I think you have understood my point of view..
I hope I am not leading you in the wrong or the incorrect direction...
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There are no limitations to mathematics. As I said, it is an abstract science, and as such, there is no limitation to it. If you don?t like this math, you are free to invent your own one, that suits your purposes better (Remember Newton? That is exactly what he did).
But if you decide to use a part of the math that has already been developed, then use it properly, and don?t trey to adapt beyond what it?s good for.
And no, your understanding does not collapse at ratios like 1/0, or 0/0, because if you apply the theorems and postulates of mathematics, such ratios simply DO NOT EXIST. Axiomatically. No more, no less.
Rep: I agree.But I do not agree that limit to 0 is same as zero.. Zero exists in reality and classicaly atleast there is nothing called tends to zero .. We can achieve perfect 0 ...Maths uses the concept of infinitesimal for its convinience to divide the undividable...
IT has rules to do so...and gives accurate results...My argument is that the process must map to the reality ...the INPUT , the PROCESS and the OUTPUT must map to the reality at every point...This statement has a very DEEP MEANING ..
Limit should not only be consitent with Maths but also with the reality...
(Please understand I am not against any of the existing concepts of Maths or Phsyics but I wish to enrich it if possible.)
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Once again, you are mixing incompatible things and concepts. First of all, bosons are pure quantum particles, and for this reason the uncertainty principle prevents you from ?squeezing? them in a volume of radius zero (that would mean you can measure exactly their position). This consideration only and it solves your problem.
Second of all, you assume that bosons interact according to classical gravitation at all distances, which for the time being is an unsupported statement. Quantum gravity effects might come into play at such distances.
Third of all, you cannot ignore the nuclear and electromagnetic forces which are much, much stronger than gravitational interaction, and which in fact prevent you once again to squeeze all bosons in a zero volume.
REP: Agree this was not a suitable example but my desire was to share the concept with simplicity...
Can a function understood at all points and becomes non-understood at certain points or at exact 0(or any other exact no.)?
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I have no idea what trick you used, but what you say is far, far away from the real picture.
The trick was to move the reference point to some other place so that we can understand the point of limit without using limit.
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Your confidence is greatly misplaced. In gravity, if you consider the symmetry invariances, it does not matter where the symmetry is located, it only matters that it exists.
REP: After transformation the position of my so called collapse has changed but it was not removed from the system.If theroy intends to remove it completely then with its current capabilities we can say that it will fail to do so...(after enough digging one will rediscover its new position)
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Those equations you talk about are classical, so by this only fact they only give an accurate picture in the range where classical arguments apply. And they do not apply in the case of your bosons. Nor is it any claim that the classical description should give an overall accurate picture in all instances. Let me put it this way: this is the reason why quantum mechanics was developed, to replace the classical description in the circumstances where the classical description failed.
REP: Give me some time I will find out a real classical case of collapse.
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dkv: ?How universe came into existence is one such point.?
I agree with you that this is a matter of interest, but for the time being there is no fully tested theory that can make any claims about the origins of the universe. There are only theories that have been validated down to the origin of the CMBR, and that?s it. They don?t offer any info about the origin of the universe. Beyond the CMBR range, there are only untested assumptions.
REP: Great.
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Pray do tell me how math dictates over the reality. And BTW, since when does math describe reality? It is physics that is concerned with the description of nature, not math.
REP: I also need to revisit this thought..
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No one is running away from inconsistencies just for convenience. Not in physics. For the time being, the tools are used until a better understanding of nature is achieved. This has always been the case in physics.
REP: What if it does not meet to reality in with its full force...Why is it that it allows certain intermediate steps in the derivation to exist independent of reality when it is describing it.. How do you explain Complex no. used extensively in Physics.
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Oh, boy. ZERO IS NOT AN ORIGIN! It is only your bias that leads you to this consideration. If you want another definition, consider it as the neutral element of the group/field of real numbers, or integers, or rationals with respect to addition.
Relabeling the quantities you deal with DOES not change any of your understanding, you just changed the language you speak, you haven?t changed what you are actually saying.
Yes Sir , I undertand that 0 is not origin .. but yes I would like to call it a reference point and there is no need to associate it with existence and non-existence...Boolean algenra is more than enough to handle such concepts...
We are more intersted in classifying the reality relative to a reference.That reference point can ever be absolute or not is a seperate question.
correct me if I am still wrong.
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Look, let?s clear up something. Mathematical consistency, even if desired for esthetical reasons, is NOT and has NEVER BEEN the fundamental driving force in physics. It is merely a tool to express our knowledge. No physicist in his right mind in this world will tell you he prefers a mathematically consistent theory instead of observation. This is the reason why at various levels theories can ?live? with singularities. The major issue is not that a mathematical singularity exists in a theory, but the physical meaning of that singularity.
REP:I am afraid that singularity can never be removed.. because there logically it can not be removed from Maths..unless it accepts that INPUT,PROCESS and OUTPUT of a derivation must map to the Reality.
Cheers
