Relative zero and Absolute Zero?

Discussion in 'Physics & Math' started by Quantum Quack, Jun 16, 2008.

  1. Quantum Quack Life's a tease... Valued Senior Member

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    Is it possible in math to describe the relativity of:
    1] Relative Zero.

    Definition: Relative Zero only exists relative to the fact that other objects of value exist.
    ie. -4 -3 -2 -1 [0] 1 2 3 4
    or a+b=[0]

    2] Absolute Zero.

    Definition: Absolute zero is non-relative to anything as no other thing exists therfore absolute zero is no-existant.
    ie. [0]

    I woud think it is relatively easy to describe the first item, relative zero as it is commonly used in math, however to show it as relative is what the question is about.
    Where as absolute zero may be considerably harder to show as non-relative. because to do so it must only by default..

    ie. a+b = [ ]
    notice the absense of value in the bracketed result of a+b

    Is it possible?
    Care to discuss?
     
    Last edited: Jun 17, 2008
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  3. Reiku Banned Banned

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    FIRST PART, i suppose. If you are saying, can we use zero as a relative frame to distinguish between \(\sqrt{1}\) and \(\sqrt{-1}\), then yes, it's being used as a ''relative'' symbol. It kind of reminds me of a notion i am on the fence about, and that is the notion (not my own, but of mainstream), that the time dimension can be considered the zeroeth dimension!

    Your second premise, is just logic, and it works well with me. But to just state ''absolute zero,'' is akin to |0| yes... and any operation like that, is really undefined... i would have thought.
     
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  5. Quantum Quack Life's a tease... Valued Senior Member

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    I honestly donot expect mathematics to be able to handle the 2nd part.

    to determine a absolute zero result purely by default would take some doing yet 1+1=2 could be said to do so.

    I am not sure if we have a method or theorum or any structure to do it with.
     
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  7. Quantum Quack Life's a tease... Valued Senior Member

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    Like to see mathematical proof that zero is relative though...which if course it is.

    not easy though I anticipate.
    and I probably wouldn't undertsand the math any way...
    but doing so opens the door to proving Absolute Zero by default.
     
  8. Reiku Banned Banned

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    Well, here is one way to do it. You can say there is in fact a 0.50/0.50 chance between \(\sqrt{-1}\) and \(\sqrt{1}\), instead of using a zero. It's similar to the notion of a superpositioning of values. You can have in physics, a thing existing as 0.50% of one thing, and 0.50% of the other, but they are also considered as things not actually real at all, and you could apply the same logic with the value of zero...

    ...but... it's difficult to say. If you want to call zero an observer, then it is an observer, but if you take it as a value, it really doesn't have a value that can be used a a relative observer at all... so...

    ... head's fried

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  9. D H Some other guy Valued Senior Member

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    Dang. I can't find any good net references on the difference between comparative, relative, and absolute scales. The laws of thermodynamics illustrate the three. The zeroth law of thermodynamics in effect defines a comparative temperature scale. With this law and some device to measure energy flow, one can say object that object A has a higher temperature than object B, which in turn has a higher temperature than object C. You can even start assigning numbers to such a scale. For the sake of argument, lets invent the frozblat temperature scale, with 300 frozblats representing something in thermal equilibrium with object A, 200 frozblats representing something in thermal equilibrium with object B, and 100 frozblats representing something in thermal equilibrium with object C.

    One problem with a comparative scale is that you need an infinite number of rather arbitrary reference points if you want to use such a scale numerically. Even if you did that, so what? How does the step from 100 to 101 frozblats compare to the step from 299 to 300 frozblats? Among other things, the first law of thermodynamics helps make the temperature scale relative. The step from 100 to 101 Centrigrade is exactly the same as the step from 299 to 300 Centrigrade.

    Even with this enhancement, there remains a problem of a missing absolute. Some scales such as distance are relative only. There is no such thing as a preferred spacial origin. This is not the case with temperature. The second law of thermodynamics provides an absolute zero. The third law says this absolute zero truly is an absolute zero.

    Edit
    Post restored to its original, thanks to QQ's archive.
     
    Last edited: Jun 17, 2008
  10. Reiku Banned Banned

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    Mmmmm...
     
  11. Prince_James Plutarch (Mickey's Dog) Registered Senior Member

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    Quantum Heraclitus:

    I don't think, mathematically, the absolute/relative zero distinguishment is meaningful.

    Do you want the mathematical explanation of what zero is in itself? As that is the closest you'd get to an "absolute zero" in math proper.
     
  12. Reiku Banned Banned

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    Not entirely true -- by a logical sense. You can say that zero could still increase so that a value of 1 is obtainable, if we are using standard logic of a counting system... So if you said, absolute zero, you really can't exceed or preceed something that is absolute. Or, i may be wrong.
     
  13. Reiku Banned Banned

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    lol - dafty

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  14. D H Some other guy Valued Senior Member

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    I used the wrong names in that first entry for different kinds of scales. I remembered the correct names on the drive home.

    SS Stevens, in his seminal paper "On the theory of scales of measurement", published in Science in 1946, defines four different kinds of scales: nominal, ordinal, interval, and ratio scales. A nominal scale provides the ability to label things: red, green, blue, for example. Two nominal measurements can be compared for equality, and that is about all one can do with nominal scales.

    An ordinal scale adds the ability to rank things. An A in a college course is better than a B, which in turn is better than a C. The zeroth law of thermodynamics defines an ordinal scale. Two objects can be tested for the same temperature (thermal equilibrium) or be hotter/colder than another via the direction of energy flow. On the other hand, the meaning of the differences is a bit unclear in an ordinal scale.

    An interval scale adds meaning to the differences in rank. The Centigrade temperature scale is an ordinal scale. Location is another kind of interval scale. Zero is rather arbitrary in an interval scale. While that is as good as one can get for things like location, it is not for other things such as mass and temperature.

    A ratio scale adds meaning to ratios. A ratio scale must have some absolute reference. There is no such thing as negative mass or negative temperatures (at least classically). Mass and absolute temperature are ratio scales.

    For more info, read the wiki page http://en.wikipedia.org/wiki/Level_of_measurement.

    That said, some have debated this whole measurement theory thing. See http://www.spss.com/research/wilkinson/Publications/Stevens.pdf, for example.
     
  15. D H Some other guy Valued Senior Member

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    Yes. Post restored. Thanks.
     
  16. Quantum Quack Life's a tease... Valued Senior Member

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    as I said in the OP I donot think math can define non-relative zero by any means other than by default.
    to end up with a formulation that allows a non answer ie 1-1=[ ] rather than 1-1=[0]
    But it is possible I feel to conclusively narrow the default result of non-relative zero by proving everthing else. How this is done in math I do not know.

    for example

    e=mc^2 is an all in all sort of formula, anything that falls outside this formula weakens it's holistic nature.

    If it is in fact a complete statement for energy, then it proves by default no-existance. or non-relative zero....if it is incomplete it fails to prove by default non-relative zero....
    tough call hey....is a form of deductive reasoning in epistemology, arriving at a solution purely by the absolute deduction of every other alternative.
     
  17. Reiku Banned Banned

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    Well, again, i will answer, the notion of zero means nothing mathematically, and in physics, something which is superpositioned is also considered non-existent, but has a split value of 0.50 and 0.50... so in a sense, quantum mechanics is saying that the values 0.50 and 0.50, let's say in this case, to determine a spin up or spin down, niether the up or down really exist, but exists simultaneously, nevertheless.

    So, if you use zero to define something, we can't really say very much about the zero value, because it is essentially meaningless. Nor can we apply rules like, let zero equal nine, because it was still zero, and that predicts a contradiction in math.

    So, if you are using zero as a counter that seperates one side of the complex plain \(\sqrt{-1}\) to distinguish it from \(\sqrt{1}\), then technically it is right, because we already use a zero notion to distinguish the complex plane as being relative to the real plane.

    But my head really is spinning now...

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  18. AlphaNumeric Fully ionized Registered Senior Member

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    This is incorrect. The concept of zero is essential. It's in all kinds of mathematical constructs and without it they fall apart.

    Zero is the identity for a binary operation which is abelian. In a group which is abelian, in other words (a,b) = (b,a) we can define the representation (a,b) = a+b. Groups, fields, rings, modules and groupoids all need an identity, something which has (a,b) = b for all b. We'd call that a 0 ofr abelian systems, since (0,b) = 0+b = b for all b. Without this you cannot have inverses either, since if 0 doesn't exist you cannot have a -b where (-b,b)=0.

    You are trying to define 0 by a measure, ie a norm such that d(0) = 0. 0 is so much more than that. To give another example, suppose we have the group of the reals under addition, ie we're considering the mathematical structure of adding numbers together. In this case we have an entity a such that (a,b)=b for all b. We call that 0 when the group operation is addition. However, this system is exactly equivalent to the group \(e^{x}\) under multiplication. This is because [te]e^{x}e^{y} = e^{x+y}[/tex], so adding x+y is mathematically identical in structure to multiplying \(e^{x}\) and \(e^{y}\). But in this case our identity is \(e^{0} = 1\), since 1*\(e^{x} = e^{x}\) for all \(e^{x}\). So our 'zero' in this case is 1. This doesn't have modulus 0 but it's the same entity as 0 in terms of the defining properties of a 0 when considering addition over the reals.
     
  19. Reiku Banned Banned

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    I just meant quantity, sorry. Me and my wording again

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    Like, zero is nothing, when 1is something...
     
  20. D H Some other guy Valued Senior Member

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    No, it does not. The modern version of the equation is \(E^2 = (mc^2)^2 + (pc)^2\), where m is the rest mass of some particle and p is the particle's momentum relative to some observer. If the particle is not moving with respect to some observer this reduces to \(E=mc^2\). However, this expression does not imply an absolute energy because it tautologically removes the energy due to relative motion.

    In older versions of the equation, \(E=mc^2\), the quantity m is the relativistic mass, and the relativistic mass depends on the relative speed of the particle with respect to some observer. There is no absolute energy regardless of the way you want to look at the equation.
     
  21. Reiku Banned Banned

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    By that QQ, he means that relativistic mass is only a change in energy, which shows there cannot be an absolute energy.
     
  22. Prince_James Plutarch (Mickey's Dog) Registered Senior Member

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    Quantum Heraclitus:

    ...Why would E=MC2 have to prove absolute zero?
     
  23. Reiku Banned Banned

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    Because theory suggests that when you add all the energy in the vacuum, you should have a zero total, but we are in fact left with more energy than we can even observe. I have a theory that it is what is left over (1), is what we see.

    (1) - So some type of renormalization value(s) which would be the ''effect'', was essentially the ''cause''

    Just a mad idea.
     

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