Now is the time, but how much have I got?

I may have read too much Isaac Asimov, Stanislav Lem, Fred Hoyle and other great Sci-Fi writers, or done too much time-travelling with that new movie “Interstellar” (which really was too noisy for my ears) and of course with the inimitable Doctor Who:

IMG_3079 Dr Who

The old style Sci-Fi of Arthur Clark and others tried to be as accurate as possible with their science, but today’s Sci-Fi seems to be free to bend or break all the rules, and at any time!  So given that new freedom, here are some thoughts on now, with assistance from a few other sources.

Despite reading many delightful books detailing creation mythologies and cosmology origin ideas, I find no certainty on where I, or we, came from in the distant past, or worse yet, where did that distant past come from?  Likewise I am equally uncertain about where the future might be, or if I will ever get there because it constantly seems to recede from my grasp?

I started wondering if there is anything else but the here and now?

The December 2014 special issue of Scientific American, “A Matter of Time”, seems to say that I’m agreeing with conventional wisdom:

Past Present Future

The Past is gone forever. The Future never comes. We only live in an ever-present now.  But a moment later that now slips into the past as we slide forward into a new now and then another, and so ad infinitum.  We have fading memories, and the written histories, in paper, wood and stone, and in fossils, rocks and galaxies, and even in the CMB (Cosmic Microwave Background) radiation left over from the Big Bang, of an ever-expanding past. (Image from Fall 2014, Scientific American):

All History

All this comprises a record of our past, but the actual living reality of that ‘past’ is long gone.  Any hard physical evidence only exists ‘now’.  It seems to me that now is our only reality.

Friend, and fellow tennis thinker, Skip found an interesting Hebrew mystic who is in total contradiction to the suggestion that there is only now.  The mystic says that as the Hebrew language, “…the Lord’s language…” has no present tense form of the verb to be: “…there is effectively no such thing as the present”.  That same mystic says: “…the present is the activity (they) are currently engaged in during every instant, with the purpose of turning the infinitely malleable future into a better past”. (It really is amazing how dogmatic those mystics can be about things that nobody else can ever know for certain)

Well, we can’t all be correct –

So if there is no present, what is ‘now’?  Is it not just the simple interface between past and future?  An expanding spherical surface that started way back at the moment of the Big Bang.

If we accept Einstein’s description of time as just another dimension, we can then think of this interface between past and future as a 2 dimensional expanding surface simply separating all the past from all the future.  The image below is from Neil Turok’s excellent book “The Universe Within”:

Turok surface

An old satire on the flatness of 1884 life, dominated by the Church of England, written by Edwin Abbot, described Mr. Square and others who lived in a 2D “Flatland”. They had interesting, if limited, lives. They could move around, and jump over each other, but like atomic particles, more than one could not occupy the same spot at the same time.  This implied, to me at least, that the Flatlanders had a very thin but finite thickness.  (I wanted to see that book rewritten with those 2D creatures having absolutely no thickness and able to pass through each other like shadows on a screen. But it would have made interactions between them very difficult and surely greatly altered the good plot line.)

It would be sad for us to contemplate that our lives are only two dimensional, and are lived out in the infinitely thin now interface between past and future.  Fortunately, and perhaps a little like the Flatlanders, we are rescued from this dilemma by the truly famous, and non-fictional, physicist Max Planck.  He is credited with the eponymous measure of an absolute minimum possible dimension: It is the length below which there is no meaning to our typical concepts of time and space, because quantum fluctuations would become dominant if you were to go shorter than this.
This Planck Dimension is only 1.62 x 10-35 meters long.
Henceforward I’ll only use scientific notation but just to show how difficult it would be without Scientific or Exponential notation:
1.62 x 10-35 meters is  0.000,000,000,000,000,000,000,000,000,000,000,638 inches
That’s not very much, but it should not be dismissed as being meaningless.  For comparison, on a logarithmic scale, the size of a Hydrogen atom is about half way between the size of the universe and the size of the Planck dimension.

Spare a moment of sympathy for the ancient Greeks who were smart enough to conceive the idea of an extremely small elemental atom. But how would they ever have measured it with what we now call “Roman Numerals”?  The Roman system did have another symbol of M with a bar over it for 1 million, but multiplication and division was nasty, and I don’t know how they ever measured anything less than 1.  Fortunately we have our exponential numbers to make the following math extremely easy.

If the size of our 2 D spherical ‘now’ surface has been expanding at the speed of light (300,000 m/s) since time began
13.8 billion years ago, (or 13.8 x 109 x 364 x 24 x 60 x 60 = 434 x 1015 seconds),
then we are living on a spherical skin of size:
300,000 m/s (the speed of light) x 434 x 1015 seconds = 130 x 1021 meters radius (r).
If that surface is not simply 2 dimensional, but does actually have a small Planck dimension thickness, then we live in a volume of:
4 x π x r2 x 1.62 x 10-35 = 4 x π x (130 x 1021)2 x 1.62 x 10-35 = 3.4 x 1012 cubic meters.
This is equivalent to living a cube with one side of 15.1 km (about 9 miles) long.

You might think that a cube of 15.1 km on each side should be big enough, but what size do we actually need for all our stuff?

Friend Ben and other cosmologists say that information is a key component of the universe, and like energy, cannot be destroyed – it can only be transformed.  So we do need room for our ‘stuff’ which is all the information about everything i.e. the position of every atom, at every instant of time.  Fortunately Planck comes to our rescue with his concept of a Planck time unit, smaller than which there is no meaning for us, thanks again to quantum effects.  So we have the size of ‘an instant of time’.  The Planck time unit is the time it takes for light to cross the Planck dimension or:
1.62 x 10-35 / 3 x 105 = 5.4 x 10-41 seconds.
There therefore have been 434 x 1015/ 5.4 x 10-41 =  8 x 1057 Planck time units since the big bang.

The universe, according to Wikipedia, contains about 1080 atoms (we’re not counting Dark Matter because nobody has yet been able to directly find it, despite considerable effort).  So the amount of data, including all my ‘stuff’ in basement and attic, to be accommodated is:
8 x 1057 x 1080 = 8 x 10138 bits of data.
Now an  ideal data storage unit (yet to be put into production) would hold one bit of data in each smallest possible space i.e. one cubic Planck Dimension.  Thus our storage unit needs to be:
8 x 10138 x (1.62 x 10-35)3 = 34 x 1033 cubic meters,
or a cube with each side of 324 million km length!  Sadly that cube won’t fit in our 15.1 km long cubic ‘now’ space!  There might be an error in the calculations, or else we just have too much stuff.  I suspect the latter.  ….

But the universe is still expanding, and presumably the number of atoms in it is not changing much, so could the future provide the needed space?  After another year we’ll need more room to store all the new positions of those same old 1080 atoms. That is going take up another:
1080 x (1.62 x 10-35)3 x 364 x 24 x 60 x 60 / 5.4 x 10-41 = 247.6 x 1021 cubic meters,
or a cube of 6,279 km on each side.  By the end of next year the universe will be:
434 x 1015 + 364 x 24 x 60 x 60 = 434.000000031 x 1015 seconds old.
So the volume of our now space will have grown by:
(4 x π x ( (434.000000031 x 1015 x 3 x 105)2  –  (434 x 1015 3 x 105 )2) x 1.62 x 10-35  = 468 cubic meters, or a cube of only 8 m on a side – Not enough for that extra information we accumulated during the same time.  Conclusion: It might be time to buy stock in a good, forward thinking, storage unit business.

I think I’m starting to prefer Woody Allen’s quote:
“Time is simply Nature’s way of preventing everything from happening all at once”.

But who cares? Last week time stood still for me when my daughter Olivia, and John, produced my first granddaughter Kiera and now she is yawning, feeding, pooping and smiling with her eyes wide open.

Kiera

Kiera and John  Kiera and Olivia

Now, isn’t that all one could ever ask for?

Kiera, welcome to our world.  May your enjoyment of now be fascinating, happy and forever.
Signed,
Grandad

2 thoughts on “Now is the time, but how much have I got?

  1. Like Nate, I will have to read, re-read, and possibly re-read again, but this will make for a good subject for the contemplative 3 am feeding hour! I’ll ask Kiera what she thinks after 12 days of life.

  2. Well, Albert Einstein was supposed to have said “Put your hand on a hot stove for a minute and it seems like an hour. Sit with a pretty girl for an hour and it seems like a minute. That’s relativity.”

    Perhaps there is a similarly profound insight regarding a grandchild and the passage of time, and perhaps your challenging post contains it.

    I will have to re-read and consider the matter, but meanwhile, congratulations and best wishes to everyone involved in the grandchild development.

    (By the way, in doubly special relativity, the Planck length is observer-invariant.)

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