Talk:Zeno's paradoxes/Quantized spacetime

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This is a special-topic page of Talk:Zeno's paradoxes

I haven't visited this article since it was restructured several months ago, but now it looks like it has been taken over by the same crowd of philosophers citing Kevin Brown and nonstandard physics. I tried to fight them a year ago, and I don't have the time or energy to do it again. However, I will take the time to make two more points for the benefit of anyone else who reads this discussion page:

(1) Very few physicists actually believe that spacetime is quantized in the sense that this article is described. Today, physics is perfectly consistent with a continuous spacetime in which any position can be recorded as the result of a measurement. (For those of you who have heard of quantized energies in quantum mechanics, there is a difference here. The Hamiltonian operator has discrete eigenvalues, but the position operator does not. If you want to keep arguing this point, please learn linear algebra and quantum mechanics rather than reading popular literature.)

As for my credentials, I have an M.S. in physics from a top-ten U.S. university and I am completing a PhD. I also know Craig Hogan personally, and one of my friends used to work for him. I am sure that the quotation above misrepresents him. If you ask him if spacetime is quantized, he will tell you that no one knows. There are strong hints that point both ways, but no hard evidence either way, so this is still an open question. More importantly, it is irrelevant to the solution of Zeno's paradox, as I will discuss below.

On this note, please ignore Steaphan. He is basically a religious figure, not a physicist, and he resorts to insulting everyone who argues with him. Please do not encourage him by arguing.

(2) There seem to be a lot of philosophers who have become obsessed with this question: "How can an infinite number of 'events' be completed sequentially?" They claim that Zeno's paradox, the continuum paradox, and other problems are all versions of this question.

These philosophers have stuck themselves in a semantic trap. The whole idea of an "event" is a conceptual label. I can label a series of events in any way that I want, but that those labels only exist in my head (not in the physical world). The physical world simply is, and it has no conceptual labels (like "event 1," "event 2," and so forth) built into it.

The fact of the matter is that an infinite number of "events" are happening sequentially between any two moments -- if you count each moment of time as an "event." If you stop counting events, you end up with a more sensible picture. You write down the equation of motion for a system, whose domain and range are continuous, and you don't suffer any anxiety from this fact because both time and space are continuous. The physics of the matter is perfectly clear.

Fundamentally, these philosophers are just uncomfortable with uncountably infinite sets in any setting, not just with sequential physical processes. Achilles's position in spacetime can be written as an infinite set: {(t,10t) | t≥0}. All the "contradictions" regarding such a set have been worked out a long time ago. Start by reading the article on Real Numbers and then come back to Zeno's paradox.

(And as a side note, the continuum paradox does not apply to the "real numbers." A year ago, someone put it to me this way: "When you move from 0 to 1, what is the first moment that you leave 0?" However, this is a completely different question. You've introduced time-words like "when" and "moment." This assumes another continuum already. For a detailed discussion, see .)

As a parting message: The number line is continuous, spacetime may be continuous, and reality is a dynamical process that doesn't care about how you label it. Get over it already.

Sthinks (talk) 18:44, 23 May 2009 (UTC)

Hi there "Sthinks" :)
I had a good honest belly-laugh with your "He is basically a religious figure, not a physicist, and he resorts to insulting everyone who argues with him."
First of all, yes, you should absolutely ignore me. But not my questions concerning why we can't track (either in theory or practice) the motion of small bits of stuff. Is this GPS at work here, again? (rhetorical question).
Secondly, me religious? Moi? Now that has still got me smiling as I write. One of my concerns when writing Awkward Truths was that I would upset too many religious folk. Anyone who knows me would resolutely not call me religious. In fact, as I argue, scientists are as bad as religious and new-age folk with their dogmas. This article explains in more detail why religion and science are "sister-belief systems".
As for the insults ... I've met some who use similar such counter arguments, that when I disagree with some dogma or untruth, I'm being defensive, argumentative or any manner of other "socially unacceptable" behaviours. I'm a belief doctor, it's my job, get over it already. :)
No, I'm just pointing out that you routinely use ad hominem attacks rather than actually arguing against the point that your opponent has made.
Once again, where is the proof that space-time is "infinitely divisible"? How do you reconcile the experimental evidence of the science of "lumps and jumps" with the idea that space-time (and thus motion, on some level) is "perfectly" smooth and continuous?
I've discussed this in almost every post, and you continue to ignore it. We don't know if space is infinitely divisible or not, but Zeno's paradox can be resolved either way. The "lumps and jumps" that we do know about are in energies of bound systems (and occasionally other observable quantities), not in spacetime. (As I said earlier, this is because the eigenvalues of a bound Hamiltonian are discrete whereas the eigenvalues of the position operator are not. If you don't understand what this means, and I'm quite sure that you don't by this point, then you have no business discussing quantum mechanics. I'm sorry, but you need to admit to yourself that you just don't understand the physics here.)
Interestingn response. From memory of my higher level physics and mathematics classes at university some years ago, I don't see why you keep on about eigenvalues, states and vectors. What have these to do with the inability to perfectly define bits of stuff - as required by the Uncertainty Principle?
Steaphen here (again): In doing some online research for my forthcoming article (on the superstitions rife within science), I found the following material which is pertinent to your (Sthinks) obsession with eigenvalues. I should add that the excerpt is from, which according to my searches, points towards a Kevin Brown being the author. "Ahh, so that why he's often quoted," I thought. From my initial perusal, I think he writes well. Anyway, his comments:
"We now recognize that position and momentum are incompatible variables, in the sense that an exact determination of either one of them leaves the other completely undetermined. According to quantum mechanics, the eigenvalues of spatial position are incompatible with the eigenvalues of momentum so, just as Zeno’s arguments suggest, it really is inconceivable for an object to have a definite position and momentum (motion) simultaneously."
As for your "We don't know" -- I think that says enough (although I would ask that you speak for yourself). And if you don't know, I suggest you avoid commenting as if you do. But your comment that Zeno's Paradoxes can be solved "either way" is rank nonsense. If you solve Zeno's Paradoxes, by taking into account the thought-experiment provided below (re Part A), then the Nobel prize is yours. About that we can be certain (inasmuch as you'll have conclusively busted the Uncertainty Principle of quantum mechanics, and in the process fully defined the indefinite, totally measured the immeasurable, and completely limited the unlimited).
I should add that I value your comments (even the nonsense ones), inasmuch as they are providing me the material for an article I intend to write (and possibly a book)Steaphen (talk) 23:58, 10 June 2009 (UTC)
As for your being an M.S. or whatever. So what. In my workshops I remind people to look out for those who use words like "perfectly" and "The fact of the matter is". I particularly liked your segue into supposition regarding "The fact of the matter is that an infinite number of "events" are happening sequentially between any two moments" Really, you have proof of this?
Yes, I too occasionally drop in to follow the process of thinking by many. Yours no exception. I find it quite interesting.
I find your replies deliciously ironic, on many levels. But the disconnects your theories rely on do immense harm in the world. While I may on occasion be a little too flippant, those disconnects, in science, religion and new-age are unsustainable ideologies. I believe the human race can no longer afford such deleterious disconnects.
with good wishes, and fond regards,
Steaphen Pirie Steaphen (talk) 00:51, 24 May 2009 (UTC)
Author, Be and Become
btw, I note that you use the rather unfortunate nom de plume "sthinks" which everytime I see I mentally think "thinking stinks". Why sneak around with such an unfortunate non de plume? Why no courage of your convictions? What's your real name? If no real name, at least change the moniker.
pps, And if you read the above cited article and want to argue that the Many Worlds Interpretation is NOT the leading interpretation of quantum physics, please cite the surveys which reveal otherwise. It's been some time since I scanned and noted the relevant surveys, but I'm happy (and grateful) to be corrected. —Preceding unsigned comment added by Steaphen (talkcontribs) 01:02, 24 May 2009 (UTC)
Yo, Sthinks. I've just reread your post. I have to ask, who is this Kevin Brown that I or others have supposedly quoted? I googled his name and mostly he seems to be some baseball player or some such. Are my ideas like curve balls to you?. And I entirely (perfectly) miss the point about you knowing "Craig Hogan" personally -- who's he? Is there some list of "in" people (presumably, Craig Hogan is "In"). And what, exactly, is "non-standard physics"? Some have suggested I'm on a different planet to most, but "Non-standard physics"... golly, that must put me in a whole different universe :)

This is Sthinks again. Five more quick responses are worth making:

(1) Kevin Brown seems to be the philosopher who flies the banner of "Zeno's paradoxes are not solved!" Whenever I see anyone arguing that Zeno's paradoxes are an open question, they all cite his book (and no one else's). I'm fairly convinced that 99% of philosophers consider the matter to be closed.

Hi. Just asked 4 philosophy professors, and 3 don't think that calculus solves Zeno's paradox. Small sample, but I doubt your 99% claim. Also, here is a quote from Joseph Mazur (a professor of Mathematics) book "Zeno's Paradox" (p.25): "Mathematicians may simply deny the paradox by claiming that the sum of ... is equal to 1, but they cannot answer the question of how the task is actually completed in reality." —Preceding unsigned comment added by (talk) 16:17, 12 June 2009 (UTC)

(2) I mentioned Craig Hogan because someone quoted him in bold above to support some kind of gobbledygook. I said that his quotation is taken out of context and misrepresents his beliefs.

(3) Steaphan: The many-worlds interpretation IS one leading interpretation of quantum mechanics. (In fact, I rather like it. If you do too, you should read Schlosshauer's textbook on decoherence and the quantum-classical transition. It's great stuff.) What I DON'T understand is how this is relevant at all. Steaphen, your posts consist solely of pasting buzzwords (like "many-worlds interpretation") together -- they do not amount to coherent arguments. The many-worlds interpretation has absolutely nothing to do with what you are arguing. It's as if I wrote a post saying, "Yes, but what about the TUNA FISH?" It's completely random.

(4) Steaphan: The post below argues that the uncertainty principle is in conflict with the "geometric series" approach to solving Zeno's paradox. The post is a tautology; let me explain why. First you assume Classical Mechanics, and then you show that Quantum Mechanics is wrong. This is obviously going to happen because you started by assuming Classical Mechanics, where each particle has a definite position at each moment in time.

However, you CAN apply the geometric series argument to a quantum setting. You just have to decompose the state of the particle into its position eigenstates: |psi> = \int <x|psi> |x> dx. Then you can apply the geometric series argument to each position component. The geometric series argument works either way; the problem is that you don't actually understand Quantum Mechanics well enough to do the calculation and see it.

(5) Steaphan: Anyone who looks at your work can see for themselves if you are a "religious figure." More specifically, I would call you a New Age self-help guru.

This is tiring. Sthinks (talk) 03:21, 7 June 2009 (UTC)

Response by Steaphen :)
1. I'm quite happy for you to make assumptions concerning my sources and influences.
2. Actually, I quoted Hogan. I'd forgotten I had, and was not bothered to again search this site for references to Hogann after your earlier oblique reference to Brown. I like talking "some kind of gobbledygook" although I would argue it is a special kind of gobbledygook. As for the reference to Craig Hogan. Please reread the quote - it says "according to Craig Hogan ..." I think even a five year old (like me) understands it's the reporter's interpretation of the evidence. Take up issue with NewScientist, not with those who quote the article. But that still avoids the issue - is space-time granular or not (it's either granular or it's not. If not, then good, Noble Prize please)
3. "many-worlds interpretation has absolutely nothing to do with what you are arguing" - "nothing"? Thank you. I always enjoy reading such comments. It telegraphs your thinking. Tuna fish? - what about whales and bowls of petunias. "It's completely random" - ah, now there's a religious statement if ever I heard one. The religion and superstition of randomness: "it just happens" - No cause, it's just magic. Self-organising systems "just happen, randomly and magically". So this is the best science can muster: that it "just happens"? Some might appreciate the irony that with the prevailing dogmas and superstitions rife within science, it took a poet to say it: "our own time is an unprecedented dark age."[1]
4.Conflict? not at all - it's quite simple: Arrow, atom, position, momentum. Assumptions? No, by your assertion, quantum theory has nothing to do with solving Zeno's Paradoxes. So, use geometric series (calculus), as per your requirement, to "perfectly" (fully and completely) define the real-world trajectory (moment-by-moment position and momentum) of an arrow - and that of its lead atom (using the thought-experiment in the section "Not seeing the trees for the forest section") - thereby thoroughly busting the Uncertainty Principle of quantum physics. That again reminds me, where's my Nobel Prize! What part of the pointy end of a million in prize money do you have trouble with? I particularly like your "You just have to decompose the state of the particle into its position eigenstates"- priceless. And I particularly liked the "you don't actually understand Quantum Mechanics". As I often say to people, treat my like a five year old, and explain in simple language so that I (and others) can understand. The use of gobbledygook and impractical sillyness welcomed and enjoyed.
5. I wasn't aware many would equate religion with New-Age. Unlike yourself I'm happy to have people review and criticise my work under my real name.
In conclusion - you appear to have a penchant for commenting on my character (some would argue I don't much have one, but I digress :). Whether I'm religious, New-Age, atheist, agnostic or whatever is irrelevant to the issue at hand: Congruent solutions to Zeno's Paradoxes. Tiring? Not at all. Light entertainment for me.Steaphen (talk) 10:05, 9 June 2009 (UTC)

Steaphan, you asked me to treat you like a five-year-old and explain what I've said in simple language. Here is a brief explanation, with a few extra notes in parentheses. If you don't like it or you don't understand it, then you really need to go and learn the physics. But here is my best attempt.

Continuity and discreteness in physics, using everyday language

In the everyday world, there are some things that come as whole units: apples, pots, etc., and some things that come in any amount that you want: water, air, etc. If you're talking about apples, then you can only have ONE apple, TWO apples, THREE apples, etc. If you are talking about water, you don't have "one water," "two waters," and so forth. You can have 1 cup of water, 1.5 cups of water, 1.52 cups of water, or any other amount that you desire. Apples are called "discrete" and water is called "continuous."

(Now, you will immediately retort that water is made of water molecules and so it is actually discrete. This is true, and I will address it in a moment. Keep in mind, however, that I'm supposed to be treating you like a five-year-old, and a five-year-old would not make this objection. The point is that all of the scalar quantities in classical physics are continuous, such as length, time, mass, velocity, and so forth.)

Up until the 19th century, physicists believed that a lot of things such as light were continuous. However, they discovered that a lot of things that were thought to be continuous were actually discrete. First, they discovered that everything is made of atoms, including water -- so water is actually discrete. Then they discovered that light and various other things were discrete. These discoveries were called "quantum mechanics."

In the 1920s, physicists discovered that they could explain ALL of the discrete things using a single equation, called the Schrödinger equation. It is the central equation of everything in quantum mechanics (along with its field-theoretic relativistic extensions like the Dirac equation, the Klein-Gordon equation, and so forth). Using the Schrödinger equation, you can actually PREDICT which things are discrete and which things are continuous. (This is where "eigenvalues" come in.)

The Schrödinger equation tells us some properties of particles (e.g. energy) can go EITHER WAY. Sometimes they are discrete and sometimes they are continuous, and it depends on the circumstances (the potential energy, or the other "forces") involved. These predictions have been proven by experiment, and they are the most accurate predictions in all of science.

Now, if you ask the Schrödinger equation if space and time are continuous or discrete, it tells you that they are both continuous. In fact, the way it is usually written, the equation doesn't even make sense if space or time is discrete. Therefore, the vast majority of physicists believe that space and time are probably continuous. Every equation that is accepted by all physicists uses continuous space and time.

However, no one has ever done an experiment which settles the matter one way or the other. So, a few physicists (such as Loop Quantum Gravity theorists and some astrophysicists) believe that space might be discrete and come in very small "lumps." This is still a new idea and no one knows whether or not it is right. But if it IS right, then it means that the Schrödinger equation (and QFT as it currently stands) is wrong in some sense. We would have to change the Schrödinger equation (and a variety of other equations) in order to make space and time discrete. No one has done it successfully.

(I hope this helps. The basic point that you are missing is that SOME THINGS are discrete, SOME THINGS are continuous, and SOME THINGS can be one or the other depending on the circumstances --- and there is a systematic way of figuring this out using the Schrödinger equation. As for the Nobel Prize that you keep mentioning: there were several, and they went to Schrödinger, Heisenberg, Dirac, Planck, Bohr, de Broglie, and all of the other geniuses who originally figured out everything I just told you.)

Why this is a moot point anyway

Even if you forget about quantum mechanics entirely, you can still solve Zeno's paradoxes. The thing you have to remember is that Nature does not think about "events." When you say that there are an "infinite number of events" happening, those events are all an idea in your head. Let me give you an example in the form of a dialogue.

A: Look! An infinite number of events just happened!

B: Really? What were they?

A: The first event was when Achilles was halfway to the finish line. The second event was when he was 3/4 of the way to the finish line. The third one was when he was 7/8 of the way to the finish line. You can see that each time he covers half the distance, there is a new event. There are an infinite number of them!

B: Well, that's funny. I only saw two events. The first one was when Achilles was halfway, and the second one was when he reached the finish line.

C: That's strange. The only event that I noticed was the moment he crossed the finish line. Why did you care about the halfway point?

D: Well, I counted everything in thirds. The first event was when he was a third of the way, the second was when he traversed a third of the remaining distance, and so forth.

P (a physicist): See, your problem is that you think in terms of counting "events," but you see that you can all choose the "events" however you want to. No one can agree on the events. But we can agree on an equation that describes Achilles' position. If Achilles is running at 10 miles per hour, and he starts at 0, then his position is given by this equation: x(t) = 10t. If you ask where Achilles is at any given time, then this equation will tell you.

A: But this equation doesn't tell me how all those events happened!

P: Of course it does. Let's say that the race is 10 miles long, so Achilles runs the whole thing in an hour. You ask where Achilles was after half an hour, you plug in t=.5, and it tells you that he was at x=5, or he had traveled 5 miles. You can do the same for any other point in time. It has ALL the information about ANY possible "event" that you might be interested in, but it doesn't present any philosophical problems!

B: A philosopher once told me that I can't use an equation like this. He said that between any two points there is another point, so it's impossible to go between two points, because you have to pass through an infinite number in between.

P: Yes, you do -- but there's no reason why you can't! You pass through an infinite number of positions at an infinite number of different times. Since both space and time are continuous, then there is no contradiction.

B: What do you mean?

P: Between 0 miles and 10 miles, there is a POINT, 5 miles. But between 0 hours and 1 hour, there is also a TIME, .5 hours, when Achilles was there. And between 0 miles and 5 miles, there is ANOTHER POINT, 2.5 miles. And there is also ANOTHER TIME, .25 hours, when Achilles was there. Do you see? There is always a time for every place. Since space and time are continuous, there is no "first point" between any two points. If you need to learn more about this, you should start by reading more about the Real Numbers.

B: Thanks, P! I'll do that!

Steaphan, do you see my point now? This is as plain as I can make it.

If you keep responding with jokes about my handle or related ad hominems, then I'll stop this discussion and hope that someone else learns something from it. But if you are genuinely interested in discussing the matter further, then we can keep discussing it.

Response by Steaphen
it seems to me a five-year-old would pick the obvious omission in your replies ... a la "why is that lady so fat" kind of thing that kids do.
all of which seems to indicate you have not understood my work in the least. As I explained previously (and in my books, and workshops), take the efficacy of the mathematics (by Schrödinger et al) as reflecting deeper reality. However, and this is the part you do not get, we are not justified in assuming the mathematics is entirely confined to, related or pointing to ONLY our physical system. Simple test: how many choices do you have regards the future? How many do you physically experience? Quantum theory shows the mathematics of possibility does not entirely match the mathematics of actuality (classical physics).
If you must insist on only once physical system (ours) -- of one probability, then please explain how we can't entirely track an everyday physical object.
A discrete, discontinuous physical reality within a continuous, infinite multiverse, makes sense, and fits ALL the observed evidence, while fully encompassing all effective mathematical frameworks.
It, for example, encompasses, accommodates and explains
  • why galaxies are distributed fractally
  • the single-photon, double-slit experimental results
  • Feymann's Sum-over-histories
  • Wheeler's delayed-choice experimental results
  • spiritual insights of gurus, intuition
  • why Gödel's and Heisenberg's theorems are obviously and necessarily going to apply,
  • where all the dark energy and matter is, and why we won't directly observe it, just as we don't directly observe (measure/detect) 'shadow photons' in the double-slit experiment
  • and why, according to Chaitin, some mathematical theorems are true for NO reason at all
... and so much more.
The mathematics of quantum theory is telegraphing something immensely important, but it seems that you (and many others) fail to appreciate the message.
Independent observers reading this material (some of whom, professional physicists, have 'quietly' approved of the thrust of my replies) will see that you are avoiding the fundamental issue of Zeno's Paradoxes.
No amount of asserting whatever theory you subscribe to will change the obvious omissions.
As for the jokes about handles, it goes to the issue of honesty, and credibility. If you are confident with your theories, then you have every reason to shout from the rooftops, but if you must do so under the cover of darkness, then so be it (better that you shout, then not at all, as some are now finding in various quarters of our little planet).
On a more serious note, your avoidance of any practical explanation of the experimental evidence of quantum physics is no better than that of religious priests in Galileo's time, who refused to offer credible explanations for the motion of planets. In a very real sense, every 'sceptic' or nay-sayer who resolutely denies nonlocal cognitive abilities is helping to fuel religious and new-age fundamentalism - as all such belief-systems are reliant on (perceptual) disconnects that limit intuitive, creative abilities and awareness - abilities that are increasingly needed to connect, cure and create a far more fulfilling world dynamic.
Steaphen (talk) 04:12, 26 June 2009 (UTC)

Final Response by Sthinks

Steaphan, we DO shout this from the rooftops. All the time. This is called "publishing in a peer-reviewed journal." You can find countless journal articles that confirm what I'm telling you.

Let me tell you why I use a handle. As soon as I start discussing things like Zeno's Paradoxes on the web, then I start to get dozens of spam messages from crackpots (such as yourself) for each post that I make. I only use a handle to keep my name private, since you can look up my email address (and my office phone number, and...) on a university website as soon as I give you my name. I don't lack "confidence" -- I just lack time to deal with this nonsense. More on this below.

My apologies for interjecting in your reply, but I will (again) address your points.
I'm happy to be labelled a crackpot. Many throughout history have been so labelled ...

Of all of the "obvious" responses you made, half of them have nothing to do with the question at hand, and the other half have been explained as far as possible (see Bell's inequality) by quantum mechanics and its various interpretations.

Example: Yes, quantum mechanics only gives us probabilities. Exactly. But it gives us probabilities in a continuous spacetime, which is the subject under discussion. (I am not questioning quantum mechanics at all; you are.)

Uhm, no, again, you are not justified in assuming a continuous spacetime. Sorry, but you have no evidence that it is continuous. Read by reply above. We may take the efficacy of mathematics (calculus) as reflecting some deeper reality, but that most certainly does not require that it only pertains to this physical system.

If you want an extended discussion of the philosophical aspects of this, you can start at Interpretations of quantum mechanics.

As you seem to forget it was my suggestion back on the archive page that one should indeed look to the various interpretations.

That is an extremely interesting discussion. However, none of the "interpretations" change the fact that quantum mechanics assumes a continuous spacetime, and it makes predictions that can be tested and have been shown to be accurate (unlike your vague theory of discrete spacetime). —Preceding unsigned comment added by Sthinks (talkcontribs) 03:13, 30 June 2009 (UTC)

See above.

Example: The fractal distribution of galaxies has absolutely nothing to do with this discussion. It is a process described entirely by classical gravitational physics, which my friends in the astronomy department are currently studying.


Example: The double-slit experiment is explained in a completely empirical way, as far as possible permitted by Bell's theorem, by quantum mechanics using a continuous spacetime and not a discrete one. The same goes for delayed-choice experiments. Look up any textbook's treatment of this problem. If it actually uses the equations of quantum mechanics, it will have plenty of integrals over a continuous spacetime.

See above. I don't argue against the efficacy of the mathematics. Only the intepretation of what those mathematical symbols actually respresent.

Example: The very ESSENCE of Feynman's sum-over-histories approach is a continuous spacetime, because it is written as a recursive integral! Anything that uses calculus assumes a continuous spacetime. But you don't realize this because you clearly have not studied quantum mechanics and do not know how to use or interpret its mathematical structure.

Sthinks, you're really on a hiding to nothing here. Again, calculus does not assume a continuous spacetime, only a continuity of the infinite numerical series (which is INCORRECTLY assumed to correspond with our physical reality). If it were an absolute 1:1 correspondence, then we could perfectly track/predict matter/energy quanta at every point. This is the point that you have continually avoided.

Example: Goedel's theorem applies to any mathematical structure containing the whole numbers, and Goedel was absolutely contemptuous of anyone who suggested that it had ANYTHING to do with Heisenberg's principle. The modern mathematical community generally has the same attitude. Similarly, Chaitin's discussion of mathematics has nothing to do with physics. Pure mathematics is a system of formal logic that may or may not have anything to do with the real world. Physics DOES have to do with the real world, and it makes testable predictions that have been confirmed over and over.

I didn't say they were related, only that a discontinuous physicality within a continuous multiverse would accommodate both, easy as.
Now here's where you contractict yourself. If "pure" mathematics, by your admission, has nothing to do with the "real" (THIS) world, then you have argued my point. You can't have it both ways with your belief-system. I argue that mathematics both relates to our real world, and to other probable systems.

Example: Heisenberg's principle is ALWAYS preserved by Quantum Mechanics. (And it is equivalent to the Fourier uncertainty theorem, once again using calculus. In other words, the formal statement of Heisenberg's principle ALSO uses a continuous spacetime since it is stated in terms of integrals. Every example you bring up just reinforces the fact that most physicists treat spacetime as continuous.)

No, again, it doesn't assume a continuous spacetime. That's why there are vigorous debates regarding the interpretation of quantum theory.

Example: Dark matter and dark energy can exist regardless of continuous or discrete spacetime. (I have friends who have worked on models of dark energy in continuous spacetime and other friends who have worked on models on a "lattice" model which begins with a discrete spacetime.) This issue can be settled one way or the other.

Good, write a peer-reviewed paper explaining exactly what dark matter is (since you say it can exist regardless). I have yet to see it settled in the least. As I understand, the missing dark-matter issue is considered one of the greatest unsolved cosmological mysteries (not by me, but hey, I'm a crackpot).

Steaphan, let me get down to the point here. First, you accused me of dodging the question. Then you wrote a rambling reply about a variety of subjects which are completely irrelevant. Once again, it's a screed about tuna fish when I asked you to refute an argument about quantum mechanics -- a subject about which you are severely miseducated.

"rambling" .. "completely irrelevant"? "miseducated" - whatever. You have again failed to counter the thought-experiment in the section below "not seeing the trees for the forest." That alone, despite all your replies, telegraphs your position and lack of clarity of world-view.

Have you ever considered that you yourself might be one of these "reincarnated Galilean priests"? You keep spouting the same falsities over and over, failing to actually LOOK at a single "telescope" of a textbook of quantum mechanics or learn the language of quantum mechanics. Which one of us is dogmatically refusing to see what has been discovered?

Possibly (reincarnated priest from Galileo's time). I note again you have not offered any credible world-view to accommodate the various facts of our reality (into one congruent philosophical framework).

(And what is a "Galilean priest" anyway? A priest contemporaneous with Galileo?)

Awh, don't get picky. A loose turn of phrase, perhaps, but it adquately conveys the point, and the irony, I would think.

At this point, this conversation is utterly useless, and it is not enhancing this article. I am going to stop posting. Undoubtedly, you will write a response claiming victory and making more pointless insults. I will leave it to the reader to see the inanity in such a post, and my optimism in humanity leads me to believe that you will be ignored. Unfortunately, I don't think that this article will be improved, but at this point there's nothing I can do about that.

The article doesn't need improving, only that you offer a credible philsophical framework to support your arguments.

Goodbye, Steaphan. Have a good life. Sthinks (talk) 03:08, 30 June 2009 (UTC)

Time will reveal who's views are shown to be congruent with deeper reality. I'm betting on me.
Again, calculus does not assume a continuous spacetime, only a continuity of numerical infinite series (which is INCORRECTLY assumed to correspond with our physical reality). If it were an absolute 1:1 correspondence, then we could entirely, completely and without exception track/predict matter/energy quanta at every point.
YOu are correct, your replies are pointless while ever you avoid that basic issue.
Steaphen (talk) 12:31, 2 July 2009 (UTC)
How can you prove that the spacetime is discrete? What is your proof of a discrete space-time? mike4ty4 (talk) 02:02, 4 July 2009 (UTC)
'Proof', in regards to the theory of movement of physical things (the key dilemma of Zeno's Paradoxes), requires supporting evidence as to any such theory. If we presume a discontinuous space-time, we might ask "well then, what sort of evidence should we see if space-time is discontinuous?" - I assert that, in line with this world-view we would see exactly the evidence as is presented in the field of quantum research. A discrete space-time can ONLY provide evidence and phenomena that would support this supposition - meaning, we should expect to see "lumps" and "jumps", in conjunction with no evidence of quanta moving completely smoothly (as would be expected by a completely continuous and contiguous space-time in which there was a direct, unambiguous and absolute 1:1 correspondence of our space-time with infinite-series/calculus).
In other words, with the evidence of quantum physics we may reasonably expect space-time is discontinuous, as there is no physical experimental evidence to support that it is entirely continuous. Within this framework, the onus is on those who assume it is continuous, to show evidence (as in the actual behaviour of physical objects/phenomena) as moving totally, completely and absolutely smoothly, without discontinuous behaviour in the least. On the one hand we have a reasonable supposition, supported by physical evidence. On the other, we have a questionable supposition, with no physical evidence to support it (other than the illusion of 'smooth' motion of macro-sized objected, which, like a car-chase in a movie, is recognised as being illusory. The former (real-world illusion) due to the relatively slow "persistence of ego", the latter due to "persistence of vision").
On that basis, I predict the acceptance of a discontinuous space-time will be, like the Copernican shift in world-view, only a matter time. As far as I'm concerned, it's a done deal. My posts and replies at this site are more about invoking dialogue and responses that reveal the reasons for the intransigence.
As explained to some extent in the section below "Clarity of Cause" those reasons are mostly due to cultural immaturity and short-term expediency.
A fuller understanding of why many are resisting this new "world-view" or Weltanschauung is covered in "The Evolution of the Human Psyche"
My ongoing interest and work will be focused on teaching a more congruent world-view that will enable far greater creativity and insight - one that will help improve personal, cultural and global circumstances.
As far as this site is concerned, I sense my work is done. To that end, I thank those who counter-argued. I'm quite grateful for those who did as the arguments presented are, I believe, representative of the opinions and beliefs held by the majority populace (at this time).
Steaphen (talk) 07:23, 4 July 2009 (UTC)
update by Steaphen.
Dear Mike4ty4, I may "jumped" too far ahead in my response (taking for granted knowledge I have acquired over 20+ years). In simplistic terms (and in respect of Occam's razor, and in view of the foregoing), by using the motion picture film metaphor, one is led to question the reasonableness of assuming, and requiring that there are an infinite - in literal and quite real terms, that's means a never-ending- number of "frames" involved when doing some everyday event such as blinking or lifting a finger.
If, however, you assume discrete space-time, then we are able to accept and assume an entirely reasonable idea ... that there are only a finite (albeit, exceptionally large) number of frames that we must progress through every time we blink. The flip side to this, however, is the question, "what's going on in between the blinks, pulses, excitations, perturbations etc (or "frames") that we experience in a collective sense as physical reality?" Once you ask that question, with a genuine sense of inquiry and discovery, you'll begin the journey into creative, subjective, felt fields and potentials that reach behind and beyond the physical - if you genuinely do that, you'll find yourself in the company of any inventor, artist, writer, entrepreneur or creative scientist worth their salt.
Steaphen (talk) 10:09, 4 July 2009 (UTC)
What exactly is the problem, though, with accepting an infinite number of "frames"? Furthermore, if time is fundamentally discrete, then it is meaningless to talk about "between" as that implies a smaller gradiation. Unless you admit a "super time" in the "super reality" behind the scenes that IS a continuum by which something like that can be measured (the relation here is akin to how real time relates to the discrete time in your computer's CPU, and thus "what happens between frames" is like asking "what happens during one tick of your CPU", i.e. what is happening in the physical world in which the CPU is implemented. So then one would be asking what happens in the super world where the physical world is "implemented".). Yet why doesn't a Zeno-like paradox also apply to this super time? Finally, the mere thinking of it as frames seems like an assumption of a discrete process from the beginning, and not a continuum one wherein one thing flows into the other. If you are assuming a discrete process from the beginning, then concluding that it is so, you have constructed a circular argument that does not actually prove anything at all. mike4ty4 (talk) 09:50, 6 July 2009 (UTC)
The problem of accepting a never-ending number of frames is just that .. they're literally never-ending. Off you go then, on your never-ending journey. Jokes aside, the never-ending aspect is best left to a multidimensional and meta-physical multiverse. That makes much more sense. I think the real issue here is that the answers you seek won't be found in some equation, as most respondents here hope. As for between the pulses, etc, no that does not imply or require other graduations ... think "everywhere and every when at once" from which individual frames are congealed, popped etc.
What's so bad about that? Why can't there be an endless amount of steps between them? An endless amount of steps, each of which takes no time to complete. And I just want some sort of answer, it doesn't have to be in the form of an equation. mike4ty4 (talk) 22:07, 6 July 2009 (UTC)
"No time to complete"? You have experience of this, in physical terms, of doing something in absolutely no-time, even faster than the Planck time? Are you serious? (btw, See previously concerning descriptions labelled "bad".)
I suppose you could also say "infinitesimal-time", but you really can't view a continuum process as one instant after another. mike4ty4 (talk) 19:59, 7 July 2009 (UTC)
Now this is getting silly. By your belief-system in which physicality adheres to infinite series, there are infinite instants along or within any time frame. That's the definition of a continuum. Complete and utter continuity, no gaps, no spaces, no blinks - no discontinuities, just absolute unending continuity, ad infinitum, forever. Which just so happens to not be reflected by the observable evidence of quantum physics research.
A continuum has no "gaps", yes. What you still haven't come up with yet is: what is in quantum physics that proves discrete space-time? I.e. what observation is there of this? Tell me what the experiment or data is (you said "observed"). mike4ty4 (talk) 00:44, 9 July 2009 (UTC)
Again, what is your evidence for a continuous space-time? I have suggested that the fundamental discontinuity of movement of quanta gives evidence of a quantized space-time. I note that you avoid answering the questions posed in my various thought-experiments. I define a "good scientist" as someone who offers theories to fit observed evidence. Those who merely regurgitate accepted theories, mathematical proofs and equations to explain anomalous phenomena I define as being "technicians" who work the machinery without really understanding it. Within this context, your inability to answer the questions posed in the various thought experiments, let alone offer any new thought-experiments to verify your beliefs, qualifies you, at best, as a "technician", but thoroughly disqualifies you as either a serious thinker, or competent scientist.
As for quantum mechanics, now that's the rub. The "jumps" (quantization) in QM have nothing at all to do with discrete spacetime! What makes you think they do? As has been pointed out to you again and again, the very theory of QM is devised in continuous spacetime -- so the theory would essentially have to be self-contradictory if it implied discrete spacetime. It would essentially rebuke itself. Because of that I do not see how you can prove discrete spacetime from QM as you seem to be claiming you can. I'd suggest a reading of, even on this Wikipedia, say, hydrogen atom for example, or even just particle in a box, to see where and how this quantization of certain measurable quantities arises. If you don't trust the Wikipedia enough, then look for some material on these things somewhere else that you consider more reliable. After doing that, reading it and make sure you actually understand what is going on there, then argue from this as to how we can deduce this quantization occurs due to discrete spacetime. If you want to revolutionize to a new paradigm, you need to understand the old one enough! mike4ty4 (talk) 09:50, 6 July 2009 (UTC)
re your "The "jumps" (quantization) in QM have nothing at all to do with discrete spacetime!" ...
"We know now, however, that it is Einstein's theory that ultimately fails. On extremely fine scales, space-time, and thus reality itself, becomes grainy and discontinuous, like a badly overmagnified newspaper photograph. The equations of general relativity simply can't handle such a situation, where the laws of cause and effect break down, and particles jump from point A to B without going through the space in between."[2] —Preceding unsigned comment added by Steaphen (talkcontribs) 02:19, 12 July 2009 (UTC)
First of all, please extend me the courtesy of not misquoting me. You asked for "proof", I responded by suggesting, as would any good scientist: Begin with a hypothesis, supposition, theory - whatever, and look for physical evidence to support said theory. Physical proofs (within the context of the universe newly banging on (see below! - pun intended)), are temporary artifacts, that come and as soon go.)
What did I misquote? mike4ty4 (talk) 22:07, 6 July 2009 (UTC)
That I suggested or implied QM "proved" the theories I espouse. It is the other way around, that the models I propose, would accommodate the results of quantum theory and experiment.
And why do you think already-existent models are incapable of accomodating those results? Also I'm not saying that QM proves it, but you seemed to be claiming that the mathematics of QM was suggesting discrete spacetime. mike4ty4 (talk) 19:59, 7 July 2009 (UTC)
If you start with the presumption of a quantized physicality, then QM makes sense, as do many other facts of reality, including the sayings of sages and spiritual types since time immemorial. It ALL starts to fit. But QM is not the final theory, only another step towards a deeper understanding. String theory is partially headed in the correct direction. Start with the idea of quantized space-time, and see where that leads your intuitions. Expect to be surprised.
Why does QM not make sense in the continuous space-time in which it is formulated? And why are you starting with this presumption -- I thought you said the mathematics of QM theory somehow required or was "telegraphing" this among other things. (If you have to start with this to get that to happen you have a circular argument (begging the question) that proves nothing, by the way.) QM is not a final theory, no, and in real science one does not claim any theory is a "final theory" as all theories are subject to revision. What I don't get is how you can spin this in the way you want to. mike4ty4 (talk) 00:44, 9 July 2009 (UTC)

Again, what is your evidence for a continuous space-time, the assumption upon which you base your arguments? I have suggested that the fundamental discontinuity of movement of quanta gives evidence of a quantized space-time. I note that you avoid answering the questions posed in my various thought-experiments.
"nothing at all" ... again, if space-time were entirely continuous, how could matter move from point to point without travelling the space in between. It's not about trusting Wikipedia, but about looking for congruent frameworks that fit the observable facts. A continuous space-time simply won't explain or accommodate the facts.
Quantum theory is not "devised in continuous spacetime". That is mere supposition: even though the mathematics give the appearance of continuity, the physical behaviour and evidence does not.
Yes it is. The mathematical framework is based on continuity of spacetime through and through. mike4ty4 (talk) 22:07, 6 July 2009 (UTC)
Again, you appear to have trouble understanding the mathematics need not only apply to our physical system. If you have physical evidence that the mathematics only relate to our physical system (e.g. physical evidence of completely smooth motion of particles), please enlighten me, and the rest of the scientific fraternity.
The question is not how accurately the theory applies to our physical world, but what sort of conclusions you can draw from the math. mike4ty4 (talk) 19:59, 7 July 2009 (UTC)
Whoa there! The issue at hand is the subject of movement of physical things. The mathematics is a side issue. If someone provides compelling conclusive evidence that it's all the result of magic spun by fairies on pinheads, then who gives a rats about the mathematics. It's the compelling evidence (aka RESULTS) that count, not your wishful thinking as to your pet theory. See above about starting with the presumption of a quantized physicality.
So again, what is the evidence here? Why are you presuming the quantized physicality? If it's Zeno's paradoxes then the flaw, and this has been pointed out again and again, is that Zeno's paradoxes think of a continuum as though you have to be able to count off "instants", but you can't. Cantor shows what the continuum is all about. Zeno's paradoxes do not refute continua, they refute a naive idea of them. mike4ty4 (talk) 00:44, 9 July 2009 (UTC)
I think you've missed the essential issue here. As Bohm and others have amply explained, "according to the quantum theory, movement is not fundamentally continuous" (Bohm's emphasis, not mine). If you have evidence that it is, provide it. Evidence shows that it is not continuous. Bohm also asserts that "Quantum theory requires non-continuity, non-causality and non-locality." Tell me, what physically exists in the middle of all that discontinuity? See the thought experiment below.
So this based on something from Bohm's interpretation? And furthermore, how do you prove from it discrete space-time? Are the discontinuities regular? As if they're not, that does not suggest a discrete spacetime, which means that there is a fundamental limit to how small any motion, continuous or discontinuous, can be. Note this is not just a limit to measurement but a fundamental limit of motion itself. What do you have to prove that? mike4ty4 (talk) 00:30, 10 July 2009 (UTC)
As for your "no gaps", and "no instants" ... ? ... what again are you suggesting is physically comprising these mythical "infinitesimals"? What exactly is their nature, their size? Their speed? From the Wikipedia article Vacuum state "According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence."
If you don't want to se infinitesimals, don't. But you have to understand that a continuum is fundamentally different from a discrete system! Thus reasoning about one cannot be applied to the other. And what does vacuum particles have to do with this? mike4ty4 (talk) 00:30, 10 July 2009 (UTC)
You appear to not understand the questions I have asked. What are these infinitesimals of which you speak? Are they leptons, quarks, Higgs particles? What's their mass, their size? You appear to think that if there were no particles, no emf, no quantum vacuum in existence, that somehow "space" and "time" would still be present ... as what?. What exactly do you believe "space" and "time" to be? Perhaps you believe that in the pre Big Bang state, with no-thing in existence, "space" and "time" were still existent? Again, this seems to suggest you belief in some form of ether, that exists to carry emf and particles through space-time?. As I argue in my books, time is the experience of consecutive pulsations, or wave-functions popping or coagulating possibilities into lived physical experience. The firing of brain neurons, of electrical potentials leaping the synapses; OF electrical potentials building and "collapsing" possibilities into actual thoughts and experience ... that is the origin and basis of your sense of time. —Preceding unsigned comment added by Steaphen (talkcontribs) 10:30, 12 July 2009 (UTC)
They are not particles of any sort. They are mathematical structure added to the spacetime to try and salvage your misperceptions of how a continuum works. For the umpteenth time, a time continuum does not involve "one instant after another", as there is no well order. But I dropped the idea, it doesn't seem really to help. mike4ty4 (talk) 16:21, 12 July 2009 (UTC)
When these "fleeting electromagnetic waves and particles" (that comprise the vacuum of say deep space) pop out of existence, (let's assume they do so in unison, as per the thought-experiment below), are you still suggesting there is "space". What are you suggesting is actually physically existent when the stuff of "empty space" (a quantum vaccuum) is non-existent? What are you suggesting is "space" when there is no-thing there? The ether, presumably? You have experimental evidence of the ether?
So now you're going to say space doesn't even exist now? First it's space is discrete. Now it's space doesn't even exist. Hmm. mike4ty4 (talk) 00:30, 10 July 2009 (UTC)
FINALLY, you appear to be getting the idea. For somewhere around 10**43 times each second, our space AND time simply ceases to be physically existent. Zip, GONE. Not here. GONE. Like a particle, the whole universe does the same. Facts, trees, rocks, cats, computers, you, me. GONE. Not here.
Prove it. And again what are you using to measure this "interval" between each disappearance if there's no time? Youseem to be saying that they pop in "when" the spacetime doesn't exist... but there is no "when" if time doesn't exist! mike4ty4 (talk) 19:31, 10 July 2009 (UTC)
Indeed, prove it (that space-time is continuous). Not with symbols on paper, but with physical, repeatable, independently-verifiable evidence. As for there being no "when" ... that is precisely the point. It is your expectation of a "when" that is limiting your awareness and understanding. An at-once perception does not insist on any "when", only deep-felt recognition of, and appreciation for an infinitely encompassing "now."
Because the way you put it seems to require "when". You say "for somewhere around 1043 times each second, our space and time simply ceases to be physically existent". But that simply does not make any sense in a discrete space-time. In a discrete space-time, Do you get what I'm saying here? As for no proof of continuous space-time, no, there isn't any hard proof, but there isn't any hard proof it is discrete either. It is technically an open question. What I am really objecting to here is the idea you can somehow deduce discrete space-time from QM (that the mathematics somehow "telegraphs" this important idea), that Zeno's paradox requires discrete space-time to be resolved, and that what we have observed now in physics is incompatible with the idea of a continuous space-time. mike4ty4 (talk) 21:14, 11 July 2009 (UTC)
Space-time is either quantized or it is continuous. Choose the one you believe to be correct, and then argue your supporting evidence. I have suggested that the fundamental discontinuity of movement of quanta gives evidence of a quantized space-time.
I'm curious: how can you observe this discontinuous motion, when any attempt to measure the particle affects it? You can't just "watch a quantum particle in flight", you know. You mention 2-slit experiments. How did you manage to pull off the feat of watching the photon fly to the slits, making little discrete steps of 10-35 m every 10-43 s, which is what would argue strongly for a discrete space-time? I'm sure there would be quite a hefty Nobel Prize waiting for you if you have pulled that off! Furthermore I don't need to choose one, I can say that there isn't enough evidence to conclusively resolve it. mike4ty4 (talk) 16:17, 12 July 2009 (UTC)
Also, I don't have to "choose" one or the other, I can say the question is open, too, and refrain from making a conclusion as to which one holds. mike4ty4 (talk) 18:53, 14 July 2009 (UTC)
It seems to me that while you may be in the process of, or having completed various qualifications in physics and mathematics, you fail in the most important of scientific credentials ... to put forward thought-experiments or theories to provide credible explanations for the reality we experience. I note that you (and other respondents at this site) have not addressed the thought-experiments I've posted, or suggested any of your own. Despite your qualifications, I must at best give you (and fellow respondents, Sthinks et al) a C- for regurgitating accepted dogma, without any original thought-experiments or suggestions concerning the nature of our reality.
What sort of thought experiments are these? You mean the one with the particles "jumping"? But that in no way requires quantized space-time. Consider a mathematical function, defined on the continuum, describing the motion of a particle in time, i.e. x(t). Suppose we set this equal to a step function. That gives a jump. The function is not continuous at that jump, yet this does not at all deny the continuity of the real-number Continuum. Even better we can try out a Dirichlet function which would describe a motion that is continuous nowhere! So discontinuous motion is readily accomodated even in a continuum. To talk about "what happens as it is jumping" doesn't make much sense as that defies what a continuum is about: they are not "one thing after another". It's like asking: what real number comes "just after" 1? Basically you need to think the "jump" must "take some time". All this suggests that it seems you are hiding an unstated assumption of discreteness in the background, and that is the problem! You cannot assume what you are trying to prove, or you don't have a proof but just some question begging. What I want to is why exactly you consider these theories about continua, and quantum mechanics, to not be credible explanations. Zeno's paradoxes, as have been pointed out to you, do not pose the type of challenge you want them to. Can you provide a better challenge, then?
Step functions are reliant on indicator functions, which are reliant on set theory. Set theory is reliant on numerical continuity, which is the root assumption that I have disallowed and dismissed throughout my posts.
And why do you dismiss that? In other words what do you see so wrong with the possibility of a continuum of any sort? What is it about a continuum that makes it so abhorrent -- i.e. why are you disallowing the possibility? mike4ty4 (talk) 16:17, 12 July 2009 (UTC)
From Thomae's function "named after Johannes Karl Thomae, also known as the popcorn function, the raindrop function, the ruler function, the Riemann function or the Stars over Babylon (by John Horton Conway) is a modification of the Dirichlet function. This real-valued function f(x) is defined as follows: ..." The Dirichlet function being an indicator function
The irony of quoting these sorts of functions is that they reinforce the validity of a discrete space-time. Thomae's function has a "non-zero" result (ie. a physically tangible result) for f(x) = 1/q IF x=p/q is a rational number, while it is zero (i.e. not physical, real, or measurable), IF x is irrational.
What precisely are you suggesting is physically occuring when x is irrational, and there is no physically tangible result (in other words, when did you last touch zero of something, when was the last time you saw physical nothingness?)
Same thing that would be happening when it is rational. The particle is at the position described by the function given, namely at position zero.
This response has qualified you as either a troll, or incompetent in rudimentary analysis. This matter/thread relates to space-time: applying a step function to space-time means that a zero result means zero space, zero time = nothingness.
(Be careful there with that "troll" comment -- Wikipedia has certain rules that you may be pushing.) You still don't seem to be grasping the concept of what the function or coordinates are describing: relative position to a reference frame. x(t) is just a function describing a spatial coordinate (i.e. x) vs. a temporal one (i.e. t). If x = 0 or t = 0 that does not mean "nothingness", it just means a point coincident with the reference point of the coordinate system and reference frame. So when x(t) is 1, it means the particle is at the point that has been labeled "1" in the coordinate system. In the standard geometric coordinate system used, that would be a point at distance 1 from the point at 0 (see Cartesian coordinates and distance formula.) When x(t) is 0, it means the particle is at the point that has been labeled "0" in the coordinate system. So when I'd set it equal to a step or Dirichlet function, that would describe a particle that jumps discontinuously between the points with coordinates 0 and 1. Have you even seen a position-vs-time graph before? Have you ever even seen or used spatial coordinates? mike4ty4 (talk) 18:53, 14 July 2009 (UTC)
What is that? Just a position or point in space who has label "0"!
see above.
See mine above. mike4ty4 (talk) 18:53, 14 July 2009 (UTC)
I.e. it is the origin of the spatial reference frame we are using! Why is position zero any more or less special than position 1/2, or -1/2 unit?
see above
See mine above. mike4ty4 (talk) 18:53, 14 July 2009 (UTC)
If you hate it so much (which makes no sense since it is an arbitrary reference frame thing. I could easily label the point that is labeled "1", "0" if I wanted, and then by your logic that position somehow becomes "bad".), then try Dirichlet's or Thomae's function + 1. I really can't believe you would make this argument -- it is the worst one you have ever made up to this point.
ah, I see now, it is the former and the latter.
The former/latter what, exactly? mike4ty4 (talk) 18:53, 14 July 2009 (UTC)
It is just... amazing in how silly it is. If you have the simple concept of a reference frame or coordinate system, how are you going to grasp something as sophisticated as modern QM theory? mike4ty4 (talk) 16:17, 12 July 2009 (UTC)
To those serious thinkers reading this section, in view of the above, you'll appreciate why I discontinued any further replies. Had I received thoughtful responses - even from those of you who understand the dilemma, and who played devil's advocate - that would have been sufficient for my continued interest. But, your lack of input sees me off, to focus and work with those who understand and appreciate the issues and the implications. For those interested you'll find that various new articles related to this subject will be linked to the main article I wrote some time back "Congruent Solutions to Zeno's Paradoxes."Steaphen (talk) 11:56, 14 July 2009 (UTC)
I have given input, you just don't seem to like it. That last statement about "grasping something as sophisticated as modern QM" was by no means the crux of my argument, just a little comment about how far this was going... (self-nitpick note to anyone: there should be the words "trouble with" between "have" and "the" in that last bit.) mike4ty4 (talk) 18:53, 14 July 2009 (UTC)
Scientists who quote these sort of mathematical suppositions, base their arguments on a house of cards, upon the illusion of physical continuity. In effect, building supposition upon supposition, or "axioms". Again, nothing you've stated above, in referring to any of those functions, supports the idea of a continuous space-time. —Preceding unsigned comment added by Steaphen (talkcontribs) 01:49, 12 July 2009 (UTC)
Please provide evidence that numerical, geometric series apply directly, with absolute 1:1 (that is ONE to ONE) correspondence to the movement of physical particles, namely quantum particles, to show at least the modicum of evidence of a space-time continuum (in literal, physical terms).
Now, in interest of complete fairness and honesty, I will mention something that may provide a better challenge. It is similar but not identical to Zeno's paradoxes. It is called Thomson's lamp. In this experiment, imagine flipping a lamp switch over a period of time, say, 1 minute. The lamp is off. After half that interval elapses (30 seconds), you flip the switch to on. Then half of that interval (15 seconds) later, you flip it off. 7.5 seconds (half of that interval) after this flip, you flip it on again. And so on, and so on. So the question then is: what is it doing after the whole minute is elapsed? You could say it's "flipping infinitely quickly" but what does that mean? We could make an argument that this only occus in an idealized realm without restrictions. One restriction that may be possible would be, as you mention, to use a discrete space-time. Then we cannot flip it infinitely fast. So at the end of the minute, it is either on or off, dependin on the size of the quantum of discrete space-time (you mention 10-43 seconds, apparently the Planck time, although this is considered an observational limit, and a limit to current theories, not necessarily a fundamental discrete "quantum of space"). However, there could be other possibilites. We could imagine the lamp switch undergoes some sort of "phase transition" and enters some weird state where it now occupies both (like a quantum flux?). We can also say there is a speed limit as to how fast we can flip the switch. Such a speed-limit has been proven to exist. It is called light speed. Or that it requires an infinite amount of energy to flip the switch and we can't have that. Perhaps a more "meta" answer may be that some infinities are allowed, like those of motion, but those that lead to real problems, like the lamp-flipping, are not. Indeed the existence of energy requirements, and of light speed, seems to point in this direction. What would be interesting is if there existed some phenomenon that could in theory undergo infinite oscillation of nonvanishing magnitude, and require only finite energy. Then an experiment could be devised to crank it up toward infinity, and see if it hits a wall. Such a wall may be an argument in favor of discrete spacetime (though it would not be a conclusive one, as something else might be inhibiting the flipping -- further work would be required, but it would definitely be an interesting result.).
I encourage you along this path, towards thinking of thought-experiments to support your theories. Elsewhere I've dismissed your arguments as reflecting those of a technician, not as a serious thinker. In this reply, where you attempt a semblance of fitting theory to reality, you concede that the lamp switch "enters some weird state". When was the last time you physically witnessed a "weird state". What theory do you have to explain quantum superpositions? Experimental evidence has revealed superpositions of molecules. Entire teams of physicists are engaged in building quantum computers, based on the reality of superpositions of solid-state elements and compounds. Superposition states are fully accommodated by a discrete space-time within an infinite multiverse. The superpositions are merely alternate system particles, molecules, universes becoming near-visible, or having high "presence density."
They can also equally well be accomodated by a continuous space-time within an infinite multiverse. I do not see the need to make it discrete for it to work. Especially considering the whole edifice of quantum theory is based on a continuum. So if quantum theory, based on a continuum, works, then why the need to switch to a discretuum to make it work? Whether there really is a discretuum or continuum is not obtainable from this. This is what I have been trying to tell you all this time: that quantum theory does not make the proofs you want, nor does it require a discretuum (which is essentially saying QM is a self-contradictory theory as the theory is built on continuous space-time as part of its model. Note that this has nothing to do with whether spacetime really IS a continuum, but with the model of QM.). mike4ty4 (talk) 16:17, 12 July 2009 (UTC)
Again, I encourage you along the path towards a credible theory for the reality we experience.
Also, once again in interest of complete fairness and honesty, you may wish to make the claim that in my arguments I am making an unstated assumption as well, namely that of a continuum. Well, I will allow you to make that claim, and I will affirm that if you do, the claim is completely correct. But -- and this is the important part -- I am not trying to prove that space is a continuum. What I am instead trying to do is break down the idea you have that the "only good way out" is a discretuum and your claims to having answered the continuum-vs-discretuum problem. And also to point out some misguided notions you have about continua. If you want to challenge the idea of a continuum, then you should also at the same time have an understanding of it. It is a good idea to understand what it is you are challenging, no? And I am trying to point you in that direction. As mentioned, it seems you are advancing that you have arguments that can close the question of continuous vs. discrete spacetime in the discrete direction. Yet from what I've seen, they don't seem to work, and some contain elementary misapprehensions of physical theory. Orthodox theory may be all wrong. I make no claim that it is the final or the complete answer. I am just saying that I don't find your arguments for why and how it is wrong persuasive and telling you why I don't. As for why I don't posit any new original theories, because that's not the reason I come here. Rather it is that I don't agree with your specific ideas about why we should throw out, and what things we should throw out of, the already-accepted theories that have already been provided by hundreds or thousands of scientists. This doesn't even mean I consider them an unassailable dogma, either. But a challenge to them should do just that: be a challenge to them. If someone is saying "2+2=5", I won't agree, but why I won't agree is not because "my neighbor's cat has white hair". The latter argument does nothing to challenge the claim, no matter how wrong the claim may be. That may have been a crappy analogy, but what I'm saying is the truth-value of a claim and the arguments used for a specific truth-value are not the same thing. mike4ty4 (talk) 21:14, 11 July 2009 (UTC)
I think it is disingenuous of you to suggest "complete fairness and honesty" while attempting to argue your case based on an assumption (of a continuous space-time) which I assert is incorrect. I have offered a theory which fits the facts. You have not. By your own words you are "not trying to prove that space is a continuum." That is because you know you cannot. Whether or not thousands of scientists accept or argue a particular point is irrelevant. What theories do you have to support your beliefs? As for not offering new theories, but discounting any new ones that do, based on your assumptions of a continuous space-time, that again discounts you as a serious thinker, or "good scientist." As for my "misapprehensions" (sic), again, it is not the theory of continua that is at issue here, but of its full applicability to only our particular physical system.
And you cannot prove it is is a discretuum either. (Nor can I.) As I mentioned, the question is not conclusively resolved. The thing I have been arguing is that I see flaws in the arguments you have presented to dismiss the continuum idea, and conclusively resolve the question in favor of a discretuum. By "misapprehensions", I mean misunderstanding not just continuum theory but physical theory, including the ones you seek to question or use to bolster your arguments, such as QM, and now as was seen earlier, something as elementary as coordinate systems. mike4ty4 (talk) 16:17, 12 July 2009 (UTC)
Class assignment (have someone read this to you - or download {tba /mp3} from the Belief Clinic site): sit quietly, eyes closed. Focus on your breathing, relax. Allow your reasoning abilities to recognise the inherent limits of thoughts. Begin by imagining "circles" that encircle particular times, physical circumstances, world-views and scientific understanding - with cultural beliefs, religious beliefs and scientific facts forming the periphery of each circle. Imagine or visualise many such circles (different times and circumstances - past, present, future) existing within some broader "super-circle" - a timeless "now." Visualise how the separate circles must "float" on something, within some greater sea. Use reason to see that for this not to be the case, disconnects between various circles ("times") would exist, with no possibility of those times being bridged or journeyed. Imagine as many of these "circles" (times, circumstances) as you want, all being "in" some greater "super-circle" ("now"). Accept the possibility of having other senses that can and do connect you with other circles, right now, at-once. Focus again on your breathing, relax. Allow yourself to let go your immediate focus on yourself and the local environment (your present local "circle"). Fall into the experience. Feel the at-once nature of your body, the world and universe, being with you now, in this supportive sea. Let your awareness "spread out" like a wave, washing over and through other "circles", other times, other places. Feel light. Float, allow yourself to drift and be carried. Slowly, return your awareness to your local "circle" (physical environment, current time, identity, thoughts). Allow around 20 minutes for the whole exercise, varying and repeating as desired (3 x 20 minutes per day recommended). Return to your logic and sciences, the better for it. Ciao.
As before the Big Bang, so after it. As in the micro, so in the macro. As in the part, so in the whole. In between, not here. Not physical, but remaining in potential, continually popping (or "collapsing") back into reality. The whole shebang. Cycling (unfolding) into physicality, then back out again (enfolding), into an "at-once" timeless, interconnecting, interdependent nonlocal ground ("implicate order").
How does any of that require discrete spacetime? How does it require "unknowability"? mike4ty4 (talk) 18:17, 10 July 2009 (UTC)
As a courtesy, I shall explain that those of your replies which are inane and poorly-considered have been ignored.Steaphen (talk) 05:46, 11 July 2009 (UTC)
That cycling (which results in our quantized physicality) would give string theorists the fuller mathematical tools to more fully map and "explain" our physical system, as well as explaining fractals, as well as providing the deeper frameworks that accommodate both relativistic and quantum physics. Hint: Think of ocean waves + Mexican waves in crowds + brain dendrites firing (electrical potentials, signals leaping synapses, thoughts) ... what is it that is cycling, and what is it that is actually moving? Apply to waves in quantum theory and you have your answer as to what is really going on. I'm not a mathematician (not interested in the details), but I'm almost of a mind to go off and do the mathematics to prove the point! —Preceding unsigned comment added by Steaphen (talkcontribs) 03:39, 10 July 2009 (UTC)
And what's that? (What you get when you apply it to waves in quantum theory?) Furthermore all the phenomena you mention are already explained with regular physics and finally you yourself said that there are key things that cannot be expressed with equations! So how pray tell are you going to possibly come up with fuller "mathematical" tools when by your OWN admission mathematics just doesn't cut the cake! mike4ty4 (talk) 18:17, 10 July 2009 (UTC)
Thought experiment "In phase with no-thing":
A particle "jumps" from point A to point B. Particle does not travel the space in between. Standard quantum theory.
Quantum theory does not say that a particle "jumps" from point A to B. Rather quantum theory describes (in one picture) a "wave function" that evolves CONTINUOUSLY in space and time. Nothing "jumps". The idea that electrons "jump" around in the orbitals of an atom, for example, is a popular misperception of quantum theory. Standard quantum theory says that in this case of such a spread wave packet, the particle is in some sense at both point A and point B at once, it does not "jump". With, say, Copenhagen interpretation, when the position is "measured" then the wave "collapses" to some point randomly, with a probability factor determined by that wave function. With MWI (many worlds interpretation which you seem to like the best), there is no "collapse", rather the particle keeps on following Schrodinger's equation, the wave function continues to spread, undulate, etc. continuously. There is no discrete, no jump, none of that. Do you mean for example the transitions between quantized energy levels of an atom? If so, such a transition is not a discrete jump either (and I don't see how it would prove discrete space time even if it was), but rather the wave develops more undulations until it stabilizes at the new energy level. mike4ty4 (talk) 22:07, 6 July 2009 (UTC)
When was the last time you physically saw a wave-function? Wave functions are a handy and reliable mathematical guess as to the underlying cause of particles popping up here and there, and not in between. The physically observed interference patterns (in double-slit experiments) occur after many particle or photon impressions. The wave is then inferred from the pattern. Yes, that which is "represented" by wave-functions evolve continuously, but not only in our space-time. If that were the case, AGAIN, we could expect completely smooth motion of quanta. We don't and we can't.
When a 2-slit experiment is done, you are only seeing the end results, the collisions of particles with the screen. You do not see the "flight path". So why do you think it is "jumping"? And furthermore how does this have to do anything with spacetime???? mike4ty4 (talk) 19:59, 7 July 2009 (UTC)
Again, it is the use of mathematics as being a concrete, absolute map of, and 1:1 correspondence with our physical system that is at issue here. THe wave-function you refer to defines the range of possibilities, NEVER the actuality. That is why we have the collapse of the wave-function (= possibility), to observed particle (= actuality.). If you can refute this, you'll have explained the cause of the wave-function collapse. Nobel prize is yours.
Depends on the interpretation you use. In MWI, there is no such thing as wave function "collapse". And if you can explain it with your model, why don't you go and claim that Nobel prize? mike4ty4 (talk) 19:59, 7 July 2009 (UTC)
Indeed, where is my Nobel Prize! MWI is partially correct, but misses the most important ingredient. To think that the universe splits or bifurcates as a result of a choice is just, well, bizarre to say the least. Not to mention a little arrogant ...
This idea of "splitting" may not be correct: [1] "The common misconception regarding the Many-Worlds Interpretation is the at some instance the universe splits into two magic, seperate copies where one universe observed the outcome of a measurement one way, and the other universe observed the outcome to be another. This represents

a fundamental misunderstanding of Everett’s ideas, because this is inconsistent with the Everett Postulate: the two separate terms in Eqn. 3 could exhibit interference." and furthermore the idea it "splits" as a result of choice looks dubious, as I've heard that it splits when there's a "measurement", which isn't so much the same as "making a choice". mike4ty4 (talk) 00:44, 9 July 2009 (UTC)

Now, let's assume that, due to a freak of nature, every particle in existence (even those near absolute zero), including those that comprise your eyes and brains, happen to move in exact synchronisation with that particle (time-wise). Now, tell me, in that moment that occurs between point A and B, which must exist physically! according to your belief system, what do you see? And what exactly are you using to see with? Furthermore, where exactly are you?
And another thing -- I have some major questions about this "paradigm" you propose. I read some of the stuff on your website. Namely in one part you say "The world around us exists with us, at-once. No science* or system of thought or philosophy can fully reveal or account for this "at-once" (nonlocal) nature of life." No system can account for it -- so then wouldn't that imply your theory/paradigm can't account for it either? And you say "As is more fully explained in our seminars8, left-wing and right-wing biases are not sustainable – favouring one side at the expense of the other ends up being at the expense of both, as required by KPLL 1 and 2." yet you mention also that things other than either-or are not knowable: "In view of the inability to fully reveal this at-once nature, KPLL No. 2 requires that there will remain aspects of, and potentials within, everyday experience that cannot be entirely reduced to any knowable order (science, equation, academic discipline, physiology, profession, body of experience etc)" (from Emphases mine.). So then basically it seems you on one hand seem to be claiming that this "either or" thing is bad and must be done away with, and yet on the other hand, you seem to be claiming that it cannot be avoided! What's up here?
"major questions" - you and the majority, I would expect.
No system, that can be boxed, labelled, or identified, can account for it = correct. However, a felt sense of something beyond ourselves (e.g. as one feels the sense of community, beyond oneself) is not contradicting the idea of both individual, finite, physical within a multidimensional, meta-physical existence that can't be fully reduced to limited concepts. They are both true, at the same time.
I think the deeper issue here is your attempt to fit the whole of all existence, into some physical, conceptual model. That attempt, from my limited understanding of religious and spiritual traditions across all cultures, is a futile endeavour.
Nope, not at all. There is no theory of EVERYthing nor must EVERYthing be limited to physical (atoms, energy, etc.). mike4ty4 (talk) 22:07, 6 July 2009 (UTC)
As for the apparent contradictions in my work, as explained in more detail in "Apparent contradictions within the TOA" (which you appear to not have read, or understood) the contradictions are only apparent due to limited, sequential perceptions of the deeper at-once nature of life.
So what about non-sequential perception of it? 22:05, 6 July 2009 (UTC)
non-sequential perception has been voiced by sages throughout the ages. It's when definitive descriptions are made concerning those experiences (e.g. by religion) that the troubles begin.
So what do you propose to be done with it in your frame-work, if it cannot be written down? mike4ty4 (talk) 19:59, 7 July 2009 (UTC)
The solution is to include or straddle both, the finite-known/knowable (science) while remaining open to that which will remain infinite & unknowable. The Taoist and Buddhist philosophies come close in this regard "if you speak the truth, it is not the truth" style of paradox, or Koans. Where the Taoists and Buddhists go wrong, so to speak, is to stay too much in that contemplative receptive state whereby nothing much of interest gets done (scientifically).
So what do you propose to do with these "unknowables" then anyway? Does anything of interest get done anyways other than scientifically? How do these unknowables factor into a search for knowledge? mike4ty4 (talk) 00:44, 9 July 2009 (UTC)
My apologies, I did not explain myself well. Any original, new scientific understanding comes first by feeling into the "unknowable", or "the great chaos" (see quote by Lagencrantz below). Einstein was first and foremost, intuitively, artistically orientated (as is amply explained in Ronald W Clark's biography of him). Einstein, as he explained, wasn't much interested in the details (he wasn't a good mathematician because he wasn't much bothered to be one) - he wanted to know the mind of God, the rest was details. Same for any inventor, scientist or entrepreneur who originates new ideas, products and services. Feelings & intuitions first, then with the details - the logic, the mathematics, the science, the technical details etc. As a general rule entrepreneurs, a famous one in particular, don't much bother with the science or logic of what they will achieve ... they employ people to work out the details after they've decided the next impossible thing they or their company will being doing.
So then how is this something wildly different than what is already done? As you mentioned, it is all what Einstein and pretty much anyone else who comes up with something new, does. I do not see the "earthshaking" here. mike4ty4 (talk) 00:30, 10 July 2009 (UTC)
Biographer Olof Lagencrantz wrote of famed Swedish writer, August Strindberg: “Strindberg’s intuitive awareness that everything is infinitely interconnected fired its lightning bolts into the great chaos—the starting-point of it all."
The Western religious tradition of blasphemy comes from this awareness of the paradox of finite-knowable within infinite-unknowable; i.e. to make some image of "God" is to attempt to describe (limit) the indescribable (infinite). Any image, written description (e.g. as contained in any religious text) or conceptualisation is therefore "not" a valid depiction of "God". That's the origin (I sense) for the punishment of those who attempt to do so. Technically speaking, even speaking the word "God" or "Allah" is a blasphemy, as any word spoken is a limiting description of that which remains beyond description. If you look closely at many traditions there is often deep wisdom within them, even though the original intent is now misunderstood, or lost. As previously explained, a quantized local physicality within a nonlocal infinite multiverse (a holodynamic systems view) accommodates religious and spiritual traditions ("He who knows himself knows his lord," (Islam); "By understanding the Self, all this universe is known" (Upanishads); and similar)
First off, I'd agree with the idea that God cannot be imaged, described, etc. But what I don't get, and can't get, is this last part, namely how _quantized space_ plus an infinite multiverse -- which is technically still physical still since you are using quantum physics to get the idea (You mention Everett's many-worlds thing) -- somehow solves religious and spiritual (which is beyond physical) matters! mike4ty4 (talk) 00:30, 10 July 2009 (UTC)
As explained above, and as a courtesy, those of your replies which are inane and poorly considered have been ignored.
I'm not sure though what makes them poorly considered or inane. And if I don't understand it, then why don't you tell me the error, so I can? mike4ty4 (talk) 21:14, 11 July 2009 (UTC)
Similarly, mathematicians' use of the concept "infinite", no matter how it is defined is invalid. The infinite not only cannot be named, voiced or conceptualised, it can't be imagined, or even alluded too. It is, if you like, "immathematical". Cantor's "transfinite" nomenclature was more appropriate.Steaphen (talk) 15:47, 8 July 2009 (UTC)
Yet you have mentioned that non-conceivable "unknowable" things exist and are important. mike4ty4 (talk) 00:30, 10 July 2009 (UTC)
As for labelling things "bad" or "good" such judgements are reliant on comparisons, which if you were to read the material at my site, is due to racial immaturity of seeing a hierarchical order as being primary to existence.
I'm not sure what is being labeled "bad" or "good" here. 22
05, 6 July 2009 (UTC)
ask yourself (see above) - it was you(?) who originally questioned "what's so bad about ..." etc.
What's that supposed to mean? I don't recall or notice where I used the terms "good" or "bad". Then again I've gotten sort of lost in this mess of posts. mike4ty4 (talk) 19:59, 7 July 2009 (UTC)
The basic message I espouse is that when one favours "one-side", it is often at the expense of the other. "Human Rights" for example, usually favours the human individual, at the expense of community cohesiveness. Notice that in your country (USA), a focus on human rights, individualism, and the right to bear arms (against whom?) is at the expense of "community rights" for a cohesive, safe environment. Eastern countries are biased towards the collective, which is why they aren't so good on individual "human rights".
This is right. So how would you propose to merge that and go beyond the "either-or"? Here I would agree. Doing this "either-or" thing here is not a good way to go. Both Western and Eastern systems are lacking and create problems in some areas. mike4ty4 (talk) 22:07, 6 July 2009 (UTC)
Same goes for New-Age beliefs.. A bias towards "higher-self" and being "spiritual" is nearly always at the expense of ego, reason, individuality and effectiveness.
And yes, again, I assert that science and religion are "sister belief-systems", because both objectify the causal agent for self-organising systems (bodies, cultures, universe) as being "outside" or independent of the system. Hence why standard evolutionary theories are not much better than saying "God caused it".Steaphen (talk) 14:41, 6 July 2009 (UTC)
The underlying issue in Western culture is one of a fundamental disconnect by both religion and science. As confirmed by a recent CNN report (Pew Research Center) "The more often Americans go to church, the more likely they are to support the torture of suspected terrorists." Replace "church" by "science"; "torture" with "experiment" and "of suspected terrorists" with "on live animals" and you'll appreciate the parallel. That's part of the reason the USA, despite being one of the most technologically developed, is also one of the most religious.
Again I might agree here as well. (Though I don't see how butchering QM is going to help.) Real science and real religion would not conflict nor would there be any disconnect. If, say, those Americans followed real religion, they would not support the torture of the terrorists. If the terrorists followed real religion they wouldn't be terrorists. If science and religion worked together, then such live animal experiments would probably not be done much if at all, because the real religion would provide a moral compass that steers away from that. It would seem that what is taught in those churches (which I never attended, by the way), is not real religion, but a fraud that causes damage. mike4ty4 (talk) 22:40, 6 July 2009 (UTC)
"Real" science implies there is some independent field of study that is objective and separate to the field of religion. If you combine both, you no longer have a "real" science or religion, but a subjective, felt appreciation for emerging probabilities within this self-organising system. A felt sense that is fully appreciative of quantum theory, and classical physics and that they are both only steps towards understanding a far deeper, nonlocal existence.Steaphen (talk) 00:13, 7 July 2009 (UTC)
What do you call "real" science? And how do you propose to understand the thing? mike4ty4 (talk) 19:59, 7 July 2009 (UTC)
Then I saw this which you mentioned to a poster earlier. You(?) seem to be suggesting there that we are responsible for all reality... yet where did we come from then? What about before we existed? Where are the quantum laws coming from? What if we were to go extinct? Just like that, poof, dead, gone? Also, this page again mentions about quantum physics/mechanics being important here. Yet how does QM imply all of this? From what I've seen of QM, I don't see how you can get this stuff out of it. Not even from MWI. mike4ty4 (talk) 09:59, 6 July 2009 (UTC)
The "quantum laws" come from "no-thing", just as the did the universe, via the Big-Bang. The TOA affirms that the universe is continually "banging on" somewhere around 10**43 times each second, so the Big-Bang was nothing special, in that context. If you understand the basic model, then you'll appreciate how it fits observable reality (and all others, in whichever state of mind or reality).
Steaphen (talk) 11:18, 6 July 2009 (UTC)
update 2, by Steaphen
Mike4ty4, your question prompted me to do something I have not previously done - to Google "evidence discrete universe". Improbable as it might seem, I've not really done much research on this issue - as I mentioned above it's a done deal as far as I'm concerned, based on straight-forward reasoning. But your question prompted my interest "is anyone else in the same ballpark?"
The google search 1st page response included a link to Jim Elvidge's book "Universe Solved" with this link revealing a section "Evidence - Our Discrete World", in which he argues our physical world/universe is discrete. The Google Books site has "search inside" which reveals some of his arguments which are, in my opinion, well formed, cogent, good.
and this page (author?) (Is Space-time discrete?... with good, balanced inquiry into the idea "... it may be possible to satisfy everyone by invoking a discrete structure of space-time without abandoning the continuum theories if the discrete-continuum duality can be resolved as it was for light and matter." (This parallels the basis of my original Table of One and All: One discrete-individual within All collective-continuum. No one has reported any exceptions to its universal applicability). —Preceding unsigned comment added by Steaphen (talkcontribs) 06:08, 5 July 2009 (UTC)
also this page (American Scientist), basically, same idea... evidence points to a discrete space-time.
Done deal, as I said. Only thing remaining is shifting the rest of the populace into gear (and given we're either at, or soon to pass through 'Peak Oil' AND 'Peak Resources' (e.g. copper), it seems this shift needs a bit of a giddy-up.
Steaphen (talk) 01:44, 5 July 2009 (UTC)

I don't want to get too deeply involved in this discussion, but I'm going to make one point and then disappear.

Steaphan, this last comment shows how little you understand the scientific process. If you find two or three sources that argue for one viewpoint, it does not make it a "Done deal." If that were the universal standard in science, then we would all believe that the Earth is a cube because it says so (or something like that) on .

There is evidence that suggests a discrete spacetime; if you look deeper, you will also find a lot of evidence that suggests a continuous spacetime. Right now, continuous spacetime describes everything that discrete spacetime does (and more). This situation may change in the future, but the vast majority of the scientific community feels absolutely no need to invoke discrete spacetime to explain anything.

In fact, the only people who are really trying (the Loop Quantum Gravity people) have gotten nowhere. As I understand it, they can't even reproduce Minkowski space, much less all of general relativity. I admire their valiant efforts, but discrete spacetime is hard to work with, and no one knows of any "new predictions" that it can make that the old continuous spacetime does not. As such, no evidence can decide between the two theories right now, and on top of that, discrete spacetime has a lot of work to do just to reproduce all of the results of continuous spacetime (which has not been done yet).

Please learn about the scientific method before you continue this (already overdrawn) conversation! —Preceding unsigned comment added by (talk) 13:17, 17 July 2009 (UTC)

  1. ^ Nicholas Wroe, “The happy pessimist,” quoting 1972 Booker Prize winning novelist John Berger, The Sydney Morning Herald, John Fairfax Holdings Ltd, Saturday April 10, 1999. Good Weekend, page 35.
  2. ^ Madeleine Nash, "Unfinished Symphony", Time, December 31, 1999, page 61