Lab 1 Dilation of Time

and

Relative Speed

Bill Chun Wai Hung

Binh An

Nimish Kumar

Friday Section

16 April 2004

Goal:-

To Investigate three different areas where the dilation of time due to relative speed make a difference.
- The lengthening of the time an unstable particle exist before decays into other particles.
- The slowing down of a cesium clock on a plane flying at a reasonably constant speed with respect to the ground.
- The effect of the time dilation of Global Positioning System.

Description of Apparatus

Computer to access Internet.

Procedure:-

Experiment #1:-

For the first experiment, access the given site and then calculate distance traveled vs velocity assuming the fact that the lifetime is a constant and then plot that graph and also add Experiment 687 data and plot these points and do a best fit for those two graphs.

Experiment #2:-

For this Experiment, access the given site and read about how the time dilation occurs, as particle moves at a speed of light or as things go around the world in a space flights. By having the data, state the results and evaluate the time difference due to kinematics time dilation and gravitational time dilation using the flight took 40 hrs at the height with the actual results given.

#3. Relativistic effects in global positioning systems and satellite clocks.
Find an article on global positioning and summarize the size of the problem- the uncertainty in position and the uncertainty in the clock time generated by time dilation.

The Global Position System (GPS) consists of 24 earth- orbiting satellites, each carrying accurate, stable atomic clocks. Four satellites are in each of six different orbital planes, of inclination fo 55 degrees with respect to earth's equator. Time Dilation of moving clocks is significant for clocks in the satellite as well as clocks at reest on earth. Also, because the earth and its satellites are in free fall gravitional frequency shifts arising from the tidal potential of the Moon and Sun are only 10 power 16. Relativistic effects on satellites clocks can be combined in such a way that only two corrections need to be considered. First, the average frequency shift of clock in orbit is corrected downward in frequency by 446.47 parts in 10 to the power 12. This is the combination of five different sources of relavistic effects:-
1. Gravitational frequency shifts of ground clock due to earth's monopole and quadrupole moments.
2. Gravitational frequency shifts of the satellite clock.
3. Second order Doppler Shifts from motion of satellites.
4. Earth fixed clocks.

At the time of launch of the first satellite which contained the cesium clock to be placed in orbit, the atomic clock was first operated for about 20 days to measure its clock rate before turning on the synthesizer. The frequency measured during that interval was 442.5 parts in 10 to the power 12 faster then measured values of the frequency shifts was ony 3.97 parts in 10 to power 12. Uncertainity of position determination in real time by using the Precise Positioning code is how about 2.4m. Averaging over time and over many satellites reduces this uncertainty to the point where some users are currently interested in modeling many effects down to millimeter level.

#4. In summary, state your opinion as to the existence of time dilation and suggest other tests of time dilation, which is the same as the relativistic Doppler Shift. (Spectroscopy of moving atoms, red shifting of light from far stars, dynamics of supernovas or quasars, etc.)

Existence of Time Dilation is very abstact consequence to imagine but it does occur where relative speed makes a difference. Time is Absolute in a single universe and varies relative to objects outside this universe. However, it is really interesting to notice of how time changes relative from one place to another and its effects to our normal life.

Part I The lifetime of Do

The data of distance traveled versus velocity assuming constant lifetime is filled out in the following table.

Velocity and Distance Travelled

Velocity	Length Travelled
29979246	1.19917E-05
59958492	2.39834E-05
89937737	3.59751E-05
119916983	4.79668E-05
149896229	5.99585E-05
179875475	7.19502E-05
209854721	8.39419E-05
239833966	9.59336E-05
269813212	0.000107925

Calculation.

The best function is y²-x² = k

Time² – space² = constant

Grade the experience using the assessment.

The pages were not very user friendly, but it doesn’t take much time to figure out what to do next. The instructions were sufficient and easy to understand. The different kind of plotting illustrates different possibilities of the function, and eventually led us to derive the original correction factor.

Part III Relativisitic effects in global positioning systems and satellite clocks

An article titled “General relativity in the global positioning system” was found at http://www.phys.lsu.edu/mog/mog9/node9.html. The article suggested a clock on earth is rotating with the surface of the earth. On the other hand, a clock in space (the satellite clock in particular) is not in the same inertial frame as the clock on earth. Since the inertial frames are different, in general relativity, the times in the two different inertial frames are different.

The time is used to determine the transmission of signals in order to determine the current position an object, like a car if Global Positioning System (GPS), so the time difference has to be corrected to yield the correct position of the car. To correct the time difference due to time dilation, the date of the position and the velocity of the satellite, the position clock, and the rotational speed of the earth have to be obtained in order to correct the time dilation due to the relativisitic effect.

Part IV. Summary of Bill Chun Wai Hung

The time dilation, or the relativistic Doppler Shift, exists. Imaging a train with an observer traveling from left to right relative to a stationary object. After the train has passed the object on x-direction, and we compare the light from the object to the train when the observer is at the front of the train and at the back of the train. Since the observer is moving, the light from the object can reach the back of the train faster than if the light has to reach the front of the train. This is a similar effect as a regular Doppler Shift.

One kind of test of time dilation is Laser Spectroscopy, http://archiv.ub.uni-heidelberg.de/volltextserver/volltexte/2002/3072/ . A fast ion beam (v=0.064c) was shot, and the pattern of the spectroscopy was studied. Change in velocity results in a different pattern of the spectroscopy. By studying the spectroscopy and eliminating error, the time dilation of general relativity can be proven.

Another kind of test of time dilation is by measuring the lifetime of muon. Cosmic ray muon has a very short lifetime, but the fact is that the lifetime of muon is much longer. This proves the time dilation of general relativity.

The third kind of test is to throw an atomic clock at high speed and compare it to a stationary clock directly to confirm the time dilation effect.

In Part I, the graph showed that when the velocity is close to the speed of light, the distance traveled is not directly proportional to distance traveled, but approaches infinity instead. The website also helped to derive the correction factor

= as well.

In part II, time dilation is illustrated by flying clocks around the world in both directions. The data from the website showed the time dilation, and also gave us a formula for the time dilation.

In part III, since time is importance to determine the current position of an object by GPS. The time dilation has to be calculated to correct the time in two different inertial frames, like the earth and the stationary satellite.

Background and Procedure

Part II The Hafele/Keating Experiment

The related website is http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html#c5