"I have a basket with 3 apples."
"How many apples are there left in the basket,
after John eats 5 apples?"
Mathematician: "I know that one: it's minus 2!"
Farmer: "Are you kidding me?"
While the answer seems mathematical correct, there is a clear problem in the real world.
And this is something that is often overlooked by mathematicians and mathematical physics.
In this case it may simply be that John picked his apples from a apple-tree,
while he was filling the basket with apples. The basket may end up with more
apples then before. But we don't know.
The answer is simply: "there is more going on than we can see".
There are many formulas in physics that use similar "impossible" constructions, but
in a different context: complex numbers. Complex numbers do not exist in the real world,
but are necessary to compute some problems in mathematics.
For example Schrödinger's equation is has a imaginary component:
What does it mean? Why is it there?
It is partially there, because Schrödinger brings together the wave and particle duality together in one
formula.
But: he does not solve the duality. He just puts it together in one formula.
It is simply telling: "there is more going on than we can see".
Another imaginary component is much older:
This is the Maxwell Faraday equation. It does not contain any complex numbers,
BUT to derive this equation we need complex function theory, which works with complex numbers.
So: "there is more going on than we can see". (even if it is about light)
From these maxwell equations we can derive the speed of light:
And from special relativity we learn that no particles can go faster than the speed of light.
Doesn't that mean that all particles and their forces are essentially made from light,
and related to electric and magnetic forces?
What are these complex number telling? That could be anything. But the most simple
solution would be to assume that these formulas describe interactions with another dimension.
After all: complex numbers adds "imaginary" dimensions to a normal number.
We can see this in the many worlds interpretation of quantum-physics.
Many scientists accept this interpretation to deny the existence of other dimensions. But the interpretation
simply adds a infinite amount of dimensions instead..
And singularities are the same thing. While we don't see singularities in real life, they pop up in many
cosmological formulas describing black holes and big bang. These singularities are never solved, but
are used by the mainstream science to assume all kinds of theoretical constructs.
This makes me feel like the farmer: Are you kidding me? There must be more going on than
we can describe in formulas or confirm with real observations.
My conclusion:
Many formulas that accurately describe some phenomena in physics are containing mathematical tricks
that hide something essential behind these phenomena.