# Thread: Special Relativity/Constancy of Speed of Light Question

1. I am a novice when it comes to theoretical physics, however, I have my degree in film production and as I write my science fiction script (will be second feature film), I want to make sure that it is completely accurate in regard to the following scenario (also, I don't mean to sound rude and pardon if I come off that way, but please only answer if you have studied physics at a University - and specifically had learned about implications of Special Relativity/Constancy of c. I am asking this because I have posted this to Facebook and many were just confused, which inadvertently produced nothing fruitful):

If I'm traveling at the head of a light beam towards a planet in distance (say millions of miles away - doesn't matter exact distance) and there is another light beam that starts at same time/space location heading to the same planet, so that it is parallel to me. Due to special relativity theory (i.e., what it would predict regarding universe's workings), I would observe the light running parellel to me hit the destination planet minutes (or whatever positive temporal value) first. This is because relativity theory predicts that no matter an observer's velocity, light will always appear to travel at a constant speed (c). It is always a constant to all observers, regardless of velocity. However, to the observer on the destination planet, both beams of light would appear to arrive at the same time (observer being equidistant between the two parellel light beams). Do I have this correct?

And if I need to add this - I realize problem with infinite mass, and if you find that problematic - just change one observer to be traveling at 1/2 of c - then you would still see the light beam hit the destination planet sooner in comparison to more stationary observer (i.e., observer with less velocity). And this is different than what Newtonian physics would have predicted. I am not concerned with gravitational time dilation (it's a very small planet : ).

Some said this was paradoxical - however, I believe it is answered by bending of space-time (just different frames). It is not paradoxical, correct?

Any help is very appreciated!

Thank you,
R

2.

3. Originally Posted by FavoriteMedia
I am a novice when it comes to theoretical physics, however, I have my degree in film production and as I write my science fiction script (will be second feature film), I want to make sure that it is completely accurate in regard to the following scenario (also, I don't mean to sound rude and pardon if I come off that way, but please only answer if you have studied physics at a University - and specifically had learned about implications of Special Relativity/Constancy of c. I am asking this because I have posted this to Facebook and many were just confused, which inadvertently produced nothing fruitful):

If I'm traveling at the head of a light beam towards a planet in distance (say millions of miles away - doesn't matter exact distance) and there is another light beam that starts at same time/space location heading to the same planet, so that it is parallel to me. Due to special relativity theory (i.e., what it would predict regarding universe's workings), I would observe the light running parellel to me hit the destination planet minutes (or whatever positive temporal value) first. This is because relativity theory predicts that no matter an observer's velocity, light will always appear to travel at a constant speed (c). It is always a constant to all observers, regardless of velocity. However, to the observer on the destination planet, both beams of light would appear to arrive at the same time (observer being equidistant between the two parellel light beams). Do I have this correct?

And if I need to add this - I realize problem with infinite mass, and if you find that problematic - just change one observer to be traveling at 1/2 of c - then you would still see the light beam hit the destination planet sooner in comparison to more stationary observer (i.e., observer with less velocity). And this is different than what Newtonian physics would have predicted. I am not concerned with gravitational time dilation (it's a very small planet : ).

Some said this was paradoxical - however, I believe it is answered by bending of space-time (just different frames). It is not paradoxical, correct?

Any help is very appreciated!

Thank you,
R
Okay, the first thing to realize is that it is meaningless to talk about what you would see while traveling at the speed of light. This is because the speed of light is not a valid reference frame in Relativity. That being said, we'll assume that you are traveling at 0.99c with respect to the destination planet. In this case, it is true that the light will travel at c with respect to you as measured by you and at 0.01c relative to you as measured by someone on the planet.

Thus if you started 30,000,000 km apart, it will take 100 sec according the destination planet for the light to travel the distance, and you will take ~101 sec, arriving ~ 1sec later. Also according to him, your clock runs ~7.1 times slower than his own, so ~14.25 sec will pass on your clock from the time you leave until you arrive and ~14.11 sec from the time the light leaves and arrives.

Now here what happens from your perspective: Because of the effects of length contraction, the 30,000,000 km will measure to be only 4232021 km to him. At .99c, this will take only 14.25 by your clock to cross. This is the same answer the destination planet got for the time on your clock. As far as the light goes, it will take ~7.1 sec to reach the destination planet by your clock (The light is rushing toward the planet at c, and the planet is rushing towards you at 0.99c). This is different than the time the destination planet says will pass on your clock during the crossing of the light.

Is this a paradox?, No. This is because of something called the Relativity of Simultaneity. What it means is that the same two event that are simultaneous according to you (the light reaching the planet and your clock reading 7.1 sec), are not simultaneous according to the destination planet. IOW, "at the same time" doesn't mean the same thing for you as it does for the planet.

The one time that you and the planet do agree as event being simultaneous is when those events happen at the same point. You both agree that when you and the light started from the same point, your clock read O, you both agree that when your ship arrives at the planet your clock reads 14.25 sec, etc.

This also means that you and the planet do not agree as to what time it is on the planet when you start your trip. Thus if according to the planet, both of your clocks read 0 upon your departure, then according to you the destination planet's clock already reads ~99 sec when you leave. It therefore accumulates 2 sec during the trip to read 101 sec upon your arrival. (and also advanced by 1 sec during the ~7.1 sec it takes for the light to make the trip so that the light arrives when the planet clock read 100 sec)

You might want to try reading this:
http://www.thescienceforum.com/physi...ty-primer.html

as it goes over how the concepts of time dilation, length contraction and the Relativity of Simultaneity are arrived at from the postulates of Relativity.

 Bookmarks
##### Bookmarks
 Posting Permissions
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts   BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Terms of Use Agreement