Two Objects at the Speed of Light

[imjustcurious]

If two objects are traveling at the speed of light in opposite directions, doesn't this mean that one object is traveling twice the speed of light relative to the other?

 

[nasu]

No, it does not.
The only two "objects" that can do this are two photons.
But you can take two material objects (objects with mass) and make them travel at .9 c in opposite directions. Use the relativistic formula to calculate their relative speed. What do you get?

 

[russ_watters]

Welcome to PF!

First, you propose an impossible scenario, so let's change it to make it possible: make the objects go slightly less than the speed of light.

Next, you didn't specify a frame of reference for the speed measurements. Let's assume a fixed observer between them.

So, the answer is, according to the fixed observer between them, they are separating at almost twice the speed of light. But separation speed isn't the speed they measure between them: that speed is still/also slightly less than the speed of light. One of the implications of Relativity is that velocities do not add linearly.

 

[Ginosko]

Let do it more interesting. 1.- Two ships start from a point that is equidistant of two planets. A----------X----------B where X is that start point and A&B the two planets. 2.- The distance between X to both planets is little less than 300,000 kilometers. 3. The distance from planet A to planet B then is little less than 600,000 kilometers. 3.- Both ships start from X at opposite directions to the two planets. 4.- One second later the ships traveling almost near the speed of light arrive to the planets. 5.- If the speed of light can't be added and so the speed of which the ships were traveling apart from each other never were more than the speed of light, how do the ships arrive to the two planets in around one second, if the distance between the planets is around 600,000? 6. And if the ships never were traveling more than the speed of light, and the first ship stay without movement in planet A, why do the second ship in plant B, will need around 2 seconds to reach the first ship in planet A, if it travel at the same speed of the first fly, when they fly apart of each other for 1 second? :)

 

[DarioC]

Gunosko, it appears you are thinking in classical physics terms about a situation that is determined by relativity. The one second and two second "times" get really jerked around when this kind of velocity is involved. Time is not the same as we normally deal with it on an everyday basis at MUCH lower velocities.

 

[baudrunner]

Remember when the auto first arrived on the civilized scene? 30 mph was considered irresponsibly fast - breakneck speed. Then when airplanes started flying, it was said that humans flying airplanes would never be able to break the speed of sound. Well, the Lockheed SR-71 Blackbird can maintain integrity in continuous flight at Mach 3.1. Now, of course, everybody likes to cite (and generally misunderstand) Einstein (and authoritatively, at that) on this matter - that superluminal speeds are physically impossible because an object traveling at c would possesses infinite mass and time would stand still for that object. Those are two quite untenable ideas, so, no go. Well, class, that is what an observer located in a static frame of reference would see. A person traveling in a spaceship at light speed exists in his own static frame of reference, and he still weighs the same as he does on Earth. Light speed is just another barrier to be broken. What happens when the light barrier is crossed is open to speculation. Hyper-space maybe? The ability to travel to distant stars in a matter of weeks, maybe? Some day, we will know.

 

[russ_watters]

Sorry, baudrunner, but that's totally wrong:
1. The speed of light and speed of sound are totally different and scientists knew there never was a scientific reason for a "sound barrier": it was strictly an engineering problem.

2. "Infinite mass" isn't a description used much anymore because it causes exactly the confusion you are having. Try that again with "infinite energy" and it will make more sense. And please note: this is not an untested hypothesis, it is a well tested theory.

 

[newjerseyrunner]

Remember that time isn't the only thing that changes at high speed, space does too. Space is actually shorter for the fast moving objects. So if you have a hadron moving in space towards another hadron at nearly the speed of light, form your perspective they travel a light year towards each other in a year and collide at 1.4c. From the point of view of the hadron however, it did not travel a full light year. It's own measurements would put the object coming towards it at just under the speed of light, but it's distance would be far less than the light year we see them separated by.

 

[Ginosko]

Let to it more specific: Both ships are traveling at 90% of speed of light (0.9 c). Also let assume these planets are without any movements, and at a distance of 0.9 light-second of point X, and at a distance of 1.8 light-seconds of each other.

I will use the formula for Time Dilatation Delta t' : Delta t / SQRT (1 - v2/v2)

1. In planet B in no movement, 1 second had passed. And they see ship B arriving.

2. In planet A in no movement, 1 second had passed. And they see ship A arriving

3. In ship B applying the formula I got 0.19 seconds had pass, and they arrives to planet B

4. In ship A traveling at the same speed also 0.19 seconds had pass and also arrives to planet A.

5. In each planet they will see the ship arriving to the other planet in 2.8 seconds. 1 second for the trip plus 1.8 seconds because the image of the arrival of the other ship, will take 1.8 seconds to arrive. That’s because the distance of the two planets.

I’m right in all these points or not?

My question is:

Which are the speed that the inhabitants of the two planets will estimate those two ships flying apart from each other? Is it 0.9 c + 0.9 c for a total of 1.8 c?

 

[jbriggs444]

5. In each planet they will see the ship arriving to the other planet in 2.8 seconds. 1 second for the trip plus 1.8 seconds because the image of the arrival of the other ship, will take 1.8 seconds to arrive. That’s because the distance of the two planets.

Yes, you are right on those points. In all cases it is clear whose clocks and rulers are being used. There is no ambiguity and the answers are correct.

Edit: I had failed to check your arithmetic. You missed a square root. The time dilation and length contraction factor is 0.43, not 0.19.

Which are the speed that the inhabitants of the two planets will estimate those two ships flying apart from each other? Is it 0.9 c + 0.9 c for a total of 1.8 c?

Yes. That is the separation velocity -- the rate at which the distance between the two ships is increasing. It is not the velocity of any single physical object as measured against an inertial reference frame. So it is not limited to the speed of light.

Separation velocities are not the same thing as relative velocities. The fact that the planet-bound observers compute a figure of 1.8 c for the rate at which the distance between the two ships is increasing does not mean that a passenger on either ship will measure a relative velocity of 1.8c when observing the other ship.

 

[Ginosko]

Thank you JBriggs!

So what's the velocity of separation does a passenger on either ship will measure against the other ship? Also 1.8 c? Only that they will understand that the speed of separation, is the sum of a relative speed of both ships of 0.9 c, against the X point of reference? Or they will measure just 1.00 c? In that last case, how would they explain the time of arrival of the other ship to the other planet?

 

[newjerseyrunner]

No, again, velocity is distance over time. You are assuming that the distance between the two objects is remaining constant. If they are a light year apart when they are not moving in relationship to each other, they are less than half of that if they are traveling towards each other at 90% the speed of light. You dilated time, you forgot to dilate space. At 1.8c from our perspective, from their own reference they are still going about .9c because they are moving half the distance they would have at non-relativistic speeds.

 

[Ginosko]

I got it. Thank you!