Does the Force Propelling a Spaceship Affect the Speed of Light Emitted from It?

[stallion]

This question is concerned with special relativity and relative velocity.
If a spaceship is traveling at 2x10 eighth m/s and someone shines a laser straight ahead out the front of the ship. Suppose someone in front of the ship
records the velocity of the light. Since the speed of light is the same in all frames of reference the speed should be 3x18 to the eighth and not 5x10 to the eighth(adding the two velocities).

Here is my question...since the ship is moving with a force which allows it
to travel at 2x10 to the eighth, doesn't this same force push on the photons in
the light and force them to travel faster?

 

[JesseM]

This question is concerned with special relativity and relative velocity.

If a spaceship is traveling at 2x10 eighth m/s and someone shines a laser straight ahead out the front of the ship. Suppose someone in front of the ship
records the velocity of the light. Since the speed of light is the same in all frames of reference the speed should be 3x18 to the eighth and not 5x10 to the eighth(adding the two velocities).

Here is my question...since the ship is moving with a force which allows it
to travel at 2x10 to the eighth, doesn't this same force push on the photons in
the light and force them to travel faster?

Leaving aside relativity, I think you're misunderstanding something about Newtonian physics here--if a ship is moving at a constant velocity through empty space with no resistance, it doesn't need a force pushing on it to maintain that speed, in Newtonian physics all objects naturally move in straight lines at constant velocity unless a force is acting on them (forces produce acceleration, which cause objects to change speed, direction, or both).

Also, there's no such thing as absolute speed. Even if the ship is moving at 2*10^8 m/s in your frame, in the ship's own frame it is at rest and you are moving at 2*10^8 m/s in the opposite direction, and both frames are equally valid.

Aside from that, it's just a property of the coordinate systems used in relativity that insure that something moving at c in one frame must be moving at c in other frames (the reason for this choice of coordinate systems is that it insures the laws of physics obey the same equations in all coordinate systems). If frame A uses coordinates (x,y,z,t) and B uses (x',y',z',t'), and the origin of B's coordinate system is moving at velocity v along the x-axis of A's coordinate system, then the transformation is:

$$x' = \gamma (x - vt)$$
$$y' = y$$
$$z' = z$$
$$t' = \gamma (t - vx/c^2)$$
where $$\gamma = 1/\sqrt{1 - v^2/c^2}$$

So say you have a light beam moving at speed c along the x-axis of A's coordinate system. At t=0 minutes, the light beam is at position x=0 light-minutes, and at t=1 minutes, the light beam is at position x=1 light-minute. So if you plug x=0, t=0 into the above transformation, you get x'=0, t'=0; if you plug in x=1, t=1 into it, you get $$x' = \gamma (1 - v)$$ and $$t' = \gamma (1 - v)$$. So, using speed = (change in position)/(change in time), you see that in both frames the speed is 1c.

 

[Entropia]

Your question is a valid one and it highlights an important concept in special relativity - the principle of the constancy of the speed of light. This principle states that the speed of light in a vacuum is the same for all observers, regardless of their relative motion. In other words, the speed of light is not affected by the motion of its source or the observer measuring it.

In the scenario you described, the spaceship is traveling at 2x10 to the eighth m/s. This means that the observer on the spaceship will measure the speed of light as 3x10 to the eighth m/s, while the observer on the ground will measure it as 3x10 to the eighth m/s as well. This is because the speed of light is always constant, regardless of the observer's motion.

To answer your question, the force that propels the spaceship does not affect the speed of light. This is because light is not a material object, it is an electromagnetic wave. It does not require a force to travel, it simply propagates through space at a constant speed. Therefore, the force that is propelling the spaceship will not cause the speed of light to increase.

In conclusion, the principle of the constancy of the speed of light is a fundamental concept in special relativity. It means that the speed of light is not affected by the motion of its source or the observer measuring it. So, the speed of light will always be measured as 3x10 to the eighth m/s, regardless of the motion of the spaceship or any other object.