Quantum Mechanics and General Relativity are compatible, and have a common origin: the expanding (hyper) balloon universe
Authors: Waugh Subhajit 
Published: December 2022

Quantum Mechanics and General Relativity appears to be incompatible
because we are using the wrong model of the universe. Nature
does not use two separate rule-books, but uses two different
viewpoints. To see how the conflicting demands of Quantum Mechanics and
General Relativity can be easily satisfied, we need the true model of
our universe.

Ever since Hubble’s law was discovered, scientists speculated that the
analogy of an expanding balloon best described the shape of our
universe. This view was rejected based on wrong assumptions and replaced
by the presently accepted model of a flat and infinite universe, which
is wrong!

We are confident that we have measured the universe to be (3d) flat
using two different methods. Unfortunately, neither method is capable of
measuring the extrinsic curvature of a 3d hyper-surface:

1)      We cannot measure the curvature of a 3 dimensional (hyper)
surface using summation of angles in a triangle. That works for a 2
dimensional surface curving in the 3rd dimension. But for our case, we
need the sum of solid angles (i.e. we need a tetrahedron, and not a
triangle). The ‘sum of angles of the triangle’ checkup which we had
applied to CMB (Cosmic Microwave Background) spots is bound to show that
our universe is (3d) flat!

2)      We cannot measure the curvature of our universe using the
critical mass-energy density method of General Relativity (General
Relativity can measure intrinsic curvature, but not the extrinsic
curvature).

That proves that the universe may not be 3d flat. But how can we be sure
that it is curved? Here is another piece of clue which finally nails it:
Our universe does have has a Center (although the Center does not lie
anywhere in our 3d space). This can be easily proved:

The Center of Mass equation is a powerful equation. In the vastness of
our cosmos, we can consider each galaxy (or maybe a galaxy cluster) as a
point mass. Even as the number of galaxies tend to infinity, we are
still left with a single point center of mass. Simply invoking infinity
isn’t going to help us escape from the conclusion that there is indeed a
Centre. And it has to lie outside the 3d hyper-surface.
Otherwise, we could have located the true center, and Hubble’s law would
not have the particular form v = HD. Also, the Big Bang
would not have appeared to have happened everywhere. In fact the cosmos
would be an irregular structure composed of an empty central region, the
“crater of the explosion,” an intermediate region containing the
galaxies and an external part containing only radiation. No structure in
the three-dimensional space, born from an explosion occurring 13.8
billion years ago, could resemble the universe we observe today.

The Minkowski SpaceTime equation  ds =
(i.c.dt) + dx +
dy + dz =
(i.c.dt) + dr (which
explains all of special relativity, including time dilation, length
contraction, and relative simultaneity) is not a statement for
4d spacetime continuum (since i cannot be used as an
independent axis). Einstein & Minkowski made that mistake, and assumed
a block universe view in which the past, the present and the future
simultaneously coexist! This view is in stark contrast to our everyday
experience, as well as with an astonishing number of observations in the
whole of science. In fact, an entire book has been written to highlight
this mistake. [The arrow of time: the quest to solve science’s
greatest mystery].

The above equation represents a dynamic 3d hyper-sheet,
moving with a velocity cin the
4dimension in an embedding 4d
hyperspace. This perfectly describes a small section of an expanding
(hyper) balloon. c is the radial expansion velocity of our
universe. Using this concept, and taking the age of our universe to be
13.8 billion years, the calculated Hubble constant value (71.002
km/s/Mpc) matches very well with accepted values (69.8 km/s/Mpc and 74
km/s/Mpc determined by two different methods).

Therefore, relativity is all about being trapped inside the
wall of the expanding (hyper) balloon. But, what is this 3d
hyper-surface made of? It is made of (scalar) fields, and particles,
which are mere resonance/excitation in that field. That is just the core
statement of stunningly accurate Quantum Field Theory (QFT) which forms
the foundation of Standard Model of Particle Physics. Thus, we get a
glimpse of the unity between relativity and Quantum Mechanics.

Copernicus broke with 1300 years of tradition, and revolutionized
science by moving from earth-centric to sun-centric view. But, moving
the viewpoint to the true center of our expanding universe explains the
origin and true nature of time itself!

Clearly there are two viewpoints: the Center of Universe
viewpoint (God’s view/nature’s view) and our viewpoint (i.e. viewpoint
of an unfortunate creature trapped inside the wall of the
hyper-balloon). From our viewpoint, the radius of the universe is an
impossible direction (which forces us to use imaginary number) and hence
it is a temporal dimension. But from the center of universe viewpoint,
the radius is a real dimension, and hence is spatial dimension. Thus
time and space dimension exchange roles. The radial expansion of the
universe appears as passage of time from our viewpoint.

From the center of universe viewpoint, simultaneity is absolute (as
demanded by Sagnac effect), and there is indeed absolute universal time
(as demanded by quantum mechanics) since the time passed since the Big
Bang is just a function of the radius of the universe. From our
viewpoint (located at an awkward position in the universe), locality is
absolute, and velocity c is the upper limit, and remains constant for
every observer. This turns (our) space and time into inseparable twins,
and makes (our) time a relative concept. This solves the time problem
which had so stubbornly resisted the reconciliation of Quantum Mechanics
and General Relativity.

The two viewpoints differ drastically. As explained later, temporal
dimension is that dimension along which any movement can be ignored. For
example, we can easily ignore the tremendous velocity with which we are
traveling along the radius of the universe. In a similar manner,
nature/universe ignores movement along the wall of the balloon whether
we travel to the moon or to the sun or to the Andromeda galaxy, because
the moon, the sun, and Andromeda galaxy are all equidistant from the
true center of the universe. This fact, combined with the fact that the
(entire) closed universe is an absolutely isolated system (Absolute
Island) and has to conserve total momentum etc. gives rise to
non-locality in entangled particles.

Relativity is our viewpoint from an awkward position of the universe,
while Quantum Mechanics is the other viewpoint. Both phenomena are like
two sides of the same coin. Relativity is inside the light cone
phenomena (since nothing can travel faster than light), while Quantum
Mechanics is outside the light cone phenomena (allowing instant
communications in ‘quantum entanglement’ experiments). Both are dictated
just by the scale (i.e. whether we use classical/human scale or
sub-atomic scale) for a very good reason (explained in detail in my
paper).

But why does the transition from Relativity to Quantum Mechanics happens
with decreasing size scale? That’s because, this is what is happens to
spatial and temporal dimensions at different scales:

3+1 (Classical regime) <=> 2+2 (Compton regime)
<=> 1+3 (Planck regime).

General Relativity makes things a bit tricky since it involves
curvature/warping of spacetime, but it does not become incompatible with
Quantum Mechanics. The only difference between the warped spacetime of
General Relativity, and the flat spacetime of Special Relativity is very
similar to the difference between a stretched rubber membrane, with and
without a metal ball placed on it. This stretching also produces the
same time dilation (as predicted by Einstein), but now it is due to the
cos and sine components of the temporal dimension. General Relativity
and Quantum Mechanics are the two pillars of modern Science. Reconciling
the two leads us to ‘Theory of Everything’.

The list of achievements in my above-mentioned paper is simply too long
to be detailed here. The ‘Principle of Least Action (PLA)’ comes closest
to the ‘theory of everything’ in physics, and from PLA, all known laws
of physics can be derived. PLA can be generalized to ‘Principle of
Maximum Proper time’, which is just the Minkowskian version of the
Euclidean statement “The least distance between two points in (hyper)
space is a straight line”.

My paper also explains why dualities like wave-particle duality, or
Lagrangian-Hamiltonian duality arises. Duality is a bedrock concept of
modern physics.

The crucial conservation laws of Physics arise from symmetries of nature
(as per Noether’s theorem). We can directly see from this simple
structure of our universe, why those symmetries (e.g. homogeneity and
isotropy) arises in the first place.

Nature, the ultimate judge, has stamped TOTALLY APPROVED on my
paper.