<< Chapter < Page Chapter >> Page >

In 1971, American physicists Joseph Hafele and Richard Keating verified time dilation at low relative velocities by flying extremely accurate atomic clocks around the world on commercial aircraft. They measured elapsed time to an accuracy of a few nanoseconds and compared it with the time measured by clocks left behind. Hafele and Keating’s results were within experimental uncertainties of the predictions of relativity. Both special and general relativity had to be taken into account, because gravity and accelerations were involved as well as relative motion.

Check Your Understanding a. A particle travels at 1.90 × 10 8 m/s and lives 2.10 × 10 −8 s when at rest relative to an observer. How long does the particle live as viewed in the laboratory?

a. Δ t = Δ τ 1 v 2 c 2 = 2.10 × 10 −8 s 1 ( 1.90 × 10 8 m/s) 2 ( 3.00 × 10 8 m/s) 2 = 2.71 × 10 −8 s .

Got questions? Get instant answers now!

b. Spacecraft A and B pass in opposite directions at a relative speed of 4.00 × 10 7 m/s . An internal clock in spacecraft A causes it to emit a radio signal for 1.00 s. The computer in spacecraft B corrects for the beginning and end of the signal having traveled different distances, to calculate the time interval during which ship A was emitting the signal. What is the time interval that the computer in spacecraft B calculates?

b. Only the relative speed of the two spacecraft matters because there is no absolute motion through space. The signal is emitted from a fixed location in the frame of reference of A , so the proper time interval of its emission is τ = 1.00 s . The duration of the signal measured from frame of reference B is then
Δ t = Δ τ 1 v 2 c 2 = 1.00 s 1 ( 4.00 × 10 7 m/s) 2 ( 3.00 × 10 8 m/s) 2 = 1.01 s.

Got questions? Get instant answers now!

Summary

  • Two events are defined to be simultaneous if an observer measures them as occurring at the same time. They are not necessarily simultaneous to all observers—simultaneity is not absolute.
  • Time dilation is the lengthening of the time interval between two events when seen in a moving inertial frame rather than the rest frame of the events (in which the events occur at the same location).
  • Observers moving at a relative velocity v do not measure the same elapsed time between two events. Proper time Δ τ is the time measured in the reference frame where the start and end of the time interval occur at the same location. The time interval Δ t measured by an observer who sees the frame of events moving at speed v is related to the proper time interval Δ τ of the events by the equation:
    Δ t = Δ τ 1 v 2 c 2 = γ Δ τ ,

    where
    γ = 1 1 v 2 c 2 .
  • The premise of the twin paradox is faulty because the traveling twin is accelerating. The journey is not symmetrical for the two twins.
  • Time dilation is usually negligible at low relative velocities, but it does occur, and it has been verified by experiment.
  • The proper time is the shortest measure of any time interval. Any observer who is moving relative to the system being observed measures a time interval longer than the proper time.

Conceptual questions

(a) Does motion affect the rate of a clock as measured by an observer moving with it? (b) Does motion affect how an observer moving relative to a clock measures its rate?

Got questions? Get instant answers now!

To whom does the elapsed time for a process seem to be longer, an observer moving relative to the process or an observer moving with the process? Which observer measures the interval of proper time?

The observer moving with the process sees its interval of proper time, which is the shortest seen by any observer.

Got questions? Get instant answers now!

(a) How could you travel far into the future of Earth without aging significantly? (b) Could this method also allow you to travel into the past?

Got questions? Get instant answers now!

Problems

(a) What is γ if v = 0.250 c ? (b) If v = 0.500 c ?

a. 1.0328; b. 1.15

Got questions? Get instant answers now!

(a) What is γ if v = 0.100 c ? (b) If v = 0.900 c ?

Got questions? Get instant answers now!

Particles called π -mesons are produced by accelerator beams. If these particles travel at 2.70 × 10 8 m/s and live 2.60 × 10 −8 s when at rest relative to an observer, how long do they live as viewed in the laboratory?

5.96 × 10 −8 s

Got questions? Get instant answers now!

Suppose a particle called a kaon is created by cosmic radiation striking the atmosphere. It moves by you at 0.980 c , and it lives 1.24 × 10 −8 s when at rest relative to an observer. How long does it live as you observe it?

Got questions? Get instant answers now!

A neutral π -meson is a particle that can be created by accelerator beams. If one such particle lives 1.40 × 10 −16 s as measured in the laboratory, and 0.840 × 10 −16 s when at rest relative to an observer, what is its velocity relative to the laboratory?

0.800 c

Got questions? Get instant answers now!

A neutron lives 900 s when at rest relative to an observer. How fast is the neutron moving relative to an observer who measures its life span to be 2065 s?

Got questions? Get instant answers now!

If relativistic effects are to be less than 1%, then γ must be less than 1.01. At what relative velocity is γ = 1.01 ?

0.140 c

Got questions? Get instant answers now!

If relativistic effects are to be less than 3%, then γ must be less than 1.03. At what relative velocity is γ = 1.03 ?

Got questions? Get instant answers now!

Questions & Answers

I'm interested in biological psychology and cognitive psychology
Tanya Reply
what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 2

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 3' conversation and receive update notifications?

Ask