SpaceTime is not a 4 dimensional continuum; mathematics is telling something else!
(INDORE, Madhya Pradesh, India-Jan. 16, 2023.) Einstein and Minkowski combined the three dimensions of space and one dimension of time into a single four-dimensional manifold called SpaceTime. This leads to a block universe view in which there is no distinction between the past, the present and the future, and all three of them 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]. This view has been challenged in a landmark paper published online by Mr. Subhajit Waugh from RRCAT, Department of Atomic Energy, Government of India. A brief summary of the research geared towards non-specialist audiences, can be found here. The original preprint paper is titled Quantum Mechanics and General Relativity are fully compatible, and have a common origin: the expanding (hyper) balloon universe. [Link1] [Link2]
The Minkowski SpaceTime Equation (MSTE) ds2=(ic dt) 2+dx2+dy2+dz2= (ic 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. That mistake occurred due to our incomplete knowledge about the true nature of imaginary numbers. An imaginary sign lies hidden within the MSTE, which distinguishes spatial dimensions from time dimension and turns the metric (+,+,+,-) instead of (+,+,+,+). Einstein’s mistake was to treat time and space exactly equally (which certainly is not the case). Unlike real numbers, imaginary number (i) cannot be used as an independent axis (this is explained in detail in the paper whose link is provided below). An independent axis means an additional dimension. Imaginary number is required only for inaccessible dimension, and does not create an additional dimension. Imaginary number is required only by a trapped creature.
MSTE is confirmed to be true in countless experiments, but is actually a mathematical statement for a (dynamic) 3D hypersheet, moving with a velocity c in the 4th dimension in an embedding 4D hyperspace. Thus MSTE perfectly describes a small section of an expanding (hyper) balloon universe, where c is the radial increment velocity of our universe. Using this balloon model, 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 separate methods). Since the crucial SpaceTime equation and Hubble’s law are both telling the same story, it should give us great confidence that we are on the right track to claim that our universe is an expanding (hyper) balloon. Since our universe is expanding at a constant rate rather than accelerating (as currently believed), we do not need dark energy, since we do not have to account for acceleration.
An immediate consequence of making the above correction (4D spacetime continuum versus dynamic 3D hypersheet) is that one dimension got freed up (which we were reserving unnecessarily). That is because if we ignore the motion of the hypersheet, then, what Einstein had assumed as a 4D structure, turns out to be a 3D one (inside a 4D embedding hyperspace). Kaluza’s miracle of obtaining Maxwell’s equation in addition to Einstein’s field equations seemed to demand a heavy price: a 5th dimension was required as an embedding space [Link1]. Actually, 4 dimensions are sufficient, and we get electromagnetic phenomena as a bonus! In fact, the implications of freeing up a dimension is much more profound, and solves the requirement of a fifth dimension popping up everywhere in physics, but stringent limit on the number of dimensions set at four from experiments and observations simply won’t allow that.
MSTE shows that relativity is all about being trapped inside the wall of the expanding (hyper) balloon, but being free to move along the wall. The question is “What is this 3D hypersurface wall of the balloon universe made of?”
It is made of (scalar) fields, and particles, which are mere resonances/excitations 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. Since every star and planets and even ourselves are ultimately made up of particles (which are mere excitations/resonances in the 3d fields), therefore, every bit of matter is eternally trapped in this 3D hypersheet, and is getting dragged with it as the (hyper) balloon universe expands. The radius of the universe is an impossible direction for us (which does not even exist for trapped creatures like us). The radial increase of the universe appears as passage of time for us.
GRAVITY AND DARK MATTER: The rubber membrane/sheet model is used to teach General Relativity in schools and colleges. Rather than taking it as an analogy, we should take it rather literally. The wall of the balloon universe behave just like a rubber membrane. The difference is that it is a 3D hypersheet rather than a 2D sheet. Massive objects like stars and planets are embedded like thin coins inside this wall itself (when viewed from the 4th dimension), and produces stretching of this wall along the 4th dimension. This stretching is seen by trapped creatures like us as warping of 4D SpaceTime fabric itself, and gives rise to gravity as General Relativity (GR) insist. This stretching also produces the same gravitational time dilation (as predicted by Einstein). But now it is due to the reduction of the net temporal motion (i.e. motion along the radius of the universe) due to the inclusion of sin(θ) or cos(θ) depending on definition of θ, whose value depends on the slope of the 3D membrane at that point.
General Relativity remains our best theory of gravity. However the greatest cosmological challenges today like dark matter, black hole singularity (leading to ‘information loss’ paradox) etc. are mere relics of our misunderstanding of General Relativity. Since the 3D hypersheet is a single continuous sheet, and since all massive objects nearby stretch this sheet in a single direction, therefore the collective stretching gets enormously amplified. The resultant huge stretching bends light rays enormously (through gravitational lensing) and gives false impression of enormous amounts of Dark Matter halo. This magically solves all dark matter related issues. Black hole singularity is just the insider viewpoint of a trapped creature. Right at the center of the naked singularity, time passes at the same rate as in deep space, far away from any gravitational sources.
IMAGE: The colored image on the RHS is the inverted image of the colored image on LHS. Just compare the inverted image with figure (d) to see how Dark Matter Halo arises. Note: Figures (a), (b), (c), (d) are cross sections of rubber membranes (RM) with balls placed on it. Massive objects are shown as balls for easy visualization, but are actually embedded like coins inside the RM.
About Mr. Subhajit Waugh
Mr. Subhajit Waugh is a Scientific Officer at RRCAT, Department of Atomic Energy, Government of India. He obtained his Master’s degree in Physics from the National Institute of Technology, Rourkela, in 2003, where he was the topper of his batch. In 1996, he was awarded the prestigious NCERT National Talent Scholarship. He appeals his viewers to watch and share his favorite (non-scientific) video.