# Fastest speed for the ship?

When John and Jade enter the Yellow Yard, she explains to him that it will take three years to cross the entire distance. She says that it will take them this long because you cannot go faster than the speed of light. According to the famous equation E=MC^2, energy is equal to mass moving at the speed of light squared. Wouldn't this mean that the ship could move at it's fastest just slower than the speed of light squared, which is many times faster than just sub the speed of light?

• `E=MC^2, energy is equal to mass moving at the speed of light squared` - this is not what the equation says. It says that the energy at rest is equal to the rest mass times the speed of light squared. The mass is not moving at the speed of light squared. I don't know where you got that idea from. – bon Mar 5 '16 at 20:18
• Having read the article you linked on the Yellow Yard, I’m not at all sure how much of my answer applies. Is the Yellow Yard three light-years across? Your first link says something about a yard, i.e. 3 feet. The other links make it sound like the yard is three light-years across though, which would mean my answer applies. – Molag Bal Mar 5 '16 at 20:45
• "The speed of light squared" would have units like square meters divided by square seconds, so it doesn't even make sense as a speed, since speed must always have units like meters divided by seconds (or some unit of length divided by some unit of time). – Hypnosifl Mar 5 '16 at 22:57
• To add to the point about why you can't treat "the speed of light squared" as itself a speed, suppose we use units of light-years for distance and years for time--then in those units, the speed of light is 1, and the speed of light squared is also 1. Whereas if you use units of kilometers and seconds, the speed of light is 299792.458, and the speed of light squared is 89875517873.681764. If you wrongly imagine those squared speeds to be speeds themselves, you'd have to conclude that whether or not the speed of light squared is any larger than the speed of light depends what units you use! – Hypnosifl Mar 6 '16 at 0:31

No, the fastest possible speed for a spaceship is just short of the speed of light.

## Real-world physics

E=mc2 is talking about your energy at rest. You need an equation for energy at relativistic speeds:

E = mc2/sqrt(1−v2/c2)

where E is the relativistic total energy, m is mass, c is the speed of light, and v is your speed. As v approaches c, E approaches infinity. If v=0, this equation reduces to E = mc2.

Note that people sometimes like to define mass m to increase as you approach the speed of light, but in the equations above, m is the “rest mass” and does not change with speed.

This is further complicated by the idea of reference frames and time dilation, so that the duration of a voyage at near light speed is different for someone on the ship than it is for someone who didn’t go. However, it appears that the comics don’t take this into account, so we can skip that part. If you want to read about it anyway, here are a couple links:

## In-universe physics

Without reading the entire series, it appears that the in-universe physics is a sort of hybrid of relativity and Newtonian mechanics: the speed of light is an arbitrary maximum speed, and time dilation does not occur. Or perhaps I misunderstood the context in the text that I read.

This all assumes that the Yellow Yard is three light-years across. I couldn’t verify whether that was true.

• The first link in the question says something about the trip taking one nanosecond from one character’s perspective and three years from the other characters’ perspective, but I don’t know how that fits anywhere... – Molag Bal Mar 5 '16 at 20:58
• Good answer, but I just wanted to note that time dilation is only relevant if you state the distance to be traveled in some other reference frame different from the rest frame of the travelers (due to length contraction, the distance will be different in different frames). If the Yellow Yard is about three light years long in the rest frame of John and Jane as they are traveling, then if their speed relative to the Yellow Yard is close to the speed of light, it would indeed take them about three years of subjective time. – Hypnosifl Mar 5 '16 at 23:03
• @Hypnosifl I think I understand what you’re saying now... anyway, I added a link to a physics.SE question in my answer that explains what I was thinking of when I wrote my answer. – Molag Bal Mar 5 '16 at 23:18
• @amaretto Since the Yellow Yard is the space between two fourth walls that is contained within a room in a parallel universe, the character in the aforementioned room just sees them zip by, but to John and Jade it takes a few years. – Cyberson Mar 6 '16 at 21:23
• Because. – OrangeDog Apr 25 '16 at 21:34