular theory of light. That is, Newton proposed that light consisted of small particles, with which he could easily explain the phenomenon of reflection. With considerably more difficulty, he could also explain refraction through a lens, and the splitting of sunlight into a rainbow by a prism. Newton's particle viewpoint went essentially unchallenged for over a century.

Young, Fresnel, and Maxwell

In the early 19th century, the double-slit experiments by Young and Fresnel provided evidence for Huygens' wave theories. The double-slit experiments showed that when light is sent through a grid, a characteristic interference pattern is observed, very similar to the pattern resulting from the interference of water waves; the wavelength of light can be computed from such patterns. The wave view did not immediately displace the ray and particle view, but began to dominate scientific thinking about light in the mid 19th century, since it could explain polarization phenomena that the alternatives could not.

In the late 19th century, James Clerk Maxwell explained light as the propagation of electromagnetic waves according to the Maxwell equations. These equations were verified by experiment by Heinrich Hertz in 1887, and the wave theory became widely accepted.

Planck's formula for black-body radiation

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In 1901, Max Planck published an analysis that succeeded in reproducing the observed spectrum of light emitted by a glowing object. To accomplish this, Planck had to make an ad hoc mathematical assumption of quantized energy of the oscillators (atoms of the black body) that emit radiation. It was Einstein who later proposed that it is the electromagnetic radiation itself that is quantized, and not the energy of radiating atoms.

Einstein's explanation of the photoelectric effect

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The photoelectric effect. Incoming photons on the left strike a metal plate (bottom), and eject electrons, depicted as flying off to the right.

In 1905, Albert Einstein provided an explanation of the photoelectric effect, a hitherto troubling experiment that the wave theory of light seemed incapable of explaining. He did so by postulating the existence of photons, quanta of light energy with particulate qualities.

In the photoelectric effect, it was observed that shining a light on certain metals would lead to an electric current in a circuit. Presumably, the light was knocking electrons out of the metal, causing current to flow. However, using the case of potassium as an example, it was also observed that while a dim blue light was enough to cause a current, even the strongest, brightest red light available with the technology of the time caused no current at all. According to the classical theory of light and matter, the strength or amplitude of a light wave was in proportion to its brightness: a bright light should have been easily strong enough to create a large current. Yet, oddly, this was not so.

Einstein explained this conundrum by postulating that the electrons can receive energy from electromagnetic field only in discrete portions (quanta that were called photons): an amount of energy E that was related to the frequency f of the light by

$E=hf\,$

where h is Planck's constant (6.626 × 10⁻³⁴ J seconds). Only photons of a high enough frequency (above a certain threshold value) could knock an electron free. For example, photons of blue light had sufficient energy to free an electron from the metal, but photons of red light did not. More intense light above the threshold frequency could release more electrons, but no amount of light (using technology available at the time) below the threshold frequency could release an electron. To "violate" this law would require extremely high intensity lasers which had not yet been invented. Intensity-dependent phenomena have now been studied in detail with such lasers.

Einstein was awarded the Nobel Prize in Physics in 1921 for his discovery of the law of the photoelectric effect.

De Broglie's wavelength

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Propagation of de Broglie waves in 1d—real part of the complex amplitude is blue, imaginary part is green. The probability (shown as the colour opacity) of finding the particle at a given point x is spread out like a waveform; there is no definite position of the particle. As the amplitude increases above zero the curvature decreases, so the amplitude decreases again, and vice versa—the result is an alternating amplitude: a wave. Top: Plane wave. Bottom: Wave packet.

In 1924, Louis-Victor de Broglie formulated the de Broglie hypothesis, claiming that all matter, not just light, has a wave-like nature; he related wavelength (denoted as λ), and momentum (denoted as p):

$\lambda ={\frac {h}{p}}$

This is a generalization of Einstein's equation above, since the momentum of a photon is given by p = ${\tfrac {E}{c}}$ and the wavelength (in a vacuum) by λ = ${\tfrac {c}{f}}$, where c is the speed of light in vacuum.

De Broglie's formula was confirmed three years later for electrons (which differ from photons in having a rest mass) with the observation of electron diffraction in two independent experiments. At the University of Aberdeen, George Paget Thomson passed a beam of electrons through a thin metal film and observed the predicted interference patterns. At Bell Labs Clinton Joseph Davisson and Lester Halbert Germer guided their beam through a crystalline grid.

De Broglie was awarded the Nobel Prize for Physics in 1929 for his hypothesis. Thomson and Davisson shared the Nobel Prize for Physics in 1937 for their experimental work.

Heisenberg's uncertainty principle

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In his work on formulating quantum mechanics, Werner Heisenberg postulated his uncertainty principle, which states:

$\Delta x\Delta p\geq {\frac {\hbar }{2}}$

where

$\Delta$ here indicates standard deviation, a measure of spread or uncertainty;

x and p are a particle's position and linear momentum respectively.

$\hbar$ is the reduced Planck's constant (Planck's constant divided by 2$\pi$).

Heisenberg originally explained this as a consequence of the process of measuring: Measuring position accurately would disturb momentum and vice-versa, offering an example (the "gamma-ray microscope") that depended crucially on the de Broglie hypothesis. It is now thought, however, that this only partly explains the phenomenon, but that the uncertainty also exists in the particle itself, even before the measurement is made.

In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions; likewise, just as it is nonsensical to discuss the wavelength of a "pulse" wave traveling down a string, particles do not have perfectly precise momenta (which corresponds to the inverse of wavelength). Moreover, when position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength (and thus momentum). And conversely, when momentum (and thus wavelength) is relatively well defined, the wave looks long and sinusoidal, and therefore it has a very ill-defined position.

de Broglie–Bohm theory

De Broglie himself had proposed a pilot wave construct to explain the observed wave–particle duality. In this view, each particle has a well-defined position and momentum, but is guided by a wave function derived from Schrödinger's equation. The pilot wave theory was initially rejected because it generated non-local effects when applied to systems involving more than one particle. Non-locality, however, soon became established as an integral feature of quantum theory (see EPR paradox), and David Bohm extended de Broglie's model to explicitly include it. In the resulting representation, also called the de Broglie–Bohm theory or Bohmian mechanics, the wave–particle duality is not a property of matter itself, but an appearance generated by the particle's motion subject to a guiding equation or quantum potential.

Wave behavior of large objects

Since the demonstrations of wave-like properties in photons and electrons, similar experiments have been conducted with neutrons and protons. Among the most famous experiments are those of Estermann and Otto Stern in 1929. Authors of similar recent experiments with atoms and molecules, described below, claim that these larger particles also act like waves.

A dramatic series of experiments emphasizing the action of gravity in relation to wave–particle duality were conducted in the 1970s using the neutron interferometer. Neutrons, one of the components of the atomic nucleus, provide much of the mass of a nucleus and thus of ordinary matter. In the neutron interferometer, they act as quantum-mechanical waves directly subject to the force of gravity. While the results were not surprising since gravity was known to act on everything, including light (see tests of general relativity and the Pound-Rebka falling photon experiment), the self-interference of the quantum mechanical wave of a massive fermion in a gravitational field had never been experimentally confirmed before.

In 1999, the diffraction of C₆₀ fullerenes by researchers from the University of Vienna was reported. Fullerenes are comparatively large and massive objects, having an atomic mass of about 720 u. The de Broglie wavelength is 2.5 pm, whereas the diameter of the molecule is about 1 nm, about 400 times larger. In 2012, these far-field diffraction experiments could be extended to phthalocyanine molecules and their heavier derivatives, which are composed of 58 and 114 atoms respectively. In these experiments the build-up of such interference patterns could be recorded in real time and with single molecule sensitivity.

In 2003, the Vienna group also demonstrated the wave nature of tetraphenylporphyrin—a flat biodye with an extension of about 2 nm and a mass of 614 u. For this demonstration they employed a near-field Talbot Lau interferometer. In the same interferometer they also found interference fringes for C₆₀F_48., a fluorinated buckyball with a mass of about 1600 u, composed of 108 atoms. Large molecules are already so complex that they give experimental access to some aspects of the quantum-classical interface, i.e., to certain decoherence mechanisms. In 2011, the interference of molecules as heavy as 6910 u could be demonstrated in a Kapitza–Dirac–Talbot–Lau interferometer. These are the largest objects that so far showed de Broglie matter-wave interference. In 2013, the interference of molecules beyond 10,000 u has been demonstrated.

Whether objects heavier than the Planck mass (about the weight of a large bacterium) have a de Broglie wavelength is theoretically unclear and experimentally unreachable; above the Planck mass a particle's Compton wavelength would be smaller than the Planck length and its own Schwarzschild radius, a scale at which current theories of physics may break down or need to be replaced by more general ones.

Recently Couder, Fort, et al. showed that we can use macroscopic oil droplets on a vibrating surface as a model of wave–particle duality—localized droplet creates periodical waves around and interaction with them leads to quantum-like phenomena: interference in double-slit experiment, unpredictable tunneling (depending in complicated way on practically hidden state of field), orbit quantization (that particle has to 'find a resonance' with field perturbations it creates—after one orbit, its internal phase has to return to the initial state) and Zeeman effect.

Treatment in modern quantum mechanics

Wave–particle duality is deeply embedded into the foundations of quantum mechanics. In the formalism of the theory, all the information about a particle is encoded in its wave function, a complex-valued function roughly analogous to the amplitude of a wave at each point in space. This function evolves according to a differential equation (generically called the Schrödinger equation). For particles with mass this equation has solutions that follow the form of the wave equation. Propagation of such waves leads to wave-like phenomena such as interference and diffraction. Particles without mass, like photons, has no solutions of the Schrödinger equation so have another wave.

The particle-like behavior is most evident due to phenomena associated with measurement in quantum mechanics. Upon measuring the location of the particle, the particle will be forced into a more localized state as given by the uncertainty principle. When viewed through this formalism, the measurement of the wave function will randomly "collapse", or rather "decohere", to a sharply peaked function at some location. For particles with mass the likelihood of detecting the particle at any particular location is equal to the squared amplitude of the wave function there. The measurement will return a well-defined position, (subject to uncertainty), a property traditionally associated with particles. It is important to note that a measurement is only a particular type of interaction where some data is recorded and the measured quantity is forced into a particular eigenstate. The act of measurement is therefore not fundamentally different from any other interaction.

Following the development of quantum field theory the ambiguity disappeared. The field permits solutions that follow the wave equation, which are referred to as the wave functions. The term particle is used to label the irreducible representations of the Lorentz group that are permitted by the field. An interaction as in a Feynman diagram is accepted as a calculationally convenient approximation where the outgoing legs are known to be simplifications of the propagation and the internal lines are for some order in an expansion of the field interaction. Since the field is non-local and quantized, the phenomena which previously were thought of as paradoxes are explained. Within the limits of the wave-particle duality the quantum field theory gives the same results.

Visualization

Below is an illustration of wave–particle duality as it relates to De Broglie's hypothesis and Heisenberg's uncertainty principle (above), in terms of the position and momentum space wavefunctions for one spinless particle with mass in one dimension. These wavefunctions are Fourier transforms of each other.

The more localized the position-space wavefunction, the more likely the particle is to be found with the position coordinates in that region, and correspondingly the momentum-space wavefunction is less localized so the possible momentum components the particle could have are more widespread.

Conversely the more localized the momentum-space wavefunction, the more likely the particle is to be found with those values of momentum components in that region, and correspondingly the less localized the position-space wavefunction, so the position coordinates the particle could occupy are more widespread.

Position x and momentum p wavefunctions corresponding to quantum particles. The colour opacity (%) of the particles corresponds to the probability density of finding the particle with position x or momentum component p.
Top: If wavelength λ is unknown, so are momentum p, wave-vector k and energy E (de Broglie relations). As the particle is more localized in position space, Δx is smaller than for Δp_x.
Bottom: If λ is known, so are p, k, and E. As the particle is more localized in momentum space, Δp is smaller than for Δx.

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Alternative views

Wave–particle duality is an ongoing conundrum in modern physics. Most physicists accept wave-particle duality as the best explanation for a broad range of observed phenomena; however, it is not without controversy. Alternative views are also presented here. These views are not generally accepted by mainstream physics, but serve as a basis for valuable discussion within the community.

Both-particle-and-wave view

The pilot wave model, originally developed by Louis de Broglie and further developed by David Bohm into the hidden variable theory proposes that there is no duality, but rather a system exhibits both particle properties and wave properties simultaneously, and particles are guided, in a deterministic fashion, by the pilot wave (or its "quantum potential") which will direct them to areas of constructive interference in preference to areas of destructive interference. This idea is held by a significant minority within the physics community.

At least one physicist considers the "wave-duality" a misnomer, as L. Ballentine, Quantum Mechanics, A Modern Development, p. 4, explains:

When first discovered, particle diffraction was a source of great puzzlement. Are "particles" really "waves?" In the early experiments, the diffraction patterns were detected holistically by means of a photographic plate, which could not detect individual particles. As a result, the notion grew that particle and wave properties were mutually incompatible, or complementary, in the sense that different measurement apparatuses would be required to observe them. That idea, however, was only an unfortunate generalization from a technological limitation. Today it is possible to detect the arrival of individual electrons, and to see the diffraction pattern emerge as a statistical pattern made up of many small spots (Tonomura et al., 1989). Evidently, quantum particles are indeed particles, but whose behaviour is very different from classical physics would have us to expect.

Afshar experiment (2007) has demonstrated that it is possible to simultaneously observe both wave and particle properties of photons.

Wave-only view

At least one scientist proposes that the duality can be replaced by a "wave-only" view. In his book Collective Electrodynamics: Quantum Foundations of Electromagnetism (2000), Carver Mead purports to analyze the behavior of electrons and photons purely in terms of electron wave functions, and attributes the apparent particle-like behavior to quantization effects and eigenstates. According to reviewer David Haddon:

Mead has cut the Gordian knot of quantum complementarity. He claims that atoms, with their neutrons, protons, and electrons, are not particles at all but pure waves of matter. Mead cites as the gross evidence of the exclusively wave nature of both light and matter the discovery between 1933 and 1996 of ten examples of pure wave phenomena, including the ubiquitous laser of CD players, the self-propagating electrical currents of superconductors, and the Bose–Einstein condensate of atoms.

Albert Einstein, who, in his search for a Unified Field Theory, did not accept wave-particle duality, wrote:

This double nature of radiation (and of material corpuscles)...has been interpreted by quantum-mechanics in an ingenious and amazingly successful fashion. This interpretation...appears to me as only a temporary way out...

The many-worlds interpretation (MWI) is sometimes presented as a waves-only theory, including by its originator, Hugh Everett who referred to MWI as "the wave interpretation".

The Template:Visible anchor of R. Horodecki relates the particle to wave. The hypothesis implies that a massive particle is an intrinsically spatially as well as temporally extended wave phenomenon by a nonlinear law.

Neither-wave-nor-particle view

It has been argued that there are never exact particles or waves, but only some compromise or intermediate between them. One consideration is that zero dimensional mathematical points cannot be observed. Another is that the formal representation of such points, the Kronecker delta function is unphysical, because it cannot be normalized. Parallel arguments apply to pure wave states. Roger Penrose states:

"Such positions states are idealised wavefunctions [...] Whereas the momentum states are infinitely spread out, the position states are infinitely concentrated. Neither is normaliseable [...]"

Relational approach to wave–particle duality

Relational quantum mechanics is developed which regards the detection event as establishing a relationship between the quantized field and the detector. The inherent ambiguity associated with applying Heisenberg's uncertainty principle and thus wave–particle duality is subsequently avoided.

Semantic artifact view

Robert Anton Wilson suggests that many of the so-called quantum paradoxes represent semantic artifacts arising from poor language choice when reporting observed phenomena in Science. Wilson frequently used the wave-particle duality example to illustrate his idea. To wit, let us propose one group of scientists performs a set of experiments and reports, "One experiment demonstrates light is a wave while another demonstrates light is a particle." Let us also propose that another group of scientists halfway around the world also perform an identical set of experiments and reports, "When constrained by one experiment, light behaved as a wave and while constrained by another experiment, light behaved as a particle." Although both groups of scientists aim to report similar empirical observations, the first group makes an existential conclusion about the 'is-ness' of light. The second group reports their observations operationally, describing what they actually observed light doing rather than jumping to an existential conclusion about what light 'is'.

Applications

Although it is difficult to draw a line separating wave–particle duality from the rest of quantum mechanics, it is nevertheless possible to list some applications of this basic idea.

• Wave–particle duality is exploited in electron microscopy, where the small wavelengths associated with the electron can be used to view objects much smaller than what is visible using visible light.

• Similarly, neutron diffraction uses neutrons with a wavelength of about 0.1 nm, the typical spacing of atoms in a solid, to determine the structure of solids.

See also

• Arago spot
• Afshar experiment
• Basic concepts of quantum mechanics
• Complementarity (physics)
• Electron wave-packet interference
• Faraday wave
• Hanbury Brown and Twiss effect
• Photon polarization
• Scattering theory
• Wavelet
• Wheeler's delayed choice experiment

Notes and references

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External links

• Animation, applications and research linked to the wave-particle duality and other basic quantum phenomena (Université Paris Sud)
• Template:Cite arxiv
• Template:Cite web
• Template:Cite web
• E.H. Carlson, Wave–Particle Duality: Light on Project PHYSNET
• Template:Cite web
• Template:Cite web

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