# [ExI] Dark mass = FTL baryons?

Stuart LaForge avant at sollegro.com
Wed Aug 16 11:25:32 UTC 2017

```My exchanges with John Clark in the last month, caused me to ask an
interesting question: What fraction of reality, by 4-D volume, lies inside
of our past lightcone? I modelled reality as a 4-D hypersphere or 4-sphere
in Planck units given by

S4. t^2+x^2+y^2+z^2 <= R^2

where t is time and R is the radius of the 4-sphere. Then I modelled the
light-cone as the bottom half of t^2-x^2-y^2-z^2 = 0 which reduces to

PLC4. t <= -sqrt(x^2+y^2+z^2)

So I was looking for 4-volume of the intersection of PLC4 & S4 divided by
the 4-volume of S4.

The 4-volume of a 4D cone with an apex angle of (pi/4) is and the radius
of its 3D spherical base is

Vc = pi*r^4/3

Where the radius of its 3D spherical base is r

The 4-volume of a 4-sphere is

Vs = pi^2*R^4/2 where R is the full radius of the 4-sphere.

R is related to r by

R = sqrt(2)*r

Substituting in R in Vs and dividing Vc by Vs and simplifying yields the
fraction of spacettime contained within the past lightcone as:

Fp = 1/(6*pi) or approximately 5.3%

What I find so surprising is that this is very close to our latest
estimates of the mass fraction of visible matter in the universe as
compared to the total mass of visible matter, dark matter, and dark
energy. The latest figures are given here:

https://arstechnica.com/science/2013/03/first-planck-results-the-universe-is-still-weird-and-interesting/

So our latest measurements have the fraction of visible matter at 4.9% and
I have shown that special relativity predicts that you should only be able
to see and be causally affected by 5.3% of the universe. Since the density
of the universe at the largest scales is pretty uniform, I would expect
that the percent 4-volume should approximate percent mass.

So that would mean that dark matter and dark energy are spacelike or
future timelike particles existing outside our past lightcone and
therefore unable to be directly detected although they should still be
able to bend spacetime with their mass.

Perhaps this "dark mass" is simply baryons moving in FTL inertial frames
that are protected from detection by event horizons and cosmic censorship?

Thoughts anyone?

Stuart LaForge

```