# Light moves at C from all frames of references?

1. Feb 20, 2008

### Bigman

there are a few things i don't get when it comes to light moving at c from all frames of reference... i mean it makes sense to me in some cases: like if an observer on the earth sees a missle going one way at half the speed of light, and a spaceship going the other way at the speed of light, the spaceship won't observe the missle's speed as the speed of light, since time goes faster on the spaceship then it does to the observer on the earth (at least that's my understanding so far from what i've read... just to double check, is everything i said in that example accurate?)

but i can think of a few examples where it doesn't work out as easily (some of them are harder to explain then others). here's one: you have a space station floating out in the middle of no where in space (this is our initial reference point... i would have used earth, but i wanted to avoid all the gravity and orbits and rotation and stuff) and a ship takes off from the station, and ends up doing about half the speed of light (from the station's frame of reference). since the ship has sped up, the clock on board the ship is now going faster then the clock on board the space station (right?). now, lets say you eject two escape pods from the ship: one out the front, and one out the back(the ship is still facing directly away from the station), and they each shoot out with a velocity which, from the ships frame of reference, has a magnitude equal to the velocity of the space station (which is less then half the speed of light, because time is moving faster on the ship then it is on the space station... right?). what confuses me is, how fast are the clocks on board each of the escape pods going in relation to the spaceship, the space station, and each other?

Last edited: Feb 20, 2008
2. Feb 20, 2008

### chroot

Staff Emeritus
Clocks do not magically change their rate simply because they are moving. If you're on-board a star ship, you will look down at your wristwatch and see it behaving perfectly normally, no matter how fast the star ship is going relative to anything else in the universe.

You must have two frames of reference in order to see any effects of time dilation. If a ship leaves a space station at half the speed of light, it will appear to observers in the space station that clocks aboard the ship are running slowly. Similarly, it will appear to observers on the ship that the clocks aboard the space station are running slowly.

Velocities do not add as simply in special relativity as you are accustomed. If an escape pod leaves the ship at 0.5c wrt the ship, and the ship is moving at 0.5c wrt the space station, the two velocities add like this:

$v = \frac{ 0.5c + 0.5c }{ 1 + \frac{ 0.5c \cdot 0.5c } { c^2 } } = 0.8c$

Observers aboard the space station will measure the escape pod as moving away with a velocity of 0.8c.

- Warren

3. Feb 20, 2008

### yuiop

No material object (anything with greater than zero rest mass) can go at the speed of light relative to any observer.

Generally the clocks on any object moving relative to an observer are measured as "ticking" slower by that observer.

slower

Use the relativistic velocity addition equation to figure out the speed of the pods and then the Lorentz transformations for time to answer this question.

See http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

4. Feb 20, 2008

### Bigman

woops, i meant to say that the ship was moving half the speed of light in the first example. in the second example, i was interested mostly in the time dilation, though i think that makes more sense to me now, after reading warren's post in another thread... so now i have a question that has more to do with light itself: lets say you have a ship flying by a space station at .5c, both the ship and the space station have big bright light bulbs protruding from them, and the moment that the ship flies by the space station, both lights flash for an instant (so basically, you have light coming from two sources, which are in virtually the same spot in space but have different velocities). i'm wondering, if you freeze frame everything a moment later, will the two spheres of light be overlapping each other? and if so, where will the center of these spheres be located, at the position of the ship or the station (or will the center's position be somehow dependant on the frame of reference)?

5. Feb 20, 2008

### Janus

Staff Emeritus

The center of the expanding spheres will depend on the frame of reference.

6. Feb 20, 2008

### Bigman

that can't be possible, can it? lets say you had two sensors attached to the spaceship, one out a mile in front of the ship and one out a mile in the back (imagine long mic booms sticking off the front and back), and you had two more sensors attached to the station in a similar fasion, and when the ship and station pass each other, the two sensors in the front are next to each other, as are the two sensors in the back. would the ship record that both it's sensors went off at the same time? if so, would an observer on the ship say that the light hit the station's front sensor before hitting the station's back sensor, since the ships sensors and the stations sensors are no longer next to each other by the time the light reaches them?

7. Feb 20, 2008

### yuiop

Imagine that the light sources are so close together at the passing point that we can treat them as one light source for practical purposes. From the point of view of the space station there is ring of light centred on the space station. From the point of view of the ship (some moments later) there is a ring of light centered on the ship.

The ship sees itself as stationary and from that point of view it initially sees the space station approaching. At the moment the space station was alongside it sees a flash and then it sees a ring of light spreading out evenly in all directions and the space station moving away.

The spacestation sees itself as stationary and from that point of view it initially sees the ship approaching. At the moment the ship was alongside it sees a flash and then it sees a ring of light spreading out evenly in all directions and the ship moving away.

See the symmetry?

This is what would really be observed, even if there is only one light source like a spark flashing across a small gap between the two craft at they moment they are closest to each other.

8. Feb 21, 2008

### Janus

Staff Emeritus
The ship will say the light hit its sensors simultaneouly, while hitting the sensors of the station at different times. Conversely, the station will say that the light hit it's sensors simultaneouly, while hitting the ships sensors at different times.

Welcome to "The Relativity of Simultaneity".

9. Feb 21, 2008

### Bigman

wow... so if someone in the ship were somehow able to instantaneously observe light, they would observe that the light hit the station's front sensor first, then the ships two sensors, then the stations back sensor(and someone in the station would observe everything i just said, with the words "station" and "ship" switched)?

10. Feb 21, 2008

### Janus

Staff Emeritus
Yes.

Also consider this:
We put clocks at these sensors, all reading a time of zero and designed to start ticking when the sensor next to it is tripped by the light. Then according to the ship, the clocks next to its sensors start at the same time and are synchronized so that they show the same time at all times. The station's clocks, however, will not start at the same time and thus will not show the same time after they are running (once running they both tick at the same rate, but one clock will lag behind the other.) According to the station, the reverse is true.