Exam 3: The Laws of Physics Are Frame-Independent Relativity

Which of the following are (at least nearly) inertial reference frames and which are not? (Respond T if the frame is inertial, F if it is non inertial, and C if it is inertial for everyday purposes. The classification could be debatable, creating an opportunity to discuss the issues involved.) -(c) A non rotating frame attached to the sun

A sealed cup of water is placed in a microwave oven. The water absorbs microwave energy, which causes its atoms to vibrate more vigorously, making the water warmer. In this process, the mass of the water in the cup:

If the space time interval between two events $A$ and $B$ is spacelike and event $A$ occurs before event $B$ in some Home Frame, then it is always possible to find an Other Frame where the events occur in the other order.

Suppose we know a particle's four-momentum $p_{t}$ and $p_{x}$ components. If we draw the particle's four-momentum arrow on an energy-momentum diagram, we can use a hyperbola to determine

Consider a Home Frame and an Other Frame that moves in the $+x$ direction with respect to the Home Frame. -(a) Observers in the Home Frame will conclude that the clocks in an Other Frame will be out of synchronization, even if the observers in the Other Frame have carefully synchronized clocks using the Einstein prescription.

(a) The squared magnitude of a four-vector could be negative.

A photon hitting an electron (mass $m$ ) at rest can create an electron-antielectron pair in addition to the original electron. Assume that the two electrons and the positron move away from the collision at rest with respect to each other afterward. What was the photon's initial energy?

The coordinate time between two given events is shortest in the inertial frame where their spatial separation is the smallest.

Suppose you are in a train traveling at one-half of the speed of light relative to the earth. Assuming that photons emitted by the train's headlight travel at the speed of light relative to you, they would (according to the Galilean velocity transformation) travel at 1.5 times the speed of light relative to the earth.

In example R9.4, a kaon (whose mass is $498 \mathrm{MeV}$ ) decays to two pions (each with a mass of $135 \mathrm{MeV}$ ). -(b) The total system's mass decreases in this process.

A light flash leaves a master clock at $x=0$ at time $t=-12 \mathrm{~s}$ , is reflected from an object a certain distance in the $-x$ direction from the origin, and then returns to the origin at $t=+8 \mathrm{~s}$ . From this information, we can infer that the spacetime coordinates of the reflection event are $[t, x]=$

A particle's mass is always either equal to or smaller than the time-component of its four-momentum.

If the space time interval between two events is time like, then the temporal order of the two events is the same in every inertial reference frame.

An object is at rest in the Home Frame. Imagine an Other Frame moving at a speed of $|\beta|=\frac{4}{5}$ with respect to the Home Frame. The object's length in the Other Frame is measured to be $15 \mathrm{~ns}$ . What is its length as observed in the Home Frame?

In figure R2.12, the object whose world line is labelled $B$ is moving along the $x$ axis.

A system consists of two photons moving in opposite directions. One photon has energy $E$ and the other has energy $4 E$ . The total system's mass $M$ is

A particle moves along the $x$ axis. The slope of the arrow representing an object's four-momentum on an energy-momentum diagram is equal to

Since the laws of physics are the same in every reference frame, an object must have the same kinetic energy in all inertial reference frames.

The absolute value of the $x$ component of a particle's four-momentum vector is always either equal to or smaller than its $t$ component.

Which of the following are (at least nearly) inertial reference frames and which are not? (Respond T if the frame is inertial, F if it is non inertial, and C if it is inertial for everyday purposes. The classification could be debatable, creating an opportunity to discuss the issues involved.) -(a) A non rotating frame floating in deep space