What would happen if you were traveling in a spaceship at just under speed of light and you turned your headlights on?

Answer 1

Simple. You would see a ray of light moving away from you at a speed that would equal the speed of light minus your speed.

Not simple. If you know anything about anything, you know that someone asking this question does so because of an apparent paradox: Modern theory asserts that the speed of light is a constant - that is, the laws of physics say that nothing may travel faster than the speed of light. This raises the issue of if you were in a vehicle travelling near the speed of light, how could photons from the headlights proceed ahead of you at the speed of light? This would apparently violate the speed of light as a constant, if you think of yourself as an outside observer of the spaceship, and add the spaceship's velocity to the constant (c).

You would also know, despite many others on this website who eagerly point out that physics do not allow a spaceship to be accelerated to the speed of light, that this is a thought experiment which is useful for imagining the nature of our universe regardless of some condition which may be unattainable (in fact, a thought experiment usually includes such a condition precisely because it is unattainable and thus can only be thought out in the mind and not actually carried out in the real world).

That said, here's some answers:

This apparent paradox is invalidated by a frequently omitted piece of information regarding c, the constant speed of light - c is a constant for all observers in all frames of reference (in a vacuum). This means that regardless of whatever speed you travel, the speed of light is always the same from your viewpoint. Thus, if you were in a spaceship travelling close to the speed of light, c would still be the same for you and you would observe the light from your headlights extend outwards in front of the ship as would be expected in any other situation.

It's tough to imagine, but you have to picture things in a much different ways because we are dealing with astronomical (literally) values in terms of velocity and space. Think about what actually constitutes speed. The speed of an object under normal circumstances is the distance it travels divided by the time it took to travel that distance. If a car drives 1km away from you in one minute its speed is 1km/minute. However, if a spaceship leaves earth, it must be travelling at escape velocity (the minimum speed to escape earth's gravity) - but wait! The earth is hurling through space around the sun at a high velocity, and the sun itself is orbiting our galaxy at yet another high velocity, and the galaxy is moving as well. Further, we might consider what speed it is travelling compared with some galaxy on the other side of the universe, when the actual amount of space in the universe is itself expanding (so to speak).

So what speed is the spaceship actually travelling at? It depends on your frame of reference. It's easy to picture the ship's velocity in terms of how fast it is moving away fromyou, but it is much more difficult to picture its velocity in reference with other planets or stars, which are themselves moving.

In fact, everything in the universe is moving - that is, you could not plot a coordinate system across the universe and expect anything to remain stationary with reference to any point in your system. Thus, there is no such thing as an absolute velocity, since the velocity of some object you are observing always depends on where you are and how fast you are moving - that is, there is no absolute velocity except for c, the constant speed of light in a vacuum.

To explore further, you may want to consider what might happen if you were watching a spaceship turn on its headlights while travelling towards you at the speed of light!

Interesting topics which are related:

-Einstein described space and time as one

-Time dilation says that objects which are moving faster than you are experience less time passing than you are, meaning that if I was born at the same time as you, and I left earth in a spaceship travelling at a high velocity, I would return to earth somewhat younger than you are. Less time has passed for me than it has for you. Why?

-Use of proper distance

-The expansion of the Universe and the Hubble constant

-Cosmic background radiation (we can actually observe the beginning of the universe - the big bang - in present day!)