Question: If, theoretically, we could travel at the speed of light. What what would be able to see?

Cesar Lopez-Monsalvo answered on 17 Jun 2011:

This is the kind of questions that motivated relativity. In fact, this is the exact same question asked by Einstein himself!
The answer to this lies in one of the key principles of relativity; “the invariance of the speed of light”.

Towards the end of the 19Th century, people believed that there was a “kind of” fluid filling up the entire universe. On this fluid, light would propagate as a wave – the same as sound does in the air. Very complicated experiments were trying to measure the speed of the earth with respect to this “aether”. The most famous one was carried out by Michelson and Morley. They made an apparatus which is called an interferometer. It is basically an L-shaped tool in which you fire a beam of light on the wedge, where the beam is split in two. Each beam will travel through each arm, and at the end of each arm there is a mirror which bounces the beam back. Then you observe what happens when the beam recombines. If the two arms of the L are of the EXACT same length, then the beam should recombine “cleanly”, without any interference. If there is a difference in the length of the arms, then the recombination won’t be perfect and you would see an interference pattern. You can see the set up here .

Ok, what is this for? Well, they thought that if the earth was moving with respect to this “aether” then they will be able to see some interference in their apparatus (because light would need to catch up with the mirror which is moving in the same direction of the earth with respect to this “aether”). They tried every possible orientation and could not find anything, as if it didn’t matter in which direction, or how fast, you are moving. This was very puzzling! This basically tells you two things: 1. that the aether does not exist, and 2. that if you are in a spacecraft and hold a mirror in front of you, no matter how fast you go, the speed of light with respect to you will ALWAYS be the same as for anybody else. Even if you are moving away from a source – a star, say – at 99.999999% of the speed of light, you would measure the same speed of light as if you were just standing still at a fixed position with respect to the star! Einstein used this principle to construct the first version of relativity, which is called SPECIAL RELATIVITY.

Here comes the answer to your question. In relativity, the “structure” of spacetime (see here http://ias.im/47.305) is given by “light rays”. So, same as in my answer to the black hole question (http://ias.im/47.747), consider two observers – you and a friend, say. Since you are the one who wants to travel at the speed of light, your friend will just have to sit and wait for you. You both have a clock with you and synchronize them before you depart. So you verify everything is set, say good by and jump into a light beam. You will disappear from sight almost instantly from your friend’s point of view and basically never come back. What happens with you? You will never noticed that you just jumped in the beam. The reason for that is that clocks on light beams never tick! There is no “proper time” for light (see here http://ias.im/47.1204 to know what proper time is). This means that, from the point of view of a “photon” (a light particle) which was emitted a million years ago, not a single second has passed in its own frame….nothing at all.

One can show that reaching the speed of light for a massive object is impossible. However, even if you actually could, you would not be able no even notice anything. Time will simply “freeze” from your point of view, your clock will never tick! This issue has profound philosophical implications about “destiny” and “free-will”…but I will stop here.