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    I was thinking earlier today about the following question:

    If the Big Bang and the universe originated from a singularity of infinite mass and energy, wouldn't the law of conservation of mass/energy suggest that the current universe, which many consider finite, also contains an infinite amount of mass and energy?

    I'm an AS student so I've probably just completely misinterpreted a fundamental facet about the Big Bang theory or the law of conservation, but I'd be grateful if someone with more knowledge on the subject could explain this?
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    Did it have infinite mass and energy?
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    (Original post by + polarity -)
    Did it have infinite mass and energy?
    Well I've seen it defined in books as a point of infinite density and temperature, so that's what I assumed.
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    My understanding is that it was considered to be incredible density (could probably word that better), but not infinite.
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    (Original post by IchiCC)
    Well I've seen it defined in books as a point of infinite density and temperature, so that's what I assumed.
    Suppose I took all the observable matter in the universe (a finite amount) and compressed it to a point. That point would have infinite density, but would still have finite mass.

    Whether there actually was a singularity at the big bang is debatable.
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    Also we don't know that the universe is spatially finite.
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    (Original post by TableChair)
    Suppose I took all the observable matter in the universe (a finite amount) and compressed it to a point. That point would have infinite density, but would still have finite mass.

    Whether there actually was a singularity at the big bang is debatable.
    Whether or not the big bang happened is also debatable.
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    (Original post by IchiCC)
    I was thinking earlier today about the following question:

    If the Big Bang and the universe originated from a singularity of infinite mass and energy, wouldn't the law of conservation of mass/energy suggest that the current universe, which many consider finite, also contains an infinite amount of mass and energy?

    I'm an AS student so I've probably just completely misinterpreted a fundamental facet about the Big Bang theory or the law of conservation, but I'd be grateful if someone with more knowledge on the subject could explain this?
    You may find this interesting
    http://www.astronomycafe.net/qadir/q1326.html
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    (Original post by mathperson)
    Whether or not the big bang happened is also debatable.
    Not really. All observations of the universe concur that there was a big bang (i.e. approximately 13.7 billion years ago, the universe was in a hot, dense state). To claim otherwise is pretty ludicrous, but I'd like to hear what evidence you have?
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    (Original post by TableChair)
    Not really. All observations of the universe concur that there was a big bang (i.e. approximately 13.7 billion years ago, the universe was in a hot, dense state). To claim otherwise is pretty ludicrous, but I'd like to hear what evidence you have?
    I don't have any evidence, you see I'm a mathematician and I don't deal with 'evidence' as scientists/engineers do, I deal in absolute proof. Now I don't have mathematical proof that the big bang didn't happen, because if I did have mathematical proof then it is unquestionable, however whether or not the big bang did happen will always be up for debate until absolute proof is found.

    I know I can't word this without sounding somewhat rude, but I don't intend it that way , however when you say it is 'ludicrous to question it because of evidence' is typical of what a scientist would say.
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    so I guess you reject all science.

    What about mathematical axioms?
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    A perfect singularity is only a mathematical model, and so far, there has been no evidence to suggest that it has a perfectly corresponding counterpart in physical reality (much like the idea of a perfect circle which is a mathematical model for the imperfect physical circles we see in real life).

    For example, consider a collapsing star. Theory tells us that under its own gravity, the star will get smaller and smaller in volume, and hence will get larger and larger in density. This process is in positive feedback, which means that every time the volume decreases, the density increases, the gravity gets stronger per unit volume, the volume decreases, the density increases, etc, etc. Of course, this feedback process would have to go on for an infinite amount of time before it became a singularity - a point mass of infinite density and 0 volume. However, infinite time doesn't exist in the universe, and so it is probably that many collapsing stars may APPROACH a singularity as time TENDS towards infinite, but will never actually get to that point. However, it will get very close, and so we can accurately model our "ALMOST" singularity in real life with a perfect singularity in the mathematical model.

    The same could be true of the singularity which set off the expansion of the universe.
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    I think the ratio of mass to size of the universe is infinite but not the mass. Because as size turns to 0 the mass/size will turn to infinity.
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    (Original post by mathperson)
    I don't have any evidence, you see I'm a mathematician and I don't deal with 'evidence' as scientists/engineers do, I deal in absolute proof. Now I don't have mathematical proof that the big bang didn't happen, because if I did have mathematical proof then it is unquestionable, however whether or not the big bang did happen will always be up for debate until absolute proof is found.

    I know I can't word this without sounding somewhat rude, but I don't intend it that way , however when you say it is 'ludicrous to question it because of evidence' is typical of what a scientist would say.
    In science and engineering, there is a thing called "beyond reasonable doubt". That is, we may never be able to acquire an absolute proof for a hypothesis, but there can be SO much evidence supporting the hypothesis that you would be going beyond reasonable doubt into unreasonable doubt to question it.

    Of course, I would never stop someone from questioning it, because you never know where an alternative hypothesis might lead... it may just be successful enough to acquire more evidence than the previous hypothesis.

    However, it is still quite ludicrous to question something for which the evidence is substantial, to the point that it is self evident.

    And yes, as someone else has already mentioned, your beautiful subject of Mathematics is founded, regardless of what field you are in, on a set of axioms. Axioms being "self-evident" starting points which, themselves are not proven. And then, from these axioms, all other theorems are proved. However, it can be seen as debatable that these axioms are "self-evident beyond reasonable doubt". You might be ludicrous to suggest so, but there is room for debate in all mathematics that springs from unproven axioms. Especially when we consider Gödel's theorems of incompleteness... we can see that the realm of the Mathematical can be deeply flawed in its basic premises.

    Of course, I presume that you have never heard of "axioms" or Gödel's theorems, and are still under the schoolboy illusion that all of mathematics is conceptually perfect, and that every question has a "right" answer. When you undoubtedly wiki these concepts, you will either have to accept the "beyond reasonable doubt" rule of thumb, or you will be forced to lose your faith in your favourite subject, because it is not the image of perfection and purity that you think it is.
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    (Original post by buckett)
    I think the ratio of mass to size of the universe is infinite but not the mass. Because as size turns to 0 the mass/size will turn to infinity.
    That ratio is called density, and you are correct that in a singularity, there is infinite density, zero volume.
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    The laws of physics that we know and love completely break down at singularities.
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    (Original post by Phugoid)
    In science and engineering, there is a thing called "beyond reasonable doubt". That is, we may never be able to acquire an absolute proof for a hypothesis, but there can be SO much evidence supporting the hypothesis that you would be going beyond reasonable doubt into unreasonable doubt to question it.

    Of course, I would never stop someone from questioning it, because you never know where an alternative hypothesis might lead... it may just be successful enough to acquire more evidence than the previous hypothesis.

    However, it is still quite ludicrous to question something for which the evidence is substantial, to the point that it is self evident.

    And yes, as someone else has already mentioned, your beautiful subject of Mathematics is founded, regardless of what field you are in, on a set of axioms. Axioms being "self-evident" starting points which, themselves are not proven. And then, from these axioms, all other theorems are proved. However, it can be seen as debatable that these axioms are "self-evident beyond reasonable doubt". You might be ludicrous to suggest so, but there is room for debate in all mathematics that springs from unproven axioms. Especially when we consider Gödel's theorems of incompleteness... we can see that the realm of the Mathematical can be deeply flawed in its basic premises.

    I really hope this doesn't come across as rude, I'm not that sort of person, and I appologise if it does . However to be honest I don't feel I can have a decent conversation with you about this subject.

    newton's law of universal gravitation was 'beyond reasonable doubt', however his approach was flawed in that his formula came from experimental observation rather than mathematical derivation. This resulted in, eventually, it being replaced with a mathematically derived theorem (note not theory) called quantum mechanics.

    "However, it is still quite ludicrous to question something for which the evidence is substantial, to the point that it is self evident." This is a typical thing that a scientist/engineer would say, and I'm not going to trouble myself to answer it, not because I don't want to assist your understanding, but I believe that unless you find out for yourself why this statement is incorrect, you will not appericiate why it is.

    Again, scientists/engineers tend not to have a full understanding of what an axiom is. They are not theorems that need proving, they are quite simply fundemental definitions that define that language that the theorems built upon them are expressed in, they do not need proving. There is no room for debate in mathematics, however as previously mentioned in this post, I shall let you figure out why.

    Take care.
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    (Original post by mathperson)
    I really hope this doesn't come across as rude, I'm not that sort of person, and I appologise if it does . However to be honest I don't feel I can have a decent conversation with you about this subject.

    newton's law of universal gravitation was 'beyond reasonable doubt', however his approach was flawed in that his formula came from experimental observation rather than mathematical derivation. This resulted in, eventually, it being replaced with a mathematically derived theorem (note not theory) called quantum mechanics.
    Lol, how about nooooo?

    Newtonian principles were INDEED beyond reasonable doubt, but then something happened independently that brought the possibility of reasonable doubt into the arena - people began to observe things that were not explained by Newtonian physics. Such things were blackbody radiation, optics, the motion of bodies at high velocities, and the physics of the microworld. These were the things that allowed reasonable doubt to be cast upon Newtonian physics, and FROM that doubt the theories of General Relativity and Quantum Mechanics were born.

    The vast majority of successful theories which supersede an existing theory only come to centre-stage once the previous theory has doubt cast upon it by some observation, and Quantum theory is no different.

    Now, the mathematics of quanta are indeed "theorems", but the hypothesis that these theorems accurately depict physical reality is a THEORY!

    Newtonian theory, btw, is not "wrong". The only thing that was "wrong" about the Newtonian philosophy was that it was considered to describe all motion in the universe, when in fact it only describes motion within a limited range of velocities, masses, etc.

    "However, it is still quite ludicrous to question something for which the evidence is substantial, to the point that it is self evident." This is a typical thing that a scientist/engineer would say, and I'm not going to trouble myself to answer it, not because I don't want to assist your understanding, but I believe that unless you find out for yourself why this statement is incorrect, you will not appericiate why it is.
    Not particularly. Unless you have grounds for reasonable doubt, you are an idiot not to take a theory on board.

    Again, scientists/engineers tend not to have a full understanding of what an axiom is. They are not theorems that need proving, they are quite simply fundemental definitions that define that language that the theorems built upon them are expressed in, they do not need proving. There is no room for debate in mathematics, however as previously mentioned in this post, I shall let you figure out why.

    Take care.
    I never said they were theorems that needed proving. I know fine well what axioms are. You may call them definitions, and that is fine, but when you try to apply mathematics to describe physical reality, those definitions become into "assumptions". You may be able to define a conceptual world in which to work, but you cannot define reality. Reality is defined already, and therefore you can do one of two things:

    1) Define a set of mathematical axioms and then ASSUME that they have counterparts in the physical world.
    2) Observe the physical world and try to determine the axioms, and self-evident truths of reality from there.

    Both, of course, have their flaws, and you are a fool if you fail to recognise that.
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    Ok we're going to get nowhere here. I think I've seen this guy in another thread, just let him be.
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    (Original post by Phugoid)
    A perfect singularity is only a mathematical model, and so far, there has been no evidence to suggest that it has a perfectly corresponding counterpart in physical reality (much like the idea of a perfect circle which is a mathematical model for the imperfect physical circles we see in real life).

    For example, consider a collapsing star. Theory tells us that under its own gravity, the star will get smaller and smaller in volume, and hence will get larger and larger in density. This process is in positive feedback, which means that every time the volume decreases, the density increases, the gravity gets stronger per unit volume, the volume decreases, the density increases, etc, etc. Of course, this feedback process would have to go on for an infinite amount of time before it became a singularity - a point mass of infinite density and 0 volume. However, infinite time doesn't exist in the universe, and so it is probably that many collapsing stars may APPROACH a singularity as time TENDS towards infinite, but will never actually get to that point. However, it will get very close, and so we can accurately model our "ALMOST" singularity in real life with a perfect singularity in the mathematical model.

    The same could be true of the singularity which set off the expansion of the universe.
    I think a singularity can form in finite (proper) time.
 
 
 
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