Hi,
I was thinking about time being the 4th spatial dimension, thanks to a book I'm reading these days.
Nothing special, till I tried to imagine this in the smallest possible scale.
So, I drawn the classic space/time graph and marked two points on each axes:
y and y+Planck lengh on the space axis
x and x+Planck time on the time axis
Now, looking at how the smallest 4 dimensional particle could be rapresentend in this graph, I figured out that it should have these attributes:
lenght, width and height equal to the Planck lenght
lenght in the 4th dimension ( or "duration" ) equal to the Planck time
But, being time just another spatial dimension, i thought this: what if somehow the Planck time is equal to the Planck lenght?
In other words, if the smallest 3D particle is like a cube, the smallest 4D particle should be an hypercube. And if the cube has equal lenght, width and height, an hypercube should have equal lenght, width, height and duration. Or not?
Furthermore, I wrote an equaltion about this.
Here it is.
Be clement, I'm really not good at math, and if this equation is completely wrong just ignore it.
If it cointains some errors that if corrected could lead to something new for all of us, then feel free to do so.
Beside all this, I feel somehow that a turtle runs as fast as a rabbit after all. The only thing that changes is that the rabbit is running more through space than through time. I feel also that for this reason, in someway, the speed of light is not only the max speed possible, but also the minimum. But I'm a bit confused about this. I hope you can help me to clarify.
So, what you guys think about all this reasoning? Is it valid? Is it meaningless?
I hope I have not waster your time ( space )
As you'll probably notice, my english is not so good. Sorry for that.