King Solomon said:
Perhaps an interesting would be: Suppose the mass of the entire universe was infinite, what implications would this at the moment of the Big Bang?
Seems to me that a more interesting question would be what an infinite universe would mean. Infinity isn't big, but beyond bog. In fact, it is so far beyond big that finity itself is more interesting IMO.
You doubt that?
Think of the biggest finite prime integer you can, expressed explicitly in some convenient positive positive integer base >3. Decimal or hex would be fine, but suit yourself. Get a few friends to help you think of bigger ones (none less than say 1000 significant digits need apply. Choose n numbers, n> 3, the more the merrier, but no prime that you choose is permitted to contain any digit smaller than three, or any string of more than thirty identical adjacent digits). Take them in some sequence and call them V1, V2...Vn and calculate P=V1^V2^V3^...Vn.
Long before this time you have an answer too large to fit into the volume of the observable universe even if the universe were filled solid with protons and each proton somehow held one digit. Now raise P to the P, and repeat that process P times. Next add the first P decimal digits of Pi, taken as expressing an integer. Multiply the result by the same number of decimal digits of the decimal expansion of the 23rd root of e, taken as expressing an integer. Call the result P'.
With negligible exceptions every FINITE number,
in fact starting with P'+1, is larger than P', whose value you don't know because you ran out of observable universe to store your calculations in before you got past the first few steps. In fact, long before you got to the final P' you did not know a single digit of any of the numbers you were working with, let alone the final value of P'.
There is in fact very little you know about P' EXCEPT that P'<P'+1.
And that no one could tell you more because we have not world enough and time. We don't even know how long it would take light to reach our planet at the centre of our globularly packed number, starting from the outside.
Now, you will no doubt be asking what all this runaround is supposed to deliver, right?
Because asking about any REAL infinity is meaningless from a whole swadge of points of view. What attribute of an infinite (not just finitely large) universe could affect us where we are? Light from more than say 1e41 LY couldn't even reach us because of red shift, and even if it could, it would take too long to be of interest. Nor could any other physical signal. But a sphere of 1e41 LY filled with proton-sized numeric digits is vanishingly tiny compared with anything like P' or a brain large enough to read or calculate any number on such a scale.
And packing space so densely would be waaayyy beyond any kind of gravitational collapse, but my mind boggles at trying even to guestimate how far we'd have to expand our P' if we wished to prevent collapse.
And P' is negligibly small, remember...
Now, if you are not yet sick of that game, have fun playing it for as long as you like, but for my part I fall off the bus just trying to imagine what a modestly large
finite universe would be like if P' is so tiny.
How could we even in principle tell the difference between our tiny P' notional universe and a modestly large one, let alone an infinite one, whatever that might mean?
In such terms just what do you see an infinite universe
meaning, let alone
existing?
