It is my honour to answer your post. I deeply respect anyone who is on a sincere search for truth. That's what science should always be about.
I'll start by telling you a couple of things about how my mind works. First, I've had a powerful conviction that we live in a unified field or unification ever since I was a teenager. It's such a strong feeling that I take it for granted that the universe is physically unified, and I find it hard to imagine it being in any other state (despite my senses constantly telling me that everything is separate). Second, I've also had a deep mistrust of present-day mathematics since my teenage years. I'm still not sure of the reason for this. Maybe this is the reason - how can a theory of unification be achieved by clinging to the old fashioned idea that this thing is separate from that thing and 1 1 = 2 separate things? This is how maths began thousands of years ago when our ancestors had no concept of anything existing beyond the things we can only see as separate.
There is no need for differentiation between similars. There is no "inner" and "outer" but only one (representing unification) and zero. Together with one, zero comprises the binary digits of base-2 mathematics (which seems to be the producer of space and time). Like a one-dimensional line drawn on two-dimensional paper, the "drawing" of space-time occurs in an extra dimension called hyperspace. The perception of extra dimensions only exists in the reality humans and their instruments detect. Nothing can be truly separate when we consider the universe as a unification caused by 1's and 0's, but our physical senses and scientific instruments don't detect binary digits and our senses/instruments thus reinforce the illusion of separateness. Even the 1's and 0's are united by the quantum entanglement existing throughout all space and time (in time, we call the entanglement "retrocausality"). On Earth in 2013, union of 1's and 0's is represented by the qubits in quantum computers. What happens when we view the universe as a unification created by ones and zeros, or qubits? There is no separation between space, time, and hyperspace - and extra dimensions are indeed a fantasy.
When I say "infinity equals the total elimination of distance", you must remember to differentiate between physical infinity (the universe going on and on forever) and what I call electronic infinity (explained below).
"The inverse-square law states that the force between two particles becomes infinite if the distance of separation between them goes to zero. Remembering that gravitation (associated with particles) partly depends on the distance between their centres, the distance of separation only goes to zero when those centres occupy the same space-time coordinates (not merely when the particles' or objects' sides are touching i.e. infinity equals the total elimination of distance). The infinite cosmos could possess this absence of distance in space and time, via the electronic mechanism of binary digits. To distinguish this definition from "the universe going on and on forever", we can call it "electronic infinity or e ".
Of course, the difference between "physical" and "electronic" infinity doesn't exist in reality, but we can speak of the difference because we live in the human world where the ones and zeros producing unification can't be seen. Failing to distinguish between the infinities causes confusion and could lead to us saying "infinity equals the total elimination of distance is logically not consistent".
It's impossible to point to the 4th dimension of time, so this cannot be physical. Since the union of space-time is well established in modern science, we can assume the 4th dimension is actually measurement of the motions of the particles occurring in the 3 dimensions of length, width, and height. The basic standard of time in the universe is the measurement of the motions of photons - specifically, of the speed of light. This is comparable to the 1960's adoption on Earth of the measurement of time as the vibration rate of cesium atoms. At lightspeed, time = 0 (it is stopped). Below 300,000 km/sec, acceleration or gravitation causes time dilation (slowing of time as the speed of light is approached). If time's 0, space is also 0 because space and time coexist as space-time whose warping (gravity) is necessarily 0 too. Spacetime/gravity form matter/mass (see next paragraph), so the latter pair can't exist at lightspeed and photons are massless. I think time dilation is real because it fits in perfectly with the revised gravitational theory I put together in my article. It's just a composite of Newton's and Einstein's ideas that explains - in nonmathematical, layman's language - gravity as a push by gravitational waves that explains dark energy, dark matter, Kepler's laws of planetary motion, tides, orbits, and apples falling on a 17th-century scientist's head. It supports Einstein's idea of gravitational-electromagnetic interaction forming mass, saying gravity is weaker at higher altitudes because it is concentrated in more and more wave packets at lower heights and below a planet's surface - where it corresponds to higher density, magnification of gravity's effects, and slowing down of time because motion of the particles is less in greater densities (particle motion increases at lower density, allowing the universe's highest speed in the vacuum of space).
Suppose Albert Einstein was correct when he said gravitation plays a role in the constitution of elementary particles (in "Do Gravitational Fields Play An Essential Part In The Structure of the Elementary Particles?" - a 1919 submission to the Prussian Academy of Sciences). And suppose he was also correct when he said gravitation is the warping of space-time. Then it is logical that 1) gravitation would play a role in constitution of elementary particles and also in the operation of the nuclear forces, and 2) the warping of space-time that produces gravity means space-time itself plays a role in the constitution of elementary particles and the nuclear forces. I think mass increase is shown to be real by ultra-high-energy cosmic rays. Mass increase at increasing accelerations is inevitable because the object is encountering more spacetime and gravity (the producers of mass; which also confer mass's equivalent [energy] on cosmic rays that travel far enough through space, turning them into ultra-high-energy cosmic rays). But mass increase cannot become infinitely large since space-time, gravity and mass don't exist at lightspeed. The object is converted into energy which means mass and energy must be equivalent and Energy must equal Mass related to the Speed of Light (E=mc^2, in the words of Albert Einstein). You point out that "As per the equation, any particle traveling at the velocity of light would acquire infinite mass." This paragraph says mass does increase up to the speed of light - but mass is totally converted to energy at Lightspeed instead of becoming infinite. So E=mc^2 appears to only be partly correct because the highest speed possible is Lightspeed. Physically speaking, it cannot be multiplied. Einstein himself proved this. The equation E=mc^2 can be considered a degenerate form of the mass-energy-momentum relation for vanishing momentum. Einstein was very well aware of this, and in later papers repetitively stressed that his mass-energy equation is strictly limited to observers co-moving with the object under study. The version of the equation applicable here is E=m/c^2*c^2. In the case of a proton travelling at Lightspeed, the equation means the energy the proton is changed into equals its mass of 938.27231 MeV/c^2 multiplied by c^2.
Length contraction (or Lorentz-FitzGerald contraction) - like time dilation, described by a pair of equations known as the Lorentz transformations (named after the Dutch physicist Hendrik Lorentz, 1853-1928) - says a vehicle reaching 90% of lightspeed will, to a non-comoving (stationary) observer, appear to be less then half as long as its rest length ("The Cosmos", a book in the series "Voyage Through The Universe" - Time-Life Books, pp. 42, 44). This is how Albert Einstein described the reality of length contraction in 1911 -
The question as to whether the Lorentz contraction really exists or not is misleading. It doesn't "really" exist, in so far as it doesn't exist for a comoving observer; though it "really" exists, i.e. in such a way that it could be demonstrated in principle by physical means by a non-comoving observer. ( "Zum Ehrenfestschen Paradoxon. Eine Bemerkung zu V. Variĉaks Aufsatz". Physikalische Zeitschrift 12: 509-510)
We are compelled to use terms like co-moving and non-comoving because we live in the human world where the ones and zeros producing unification can't be seen. What would happen to length contraction, mass increase and time dilation if we could perceive the ones and zeros? All 3 Relativistic effects might disappear, to be replaced by an endless number of ones and zeros at rest (an infinite universe where time is "at rest" i.e. every second that ever existed, or will exist, resembles a frame in a movie film). This "rest" could also be viewed as confirmation of Hidden Variables - an interpretation of quantum mechanics which is based on belief that the theory is incomplete (Albert Einstein is the most famous proponent of hidden variables) and it says there is an underlying reality with additional information of the quantum world. Their identification would lead to problems having exact, instead of merely probabilistic, outcomes - and could also restore a reality that exists independently of observation ("Quantum" by Manjit Kumar - Icon Books 2008, p.379) Exact outcomes that are independent of observation could eliminate variables such as co-moving and non-comoving. I suggest this underlying reality is the binary digits generated in 5D hyperspace.
I hope my answers give you things to think about. Best wishes to you.