## Journal Journal: Tea, Earl Grey, Hot. 5

I got myself involved in a discussion on Fark over replicators and ended up trying to consider them from a practical point of view. I did the math on trying to make matter from energy and managed to convince myself that the idea is just insane. It was the first time I had ever done it and I thought it was interesting enough that I would come back here and share.

Ok, so to start with take the equation from Special Relativity which we all know and love:

E=mc^2

Now, for the moment, I am going to assume that Captain Picard's cup of tea is really big. It's a 1 kilogram cup of tea. We can chop this down later, but this makes the math easier. Also, it doesn't matter all that much.

Next, we will use 300,000,000 m/s as the value for the speed of light. I know this technically wrong, but it's close enough and makes the math less messy. Again, feel free to go back and do this with 299,792,458 m/s you'll find that it's close enough.

So:

E=mc^2

E=1 Kg * (300,000,000 m/s)^2

E=1 Kg * 90,000,000,000,000,000 m^2/s^2

E= 90,000,000,000,000,000 Kg*m^2 / s^s

Ok, the reason I choose kilograms, meters and seconds for the units is that 1 Kg*m^2/s^ = 1 Joule, a well known unit of energy. So:

E=90,000,000,000,000,000 J

Now, this is a big number, but what does it mean? We can jump over to Wikipedia (yes, I know, wikipedia bad.) and get the energy equivalent of TNT, a unit which people seem to deal with better. Well, the energy equivalent of 1 Megaton of TNT is 4.184 * 10^15 J. So, stick this in our formula:

E=90,000,000,000,000,000 J / 4,184,000,000,000,000 J/Mt

E=~21.5Mt

This means that, for every kilogram you need to replicate, you need the energy equivalent to a large thermonuclear bomb. For comparison sake, the largest device ever detonated was the Tsar Bomba at 50Mt. So, if the Captain goes off his rocker and decides to get a whole pot of tea at once, the engine room is going to need to generate more energy than the largest nuclear device we have detonated to date. And not turn into a huge fireball in space in the process.

Now, this doesn't mean that it's impossible; but, trying to generate and contain that amount of energy, and do it in a reasonable time scale, just seems a bit ridiculous. The better part is trying to create safe failure modes. Let's go with the Star Trek idea of anti-matter. So, you dump half a kilogram of anti-protons in one side of your reactor and half a kilogram of protons in the other. And, because this reactor was built by the lowest bidder, with substandard welding, and poor maintenance, the reaction vessel fails. So, how do you plan a failure mode for a 21Mt explosion in a cracked reaction vessel? Again, not an impossible problem, but this seems like an awful lot of work for a cup of tea.

Ok, so to start with take the equation from Special Relativity which we all know and love:

E=mc^2

Now, for the moment, I am going to assume that Captain Picard's cup of tea is really big. It's a 1 kilogram cup of tea. We can chop this down later, but this makes the math easier. Also, it doesn't matter all that much.

Next, we will use 300,000,000 m/s as the value for the speed of light. I know this technically wrong, but it's close enough and makes the math less messy. Again, feel free to go back and do this with 299,792,458 m/s you'll find that it's close enough.

So:

E=mc^2

E=1 Kg * (300,000,000 m/s)^2

E=1 Kg * 90,000,000,000,000,000 m^2/s^2

E= 90,000,000,000,000,000 Kg*m^2 / s^s

Ok, the reason I choose kilograms, meters and seconds for the units is that 1 Kg*m^2/s^ = 1 Joule, a well known unit of energy. So:

E=90,000,000,000,000,000 J

Now, this is a big number, but what does it mean? We can jump over to Wikipedia (yes, I know, wikipedia bad.) and get the energy equivalent of TNT, a unit which people seem to deal with better. Well, the energy equivalent of 1 Megaton of TNT is 4.184 * 10^15 J. So, stick this in our formula:

E=90,000,000,000,000,000 J / 4,184,000,000,000,000 J/Mt

E=~21.5Mt

This means that, for every kilogram you need to replicate, you need the energy equivalent to a large thermonuclear bomb. For comparison sake, the largest device ever detonated was the Tsar Bomba at 50Mt. So, if the Captain goes off his rocker and decides to get a whole pot of tea at once, the engine room is going to need to generate more energy than the largest nuclear device we have detonated to date. And not turn into a huge fireball in space in the process.

Now, this doesn't mean that it's impossible; but, trying to generate and contain that amount of energy, and do it in a reasonable time scale, just seems a bit ridiculous. The better part is trying to create safe failure modes. Let's go with the Star Trek idea of anti-matter. So, you dump half a kilogram of anti-protons in one side of your reactor and half a kilogram of protons in the other. And, because this reactor was built by the lowest bidder, with substandard welding, and poor maintenance, the reaction vessel fails. So, how do you plan a failure mode for a 21Mt explosion in a cracked reaction vessel? Again, not an impossible problem, but this seems like an awful lot of work for a cup of tea.