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Define Distance

  1. May 12, 2007 #1
    I believe very fundamentally basic units such as time cannot be defined. Of course there are definitions for time. But none can capture the meaning in which time is something that passes, like days rolling by... In the same sense does that mean that distance also cannot be defined?
  2. jcsd
  3. May 12, 2007 #2

    In terms of gravitation it is actually impossible to distinguish between space and time. Mass, distance and time simply cannot be measured by gravitation alone since they are all interrelated. This is due to the diffeomorphism invariance of general relativity.

    The only known absolute measure of distance is in terms of electromagnetism by using the fine structure constant and the Planck length.
    Last edited: May 12, 2007
  4. May 12, 2007 #3


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    I guess "distance" is how far apart two points in space are. if there are many points then you will need to just pick two first and then the distance between these two will become the standard "unit" that you use to measure all other distances between points.

    As to what we really mean by distance: firstly it really depends on your taste, mine is probably the number of "ticks" it takes for a photon to get one point to another. one "tick" being (say) the pulse of a Pulsar....
  5. May 12, 2007 #4
    mjsd, those definitions would only work in euclidean geometry.

    Let's take an example. Einstein showed that the formula for gravity found by Newton was a poor approximation at some instances, because it relied on the instantaneous separation between to objects with mass. Using Special and General Relativity, two questions needed to be posed for the Newtonian definition. Instantaneous according to...? The separation at what time? Long story short, simultaneity as its classical description in non relativistic mechanics is quite meaningless in relativity.
  6. May 12, 2007 #5
    The universe (IS) the definition of time. It stands as markers for time. The universe (markers) exist, and time (NOTHING) does not.
  7. May 12, 2007 #6
    I agree with prasannapakkiam. I think that time should be treated as just another spatial axis. Perhaps the reason time seems to flow is because we are caught in some temporal gravitational well.
  8. May 12, 2007 #7
    Well, I have written a PDF on the Mathematics of SR. In the Glossary section, I said time can be thought of as a parameter, and that every vector in 3D Space can be defined from it - just as a function can be defined parametrically, in which every interval is drawn for each interval of the parameter. As for distance, it is quite hard. I tend not to agree with msjd's definition as it seems to just say distance is distance...
  9. May 12, 2007 #8


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    hey, I thought this is supposedly a philosophy thread not a "physics" thread... besides, photon always travel on the geodesic whether it is flat or curve space... so I don't see a big issue there. Of course there is an issue about time, but that's not the point here I believe... we all know that different observer measure different distance and time based on their reference frame. What I believe the OP was getting at was that how do we make sense of the thing refer to as "distance"?

    well... what do you have in mind? distance is not distance as we know it but distance is just some abstract quantity we use to parametarise something else? I am not saying that my definition is correct, I was just throwing in some ideas, because I don't understand what you are really getting at.
  10. May 12, 2007 #9
    Well, all I am saying is that, you cannot define something with the original word itself. For example, one definition of time is: the period it takes for an event/action to occur. This effectively says time is time - i.e. what is period, the time... So that is why I did not agree with your definition of distance. But that is probably the closest definition we can come up with...
  11. May 13, 2007 #10


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    in order to use "distance" or "time" to discuss the relation between "events", one needs a "definition" that has practical value, that help us in defining something else in a logical way. If you do not care about applications or relation to other stuffs, then you don't need a definition for "distance" or "time", whether you can "define" them is irrelevant. At the end of the day, you may tag any concepts to the word "distance" or "time", if your choice is useful enough for your specific purposes then it will be just as good as any other choices. There is probably no such thing as the universally "best" definition in this world.
  12. May 13, 2007 #11
  13. May 13, 2007 #12


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    What is a definition?

    You have a set of strings in your language. You have a set of objects in your model (i.e., whatever you are trying to define, say, the real world). I'll assume neither are empty. You map the strings to the objects. A definition is either (i) this mapping from a string to an object or (ii) some relation on your strings (an equivalence relation or perhaps an operation or whathaveyou). So to say that one of your strings cannot be defined means either that (i) you just didn't map it to any object for some reason or (ii) your definition relation is partial (i.e., a string is not in the domain of your definition relation).

    Is it one of those?

    Or do you mean defined in some other sense, perhaps that some theories have atomic objects, which are take as undefined?

    Or maybe you are thinking of definition as being an operation that adds some structure to your strings as, say, you might think of multiplication on the integers as adding structure to them, and you are thinking of "fundamental" strings as being like primes in that case or something?

    At any rate, I don't see why this has anything to do with your model (i.e., something special about the things that you call time, space, etc.). Rather, the peculiarity seems to lay in the theories that you choose to use to interpret your model.

    (Hah, science and model theory use "model" in somewhat opposite ways. I might have used both. I hope it does not cause confusion. That last sentence made me do a double take. In MT, it's the theory that gets interpreted (and some interpretations are models).)
  14. May 14, 2007 #13


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    My personal prognosis is that we should find a common denominator for measure of time ans configuration spaces. I think the measure will have a probabilistic interpretations similiar to a measure of distinguishability.

    Some people have toyed with these ideas, where you define a distance metric by the probability of mixing up the data. Thus by construction remote points are not likely to be mixed up, also giving locality a statistical status. Intuitively when you starting thinking along these lines, gravity interactions are not far away.

    The logical problem I see, is how to make a consistent decomposition of space, from the rest of general configuration space. They way I see it, this way of construction suggest to me it's all blurred and inherently relational. Any artificial picking out a background space time, and consider physics ontop of that seems to somehow be ambigous, because all measures are bound to be related.

    I picture time as a parametrization of progress, relative to expectations. I think the local information would suggest an optimal bet. Classically time might a parametrization along the "bet-line", and otherwise it might be like a random walk averaging around the optimum bet-line.

    I think prasannapakkiam's questions will be seen a proper answer eventually.

    To my knowledge nonone yet derived classical GR in terms of the information geometric approach?

    I suspect the obvious problem in doing thta, is howto subtract the rest of the dynamics from the supposed "spacetime" geometry.

    Anyone know? I know Ariel Caticha thought this would be possible, but I don't know if he is still wokring on it, or if he has given up?
    http://arxiv.org/abs/gr-qc/0301061. I'm not sure it's necessary to decomposing it though, perhaps the decomposition beeing inherently ambigous is why we have a hard time merging the theories in the semiclassical synthesis.

    Disclaimer: I recently resumed this so I am still working on the formalism to back up my intuition above, but I would be interested to hear if someone else know what progress has ben made on this? Specifically explaining the GR logic in terms of information geometry and first principles.

  15. May 14, 2007 #14


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    I personally see part of the problem that since in general, the conditional probabilities P(x1|x2) != P(x2|x1), the most general correlation kind of bundles the geometry with the dynamics. Seeing x2, given x1 may be more likely than the other way around, because not only does it include the geometry it also includes the full dynamics. I guess one would need to split the transition probabilti into a proper metric corresponding to a normal geometry, and the residual term for the additional dynamics. To what extent this can be done in a unique way without coupling is an interesting question? It seems all the dynamics is floating ontop of the floating ground, but exactly where does the ground ened, and the superpositioned dynamics start?

  16. May 14, 2007 #15


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    Distance is the separation along any dimension of measurement between two things. These "things" can be events (the US Civil War and the Battle of Thermopylae are distant in time from one another), objects (I am distant from the fan at the other side of the room from me), or anything else of which we can intelligibly speak of distance between them (there is a gap in thinking between Ann Coulter and Gloria Steinem). Note, the dimension of measurement in the last example is wholly qualitative, in that there are no units, and there probably can be no units, of intellectual agreement and disagreement, although you can still map a political spectrum and give chart units to a person's position if you please (many online tests do just this) and give the distance a visual representation.
  17. May 25, 2007 #16
    time may not even exist for all we know, it is a measurement, nothing esle. there are things in between that give us a sense of time. destination, distance, day and night etc... time, like mathematics, is only a guideline. humans (we) are born with the thought/teaching that we must have a beginning and end, when really, in fact, we don't need to. we see new borns and people dying etc... we claim hypotheses for the universe's beginning and end, when, infinity, has two sides and we are somewhere in it. however, the location in infinity where we stand, is no different than any other point, there is no lesser or greater point. usually when we think of inifnity, we only think of present time to future, and never take account the past simultaneously.
  18. May 25, 2007 #17
    Exactly. It is just a perception that we seem to have taken for granted; and built everything upon it...
  19. May 25, 2007 #18
    This is really a good one, and I think I would have red the question more like: "What is time ?"

    Well, I think a good place to start will be to ask some other questions:

    "What is an explaination ?", "what will the meaning 'mean' ?", and "what is then a 'definition' ?"

    Possibly it could be like that, the nature of the "time" is not a sequence of words and it neither a mathematical formula.

    To explain: Lets say I show you a picture of a car - its a green one of a certain modell and you can read the registration plates, and I ask you: Is this your car ?

    Your answer might be: No this is not my car, this is a pice of cartoon with some color on it, my car is made of steel.

    Your car might have more than one side, so it might be needed more than one picture to give a bether understanding of your car, one from each side, one from the inside, one from the engine compartment etc.

    The collection of pictures will give some ideas about your car, but still they will not be your car.

    In a simualr way, an explanation of time will not be the time itself but a more or less accurate or applicable picture of the time.

    As it might be required more than one picture to explain or describe your car, it might be needed more than one picture, sentence or formula to explain the time. But still, like the description of your car will not be your car, the description of time will not be the time.
    Last edited: May 25, 2007
  20. May 26, 2007 #19
    :approve::smile::approve: WOW. Well I guess it doesn't get closer than this!
  21. Jun 6, 2007 #20
    The problem is that when a 'thing' or an 'entity' or an 'event' is 'Super-positioned', space distance and time always have zero values. This is also metaphysically and epistomologicallly equivalent to implying that the thing or entity or event has zero-history (that is, acting or occuring whithout leaving a single trace of spatio-temporal history). Under this superstate, the notion of distance or time flies out of the window. It's pointless thinking about it.
    Last edited: Jun 6, 2007
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