View Full Version : Simple relativity question

Chief Engineer Scott
2001-Dec-05, 01:01 PM
I should remember how the frames reference on the following question, but my brain seems to have gone into a complete fugue state :-
If you are travelling at 60mph and turn on your headlights, then that light is at c relative to you, what velocity is it to a static observer you are just passing?

2001-Dec-05, 01:24 PM
I assume you mean how fast is the light travelling. The speed of light is alwasys the speed of light. That's why it's called the speed of light /phpBB/images/smiles/icon_smile.gif

In other words, the speed of light (in a vacuum) is always c, regardless of the motion of the source or the observer.

This might not seem intuitive, but time is not invariant. Time slows down for travelers approaching the speed of light and the distance they measure changes as well, so the usual equation v = d/t always works out to c.


2001-Dec-05, 03:36 PM
Yup, the speed of light is c for all observers. If you look at the three specific events:

1) driver turns on his headlights
2) light from headlights reaches 'stationary' observer
3) car reaches 'stationary' observer

The two observers would disagree on how much time passed between any two of the events, and they would also disagree on the distance the car was from the stationary observer when the lights were turned on, but they'd both agree on c being the velocity of the light.

At least, according to Einstein. /phpBB/images/smiles/icon_smile.gif

Pi Man
2002-Jun-30, 01:41 AM
When Einstein was first formulating his theory of(fanfare here please) Special Relativity, he looked at Maxwell's equations(about which you can find out more here (http://www.pact.cpes.sussex.ac.uk/users/markh/RQF1/node16.html)), and observed that the speed at which light would go(in a vacuum) was c. Scientists then asked, "Speed c relative to what? /phpBB/images/smiles/icon_confused.gif" They came up with Ether(about which you can find out more here (http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node67.html)) as being a substance relative to which light went at speed c. However, that meant that somebody could(with powerful enough rockets) catch up to a light beam, and thus see it as stationary. Einstein noted that a stationary(or slower than c in a vacuum) beam of light was not a solution to Maxwell's equations. So, he hypothesized(hypothecized, hypothasyzed, hypethysezed? /phpBB/images/smiles/icon_biggrin.gif) that *anybody* trying to study light had to see it going at speed c. All of Special Relativity and General Relativity was just an extrapolation of this hypothesis.
Pi=Epsilon (4/(4n+1)-4/(4n+3))

<font size=-1>[ This Message was edited by: Pi Man on 2002-06-29 21:42 ]</font>

David Hall
2002-Jun-30, 11:57 AM
The problem is that in this kind of situation, you expect something to change. Common sense tells you that the speed of the car adds to the speed of light in some way.

But since light always travels at the Universal Speed Limit, it's not possible for it to go any faster. So where does that extra speed go? Well, simply, the extra 60 mph energy instead shifts the wavelength of that light up to a more energetic level.

In the example you asked about. When the car is moving towards the observer, the light is blueshifted by whatever amount 60 mph adds. After you pass the observer, light is then redshifted by that same amount.
David Hall
"Dave... my mind is going... I can feel it... I can feel it." (http://www.occn.zaq.ne.jp/cuaea503/whatnots/2001_feel_it.wav)

<font size="-1">(changed last paragraph)</font>

<font size=-1>[ This Message was edited by: David Hall on 2002-06-30 08:01 ]</font>

2002-Jun-30, 06:14 PM
I know a bit about SR, but this thought just popped into my head: Would the
two observers disagree about how fast they were moving relative to each other?

Oh, and remember the other founding principle of SR: The laws of physics should be the same for any observer (or something similar to that).

2002-Jun-30, 07:26 PM
On 2002-06-30 14:14, xriso wrote:
I know a bit about SR, but this thought just popped into my head: Would the
two observers disagree about how fast they were moving relative to each other?

Fortunately, symmetry prevails, and so, no. Each is justified in thinking, "I'm not actually moving at all; he is." But the speed perceived would be the same.