Masa hidup relativistik, energi dan pergeseran Doppler
GRE Subject Test · GRE Physics Topik 22 6:01 Narasi bahasa Inggris · Subtitle bahasa Inggris + 中文 disematkan langsung
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A fast unstable particle can travel farther in the laboratory than its rest-frame lifetime times its speed would suggest.
高速运动的不稳定粒子在实验室中可以飞行得比"静止寿命乘速度"更远。
This topic relates proper lifetime to laboratory time and distance, uses the invariant energy-momentum relation and relativistic kinetic energy, and infers a recession speed from a wavelength ratio.
本主题把固有寿命与实验室时间和距离联系起来，使用不变的能量-动量关系和相对论动能，并由波长比推出退行速度。
For relative speed v, define beta equals v over c, and gamma equals 1 over the square root of 1 minus beta squared.
对于相对速度 v，定义 β 等于 v 除以 c，γ 等于 1 除以根号下 1 减 β 平方。
Proper time is measured along the particle's worldline by a clock at rest with it.
固有时是由与粒子相对静止的时钟沿其世界线测得的时间。
If its proper mean lifetime is tau nought, its laboratory mean lifetime is gamma tau nought, and its mean travel distance is v gamma tau nought at constant speed.
若固有平均寿命为 τ0，则实验室平均寿命为 γ τ0，匀速时的平均飞行距离为 v γ τ0。
The decay is statistical; mean lifetime is not a guaranteed decay time for each particle.
衰变是统计性的：平均寿命并不是每个粒子确定的衰变时间。
At beta equals 0.8, gamma equals five thirds.
当 β 等于 0.8 时，γ 等于三分之五。
Compute spacetime events consistently in one frame; proper time and coordinate time are different quantities.
要在同一参考系中一致地计算时空事件；固有时与坐标时是不同的物理量。
Total energy is E equals gamma m c squared, momentum is p equals gamma m v, and the invariant is E squared minus p squared c squared equals m squared c to the fourth.
总能量 E 等于 γ m c 平方，动量 p 等于 γ m v，不变量为 E 平方减 p 平方 c 平方等于 m 平方 c 的四次方。
When E and p c are expressed in the same energy units, find m c squared as the square root of E squared minus p c squared, not E minus p c.
当 E 和 pc 用相同能量单位表示时，m c 平方等于 E 平方减 pc 平方的平方根，而不是 E 减 pc。
The nonnegative square root is required for positive rest mass.
必须取非负平方根，以保证静止质量为正。
For E equal to 13 G e V and p c equal to 12 G e V, the rest energy is 5 G e V and the mass is 5 G e V over c squared.
例如 E 等于 13 GeV、pc 等于 12 GeV 时，静能为 5 GeV，质量为 5 GeV 除以 c 平方。
A massless particle has E equal to p c but need not have zero energy or momentum.
无质量粒子满足 E 等于 pc，但其能量或动量不一定为零。
These relations concern isolated-particle four-momentum, not classical m v at relativistic speed.
这些关系描述的是孤立粒子的四动量，而不是相对论速度下的经典 mv。
Work accelerating a particle from rest equals the kinetic energy K, which is E minus m c squared, or gamma minus 1, times m c squared.
把粒子从静止加速所做的功等于动能 K，即 E 减 m c 平方，也就是 γ 减 1 再乘以 m c 平方。
At beta equals 0.6, gamma is 1.25 and K is 0.25 m c squared, while the classical one half m v squared gives 0.18 m c squared.
当 β 等于 0.6 时，γ 为 1.25，K 为 0.25 m c 平方，而经典公式二分之一 m v 平方给出 0.18 m c 平方。
Classical kinetic energy is the low-speed expansion and becomes inaccurate near c.
经典动能只是低速展开，在接近光速时不再准确。
Finite acceleration work increases gamma rather than allowing a massive particle to reach or exceed c.
有限的加速功只会增大 γ，而不能使有质量的粒子达到或超过光速。
Keep total energy, rest energy and kinetic energy distinct when interpreting answer units.
解读答案单位时，要区分总能量、静能和动能。
For purely longitudinal relative recession in special relativity, the wavelength ratio r equals lambda observed divided by lambda emitted, which is equal to the square root of the quantity one plus beta, all over one minus beta.
在狭义相对论中，对于纯纵向相对退行情况，波长比 r 等于观测波长 λ_observed 除以发射波长 λ_emitted，即等于 (1+β)/(1−β) 的平方根。
Rearranging gives beta equals r squared minus one, all over r squared plus one.
整理后得到 β = (r²−1)/(r²+1)。
A ratio r equals 2 gives beta equals three fifths, not c times r minus one from a low-speed approximation.
当比值 r = 2 时，β = 3/5，而非低速近似下的 c(r−1)。
Blueshift uses r less than 1 and a negative recession parameter under this convention.
在此约定下，蓝移对应 r < 1 及负值的退行参数。
The formula assumes the shift is entirely kinematic.
该公式假设频移完全是运动学效应。
Cosmological expansion or gravitational redshift requires a different model.
宇宙学膨胀或引力红移需要不同的模型。
State the question's stipulated model before interpreting a spectral ratio.
在解读光谱比之前，请先明确题目所指定的物理模型。
Energy and momentum fix the rest energy: m c squared is the square root of E squared minus p c squared, never E minus p c.
能量和动量决定静能：m c 的平方等于 E 的平方减 p c 的平方再开方，而绝不是 E 减 p c。
For E of 17 GeV and p c of 15, m c squared is the square root of 289 minus 225, which is 8 GeV.
当 E 为 17 GeV、p c 为 15 GeV 时，m c 的平方等于 289 减 225 的平方根，即 8 GeV。
The kinetic energy is E minus m c squared: 17 minus 8, which is 9 GeV.
动能等于 E 减 m c 的平方：17 减 8，等于 9 GeV。
The rest mass is 8 GeV over c squared.
静质量是 8 GeV 除以 c 的平方。
Two photons of equal energy E collide, with their directions separated by an angle theta.
两个能量都为 E 的光子相撞，它们的传播方向夹角为 θ。
Derive the invariant mass of the pair, and check the parallel and head-on limits.
推导这对光子的不变质量，并检验平行和正面对撞两种极限。
Four marks.
共 4 分。
Total energy is 2E.
总能量为 2E。
Total momentum magnitude is 2E over c, times the absolute value of cosine of theta over 2.
总动量大小为 2E 除以 c，再乘以 cos(θ/2) 的绝对值。
M squared c to the fourth power equals 4E squared minus 4E squared times cosine squared of theta over 2, which simplifies to 4E squared times sine squared of theta over 2.
M²c⁴ = 4E² − 4E²cos²(θ/2) = 4E²sin²(θ/2)。
Thus, M c squared equals 2E times sine of theta over 2, for theta between 0 and pi inclusive.
因此 Mc² = 2E sin(θ/2)，其中 0 ≤ θ ≤ π。
Parallel photons have zero pair invariant mass. Head-on photons have M c squared equal to 2E.
平行光子对的不变质量为零；对撞光子的 Mc² = 2E。
Award vector momentum, invariant, result, and limits.
需给出矢量动量、不变量、结果及极限条件。
Each photon remains massless.
每个光子仍保持无质量。
Do not use the proper lifetime as laboratory time, subtract pc from E to find rest mass, or apply the classical Doppler approximation to a large wavelength ratio.
不要将固有寿命当作实验室时间。 不要用E减去pc来求静止质量。 也不要在大波长比的情况下使用经典多普勒近似。
Proper time, 固有时, is the time recorded by a clock moving with the object along its worldline.
固有时。 由随物体沿其世界线运动的时钟记录的时间。
Rest energy, 静能, is the energy m c squared associated with an object's rest mass.
静能。 与物体静止质量相关的能量mc²。
Retrieve the meanings without reading the definitions, then change a parameter in the original transfer and test the limiting case.
在不阅读定义的情况下回忆其含义，然后改变原始传递中的一个参数并检验极限情况。