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| [[File:Gravitational red-shifting2.png|thumb|200px|The gravitational redshift of a light wave as it moves upwards against a gravitational field (produced by the yellow star below).]]
| | With all the buzz about Green Coffee Bean Extract, I had to take a chance plus give it a try. Who wouldn't like to lose a few pounds with absolutely no diet or exercise? The complete thing souded too wise to be true. Something had to be wrong with this theory. I set my notice to go ahead and try it, thinking that I was going to prove Dr. Oz and everyone else incorrect. Well, to my surprise it really worked! I couldn't believe it.<br><br>These are delicious raspberry yogurt muffins. The right thing about them is they are only 133 calories each. The total recipe is about 1595 calories thus you can function out how much will be inside smallermuffins.Enjoy!<br><br>raspberry ketone is the latest fad among the fat watchers. Unlike different fat burners plus fat loss pills, it is very 1 product which seems to be efficient plus secure at the same time.<br><br>In fact, much of which spam misspells ketone as keytone, perhaps to encourage you to buy something to tone you up. That doesnt grow the self-confidence in the slim underlying science.<br><br>If youre not really sure regarding using Absonutrix [http://safedietplansforwomen.com/raspberry-ketones raspberry ketone], thats okay, theres a great deal of skeptics available. However, dont be so rapid to judge, try it out. The all-natural supplement originates from the berry and assists stimulate the release of hormones that help break down fat with a ideal response. Youll burn calories, youll run from hoops, and the muscles may thank you.<br><br>For my exercise - I would go to the gym for at least 1 hour, each day. There are no days off. I would do at least 20-30 minutes of cardio followed by muscle confusion strength training, functioning almost raspberry ketone diet every area of the body at when. Every day, I would change course and speed.<br><br>Especially for Type II diabetics, exercising is regarded as the number one techniques to lower blood sugars degrees. Exercise will enhance blood glucose degrees in many methods. First, whenever you work aerobic exercise, muscles take up glucose 20 occasions quicker. Secondly, stength training will assist build more muscle. Consequently, the more muscle we have, the more glucose is burned. In 1 recent research of Hispanic men and women, experts found that 16 weeks of strength training improved blood sugar degrees similar to taking diabetes drugs. However, when the blood glucose level is 250 mg/dL or above, check your ketones initially. If ketones are obvious, never exercise. Furthermore, when a blood sugar 300 mg/dL or high, even without any evidence of ketones, never exercise.<br><br>Some people report headaches taking the Hydroxycut Caffeine Free, but I did not experience any bad negative effects different than periodic sleepiness. If you do experience any side effects, decrease dosage or stop taking plus talk to the doctor. |
| In [[astrophysics]], '''gravitational redshift''' or '''Einstein shift''' is the process by which [[electromagnetic radiation]] originating from a source that is in a [[gravitational field]] is reduced in [[frequency]], or [[redshift]]ed, when observed in a region of a weaker gravitational field. This is a direct result of [[Gravitational time dilation]] - as one moves away from a source of gravitational field, the rate at which time passes is increased relative to the case when one is near the source. As frequency is inverse of time (specifically, time required for completing one wave oscillation), frequency of the electromagnetic radiation is reduced in an area of a higher gravitational potential (i.e., equivalently, of lower gravitational field) . There is a corresponding reduction in energy when electromagnetic radiation is red-shifted, as given by [[Planck's relation]], due to the electromagnetic radiation propagating in opposition to the gravitational gradient. There also exists a corresponding [[blueshift]] when electromagnetic radiation propagates from an area of a weaker gravitational field to an area of a stronger gravitational field.
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| If applied to optical wavelengths, this manifests itself as a change in the colour of visible light as the wavelength of the light is increased toward the red part of the [[light spectrum]]. Since frequency and wavelength are inversely proportional, this is equivalent to saying that the frequency of the light is reduced towards the red part of the light spectrum, giving this phenomenon the name [[redshift]].
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| ==Definition==
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| [[Redshift]] is often denoted with the [[dimensionless]] variable <math>z\,</math>, defined as the fractional change of the wavelength<ref>
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| See for example equation 29.3 of ''[[Gravitation (book)|Gravitation]]'' by Misner, Thorne and Wheeler.
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| </ref>
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| <math>z=\frac{\lambda_o-\lambda_e}{\lambda_e}</math> | |
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| Where
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| <math>\lambda_o\,</math> is the wavelength of the [[electromagnetic radiation]] ([[photon]]) as measured by the observer.
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| <math>\lambda_e\,</math> is the wavelength of the [[electromagnetic radiation]] ([[photon]]) when measured at the source of emission.
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| The gravitational redshift of a photon can be calculated in the framework of [[General Relativity]] (using the [[Schwarzschild metric]]) as | |
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| <math>\lim_{r\to +\infty}z(r)=\frac{1}{\sqrt{1-\frac{r_s}{R^*}}}-1</math> | |
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| with the [[Schwarzschild radius]]
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| <math>r_s=\frac{2GM}{c^2}</math>,
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| where <math>G</math> denotes Newton's [[gravitational constant]],
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| <math>M</math> the [[mass]] of the gravitating body,
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| <math>c</math> the [[speed of light]], and
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| <math>R^*</math> the distance between the center of mass of the gravitating body and the point at which the photon is emitted. The redshift is not defined for photons emitted inside the Schwarzschild radius, the distance from the body where the [[escape velocity]] is greater than the speed of light. Therefore this formula only applies when <math>R^*</math> is at least as large as <math>r_s</math>. When the photon is emitted at a distance equal to the Schwarzschild radius, the redshift will be infinitely large. When the photon is emitted at an infinitely large distance, there is no redshift.
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| In the Newtonian limit, i.e. when <math>R^*</math> is sufficiently large compared to the Schwarzschild radius <math>r_s</math>, the redshift can be approximated by a [[binomial expansion]] to become
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| <math>\lim_{r\to +\infty}z_\mathrm{approx}(r)=\frac{1}{2}\frac{r_s}{R^*} = \frac{GM}{c^2R^*}</math>
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| ==History==
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| The gravitational weakening of light from high-gravity stars was predicted by [[John Michell]] in 1783 and [[Pierre-Simon Laplace]] in 1796, using [[Isaac Newton]]'s concept of light corpuscles (see: [[emission theory]]) and who predicted that some stars would have a gravity so strong that light would not be able to escape. The effect of gravity on light was then explored by [[Johann Georg von Soldner]] (1801), who calculated the amount of deflection of a light ray by the sun, arriving at the Newtonian answer which is half the value predicted by [[general relativity]]. All of this early work assumed that light could slow down and fall, which was inconsistent with the modern understanding of light waves.
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| Once it became accepted that light is an electromagnetic wave, it was clear that the frequency of light should not change from place to place, since waves from a source with a fixed frequency keep the same frequency everywhere. One way around this conclusion would be if time itself were altered—if clocks at different points had different rates.
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| This was precisely [[Albert Einstein|Einstein's]] conclusion in 1911. He considered an accelerating box, and noted that according to the [[special theory of relativity]], the clock rate at the bottom of the box was slower than the clock rate at the top. Nowadays, this can be easily shown in [[Rindler space|accelerated coordinates]]. The metric tensor in [[natural units|units where the speed of light is one]] is:
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| :<math>
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| ds^2 = - r^2 dt^2 + dr^2
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| \,</math>
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| and for an observer at a constant value of r, the rate at which a clock ticks, R(r), is the square root of the time coefficient, R(r)=r. The acceleration at position r is equal to the curvature of the hyperbola at fixed r, and like the curvature of the nested circles in polar coordinates, it is equal to 1/r.
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| So at a fixed value of g, the fractional rate of change of the clock-rate, the percentage change in the ticking at the top of an accelerating box vs at the bottom, is:
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| :<math>
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| {R(r+dr) - R(r) \over R} = {dr\over r} = g dr
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| \,</math>
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| The rate is faster at larger values of R, away from the apparent direction of acceleration. The rate is zero at r=0, which is the location of the [[horizon|acceleration horizon]].
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| Using the [[principle of equivalence]], Einstein concluded that the same thing holds in any gravitational field, that the rate of clocks R at different heights was altered according to the gravitational field g. When g is slowly varying, it gives the fractional rate of change of the ticking rate. If the ticking rate is everywhere almost this same, the fractional rate of change is the same as the absolute rate of change, so that:
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| :<math>
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| {dR \over dx} = g = - {dV\over dx}
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| \,</math>
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| Since the rate of clocks and the gravitational potential have the same derivative, they are the same up to a constant. The constant is chosen to make the clock rate at infinity equal to 1. Since the gravitational potential is zero at infinity:
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| :<math>
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| R(x)= 1 - {V(x) \over c^2}
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| \,</math>
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| where the speed of light has been restored to make the gravitational potential dimensionless.
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| The coefficient of the <math>dt^2</math> in the [[metric tensor (general relativity)|metric tensor]] is the square of the clock rate, which for small values of the potential is given by keeping only the linear term:
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| :<math>
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| R^2 = 1 - 2V
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| \,</math>
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| and the full metric tensor is:
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| :<math>
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| ds^2 = - \left( 1 - {2V(r)\over c^2} \right) c^2 dt^2 + dx^2 + dy^2 + dz^2
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| </math>
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| where again the c's have been restored. This expression is correct in the full theory of general relativity, to lowest order in the gravitational field, and ignoring the variation of the space-space and space-time components of the metric tensor, which only affect fast moving objects.
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| Using this approximation, Einstein reproduced the incorrect Newtonian value for the deflection of light in 1909. But since a light beam is a fast moving object, the space-space components contribute too. After constructing the full theory of general relativity in 1916, Einstein solved for the space-space components in a [[post-Newtonian approximation]], and calculated the correct amount of light deflection – double the Newtonian value. Einstein's prediction was confirmed by many experiments, starting with [[Arthur Eddington]]'s 1919 solar eclipse expedition.
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| The changing rates of clocks allowed Einstein to conclude that light waves change frequency as they move, and the frequency/energy relationship for photons allowed him to see that this was best interpreted as the effect of the gravitational field on the [[mass–energy equivalence|mass–energy]] of the photon. To calculate the changes in frequency in a nearly static gravitational field, only the time component of the metric tensor is important, and the lowest order approximation is accurate enough for ordinary stars and planets, which are much bigger than their [[Schwarzschild radius]].
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| ==Important things to stress==
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| * The receiving end of the light transmission must be located at a higher [[gravitational potential]] in order for gravitational redshift to be observed. In other words, the observer must be standing "uphill" from the source. If the observer is at a ''lower'' gravitational potential than the source, a gravitational [[blueshift]] can be observed instead.
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| * Tests done by many universities continue to support the existence of gravitational redshift.<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html General Relativity]</ref>
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| * Gravitational redshift is not only predicted by [[general relativity]]. Other theories of gravitation require gravitational redshift, although their detailed explanations for why it appears vary.{{Citation needed|date=September 2007}} (Any theory that includes [[conservation of energy]] and [[mass–energy equivalence]] must include gravitational redshift.)
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| * Gravitational redshift does not assume the [[Schwarzschild metric]] solution to [[Einstein's field equation]] – in which the variable <math>M\;</math> cannot represent the mass of any rotating or charged body.
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| ==Initial verification==
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| A number of experimenters initially claimed to have identified the effect using astronomical measurements, and the effect was eventually considered to have been finally identified in the spectral lines of the star [[Sirius B]] by [[Walter Sydney Adams|W.S. Adams]] in 1925. However, measurements of the effect before the 1960s have been critiqued by (''e.g.'', by C.M. Will),{{citation needed|date=August 2010}} and the effect is now considered to have been definitively verified by the experiments of [[Robert Pound|Pound]], Rebka and Snider between 1959 and 1965.
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| The [[Pound–Rebka experiment]] of 1959 measured the gravitational redshift in spectral lines using a terrestrial [[Iron-57|<sup>57</sup>Fe]] [[gamma rays|gamma]] source. This was documented{{citation needed|date=August 2010}} by scientists of the Lyman Laboratory of Physics at [[Harvard University]]. A commonly cited experimental verification is the Pound–Snider experiment of 1965. [[James W. Brault]], a graduate student of [[Robert Dicke]] at [[Princeton University]], measured the gravitational redshift of the sun using optical methods in 1962.
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| More information can be seen at [[Tests of general relativity]].
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| ==Application==
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| Gravitational redshift is studied in many areas of [[astrophysics|astrophysical]] research.
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| ==Exact Solutions==
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| A table of exact solutions of the [[Einstein field equations]] consists of the following:
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| {| class="wikitable"
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| | Non-rotating
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| | Rotating
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| |-
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| | Uncharged
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| | [[Schwarzschild metric|Schwarzschild]]
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| | [[Kerr metric|Kerr]]
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| |-
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| | Charged
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| | [[Reissner–Nordström metric|Reissner–Nordström]]
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| | [[Kerr–Newman metric|Kerr–Newman]]
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| |}
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| The more often used exact equation for gravitational redshift applies to the case outside of a non-rotating, uncharged mass which is spherically symmetric. The equation is:
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| <math>\lim_{r\to +\infty}z(r)=\frac{1}{\sqrt{1-\left(\frac{2GM}{R^*c^2}\right)}}-1</math>, where
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| * <math>G\,</math> is the [[gravitational constant]],
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| * <math>M\,</math> is the [[mass]] of the object creating the gravitational field,
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| * <math>R^*\,</math> is the radial coordinate of the point of emission (which is analogous to the classical distance from the center of the object, but is actually a [[Schwarzschild coordinates|Schwarzschild coordinate]]),
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| * <math>r,</math> is the radial coordinate of the observer (in the formula, this observer is at an infinitely large distance), and
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| * <math>c\,</math> is the [[speed of light]].
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| ==Gravitational redshift versus gravitational time dilation==
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| When using [[special relativity]]'s [[relativistic Doppler]] relationships to calculate the change in energy and frequency (assuming no complicating [[route-dependent]] effects such as those caused by the [[frame-dragging]] of [[rotating black hole]]s), then the Gravitational redshift and [[blueshift]] frequency ratios are the inverse of each other, suggesting that the "seen" frequency-change corresponds to the [[gravitational time dilation|actual difference in underlying clockrate]]. Route-dependence due to [[frame-dragging]] may come into play, which would invalidate this idea and complicate the process of determining globally agreed differences in underlying clock rate.
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| While gravitational redshift refers to what is seen, [[gravitational time dilation]] refers to what is deduced to be "really" happening once observational effects are taken into account.
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| ==See also==
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| * [[Tests of general relativity]]
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| * [[Equivalence principle]]
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| * [[Gravitational time dilation]]
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| * [[Redshift]]
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| ==Notes==
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| {{Reflist}}
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| ==Primary sources==
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| * {{Cite journal
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| |last=Michell, John
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| |year=1784
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| |title=On the means of discovering the distance, magnitude etc. of the fixed stars
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| |journal=Philosophical Transactions of the Royal Society
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| |pages = 35–57
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| }}
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| * {{Cite book
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| |last=Laplace, Pierre-Simon
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| |year=1796
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| |title=The system of the world (English translation 1809)
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| |volume=2
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| |pages = 366–368
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| |location=London
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| |publisher=Richard Phillips
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| |url=http://books.google.com/?id=f7Kv2iFUNJoC}}
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| * {{Cite journal
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| |last=Soldner, Johann Georg von
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| |year=1804
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| |title=[[s:On the Deflection of a Light Ray from its Rectilinear Motion|On the deflection of a light ray from its rectilinear motion, by the attraction of a celestial body at which it nearly passes by]]
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| |journal=Berliner Astronomisches Jahrbuch
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| |pages =161–172}}
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| * Albert Einstein, "Relativity: the Special and General Theory." [[gutenberg:5001|(@Project Gutenberg)]].
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| * R.V. Pound and G.A. Rebka, Jr. "Gravitational Red-Shift in Nuclear Resonance" Phys. Rev. Lett. '''3''' 439–441 (1959)
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| * R.V. Pound and J.L. Snider "Effect of gravity on gamma radiation" Phys. Rev. '''140 B''' 788–803 (1965)
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| * R.V. Pound, "Weighing Photons" Classical and Quantum Gravity '''17''' 2303–2311 (2000)
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| ==References==
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| * {{Cite book | last1 = Misner | first1 = Charles W. | last2 = Thorne | first2 = Kip S. | last3 = Wheeler | first3 = John Archibald | title = Gravitation | publisher = W. H. Freeman | location = San Francisco | year = 1973 | month = 1973-09-15 | isbn = 978-0-7167-0344-0 }}
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| [[Category:Albert Einstein]]
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| [[Category:Effects of gravitation]]
| |
With all the buzz about Green Coffee Bean Extract, I had to take a chance plus give it a try. Who wouldn't like to lose a few pounds with absolutely no diet or exercise? The complete thing souded too wise to be true. Something had to be wrong with this theory. I set my notice to go ahead and try it, thinking that I was going to prove Dr. Oz and everyone else incorrect. Well, to my surprise it really worked! I couldn't believe it.
These are delicious raspberry yogurt muffins. The right thing about them is they are only 133 calories each. The total recipe is about 1595 calories thus you can function out how much will be inside smallermuffins.Enjoy!
raspberry ketone is the latest fad among the fat watchers. Unlike different fat burners plus fat loss pills, it is very 1 product which seems to be efficient plus secure at the same time.
In fact, much of which spam misspells ketone as keytone, perhaps to encourage you to buy something to tone you up. That doesnt grow the self-confidence in the slim underlying science.
If youre not really sure regarding using Absonutrix raspberry ketone, thats okay, theres a great deal of skeptics available. However, dont be so rapid to judge, try it out. The all-natural supplement originates from the berry and assists stimulate the release of hormones that help break down fat with a ideal response. Youll burn calories, youll run from hoops, and the muscles may thank you.
For my exercise - I would go to the gym for at least 1 hour, each day. There are no days off. I would do at least 20-30 minutes of cardio followed by muscle confusion strength training, functioning almost raspberry ketone diet every area of the body at when. Every day, I would change course and speed.
Especially for Type II diabetics, exercising is regarded as the number one techniques to lower blood sugars degrees. Exercise will enhance blood glucose degrees in many methods. First, whenever you work aerobic exercise, muscles take up glucose 20 occasions quicker. Secondly, stength training will assist build more muscle. Consequently, the more muscle we have, the more glucose is burned. In 1 recent research of Hispanic men and women, experts found that 16 weeks of strength training improved blood sugar degrees similar to taking diabetes drugs. However, when the blood glucose level is 250 mg/dL or above, check your ketones initially. If ketones are obvious, never exercise. Furthermore, when a blood sugar 300 mg/dL or high, even without any evidence of ketones, never exercise.
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