# General & Special Relativity, Everyday Examples

#### sciroccokid

Does anyone have any original everyday examples of General and Special Relativity? It seems like often the same examples are used over and over. One great example I came across recently was how GPS uses both general & special relativity. Anyone else have any everyday applications or examples of these theories?

Related Special and General Relativity News on Phys.org

#### mgb_phys

Homework Helper
In a CRT (ie. tv with a tube) the electrons are relativistic enough to take this into account when calculating the deflector fields.

A measurable effect - though not particularly practical - we detect cosmic rays at ground level that shouldn't have lived long enough to reach us from the upper atmsophere where they are formed, except for time dilation.

#### sciroccokid

In a CRT (ie. tv with a tube) the electrons are relativistic enough to take this into account when calculating the deflector fields.
Hmm, this is great. Can you elaborate on this a bit. The idea here is to explain special & general relativity in practical terms to someone who is unfamiliar with the concept.

Thanks! Any other ideas?

Another good example I have come across, is that your time runs faster atop a building then it does 70 stories down at street level.

Last edited by a moderator:

Homework Helper

#### sciroccokid

And, of course, GPS systems have to take relativistic effects into account.
See
http://www.phys.lsu.edu/mog/mog9/node9.html
Yes sir. Great link. I think satellites are a great example as they use both GR & SR. People understand they travel at high speeds and "very high up".

Thanks!

#### Dale

Mentor
Another thing to point out wrt GPS is not just the altitude and the speed, but also the precision of the time required. If you want to get your location to within say 50 feet then your timing needs to be accurate to within 50 nanoseconds! So if you did not take relativity into account your GPS "position" would drift by something like 7 miles/day!

#### sylas

Thanks! Any other ideas?

Another good example I have come across, is that your time runs faster atop a building then it does 70 stories down at street level.
If you like this example, then you'll love this one. A physicist took his kids for a weekend holiday up Mt Rainier, along with three atomic clocks, while Mum stayed home to work on her thesis in peace and quiet... and to supervise atomic clocks left in the kitchen.

Story, and pictures, and links, in [post=2177891]msg #10[/post] of thread "Gravitational Time Dilation - Confused".

The full story offsite at Project GREAT: General Relativity Einstein/Essen Anniversary Test -- Clocks, Kids, and General Relativity on Mt Rainier.

Felicitations -- sylas

#### crx

Another thing to point out wrt GPS is not just the altitude and the speed, but also the precision of the time required. If you want to get your location to within say 50 feet then your timing needs to be accurate to within 50 nanoseconds! So if you did not take relativity into account your GPS "position" would drift by something like 7 miles/day!

...or could be just a simple myth , as shown here : http://www.physicsmyths.org.uk/gps.htm

#### mgb_phys

Homework Helper
Not sure I'm convinced by that.
Yes to get your position relative to the satelites then all you need is for their clocks to be in sync - their absolute time doesn't matter and them running fast/slow only changes the units of distance slighty.
But if you want your position on Earth then you need to compare that relative position with the satelites known orbital position which they calculate from absolute time, and this would drift without the relativistic correction.

In practice the onboard empheris is updated pretty regularly by the ground stations so this wouldn't be a big problem

#### Dale

Mentor
The math there doesn't hold up. This is simply not how GPS coordinates are determined.

First, you never have a 1D situation where the receiver is in line between two transmitters since that would require one of the transmitters to be below the horizon. Also, it takes a minimum of four satellites to localize a GPS receiver. Because it takes four and because all four are in somewhat of the same direction (i.e. all are above the horizon) the errors do not simply cancel out like this site suggests. It is likely that the error is less than the 7 miles/day, but the geometry is not such that they completely cancel.

Last edited:

#### russ_watters

Mentor
Particulars of how the position is calculated aside, there is a more practical reason why Relativity is important in GPS satellites: the sample calculations in the website assume the satellites' clocks can be/remain synchronized with or without relativistic calculations. But since they are built in one frame of reference and launched into others (not the same frames, counter to the claim on the website), often years apart, there probably isn't a practical way to make/keep them synchronized except via a ground station.

Also, it seems to me that the website discards time dilation but still assumes a constant speed of light...

#### Cleonis

Gold Member
I think satellites are a great example as they use both GR & SR. People understand they travel at high speeds and "very high up".
I feel I should point out that GR has subsumed SR.

In the case of a satellite it is customary to attribute a velocity time dilation effect to the fact that it has a velocity relativity to the Earth, and a gravitational time dilation effect to the fact that the satellite is located higher in the gravitational well than clocks on the surface of the Earth. GR accounts for both effects, so it's certainly not an SR effect side by side with an GR effect.

In fact several years ago a discussion was posted on Usenet, showing that in GR you also have the option to find the total time dilation without separating in velocity time dilation and gravitational time dilation. The separation in velocit time dilation and gravitational time dilation is to an extent artificial. In GR you have the option of treating that as a single time dilation effect.

Here is where to find the discussion of 'relativistic time on satellites':
Usenet group: sci.physics
Message author: Kevin Brown
Time 9:00 am Date: 8 april 1997
I located the message in the Google Usenet archive by entering the following combination of search strings: '"Kevin Brown"' 'relativity' 'subsumes'

Cleonis

#### mgb_phys

Homework Helper
I feel I should point out that GR has subsumed SR.
I have some vague memory that this is only true for something in free fall - or I suppose an orbit counts.
I think the problem was to calculate the trajectory of an object that minimizes time from the objects point of view - it turns out to be a classical newtonian parabola

#### Dale

Mentor
I think Cleonis' point is correct in general, not just for free falling observers. You would just use the appropriate metric for whatever coordinate system you want.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving