邮票上的物理学史——伽利略(续)

６）引力质量和惯性质量的等价性．伽利略之所以详细研究自由落体运动,是为了批驳亚里士多德的错误理论：重物体下落比轻物体快,落体速度与其重量成正比．传说伽利略曾在比萨斜塔（图１０,意大利,１９７３年）上做实验,把同样大小的铁球和木球同时放下,观众看到二者...     

物理学中的三种质量

经典物理学中有三种质量:惯性质量、引力质量和测度质量.下面我们对它们的等效性和不同点进行介绍.1惯性质量惯性质量是物体惯性的量度.牛顿第二定律F=ma中的m就是惯性质量.     

邮票上的物理学史⑦ --伽利略(续)

6) 引力质量和惯性质量的等价性.伽利略之所以详细研究自由落体运动,是为了批驳亚里士多德的错误理论:重物体下落比轻物体快,落体速度与其重量成正比.传说伽利略曾在比萨斜塔(图10,意大利,1973年)上做实验,把同样大小的铁球和木球同时放下,观众看到二者同时落地,但历史考证对这一传说存疑.不过伽利略早年(1591年)写的<论运动>小册子中的确记载有这类实验.     

用气轨系统与Spss标定物体的惯性质量

通过对气轨系统的改进与调试,用气垫导轨测量物体做简谐振动的周期,由实验原理及其不确定度的分析,结合测量数据,应用Spss软件分析给出周期的平方与其惯性质量的定标曲线,验证了物体在气垫导轨上做简谐振动周期的平方与其惯性质量存在线性关系,进一步验证了物体的惯性质量与其引力质量相等的关系.     

弱等效原理的实验检验

惯性质量与引力质量相等是广义相对论基本理论假设之一，这个假设称为等效原理。本文介绍等效原理的检验实验的框架以及检验实验的历史、现状和未来。     

浅谈广义相对论的创立之一 等效原理的发现与应用

简述了惯性质量同引力质量相等的经典实验;介绍了爱因斯坦发现等效原理的思路历程;说明了等效原理在分析引力场中时间延缓,星光谱线的引力红移和光线偏转等问题上的应用.     

用气轨测定惯性质量

惯性质量是根据牛顿第二定律定义的,即m=F/a(m称为物体的惯性质量,F为作用于物体的合外力,a为物体所获得的加速度),它是物体对运动状态发生变化的抵抗能力的量度.物体的惯性质量的大小,不能用天平测定,因为天平测定的是物体的引力质量,故必须用动态法测定.在普通物理实验中,通常使用专门仪器——惯性秤测定.我们用气垫导轨装置进行实验所获得的结果表明:气垫导轨装置不但可以测量物体的惯性质量,而且测量精度比惯性秤高,值得推荐.本文着重论述用气垫导轨装置测定物体的惯性质量的实验原理,同时具体介绍实验所用仪器和实验结果.一、实验原理…     

“光”有“重量”吗?

 四百年前,伽利略曾利用实验深入地研究了落体和抛体的运动.后来,从盛传的比萨斜塔实验中,人们发现任何物体的惯性质量m_I都等于引力质量m_G.大约80年前,上述发现又成了广义相对论的基本出发点--等效原理.爱因斯坦还告诉我们,光子在引力场中也遵循这一原理.     

关于伽利略的一个推理

伽利略曾用思辨方法指出了亚里士多德落体理论中的一个矛盾．本文用现代力学概念分析伽利略的推理，讨论这一问题与惯性质量和引力质量的等效性关系。指出这一推论虽有启发性，但严格的物理理论仍须建立在实验基础上．     

验证爱因斯坦是对还是错?

 传说16世纪末叶意大利科学家伽利略做过一个简单实验:从比萨斜塔上让一颗铅球和一颗木球同时下落,证明不同的质量同时到达地面.而今,两位斯坦福物理学家C.W.弗朗西斯·埃弗里特和保罗·沃尔登建议对这一原理（现在人们熟知的惯性质量和引力质量等价）进行验证,并宣称他们的实验精度为伽利略的10¹⁴倍.     

Gravity and the quantum vacuum inertia hypothesis

In previous work it has been shown that the electromagnetic quantum vacuum, or electromagnetic zero‐point field, makes a contribution to the inertial reaction force on an accelerated object. We show that the result for inertial mass can be extended to passive gravitational mass. As a consequence the weak equivalence principle, which equates inertial to passive gravitational mass, appears to be explainable. This in turn leads to a straightforward derivation of the classical Newtonian gravitational force. We call the inertia and gravitation connection with the vacuum fields the quantum vacuum inertia hypothesis . To date only the electromagnetic field has been considered. It remains to extend the hypothesis to the effects of the vacuum fields of the other interactions. We propose an idealized experiment involving a cavity resonator which, in principle, would test the hypothesis for the simple case in which only electromagnetic interactions are involved. This test also suggests a basis for the free parameter η(ν) which we have previously defined to parametrize the interaction between charge and the electromagnetic zero‐point field contributing to the inertial mass of a particle or object.     

Nordström’s scalar theory of gravity and the equivalence principle

General Relativity obeys the three equivalence principles, the “weak” one (all test bodies fall the same way in a given gravitational field), the “Einstein” one (gravity is locally effaced in a freely falling reference frame) and the “strong” one (the gravitational mass of a system equals its inertial mass to which all forms of energy, including gravitational energy, contribute). The first principle holds because matter is minimally coupled to the metric of a curved spacetime so that test bodies follow geodesics. The second holds because Minkowskian coordinates can be used in the vicinity of any event. The fact that the latter, strong, principle holds is ultimately due to the existence of superpotentials which allow to define the inertial mass of a gravitating system by means of its asymptotic gravitational field, that is, in terms of its gravitational mass. Nordström’s theory of gravity, which describes gravity by a scalar field in flat spacetime, is observationally ruled out. It is however the only theory of gravity with General Relativity to obey the strong equivalence principle. I show in this paper that this remarkable property is true beyond post-newtonian level and can be related to the existence of a “Nordström-Katz” superpotential.     

Gravitational mass and energy gradient in the ultra-strong magnetic fields

The paper aims to apply the complex octonion to explore the influence of the energy gradient on the Eötvös experiment, impacting the gravitational mass in the ultra-strong magnetic fields. Until now the Eötvös experiment has never been validated under the ultra-strong magnetic field. It is aggravating the existing serious qualms about the Eötvös experiment. According to the electromagnetic and gravitational theory described with the complex octonions, the ultra-strong magnetic field must result in a tiny variation of the gravitational mass. The magnetic field with the gradient distribution will generate the energy gradient. These influencing factors will exert an influence on the state of equilibrium in the Eötvös experiment. That is, the gravitational mass will depart from the inertial mass to a certain extent, in the ultra-strong magnetic fields. Only under exceptional circumstances, especially in the case of the weak field strength, the gravitational mass may be equal to the inertial mass approximately. The paper appeals intensely to validate the Eötvös experiment in the ultra-strong electromagnetic strengths. It is predicted that the physical property of gravitational mass will be distinct from that of inertial mass.     

A New Proposal to Redefine Kilogram by Measuring the Planck Constant Based on Inertial Mass

A novel method to measure the Planck constant based on inertial mass is proposed here, which is distinguished from the conventional Kibble balance experiment which is based on the gravitational mass. The kilogram unit is linked to the Planck constant by calculating the difference of the parameters, i.e. resistance, voltage, velocity and time, which is measured in a two-mode experiment, unloaded mass mode and the loaded mass mode. In principle, all parameters measured in this experiment can reach a high accuracy, as that in Kibble balance experiment. This method has an advantage that some systematic error can be eliminated in difference calculation of measurements. In addition, this method is insensitive to air buoyancy and the alignment work in this experiment is easy. At last, the initial design of the apparatus is presented.     

Inertial and gravitational masses in the bimetric theory of gravitation

The inertial mass of a static spherically symmetric body is evaluated in the framework of Rosen's bimetric theory of gravitation. It is shown that the inertial mass equals the gravitational mass independently of the specific equation of state chosen, and hence that the theory satisfies the equivalence principle.     

Some remarks concerning the equivalence principle of general relativity with respect to quantum mechanical one-particle state

We discuss a recent experiment with interfering neutron beams in the gravitational field of the earth, and show how the explanation of the interference pattern can be obtained by an application of the equivalence principle to the one-particle states. The calculation is carried out in the coordinate system where the gravitational field has been transformed away.     

Freely Falling 2-Surfaces and the Effective Gravitational Mass

We derive an expression for the effectivegravitational mass for any closed spacelike 2-surface.This effective gravitational energy is defined directlythrough the geometrical quantity of the freely falling 2-surface and thus is well adapted to intuitiveexpectation that the gravitational mass should bedetermined by the motion of a test body moving freely inthe gravitational field. We find that this effective gravitational mass has a reasonable positivevalue for a small sphere in the non-vacuum space-timesand can be negative for the vacuum case. Further, thiseffective gravitational energy is compared with the quasi-local energy based on the (2 + 2)formalism of General Relativity. Although some gaugefreedoms exist, analytic expressions of the quasi-localenergy for vacuum cases are the same as the effective gravitational mass. Especially, we see that thecontribution from the cosmological constant is the samein general cases.     

矢引力子场度规场引力理论的共形平直静止解及引力场的能量动量赝张量的正常性

本文求出了VGM引力理论的共形平直静止解。文中把胡宁表达式引入VGM,它同样是守恒的能量动量表达式。对于单个集中质量的引力场,与GR一样,可证实引力质量与惯性质量相等。但Einstein的等效原理在这理论中并不成立。利用所求得的解,可知当n<1/4时,引力场的能量动量赝张量就是正常的。 关键词：     

Toward improving the accuracy of testing the equivalence of the inertial and the gravitational mass under terrestrial conditions

An experiment aimed at testing the equivalence of the inertial and the gravitational mass is considered in which use is made of a facility including a vacuum chamber with two coupled oscillators (a pendulum and dynamical damper that form a vibrational system featuring two degrees of freedom) and falling onto the Sun. The layout of the facility and its basic parameters are presented. The pendulum and the dynamical damper have the same natural frequency, which is equal to the frequency of their rotation about the Sun. This frequency is dependent on the date of the experiment and can be calculated on the basis of the time equation. In the proposed facility, the amplitude of oscillations of the damper is 1.2×10^?5 rad, which is much greater than the value of 10^?7 rad previously achieved in the experiment that tested the equivalence principle to the highest precision of about 10^?12. This precision can be considerably improved. The result is presented that was obtained from a measurement during the solar eclipse in Moscow on August 11, 1999.