swans on tea

Just another SFN Blogs site
  • Home
  • A very little about me
  • Sample Page

The Relativistic Van

Published by swansont on January 28, 2008 04:14 pm under Physics, The Lab, Time

Who cares about gas mileage? This sucker warps time!

When relativity is discussed in popular literature it’s often couched in terms of affecting objects moving at a significant fraction of the speed of light, and that’s a true statement: kinematic time dilation cannot generally be ignored in that situation. But the implication that the opposite is true — that you can ignore these effects under other circumstances — doesn’t hold. At least, it doesn’t hold if you have some expensive toys at your disposal.

Let’s say you were going to drive across the US and back, and you had the aforementioned expensive toys. Maybe you wanted to calibrate clocks and check on the reliability of a satellite time-transfer system, and you have a mobile system that would do time transfer at the source and at the target site, allowing you to check on that calibration. Or something like that.

The time dilation in question gives a fractional frequency shift that goes with the square of the speed, as compared to the square of speed of light. That’s normally very small, and has to be under this approximation (c is big, v/c is small, (v/c) squared is reeaaally small), so you can usually ignore it, right? Not everyone can. The famous Hafele-Keating experiment that used airplanes and around–the–world travel was able to measure kinematic dilations. A trip across the US is ~2700 miles, and at 600 mph you’d get a frequency shift of 4 parts in 10^13 and a dilation of about 13 nanoseconds on your round-trip due to traveling at that speed. (one thing to note is that I’m using a different coordinate system than is used in the H-K writeup, in case you want to play along at home. The answer will be the same, but the east vs west contributions are accounted for differently, and I’m not showing that detail)

But what about a van? At 60 mph this will take you ~90 hours of road time round-trip. (It doesn’t matter if you do this all at once, so feel free to stop off and take pictures of the Grand Canyon or drop a few dollars in Vegas if that’s your thing.) This gives a change in the frequency of your clock of 4 parts in 10^15. So far, so good — the speed dropped by an order of magnitude and our frequency shift is the square of that, i.e. 100 times smaller. But here’s what I glossed over before: for the total time shift you have to integrate over the whole trip. If you are going 1/10 of the speed, the trip will take you 10 times longer. It turns out that because of this, the total time delay goes linearly with speed, not quadratically. Your time delay is 1.3 ns, which is still something that you can measure with an atomic clock, and is something for which you have to account if you are doing clock calibrations.

I haven’t mentioned gravitational time dilation at all, which is a much larger effect and more easily measured. And lest you think that only government labs would do this exercise, there are amateurs out there who do this sort of thing, like measure the 22 nanosecond gravitational time dilation due to a day-trip to Mt. Ranier.

No Comment

  1. Science is close-minded - Page 10 - Science Forums on June 13th, 2008

    […] car or van results in time dilation, and you can learn A LOT by reading that. Here is the link: Swans on Tea The Relativistic Van Here are a few additional studies supporting the idea: Haefele and Keating, Nature 227 (1970), […]

  2. That Time Problem?? - Science Forums on June 20th, 2008

    […] automobiles. __________________ Remember, we cannot see everything even when it is there right in front of […]

Posting your comment.

  • Recent Posts

    • When Does the Decade End?
    • This is the Hardest Job a Manager Has …
    • 5 Things You Should Know About Light
    • See Spot "Run"
    • The System Works
  • Recent Comments

    • Joey Cook on One Ringy-Dingy, Two Ringy-Dingy
    • Science Fanatic on Talk Like a Physicist Day
    • Chris Gould on Brian Cox is Full of **it
    • LaurieAG on Inmates Running the Asylum
    • Uncle Al on Curious About Curies
  • Archives

    • December 2019
    • February 2015
    • January 2015
    • December 2014
    • November 2014
    • October 2014
    • September 2014
    • August 2014
    • July 2014
    • June 2014
    • May 2014
    • April 2014
    • March 2014
    • February 2014
    • January 2014
    • December 2013
    • November 2013
    • October 2013
    • September 2013
    • August 2013
    • July 2013
    • June 2013
    • May 2013
    • April 2013
    • March 2013
    • February 2013
    • January 2013
    • December 2012
    • November 2012
    • October 2012
    • September 2012
    • August 2012
    • July 2012
    • June 2012
    • May 2012
    • April 2012
    • March 2012
    • February 2012
    • January 2012
    • December 2011
    • November 2011
    • October 2011
    • September 2011
    • August 2011
    • July 2011
    • June 2011
    • May 2011
    • April 2011
    • March 2011
    • February 2011
    • January 2011
    • December 2010
    • November 2010
    • October 2010
    • September 2010
    • August 2010
    • July 2010
    • June 2010
    • May 2010
    • April 2010
    • March 2010
    • February 2010
    • January 2010
    • December 2009
    • November 2009
    • October 2009
    • September 2009
    • August 2009
    • July 2009
    • June 2009
    • May 2009
    • April 2009
    • March 2009
    • February 2009
    • January 2009
    • December 2008
    • November 2008
    • October 2008
    • September 2008
    • August 2008
    • July 2008
    • June 2008
    • May 2008
    • April 2008
    • March 2008
    • February 2008
    • January 2008
  • Categories

    • admin
    • Antiscience
    • Art
    • Blog Compendia
    • Blogging
    • Body
    • Books
    • Bureaucracy
    • Business
    • Cartoon
    • Conference stories
    • Cool stuff
    • DIY science
    • Education
    • Environment
    • Experiments
    • Food
    • Game
    • Geocaching
    • History
    • Humor
    • Illusions
    • Journalism
    • Lab Stories
    • Language
    • Links
    • Math
    • Metaphysics
    • Misc
    • Movies
    • Music
    • Navy
    • Not Really Science at All
    • Other science
    • peeve
    • photography
    • Photos
    • Physics
    • Politics
    • Quotes
    • Rants
    • Religion
    • Satire
    • Sci-Fi
    • Science-general
    • science-y observation
    • Security
    • Shameless self promotion
    • Sick sick sick
    • Silly
    • Sports
    • Tech
    • The Lab
    • Thermal IR
    • Time
    • TMI
    • Toys
    • trivia
    • TV
    • TYAGFITI
    • Typography
    • Uncategorized
    • Video
    • Weird
    • World Events
    • Writing
  • Meta

    • Log in
    • Entries feed
    • Comments feed
    • WordPress.org

Copyright © 2023 swans on tea
WordPress Theme based on Light Theme