It is not true that “all the theories speak of the ‘speed of light’ required for time travel.” Certainly, time travel to the future does not require traveling at the speed of light. Traveling at any speed with respect to an observer involves unsynchronized clocks. It’s the basis of Special Relativity.
Traveling to the past, on the other hand, requires a theory that allows for such travel. So far there is no such theory. General Relativity has solutions that seem to indicate time travel to the past. However the number of solutions to General Relativity are infinite. If you fully analyze those solutions they end up describing universes that are not this particular universe. It might be wonderful that in some other universe you can time travel to the past but that’s not much help if you live in this universe.
And frankly, you really don’t want to attempt time travel by moving at the speed of light. That’s a fairly straight forward Special Relativity problem if taken at a very crude form. It involves the Lorentz Factor (Gamma) which tells you the ratio between proper time Tau (your clock) and coordinate time t (the stationary clock you observe as you pass by it).
Gamma = 1/sqrt(v^2/c^2)
v is your velocity relative to the stationary clock
c is the speed of light
This will tell you how fast you observe time passing outside your “light” ship. As you can see, in the denominator sqrt(v^2/c^2) in the limit as v —> c the denominator gets smaller and smaller until just before v=c it gets vanishingly small and the passing of time, from your perspective, outside the ship begins to approach ticking off time infinitely fast. At the instant that v=c time outside the ship will appear to be running infinitely fast. You will no longer experience time. Instead you will instantly be confronted with the end of the universe.
Will this actually happen? No one knows. Special Relativity and General Relativity are classical theories - they do not in their basic forms include quantum mechanical effects. But you don’t have to travel at the speed of light to be instantly vaulted to the end of the universe. It takes a few milliseconds for your brain to register outside events so if you’re traveling so close to the speed of light that it takes a nanosecond to advance to the infinite future you’ll never know.
As to “it will come when numbers and measurements are not used” I’m sorry but that simply isn’t true. It is true that the world doesn’t care about what we say or do because it will follow the laws of physics in any case. But mathematics is the language of physics. Mathematics is used to both unambiguously describe physical systems and theories and to extend our theoretical understanding of physical systems and theories based on the implications of the math of current tested theories. No math = no physics language = no unambiguous description of the theory. Why does math and only math properly describe physics? No one knows. We do know that it is the only way for physicists to properly communicate their theories. As Professor John Baez lists in his Crackpot Science Index, "20 points for every statement along the lines of “I have a wonderful physics theory. I just need a mathematician to figure out and write the equations for me.” To understand physics you have to understand the math underlying physics. You don’t invent a theory and have someone else, who does understand the math, fill in the blanks for you.
The final proof of the pudding is the experiment. No matter how beautiful and elegant your thoughts are, what you’ve let go of or how super your mathematics is; if you run the experiment and it fails the theory is wrong. Be satisfied that you learned something new - this theory is not the answer.