Just how much power does it take to form a Reality Marble?

reality marble
inside of a reality marble

            While at the Colorado Anime Fest, I was asked to look into the science behind some of the powers in the Fate Series.  At first, I wasn’t really sure what I could do with it, because it is a magical series with crazy powers and not very many good reference scenes to measure what is happening.  Plus, there is the fact that I haven’t watched much of the Fate series beyond the original anime series from the early 2000’s and the much more recent Fate/Apocrypha.  That being said I went for a run the other day and got to thinking.

Just what is a Reality Marble?

            In the Fate series a Reality Marble is essentially a pocket universe created by a mage/servant through the use of magic.  The new universe is completely separate and sealed off from the real world as long as it is active.  (I know in Fate series canon it is a bit more complicated, but the basics are sound.)

How big is a Reality Marble?

            There are no hard numbers on just how big a Reality Marble is in any of the Fate series, but there are a few screen shots that will allow me to speculate a bit.  Archers Reality Marble, Unlimited Blade Works is a hill in the center of a field filled with swords, seen bellow.

reality marble

            In this particular image we can see all the way to the horizon.  In the real world when you are standing on a flat plane the horizon is 4.7km away for an individual who has an eye level of 1.70m.  I know that Shirou is technically 1.67m tall, and there is the hill to contend with but we don’t know how high the hill actually is.  As a result, I am going to round the distance up to 5km even to make the math a little easier.  Additionally, it is safe to assume that they were summoned to the middle of Unlimited Blade works, thus it has a diameter of 10km.

What is the shape of a Reality Marble?

            The next big question is the shape of the Reality Marble; is it a sphere, a dome, or something else entirely?  There is no absolute way to be sure; however, there are some clues in Fate/Apocrypha.  Achilles, the famous hero from Greek legend, has a shield (Akhilleus Kosmos) that while not technically a reality marble, is described as being very similar to one.

Fate Apocrypha

            The shield defends against attacks by creating a miniature world.  In Fate/Apocrypha the world appears like a sphere from the outside.

Fate Apocrypha

            I know that it is not a Reality Marble but I think it is close enough to one to safely assume that a Reality Marble would have a spherical shape.

Volume of a Reality Marble

            It we combine the diameter measurement from Unlimited Blade Works and the shape from Akhilleus Kosmos, we can start to get an idea of how big a Reality Marble is.  (FYI- I will be converting km to cm to make the math easier down the road.)

Volume of a sphere

V=4/3πr^3

V=(4/3) x π x (5,000)^3

V= 5.24×10^17cm^3

Mass of a Reality Marble

            Since people can survive inside of a Reality Marble, it is safe to say that it has conditions similar to that of Earth, which means I can use the average density of the Earth to figure out how much mass is in the Reality Marble.

Mass of the Reality Marble = Density of the Earth x Volume of a Reality Marble

Mass = 5.51 g/cm³ x V= 5.24×10^17cm^3

Mass = 2,887,240,000,000,000,000 grams

Or

Mass = 2,887,240,000,000,000 kilograms

Energy needed to create a Reality Marble

           Leaving aside the energy to create a pocket universe, the Reality Marble leaves the real world completely unaffected, which means that all of the mass in the Reality Marble has to come from somewhere.  That somewhere in this case is energy, and the energy needed to create all of the mass can be calculated using Einstein’s Theory of Relativity, or E=mc^2

Energy = Mass x Speed of Light squared

Energy = 2,887,240,000,000,000kg x (299,792,458m/s x 299,792,458m/s)

Energy = 2,887,240,000,000,000kg x 8.99×10^16m^2/s^2

Energy = 2.59×10^32 joules

            For a frame of reference that is just a bit more than the gravitational binding energy of the Earth, or the amount of energy that is holding the planet together.  It also happens to be just a bit less than the amount of energy released by the sun in one year.

Conclusion

            I’m really not surprised by just how ridiculous the numbers were, and I can’t really take it any further as it’s entering theoretical physics, and sparkly magical bullshit territory.  That being said I do have another Science of Fate post I am working on, namely Frankenstein, which is based on some interesting real-world science that I read about recently.