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Quantum Mechanics and General Relativity are compatible, and have a common origin: the expanding (hyper) balloon universe
  • Subhajit Waugh
Subhajit Waugh
Dept. of Atomic Energy, Raja Ramanna Centre for Advanced Technology (RRCAT)

Corresponding Author:[email protected]

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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 = H0D. 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  ds2 = (i.c.dt)2 + dx2 + dy2 + dz2 = (i.c.dt)2 + dr2 (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 c in the 4th dimension 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.
Published in SSRN Electronic Journal. 10.2139/ssrn.4158771