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| | In [[physics]], '''relativistic mechanics''' refers to [[mechanics]] compatible with [[special relativity]] (SR) and [[general relativity]] (GR). It provides a non-[[quantum mechanics|quantum mechanical]] description of a system of particles, or of a [[fluid]], in cases where the [[velocity|velocities]] of moving objects are comparable to the [[speed of light]] ''c''. As a result, [[classical mechanics]] is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of [[electromagnetism]] with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at ''any'' speed, including faster than light. The foundations of relativistic mechanics are the [[postulates of special relativity]] and general relativity. The unification of SR with quantum mechanics is [[relativistic quantum mechanics]], while attempts for that of GR is [[quantum gravity]], an [[list of unsolved problems in physics|unsolved problem in physics]]. |
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| == Run for the Wife Ray Ban Sale Online == | | :<math>\gamma(\mathbf{v}) = \frac{1}{\sqrt{1 - \mathbf{v}\cdot\mathbf{v}/c^2}}\,\rightleftharpoons\,\gamma(v) = \frac{1}{\sqrt{1 - (v/c)^2}}.</math> |
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| | ===Relativistic energy and momentum=== |
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| | The [[four-momentum]] of an object is straightforward, identical in form to the classical momentum, but replacing 3-vectors with 4-vectors: |
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| | E &= \gamma(\mathbf{v}) m_0 c^2 \\ |
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| | \mathbf{p} &= \gamma(\mathbf{v}) m_0 \mathbf{v} |
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| | The factor of γ('''v''') comes from the definition of the four-velocity described above. The appearance of the γ factor has an alternative way of being stated, explained next. |
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| | ===Rest mass and relativistic mass=== |
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| | This makes the relativistic relation between the spatial velocity and the spatial momentum look identical. However, this can be misleading, as it is ''not'' appropriate in special relativity in ''all'' circumstances. For instance, kinetic energy and force in special relativity can not be written exactly like their classical analogues by only replacing the mass with the relativistic mass. Moreover, under Lorentz transformations, this relativistic mass is not invariant, while the rest mass is. For this reason many people find it easier use the rest mass (thereby introduce γ through the 4-velocity or coordinate time), and discard the concept of relativistic mass. |
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| | Other physicists, including [[Wolfgang Rindler]] and [[T. R. Sandin]], have argued that relativistic mass is a useful concept and there is little reason to stop using it.<ref>{{Cite journal | title = In defense of relativistic mass | author = T. R. Sandin | journal = American Journal of Physics | volume = 59 | issue = 11 | date = November 1991 | url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000059000011001032000001&idtype=cvips&gifs=yes | format = subscription required | pages = 1032 | doi = 10.1119/1.16642 | postscript = <!--None-->|bibcode = 1991AmJPh..59.1032S }}</ref> |
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| | See [[mass in special relativity]] for more information on this debate. |
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| == IS LOCAL 6 Abercrombie Store Melbourne == | | Some authors use ''m'' for relativistic mass and ''m''<sub>0</sub> for rest mass,<ref>See, for example: {{cite book |last=Feynman |first=Richard |authorlink=Richard Feynman |title=[[The Feynman Lectures on Physics#Six Not-So-Easy Pieces (1998)|Six Not-So-Easy Pieces]] |year=1998 |isbn=0-201-32842-9 |chapter=The special theory of relativity |publisher=Perseus Books |location=Cambridge, Mass.}}</ref> others simply use ''m'' for rest mass. This article uses the former convention for clarity. |
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| | A particle whose rest mass is zero is called ''massless''. [[Photon]]s and [[graviton]]s are thought to be massless; and [[neutrino]]s are nearly so. |
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| | The inertial frame in which the momenta of all particles sums to zero is called the [[center of momentum frame]]. In this special frame, the relativistic energy-momentum equation has '''p''' = 0, and thus gives the invariant mass of the system as merely the total energy of all parts of the system, divided by ''c''<sup>2</sup> |
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| | This is the invariant mass of any system which is measured in a frame where it has zero total momentum, such as a bottle of hot gas on a scale. In such a system, the mass which the scale weighs is the invariant mass, and it depends on the total energy of the system. It is thus more than the sum of the rest masses of the molecules, but also includes all the totaled energies in the system as well. Like energy and momentum, the invariant mass of isolated systems cannot be changed so long as the system remains totally closed (no mass or energy allowed in or out), because the total relativistic energy of the system remains constant so long as nothing can enter or leave it. |
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| | An increase in the energy of such a system which is caused by translating the system to an inertial frame which is not the [[center of momentum frame]], causes an increase in energy and momentum without an increase in invariant mass. ''E'' = ''m''<sub>0</sub>''c''<sup>2</sup>, however, applies only to isolated systems in their center-of-momentum frame where momentum sums to zero. |
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| | Taking this formula at face value, we see that in relativity, mass is simply energy by another name (and measured in different units). In 1927 Einstein remarked about special relativity, "Under this theory mass is not an unalterable magnitude, but a magnitude dependent on (and, indeed, identical with) the amount of energy."<ref>[http://www.pbs.org/wgbh/nova/newton/einstein.html Einstein on Newton]</ref> |
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| | In a "totally-closed" system (i.e., [[isolated system]]) the total energy, the total momentum, and hence the total invariant mass are conserved. Einstein's formula for change in mass translates to its simplest Δ''E'' = Δ''mc''<sup>2</sup> form, however, only in non-closed systems in which energy is allowed to escape (for example, as heat and light), and thus invariant mass is reduced. Einstein's equation shows that such systems must lose mass, in accordance with the above formula, in proportion to the energy they lose to the surroundings. Conversely, if one can measure the differences in mass between a system before it undergoes a reaction which releases heat and light, and the system after the reaction when heat and light have escaped, one can estimate the amount of energy which escapes the system. |
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| == Sports Illustrated Beats Wireless Price In Australia == | | ====Chemical and nuclear reactions==== |
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| | In both nuclear and chemical reactions, such energy represents the difference in binding energies of electrons in atoms (for chemistry) or between nucleons in nuclei (in atomic reactions). In both cases, the mass difference between reactants and (cooled) products measures the mass of heat and light which will escape the reaction, and thus (using the equation) give the equivalent energy of heat and light which may be emitted if the reaction proceeds. |
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| == First Church Oakley Sunglasses Sydney Australia == | | In chemistry, the mass differences associated with the emitted energy are around 10<sup>−9</sup> of the molecular mass.<ref>{{cite book|title=Modern Physics: Second Edition|page=38|year=2008|publisher=Pearson Addison-Welsey|isbn=0-8053-0308-1|author=Randy Harris}}</ref> However, in nuclear reactions the energies are so large that they are associated with mass differences, which can be estimated in advance, if the products and reactants have been weighed (atoms can be weighed indirectly by using atomic masses, which are always the same for each [[nuclide]]). Thus, Einstein's formula becomes important when one has measured the masses of different atomic nuclei. By looking at the difference in masses, one can predict which nuclei have stored energy that can be released by certain [[nuclear reaction]]s, providing important information which was useful in the development of nuclear energy and, consequently, the [[nuclear bomb]]. Historically, for example, [[Lise Meitner]] was able to use the mass differences in nuclei to estimate that there was enough energy available to make nuclear fission a favorable process. The implications of this special form of Einstein's formula have thus made it one of the most famous equations in all of science. |
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| | ====Center of momentum frame==== |
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| == 755 8th Avenue South Nike Air Max 2013 == | | The equation ''E'' = ''m''<sub>0</sub>''c''<sup>2</sup> applies only to isolated systems in their [[center of momentum frame]]. It has been popularly misunderstood to mean that mass may be ''converted'' to energy, after which the ''mass'' disappears. However, popular explanations of the equation as applied to systems include open (non-isolated) systems for which heat and light are allowed to escape, when they otherwise would have contributed to the mass ([[invariant mass]]) of the system. |
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| | Historically, confusion about mass being "converted" to energy has been aided by confusion between mass and "[[matter]]", where matter is defined as [[fermion]] particles. In such a definition, electromagnetic radiation and kinetic energy (or heat) are not considered "matter". In some situations, matter may indeed be converted to non-matter forms of energy (see above), but in all these situations, the matter and non-matter forms of energy still retain their original mass. |
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| | For isolated systems (closed to all mass and energy exchange), mass never disappears in the center of momentum frame, because energy cannot disappear. Instead, this equation, in context, means only that when any energy is added to, or escapes from, a system in the center-of-momentum frame, the system will be measured as having gained or lost mass, in proportion to energy added or removed. Thus, in theory, if an atomic bomb were placed in a box strong enough to hold its blast, and detonated upon a scale, the mass of this closed system would not change, and the scale would not move. Only when a transparent "window" was opened in the super-strong plasma-filled box, and light and heat were allowed to escape in a beam, and the bomb components to cool, would the system lose the mass associated with the energy of the blast. In a 21 kiloton bomb, for example, about a gram of light and heat is created. If this heat and light were allowed to escape, the remains of the bomb would lose a gram of mass, as it cooled. In this thought-experiment, the light and heat carry away the gram of mass, and would therefore deposit this gram of mass in the objects that absorb them.<ref>E. F. Taylor and J. A. Wheeler, '''Spacetime Physics''', W.H. Freeman and Co., NY. 1992. ISBN 0-7167-2327-1, see pp. 248-9 for discussion of mass remaining constant after detonation of nuclear bombs, until heat is allowed to escape.</ref> |
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| | ===Angular momentum=== |
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| | {{main|Relativistic angular momentum}} |
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| | In relativistic mechanics, the time-varying mass moment |
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| </ul>
| | :<math>\mathbf{N} = m \left( \mathbf{x} - t \mathbf{v} \right) </math> |
| | |
| | and orbital 3-angular momentum |
| | |
| | :<math>\mathbf{L} = \mathbf{x}\times \mathbf{p}</math> |
| | |
| | of a point-like particle are combined into a four dimensional [[bivector]] in terms of the 4-position '''X''' and the 4-momentum '''P''' of the particle:<ref>{{cite book |author=R. Penrose| title=[[The Road to Reality]]| publisher= Vintage books|pages=437–438, 566–569| year=2005 | isbn=978-00994-40680}} '''Note:''' Some authors, including Penrose, use ''Latin'' letters in this definition, even though it is conventional to use Greek indices for vectors and tensors in spacetime.</ref><ref>{{cite book|title=Special Relativity and How it Works|author=M. Fayngold|year=2008|publisher=John Wiley & Sons|page=137-139|isbn=3527406077|url=http://books.google.co.uk/books?id=Q3egk8Ds6ogC&pg=PA137&dq=angular+momentum+in+special+relativity&hl=en&sa=X&ei=2QOhUbSENeGO0AWVqoGADg&ved=0CDQQ6AEwAA#v=onepage&q=angular%20momentum%20in%20special%20relativity&f=false}}</ref> |
| | |
| | :<math>\mathbf{M} = \mathbf{X}\wedge\mathbf{P}</math> |
| | |
| | where ∧ denotes the [[exterior product]]. This tensor is additive: the total angular momentum of a system is the sum of the angular momentum tensors for each constituent of the system. So, for an assembly of discrete particles one sums the angular momentum tensors over the particles, or integrates the density of angular momentum over the extent of a continuous mass distribution. |
| | |
| | Each of the six components forms a conserved quantity when aggregated with the corresponding components for other objects and fields. |
| | |
| | === Force === |
| | |
| | In special relativity, [[Newton's second law]] does not hold in the form '''F''' = ''m'''''a''', but it does if it is expressed as |
| | :<math> \mathbf{F} = \frac{d\mathbf{p}}{dt} </math> |
| | where '''p''' = γ('''v''')''m''<sub>0</sub>'''v''' is the momentum as defined above and ''m''<sub>0</sub> is the [[invariant mass]]. Thus, the force is given by |
| | |
| | :<math>\mathbf{F} = \gamma(\mathbf{v})^3 m_0 \, \mathbf{a}_\parallel + \gamma(\mathbf{v}) m_0 \, \mathbf{a}_\perp </math> |
| | |
| | :{| class="toccolours collapsible collapsed" width="80%" style="text-align:left" |
| | !Derivation |
| | |- |
| | | |
| | Starting from |
| | :<math> \mathbf{F} = m_0 \frac{d(\gamma(\mathbf{v}) \, \mathbf{v})}{dt} = m_0 \left( \frac{d \gamma(\mathbf{v})}{dt} \, \mathbf{v} + \gamma(\mathbf{v}) \frac{d\mathbf{v}}{dt} \right).</math> |
| | |
| | Carrying out the derivatives gives |
| | |
| | :<math> \mathbf{F} = \frac{\gamma(\mathbf{v})^3 m_0}{c^2} \left( \mathbf{v} \cdot \mathbf{a} \right) \, \mathbf{v} + \gamma(\mathbf{v}) m_0\, \mathbf{a}.</math> |
| | |
| | If the acceleration is separated into [[Acceleration#Tangential and centripetal acceleration|the part parallel to the velocity ('''a'''<sub>∥</sub>) and the part perpendicular to it ('''a'''<sub>⊥</sub>)]], so that: |
| | |
| | :<math> \mathbf{a} = \mathbf{a}_\parallel + \mathbf{a}_\perp\,,\quad \mathbf{v}\cdot\mathbf{a}_\perp = 0 \,,\quad \mathbf{v}\cdot\mathbf{a} = \mathbf{v}\cdot\mathbf{a}_\parallel \,, </math> |
| | |
| | one gets |
| | |
| | :<math> \mathbf{F} = \frac{\gamma(\mathbf{v})^3 m_0}{c^2} \left( \mathbf{v} \cdot \mathbf{a}_\parallel \right) \, \mathbf{v} + \gamma(\mathbf{v}) m_0\, (\mathbf{a}_\perp + \mathbf{a}_\parallel ) \, . </math> |
| | |
| | By construction '''a'''<sub>∥</sub> and '''v''' are parallel, so ('''v'''·'''a'''<sub>∥</sub>)'''v''' is a vector with magnitude ''v''<sup>2</sup>''a''<sub>∥</sub> in the direction of '''v''' (and hence '''a'''<sub>∥</sub>) which allows the replacement: |
| | |
| | :<math> (\mathbf{v}\cdot\mathbf{a}) \mathbf{v} = v^2 \mathbf{a}_\parallel </math> |
| | |
| | then |
| | |
| | :<math>\begin{align} |
| | \mathbf{F} & = \frac{\gamma(\mathbf{v})^3 m_0 v^{2}}{c^2} \, \mathbf{a}_{\parallel} + \gamma(\mathbf{v}) m_0 \, (\mathbf{a}_{\parallel} + \mathbf{a}_{\perp})\\ |
| | & = \gamma(\mathbf{v})^3 m_0 \left( \frac{v^2}{c^2} + \frac{1}{\gamma(\mathbf{v})^2} \right) \mathbf{a}_{\parallel} + \gamma(\mathbf{v}) m_0 \, \mathbf{a}_{\perp} \\ |
| | & = \gamma(\mathbf{v})^3 m_0 \left( \frac{v^{2}}{c^2} + 1 - \frac{v^{2}}{c^2} \right) \mathbf{a}_{\parallel} + \gamma(\mathbf{v}) m_0 \, \mathbf{a}_{\perp} \\ |
| | & = \gamma(\mathbf{v})^3 m_0 \, \mathbf{a}_{\parallel} + \gamma(\mathbf{v}) m_0 \, \mathbf{a}_{\perp} |
| | \end{align}\,</math> |
| | |
| | |} |
| | |
| | Consequently in some old texts, γ('''v''')<sup>3</sup>''m''<sub>0</sub> is referred to as the ''longitudinal mass'', and γ('''v''')''m''<sub>0</sub> is referred to as the ''transverse mass'', which is numerically the same as the [[relativistic mass]]. See [[mass in special relativity]]. |
| | |
| | If one inverts this to calculate acceleration from force, one gets |
| | |
| | :<math> \mathbf{a} = \frac{1}{m_0 \gamma(\mathbf{v})} \left( \mathbf{F} - \frac{ ( \mathbf{v} \cdot \mathbf{F} ) \mathbf{v} }{c^2} \right) \,.</math> |
| | |
| | The force described in this section is the classical 3-D force which is not a [[four-vector]]. This 3-D force is the appropriate concept of force since it is the force which obeys [[Newton's laws of motion#Newton's third law|Newton's third law of motion]]. It should not be confused with the so-called [[four-force]] which is merely the 3-D force in the comoving frame of the object transformed as if it were a four-vector. However, the density of 3-D force (linear momentum transferred per unit [[Four-dimensional space|four-volume]]) ''is'' a four-vector ([[tensor density|density]] of weight +1) when combined with the negative of the density of power transferred. |
| | |
| | ===Torque=== |
| | |
| | The torque acting on a point-like particle is defined as the derivative of the angular momentum tensor given above with respect to proper time:<ref>{{cite paper|title=Torque and angular momentum on a system at equilibrium in special relativity|author=S. Aranoff|journal=American journal of physics|volume=37|year=1969|url=http://www.researchgate.net/publication/237053370_Torques_in_Special_Relativity}} This author uses '''T''' for torque, here we use capital Gamma '''Γ''' since ''T'' is most often reserved for the [[stress-energy tensor]].</ref><ref>{{cite paper|title=Equilibrium in special relativity|author=S. Aranoff|journal=Nuovo Cimento|volume=10|year=1972|url=http://www.analysis-knowledge.com/Physics/Equilibrium%20in%20Special%20Relativity.pdf|page=159}}</ref> |
| | |
| | :<math>\boldsymbol{\Gamma} = \frac{d \mathbf{M}}{d\tau} = \mathbf{X}\wedge \mathbf{F}</math> |
| | |
| | or in tensor components: |
| | |
| | :<math>\Gamma_{\alpha\beta} = X_\alpha F_\beta - X_\beta F_\alpha </math> |
| | |
| | where '''F''' is the 4d force acting on the particle at the event '''X'''. As with angular momentum, torque is additive, so for an extended object one sums or integrates over the distribution of mass. |
| | |
| | ===Kinetic energy=== |
| | |
| | The ''[[work-energy theorem]]'' says<ref>R.C.Tolman "Relativity Thermodynamics and Cosmology" pp47-48</ref> the change in [[kinetic energy]] is equal to the work done on the body. In special relativity: |
| | |
| | :<math>\begin{align} |
| | \Delta K = W = [\gamma_1(v_1) - \gamma_0(v_0)] m_0c^2.\end{align}</math> |
| | |
| | :{| class="toccolours collapsible collapsed" width="80%" style="text-align:left" |
| | !Derivation |
| | |- |
| | | |
| | :<math>\begin{align} |
| | \Delta K = W &= \int_{\mathbf{x}_0}^{\mathbf{x}_1} \mathbf{F} \cdot d\mathbf{x} \\ |
| | &= \int_{t_0}^{t_1} \frac{d}{dt}(\gamma m_0 \mathbf{v})\cdot\mathbf{v}dt \\ |
| | &= \left. \gamma m_0 \mathbf{v} \cdot \mathbf{v} \right|^{t_1}_{t_0} - \int_{t_0}^{t_1} \gamma m_0\mathbf{v} \cdot \frac{d\mathbf{v}}{dt} dt \\ |
| | &= \left. \gamma m_0 v^2 \right|^{t_1}_{t_0} - m_0\int_{v_0}^{v_1} \gamma v\,dv \\ |
| | &= m_0 \left( \left. \gamma v^2 \right|^{t_1}_{t_0} - c^2\int_{v_0}^{v_1} \frac{2v/c^2}{2\sqrt{1-v^2/c^2}}\,dv \right) \\ |
| | &= \left. m_0\left(\frac {v^2}{\sqrt{1-v^2/c^2}} + c^2 \sqrt{1-v^2/c^2} \right) \right|^{t_1}_{t_0} \\ |
| | &= \left. \frac {m_0c^2}{\sqrt{1-v^2/c^2}} \right|^{t_1}_{t_0} \\ |
| | &= \left. {\gamma m_0c^2}\right|^{t_1}_{t_0} \\ |
| | &= \gamma_1 m_0c^2 - \gamma_0 mc^2.\end{align}</math> |
| | |} |
| | |
| | If in the initial state the body was at rest, so ''v''<sub>0</sub> = 0 and γ<sub>0</sub>(''v''<sub>0</sub>) = 1, and in the final state it has speed ''v''<sub>1</sub> = ''v'', setting γ<sub>1</sub>(''v''<sub>1</sub>) = γ(''v''), the kinetic energy is then; |
| | :<math>K = [\gamma(v) - 1]m_0 c^2\,,</math> |
| | a result that can be directly obtained by subtracting the rest energy ''m''<sub>0</sub>''c''<sup>2</sup> from the total relativistic energy γ(''v'')''m''<sub>0</sub>''c''<sup>2</sup>. |
| | |
| | ===Classical limit=== |
| | The Lorentz factor γ(''v'') can be expanded into a [[Taylor series]] or [[binomial series]] for (''v''/''c'')<sup>2</sup> < 1, obtaining: |
| | |
| | :<math>\gamma = \dfrac{1}{\sqrt{1 - (v/c)^2}} = \sum_{n=0}^{\infty} \left(\dfrac{v}{c}\right)^{2n}\prod_{k=1}^n \left(\dfrac{2k - 1}{2k}\right) = 1 + \dfrac{1}{2} \left(\dfrac{v}{c}\right)^2 + \dfrac{3}{8} \left(\dfrac{v}{c}\right)^4 + \dfrac{5}{16} \left(\dfrac{v}{c}\right)^6 + \cdots</math> |
| | |
| | and consequently |
| | :<math>E - m_0 c^2 = \frac{1}{2} m_0 v^2 + \frac{3}{8} \frac{m_0 v^4}{c^2} + \frac{5}{16} \frac{m_0 v^6}{c^4} + \cdots ;</math> |
| | :<math>\mathbf{p} = m_0 \mathbf{v} + \frac{1}{2} \frac{m_0 v^2 \mathbf{v}}{c^2} + \frac{3}{8} \frac{m_0 v^4 \mathbf{v}}{c^4} + \frac{5}{16} \frac{m_0 v^6 \mathbf{v}}{c^6} + \cdots .</math> |
| | |
| | For velocities much smaller than that of light, one can neglect the terms with ''c''<sup>2</sup> and higher in the denominator. These formulas then reduce to the standard definitions of Newtonian [[kinetic energy]] and momentum. This is as it should be, for special relativity must agree with Newtonian mechanics at low velocities. |
| | |
| | ==See also== |
| | |
| | *[[Introduction to special relativity]] |
| | *[[Twin paradox]] |
| | *[[Relativistic equations]] |
| | *[[Relativistic heat conduction]] |
| | *[[Classical electromagnetism and special relativity]] |
| | *[[Relativistic system (mathematics)]] |
| | |
| | ==References== |
| | |
| | ===Notes=== |
| | |
| | {{reflist}} |
| | |
| | * {{cite article|title=Center of mass in special and general relativity and its |
| | role in an effective description of spacetime|author=C. Chryssomalakos, H. Hernandez-Coronado, E. Okon |
| | |year=2009|location=Mexico|journal= J.Phys.Conf.Ser.|url=http://arxiv.org/pdf/0901.3349v1.pdf|arxiv=0901.3349|doi=10.1088/1742-6596/174/1/012026}} |
| | |
| | ===Further reading=== |
| | |
| | ;General scope and special/general relativity |
| | |
| | * {{cite book| author=P.M. Whelan, M.J. Hodgeson| title=Essential Principles of Physics| publisher=John Murray|edition=2nd| year=1978 | isbn=0-7195-3382-1}} |
| | * {{cite book| author=G. Woan| title=The Cambridge Handbook of Physics Formulas| publisher=Cambridge University Press|edition=| year=2010| isbn=978-0-521-57507-2}} |
| | * {{cite book|page=| author=P.A. Tipler, G. Mosca| title=Physics for Scientists and Engineers: With Modern Physics| publisher=W.H. Freeman and Co|edition=6th| year=2008| isbn=9-781429-202657}} |
| | * {{cite book|page=| author=R.G. Lerner, G.L. Trigg| title=Encyclopaedia of Physics| publisher=VHC Publishers, Hans Warlimont, Springer|edition=2nd| year=2005| isbn=978-0-07-025734-4}} |
| | *Concepts of Modern Physics (4th Edition), A. Beiser, Physics, McGraw-Hill (International), 1987, ISBN 0-07-100144-1 |
| | * {{cite book|page=| author=C.B. Parker| title=McGraw Hill Encyclopaedia of Physics| publisher=McGraw Hill|edition=2nd| year=1994| isbn=0-07-051400-3}} |
| | * {{cite book|title=The Geometry of Physics |author=T. Frankel|publisher=Cambridge University Press|year=2012|edition=3rd|isbn=978-1107-602601}} |
| | * {{cite book|title=Physics with Modern Applications|author=L.H. Greenberg|publisher=Holt-Saunders International W.B. Saunders and Co|year=1978|isbn=0-7216-4247-0}} |
| | * {{cite book| author=A. Halpern| title=3000 Solved Problems in Physics, Schaum Series| publisher=Mc Graw Hill|edition=| year=1988| isbn=978-0-07-025734-4}} |
| | |
| | ;Electromagnetism and special relativity |
| | |
| | * {{cite book|title=Electricity and Modern Physics |edition=2nd|author=G.A.G. Bennet|publisher=Edward Arnold (UK)|year=1974|isbn=0-7131-2459-8}} |
| | * {{cite book|title=Electromagnetism|edition=2nd|author=I.S. Grant, W.R. Phillips, Manchester Physics|publisher=John Wiley & Sons|year=2008|isbn=978-0-471-92712-9}} |
| | * {{cite book|title=Introduction to Electrodynamics|edition=3rd |author=D.J. Griffiths|publisher=Pearson Education, Dorling Kindersley, |year=2007|isbn=81-7758-293-3}} |
| | |
| | ;Classical mechanics and special relativity |
| | |
| | * {{cite book|title=Dynamics and Relativity|author=J.R. Forshaw, A.G. Smith|publisher=Wiley, |year=2009|isbn=978-0-470-01460-8}} |
| | * {{cite book|title=An Introduction to Mechanics|author=D. Kleppner, R.J. Kolenkow|publisher=Cambridge University Press|year=2010|isbn=978-0-521-19821-9}} |
| | * {{cite book|title=Analytical Mechanics|author=L.N. Hand, J.D. Finch|publisher=Cambridge University Press|year=2008|isbn=978-0-521-57572-0}} |
| | |
| | ;General relativity |
| | |
| | * {{cite book|title=Relativity DeMystified|author=D. McMahon|publisher=Mc Graw Hill|year=2006|isbn=0-07-145545-0}} |
| | * {{cite book|title=[[Gravitation (book)|Gravitation]]|author=J.A. Wheeler, C. Misner, K.S. Thorne|publisher=W.H. Freeman & Co|year=1973|isbn=0-7167-0344-0}} |
| | * {{cite book|title=Gravitation and Inertia|author= J.A. Wheeler, I. Ciufolini|publisher=Princeton University Press|year=1995|isbn=978-0-691-03323-5}} |
| | * {{cite book|title=Relativity, Gravitation, and Cosmology|author= R.J.A. Lambourne|publisher=Cambridge University Press|year=2010|isbn=9-780521-131384}} |
| | |
| | [[Category:Theory of relativity]] |
Template:Further2
In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light c. As a result, classical mechanics is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of electromagnetism with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at any speed, including faster than light. The foundations of relativistic mechanics are the postulates of special relativity and general relativity. The unification of SR with quantum mechanics is relativistic quantum mechanics, while attempts for that of GR is quantum gravity, an unsolved problem in physics.
As with classical mechanics, the subject can be divided into "kinematics"; the description of motion by specifying positions, velocities and accelerations, and "dynamics"; a full description by considering energies, momenta, and angular momenta and their conservation laws, and forces acting on particles or exerted by particles. There is however a subtlety; what appears to be "moving" and what is "at rest"—which is termed by "statics" in classical mechanics—depends on the relative motion of observers who measure in frames of reference.
Although some definitions and concepts from classical mechanics do carry over to SR, such as force as the time derivative of momentum (Newton's second law), the work done by a particle as the line integral of force exerted on the particle along a path, and power as the time derivative of work done, there are a number of significant modifications to the remaining definitions and formulae. SR states that motion is relative and the laws of physics are the same for all experimenters irrespective of their inertial reference frames. In addition to modifying notions of space and time, SR forces one to reconsider the concepts of mass, momentum, and energy all of which are important constructs in Newtonian mechanics. SR shows that these concepts are all different aspects of the same physical quantity in much the same way that it shows space and time to be interrelated. Consequently, another modification is the concept of the center of mass of a system, which is straightforward to define in classical mechanics but much less obvious in relativity - see relativistic center of mass for details.
The equations become more complicated in the more familiar three dimensional vector calculus formalism, due to the nonlinearity in the Lorentz factor, which accurately accounts for relativistic velocity dependence and the speed limit of all particles and fields. However, they have a simpler and elegant form in four-dimensional spacetime, which includes flat Minkowski space (SR) and curved spacetime (GR), because three dimensional vectors derived from space and scalars derived from time can be collected into four vectors, or four dimensional tensors. However, the six component angular momentum tensor is sometimes called a bivector because in the 3D viewpoint it is two vectors (one of these, the conventional angular momentum, being an axial vector).
Relativistic kinematics
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The relativistic four-velocity, that is the four-vector representing velocity in relativity, is defined as follows:
In the above, τ is the proper time of the path through spacetime, called the world-line, followed by the object velocity the above represents, and
is the four-position; the coordinates of an event. Due to time dilation, the proper time is the time between two events in a frame of reference where they take place at the same location. The proper time is related to coordinate time t by:
where γ(v) is the Lorentz factor:
(either version may be quoted) so it follows:
The first three terms, excepting the factor of γ(v), is the velocity as seen by the observer in their own reference frame. The γ(v) is determined by the velocity v between the observer's reference frame and the object's frame, which is the frame in which its proper time is measured. This quantity is invariant under Lorentz transformation, so to check to see what an observer in a different reference frame sees, one simply multiplies the velocity four-vector by the Lorentz transformation matrix between the two reference frames.
Relativistic dynamics
Relativistic energy and momentum
There are a couple of (equivalent) ways to define momentum and energy in SR. One method uses conservation laws. If these laws are to remain valid in SR they must be true in every possible reference frame. However, if one does some simple thought experiments using the Newtonian definitions of momentum and energy, one sees that these quantities are not conserved in SR. One can rescue the idea of conservation by making some small modifications to the definitions to account for relativistic velocities. It is these new definitions which are taken as the correct ones for momentum and energy in SR.
The four-momentum of an object is straightforward, identical in form to the classical momentum, but replacing 3-vectors with 4-vectors:
The energy and momentum of an object with invariant mass m0 (also called rest mass), moving with velocity v with respect to a given frame of reference, are respectively given by
The factor of γ(v) comes from the definition of the four-velocity described above. The appearance of the γ factor has an alternative way of being stated, explained next.
Rest mass and relativistic mass
The quantity
is often called the relativistic mass of the object in the given frame of reference.[1]
This makes the relativistic relation between the spatial velocity and the spatial momentum look identical. However, this can be misleading, as it is not appropriate in special relativity in all circumstances. For instance, kinetic energy and force in special relativity can not be written exactly like their classical analogues by only replacing the mass with the relativistic mass. Moreover, under Lorentz transformations, this relativistic mass is not invariant, while the rest mass is. For this reason many people find it easier use the rest mass (thereby introduce γ through the 4-velocity or coordinate time), and discard the concept of relativistic mass.
Lev B. Okun suggested that "this terminology [...] has no rational justification today", and should no longer be taught.[2]
Other physicists, including Wolfgang Rindler and T. R. Sandin, have argued that relativistic mass is a useful concept and there is little reason to stop using it.[3]
See mass in special relativity for more information on this debate.
Some authors use m for relativistic mass and m0 for rest mass,[4] others simply use m for rest mass. This article uses the former convention for clarity.
The energy and momentum of an object with invariant mass m0 are related by the formulas
The first is referred to as the relativistic energy–momentum relation. While the energy E and the momentum p depend on the frame of reference in which they are measured, the quantity E2 − (pc)2 is invariant, and arises as −c2 times the squared magnitude of the 4-momentum vector which is −(m0c)2.
It should be noted that the invariant mass of a system
is different from the sum of the rest masses of the particles of which it is composed due to kinetic energy and binding energy. Rest mass is not a conserved quantity in special relativity unlike the situation in Newtonian physics. However, if an object is not changing internally, then its rest mass will not change and can be calculated with the same result in any frame of reference.
A particle whose rest mass is zero is called massless. Photons and gravitons are thought to be massless; and neutrinos are nearly so.
Mass–energy equivalence
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The relativistic energy-momentum equation holds for all particles, even for massless particles for which m0 = 0. In this case:
When substituted into Ev = c2p, this gives v = c: massless particles (such as photons) always travel at the speed of light.
Notice that the rest mass of a composite system will generally be slightly different from the sum of the rest masses of its parts since, in its rest frame, their kinetic energy will increase its mass and their (negative) binding energy will decrease its mass. In particular, a hypothetical "box of light" would have rest mass even though made of particles which do not since their momenta would cancel.
Looking at the above formula for invariant mass of a system, one sees that, when a single massive object is at rest (v = 0, p = 0), there is a non-zero mass remaining: m0 = E/c2.
The corresponding energy, which is also the total energy when a single particle is at rest, is referred to as "rest energy". In systems of particles which are seen from a moving inertial frame, total energy increases and so does momentum. However, for single particles the rest mass remains constant, and for systems of particles the invariant mass remain constant, because in both cases, the energy and momentum increases subtract from each other, and cancel. Thus, the invariant mass of systems of particles is a calculated constant for all observers, as is the rest mass of single particles.
The mass of systems and conservation of invariant mass
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For systems of particles, the energy-momentum equation requires summing the momentum vectors of the particles:
The inertial frame in which the momenta of all particles sums to zero is called the center of momentum frame. In this special frame, the relativistic energy-momentum equation has p = 0, and thus gives the invariant mass of the system as merely the total energy of all parts of the system, divided by c2
This is the invariant mass of any system which is measured in a frame where it has zero total momentum, such as a bottle of hot gas on a scale. In such a system, the mass which the scale weighs is the invariant mass, and it depends on the total energy of the system. It is thus more than the sum of the rest masses of the molecules, but also includes all the totaled energies in the system as well. Like energy and momentum, the invariant mass of isolated systems cannot be changed so long as the system remains totally closed (no mass or energy allowed in or out), because the total relativistic energy of the system remains constant so long as nothing can enter or leave it.
An increase in the energy of such a system which is caused by translating the system to an inertial frame which is not the center of momentum frame, causes an increase in energy and momentum without an increase in invariant mass. E = m0c2, however, applies only to isolated systems in their center-of-momentum frame where momentum sums to zero.
Taking this formula at face value, we see that in relativity, mass is simply energy by another name (and measured in different units). In 1927 Einstein remarked about special relativity, "Under this theory mass is not an unalterable magnitude, but a magnitude dependent on (and, indeed, identical with) the amount of energy."[5]
Closed (isolated) systems
In a "totally-closed" system (i.e., isolated system) the total energy, the total momentum, and hence the total invariant mass are conserved. Einstein's formula for change in mass translates to its simplest ΔE = Δmc2 form, however, only in non-closed systems in which energy is allowed to escape (for example, as heat and light), and thus invariant mass is reduced. Einstein's equation shows that such systems must lose mass, in accordance with the above formula, in proportion to the energy they lose to the surroundings. Conversely, if one can measure the differences in mass between a system before it undergoes a reaction which releases heat and light, and the system after the reaction when heat and light have escaped, one can estimate the amount of energy which escapes the system.
Chemical and nuclear reactions
In both nuclear and chemical reactions, such energy represents the difference in binding energies of electrons in atoms (for chemistry) or between nucleons in nuclei (in atomic reactions). In both cases, the mass difference between reactants and (cooled) products measures the mass of heat and light which will escape the reaction, and thus (using the equation) give the equivalent energy of heat and light which may be emitted if the reaction proceeds.
In chemistry, the mass differences associated with the emitted energy are around 10−9 of the molecular mass.[6] However, in nuclear reactions the energies are so large that they are associated with mass differences, which can be estimated in advance, if the products and reactants have been weighed (atoms can be weighed indirectly by using atomic masses, which are always the same for each nuclide). Thus, Einstein's formula becomes important when one has measured the masses of different atomic nuclei. By looking at the difference in masses, one can predict which nuclei have stored energy that can be released by certain nuclear reactions, providing important information which was useful in the development of nuclear energy and, consequently, the nuclear bomb. Historically, for example, Lise Meitner was able to use the mass differences in nuclei to estimate that there was enough energy available to make nuclear fission a favorable process. The implications of this special form of Einstein's formula have thus made it one of the most famous equations in all of science.
Center of momentum frame
The equation E = m0c2 applies only to isolated systems in their center of momentum frame. It has been popularly misunderstood to mean that mass may be converted to energy, after which the mass disappears. However, popular explanations of the equation as applied to systems include open (non-isolated) systems for which heat and light are allowed to escape, when they otherwise would have contributed to the mass (invariant mass) of the system.
Historically, confusion about mass being "converted" to energy has been aided by confusion between mass and "matter", where matter is defined as fermion particles. In such a definition, electromagnetic radiation and kinetic energy (or heat) are not considered "matter". In some situations, matter may indeed be converted to non-matter forms of energy (see above), but in all these situations, the matter and non-matter forms of energy still retain their original mass.
For isolated systems (closed to all mass and energy exchange), mass never disappears in the center of momentum frame, because energy cannot disappear. Instead, this equation, in context, means only that when any energy is added to, or escapes from, a system in the center-of-momentum frame, the system will be measured as having gained or lost mass, in proportion to energy added or removed. Thus, in theory, if an atomic bomb were placed in a box strong enough to hold its blast, and detonated upon a scale, the mass of this closed system would not change, and the scale would not move. Only when a transparent "window" was opened in the super-strong plasma-filled box, and light and heat were allowed to escape in a beam, and the bomb components to cool, would the system lose the mass associated with the energy of the blast. In a 21 kiloton bomb, for example, about a gram of light and heat is created. If this heat and light were allowed to escape, the remains of the bomb would lose a gram of mass, as it cooled. In this thought-experiment, the light and heat carry away the gram of mass, and would therefore deposit this gram of mass in the objects that absorb them.[7]
Angular momentum
Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.
In relativistic mechanics, the time-varying mass moment
and orbital 3-angular momentum
of a point-like particle are combined into a four dimensional bivector in terms of the 4-position X and the 4-momentum P of the particle:[8][9]
where ∧ denotes the exterior product. This tensor is additive: the total angular momentum of a system is the sum of the angular momentum tensors for each constituent of the system. So, for an assembly of discrete particles one sums the angular momentum tensors over the particles, or integrates the density of angular momentum over the extent of a continuous mass distribution.
Each of the six components forms a conserved quantity when aggregated with the corresponding components for other objects and fields.
Force
In special relativity, Newton's second law does not hold in the form F = ma, but it does if it is expressed as
where p = γ(v)m0v is the momentum as defined above and m0 is the invariant mass. Thus, the force is given by
Consequently in some old texts, γ(v)3m0 is referred to as the longitudinal mass, and γ(v)m0 is referred to as the transverse mass, which is numerically the same as the relativistic mass. See mass in special relativity.
If one inverts this to calculate acceleration from force, one gets
The force described in this section is the classical 3-D force which is not a four-vector. This 3-D force is the appropriate concept of force since it is the force which obeys Newton's third law of motion. It should not be confused with the so-called four-force which is merely the 3-D force in the comoving frame of the object transformed as if it were a four-vector. However, the density of 3-D force (linear momentum transferred per unit four-volume) is a four-vector (density of weight +1) when combined with the negative of the density of power transferred.
Torque
The torque acting on a point-like particle is defined as the derivative of the angular momentum tensor given above with respect to proper time:[10][11]
or in tensor components:
where F is the 4d force acting on the particle at the event X. As with angular momentum, torque is additive, so for an extended object one sums or integrates over the distribution of mass.
Kinetic energy
The work-energy theorem says[12] the change in kinetic energy is equal to the work done on the body. In special relativity:
If in the initial state the body was at rest, so v0 = 0 and γ0(v0) = 1, and in the final state it has speed v1 = v, setting γ1(v1) = γ(v), the kinetic energy is then;
a result that can be directly obtained by subtracting the rest energy m0c2 from the total relativistic energy γ(v)m0c2.
Classical limit
The Lorentz factor γ(v) can be expanded into a Taylor series or binomial series for (v/c)2 < 1, obtaining:
and consequently
For velocities much smaller than that of light, one can neglect the terms with c2 and higher in the denominator. These formulas then reduce to the standard definitions of Newtonian kinetic energy and momentum. This is as it should be, for special relativity must agree with Newtonian mechanics at low velocities.
See also
References
Notes
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
Further reading
- General scope and special/general relativity
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- Concepts of Modern Physics (4th Edition), A. Beiser, Physics, McGraw-Hill (International), 1987, ISBN 0-07-100144-1
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- Electromagnetism and special relativity
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- Classical mechanics and special relativity
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- General relativity
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- ↑ Template:Cite web Note that in 2008 the last editor, Don Koks, rewrote a significant portion of the page, changing it from a view extremely dismissive of the usefulness of relativistic mass to one which hardly questions it. The previous version was: Template:Cite web
- ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
- ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
- ↑ See, for example: 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- ↑ Einstein on Newton
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- ↑ E. F. Taylor and J. A. Wheeler, Spacetime Physics, W.H. Freeman and Co., NY. 1992. ISBN 0-7167-2327-1, see pp. 248-9 for discussion of mass remaining constant after detonation of nuclear bombs, until heat is allowed to escape.
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Note: Some authors, including Penrose, use Latin letters in this definition, even though it is conventional to use Greek indices for vectors and tensors in spacetime.
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
- ↑ Template:Cite paper This author uses T for torque, here we use capital Gamma Γ since T is most often reserved for the stress-energy tensor.
- ↑ Template:Cite paper
- ↑ R.C.Tolman "Relativity Thermodynamics and Cosmology" pp47-48