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Can the proggression of time be described purely as a mathematical function?

  1. Nov 30, 2008 #1
    I am not too good at maths, but I have noticed a few patterns in some basic functions.

    For example, when comparing a function to the inverse of that function, the inverse of the function can often come out with multiple values, but the original one always leads to one definite number. For example, the 'square' and 'square-root' function. The square root is usually "plus or minus" the square root, and hence the two possible values. The same with trigonometric functions.

    Another pattern I noticed when comparing the inverse function to the original one is that it doesn't matter about the order of the computation of the normal function, but then when calculating the inverse, the order matters. e.g.

    7*23*4*5 is the same as 7*(23*(4*5)), but 7/(23/(4/5)) is not the same as (7/23)/(4/5).

    Another point: every function has a 'base', for example the multiplication function can be written as f[y](x)= x*y (where [y] is the 'base'). The inverse of SOME functions can be found simple by changing the base of the original function to [1/y]:

    f[1/y](x) = x*(1/y) = x/y

    But other functions do not work in the same way. For example with logarithms:

    log[a](x)= y
    but,
    log[1/a](y) does not = x

    Does this mean that all the different functions can be sorted into different groups? Sorted into groups that share properties.
    ------
    And now onto the physics:

    Could someone calculate a function that simulates the passing of time? In which the necessary values of the universe (perhaps the velocities and positions of particles?) are changed to give the values of the particles a second later? Obviously to develop a single function to do this would be mind boggling, so this is only a theoretical question.

    What would this function act like? Would the inverse of this function lead to even more possible values that the forward version? (seeing as quantum mechanics adds an inherent randomness, and hence multiple values). And could it possibly lead to less values than the forward version?

    I welcome any help or information on this ponder of mine, including criticisms. As I said, I'm not an experienced mathematician so I might have got something wrong.
     
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  3. Nov 30, 2008 #2

    ZapperZ

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    You are making connections where such connections do not exist.

    For example, what's so special about "square" and "square root"? It's not as if "cube", "cube root", etc... etc. do not exist. Those are multi-valued as well, as anyone who has taken complex algebra can tell you. There's nothing special about square and square root.

    What you are doing is similar to arranging letters of the alphabet, and then finding some odd pattern and deducing the law of the universe from it just because it happened to spell something similar to a physics concept.

    Zz.
     
  4. Dec 1, 2008 #3
    I think you have missunderstood me. Im not trying to make conections, I'm simply observing. there are many functions, including all the "power" functions, that are not multi valued, unless it is the inverse of the function. I am simple observing different properties that a function can have.

    What I am asking, is what would the properties of the "Time function" be? e.g.

    If we knew all the properties of every particle in the world, then how many possible out comes would there be? Would it be an infinite range? And the inverse of that function would tell us what previously has happened. So would there be just as many possible values for that?

    I am not trying to conclude anything about the laws of the universe, so you are wrong about the "arranging letters of the alphabet" analogy.

    Maby I shouldn't have called them "patterns", but never mind.
     
  5. Dec 1, 2008 #4

    ZapperZ

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    So if your observation has no profound ideas behind it, then I don't see why you would even want to bring it up. I observe patterns in the clouds. The observation ends there without any attempt on my part to try to dig any meaning into it.

    You will have to define what is meant by "time function". Do you also have a "space function" to go along with that? After all, per SR, they are on equal footing.

    Why is this inverse function so fascinating to you? If you have looked at classical E&M alone, you'll see many other "functions". Try solving the E field for, say an infinite plane of charge, for example. No inverse function there. Or what about a harmonic potential we use in solid state physics? No inverse function there either.

    So what's with the "time function" and the fascination with the "inverse function"? If this is only pure mathematical curiosity or numerology, shouldn't this thread be in the mathematics forum?

    Zz.
     
  6. Dec 1, 2008 #5

    atyy

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    What time should we use? The beating of a heart or an atomic clock? We choose a clock that makes the laws of motion simple (ie. F=ma). Compare equations (1.24), (1.25), (1.26) in the following, where different choices of time have been made: http://books.google.com/books?id=WAW-4nd-OeIC&printsec=frontcover#PPA6,M1
     
  7. Dec 1, 2008 #6
    But you see, we don't know all the properties of every particle. Hell, we don't even know all the properties of a single particle. However, I do like what you are trying to do here in the sense that you are stepping back and looking for universals. What I don't like is that you are treating the passage of time as a mathematical function.

    The biggest fallacy in all of physics (in my humble opinion) is the belief that the laws of nature are constant. It is just a belief, based upon the experience of what we've seen in our brief period of existence true, but it is carrying a lot of weight and the branch is pretty thin. And the conclusions that we've made based upon this premise encompass literally everything we know, or think we know.
    We assume that mathematics models existence perfectly. But that assumption is based upon the belief that the rules don't change. If they do, and so far we've seen nothing that doesn't change so why assume the rules don't.... what does that do to our worship of mathematics? Mathematics works great, for now and for handling the things that need to be handled. But it is not a wizard's staff.
     
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  8. Dec 1, 2008 #7

    ZapperZ

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    But the assumption that they DO change is also based on a "belief". So what's the difference?

    Considering that there are MORE empirical evidence that things haven't changed, it appears that the acceptance that they have changed is based on a belief based on flimsy or lack of evidence.

    It doesn't mean that we haven't been looking for such a change. There have been several observations in looking to see if the fine structure constant has, in fact, changed with time. This clearly shows that no one worship anything if we ourselves are trying to see if something as fundamental as the value of this might have changed.

    Nothing is held sacred in physics. But to challenge it, it must be based on solid grounds, i.e. experimental observations, not simply with idle speculation.

    If this thread continues in this line and not get back to actual physics content, it will be moved into the Philosophy forum.

    Zz.
     
  9. Dec 1, 2008 #8

    Vanadium 50

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    We can look at the universe as it was long ago and determine that the laws of nature then are identical to the laws of nature now. Your humble opinion is unfounded.
     
  10. Dec 1, 2008 #9
    I'm curious how you determined that we've looked at the universe long ago and determined that nothing has changed since then. The term 'long ago' is relative. We might think that 'big' is Mt. Everest. But compared to our little tiny solar system, it's miniscule. Compare that to the Milky Way, etc. We have attached an age to the universe which might be completely false if any of the assumptions on which that age is based are not true.
    Just 50 years ago cosmology considered the activity of our solar system to be very much like a well oiled machine, a clock as it were, and that we could accurately predict using retrograde analysis the precise structure and location of all of the planets going back as far as we wanted. Catastrophic events as harbingers of change were beginning to be proposed by some people but were mocked, viciously, as ridiculous and anyone who believed such nonsense were considered crackpots. When the normal order of things is challenged, that is the standard response. Just 50 years ago we were looking at the past and not seeing what was there. What makes you think we've now become accurate in our understanding of the past?

    If the units being used to measure change were themselves changing, then the possibility exists that we might not detect any change even though a change was taking place.
    But perhaps you are correct and some things don't change. Human nature, for instance.

    I do agree that this should be moved to the philosphy forum.
     
  11. Dec 1, 2008 #10

    ZapperZ

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    How about 6.5 billion years ago[1]? By current estimate, that's about half of the age of the universe, which is subtantial and not miniscule.

    Zz.

    [1] Flambaum and Kozlov, Phys. Rev. Lett. 98, 240801 (2007).
     
  12. Dec 1, 2008 #11

    Vanadium 50

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    It's not very good philosophy. "We made mistakes in the past, so therefore we know nothing" is hardly profound. Or correct. "Maybe you're wrong!" is hardly a good argument in any event.

    There are two possibilities. One is that we are able to observe the universe as it was long ago and infer that many of the laws of physics are the same. The other is that the laws of physics change, in exactly the right way so that it appears that many of the laws of physics are the same.
     
  13. Dec 1, 2008 #12

    Vanadium 50

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    The problem is that one can always counter with, "Ah...but maybe the universe isn't really 6.5 billion years old. The laws of physics changed to make it look that old." Once you go with this line of argument, you might as well toss all of science, as the argument really boils down to "maybe the universe is different from the way your observations indicate."
     
  14. Dec 1, 2008 #13

    ZapperZ

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    Ah, by then, we can play the speculation game, and I can easily make as valid a speculation as any about the mental state of the poster. :)

    Zz.
     
  15. Dec 1, 2008 #14
    Those are good points guys/gals. How about if we just maintain an element of doubt and call it a day, eh?
    I really do like "maybe the universe is different from the way your observations indicate" because it says that we understand that our understanding is based solely upon our observations. It really doesn't invalidate science, it just simply appreciates the idea that our observations can be flawed. And that means we must maintain vigilance against giving ourselves an omniscience that we don't really have.
    I was warned off of one post because I brought up Mark McCutcheon's "The Final Theory" because I violated one of the rules of this forum by mentioning someone who those who are omniscient have deemed a crackpot. That's ok. He's in some pretty good company and I'm not worried about the unfairness of the label. Perhaps it's just my mental state :) but I have a strong suspicion you haven't heard the last of him. Unlike those of you who consider him a crackpot, I have read his work. And I understand most of it. I understand a lot more about a great many things after having read him than I did before I read him. And I know that he might be wrong. I simply took the time to consider what he was saying, which is more than what many others have done. To understand that one's perception of existence might be flawed for a very fundamental reason is a frightening thought, one that not a lot of people can deal with.
    And as far as this not being good philosophy, well, to understand our relationship to existence we must consider our nature as observational creatures whose mode of survival is the interpretation of observation. Anything that sheds light on that process is fundamental to philosophy.
     
  16. Dec 1, 2008 #15
    (1) I found the patterns/properties, and I asked this forum about them, to see if you could make any sense from them. From what I have heard so far, the properties mean nothing about the function. And nobody has attempted to list the functions of maths in a table with similar properties. (This is what I was hoping for)

    (2) A definition of the function could be: A function that manipulates the nessacary values of the universe in the same way that the passage of time does.

    What is to the right of an object is independent on what the object is. You could not create a function to predict what you will find as you move through a space dimension. Whereas what happens in the future IS dependant on what happened in the past, so a function exists? right? Correct me if I'm wrong, but I don't think time and space are on completely equal footing here.

    (3) I don't know what your talking about here, ha-ha, I have only done GCSE and AS Maths. I am not 'fascinated' with the inverse of a function, I just mentioned that if a function existed to describe time, the inverse of this would predict the past.

    (4) I did consider putting it in the maths section, but I decided against it, as a mathematician may not be able to answer the relation with time.

    Well this is my original question: Why do you not like it? Is it not possible?

    This is what I am interested in.
     
  17. Dec 1, 2008 #16
    To the OP,

    You should try your hand at learning a little more about math and physics before trying to come up with theories of your own. You'll learn a lot more from studying two hundred years of scientific progress than you will with months or years of trying to figure it all out yourself.

    In this case, let's look at what you have here.

    First, you're talking a lot about mathematical functions, but you don't seem to have a clear grasp of the general notion. To you, like many people a "function" is a button on your calculator =-) But functions like square root and log are just the most useful for engineering disciplines. You can define a function however you'd like as long as it assigns a SINGLE output to each possible input. For example, f(x) is 0 when x is rational and 1 when x is irrational. It's not continuous. It's not useful at all to a physicist, but it's a function.

    Somethings, we talk about "multi-valued" functions, but these are not functions in the strict mathematical sense. These so-called multi-valued functions arise when you need to "undo" a function with no inverse.

    Functions can be classified into two important categories in math: surjective (aka onto) and injective (aka one-to-one). A function which is both one-to-one and onto is called bijective. A only injective functions can have inverses, because it guarantees that when you "flip" the x and y axis, your function is still single-valued, and thus, it's still a function. Logarithms, exponents, and x^k where k is an odd integer are all injective. Square roots, x^k where k is even, absolute value, and sine and cosine are *not* injective, and so their inverses turn out to be "multi-valued".


    For your physics question, consider this. Let's say at any given moment, the universe has a definite state. Think of a state as a single frame of a movie. The state tells you where everything in the universe is and what it's doing at that instant in time. We could imagine, then, that the universe is a function which maps points in time to states of the universe. Such a model of the world seems totally plausible. In fact, many computer-simulations use this kind of technique. It allows you to pause or rewind time in the simulation at your whim.

    However, to make a statement that says that's REALLY how the world works will get you in trouble on these forums, and it shows you haven't gotten terribly deep in physics (yet!).

    First, spacetime is not Euclidean. Relativity shows that time plays tricks on you when you start moving faster and faster. For instance, if two people see a planet explode, they will disagree on WHEN it exploded, and there is provably no way to determine who is right.

    Quantum mechanics makes things even harder. (QM is something like mother nature telling scientists to get off her back). Part of the implication of QM is that the state of your universe is inherently unknowable. If the universe function from time to states, the joke is that we can't even know exactly what state it's in!

    So while your "time function" theory isn't completely crazy, it is, unfortunately, completely useless. But don't be discouraged. I had ideas like that when I was younger too. The universe doesn't work exactly like you think it does, and you should go out and learn more about how it *does*. Reality is stranger than fiction, and as long as you're patient, it will be worth it ;-)
     
  18. Dec 1, 2008 #17
    The word function (at least to a mathematician) has a very precise meaning. It is a fundamental kind of mathematical object. It's one of the most powerful abstractions in the history of mankind.

    Most of mathematics is the study of particular classes of functions, such as polynomials (algebra), trigonometric functions (trigonometry), continuous functions (point-set topology), real- or complex-valued functions (real or complex analysis), linear transformations (linear algebra), homomorphisms (group theory), bijections (set theory), morphisms (category theory), transformations on real or complex functions (calculus), computatable functions (theory of computation), and I'm sorry if I left any important ones out.

    While a physicist likes to think about things that are always changing, in math, a function doesn't actually change what it acts on. If f(x) = |x|, then f(-5) = 5. But that doesn't mean I "changed" -5 into 5. -5 is still negative, 5 is still positive. Functions don't change their inputs. Functions don't change anything at all. But when you think out a problem, you tend to work it out step by step, and it comes across as if that number was actually changing. But it's not.
     
  19. Dec 1, 2008 #18
    Thanks for the Constructive reply. I have already heard of and (partly) understood the basics of quantum theory and special/general relativity. I also did not mean to be "trying to come up with theories of my own" I was just asking people questions. I never presumed I was right.
    I want to learn, and when I have ideas and ponders, I come here to find out what is wrong and right with them.
     
  20. Dec 1, 2008 #19
    OK, so the passage of time (I will stop calling it a function) does not destroy the past and create the present, I understand that. But just like f(-5) = |-5| = 5, f(x) depends on the value of x, just like the future depends on the past (or present).

    Does this make sense?
    How would I word it?
     
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