If a vehicle were traveling through space at/near the speed of light, then what would happen if it turned its headlights on?

That's the neat thing. The speed of light is constant. It doesn't change. It's always 1c whether you're traveling at +1c, - 1c, or 0c. Buckle up for some relativity. The wavelength can compress or expand, but it always travels at 1c.

Let's say you're on a ship capable of moving at any speed between 0c and 1c. You're passing a particular star and want to travel to a planet 1ly away. You have a powerful laser and the other planet has a powerful telescope to detect it. There are calibrated timers on both the planet and on your ship that are synced to each other. .

T minus zero. You flash the laser at the planet as you fly at 0.5c, or 1/2 lightyear per year. The light travels at 1c, or 1ly per year.

1 year after the flash, the planet sees the flash. It traveled 1ly in 1 year. 2 years after the flash, the planet sees your ship arrive. All is normal so far.

From the ship, you know the light traveled at 1c away from you. You arrive at the planet 1 year after the flash, according to your on board timer. One. The light took half as long as you.

Time is not constant, c is constant. The faster you go, the slower time passes. In 1 year of fast travel, you arrive 2 years later, according to the stationary planet. So all of the light physics apply the same, no matter the speed. Time dilates to make up the logical difference. If you reach 1c, time effectively stops and you arrive instantaneously, from your perspective. When we look up at the Andromeda galaxy, some 2.5 million lightyears away, the light we see was emmited 2.5 million years ago - from our perspective. If we see a star go supernova in Andromeda, it happened 2.5 million years ago. But those photons of light, created by a star that died 2.5 million years ago, experience no time passage at all. They instantaneously go from the star to your retina, from their perspective.

That's basically why lightspeed travel is effectively impossible within our current models. Traveling faster is out of the question because none of it makes sense. It's not a simple matter of making a new model or believing scientists are idiots. There are many experiments that hold true to the model (such as the atomic clocks used on a plane to test the effect of speed and gravity on time dilation) as well as satellites using the current model to maintain time accuracy. The energy required to get to those speeds is not even remotely feasible. The fastest man made object at 450,000+mph, the Parker solar probe, is still in the 0.0005c range. We tried our best and it's still just a tiny fraction of 1c. And that's by using some gravity slingshots and spiraling down into the sun's gravity well, nothing about leaving the solar system. The Voyager probes that slingshotted out of the sun's gravity well are down to under 40,000mph.

You would see your normal headlights because your subjective experience of time wouldn’t change.

Nothing. The speed of light is so fast that our intuitive understanding of the world doesn't apply, when going that fast.

Light travels at the speed of light relative to you. It doesn't matter where you are or how fast you're moving light will travel around you at the speed of light.

Imagine you're in a space ship passing a planet at half the speed of light. You would measure your headlight's beam as travelling away from you at the speed of light. Someone on the planet would see you going 0.5c and your headlights going 1c, and would conclude your headlight beam is traveling away from you at half the speed of light.

How does the universe deal with these contradictory observations? Time dilation. Time will flow at a different rate on your ship than the planet. The universe is weird at high speeds.

As far as your speed, it would be the same as turning on the headlights of your car. The lights will slow you down, but such a small amount you need a special lab to even measure it.

That's the fun part of light, it is the same speed regardless of reference frame.

Just wanted to say this was an awesome thread with a lot of great explanations- really interesting read, thanks for the great question!

If you are in the car, the headlights would look normal. If the car is driving towards you, the light would be blue shifted. If it is driving away from you (I guess you would be seeing the taillights), they would be red shifted. That is what happens when you look at the light from distant galaxies. Because the universe is expanding, the galaxies are moving away from us rather fast. Because you know the emission spectra of the stars in them, you can calculate the red shift, and that tells you how far away the galaxy is.

Where would you be located relative to the light?

If you were observing as a third person watching in the slowest of slow motion, would the light from the headlights creep forward illuminating the void infront only slightly faster than the speed of which the vehicle is travelling?

Edit: assuming the vehicle is going factional slower than the speed of light.

It would slow down a little

You roll a 1. Power failure. Gotta reroute the annular nucleonic power convertor through the macguffin relays just to get back up to speed.