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Singularity (Wikipedia and Mathworld definitions)

  1. Aug 26, 2007 #1


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    This post is just concerned with definition of terms, for them as wants it. If you are NOT confused about what is meant by a singularity in math/physics, please ignore this. Sometimes a good online source, if you want the meaning of math and physics terms, is Wolfram Mathworld. Wolfram also has a comparable reference for Physics terms. However the term singularity came into physics from mathematics, over a hundred years ago, so the place to look it up is Mathworld.


    The primary meaning is a place (point or region) where a function blows up and fails to give meaningful results. This was taken over into physics: a place where a man-made mathematical model blows up and fails to give meaningful results.

    Of course the word has other meanings in ordinary non-technical speech (it can mean oddness or peculiarity) but that is outside of physics and cosmology.

    Wikipedia says this
    a singularity is in general a point at which a given mathematical object is not defined
    and they give the example of the function f(x) = 1/x, which is not defined at x = 0 and which blows up there.

    the point to remember is that a singularity is not something which exists in nature.

    it is a point where a man-made mathematical model breaks down and fails to compute.

    Historically, in the mathematical sciences there has been a process of singularity removal or resolution. In a number of cases people have gotten rid of singularities by improving the model. You replace the model with a better version which does not break down---and so does not have the singularity---and that gets rid of the problem.

    Mathematicians and physicists have been dealing with singularities for hundreds of years. Just to take one example, Quantum Mechanics has its roots in several inventions of mathematical ways to resolve singularities-----the Planck radiation curve (1900) replaced earlier models of thermal radiation that blew up----the Bohr model atom (1913) took care of an instability in the classical model atom. This process of singularity resolution, by improving theory, is generally expected to continue as in the past.

    The word singularity, as a technical term in mathematics and the mathematical sciences, has had the same meaning for hundreds of years. If you look at what Wolfram Mathworld says, you will see that singularities do not always occur as ISOLATED POINTS.
    The bad points where something doesnt work can sometimes occur connected in a line or surface or hypersurface.

    That is, a mathematical model can blow up and fail to apply in a WHOLE REGION.

    Sometimes people get the mistaken idea that because the word "singularity" sounds like the word "single", a singularity must somehow refer to a single isolated point. That isn't so.
    Last edited: Aug 26, 2007
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  3. Aug 26, 2007 #2


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    I posted the above because today I got a PM indicating that someone was confused about the meaning of the word and thought that we at PF were using it in a new sense :smile:

    So I thought there might be others in the same fix. Otherwise I would not have bothered, and would just have assumed that everybody at Cosmology forum knew the usual meaning (in math sciences context.)

    Sorry if this post seems unnecessary or too obvious. It is meant for anyone in the same mental boat as the person who wrote the PM, in case there are others.
    Last edited: Aug 27, 2007
  4. Aug 26, 2007 #3


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    There is a common usage along the lines of 'the central singularity of the/a black hole' that is often phrased in such a way as to make 'the singularity' sound like a real location existing in the hole. In think this often causes a fair bit of confusion, though not as much as the singularity at t=0 in the FLRW model!
  5. Aug 26, 2007 #4
    Hi Marcus:

    I appreciate your kind explanation of singularities, however I PM’d you because I am writing a play wherein the non-existence of time as well as so-called "alternate realities" are part of the conceptual backdrop so I have been doing some research looking for elegant quotations I might be able to use.

    I happened into this forum following a very unsatisfying visit to Rovelli’s homepage (http://www.cpt.univ-mrs.fr/~rovelli/) and was horrified to learn (from you) that the term (or concept) of “singularity” (as in the singularity that "preceeded" the Big Bang) was outdated or renamed. I’ve visited so many pages and forums today I have only been able to relocate one of you quotations, but here it is:

    QUOTE MARCUS:(https://www.physicsforums.com/showthread.php?t=120324&page=2)

    ‘It is more like asking simply "what was the situation one hour or one year before what USED TO BE CALLED the singularity?"’

    Fearful that I am about to spend (at least) a year basing an entire conceptual play on outdated thinking (or terminology) I thought I’d better ask you for the new term (or concept) so I can research it.

    I’m no scientist, but I do understand that the singularity which “preceded” (in time terms) the Big Bang was “where” the laws of physics break down, and I must say I have long been shocked that science is willing to base so much theory and painstaking math in order to to get to a point where it all breaks down. I think I understand that you feel "singularity" is generally inaccurate and will be resolvable with new knowledge -- but I still need to know the new term if there is one.

    I am non-the-less very grateful for the 101 on singularities, because it is always helpful to read something defined in clear terms.

    Thanks again for your time,

    M. B.
  6. Aug 26, 2007 #5


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    we definitely need a word for the PIT of a black hole (where the classical model blows up).
    I recently heard a term for it, I forget what it was and where i heard it unfortunately!
    Could have been a recorded talk at one of several conferences I've been sampling.
    It wasn't "pit".

    this has become kind of a professional sideline of yours I think, getting concepts and language sorted out. needs to be done all right.
  7. Aug 26, 2007 #6
    Okay, now I'm ready to sound really dumb.

    I've always thought that black holes take in matter from our universe, condense it and dump it into other dimensions, or alternate universes, causing a "big bang" on that side.

    Should I commit suicide immediately?
  8. Aug 26, 2007 #7
    Oh, I just found this. (It's so funny -- google keeps taking me to posts by Marcus)

    Quote Marcus:
    "There is also Leonardo Modesto, postdoc at Rovelli's institute in Marseille.
    He has written a couple of papers removing the BH singularity. There is a tension between the Modesto picture (where spacetime continues at the pit of a black hole, where the classicial singularity used to be, and may inflate from there to form a new universe) https://www.physicsforums.com/archive/index.php/t-47885.html

    So, it that a scientific way of saying what I put in layman's terms?
  9. Aug 26, 2007 #8


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    I'm sure that won't be necessary!

    As to what happens to material that crosses the event horizon of a Black Hole, the short answer is that we do not know. Highly imaginative ideas involving other dimensions, other Universes, wormholes etc etc have been suggested in regards to Black Holes but they are little more than speculation.

    We have a solution to the equations of General Relativity for a finite mass squashed into an infinitely small volume. Relativity predicts what the result of dropping stuff into these things would look like from afar and we have observed behavior consistent with these predictions using modern telescopes. This is about all that we know about Black Holes, though there is plenty of speculation. I highly doubt that when and if we can more satisfactorily describe Black Holes with a theory that does not 'blow up' at any point that Black Holes will turn out to be the mystical Universe linking Stargates that they are often romanticised to be!
  10. Aug 26, 2007 #9


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    We have competing proposals for how to resolve the Big Bang singularity, and that influences how people talk about it. Some refer to what replaces the singularity as a BOUNCE.

    A more colorless objective way to refer to that moment would be "the beginning of expansion"

    that would include the idea of a bounce as one possibility, but it would also permit one to think as some people do (a very poetic notion) that our expanding region of spacetime began with a QUANTUM FLUCTUATION in some other region.

    Have a look/listen at this illustrated ROGER PENROSE talk. he doesnt like the bounce idea and is more drawn to the fluctuation idea
    My leanings are the opposite of Penrose, but its only fair to hear several different viewpoints.

    A colorless unpoetical unevocative generic expression is "the beginning of expansion"
    and that could be interpreted according to several people's scenarios.

    Anyway you no longer need be shocked that cosmologists would LEAVE things at a point where the classical model breaks down! Quite a few are pushing back into earlier time and modifying the laws of physics so that they are more robust and don't fail. The main weakness was General Relativity which blew up and predicted infinite density, infinite pressure and other nonsense. Quantizing GR can seemingly fix that---it is work in progress.

    Other people here may think differently but my feeling is that dramatic arts is general audience entertainment and you have to talk concepts you think the audience will understand. So you might sort of mythologize and talk about the
    as if it were something real, that really happened in nature.
    The audience will already have some concept in mind that popular science writers have taught them to believe.

    NEVER FEAR! In the public at large "singularity" is a very popular word as you must know. (but not used in correct scientific sense)
    It has even become something of a buzzword anyway lately. there is that guy who is talking about a "technological singularity" like some approaching millennial climax when we all turn into the scintillating cells of a planetsize brain. I would say the notion is only "outdated" in the context of Cosmology where one is trying to understand what actually happened. In the myth-world of the public mind it is a very firmly rooted idea and not at all outdated.

    Other's may have different advice, but I would say that you should use the language which has been fed to the public by people like Stephen Hawking, Brian Greene, Leonard Susskind (in his popular writing).
    I think those influences are harmful and I repeatedly find people who have read such pop sci are kind of brain damaged by it and have a hard time grasping what is really going on. So I don't CONDONE writing new age pop sci or any other kind of pop sci in that vein. It is part of the problem.

    On the other hand, you want to have a successful play, right? what can you do?
    You can't be pedantic, you have to talk to your audience as directly as you can.

    Last edited: Aug 26, 2007
  11. Aug 26, 2007 #10
    Well, anyway, I must sound really dumb to you. However if anyone has any wonderful quotations (especially older ones I might not need permission to use) that illuminate the "there is no time" and "alternate realities do exist and can occupy the same space" concepts, I would appreciate if you would PM them to me. Otherwise, I will let you get back to your better-educated exchanges, which I am surely interrupting (and probably making spelling errors to boot.)

    Thanks again,

    Kathy (MediumBang)
  12. Aug 26, 2007 #11
    But, the "new" universe probably wouldn't be just like ours. I mean it could be denser or much much smaller, (at least to start.)

    I truly believe (here I go again) that we currently share "space" with other universes that are much less dense than we are, so we can't see them. By the same standard -- much denser universes, might not perceive our existence as being "real."

    Some theorists (is that a word?) say that our ability to see our universe is as much faith and perception as anything else -- since we are composed mostly of empty space.

    Wouldn't a "being" from a "parallel" universe which is much less dense than ours be able to walk through our walls -- or even float in our air, or even walk on it?

    It's really hard for me to believe in "one true reality" with all these possibilities banging around in my head (causing brain damage, I'm sure.)
  13. Aug 26, 2007 #12


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    I think that is possible but it has not been proven. I wouldn't call the new region of spacetime that expands from the pit of the hole an "other dimension" or an "alternative universe". personally i guess I'd call it just part of the same universe. a continuation.

    However Penrose doesnt think that happens. Check out his November 2005 talk at Cambridge. He gives reasons. (I think he may be wrong but he has an argument.)
    Last edited: Aug 27, 2007
  14. Aug 26, 2007 #13


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    That is more or less right. You put it in layman's terms Kathy.
    (but what i said was not in very scientific terms----you'd have to read the technical papers to see it in all the gory math detail.)

    Lee Smolin wrote a book about this called The Life of the Cosmos.

    his idea is that spacetime regions reproduce.
    black holes are the reproductive mechanism (like budding)
    the characteristics of the universe can gradually evolve, like some species of plant, to reproduce more prolifically---have more baby universes

    this explains why our universe is so good at being longlived and having lots of matter and condensing lots of galaxies and stars (because many of they stars ultimately collapse to hole, making offspring similar to the parent----other details too.

    I dont agree with what you say about "alternate universes occupying the same space"
    that is not part of the black hole baby universe picture
    the spacetime that comes out the backdoor of a black hole is not in our space, it is a different outgrowth. there is no conflict.
    Gen Relativity is a dynamic theory of space that allows it to grow. there does not have to be a big room in which everything happens (and where things might collide). Since there is no big room there is no chance of collision.
    Alternate universes occupying the same space sounds weird to me.

    there is the Many Worlds Interpretation of Quantum Mechanics, but I think that is wacky. One doesnt need it in cosmology.
    there is a lot of new age garbage floating around but for cosmology all you really need is one universe. If it came from a bounce OK then there is a part of it before the bounce, but it is all the same. If black holes bounce babies out the back door well that is kind of strange but still OK and still part of the same thing. It is just like a tree able to branch. But no "alternative universes" for me---I just need the one.
    Last edited: Aug 27, 2007
  15. Aug 26, 2007 #14


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    But what evidence do you have for any of this? I'm not one to pretend that the Utopic ideal of objective scientific method bears much resemblance to the actual processes that go on in research, but science does none the less demand both a theoretical framework for its ideas that are coherent and concrete as well as experimental or observational confirmation, or at least the in principle confirmableness of an idea
    regardless of whether it can be done at present. This is why the ideas you present above are not the kind of thing that scientists would bother with in terms of research.

    That being said there's nothing to stop the imagination speculating on this is a literary sense. I hope that doesn't come across as condescending!
  16. Aug 27, 2007 #15
    Yep. That was my dropping off point.

    No, but if my research keeps going like it has been, I might be asking permission to use some of your quotations.

    I think it's pretty obvious I'm in no position to educate anyone in the matters of scientific theory -- that is not my intention. However, extremely simple quotations from solid sources that greatly illuminate the theories behind my story would be helpful.

    Please define "brain" in that context. (I'm kidding)

    In the past, Hawking's thinking has always been too linear for me. However, I've heard he has had a change of mind since he was unconscious (thus "out of body" or, at least, out of conscious contact with "body") and he is finally ready to consider the possibility that "real" might include things we can't see -- even with a microscope or telescope, or even that existence might possibly be all in the perception. Maybe the tree doesn't make a sound if there is no consciousness to perceive the brain impulses that receive signals from the ear that is aware of vibrations in it's environment.

    To be honest that's not likely to happen no matter what I do.
    And yet I continue to move forward. (Sort of like coral that can never go very far but might, just by existing, become part of something far greater.)

    Sorry to get mushy, but YOU ASKED!!!

    Thanks for all the input, guys.
  17. Aug 27, 2007 #16


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    That does it! Wallace YOU have to write the play!

    Actually sometimes departments have these departmental picnics where they do skits, lampooning various rival theories and even their own professors.
    Sometimes they adapt show tunes or Gilbert and Sullivan.

    A real Astronomy Department christmas party skit, or some such, might be quite entertaining.

    I will leave you and Kathy to plan it.:smile:
  18. Aug 27, 2007 #17
    Oh, right! And you scientific types never say anything weird?

    The idea of only one universe in infinity seems unlikely to me. But no matter how many there might or might not be, or what type of "space" they do or do not occupy, there is always an infinite "whole" we are (and have always been) a part of.
  19. Aug 27, 2007 #18


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    Never. It is very tempting to continue the conversation. How should I picture your play. What situation? Like, a doctor's waiting room? A train station?
  20. Aug 27, 2007 #19
    Here, let me say something which I hope won't piss you off. It's a quote by.... me!

    It is sometimes easier for an uneducated mind to see the obvious.


    You see, you educated types have to contend with the sum total of all the brilliant thinking as well as all the crappy thinking of all time. As for me, I can just look up at the sky and say "There are too many planets in the universe to make it likely that there is life on only one."

    By the same token I can just think "You can't make something out of nothing, nor can you create something made of one group of substances from something made of other substances. Thus, our universe MUST HAVE come from something made of the same stuff. It might have been crunched down really small, or expanded so huge that only a single cell of it exists in our entire universe -- but it MUST COME FROM SOMEWHERE NEAR WHERE WE ARE, AND IT MUST COME FROM SOMETHING MADE OF THE SAME STUFF.

    This is not rocket science.

    Okay, then, quid pro quos, give me convincing evidence that we are really having this conversation and that this exchange is not all just a dream. When you do that, I will use the same evidence to support my position(s.)

    Actually, you guys don't seem condecending to me at all. I have really been enjoying your posts.

    I've seen science documentaries which reflect some agreement with my thinking on Discovery Channel, but those shows might not be relevant at your level of study.

    Okay, my brain is worn out. Time to sleep. What say we continue this conversation in our dreams? (smile.)

  21. Aug 27, 2007 #20


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    good nite
    play write
    don't let the bugs bite

    Wallace is in Oz so it is not his bedtime yet
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