力和描述力如何工作的牛顿三定律通常被视为经典力学的核心组成部分。但在一项新的提议中,一个物理学家小组建议,首先向学习力学的学生介绍涉及能量的概念,并通过从能量方程推导出力来教授力。研究人员现在提出证据表明,这种基于微积分的“能量优先”入门课程提高了数学能力较弱的学生的成绩,并提高了物理和工程课程后期的成绩。 文章来源: https://physics.aps.org/articles/v12/100 N.-L. Nguyen and D. E. Meltzer, “Initial understanding of vector concepts among students in introductory physics courses,” Am. J. Phys. 71 , 630 (2003) . C. J. Fischer, The Energy of Physics, Part I: Classical Mechanics and Thermodynamics, 2nd Edition (2019) . C. J. Fischer, The Energy of Physics, Part II: Electricity and Magnetism, 2nd Edition (2020) . E. Brewe, “Energy as a substancelike quantity that flows: Theoretical considerations and pedagogical consequences,” Phys. Rev. ST Phys. Educ. Res. 7 , 020106 (2011) . J. Solbes, J. Guisasola, and F. Tarín, “Teaching energy conservation as a unifying principle in physics,” J. Sci. Ed. Technol. 18 , 265 (2009) . 让汉字也能进行数学及物理运算 链接: http://wap.sciencenet.cn/blog-3364677-1162318.html
在网上经常看到有人说 : 震级每增加一级,释放的能量增加约 31.6 倍;一次 6.5 级地震释放的能量是一次 5.5 级地震的 约 32.6 倍。那么,这些说法严谨吗 ? 实际上,一次地震释放的能量(地震能)包括地震波辐射能、摩擦热能与表面能等,地震波辐射能仅占地震能的一小部分。因为震级对应的能量为地震波辐射能,故“释放的能量”说法不严谨,科学家伙不宜这样笼统地说。 据有关学者的研究,地震波辐射能与震级的关系为: lg E =1.5 M S +constant lg E =1.5 M L +constant lg E =1.5 M W +constant lg E =2.4 m b +constant 式中, E 表示地震波辐射能, M S 表示 面波震级, M L 表示 地方震级或近震震级, M W 表示 矩震级, m b 表示 短周期体波震级。 由上述公式知, 当两次地震的震级标度均为 M S 或 M L 或 M W 时 ,其震级差( D M , D M ≥0 )与相应地震波辐射能之比( E 2 / E 1 , E 2 ≥ E 1 )的关系为: E 2 / E 1 =10 1.5 D M ( 1 ) 当两次地震的震级标度均为 m b 时,其震级差( D m , D m ≥0 )与相应地震波辐射能之比( E 2 / E 1 , E 2 ≥ E 1 )的关系为: E 2 / E 1 =10 2.4 D m ( 2 ) 可看出,地震波辐射能之比与震级标度有关。 由式( 1 )知,震级每增加一级,地震波辐射能之比约为 32.6 ;而由式( 2 )知,震级每增加一级,地震波辐射能之比约为 251.2 。 再回到本文开头提出的问题,严谨的说法是:( 1 )以 M S 或 M L 或 M W 表示的震级每增加一级,地震波辐射能增加约 31.6 倍;以 m b 表示的震级每增加一级,地震波辐射能增加约 250.2 倍。( 2 )一次 M S 6.5 或 M L 6.5 或 M W 6.5 地震的地震波辐射能分别是一次 M S 5.5 或 M L 5.5 或 M W 5.5 地震的约 32.6 倍 ; 而 一次 m b 6.5 地震的地震波辐射能是一次 m b 5.5 地震的 约 251.2 倍。 综上,科学家伙科普震级与能量关系时,应注意关键词“震级标度”与“地震波辐射能”,否则会以讹传讹,给公众传播不靠谱的知识。 参考(略)
以下内容是科学网博客上的留言,鉴于回答的问题很重要而且具有普遍性,现以博文的形式发表。 刘吉斌 2015-5-21 23:25 刘教授: 请你注意英捷特数据库平台(ingentaconnect) 中physics today68卷第6期以封面文章发表(31日前)名为 A new approach to the correction of Galilean transformation的文章,其属下期刊physics Essays已在线发表。我认为这文章的内容值得人们关注,故作此留言。如果你们能细读这文章,也许会给你们带来一些重要的课题和机遇。文章作者——刘圣。 博主回复(2017-7-5 21:17) : 看了刘圣先生的文章,有两点看法:1. 能量是物质运动的惯性的量度,质量只能近似描述惯性,其实质量不是一个真实的物理量(请参阅我的论文“ 质量是一个真实的物理量吗? ”),所以没有质量的物质是有能量的,从而是有惯性的。有了这一点,他的论文的前提就不成立了;2. 时空结构是由参照系的运动状态决定的,与物质是否有质量无关,与物质是什么类型的物质无关,认为不同的物质应满足不同的时空变换是不可信的; 3. 由时空的均匀性、各向同性及惯性系等价原理就可推出“准洛伦兹变换”(里面有个常数V,而不是C),但可以通过实验来确定这个常数V, 比如通过测量高速运动粒子的寿命来确定,也可以要求麦克斯韦方程在这个变换下协变来确定,巧合的是这个V正好就是等于光速C, 从而得到洛伦兹变换。 刘圣先生的论文链接: https://www.researchgate.net/publication/289674860_A_new_approach_to_the_correction_of_Galilean_transformation 请参阅我的论文“ A new approach to special relativity ”和“ Is mass a real physical quantity ”
论文摘要 尽管质量是一个非常普通和基本的概念,但是质量问题仍然是现代物理的关键问题之一,到目前为止,专家们还是没能达成一致。在这篇论文中,我们讨论了有关质量,能量和物质的问题,意识到质量既不是一个物体所含物质的量,也不是物体惯性的量度,也不是引力场的源,而能量是一个物体惯性的量度,也是引力场的源。以前,质量的概念被用于度量惯性和计算引力只是一种仅当物体和粒子作慢速运动,其静止能量远大于其动能时的近似方法。其实,质量的概念是一个多余的人造概念,它等于静止能量除以一个常数 c 的平方 (如果选择 c=1,质量就精确地等于静止能量),没有任何其它物理意义。如果质量的概念完全由能量的概念来取代(更准确地讲,应该是静止能量),所得物理方程是非常完美的,其物理意义更加清楚,一些困惑,诸如质量和能量的关系,物质的本质,弱等效原理的实质和黑格子机制的物理意义,等等,都会变得更清楚。 目录 1. Introduction 引言 2. Should the concept of relativistic mass be introduced into Physics? 动质量的概念应该被引入到物理学中吗? 3. Is mass the amount of matter an object has? 质量是物体所含物质之量吗? 4. Is mass the measure of inertia? 质量是惯性的量度吗? 5. What is the essence of gravitational mass? 引力质量的本质是什么? 6. If there is no concept of mass in Physics 如果在物理学中没有质量的概念 7. Summary 总结 全文下载
之前一直疑惑我计算的声子谱纵坐标是什么,别人的是频率单位,我的数值和别人不一样,看文献还有人用波矢的单位(cm-1),现在终于搞懂了,分享给大家! 转载自新浪博客: 点击可以查看更多信息。 http://blog.sina.com.cn/s/blog_5f15ead20100cwwo.html Magnitude Unit name MKS value mass Kg 1.E0 mass g 1.E-3 mass amu 1.66054E-27 length m 1.E0 length cm 1.E-2 length nm 1.E-9 length Ang 1.E-10 length Bohr 0.529177E-10 time s 1.E0 time fs 1.E-15 time ps 1.E-12 time ns 1.E-9 energy J 1.E0 energy erg 1.E-7 energy eV 1.60219E-19 energy meV 1.60219E-22 energy Ry 2.17991E-18 energy mRy 2.17991E-21 energy Hartree 4.35982E-18 energy K 1.38066E-23 energy kcal/mol 6.94780E-21 energy mHartree 4.35982E-21 energy kJ/mol 1.6606E-21 energy Hz 6.6262E-34 energy THz 6.6262E-22 energy cm-1 1.986E-23 energy cm**-1 1.986E-23 energy cm-1 1.986E-23 force N 1.E0 force eV/Ang 1.60219E-9 force Ry/Bohr 4.11943E-8 Magnitude Unit name MKS value pressure Pa 1.E0 pressure MPa 1.E6 pressure GPa 1.E9 pressure atm 1.01325E5 pressure bar 1.E5 pressure Kbar 1.E8 pressure Mbar 1.E11 pressure Ry/Bohr**3 1.47108E13 pressure eV/Ang**3 1.60219E11 charge C 1.E0 charge e 1.602177E-19 dipole C*m 1.E0 dipole D 3.33564E-30 dipole debye 3.33564E-30 dipole e*Bohr 8.47835E-30 dipole e*Ang 1.602177E-29 MomInert Kg*m**2 1.E0 MomInert Ry*fs**2 2.17991E-48 Efield V/m 1.E0 Efield V/nm 1.E9 Efield V/Ang 1.E10 Efield V/Bohr 1.8897268E10 Efield Ry/Bohr/e 2.5711273E11 Efield Har/Bohr/e 5.1422546E11 angle deg 1.d0 angle rad 5.72957795E1 torque eV/deg 1.E0 torque eV/rad 1.745533E-2 torque Ry/deg 13.6058E0 torque Ry/rad 0.237466E0 torque meV/deg 1.E-3 torque meV/rad 1.745533E-5 torque mRy/deg 13.6058E-3 torque mRy/rad 0.237466E-3
之前一直疑惑我计算的声子谱纵坐标是什么,别人的是频率单位,我的数值和别人不一样,看文献还有人用波矢的单位(cm-1),现在终于搞懂了,分享给大家! 转载自新浪博客: http://blog.sina.com.cn/s/blog_5f15ead20100cwwo.html,点击可以查看更多信息。 Magnitude Unit name MKS value mass Kg 1.E0 mass g 1.E-3 mass amu 1.66054E-27 length m 1.E0 length cm 1.E-2 length nm 1.E-9 length Ang 1.E-10 length Bohr 0.529177E-10 time s 1.E0 time fs 1.E-15 time ps 1.E-12 time ns 1.E-9 energy J 1.E0 energy erg 1.E-7 energy eV 1.60219E-19 energy meV 1.60219E-22 energy Ry 2.17991E-18 energy mRy 2.17991E-21 energy Hartree 4.35982E-18 energy K 1.38066E-23 energy kcal/mol 6.94780E-21 energy mHartree 4.35982E-21 energy kJ/mol 1.6606E-21 energy Hz 6.6262E-34 energy THz 6.6262E-22 energy cm-1 1.986E-23 energy cm**-1 1.986E-23 energy cm-1 1.986E-23 force N 1.E0 force eV/Ang 1.60219E-9 force Ry/Bohr 4.11943E-8 Magnitude Unit name MKS value pressure Pa 1.E0 pressure MPa 1.E6 pressure GPa 1.E9 pressure atm 1.01325E5 pressure bar 1.E5 pressure Kbar 1.E8 pressure Mbar 1.E11 pressure Ry/Bohr**3 1.47108E13 pressure eV/Ang**3 1.60219E11 charge C 1.E0 charge e 1.602177E-19 dipole C*m 1.E0 dipole D 3.33564E-30 dipole debye 3.33564E-30 dipole e*Bohr 8.47835E-30 dipole e*Ang 1.602177E-29 MomInert Kg*m**2 1.E0 MomInert Ry*fs**2 2.17991E-48 Efield V/m 1.E0 Efield V/nm 1.E9 Efield V/Ang 1.E10 Efield V/Bohr 1.8897268E10 Efield Ry/Bohr/e 2.5711273E11 Efield Har/Bohr/e 5.1422546E11 angle deg 1.d0 angle rad 5.72957795E1 torque eV/deg 1.E0 torque eV/rad 1.745533E-2 torque Ry/deg 13.6058E0 torque Ry/rad 0.237466E0 torque meV/deg 1.E-3 torque meV/rad 1.745533E-5 torque mRy/deg 13.6058E-3 torque mRy/rad 0.237466E-3
Regenauer-Lieb K, Weinberg R F, Rosenbaum G. The effect of energy feedbacks on continental strength . Nature, 2006, 442(7098): 67-70. http://www.nature.com/nature/journal/v442/n7098/full/nature04868.html 【Abstract】The classical strength profile of continents1, 2 is derived from a quasi-static view of their rheological response to stress—one that does not consider dynamic interactions between brittle and ductile layers. Such interactions result in complexities of failure in the brittle–ductile transition and the need to couple energy to understand strain localization. Here we investigate continental deformation by solving the fully coupled energy, momentum and continuum equations. We show that this approach produces unexpected feedback processes, leading to a significantly weaker dynamic strength evolution. In our model, stress localization focused on the brittle–ductile transition leads to the spontaneous development of mid-crustal detachment faults immediately above the strongest crustal layer. We also find that an additional decoupling layer forms between the lower crust and mantle. Our results explain the development of decoupling layers that are observed to accommodate hundreds of kilometres of horizontal motions during continental deformation.
How to Attract Positive Energy and Dispel Negative Energy 养生之道:如何吸收正能量,驱除负能量 急切需要“个性化方法” 原则上,你可以采取任何有效于你的方法增进你的“正能量”... 以下是来自网络的一些建议性的东西,我觉得这些不一定适合你。 Written by: Sen - CalmDownMind.com Every moment you have a choice –to be at peace or to be in resistance. When you are at peace you attract positive energy and when you resist you create negative vibes that reflect back on your being. It’s a simple choice and yet most people unconsciously choose to live in negativity. It’s not your boss, colleagues, parents, ex or the traffic, but your own perception that creates stress and negative energy. Circumstances are neutral. You will generate positive vibes when your inner state is one of alignment and congruence, instead of being resistive. 养生之道:如何吸收正能量,驱除负能量 Start Your Day With Meditation冥思 Any form of meditation is helpful but it’s best to keep it simple. Just practice the meditation of becoming aware of your presence. You don’t have to sit in any strident posture, just relax and feel your consciousness or presence in the midst of the thoughts and emotions. This is a very powerful practice that creates a positive vibe throughout the body. Treat Everyone the Way You Want to be Treated A day is easily ruined when you start holding resentment against someone. Know that everything is oneness and though we appear as different forms, everything is the manifestation of the one true essence. When you see others as yourself you will not harbor negative feelings and in turn your attitude will attract positive energy from the people around you. Let Go of Your Need to Control Life is a flux and its nature is change. The more you resist the more you will suffer. Whenever you try to control a life situation, you will feel stressed out and this will generate a lot of negative energy. Just imagine life to be a raging river, does it serve any purpose to struggle? Wouldn’t it be much more relaxing and peaceful if you just let go and allow yourself to float with the flow? People who stay surrendered and relaxed generate a lot of positive energy and attract the grace of life. See the Positive in Every Situation Know that good and bad are just perceptions created in the conditioned mind. In reality every life situation is pure grace and is the manifestation of the one truth – call it god or spirit or energy. When you see every situation with this innocence, it will reveal its grace to you. Visualize a Peaceful Life Your mind might be addicted to negative thinking, most minds are. You will have to consciously break out of this addiction if you want to attract positive energy within you. Stay conscious and see your mind churning out fearful images. Stop thinking these thoughts and focus your attention on visualizing a peaceful flow of life. You will be amazed at the positive vibes you feel in your body. Stop Worrying About the Future Worry has not served any purpose to this date for anyone. Whatever has to happen will happen, there is nothing you will achieve by worrying about it. In fact what you worry about will not even happen most of the times. So why waste energy dwelling on worries? You are unconsciously creating a lot of negative energy inside you which is harmful to your whole being. Just plan practically and leave the rest to life. Drop the Resentment Within The past is past, it has no reality than as a memory trace. Can you live in such simplicity? After all if you don’t continuously think up a bad memory you will not feel any resentment within. So just learn to forgive and move on. There is a lot positive energy in the simple act of forgiveness. Stay as the Presence Instead of the Ego While interacting with people try to stay as the conscious presence instead of dwelling in your mind. Be the unconditioned presence, allowing people to talk or interact with you without taking offence or protecting opinions. People will get attracted to your calm nature as it radiates a lot of positive energy. Look at the Nature If you want to attract positive energy just look at the nature for a while. A tree or a flower, it just rests in stillness and moves with the wind. There is a peace that radiates from their being. This peace will ignite your own inner true nature of stillness. Feel the Spaciousness in Your Body Just close your eyes and try to feel your body from within. You will be surprised at the spaciousness of your body. It feels like a lot of empty space with a few sensations here and there. This inner body realization will free up any stored negative energy. After a few moments of inner body realization you will feel light and at ease. These are some simple techniques to attract positive energy into your being. Remember that staying conscious and dwelling in presence is your true nature, and it’s always peaceful and radiant of positive energy. (来自网络,仅供参考)
心理学杂谈:呼唤“正能量”就是Positive Psychology来到中国? 什么是Positive Psychology? Positive Psychology 的目的在于帮助人们改负面思维,使人们感觉更幸福,更有力量和勇气面对人生。 Positive Psychology脱胎于人本主义心理学,把希望借助现代自然科学的方法论来寻找环境中或现实中能够增进健康人群的精神福祉,使人们感觉更幸福,更有力量。 Positive Psychology之父 被认为是美国宾西法尼法大学的 Martin E. P. Seligman(昵称 Marty)。此人在1998年率先在美国出版了一系列的关于“自我帮助”的书籍。在这些书籍里他阐述了一种“Learned Helplessness( 习得的无助感)的心理学观念。 在他看来人类和动物在遭遇逆境或坎坷之后喜倾向于进行“内归因),即习惯性地认为自我是无助者 ( act or behave helplessly in a particular situation) usually after experiencing some inability to avoid an adverse situation —甚至当该个体完全有能力改变局面的时候,也总是西习惯性寻找自己的原因,把自己条定在孤立无援这种可怜兮兮的地位。他发现这种情况及其类似于严重抑郁病患者的表现,而造成这种心理状态的根本原因是个体对环境的无法控制/改变。 与人本主义心理学家马斯洛不同,他提出了 美好人生 五要素说:1、 P ositive emotion —by writing down, every day at bed time, three things that went well, and why ;2、 E ngagement —by preferentially using one's highest strengths to perform the tasks which one would perform anyway ;3、 R elationships — but not in a way that can be explained briefly; listen to timestamp 15:12 and following of the audio ;4、 M eaning — belonging to and serving something bigger than one's self ;5、 A chievement — determination is known to count for more than IQ
20世纪初期,晴朗的物理学上空飘着“两朵乌云”,它们是: 黑体辐射研究中的紫外灾难 以太漂移实验中的零结果。 后来出现了量子论,普朗克后来NB了:获得NB物理学奖。 后来出现了相对论,爱因斯坦也NB了:获得NB物理学奖。 如今,21世纪初期,天朝物理学上空飘来了两个“正能量”: 1)以包括科学网博主邢LRJ物理学家在内的、中科院物理学家为主体的大亚湾中微子实验研究国际合作成果 2)以T大XUE院士为主的国际合作团队“量子反常霍尔效应”研究获突破 http://www.sciencemag.org/content/early/2013/03/13/science.1234414 相关报道: http://news.tsinghua.edu.cn/publish/news/4204/2013/20130315085129032737847/20130315085129032737847_.html http://paper.sciencenet.cn/htmlpaper/201331513142223128244.shtm Prediction: The 2reach the NB level, and have possibility to win NB prize .
在分子模拟中,当体系非常庞大时,单机计算就显得非常缓慢,这时候就要用到多核/多机并行运算。MPI就是一种很好的并行实现方式,它通过网络把许多计算机连接起来,把任务分配给许多CPU以实现加速。下面用一个例子说明在分子模拟中如何利用MPI来计算体系的能量。 假定体系有1 000 000个原子,那么要计算原子间总的相互作用就需要进行5$\times$10$^{11}$次计算,单机运行起来很慢。 do iAtom = 1, 1000000-1 do jAtom = iAtom + 1, 1000000 uTot = uTot + getEn(iAtom, jAtom) end do end do 但是如果我们有10个CPU,那么每个CPU只要计算$\frac{1}{10}$的相互作用就可以了,理论上可以提速十倍。对每台机器来说,只要运行 do iAtom = iProc + 1, 1000000-1, nProcs do jAtom = iAtom + 1, 1000000 uTot = uTot + getEn(iAtom, jAtom) end do end do 其中iProc是当前CPU的序号,nProcs是要使用的CPU的总数。每个CPU得到各自的结果后,用MPI_Reduce把大家的结果都加起来,就得到了体系的总能量。
VASP中各种能量 2012-08-19 14:07:22| 分类: VASP | 标签:vasp计算 电子结构 |字号 订阅 【转自】:http://cms.mpi.univie.ac.at/vasp-forum/forum_viewtopic.php?4.273 Dear colleague, TOTEN includes ALL energy contributions (listed separately in OUTCAR), namely: -- alpha Z and the Ewald energy: the electrostatic interaction of the ions in a compensating electron gas. -- the Hartee and exchange correlation energy as defined in the Kohn-Sham hamiltonian -- The entropy part steems from the smearing (using the free energy as varionational parameter), -- EBANDS are the KS-eigenvalues and -- EATOM is the reference energy for the potential (which is defined in the POTCAR file). Furthermore, if you do MD, ETOTAL includes the following terms in addition to TOTEN: EKIN the kinetic energy (at the given T) ES the Nose potential EPS the Nose kinetic or a detailed overview I recommend to read first the VASP theory papers and afterwards studying the source code especially pot.F, ebs.F, main.F. -- EBAND is explicitely written in OUTCAR (but it is not the total elecron energy) -- the electrostatic contributions have to be obtained by subtracting all parts that do not contribute to OUTCAR中计算结果显示: Free energy of the ion-electron system (eV) --------------------------------------------------- alpha Z PSCENC = 472.40550564 Ewald energy TEWEN = -5073.64932000 -1/2 Hartree DENC = -395.84178320 -V(xc)+E(xc) XCENC = -1485.40951914 PAW double counting = 4089.61537183 -2348.49082964 entropy T*S EENTRO = 0.02077590 eigenvalues EBANDS = 433.09482024 atomic energy EATOM = 4005.65773062 --------------------------------------------------- free energy TOTEN = -302.59724774 eV energy without entropy = -302.61802364 energy(sigma-0) = -302.60417304 其分别表示: alpha Z and the Ewald energy define the electrostatic interaction of the ions in a compensating electron gas. The alpha Z component deals with the divergent parts (G=0). The following parts are the Hartree and exchange correlation energy as defined in the Kohn-Sham Hamiltonian. The entropy part stems from the smearing (using the free energy as variational parameter, electronic entropy), EBANDS from Kohn-Sham eigenvalues, and EATOM is the reference energy for the potential (which is defined in the POTCAR file). Furthermore, you find a documentation of the respective terms of the Schroedinger equation in the handouts of the VASP-workshop, http://cms.mpi.univie.ac.at/vasp-workshop especially in the session about dft (download especially comput_mat.pdf, dft_introd.pdf, and accuracy.pdf (p.4 for EATOM))
当前震级标度有以下几种:地方性震级 M L , 短周期体波震级 m b 、长周期体波震级 m B 、面波震级 M S 、矩震级 M W 以及持续时间震级 M D ,常见震级标度换算公式如下: 对于 M W 震级的转换采用以下方法,在大多数破坏性地震的震级测定中,当 6.4 < M S < 7.8 时, M W = M S ;当 M S = 6 时, M W ≈ M S ,相差很小;在较小震级范围内 M W = M L 。 震级 M L 、地震矩 M 0 、地震能量 E 和 Benioff Strain 之间换算关系如下: 当不同的震级标度统一换算为 M L 时,表 1 给出了震级及相应的能量、 Benioff 应变值。 表 1 震级 - 能量 - Benioff 应变换算表 震级 ( M L ) 地震距 M 0 能量 E Benioff 应变 1 3.55E+10 1.77E+06 1.33E+03 2 1.12E+12 5.61E+07 7.49E+03 3 3.55E+13 1.77E+09 4.21E+04 4 1.12E+15 5.61E+10 2.37E+05 5 3.55E+16 1.77E+12 1.33E+06 6 1.12E+18 5.61E+13 7.49E+06 7 3.55E+19 1.77E+15 4.21E+07 8 1.12E+21 5.61E+16 2.37E+08 9 3.55E+22 1.77E+18 1.33E+09
众所周知 , 热力学第一定律和热力学第二定律是人类宏观经验总结 . 例如 , 王竹溪的“热力学”教科书中说 : “ … 把一个不可逆过程所产生的改变完全恢复原状 , 这是不可能的 . 这个经验事实是热力学第二定律的基础 , 它的准确性由无数的热力学第二定律的推论都与实际现象符合而得到保障 . ” 傅献彩等的“物理化学”教科书中也明确地说 : “ 热力学第二定律和热力学第一定律一样 , 是建立在无数事实的基础上 , 是人类经验的总结 . 它不能从其它更普遍的定律推导出来 . ” 人类的大量日常经验可以归纳为两句话: (1) 能量是守恒的 , 不生不灭 , 一种能量形式的减少或消失 , 就一定伴随着另一种能量形式的增加或生成 . (2) ( 有效 ) 能量是耗散的 , 单向的 , 不可逆的 , 不可能取之不尽 , 用之不竭 . 一旦 ( 有效 ) 能量转换成环境温度的废热 , 就不可能再被利用来对外作功 . 实际上 , 这就是热力学第一定律和热力学第二定律 . 其中 , 有效能量又称可利用的能量 (available energy) 就是指体系中可以被利用来对外作功的能量部分 . “ 能量的耗散 (energy dissipation)” 就是开尔文所说 “ 能量的退化 (energy degradation)” 而不是能量的减少或消失 . 简而言之, 热力学第一定律和热力学第二定律就是 : (1) 能量是守恒的 , 不生不灭 . (2) 能量是耗散的 , 一旦转变成废热 , 就不能再被利用 . 绝大部分热力学教科书中,讨论热力学第二定律的文字表述时列举了一种 “克劳修斯的表述”,两种“开尔文的表述”。即 热力学第二定律的“克劳修斯表述”: “不可能把热从低温传到高温物体,而不引起其它变化。” 热力学第二定律的“开尔文第一种表述”: “不可能从单一热源取出热使之完全变为功,而不引起其它变化。” 热力学第二定律的“开尔文第二种表述”: “第二类永动机是不可能得到的。” 可是这里所指的第二类永动机就是很狭义地重复前面两种表述. 必须加上 1865 年热力学第二定律的“克劳修斯第二种表述”: “第二基础原理,在我所给出的形式中,断定所有在自然界中的转变可以按一定的方向, 就是我已经假定是正的方向, 不需要补偿地由它们自己进行;但是对相反的方向,就是负的方向,它们就只可能在同时发生的正转变的补偿下进行。 (The second fundamental theorem, in the form which I have given to it, asserts that all transformations occurring in nature may take place in a certain direction, which I have assumed as positive, by themselves, that is, without compensation; but that in the opposite, and consequently nega-tive direction, they can only take place in such a manner as to be compensated by simultaneous occurring positive transformations.) ” 显然,克劳修斯所讨论的体系中至少包含两个(或两类)过程: 1. “正的方向”的“不需要补偿地由它们自己进行”的自发过程, 又称正耗散过程;和 2. “负的方向”的“在同时发生的正转变的补偿下进行”的非自发过程, 又称负耗散过程。但是体系永远不可能是负耗散的. 因此 热力学第二定律的最概括表述为一句话 : 负耗散体系是不存在的 , 所谓的 “ 负耗散体系 ” 就是第二类永动机 .
再谈质能关系,推荐一本好书,建议自我检试 本次博文将再次讨论相对论中质量能量关系。很多人都对相对论中质量、能量和它们的关系感到兴趣,包括科学网博客在内的不少网上博客或论坛常有博文讨论这些问题。虽然大家都认为质量、能量是物理学上最基本的概念,质能关系是物理学上最基本的规律;可是仍然有不少人对相对论中质量、能量和它们的关系存在相当程度、或多或少的误解。Lev B Okun 教授(曾任莫斯科理论与实验物理研究所基本粒子理论实验室主任,欧洲核子研究中心的客座正式成员)于1989年在Physics Today 上发表的一篇论文《The Concept of Mass》中,最早强调指出,人们对相对论中质量、能量和它们的关系存在一些错误的理解。这是由于物理学发展中出现的一些模糊概念和习惯势力的影响所造成的。他通过详细的理论分析和对历史文献的解读,明确指出:1、与牛顿力学相同,相对论中的(惯性)质量没有静止质量和运动质量之分,2、相对论中的能量则有静止能量和运动能量之分,3、在相对论中质能关只是 静止能量=(质量)乘(光速平方)。 前不久,我才读到Lev B Okun 教授于1989年在Physics Today 上发表的论文《The Concept of Mass》;但在两年前我看到过别人对这篇论文的介绍,特别是关于在相对论中,质量没有静止质量和运动质量之分、能量则有静止能量和运动能量之分、静止能量=(质量)乘(光速平方)之主要观点的介绍。经过自己思考,很快我就接受了Okun 教授的上述主要观点。Okun 教授认为,正确的概念和正确的关系对规律的认识、理解和掌握是非常重要的,错误的概念和错误的关系往往会妨碍对规律的认识、理解和掌握;我完全赞同Okun 教授的这些看法。 半年之前在我的博客中,曾发表过几篇博文,企图阐明Okun 教授的上述主要观点。其效果看来不够理想,还遭到反驳和讥讽,这可能是由于我的博文写得不好以及人微言轻的缘故吧?前不久,我在大连理工大学图书馆借到了Okun 教授于2009年新出版的一本专著《Energy and Mass in Relativity Theory》(Published by World Scientific Publishing Co.Pte.Ltd.)。这本专著除了收有Okun 教授于1989年在Physics Today 上发表的论文《The Concept of Mass》(我就是在这本书上读到这篇论文的)之外,还收有Okun 教授、他的学生、以及其他学者在1968-2008年间所发表的关于相对论中质量、能量和质-能关系的论文。我觉得这是一本好书,对澄清当前人们对相对论中质量、能量和它们的关系所存在一些错误的理解,必定会起到较大的影响,特向广大网友推荐。 Okun 教授在论文《The Concept of Mass》之中,写出了4个可能的质量能量关系,其中只有一个关系是正确的,但有两个关系虽是错误的、却仍有不少人还在相信和继续采用。对这4个可能的质量能量关系是对是错的判断可以检验出对相对论的理解是否正确,建议有兴趣者不妨自我检试一下。 Okun 教授对这4个可能的质量能量关系是直接写出的,有可能与现有的一些模糊概念相混淆而影响对正确关系的理解。下面我们通过逻辑分析来得出这4个可能的质量能量关系。 一个质点的(惯性)质量是否与该质点的运动速度有关,只有两种可能:
最近我一直在研究量子力学中薛定谔方程的推导。物理学家一般不太关心这件事,只管应用方程做计算就行了。但对于做物理学基础研究的我来说,这是一个十分具有挑战性的重要问题。其中涉及到了能量(E)与动量(p)之间关系的来源问题。尽管能量-动量关系被广泛用于相对论和量子理论中,但似乎没有一个令人满意的基本推导。十多年前我就就意识到这个问题,并曾做过尝试。最近,我写了一篇文章,利用时空平移不变性和相对论不变性进一步完善了以前的推导。文章的另一个推论是,爱因斯坦的著名方程E=mc 2 实际上只是一个定义,而质量原则上可以从物理学中消失。 Momentum and energy are two of the most important concepts of modern physics. Their relation has been widely used in Newtonian mechanics and quantum mechanics in an approximate form, as well as in relativistic mechanics and quantum field theory in an exact form. Yet, as far as we know, a fundamental derivation of this pivotal relation seems still missing in the literature. Most ``derivations" are based on the somewhat complex analysis of an elastic collision process. Moreover, they resort to either some Newtonian limit (e.g. $p=mv$) or some less fundamental relation (e.g. $p=Eu/c^2$) or even some mathematical intuition (e.g. four-vectors) . As we think, the logic of these ``derivations" seems a little upside-down, and they are only heuristic demonstrations of the energy-momentum relation. So simple and fundamental relation the energy-momentum relation is, and thus its derivation should be simpler, based on more fundamental postulates. In this short note, we will present such a derivation, based only on spacetime translation invariance and relativistic invariance. Derivation of the energy-momentum relation
仅就物质场而言 , 在一般情况下 , 其能量不守恒 为什么这样说呢?首先要注意必须满足两个条件: 1 ), 仅就物质场而言, 2 ),在一般情况下。我们是在这 两个条件下来谈论 物质场的能量不守恒的。如果我们讨论一个引力体系(即既有物质场又有引力场的体系),由于任一引力体系肯定遵守 Lorentz 与 Levi-Civita 守恒定律或 爱因斯坦 守恒定律 , 因此就可推出 , 在一般情况下,所讨论的体系总体的能量必定是守恒的。但若仅就物质场而言,在一般情况下,由于物质场要与引力场交换能量 , 因之物质场单独的能量便不守恒了。下面我们用数学公式来说明这个陈述。 可以证明 , 对于任一引力体系 , 若 其作用量在时空局域平移变换下具有不 变性 , 则存在 Lorentz 与 Levi-Civita 守恒定律 这也表明体积 V 中能量的总量也保持不变 , 流经封闭面 S 的总动量流也为零。因之, 仅就物质场而言,在一般情况下,物质场单独的能量也是不守恒的。 从上述轮证中,我们已经看到,仅就物质场而言 , 在一般情况下 , 其能量是 不守恒的;那么,当引力场存在时,在什么样的特殊情况下 , 仅就物质场而言 , 其能量可以守恒呢?这个问题留待下次博文讨论。 参考文献 Chen F. P. 2008, Field equations and conservation laws derived from the generalized Einsteins Lagrangian density for a gravitational system and their implications to cosmology. Int.J.Theor.Phys.47,421. Chen F. P. 2008, A Further Generalized Lagrangian Density and Its Special Cases. Int.J.Theor.Phys.47 , 2722. 陈方培 .2008, 引力体系的拉氏量与能动张量密度守恒定律及场方程 ( 引力体系协变的能动张量密度及其守恒定律与某些应用 I ). 中国科技论文在线 200802-56.