If I travel at 0.5c from the sun, why does redshifted light still reach me at c?

[Frederick T]

It's come to my attention that if we were to travel in a spaceship at 0.5c directly away from our sun, I would observe that the light from the sun as being red shifted. What I would also observe was that this red shifted electromagnetic wave would in fact travel away from me in the spaceship traveling at 0.5c at the speed of light with its new redshifted properties. I would be lead to conclude that light does not, in fact, have a speed limit, but the speed limit exists only as a spacetime limitation to the inertial frame of reference.

 

[jedishrfu]

You can conclude that. Light travels at the same speed in all inertial frames. What you observe as red shifted light ie lower energy might be observed in another inertial frame as blue shifted light and yet it’s the same light, the same photons. In all cases, the speed is the speed of light but the energy is different.

 

[Ibix]

What I would also observe was that this red shifted electromagnetic wave would in fact travel away from me in the spaceship traveling at 0.5c at the speed of light with its new redshifted properties.

No you would not. This would be true under Galilean relativity, but that is not an accurate description of reality. You need to use Einstein's relativity, and time dilation, length contraction, and the relativity of simultaneity conspire to make your measurements of the speed of light invariant. This has been extensively tested - see the FAQ linked in the sticky thread in this forum.

This is covered in all introductions to SR.

Edit: having read Nugatory's and Dale's responses below, it's possible I'm misreading the OP. The above response may or may not be relevant to the question actually being asked.

 

[Nugatory]

wave would in fact travel away from me in the spaceship traveling at 0.5c at the speed of light with its new redshifted properties.

The syntax is a bit tangled here, but if what you mean is:
1) relative to the earth, the spaceship is moving at .5c and the flash of light is moving at c.
2) relative to the spaceship, the Earth is moving backwards at .5c and the flash of light is moving at c.
then you have it right.

 

[Dale]

What I would also observe was that this red shifted electromagnetic wave would in fact travel away from me in the spaceship traveling at 0.5c at the speed of light with its new redshifted properties

I don’t understand what you mean to say here. Can you please clarify?