什么是时空弯曲？
What is the curvature of spacetime?
在广义相对论中，时空不是平坦的背景，而是可被质量能量弯曲的四维结构。物体和光都沿着弯曲时空中的测地线运动，引力即表现为时空的弯曲。
In general relativity, spacetime is not a flat background but a four-dimensional structure curved by mass and energy. Objects and light follow geodesics in this curved spacetime, and gravity is precisely that curvature.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#时空弯曲 #测地线 #引力
广义相对论里“电梯思想实验”想说明什么？
What does the elevator thought experiment illustrate in general relativity?
爱因斯坦说在封闭电梯里，你分不清自己是受引力还是正在加速。局部来看，引力和加速度等效，这正是等效原理，也是广义相对论把引力解释为时空弯曲的起点。
Einstein noted that inside a closed elevator you can't tell gravity from acceleration. Locally, gravity and acceleration are equivalent—the equivalence principle—and it starts general relativity's view of gravity as curved spacetime.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 4 条独立证据
来源 · Source
Halliday, Resnick, Walker,《Fundamentals of Physics》第10版,Wiley,2013
David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, 10th ed., Wiley, 2013
独立核验依据 · Independent verification: 核验依据 3 angusrobertson.com.au
#等效原理 #广义相对论 #时空弯曲
等效原理如何导出时空弯曲？
How does the equivalence principle lead to curved spacetime?
局部无法区分均匀引力与加速参考系（等效原理），但全局不同引力场有潮汐效应，只能用黎曼几何描述——物质告诉时空如何弯曲，弯曲的时空告诉物质如何运动（爱因斯坦方程）。
Locally gravity equals acceleration (equivalence principle), but global tidal effects require Riemannian geometry: matter curves spacetime, and curved spacetime dictates motion via Einstein's equations.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#相对论 #等效原理 #曲率
为什么黑洞附近时间会变慢？
Why does time slow down near a black hole?
广义相对论说强引力会弯曲时空，引力越强的位置时间流逝越慢（引力时间膨胀）。靠近黑洞时这种效应极其明显。
General relativity says strong gravity curves spacetime, and time runs slower where gravity is stronger (gravitational time dilation). Near a black hole this effect is extreme.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
Einstein，《广义相对论的基础》，Annalen der Physik 49 (1916)
Einstein, 'Die Grundlage der allgemeinen Relativitatstheorie', Annalen der Physik 49 (1916)
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL10275999W：Die Grundlage der allg
#时间膨胀 #黑洞 #相对论
为什么没有什么能比光更快？
Why can nothing travel faster than light?
狭义相对论把光速设为宇宙速度上限。物体质量随速度接近光速而趋于无穷，加速到光速需要无限能量，所以无法超越。
Special relativity sets light speed as the cosmic limit. An object's mass grows toward infinity near light speed, requiring infinite energy to reach it, so surpassing it is impossible.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
Einstein，《论动体的电动力学》，Annalen der Physik 17 (1905)
Einstein, 'Zur Elektrodynamik bewegter Korper', Annalen der Physik 17 (1905)
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL10276008W：Zur Elektrodynamik bew
#光速极限 #相对论 #质量
闵可夫斯基时空的几何结构是怎样的？
What is the geometric structure of Minkowski spacetime?
闵可夫斯基时空把三维空间和一维时间合并为四维流形，其度量带有负号：ds²=c²dt²−dx²−dy²−dz²。这种伪黎曼几何让光锥划分出类时、类光和类空区域，决定了因果可达性。它是狭义相对论的几何语言。
Minkowski spacetime merges three space dimensions and one time dimension into a four-dimensional manifold with a metric carrying a minus sign: ds²=c²dt²−dx²−dy²−dz². This pseudo-Riemannian geometry uses light cones to separate timelike, lightlike, and spacelike regions, fixing causal accessibility. It is the geometric language of special relativity.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#闵可夫斯基 #伪黎曼几何 #光锥
为什么 GPS 卫星上的钟比地面快，却要靠相对论修正？
Why do GPS satellite clocks run faster than ground clocks, yet need relativity corrections?
卫星离地球更远，引力更弱，按广义相对论它的钟走得快；但速度又让它变慢，两者叠加净快约每天 38 微秒。若不修正，定位每天会偏差约 10 公里。
Higher up, gravity is weaker so by general relativity the satellite clock runs fast; its speed slows it, and the net is about 38 microseconds fast per day. Without correction, GPS position would drift about 10 km daily.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-06
来源 · Source
Ashby，《全球定位系统中的相对论》，Living Reviews in Relativity 6 (2003)
Ashby, 'Relativity in the Global Positioning System', Living Reviews in Relativity 6 (2003)
独立核验依据 · Independent verification: 核验依据 1 DOI 10.12942/lrr-2003-1
#引力红移 #GPS #相对论修正
黑洞的“事件视界”是什么，为什么进去就出不来？
What is a black hole's event horizon, and why is there no return past it?
事件视界是逃逸速度超过光速的边界；一旦越过，连光也无法逃出，因局部时空被极度弯曲。视界本身不是实体，而是“有去无回”的单向膜。
The event horizon is the boundary where escape speed exceeds light; cross it and not even light gets out, because spacetime is bent that sharply. It is not a solid surface but a one-way point of no return.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#事件视界 #黑洞 #逃逸速度
四维时空中的时空间隔为什么是不变量？
Why is the spacetime interval invariant in four-dimensional spacetime?
在闵可夫斯基时空中，两个事件之间的间隔定义为c²Δt²−Δx²−Δy²−Δz²。洛伦兹变换保持这个量不变，就像旋转保持欧几里得距离不变一样。因此所有惯性观察者都同意时空间隔，尽管他们对时间和空间的单独测量可能不同。
In Minkowski spacetime the interval between two events is defined as c²Δt²−Δx²−Δy²−Δz². Lorentz transformations preserve this quantity, just as rotations preserve Euclidean distance. Thus all inertial observers agree on the interval even though their separate measures of time and space differ.
难度 专业 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#时空间隔 #闵可夫斯基 #洛伦兹
引力波是什么，怎么被直接探测到的？
What are gravitational waves, and how were they directly detected?
引力波是时空本身的涟漪，由双黑洞等剧烈加速的质量产生，以光速传播。LIGO 在 2015 年用相距千里、长度几公里的激光干涉仪测到 10⁻¹⁸ 米量级的微小拉伸。
Gravitational waves are ripples in spacetime made by violently accelerating masses like merging black holes, traveling at light speed. In 2015 LIGO detected them with kilometer-scale laser interferometers thousands of km apart, sensing stretches of order 10⁻¹⁸ m.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：此条未指向带版次的可引用著作（通识性内容、机构文件或未展开的英文书名），本库不提供独立书目出处；如需精确引用，需由编辑补全具体篇目与版次。
激光干涉引力波天文台（LIGO）
LIGO
#引力波 #LIGO #时空涟漪
GPS 卫星为什么要校正相对论效应？
Why must GPS satellites correct for relativistic effects?
卫星高速运动产生狭义相对论的时间变慢，而较弱的引力场又按广义相对论使星上钟变快，两种效应叠加约每天快 38 微秒。若不校正，定位误差每天会累积到约十公里量级。
The satellites' high speed slows their clocks by special relativity, while the weaker gravity speeds them up by general relativity, netting about +38 microseconds per day. Without correction the positioning error would grow by roughly ten kilometres per day.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
Misner、Thorne、Wheeler《引力》；美国国家标准与技术研究院（NIST）
Misner, Thorne & Wheeler, Gravitation; US NIST
#GPS #引力时间膨胀 #狭义相对论
彭罗斯图如何描述黑洞和白洞？
How do Penrose diagrams describe black holes and white holes?
彭罗斯图把无限的时空压缩到有限图中，用45度光线边界表示因果结构。它能清晰显示黑洞的事件视界、奇点以及理论上的白洞和虫洞区域。它帮助物理学家直观理解时空的全局因果拓扑。
A Penrose diagram compresses infinite spacetime into a finite picture, with 45-degree light lines marking causal structure. It clearly shows a black hole's event horizon, singularity, and the theoretical white-hole and wormhole regions. It helps physicists visualize the global causal topology of spacetime.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#彭罗斯图 #黑洞 #白洞
黑洞事件视界附近的时间对远方观察者为何冻结？
Why does time appear frozen at a black hole's horizon to a distant observer?
在施瓦西度规中，远处的坐标时与自身时之比在接近视界时趋于无穷；下落者穿过视界有限自身时，但远方看到其信号无限红移、节奏无限变慢。
In Schwarzschild coordinates the time dilation diverges at the horizon; the infaller crosses in finite proper time, but a distant observer sees signals infinitely redshifted and slowed.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#相对论 #黑洞 #视界
用广义相对论的测地线方程，为什么自由落体者感觉不到重力？
By the geodesic equation, why does a free-faller feel no gravity?
测地线方程是 ∇_u u=0，自由下落者沿测地线运动，自身参考系中唯一的力是测地偏离（潮汐）；局部等效原理让他处于惯性系，故失重。感受重力其实是支撑力（非测地运动）造成的。
The geodesic equation ∇_u u=0 means a free-faller follows inertial motion; locally they feel weightless (equivalence principle). Weight is felt only when a support force pushes them off a geodesic.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#相对论 #自由落体 #测地线
在强引力场中，光的频率为什么会发生“引力红移”——从地面向高处传播的光频率会变低？
In a strong gravitational field, why does light suffer 'gravitational redshift'—why does light travelling upward arrive at a lower frequency?
广义相对论中时钟在引力势低处走得更慢，光子往上爬出引力井时要“付出”能量，频率随之降低、波长变长，即红移。庞德–雷布卡实验在哈佛塔用伽马射线精确测到了这一微小频移，直接验证了等效原理。
In general relativity clocks run slower deeper in a gravitational well; a photon climbing upward pays energy, so its frequency drops and wavelength stretches—a redshift. The Pound–Rebka experiment in the Harvard tower measured exactly this tiny shift with gamma rays, directly confirming the equivalence principle.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
R. V. Pound & G. A. Rebka,《Apparent Weight of Photons》,Phys. Rev. Lett. 4,337(1960)
R. V. Pound & G. A. Rebka, 'Apparent Weight of Photons', Phys. Rev. Lett. 4, 337 (1960)
独立核验依据 · Independent verification: 核验依据 1 CROSSREF 标识 10.1103/physrevlett.4.337：Apparent Weight of
#引力红移 #等效原理 #引力时间膨胀
一对相互绕转的中子星为什么会因为辐射引力波而慢慢“靠近”，最终轨道收缩？
Why do two orbiting neutron stars slowly spiral inward, their orbit shrinking, because of gravitational waves?
加速的质量四极矩会辐射引力波并带走能量与角动量，这是广义相对论的预言。赫尔斯–泰勒双脉冲星（PSR B1913+16）的轨道周期被测出以精确速率减小，减少量恰与引力波辐射的理论相符，成为引力波存在的最早间接证据。
An accelerating mass quadrupole radiates gravitational waves and carries away energy and angular momentum, as general relativity predicts. The Hulse–Taylor binary pulsar (PSR B1913+16) shows its orbital period shrinking at exactly the rate expected from gravitational-wave loss, the first indirect evidence for gravitational waves.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
J. M. Weisberg, D. J. Nice & J. H. Taylor,《Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16》,ApJ 722,1030(2010)
J. M. Weisberg, D. J. Nice & J. H. Taylor, 'Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16', ApJ 722, 1030 (2010)
独立核验依据 · Independent verification: 核验依据 1 DOI 10.1088/0004-637x/722/2/1030
#引力波 #双星系统 #轨道衰减
闵可夫斯基时空的度规为什么是 diag(-1,1,1,1)？
Why is the Minkowski metric diag(-1,1,1,1)?
它编码了光速不变：时空间隔 ds²=-c²dt²+dx²+dy²+dz² 在不同惯性系下保持不变，负号把时间与空间区分开，使得光的轨迹满足 ds=0。符号约定（如+---）只是整体符号的选择。
It encodes light-speed invariance: the interval ds²=-c²dt²+dx²+dy²+dz² is frame-independent; the minus sign distinguishes time and makes light paths null (ds=0). The sign convention is a choice.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
Herbert Goldstein、Charles Poole 与 John Safko 著《Classical Mechanics》（经典力学）
Herbert Goldstein, Charles Poole & John Safko, Classical Mechanics
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL6211080W：Classical mechanics（首版
#相对论 #度规 #闵可夫斯基
同时性的相对性是什么意思？
What does the relativity of simultaneity mean?
在一个参考系中同时发生的两件事，在另一个相对运动的参考系中未必同时。这是因为光信号到达观察者需要时间，而不同地点的现在无法绝对定义。它是相对论打破绝对时间观的核心。
Two events simultaneous in one reference frame need not be simultaneous in another frame moving relative to it. This is because light signals take time to reach an observer, so a universal now across locations cannot be defined absolutely. It is central to relativity's rejection of absolute time.
难度 专业 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#同时性 #参考系 #时间
洛伦兹变换如何从相对性原理和光速不变推导出来？
How is the Lorentz transformation derived from the relativity principle and invariant light speed?
假设两个惯性系之间的坐标变换是线性且保持空间各向同性，再要求光速在任一惯性系中都是c，就唯一确定了洛伦兹变换的形式。它把时间也纳入变换，取代了伽利略变换。由此自然导出时间膨胀与长度收缩。
Assuming the coordinate transformation between inertial frames is linear and preserves spatial isotropy, and requiring that light speed is c in every frame, uniquely fixes the form of the Lorentz transformation. It incorporates time into the transformation, replacing the Galilean one, and naturally yields time dilation and length contraction.
难度 专业 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#洛伦兹变换 #相对性原理 #光速不变
为什么说“同时”是相对的？
Why is simultaneity relative?
狭义相对论指出，两个在不同地点同时发生的事件，对运动速度不同的观察者可能不再同时；光速不变导致时间顺序随参考系而变。
Special relativity says two events simultaneous in one frame may not be in another moving frame, because the constant speed of light changes the order of distant events.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
Einstein，《论动体的电动力学》，Annalen der Physik 17 (1905)
Einstein, 'Zur Elektrodynamik bewegter Korper', Annalen der Physik 17 (1905)
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL10276008W：Zur Elektrodynamik bew
#同时性 #相对论 #参考系
广义相对论如何解释引力？
How does general relativity explain gravity?
广义相对论认为质量和能量会弯曲周围的时空，物体沿弯曲时空中的最短路径运动，这就是我们感受到的引力。它成功预言了光线在太阳附近偏折和水星轨道的异常。
General relativity holds that mass and energy curve the spacetime around them, and objects follow the shortest paths in that curved spacetime, which we experience as gravity. It correctly predicted light bending near the Sun and Mercury's orbital anomaly.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#广义相对论 #时空 #引力
「双生子佯谬」里，为什么去太空旅行的人回来会更年轻？
In the twin paradox, why does the space-traveling twin return younger?
狭义相对论的时间膨胀说，运动越快、时间走得越慢。双生子之一坐飞船以接近光速往返，他的「固有时」比留在地球的那位更短，所以回来更年轻。看似对称的悖论其实不对称：旅行的那位经历过加速、调头，不在单一的惯性系里，因此并非真的平等。实验上用快速运动的原子钟已验证这种效应。
Special relativity's time dilation says faster motion slows time. The twin who rides a near-light-speed round trip accumulates less 'proper time' than the one on Earth, returning younger. The apparent symmetry breaks because the traveler accelerates and turns around, leaving a single inertial frame, so the cases are not equal. Fast-moving atomic clocks have confirmed the effect.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
A. 爱因斯坦 1905 年狭义相对论论文；S. 温伯格《引力和宇宙学》相关章节
A. Einstein (1905) special relativity paper; S. Weinberg, 'Gravitation and Cosmology', on time dilation
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL3398933W：Gravitation and cosmolo
#双生子佯谬 #时间膨胀 #固有时
相对论质量与不变质量有什么区别？
What is the difference between relativistic mass and invariant mass?
现代物理学倾向于只使用不变质量（静质量），它是所有参考系下都相同的标量。所谓相对论质量随速度增大，容易引起误解，现已较少使用。能量和动量通过E²=p²c²+m²c⁴与不变质量联系。
Modern physics prefers the single invariant mass (rest mass), a scalar identical in all frames. The older relativistic mass grows with speed and is now discouraged because it misleads. Energy and momentum relate to invariant mass via E²=p²c²+m²c⁴.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#不变质量 #相对论质量 #动量
为什么物体的“惯性质量”会随着速度逼近光速而急剧增大，使继续加速越来越难？
Why does an object's 'inertial mass' grow sharply as its speed approaches light, making further acceleration harder?
现代表述中质量是不变量，真正随速度变化的是动量：p = γmv，其中 γ = 1/√(1−v²/c²)。速度越接近光速，γ 越大，同一个力带来的加速度越小，早期文献便把这种“越来越难推动”记作“相对论质量增大”。由于 v→c 时 γ→∞，把有质量物体加速到光速需要无穷大的能量，这正是光速成为速度上限的原因。
In modern usage mass is an invariant; what really grows with speed is momentum, p = γmv with γ = 1/√(1−v²/c²). The closer v gets to c, the larger γ becomes and the less a given force accelerates the body—an effect older texts labelled 'relativistic mass increase'. Because γ → ∞ as v → c, accelerating a massive object to light speed would take infinite energy, which is why c is the speed limit.
难度 进阶 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
R. Resnick,《Introduction to Special Relativity》(Wiley,1968),第3章(相对论动力学)
R. Resnick, 'Introduction to Special Relativity' (Wiley, 1968), Ch.3 (Relativistic dynamics)
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780471717256 (1968)
#洛伦兹因子 #相对论动量 #光速极限
引力波是怎么产生的，为何1916年预言2015年才探测到？
How are gravitational waves produced and why detected only in 2015?
加速的质量四极矩变化会辐射时空涟漪，但强度极弱；黑洞并合在千分之一秒内释放约3倍太阳质量的能量，使臂长4公里的法布里-珀罗臂改变不到质子直径的千分之一，需激光干涉仪才能达到该灵敏度。
Changing mass quadrupole radiates ripples, but they are extremely weak; the 2015 black-hole merger released ~3 solar masses in energy, shifting a 4-km arm by less than a thousandth of a proton, demanding exquisite laser interferometry.
难度 进阶 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：此条未指向带版次的可引用著作（通识性内容、机构文件或未展开的英文书名），本库不提供独立书目出处；如需精确引用，需由编辑补全具体篇目与版次。
LIGO 2015
LIGO 2015
#相对论 #引力波 #LIGO
为什么运动的钟会变慢？
Why do moving clocks run slow?
在相对论中，时间和空间是统一的四维时空，不同运动状态的观察者沿不同的世界线穿越时空。运动的观察者把更多时空路程花在空间方向上，留给时间方向的就越少，于是其固有时间流逝得更慢。这对所有过程的钟都同样成立。
In relativity, space and time form a unified four-dimensional spacetime, and observers in different motion follow different worldlines. A moving observer spends more of the spacetime interval on the spatial direction, leaving less for the time direction, so their proper time flows slower. This applies equally to all kinds of clocks.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#时间膨胀 #固有时间 #世界线
快子（假想的超光速粒子）为什么被认为会违背因果律？
Why are tachyons (hypothetical faster-than-light particles) thought to violate causality?
如果存在超光速粒子，在某些参考系中它的运动方向会反转，可能让结果发生在原因之前。这会破坏因果顺序，导致逻辑悖论。因此快子未被证实，也通常被视为理论上的警示而非真实粒子。
If faster-than-light particles existed, in some reference frames their direction of motion would reverse, letting an effect precede its cause. This would destroy causal order and create paradoxes. Tachyons are unconfirmed and usually treated as a theoretical warning rather than real particles.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#快子 #超光速 #因果律
长度收缩是真实的还是只是视觉错觉？
Is length contraction real or just a visual illusion?
长度收缩不是眼睛看起来的错觉，而是不同惯性系对同时测量物体两端所得结果的客观差异。在运动方向上，物体在其静止系测得的长度比在地面系测得的更长。它是时空几何的真实属性，而非观测假象。
Length contraction is not a mere optical illusion but an objective difference arising because endpoints are measured simultaneously in different inertial frames. Along the direction of motion, an object's rest-frame length exceeds its length measured from the ground frame. It is a real property of spacetime geometry, not an observational artifact.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#长度收缩 #同时性 #参考系
卫星定位（GPS）为什么还要动用爱因斯坦的相对论？
Why does GPS navigation need Einstein's relativity?
导航卫星在约2万公里高空高速飞行，它的时钟相对地面每天快约38微秒：狭义相对论（高速运动）贡献约7微秒，广义相对论（远离地球、引力更弱）贡献约45微秒，一快一慢合计净快38微秒。若不修正，定位误差每天会累积约10公里。所以卫星上的原子钟都要按相对论校准后再工作。
Orbiting about 20,000 kilometers up at high speed, a GPS satellite's clock gains roughly 38 microseconds per day relative to the ground: special relativity (fast motion) adds about 7, general relativity (weaker gravity high above Earth) adds about 45, netting +38. Uncorrected, that would drift positions by some 10 kilometers each day. The satellites' atomic clocks are therefore tuned using relativity before they ever navigate.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 4 条独立证据
来源 · Source
Halliday, Resnick, Walker,《Fundamentals of Physics》第10版,Wiley,2013
David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, 10th ed., Wiley, 2013
独立核验依据 · Independent verification: 核验依据 3 angusrobertson.com.au
#时间膨胀 #GPS #广义相对论
黑洞的「事件视界」是什么，进了就真的出不来吗？
What is a black hole's event horizon, and is it truly impossible to escape once inside?
事件视界是黑洞周围的一道边界：在它之内，连光都无法挣脱引力的束缚，因为任何逃向外的路径都被时空弯曲折回到内部。越过视界便与外面宇宙断开因果联系，再无返回之路（至少按广义相对论）。2019年事件视界望远镜（EHT）首次拍到 M87* 黑洞的「阴影」，正是视界附近光被弯折形成的暗区。
The event horizon is the boundary around a black hole inside which not even light can escape gravity, because spacetime curvature bends every outward path back inward. Crossing it severs causal contact with the outside universe, with no return under general relativity. In 2019 the Event Horizon Telescope captured the shadow of M87*, the dark region shaped by light bent near the horizon.
难度 进阶 · 适合 小学高段(9-12)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：此条未指向带版次的可引用著作（通识性内容、机构文件或未展开的英文书名），本库不提供独立书目出处；如需精确引用，需由编辑补全具体篇目与版次。
事件视界望远镜（EHT）合作组 2019 年 M87* 黑洞成像成果（ApJL 专刊）
Event Horizon Telescope (EHT) Collaboration (2019), M87* imaging, Astrophysical Journal Letters special issue
#事件视界 #黑洞 #广义相对论
为什么在匀速前进的火车上，车头和车尾“同时”发生的两件事，在站台上的人看来却不再同时？
Why do two events simultaneous at the front and back of a moving train appear not simultaneous to someone on the platform?
设想车厢正中亮起一次闪光：车上的人看到光同时到达车头和车尾，两事件同时发生。站台上的人看到车尾正迎着光运动、车头在远离，于是光先到车尾，两事件不再同时。这不是“信号传播延迟造成的错觉”，而是洛伦兹变换的必然结果（Δt′ = −γvΔx/c²）：同时性只能相对某个参考系才有定义。
Imagine a flash at the middle of the carriage: the passenger sees the light reach the front and the rear together, so the two events are simultaneous. The platform observer sees the rear wall moving toward the light and the front moving away, so the light arrives at the rear first and the events are not simultaneous. This is not an illusion caused by signal delay but a direct consequence of the Lorentz transformation (Δt′ = −γvΔx/c²): simultaneity is only defined relative to a frame.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
A. Einstein,《Zur Elektrodynamik bewegter Körper》,Annalen der Physik 322,891(1905)
A. Einstein, 'Zur Elektrodynamik bewegter Körper', Annalen der Physik 322, 891 (1905)
独立核验依据 · Independent verification: 核验依据 1 INSPIRE 标识 10.1002/andp.19053221004：Zur Elektrodynamik b
#同时性的相对性 #参考系 #狭义相对论
双生子佯谬是怎么回事？
What is the twin paradox about?
双生子佯谬设想一名宇航员以接近光速远行并返回，结果比留在地球上的双胞胎更年轻。这看似矛盾，其实是因为旅行的双胞胎经历了加速和参考系切换，两个人的世界线长度不同。广义相对论表明，经历加速度的那一方确实流逝的时间更少。
The twin paradox imagines an astronaut traveling near light speed and returning younger than the twin who stayed on Earth. It seems contradictory, but the traveling twin undergoes acceleration and changes reference frames, so their worldlines have different lengths. General relativity confirms that the twin who experiences acceleration really ages less.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#双生子佯谬 #时间膨胀 #世界线
洛伦兹力如何从相对论自然导出？
How is the Lorentz force derived naturally from relativity?
在不同惯性系中切换时，纯电场会部分表现为磁场，电荷所受的力随之同时包含电力和磁力。由此相对论统一了电与磁，洛伦兹力 F=q(E+v×B) 正是同一电磁场变换后的表现。磁本质上是电的相对论效应。
When switching inertial frames, a pure electric field partly appears as a magnetic field, and the force on a charge then includes both electric and magnetic parts. Relativity thus unifies electricity and magnetism, and the Lorentz force F=q(E+v×B) is exactly how the same electromagnetic field looks after transformation. Magnetism is essentially a relativistic effect of electricity.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Griffiths,《Introduction to Electrodynamics》第4版,Cambridge University Press,2017
D. J. Griffiths, Introduction to Electrodynamics, 4th ed., Cambridge University Press, 2017
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-1-108-35938-2 (4th ed., Cambridge Univ. Press)
#洛伦兹力 #相对论 #电磁统一
质能方程 E=mc² 到底在说什么？
What does the mass-energy equation E=mc² actually say?
它表示质量与能量是同一物理量的两种表现，静止物体蕴含的固有能量等于其质量乘以光速平方。核反应里极小的质量亏损就能释放巨大能量，正是这一等价关系的体现。
It says mass and energy are two aspects of the same quantity, with a body's rest energy equal to its mass times the speed of light squared. Tiny mass losses in nuclear reactions release enormous energy precisely because of this equivalence.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
爱因斯坦 1905 年《物体的惯性》论文
Einstein, 'Does the inertia of a body depend upon its energy content?' (1905)
独立核验依据 · Independent verification: 核验依据 1 ARCHIVE 标识 einstein-e_mc2-inertia-body-energy：Einstein:
#质能等价 #E=mc² #核能
什么是长度收缩？
What is length contraction?
根据狭义相对论，相对于观察者高速运动的物体，在其运动方向上的长度会看起来缩短，这叫长度收缩。这一效应只有在速度接近光速时才明显。
By special relativity, an object moving at high speed relative to an observer appears shortened along its direction of motion; this is length contraction. The effect is noticeable only near light speed.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#长度收缩 #相对论 #高速
在引力强的地方，时间真的会变慢吗？
Does time really run slower where gravity is stronger?
会，这是广义相对论的预言：质量会弯曲时空，引力越强的位置，时间流逝越慢。地球上的实验已经证实——放在低处的铯原子钟比放在高楼顶的走得略慢。黑洞附近这个效应极端放大，《星际穿越》里在黑洞旁一小时等于地球上七年的设定正是基于引力时间膨胀。
Yes — general relativity predicts that mass warps spacetime, and the stronger the gravity, the slower time flows. Experiments on Earth confirm it: atomic clocks tick slightly slower at ground level than atop a tall building. Near a black hole the effect becomes extreme, and Interstellar's one hour on the planet equals seven years on Earth is exactly gravitational time dilation.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-06
来源 · Source
Ashby，《全球定位系统中的相对论》，Living Reviews in Relativity 6 (2003)
Ashby, 'Relativity in the Global Positioning System', Living Reviews in Relativity 6 (2003)
独立核验依据 · Independent verification: 核验依据 1 DOI 10.12942/lrr-2003-1
#引力时间膨胀 #时空弯曲 #广义相对论
质能方程 E=mc² 到底在说什么——为什么核反应里“消失的质量”会变成巨大能量？
What does E=mc² really say—why does 'lost mass' in a nuclear reaction become huge energy?
这个方程表明质量本身就是一种能量形式，二者通过光速平方换算。核裂变或聚变中，产物总质量略小于反应物，差额 Δm 按 E=Δmc² 释放为能量，因 c² 极大，微小质量差就对应惊人能量。它统一了“质量守恒”与“能量守恒”。
The equation says mass is itself a form of energy, convertible through the square of light speed. In fission or fusion the products weigh slightly less than the reactants; that deficit Δm is released as energy E=Δmc², and because c² is enormous, a tiny mass loss means vast energy. It unifies conservation of mass and of energy.
难度 进阶 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
A. Einstein,《Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?》,Annalen der Physik 323,639(1905)
A. Einstein, 'Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?', Annalen der Physik 323, 639 (1905)
独立核验依据 · Independent verification: 核验依据 1 DOI 10.1002/andp.19053231314
#质能方程 #质量亏损 #核能量
巨大的星系怎么像透镜一样弯曲远处星光？
How can a massive galaxy bend distant starlight like a lens?
广义相对论说质量弯曲时空，光沿弯曲时空走，于是大质量天体把背后天体的光汇聚、放大甚至拉成弧。天文学家借此看见了本看不见的遥远星系。
General relativity says mass curves spacetime, and light follows that curve, so a massive object focuses, magnifies, and even arcs the light of objects behind it. Astronomers use this to see galaxies otherwise too faint.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#引力透镜 #时空弯曲 #广义相对论
什么是时间膨胀？
What is time dilation?
根据狭义相对论，运动速度越快的时钟走得越慢，相对于静止观察者时间被拉长，这叫时间膨胀。高速飞行的原子钟确实比地面上的钟走得稍慢。
By special relativity, a clock moving faster ticks more slowly, so time stretches relative to a stationary observer; this is time dilation. Fast-moving atomic clocks are indeed measured to run slightly slower than ground clocks.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#时间膨胀 #相对论 #速度
高速运动的钟真的会比静止的钟走得更慢吗？
Does a fast-moving clock really tick slower than a resting one?
是的，这是时间膨胀：相对你运动的钟走得更慢，公式含因子 √(1−v²/c²)。卫星上的原子钟就比地面略快（还要叠加引力效应），GPS 必须修正它。
Yes—time dilation: a clock moving relative to you runs slow by the factor √(1−v²/c²). Satellite atomic clocks run measurably differently from ground ones, and GPS must correct for it.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#时间膨胀 #相对论 #GPS
广义相对论预言光线经过太阳边缘会被偏折，1919年的日食观测是怎么证实这一点的？
General relativity predicts starlight bends past the Sun's edge—how did the 1919 eclipse observation confirm it?
爱因斯坦算出星光擦过太阳时会被偏折约 1.75 角秒。1919年爱丁顿团队在日全食时拍摄太阳附近的恒星位置，发现它们相对平时偏移的角度与广义相对论吻合、远超牛顿引力预言。这次观测让广义相对论一举成名。
Einstein calculated that starlight grazing the Sun would bend by about 1.75 arcseconds. During the 1919 total eclipse, Eddington's team photographed stars near the Sun and found their shift matched general relativity and far exceeded the Newtonian prediction. The result made general relativity famous.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
F. W. Dyson, A. S. Eddington & C. Davidson,《A Determination of the Deflection of Light by the Sun's Gravitational Field》,Phil. Trans. R. Soc. A 220,291(1920)
F. W. Dyson, A. S. Eddington & C. Davidson, 'A Determination of the Deflection of Light by the Sun's Gravitational Field', Phil. Trans. R. Soc. A 220, 291 (1920)
独立核验依据 · Independent verification: 核验依据 1 DOI 10.1017/9781316424254.003
#光线偏折 #日全食 #广义相对论验证
为什么说光速对任何观察者都一样？
Why is the speed of light the same for all observers?
爱因斯坦的狭义相对论假设：无论光源或观察者如何运动，真空中光速都恒为约每秒 30 万公里。这一看似违反直觉的结论已被大量实验证实。
Einstein's special relativity assumes that, regardless of how the source or observer moves, light in a vacuum is always about 300,000 km/s. This counterintuitive claim has been confirmed by many experiments.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#光速不变 #狭义相对论 #爱因斯坦
双生子佯谬真的矛盾吗？
Is the twin paradox really a contradiction?
并不矛盾。乘飞船高速往返的一方经历了加速与变速，参考系并不对称，因此回来时比留在地球的一方更年轻。Langevin 在 1911 年就以这一思想实验通俗说明时间膨胀。
It is not a contradiction. The traveling twin undergoes acceleration and turnaround, so the frames are not symmetric, and returns younger than the Earth-bound twin. Langevin used this thought experiment in 1911 to illustrate time dilation.
难度 进阶 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
Langevin 1911 年论文；Taylor 与 Wheeler《时空物理》
Langevin (1911); Taylor & Wheeler, Spacetime Physics
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL143107W：Spacetime physics（首版 196
#双生子佯谬 #时间膨胀 #参考系
为什么速度越快时间过得越慢？
Why does time pass more slowly at higher speed?
狭义相对论中时间膨胀源于光速不变：对运动参考系中的时钟，静止观察者测得它走得更慢，因子为 1/√(1−v²/c²)。这一效应已在粒子加速器和原子钟环球飞行实验中得到验证。
In special relativity time dilation follows from the constancy of light speed: a moving clock is measured by a stationary observer to run slower by the factor 1/√(1−v²/c²). This has been confirmed with particle accelerators and circumnavigating atomic clocks.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
爱因斯坦 1905 年论文；Taylor 与 Wheeler《时空物理》
Einstein (1905); Taylor & Wheeler, Spacetime Physics
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL143107W：Spacetime physics（首版 196
#时间膨胀 #狭义相对论 #光速不变
时间膨胀在现实中如何被验证？
How is time dilation verified in reality?
把极其精确的原子钟放在飞机或卫星上绕地球飞行，再与地面的钟比较，会发现运动的钟走得更慢，与相对论预言吻合。高能粒子如μ子在大气中能到达地面，也是因为它们自身的时间被膨胀、寿命相对延长。这些实验反复验证了时间膨胀。
Extremely precise atomic clocks flown on aircraft or satellites and compared with ground clocks show the moving clocks run slower, matching relativistic predictions. Fast cosmic muons reach Earth's surface because time dilation extends their lifetime in our frame. Such experiments repeatedly confirm time dilation.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#时间膨胀 #原子钟 #μ子
引力为什么会让光偏折？
Why does gravity bend light?
在广义相对论里光沿测地线运动，而质量使时空弯曲，测地线不再是直线，所以远处的光经过大质量天体附近时路径看起来被弯折。
Light follows geodesics, and mass curves spacetime so geodesics bend; passing a massive body, light's path appears deflected.
难度 进阶 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#相对论 #引力透镜 #测地线
为什么光速是宇宙中最快的速度？
Why is the speed of light the fastest speed in the universe?
根据狭义相对论，物体的能量会随速度增加而增大，要加速到光速需要无穷大的能量。任何有质量的物体都无法达到或超越光速。光速约每秒30万公里，是信息、因果和能量传递的速度上限。
According to special relativity, an object's energy grows as its speed increases, so reaching the speed of light would require infinite energy. Anything with mass can never attain or exceed the speed of light. At about 300,000 km/s, light speed is the universal limit for information, causality, and energy.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#光速 #相对论 #因果
什么是质能方程 E=mc²？
What is the mass-energy equation E=mc²?
E=mc²表示质量和能量是同一事物的两种表现，可以互相转化。c是光速，平方意味着极小的质量也蕴含巨大的能量。核反应和太阳发光都是这个方程的现实体现。
E=mc² states that mass and energy are two aspects of the same thing and can be converted into each other. With c being the speed of light, the square means a tiny mass holds enormous energy. Nuclear reactions and the Sun's shine are real manifestations of this equation.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#质能方程 #质量 #能量
为什么我们平时感觉不到相对论效应？
Why don't we normally notice relativistic effects?
因为我们在日常生活中接触的速度远小于光速，相对论修正量极小，可以忽略。只有在接近光速或极强引力场中，这些效应才变得明显。所以牛顿力学在低速弱场下足够准确。
Because the speeds we encounter daily are far below light speed, relativistic corrections are tiny and negligible. The effects become significant only near light speed or in very strong gravity. Thus Newtonian mechanics is accurate enough at low speeds and weak fields.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#低速近似 #牛顿力学 #相对论
爱因斯坦的 E=mc² 到底在说什么？
What does Einstein's E = mc² actually say?
它说质量本身就是一种能量：一个静质量为 m 的物体，蕴含着 m 乘以光速平方的能量，数量极其巨大。质量可以转化（不是「消失」）为其他形式的能量，如核裂变、核聚变中一小部分质量变成巨大热能和光。这也是为什么太阳能燃烧数十亿年、原子弹释放惊人威力的根源。
It says mass is itself a form of energy: a body of rest mass m contains m times the speed of light squared—an enormous amount. Mass can convert (not vanish) into other energy, as in fission or fusion where a small fraction becomes huge heat and light. It is why the Sun shines for billions of years and why atomic bombs release staggering energy.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
A. 爱因斯坦 1905 年《物体的惯性同它所含的能量有关吗？》论文
A. Einstein (1905), 'Does the inertia of a body depend upon its energy content?'
独立核验依据 · Independent verification: 核验依据 1 ARCHIVE 标识 einstein-e_mc2-inertia-body-energy：Einstein:
#质能等价 #核能 #相对论
双生子佯谬到底谁更年轻？
In the twin paradox, who is actually younger?
那个真的加速、调头返回地球的双胞胎更年轻，因为他的世界线在时空间隔上更短；看似对称其实不对称，因为一方经历了加速度、换了参考系。
The twin who accelerates and turns around is younger, because their spacetime path has a shorter proper time; the situation is not symmetric since one changed frames.
难度 入门 · 适合 小学低段(6-8)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#相对论 #双生子 #固有时
为什么无论你跑多快，测得的光速都一样？
Why is the speed of light the same no matter how fast you move?
这是狭义相对论的实验基石：真空中光速约 30 万公里每秒，对所有匀速运动的观测者都相同。它不随光源或观测者速度改变，颠覆了日常的速度叠加直觉。
It is the experimental cornerstone of special relativity: light in vacuum is about 300,000 km/s for every uniformly moving observer, regardless of the source or observer's speed. This breaks ordinary velocity addition.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 4 条独立证据
来源 · Source
Halliday, Resnick, Walker,《Fundamentals of Physics》第10版,Wiley,2013
David Halliday, Robert Resnick, Jearl Walker, Fundamentals of Physics, 10th ed., Wiley, 2013
独立核验依据 · Independent verification: 核验依据 3 angusrobertson.com.au
#光速不变 #狭义相对论 #参考系
什么是相对论？
What is the theory of relativity?
相对论是爱因斯坦在20世纪初提出的物理理论，用来描述高速运动和强引力下的空间、时间与物质规律。它分为狭义相对论和广义相对论两部分。狭义相对论处理匀速运动，广义相对论把引力解释为时空的弯曲。
Relativity is a physical theory proposed by Einstein in the early 20th century that describes space, time, and matter under high speeds and strong gravity. It has two parts: special relativity and general relativity. Special relativity deals with uniform motion, while general relativity explains gravity as the curvature of spacetime.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
A. Einstein, 《Zur Elektrodynamik bewegter Körper》, Annalen der Physik 17, 891 (1905)
A. Einstein, 'Zur Elektrodynamik bewegter Körper', Annalen der Physik 17, 891 (1905)
独立核验依据 · Independent verification: 核验依据 1 INSPIRE 标识 10.1002/andp.19053221004：Zur Elektrodynamik b
#相对论 #时空 #爱因斯坦
接近光速时为什么物体看起来变蓝、质量好像变重？
Why do fast objects look bluer and seem heavier near light speed?
相对论性多普勒效应让迎面而来的光蓝移；而物体的能量随速度增加而上升，要再加速需要更多能量，表现为质量增加的等效说法（更准说是动量增加）。
Relativistic Doppler shift blueshifts oncoming light; the object's energy rises with speed so further acceleration needs more energy, often described as increased mass (more precisely, momentum).
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Stephen Hawking,《A Brief History of Time》,Bantam Books,1988
S. W. Hawking, A Brief History of Time, Bantam Books, 1988
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL1892617W：A Brief History of Time
#相对论 #多普勒 #质能