In this scene, E = mc2 and you probably recognize that the letter c in that equation refers to a speed; specifically, the speed of light.
Now, you also know that the little number two: 2 means squared, which is the same as saying "times itself"
We can re-write that equation as:
Normally when you think of speed, you think of it in terms of some fraction - that is, "some distance per time" as in: "miles per hour" or "meters per second" or "furlongs per fortnight" - whatever you want, speed is typically expressed as some quantity of distance being covered in some amount of time.
That distance could be in any direction, in three dimensions; it doesn't have to be in only one dimension. Normally you drive straight ahead, but you could go left-and-right, forward-and-backwards, or even up-and-down if you're flying - so speed can be thought of as an amount of space being covered in a given time.
We could say that:
Exactly how much space being covered, and passing time,
the speed of light contains is not imporant -
whatever the
exact numbers are, we don't care for now; we just need
to understand that the letter c refers to
some amount of
Substituting that fraction for c in the equation, we should get:
E = m ·
With a little algebra, we can move one of those fractions to the other side:
This is the relationship between energy E and mass m used for the computations in this scene. Energy and mass are proportional to eachother in this way:
When you have a fraction, it means that one thing is divided up over some other thing - if you have, say $80, and you 'divided it up' among ten people, what that means is, you're 'spreading out' the eighty dollars over the ten people.
If a farm has 30,000 stalks of corn 'per acre' that means the stalks are spread out over the acres.
What we mean by
Saying that something is 'evenly distributed over time' just means that the thing exists.
If an object did not persist for any amount of time, then it wouldn't exist by the standards of what the term 'exist' typically means. That an object has length and width and depth is only applicable if it also has persistence.
Your company leases a storage unit - the unit is rented based on its dimensions, length, width, height, but also by its duration, that is, the time of the lease. If you have a six-month lease on a storage unit, sure your company has access to 8×10×12 feets of space, but after that six months expires, it's no longer applicable to anything your company does.
Similarly, if there weren't any dimension for an object to exist in, then it wouldn't exist. If you only had two dimensions, then 'spheres' would only exist as whatever circle happens to be intersecting the plane of your existence. There needs to be some space for mass to occupy. Your company better rent a storage unit with enough dimensions to hold whatever you need to store.
By saying
On the other side of the equation, we have
In this scene, the universe has had a grid laid out over it, in order for you to visualize it more easily - each section of the grid contains some amount of energy as well as some time.
Scrolling over the scene causes specific locations to begin consuming the universe around them. [Scroll left-to-right over the scene, or drag the slider - click in the slider bar to animate.]
These locations devour the surrounding grid and convert that into an object; an object that occupies the dimensions that were converted from the space around them, and which persists throughout the time which was also pulled through from the grid.
That is to say, when you start scrolling, things start moving from one side of the equation to the other.
Initially, nothing exists on the mass side of the equation. When you start scrolling, objects get formed; those objects need some dimensions to occupy. The dimensions they occupy are the ones sucked through from the space on the other side of the equation. The objects and the dimensions need to persist for some time; the time they exist during is the time from the other side of the equation.
Again, the masses ingest the grid, and turn it into more mass - this consumption causes the grid to warp. Eventually, the distortion forms a very strong and noticable connection between the centers of each object.
The grid does not warp to accomodate the mass; neither does the presence of the mass cause space to warp.
The masses are the wrapping of space up into a ball. Energy and time-space are sucked through to the opposite side of the equation, and that forms an object.
The 'attraction' the objects have towards eachother's center is the distortion that occurs as the objects swallow the surrounding grid-space.
If space-time is a 'fabric', imagine that
fabric laid out on a table. Then, pinch
the fabric somewhere in the middle and start
crumpling it up into a ball in your hand.
Eventually, the fabric will be distorted and
wrinkled up, and there will appear to be a ball
in the middle of it. There isn't a ball,
or an object, or a mass, or anything - it's just
the fabric being crunched up. The fabric isn't
distorting because of some object that's inside
it - the object IS the distortion of the fabric.
Now imagine that someonelse also starts
pinching the fabric in a different place.
[This is a big piece of fabric - imagine it's
a large bed sheet, and it's spread out on
a hard wooden floor.]
You both pinch the sheet at a different place
somewhere in the
middle and start crumpling it up into a ball.
After a little while, your hands are
going to start getting closer to eachother.
That is, since you're both pulling the sheet
into your hands, the part of the sheet that's
between your two hands is getting pulled into
both of your hands at once; unless you tear
the sheet [don't tear the sheet! you'll get
in trouble], your hands will start getting
closer to eachother until the two wads of
fabric you're both crunching up touch one another,
and become a single big ball.
If we're both eating the same string of spaghetti,
from opposite sides, either the spaghetti is going
to snap, or we're going to kiss.
Again, there is no force pulling the two things
together - the 'pulling force' is the wadding
up of the sheet into a ball. It's the
drawing up of the sheet into your hand
that appears to draw the two things together.
And there aren't 'things' - there just
appear to be things because the sheet is
crunched up in different places.
[Note that this animation does not show the
part where the masses start getting closer
to eachother - though it could, ofcourse, do
that from the same calculation; it's simply
intended to emphasize, for now, the
grid-becoming-mass portion of what's happening.
You should also be able to see that the masses
are 'attracted' in many directions
at once - along every different line in the
grid, in fact - it's just that a preponderance
of grid-lines has been concentrated between
the 'centers of mass' of each object.]
Make a box ...
It's a box; it's got all the parts, length, width, height - it even exists for some period of time. It contains all of the dimensions that a box usually has.
Now, conceptually, collapse the box, in one direction; squoosh it down into a square ...
Now do that same thing with another box; a different box that has been divided up using a grid ...
At this point, we have two different planes of existence. We have two squares, or planes, that are representative of fully-dimensional realms.
Take the two planes, and intersect them...
There are two separate realms of existence. One of them is the 'mass realm', the
Initially, the mass-realm is completely empty; there is nothing in it - no length or width or height or mass. At first, the mass-realm doesn't even exist because it doesn't even have the time it would need in order to exist.
In the beginning of the scene, the energy-realm exists. It has a grid laid out over it; time and energy are spread throughout the space. That particular realm is teaming with energy and time, and all of that is contained in dimensions. Here, we've visualized that as a grided-plane.
As the grid gets ingested, things begin to 'transfer' into the mass-realm. Things from the Energy side of the equation begin projecting into the mass-realm...
This happens with every mass in the scene.
It would either be confusing or impractical to attempt to show two different three-dimensional realities intersecting eachother at right angles, which is why they were reduced to planes for this example.
Again, the masses are not masses - they are conceptual locations, indicated by coordinates, that consume the grid in all directions, then spit it back out into the mass-realm. It's more like the grid-lines are threads that get pulled in through a pin hole, and make little thread-loops.
With the grid-lines turned off, it's also easier to see that the loops change shape through the progression. When viewed initially, it seems like the masses have a 'pattern' on them, and that they simply grow larger. Infact, your view is not 'zooming in' on the mass objects at all; more and more lines are getting drawn inside the mass-area each time, producing more and more of the apparent field-loop pattern.
[You can double-click the scene, or click here to toggle a menu that allows for adjusting what gets displayed. If you want to, you can also animate the line, which might also help.]
A mask has been placed over each area where the mass-lines appear in order to cover the lines from the grid and make the view less cluttered. Unmasking the masses will allow you to see that all the grid-lines are still being drawn on the grid-plane.
In this configuration, the mass-lines give the impression that each mass has a pattern drawn on it, and that progressing through the animation enlarges your view of that pattern.
If we recalculate the scene with only one mass, and increase the universal constant, it will be more obvious that the number of lines within the mass-area increases as more grid-lines get sucked in, and that the lines increase in size, as opposed to being simply a pattern that gets magnified.
You can recalculate with some new randomly placed mass locations aswell, if you don't mind sitting through the recalculation.
Remember back when we said that we were not going to be concerned at the time with exactly what values were contained in the E = mc2 equation? Well, now we've finally reached the point where we actually still don't care!
The calculation in the scene werks not by knowing how far light moves in a second but by using the speed of mass. And it's not even that; it's not even the speed of mass - it's the relative rate of the speed of mass compared to the speed of light.
For this equation, it doesn't matter what the speed of light is, it only matters what percent of the speed of light the speed of mass is. Maybe mass only expands at ten percent the speed of light, or maybe only one percent - or maybe a much, much smaller percent; it doesn't matter what the actual value is, just the relative percent.
This 'universal constant' of the speed of mass can be adjusted - which was done, for instance, to allow you to more clearly see the expansion of mass in the scene.
Mass-locations begin consuming the grid at the
rate of the 'inverse square'. The supposed masses
are simply coordinate designations; the grid-points
are also nothing more than coordinates.
That is to say, there is no 'm1'
or 'm2' or any mass involved in the
computation - there is no 'big G' or gravitational
constant. The coordinate locations of the masses
begin eating up the grid at the rate of
The grid does not warp to accomodate the mass. The masses do not distort the grid with their presence. The objects are not drawn towards eachother. There is no gravity. There are no objects.
~queviva