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4.10: Experimental Evidence
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/04%3A_Trip_to_Canopus/4.10%3A_Experimental_Evidence
When the radioactive particle moves at high speed in the laboratory, its average lifetime is significantly longer as measured on laboratory clocks than when the particle is at rest The amount of lengt...When the radioactive particle moves at high speed in the laboratory, its average lifetime is significantly longer as measured on laboratory clocks than when the particle is at rest The amount of lengthening of this lifetime is easily calculated from the particle speed in the same way the astronaut calculates time stretching on the way to and from Canopus.
3.3: What Is the Same in Different Frames
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/03%3A_Same_Laws_for_All/3.03%3A_What_Is_the_Same_in_Different_Frames
For example, the relation between the force acting on a particle and the change in velocity per unit time of that particle follows the same law in the laboratory frame as in the rocket frame. Instead,...For example, the relation between the force acting on a particle and the change in velocity per unit time of that particle follows the same law in the laboratory frame as in the rocket frame. Instead, today the speed of light ranks as mere conversion factor between the meter and the second, like the factor of conversion from the centimeter to the meter.
2.1: Floating to Moon
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/02%3A_Floating_Free/2.01%3A_Floating_to_Moon
Less than a month after the surrender at Appomattox ended the American Civil War (1861-1865), the French author Jules Verne began writing A Trip From the Earth to the Moon and A Trip Around the Moon.
8.1: The System
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/08%3A_Collide._Create._Annihilate./8.01%3A_The_System
What the action starts with, what particles there are, what speeds they have, what directions they take: that’s the story of the system at the start of the action. We do not open up in this book the m...What the action starts with, what particles there are, what speeds they have, what directions they take: that’s the story of the system at the start of the action. We do not open up in this book the more complex story of the forces, old and new, that govern the chances for this, that, and the other outcome of a given encounter.
8.4: Energy Without Mass- Photon
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/08%3A_Collide._Create._Annihilate./8.04%3A_Energy_Without_Mass-_Photon
In brief, the lightlike character of the arrow of photon momenergy tells us that (1) photon mass equals zero and (2) the magnitude of momentum, or punch-delivering power, of the photon is identical in...In brief, the lightlike character of the arrow of photon momenergy tells us that (1) photon mass equals zero and (2) the magnitude of momentum, or punch-delivering power, of the photon is identical in value with the energy of the photon:
3.8: Invariance of the Interval for All Free-float Frames
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/03%3A_Same_Laws_for_All/3.08%3A_Invariance_of_the_Interval_for_All_Free-float_Frames
In spite of the difference in space separation observed in the three frames $(0$ meters for the rocket, 8 meters for the laboratory, 20 meters for the super-rocket) and the difference in time separa...In spite of the difference in space separation observed in the three frames $(0$ meters for the rocket, 8 meters for the laboratory, 20 meters for the super-rocket) and the difference in time separation ( 6 meters for the rocket, 10 meters for the laboratory, $20.88$ meters for the super-rocket), the interval between the two events has the same value for all three observers:
3.S: Same Laws for All (Summary)
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/03%3A_Same_Laws_for_All/3.S%3A_Same_Laws_for_All_(Summary)
\[\begin{align*} (\text { interval })^{2} &=\left( $\begin{array}{c} \text { separation } \\ \text { in lab } \\ \text { time } \end{array}$ \right)^{2}-\left(\begin{array}{c} \text { separation } \\ \tex...\[\begin{align*} (\text { interval })^{2} &=\left( $\begin{array}{c} \text { separation } \\ \text { in lab } \\ \text { time } \end{array}$ \right)^{2}-\left( $\begin{array}{c} \text { separation } \\ \text { in lab } \\ \text { position } \end{array}$ \right)^{2} \\[10pt] &=\left( $\begin{array}{c} \text { separation } \\ \text { in moving- } \\ \text { particle time } \end{array}$ \right)^{2}-\left( $\begin{array}{c} \text { separation } \\ \text { in moving- } \\ \text { particle position } \end{array}$ \r…
8.3: Mass of a System of Particles
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/08%3A_Collide._Create._Annihilate./8.03%3A_Mass_of_a_System_of_Particles
System a: System energy equals the rest energy of the two particles (the sum of their masses) plus the kinetic energy of the moving particle: $E_{\text {system }}=(m+m)+3 m=5 m .$ Squared momentum o...System a: System energy equals the rest energy of the two particles (the sum of their masses) plus the kinetic energy of the moving particle: $E_{\text {system }}=(m+m)+3 m=5 m .$ Squared momentum of the system equals that of the moving particle: $p_{\text {system }}^{2}=p^{2}=$ $E^{2}-m^{2}=(4 m)^{2}-m^{2}=15 m^{2} .$ Mass of the system is reckoned from the difference between the squares of energy and momentum:
8.S: Collide. Create. Annihilate. (Summary)
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/08%3A_Collide._Create._Annihilate./8.S%3A_Collide._Create._Annihilate._(Summary)
"Mass can be converted into energy and energy can be converted into mass" - this is a loose and sometimes misleading way to summarize some consequences of the two principles that are basic and really ..."Mass can be converted into energy and energy can be converted into mass" - this is a loose and sometimes misleading way to summarize some consequences of the two principles that are basic and really accurate: (1) The total momenergy of an isolated system of particles remains unchanged in a reaction; (2) The invariant magnitude of the momenergy of any given particle equals the mass of that particle.
2.E: Floating Free (Exercises)
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/02%3A_Floating_Free/2.E%3A_Floating_Free_(Exercises)
This horizontal force causes a static deflection of the plumb line from the vertical by the small angle $\varepsilon$ . (Similar practical example: In northern India the mass of the Himalaya Mountain...This horizontal force causes a static deflection of the plumb line from the vertical by the small angle $\varepsilon$ . (Similar practical example: In northern India the mass of the Himalaya Mountains results in a slight sideways deflection of plumb lines, causing difficulties in precise surveying.) The sphere is now rolled around to a corresponding position on the other side of the room (right), causing a static deflection of the plumb by an angle $\varepsilon$ of the same magnitude but in …
7.3: Momenergy Components and Magnitude
https://phys.libretexts.org/Bookshelves/Relativity/Spacetime_Physics_(Taylor_and_Wheeler)/07%3A_Momenergy/7.03%3A_Momenergy_Components_and_Magnitude
\[\begin{aligned} & =(\text { mass }) \times \frac{\text { (eastward displacement) }}{\text { (proper time for that displacement) }} \\ & \left(\begin{array}{c}\text { northward } \\\text { component ...\[\begin{aligned} & =(\text { mass }) \times \frac{\text { (eastward displacement) }}{\text { (proper time for that displacement) }} \\ & \left( $\begin{array}{c}\text { northward } \\\text { component } \\\text { of } \\\text { momenergy }\end{array}$ \right)=\left( $\begin{array}{c}\text { northward } \\\text { component } \\\text { of } \\\text { momentum }\end{array}$ \right) \\ & =\text { (mass) } \times \frac{\text { (northward displacement) }}{\text { (proper time for that displacement) }} \\ & …

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