Stenger: Space/Time discrete, not Continuous
by BilboI'm enjoying Victor J. Stenger's (emeritus professor of physics and astronomy) book, Quantum Gods; Creation, Chaos, and the Search for Cosmic Consciousness. However, he presents the philosopher in me with a puzzle:
…we cannot continue to divide time into smaller and smaller units. Because of both relativity and quantum mechanics, which we will describe later, the smallest operationally definable time interval is the Planck time, 6.4 x 10-44 second. This means that, fundamentally, time is an integer number of Planck units. It is (by definition) discrete, occurring in jumps, rather than continuous…. (p.68)
…This distance, 1.9 x 10-35 meter, is called the Planck length.
And, just as a time interval can fundamentally be viewed as an integer number of Planck times, so a space interval can fundamentally be viewed as an integer number of Planck lengths. As with time, space is discrete. And, as with time, the fact that distance is usually thought of as a continous variable is an approximation that is fine for most purposes but breaks down at the Planck scale. In other words, there exists no "space-time continuum" in any proper model describing physical events. We can get away with assuming a continuum for most applications but we should be warned not to draw any universal or metaphysical conclusions from such models. (p.75)
So the question that comes to mind is, what about things that are smaller than the Planck time or Planck length?
By the way, my thanks to the commenter (I forgot who it was) at Panda's Thumb for how to write exponential numbers: sup and /sup, with greater and lesser signs. .
February 24th, 2010 at 4:19 pm
Like the list of evidence supporting blind, undirected processes.
Right. Good point.
How do we quantify that?
But seriously folks-
I would think that the smallest you can get is up until the point in which falling edge is indistinguishable from the rising edge.
What are these things that lay between Plank and that scenario- strings and branes perhaps…
And thank you- now I know "whatsup"
Comment by ID guy — February 24, 2010 @ 4:19 pm
February 24th, 2010 at 9:08 pm
Sounds like a restatement of Zeno's paradox of space and motion.
Comment by SteveK — February 24, 2010 @ 9:08 pm
February 24th, 2010 at 11:27 pm
I don't understand this.
1. Why is time discrete by definition.
2. Why is it that something continuous cannot occur in steps or be divided?
Are the terms "discreet" and "continuous" mathematically related?
Comment by Mung — February 24, 2010 @ 11:27 pm
February 25th, 2010 at 9:38 am
Quantum time is still conjectural, though it seems to fit a number of current theories.
Turns out that some phenomena only occur in discrete quantities. Light is only found in discrete packets called photons, though the energy of a free photon can vary continuously.
Comment by Zachriel — February 25, 2010 @ 9:38 am
February 25th, 2010 at 5:41 pm
But usually we think of space and time as being the medium in which discrete quantities have their existence. If space and time are also discrete quantities, then in what medium do they exist?
Comment by Bilbo — February 25, 2010 @ 5:41 pm
February 25th, 2010 at 10:26 pm
If you remember your Special Relativity, distance and time are observer dependent. At very small scales, below the Planck length, this renders common notions of space and time rather quaint. According to theory, at high enough energies, time, space, matter, forces are all the same thing. This is still speculative, though. The unification of gravity with the other fundamental forces is still elusive.
Comment by Zachriel — February 25, 2010 @ 10:26 pm
February 26th, 2010 at 9:49 am
No, I keep forgetting my Special Relativity, and I don't remember where I put it. I do remember the meaning of "discrete." And unless physicists are using it in a different sense, it sounds like they're saying that the universe goes in and out of existence rather frequently.
Comment by Bilbo — February 26, 2010 @ 9:49 am
February 26th, 2010 at 10:10 am
Heh. Certainly within your light-cone, we hope, otherwise, you may never find it.
Discrete being the contrary of continuous.
Not sure what you mean there, but the universe sits, as it were, in the quantum vacuum, a spacetime foam where things do pop in and out of existence on the Planck scale. It's possible the Cosmos was just such an event. We have a fairly good idea of the Big Bang back to the end of the Planck Era, after gravity and spacetime congealed, but before then it's still speculative.
Comment by Zachriel — February 26, 2010 @ 10:10 am
February 27th, 2010 at 12:00 am
The problem with math as natural science:
I don't really believe in special or non-special relativity… I don't think Einstein did toward the end either:
And Mr. Hubble (he of "redshift, blueshift") surely changed his mind toward the end as well:
"The assumption that red shifts are not velocity shifts but represent some hitherto unknown principle operating in space between the nebulae leads to a very simple, consistent picture of a universe so vast that the observable region must be regarded as an insignificant sample."
My favorite reading on the issue of space, planets, and what it all is made of is this guy (or these guys):
http://www.holoscience.com/new...
The author of these papers, Wal Thornhill comprehends and transmits this information beautifully (he's much better than I am at this stuff – really quite brilliant, in my opinion, but you've got to read whole pieces, not just quotes):
Comment by Liam — February 27, 2010 @ 12:00 am
February 27th, 2010 at 5:20 pm
OK, that "spacetime foam" thing. Does that constitute a continuum of some kind?
Comment by Bilbo — February 27, 2010 @ 5:20 pm
February 27th, 2010 at 5:39 pm
The notion of a continuum doesn't even make sense. Fuggedaboutit.
Comment by kornbelt888 — February 27, 2010 @ 5:39 pm
February 27th, 2010 at 5:52 pm
kornbelt888 wrote:
Exactly. And it's so hard to wrap one's brain around irrational numbers that we should ban them outright.
Comment by olegt — February 27, 2010 @ 5:52 pm
February 27th, 2010 at 5:59 pm
If we forget about a continuum, then we seem to have the following problem:
Finite quantity A, followed by finite quantity B. But A and B are discontinuous, which means that they do not overlap. So there is a border of some kind in between A and B. How large is this border? And what is it made of?
Comment by Bilbo — February 27, 2010 @ 5:59 pm
March 10th, 2010 at 1:15 pm
Bilbo:
Hi, Bilbo. It's sort of like the difference between wave and particle, which all things seem to be – depending on how you choose to measure and/or describe them. Wavefunction is continuous, a field of influence extended in spacetime. A particle is discrete, a packet of pure Is-ism. Quantatively speaking, it all depends on how you care to look at it. Relatively speaking, it's all about where you're looking at it from and how fast you're going.
Or, as I picture things, the difference is between considering the background a continuum in all directions like a film photograph, or a matrix composed of infinitesimal 'dots' like that same photo reproduced by a printing press (or pixels on a computer screen/printer).
On an FAPP scale, we think of the milieu as a dimensional continuum called "space-time." On a Planck-level scale the space is discrete and time exists ('ticks', 'moves', 'runs') on the boundaries.
Comment by Joy — March 10, 2010 @ 1:15 pm
March 11th, 2010 at 4:40 pm
While thinking about this I thought about a song, that is made of both a melody and words. The words are sung according to the melody. If there were no musical accompaniment, then the minute someone stopped singing, there would be no melody as well as no words. The words are the melody, the melody is expressed as the words are sung.
Comment by Bilbo — March 11, 2010 @ 4:40 pm