What is Quantum Wave Cosmology discussion thread

Discussion in 'Pseudoscience Archive' started by quantum_wave, Jul 13, 2009.

  1. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    This post, http://www.sciforums.com/showpost.php?p=2311129&postcount=66, is incorporated in the Google.doc by reference to support one of the main features of QWC:

    QWC is constructed on the very basis that the universe exists and did not come from nothing, therefore it has always existed.

    That post discusses the presented link that supported my thinking that the universe has always existed. You might remember that link was one a many different opinions about the origin of the universe, but it is in line with my primary objective of having an internally consistent set of speculations that go beyond where the consensus of science has taken us so far.

    The next step and actually the first step in the speculations of Quantum Wave Cosmology is the cause of the initial expansion of our observable universe.

    Expansion is observable. The nature of our arena in space which is referred to by the standard cosmology as our “universe” is demoted to an arena that exists within a greater universe. That is a conclusion in QWC based on the idea that if the universe has always existed then space, time and energy too have always existed. Those are characteristics of the greater universe within which our arena exists and within which our observable universe got its initial expansion momentum. In QWC the greater universe is potentially infinite spatially and so our tiny arena consisting of a finite amount of energy is considered infinitesimal relative to that spatial infinity. That brings up the concept of the multiverse which simply means that in QWC there are considered to be a potentially infinite number of arenas similar to our own.

    Step one of QWC is to select from the various multiverses that have been theorized and contemplated. That is why I give you the “multiverse” link in a recent post.

    If you read that link you see that there are many choices that fit the multiverse concept but when you add the requirement that the arenas exist within the same greater universe that contains all space, then there only needs to be three dimensions of space to host the entire universe and all of its arenas. That eliminates the multi-dimensional cosmologies.

    Out of all of the possibilities, we can also eliminate those that require a beginning of time since QWC includes the idea that the universe has always existed. The inflationary scenarios are fine as far as they go but if they don't say what caused the initial expansion they too are eliminated from consideration in QWC. So from my view, if a cosmology doesn't address the issue of its beginning it is not complete. As mentioned throughout the thread, that is the motivation for QWC, i.e. to have a physical picture of a complete and internally consistent cosmology.

    Several models refer to ways that our arena might have come into existence and how expansion might have been initiated though none of the models in the link actually say that they are based on a universe that has always existed and that includes infinite space, time and energy.

    Do you agree that there are no alternative cosmologies that come right out and say that? That is what QWC comes right out and says. So step one is to define the circumstances within such a universe that could give rise to our arena. That is what I have done. I refer to it as step one which appears in the Google.doc after the introductory section on “What is Quantum Wave Cosmology”.

    You can view the updated Google.doc: http://docs.google.com/View?id=dgzb43gp_6dtnkzxg9
     
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  3. AlphaNumeric Fully ionized Registered Senior Member

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    Then it has no predictive power. If it's something deep and fundamental, enough to reach beyond what current science can do, then it must have basic postulates from which you derive your implications, your predictions. Now if all you do is look at experimental results and twist a wordy explaination to fit the results, what predictive power have QWC got?

    An experiment says "X = 4" and you say "QWC says X=4". Then the next day another experiment says "X=5", do you change and say "QWC says X=5, QWC explains X" ? Because if you do then you're basically saying QWC is useless, without predictive power, without coherent structure, without any explanatory power at all.

    QWC, so you say, is all about talking about the areas where current science doesn't tread much, such as pre-BB. Now if the results of QWC are so fluid and mailable then how can we take any result you claim seriously, when you could just change it to be something else?

    Give me a single precise prediction of QWC and explain why it's that and not something else which I could suggest.
     
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  5. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    I understand exactly what you are saying. And yes, if the standard cosmology, BBT ever is replaced by a new consensus then I will modify QWC. The modification will center around just how much the new standard cosmology does to address the cause of the initial expansion of our observable universe, the cause of mass, and the cause of gravity.

    As for your question about how QWC can be taken seriously by professionals like yourself in the light of the fact that I can change it on my whim, think about what you just asked. There aren't any professionals that are interested in QWC except you, Prometheus and Oli whose role it is to discredit it so that our youth are not mislead by the treacherous QW, right.

    As for the predictive power of QWC, it is all prediction of the unknown. When science stops short of forming a consensus then I call that the unknown from my non-professional view point. A professional has a different methodology to claim predictive power. My methodology, when applied faithfully yields a cosmology that is satisfactory to me and that fulfills the prime objective.

    Part of the methodology is to envision a physical picture of how the universe works that satisfies me at the moment and that can continually be improved by continuing to apply the methodology. If you or anyone contributes something I can use I appreciate it. But it is unlikely that professionals would bother. In addition QWC uses no ones theory and professionals are seeped in their theories.

    Math can be made to say up is down or sideways, but unless the math has a perfect correspondence to reality, it cannot accurately predict reality. That is why QWC is a bottom up, step-by-step collaborative process of reasonable and responsible speculation. Accidentally maybe, I address things that there are already theories for beyond the consensus but that is only because observations lead to ideas and neither science nor I claim to have a corner on the idea market.

    It is entirely possible that I will talk about existing theories in my physical picture without acknowledging who's theory it is or what has been said by it or what the math might be. But I tie in my ideas (new or not) with the entire body of QWC so I can envision it having internal consistency where if the math were put to it, the math would all work together.
    This is so boring. Your ego needed a little boost didn't it. Just saying that made you get a tingly feeling I bet. Give me one reason I should engage with anyone with a record of just waiting to strike (rhetorical).
     
    Last edited: Jul 18, 2009
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  7. Ophiolite Valued Senior Member

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    Mental institutions used to be full of people who thought they were Napoleon. They were perfectly happy, but they weren't Napoleon.
     
  8. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    Come on Ophiolite, Napoleon? I'm trying to write into this that this is my own view of cosmology and that I am trying to make it a physical picture that I can visualize where a possible cause of expansion is the starting point. Then going from there step by step using a stated methodology of speculation and not using existing theory except what fits together to maintain internal consistency.

    I gave you links to support the view that nothing can come from nothing, I did some math to show that math can be made to say anything, I gave you links to alternative cosmologies that are already well known, and gave you my Google.doc which is open for you to help shape.

    Now I am about to actually get into the steps and I want views from the community about each step.

    But maybe you are saying that the Napoleon part is that I have a prime objective, or the fact that only I can maintain the document, or maybe the outward view that I won't engage with Prom/AN though I actually am when it is necessary to keep them around.

    Or is it still that my writing is crap and you haven't been able to discern anything from it because it causes you nausea? I did start applying your advice and set up an introduction, I incorporated your improved text in the first paragraph, I added a caution to parents and youth which should be sufficient to tell people this is dangerous stuff.

    I have fulfilled my prime objective and I plan to maintain my satisfaction as I just keep improving the document by continuing to apply the methodology and to fill out the as yet unpresented ideas. It is just a game now. You don't have to play and I don't have to engage anyone who doesn't want to play by my rules. Didn't Napoleon venture out and try to concur the world? I'm happy just staying in my threads, occasionally adding my two cents on other threads as long as I don't violate forum rules, etc.

    :humor: But if keeping you around means taking your hurtful jabs and having to feel remorse about how bad a job I do on my threads, feeling the dejection from people like you and never getting any attaboys like the self proclaimed forum experts get when they dis me, then so be it :bawl:.
     
  9. prometheus viva voce! Registered Senior Member

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    Apologies for the rudeness, but this is bollocks.
     
  10. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    Is not.
     
  11. AlphaNumeric Fully ionized Registered Senior Member

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    So it's the physics version of 'God of the Gaps'. It explains things we don't understand and when we expand our understanding, it's pushed into being applied to smaller and smaller regions of applicability, each time providing nothing other than a buzzword laddened version of "God did it", which is an 'explanation' which explains nothing.

    You have no grasp of how maths and physics intertwine or how you use maths as a language to describe physics, due to your unwillingness or inability to see how physics has been done by professionals.

    It's 'boring' and inappropriate of me to ask you to provide one result from your work for which you couldn't just as easily have provided to exact opposite/negation of instead? I'm asking you to show your work is more than just your guess work about things which you don't understand but I guess something you said sums it up :

    In other words you dislike mainstream physics (for reasons I'd imagine are close to the fact that you can't understand it) so you're going to provide explainations for things which you find palettable. And what if the universe isn't to your liking? You're basically saying "I'm going to ignore reality and just come up with stuff I like", irrespective of the truth.
     
  12. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    Let me refer you to the OP and the Google.doc.
     
  13. AlphaNumeric Fully ionized Registered Senior Member

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    That does nothing to negate or address what I've said. If all you're doing is writing stories which you find more acceptable than what nature is perhaps actually like then why should anyone read the Google document? Why should anyone want to listen to your fiction writing skills if they are interested in science?
     
  14. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    Because they wonder what on Earth could be so treacherous that you would try to keep them from reading it? http://docs.google.com/View?id=dgzb43gp_6dtnkzxg9
     
    Last edited: Jul 19, 2009
  15. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    The last meaningful post was:

    http://www.sciforums.com/showpost.php?p=2313378&postcount=81

    To summarize, QWC is constructed on the very basis that the universe exists and did not come from nothing, therefore it has always existed. This link presents support for that idea:

    http://www.thekeyboard.org.uk/Where%...rse from.htm

    I discussed that link here:

    http://www.sciforums.com/showpost.php?p=2311129&postcount=66

    The next step and actually the first step in the speculations of Quantum Wave Cosmology is the cause of the initial expansion of our observable universe.

    As described earlier, QWC demotes our expanding observable universe to an unremarkable arena within the greater universe and brings us to the discussion of multiverses:

    http://www.google.com/search?hl=en&q...tivers&aqi=g10

    1.5 million Links discuss multiverses but this one covers the topic nicely:

    http://en.wikipedia.org/wiki/Multiverse and is discussed in post 81 linked above.

    QWC comes right out and describes the ideas about the circumstances that preceded the Big Bang event. Please notice that is something that Big Bang Theory, which is touted by most professional scientists, will not do. It is clear that the reason they don’t discuss “before” the Big Bang or what caused the Big Bang is that the theory they tout says there was no “before” and that it is nonsense to even talk about it. If they tout the theory they have to agree that there was a beginning (something from nothing?), and that space and time are coupled into a continuum that is warped by the presence of mass.

    I personally conclude that it is not just that BBT is the best we can do so far, I also conclude that it is peer pressure and that working science professionals cannot speculate about “before” the Big Bang because if they do they are ridiculed. To a professional, that kind of ridicule can effectively end their career. At least it could block their advancement unless their focus is in areas that attempt to reconcile that thinking with other theories that are mathematically incompatible with BBT but that are also considered mainstream.

    Being a non-professional I can rely on what people say “off the record” and there is a large “off the record” body of speculation out there.

    What this post is getting around to saying is that from all of the alternative cosmologies and multiverse ideas, QWC finds the best logic in the idea that the expansion of our observable universe was preceded by a big crunch.

    Comment now if you disagree with the idea of a big crunch preceding the Big Bang and state why you disagree.

    In the Google.doc I begin the discussion of the big crunch in I. "Step One of QWC": http://docs.google.com/View?id=dgzb43gp_6dtnkzxg9 .

    Read I. "Step One of QWC" now and remember, you must be 18 years of age or be accompanied by an adult to read this document according to Prometheus, AlphaNumeric, Oli and a host of others who say it is nonsense to talk about “before” the Big Bang.
     
  16. AlphaNumeric Fully ionized Registered Senior Member

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    I never said that. I have been trying to make the point that why should anyone believe your 'results' are better and more worthy of their attention than simply making things up?

    There's a lot of information in the world of physics, much much more than any one person can get through in their lifetime so people prioritise, looking first at what they view will be the most promising, more useful, more interesting. You have freely admitted that QWC is pure speculation and, despite my repeated requests, you cannot derive a single result in a logical manner from any postulates. If you truely want to be taken seriously you have to convince actual physicists your work is worth looking at, that it's better for them to spend time reading your work than doing their current research. Given you've utterly failed to provide any reason for such action to any of the people here who have research related real lives (ie myself, Prom, Ben, Guest, DH etc) you have failed to reach your goal. Unless your goal is just to make claims you can't back up?

    Your work is better than Guest's 'fairy theory' why? Why should I spend time reading your work, instead of talking to Guest about fairies? What makes your work superior to that? Nothing.
     
  17. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    Among the proud claims of Big Bang Theory advocates is that BBT is the best that we can do, the math works at all scales right down to the Planck regime, the theory explains what we observe without needing any new physics, the theory has made many predictions that have proven to be correct, and the theory brands as nonsense any discussion about other origins of the universe besides “it came from nothing” because they don’t know what that “nothing” was.

    Buy why are they so proud? Ask what preceded the Big Bang and they confidently say “nothing”. And I don’t mean they stand silent before you, I mean they say that nothing preceded the Big Bang because the Big Bang was the beginning of space and time. They tout their main theory of cosmology by saying that they don’t know what caused the initial expansion of our observable universe but whatever it was it was nothing but the beginning.

    That is why I have a personal cosmology called Quantum Wave Cosmology:

    In the Google.doc I discuss my motivation and methodology and I begin the discussion the steps of QWC with the big crunch in I., "Step One of QWC": http://docs.google.com/View?id=dgzb43gp_6dtnkzxg9.

    According to the methodology that I employ, you are able to shape QWC by commenting and explaining your comments. Changes to the document are made by me based on your comments if I find that you have added something useful.
     
  18. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    Several people have read the last meaningful post on this thread. This thread has been viewed only about 20 times by people other than me since that last content post. AlphaNumeric viewed that post and posted to the thread accounting for maybe 4 views, and I saw D H reading it so that accounts for one or two more views. Maybe Prometheus, Ophiolite, and Oli viewed it but I don’t know that for sure. That says that there may be three or four other people who viewed the thread to see what was said, and maybe two or three just clicking on it momentarily but having no interest in it.

    Not one member of the community sees anything worth commenting on in Step I. which identifies a big crunch as the circumstances that preceded the Big Bang?

    I mentioned and you know that science professionals by and large remain advocates of BBT and the fact is that if they didn’t they would lose stature with their peers. No one denied that when I said it. So we can’t expect any professionals to condone my speculations, and we can expect the self proclaimed experts who say they know what is and is not cosmology to weigh in “against” the idea that the Big Bang was preceded by a big crunch.

    We have to imagine that off the record there are conversations and debates among scientists in many quarters that are planning the evolution of BBT to move it forward without abandoning the start of space and time, i.e. a beginning that is required by General Relativity. The equivocation of their stance and the acknowledged need for evolution of BBT must be a fact of life within scientific circles. But it is a sticky matter to bring about that evolution.

    Name a professional who wants to be the first to say that maybe something physical preceded the expansion of our observable universe? Who wants to be the first to suggest that space might have pre-existed? Who wants to say that matter cannot come from empty space so if empty space did pre-exist the Big Bang, where did the energy come from? How could matter exist in empty space if they don’t insist that there can be infinite density within empty space that does not itself occupy space? If they were to take those stances they would be limiting their careers in the short term.

    That is why change comes slowly to the standard cosmology. Until they evolve BBT they can’t hope to explain the cause of the Big Bang. Can you wait for them to move? You will be dead before the standard cosmology addresses the cause of the initial expansion of our observable universe.

    Jump in and say it wasn’t a big crunch because you have a different idea. Or jump in and say it just might have been a big crunch. Or weigh in with the professionals and say that “nothing” preceded the Big Bang. I don’t want you to come back later and say the big crunch idea is crap. Say it is crap now and say why it is crap.
     
  19. Ophiolite Valued Senior Member

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    All of your writing has the appearance of speculation that is devoid of any consideration of reality. You may be being imaginative, but it is the same imagination that generates fantasy stories. There is nothing wrong with fantasies, until we start thinking they may be real.

    They do not prove that nothing can come from nothing, therefore they do not provide a rock solid foundation for your entire thesis. This is akin to what Oli(?) pointed out, that your axioms were not actually axioms.

    As prometheus said, bollocks. If you actually believe that you demonstrated that you are even more foolish and uneducated than I gave you credit for.

    No, the reference to Napoleon is that you are ****ing delusional.
    You said you were perfectly happy with how things were going with QWC.
    I pointed out that some people thought they were Napoleon. They were happy, but they weren't Napoleon. i.e. you may be happy with QWC that does not mean that anything about it is correct.

    Dangerous?

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    You credit yourself and your ideas with way to much importance.
    More self indulgence.
     
  20. Ophiolite Valued Senior Member

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    You really have to be called to account for this persistent strawman.

    Most Big Bang proponents do not have anything to say about what came before the Big Bang.
    This is pretty much the same as evolutionists. They do not have much to say about how life originated. They might be intrigued about how it arose, but it is a subject well outside their speciality. Are you going to continue to be like the religious nutters who conflate abiogenesis and evolution?

    Most Big Bang proponents do not claim that Big Bang originated from nothing. Those who express a view are more likely to say that they have no bloody idea.

    Some Big Bang proponents are starting to envisage ways in which we might probe the reality 'before' the Big Bang. It is highly speculative, but the speculations are founded on valid observations and the IFs are very well highlighted, not taken as axiomatic.

    So please stop putting false words into the mouths of BBT proponents and then attacking those false words. It is a cheap and ignorant trick.
     
  21. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    Prometheus and now you are denying the obvious. Math can be made to say anything, period. You are delusional if you think otherwise. You are intellectually dishonest if you say that and know otherwise.
    You are not following closely enough. The fear for our children has been voiced by Prometheus, AN, and Oli. Go back and read what you are so anxious to discredit.

    Talk about straw men.
    You should try to familiarize yourself with BBT. They don't have to say it came from nothing anymore than they say what caused the expansion in the first place. They don't say. But look at the writing about BBT over the years and you will see that they do not deny that it is implied that the entire universe emerged from an infinitely dense zero volume point in space. I call that nothing. What exactly do you call it? Would you answer that for me; of course not.
    I seem to be more aware than you are of where the professionals are going with this and why. You seem to be talking about my lack of understanding when it is much more likely that you are the one that doesn't know what you are talking about.
    Most scientific professionals are able to put their science into perspective with the past and the future, realizing that “tentativeness” is a major part of life for scientists. They don’t lash out at anyone who is discussing alternatives with a sound methodology. Speculation requires a methodology just like science theory requires the scientific method. Do you understand that?

    You have either decided to ignore what I have been saying or simply jump on the band wagon with the professionals. Professional scientists by a wide margin accept BBT. You seem to agree.

    Professionals who step out of the fold and put forth alternative ideas become career disadvantaged and you don't deny that. When a tiny segment of so called professionals lash out at alternative ideas presented for discussion it makes me wonder.

    Are you aware that there is a movement that is gaining support within the scientific community to reconcile GR and particle physics and they are saying that particle physics is likely to come out on top? Look at the last paragraph in the link below. Are you familiar with String Theory? Are you familiar with the incompatibility between GR and particle physics?

    When you read links like this, http://preposterousuniverse.blogspot.com/2004/08/testing-general-relativity.html, do you still insist that BBT is the "be all and end all" of cosmology? If so, you are the one who is deluded.

    This rampage from a self proclaimed communications expert says to me that you have some issues that go beyond communication. Are you also committed to a dying theory and don’t want to let it go for some reason? What possible reason could there be to cling to BBT to the extent that you absolutely can't stand to have someone say it is not the "be all and end all" that you seem to want it to be?

    Can I take you poor excuse of a post as an objection to step one in QWC, i.e. that it was a big crunch that preceded the initial expansion of our observable universe?
     
    Last edited: Jul 21, 2009
  22. AlphaNumeric Fully ionized Registered Senior Member

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    No, it doesn't. As said, saying "BB proponents must comment on what happened before the BB!" is like telling an evolution proponent "You must explain how life started!". Its not true. The BB theory is about the fact that all the physics we currently know allows us to wind time back and we find it was small and hot about 14 billion years ago. We can find time back such that the universe gets so small and hot it reaches energy scales which are the limits of our understanding. We can also extrapolate, in a vague way, that if you could wind time back further it would seem our theories break down about a billionth of a second away from the universe having zero size.

    That's it. No "The BB theory says the universe was a singular point" or "The universe came from nothing". We trust our theories enough to wind back to a particular point in time. Beyond that we have only arm waving and vague guess work. The universe may not have been a singularity but we can't analyse it because our models break down.

    Just as evolution says "Life began somehow. What does it do then?" cosmology says "The universe began somehow and became small and hot. What does it do then?".

    Before the moment in time where our theories allow us to wind time forwards we can't so much with confidence. If you cling to general relativity still then you end up with a singularity where time and space lose their meaning so it's fruitless to ask "What happened before that" because the context of 'before' is lost. This has arisen because you've trusted a theory in an area where it's no longer trustworthy.

    Here's a simpler example, accelerating particles. The Newtonian KE of an object is \(\frac{1}{2}mv^{2}\). Put in v=c and you get \(\frac{1}{2}mc^{2}\). Large but finite. Relativity says v=c gives infinite energy, you can't get to v=c. Now if you trusted Newtonian mechanics too much you'd think you could examine speeds of v=c or v>c, that it's physically meaningful to do so but when you learn of the more powerful theory of relativity you find it's not a wise thing to do. Just as trusting general relativity when quantum mechanics is important is not too wise.

    So it's a personal story you've invented in order to make you feel that the question has an answer you can grasp. Just like religious people invent supernatural explainations like "God did it" when something they don't grasp occurs.

    Yes, it's one giant intimidation supported conspiracy.

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    It's nothing at all to do with the fact your 'work' doesn't resemble science at all.

    Neil Turok and Stephen Hawking. Both of them have put forword ideas about how our 4d universe came about. Welcome to last century.

    If gravity or dark energy are negative then they can counterbalance the positive energy of matter. Again, welcome to last century.

    Yeah, Turok and Hawking limited their careers to being professors at Cambridge. I bet they regret that!

    By your logic people studying the evolution of diseases are wasting time because they don't know the origin of the first bacteria.

    It is clear that you have spent no time reading up about what other ideas people have given for the origin of our space-time because you seem to be under the impression that if you asked anyone in academia the only proposed thing you'd get was "Nothing, it came from nowhere", which is false. And that's what makes the following all the more hypocritical :

    You should familiarise yourself with cosmology. The BB theory is about the universe once being small and hot. Where that small, hot entity came from is another thing, just as ambiogenesis is different from evolution. And when you say "look at the writing about BBT" you mean "Go read pop science magazines or newspaper interviews or watch a TV documentary where they remove all the quantitative stuff, remove most of the details, twist some of the statements and only talk to a small number of physicists.". The real 'writing on cosmology' are found on ArXiv or in journals.

    You're telling people to do something you yourself haven't done.

    No, you aren't more aware of what the professionals say. What was the last published paper you read on this stuff? Give a citation.

    'Sound methodology'? Since when is simply making stuff up and refusing (or being unable) to use precise logic 'sound'?

    Oh and I bet you're a real whiz at string theory and have first hand experience of doing renormalisations (or attempted renormalisations) of gravity theories? Did you intentionally word that so it seems like you're familiar with those areas of physics or was it an unfortunate unintended result and infact you aren't trying to pretend you know much much more than you actually do about mainstream physics? If you knew about string theory in even a vaguely decent qualitative way you'd know it provides at least one possible explaination for the creation of our universe, put forth by the aforementioned Professor Turok of Cambridge University.
     
  23. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    One question, can you state my prime objective and the methodology I use to achieve it?

    No one objects then to the big crunch preceding the Big Bang so now we move on to step II. of Quantum Wave Cosmology, "The formation and burst of a big crunch into an expanding arena like our own."

    Read the entire section in the Google.doc: http://docs.google.com/View?id=dgzb43gp_6dtnkzxg9

    I am going to be covering each of the 36 steps individually and will revise them as I get useful feedback from the community. As we go through them I will also be updating them to better reflect the stages of the arena wave and the arena particle in each step. The arena particle is the core of the big crunch, and the corresponding particle at the quantum level is the high density spot. The wave form at both levels is the same and the physics are strikingly similar with only some limiting factors to avoid the catastrophe of infinite regression.


    The arena wave at the arena level is very similar to the quantum wave or gravity wave at the quantum level. I want to make sure that the Step II. detail will correspond to the Step III. detail to make that point obvious when we get into Step III.

    Thanks in advance for you constructive comments about Step II. and for staying around to at least give me an audience.
     

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