Choose the option from each pair that makes the following statement correct. According to an observer at rest, moving clocks run more [(a) slowly; (b) quickly] than stationary clocks and moving rods are [ (c) longer; (d) shorter] than stationary rods.

Question

Want to see more full solutions like this?

Answer 1

Textbook Question

Chapter 26, Problem 1CQ

Choose the option from each pair that makes the following statement correct. According to an observer at rest, moving clocks run more [(a) slowly; (b) quickly] than stationary clocks and moving rods are [ (c) longer; (d) shorter] than stationary rods.

Expert Solution & Answer

To determine

The time measured by moving clocks versus the time measured by the stationary clock.

Answer to Problem 1CQ

According to an observer at rest, moving clocks run more (b) quickly than the stationary clocks.

According to an observer at rest, moving rods are (d) shorter than stationary rods.

Explanation of Solution

Time dilation: According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other or by being differently situated relative to a gravitational field.

Length contraction: Length contraction is the phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length which is the length as measured in the object’s own rest frame.

Conclusion:

The time measured by the observer at the rest frame with the stationary clocks is the proper time. The proper time measured by the stationary clocks will be slower than the time measure in the moving clocks. Thus, the choice (b) is correct.

The time measured by the moving clocks will be shorter than the time measured by the stationary clocks according to the time dilation. Thus, the choice (a) is incorrect.

The length of the rod measured when it is at rest is its proper length. When the rod is moving with a speed near to the speed of light, the length will appear shorter according to the length contraction. Thus, the choice (d) is correct.

The length of a stationary rod measures according to the rest frame is longer compared to the moving rod with respect to the rest frame. Thus, the choice (c) is incorrect

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Question B3 Consider the following FLRW spacetime: t2 ds² = -dt² + (dx² + dy²+ dz²), t2 where t is a constant. a) State whether this universe is spatially open, closed or flat. [2 marks] b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function of time t, starting at t = 0. [3 marks] c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect to galaxy A. d) The Friedmann equations are 2 k 8πG а 4πG + a² (p+3p). 3 a 3 [5 marks] Use these equations to determine the energy density p(t) and the pressure p(t) for the FLRW spacetime specified at the top of the page. [5 marks] e) Given the result of question B3.d, state whether the FLRW universe in question is (i) radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv) none of the previous. Justify your answer. f) [5 marks] A conformally…

SECTION B Answer ONLY TWO questions in Section B [Expect to use one single-sided A4 page for each Section-B sub question.] Question B1 Consider the line element where w is a constant. ds²=-dt²+e2wt dx², a) Determine the components of the metric and of the inverse metric. [2 marks] b) Determine the Christoffel symbols. [See the Appendix of this document.] [10 marks] c) Write down the geodesic equations. [5 marks] d) Show that e2wt it is a constant of geodesic motion. [4 marks] e) Solve the geodesic equations for null geodesics. [4 marks]

Page 2 SECTION A Answer ALL questions in Section A [Expect to use one single-sided A4 page for each Section-A sub question.] Question A1 SPA6308 (2024) Consider Minkowski spacetime in Cartesian coordinates th = (t, x, y, z), such that ds² = dt² + dx² + dy² + dz². (a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V. (b) Consider now the coordinate system x' (u, v, y, z) such that u =t-x, v=t+x. [2 marks] Write down the line element, the metric, the Christoffel symbols and the Riemann curvature tensor in the new coordinates. [See the Appendix of this document.] [5 marks] (c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify explicitly that V. V is invariant under the coordinate transformation. Question A2 [5 marks] Suppose that A, is a covector field, and consider the object Fv=AAμ. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation. [5 marks] (b)…

Answer 2

Textbook Question

Chapter 26, Problem 1CQ

Choose the option from each pair that makes the following statement correct. According to an observer at rest, moving clocks run more [(a) slowly; (b) quickly] than stationary clocks and moving rods are [ (c) longer; (d) shorter] than stationary rods.

Expert Solution & Answer

To determine

The time measured by moving clocks versus the time measured by the stationary clock.

Answer to Problem 1CQ

According to an observer at rest, moving clocks run more (b) quickly than the stationary clocks.

According to an observer at rest, moving rods are (d) shorter than stationary rods.

Explanation of Solution

Time dilation: According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other or by being differently situated relative to a gravitational field.

Length contraction: Length contraction is the phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length which is the length as measured in the object’s own rest frame.

Conclusion:

The time measured by the observer at the rest frame with the stationary clocks is the proper time. The proper time measured by the stationary clocks will be slower than the time measure in the moving clocks. Thus, the choice (b) is correct.

The time measured by the moving clocks will be shorter than the time measured by the stationary clocks according to the time dilation. Thus, the choice (a) is incorrect.

The length of the rod measured when it is at rest is its proper length. When the rod is moving with a speed near to the speed of light, the length will appear shorter according to the length contraction. Thus, the choice (d) is correct.

The length of a stationary rod measures according to the rest frame is longer compared to the moving rod with respect to the rest frame. Thus, the choice (c) is incorrect

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 26, Problem 1CQ

Choose the option from each pair that makes the following statement correct. According to an observer at rest, moving clocks run more [(a) slowly; (b) quickly] than stationary clocks and moving rods are [ (c) longer; (d) shorter] than stationary rods.

Expert Solution & Answer

To determine

The time measured by moving clocks versus the time measured by the stationary clock.

Answer to Problem 1CQ

According to an observer at rest, moving clocks run more (b) quickly than the stationary clocks.

According to an observer at rest, moving rods are (d) shorter than stationary rods.

Explanation of Solution

Time dilation: According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other or by being differently situated relative to a gravitational field.

Length contraction: Length contraction is the phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length which is the length as measured in the object’s own rest frame.

Conclusion:

The time measured by the observer at the rest frame with the stationary clocks is the proper time. The proper time measured by the stationary clocks will be slower than the time measure in the moving clocks. Thus, the choice (b) is correct.

The time measured by the moving clocks will be shorter than the time measured by the stationary clocks according to the time dilation. Thus, the choice (a) is incorrect.

The length of the rod measured when it is at rest is its proper length. When the rod is moving with a speed near to the speed of light, the length will appear shorter according to the length contraction. Thus, the choice (d) is correct.

The length of a stationary rod measures according to the rest frame is longer compared to the moving rod with respect to the rest frame. Thus, the choice (c) is incorrect

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 26, Problem 1CQ

Choose the option from each pair that makes the following statement correct. According to an observer at rest, moving clocks run more [(a) slowly; (b) quickly] than stationary clocks and moving rods are [ (c) longer; (d) shorter] than stationary rods.

Expert Solution & Answer

To determine

The time measured by moving clocks versus the time measured by the stationary clock.

Answer to Problem 1CQ

According to an observer at rest, moving clocks run more (b) quickly than the stationary clocks.

According to an observer at rest, moving rods are (d) shorter than stationary rods.

Explanation of Solution

Time dilation: According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other or by being differently situated relative to a gravitational field.

Length contraction: Length contraction is the phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length which is the length as measured in the object’s own rest frame.

Conclusion:

The time measured by the observer at the rest frame with the stationary clocks is the proper time. The proper time measured by the stationary clocks will be slower than the time measure in the moving clocks. Thus, the choice (b) is correct.

The time measured by the moving clocks will be shorter than the time measured by the stationary clocks according to the time dilation. Thus, the choice (a) is incorrect.

The length of the rod measured when it is at rest is its proper length. When the rod is moving with a speed near to the speed of light, the length will appear shorter according to the length contraction. Thus, the choice (d) is correct.

The length of a stationary rod measures according to the rest frame is longer compared to the moving rod with respect to the rest frame. Thus, the choice (c) is incorrect

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

The time measured by moving clocks versus the time measured by the stationary clock.

Answer to Problem 1CQ

According to an observer at rest, moving clocks run more (b) quickly than the stationary clocks.

According to an observer at rest, moving rods are (d) shorter than stationary rods.

Explanation of Solution

Time dilation: According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other or by being differently situated relative to a gravitational field.

Length contraction: Length contraction is the phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length which is the length as measured in the object’s own rest frame.

Conclusion:

The time measured by the observer at the rest frame with the stationary clocks is the proper time. The proper time measured by the stationary clocks will be slower than the time measure in the moving clocks. Thus, the choice (b) is correct.

The time measured by the moving clocks will be shorter than the time measured by the stationary clocks according to the time dilation. Thus, the choice (a) is incorrect.

The length of the rod measured when it is at rest is its proper length. When the rod is moving with a speed near to the speed of light, the length will appear shorter according to the length contraction. Thus, the choice (d) is correct.

The length of a stationary rod measures according to the rest frame is longer compared to the moving rod with respect to the rest frame. Thus, the choice (c) is incorrect

Answer 8

Expert Solution & Answer

To determine

The time measured by moving clocks versus the time measured by the stationary clock.

Answer to Problem 1CQ

According to an observer at rest, moving clocks run more (b) quickly than the stationary clocks.

According to an observer at rest, moving rods are (d) shorter than stationary rods.

Explanation of Solution

Time dilation: According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other or by being differently situated relative to a gravitational field.

Length contraction: Length contraction is the phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length which is the length as measured in the object’s own rest frame.

Conclusion:

The time measured by the observer at the rest frame with the stationary clocks is the proper time. The proper time measured by the stationary clocks will be slower than the time measure in the moving clocks. Thus, the choice (b) is correct.

The time measured by the moving clocks will be shorter than the time measured by the stationary clocks according to the time dilation. Thus, the choice (a) is incorrect.

The length of the rod measured when it is at rest is its proper length. When the rod is moving with a speed near to the speed of light, the length will appear shorter according to the length contraction. Thus, the choice (d) is correct.

The length of a stationary rod measures according to the rest frame is longer compared to the moving rod with respect to the rest frame. Thus, the choice (c) is incorrect

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

The time measured by moving clocks versus the time measured by the stationary clock.

Answer 12

Answer to Problem 1CQ

According to an observer at rest, moving clocks run more (b) quickly than the stationary clocks.

According to an observer at rest, moving rods are (d) shorter than stationary rods.

Answer 13

Explanation of Solution

Time dilation: According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other or by being differently situated relative to a gravitational field.

Length contraction: Length contraction is the phenomenon that a moving object’s length is measured to be shorter than its proper length, which is the length which is the length as measured in the object’s own rest frame.

Conclusion:

The time measured by the observer at the rest frame with the stationary clocks is the proper time. The proper time measured by the stationary clocks will be slower than the time measure in the moving clocks. Thus, the choice (b) is correct.

The time measured by the moving clocks will be shorter than the time measured by the stationary clocks according to the time dilation. Thus, the choice (a) is incorrect.

The length of the rod measured when it is at rest is its proper length. When the rod is moving with a speed near to the speed of light, the length will appear shorter according to the length contraction. Thus, the choice (d) is correct.

The length of a stationary rod measures according to the rest frame is longer compared to the moving rod with respect to the rest frame. Thus, the choice (c) is incorrect

Answer 14

Ch. 26.3 - Prob. 26.1QQ Ch. 26.4 - Suppose youre an astronaut being paid according to...Ch. 26.4 - True or False: People traveling near the speed of...Ch. 26.4 - You are packing for a trip to another star, and on...Ch. 26.4 - You observe a locket moving away from you. (i)...Ch. 26.7 - Prob. 26.6QQ Ch. 26.7 - Prob. 26.7QQ Ch. 26 - Choose the option from each pair that makes the...Ch. 26 - Choose the option that makes the following...Ch. 26 - Choose the option that makes the following...

Choose the option from each pair that makes the following statement correct. According to an observer at rest, moving clocks run more [(a) slowly; (b) quickly] than stationary clocks and moving rods are [ (c) longer; (d) shorter] than stationary rods.

Videos

Answer to Problem 1CQ

Explanation of Solution

Want to see more full solutions like this?

Chapter 26 Solutions