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Philosophic comments on time in Relativity.

  1. May 2, 2009 #1
    Hello all.

    I was bored and so did a little browsing on the subject of time in relativity and came across this article entitled “The Problem of Time in Science and Philosophy” by Oliver L. Reiser. Which appeared in The Philosophical Review. Vol 35 issue 3 (May 1926) It comes from the JSTOR archive. The following is an extract from the article. I believe the author has written many “well received” philosophical books.

    My question is whether this is an example of a philosopher knowing little physics and mathematics or are there subtleties which I am failing to appreciate.

    ----In the theory of relativity the ideal simplification of nature is carried to its highest state of perfection. In this physical doctrine space coordinates are tied up with time in one equation. Here any one coordinate could be said to depend on the other three. Analytically, such equations are dealt with in the same way as those of three dimensions. Under such conditions it is hard to state which is the independent variable and which the dependent. Time seems to be turned into space merely by giving it a minus sign. This clearly shows that it is not easy to state just what time really does mean in physics, and hence to say that it must necessarily function as an independent variable is inaccurate. Whether, in the last analysis, the Newtonian concept of an absolute and evenly flowing time must be reintroduced into relativity theory, in the form perhaps of the velocity of light, and whether “simultaneity” can be given an absolute meaning, are matters which the physicists have been unable to decide.-----

  2. jcsd
  3. May 2, 2009 #2


    Staff: Mentor

    I think that is consistent with the geometric interpretation. You can parameterize a 1D curve, such as the worldline of a point particle, with one parameter and that parameter need not be "time". All 4 components of the four-vector position of such a particle can then be considered dependent variables and the parameter can be considered the independent variable. You can also consider the worldline to be a simple geometric object where the ideas of dependent and independent variables don't even really apply.
    Last edited: May 2, 2009
  4. May 2, 2009 #3
    Hello Dalespam.

    I appreciate your point. I was more concerned about the staement "Time seems to be turned into space merely by giving it a minus sign.". I know that the minus sign in the signature gives the four dimensional structure its essential characteristics, but chageing time into space?

  5. May 2, 2009 #4
    evening M;

    The expression starts as an equality, x^2 + y^2 + z^2 - (ct)^2 = 0. The time element is transformed to a complex quantity via i^2, resulting in all positive components of a 4D vector. It facilitates mathematical manipulation, but does not change the character of the variables, i.e. time is not a dimension. I'll find some quotes later.
  6. May 2, 2009 #5

    Hello phyti

    Thanks for your reply. I understand the interval and its derivation and its invariance but I am not altogether happy with your explanation of how the time coordinate transforms.

    Time here is modelled as a dimension mathematically but as for time being a "real" or "physical" dimension, that's an argument I don't want to get into.

  7. May 3, 2009 #6


    Staff: Mentor

    Although that statement is essentially correct, I don't believe that it is particularly important. An equivalent geometric statement would be "a hyperboloid seems to be turned into an ellipsoid merely by giving it a minus sign". Despite that fact, a hyperboloid is not an ellipsoid. The presence of the minus sign is not an optional whim but an essential reflection of the geometry.
    Last edited: May 3, 2009
  8. May 3, 2009 #7
    I see the geometry of the situation. It is the physical reference that I do not see. I.e turning space into time. I have no problem with spactime viewed as a whole but not with time and space viewed seperately and one being turned into the other. The following is a quote from Tolman, Relativity,Thermodynamics and Cosmology which, I think, puts forward a similar objection

    ---That there must be a difference between the spatial and temporal axes in our hyper-space is made evident, by contrasting the physical possibility of rotating a meter stick from a direction in which it measures distances in the x direction to one where it measures distances in the y direction, with the impossibility of rotating it into a direction where it would measure time intervals. In other words the impossibility of rotating a meter stick into a clock.-----

  9. May 3, 2009 #8


    Staff: Mentor

    Sorry about accidentally editing my above after you had replied. I hope I restored it. Anyway, I think this is still relevant, but I will read and reply in depth tomorrow:

    The really important feature of the spacetime interval is not meremy that time has a minus sign, but that it is there at all. In other words, that space and time are part of a unified spacetime on which a single combined measure of "distance" can be used to describe both physical clocks and rods.
  10. May 4, 2009 #9
    Thanks Dalespam.

    I am completely at home with the interval and the idea of treating spacetime as a four dimensional manifold. As you say the minus sign in the metric gives it its, at first encounter, surprising properties. (I know some authors use +--- instead of -+++) However I am always aware that my belief that I know something is not always reflected in fact and so I am always interested in any comments or assistance that you, and others may offer.

  11. May 4, 2009 #10


    Staff: Mentor

    I agree. You cannot turn time into space any more than you can turn a hyperboloid into a sphere. You cannot rotate a rod into a clock any more than you can rotate a hyperboloid of one sheet into a hyperboloid of two sheets, even permitting hyperbolic angles and hyperbolic rotations.

    There is a difference between time and space, and it is described by that minus sign.
  12. May 4, 2009 #11
    So in answer to my original question, in the extract above, the author is OK with his mathematics and physics.


  13. May 4, 2009 #12


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    I wouldn't agree with that. Physicists have been able to decide, and the answer is "no". Mind you, he was writing in 1926, so maybe things weren't so clear back then.
  14. May 4, 2009 #13


    Staff: Mentor

    No, as I mentioned above I do not think that it is physically correct to talk about turning time into space by "giving it a minus sign" any more than it is mathematically correct to talk about turning an ellipsoid into a hyperbolid by "giving it a minus sign". If you did that it wouldn't be a hyperboloid any more.

    It is correct that time and space are part of the same spacetime interval formula. It is correct that time is distinguished from space by the minus sign in the formula. It is incorrect that it is particularly physically or mathematically meaningful to talk about changing the minus sign and thereby changing time into space.
  15. May 4, 2009 #14

    Thanks Dalespam.

    I must have misread tour earlier reply. There have been some interesting replies which have answered my concerns about the original quote.

  16. May 4, 2009 #15
    Because time is treated as a dimension in the mathematical model, does not imply a literal
    If you checked your Funk & Wagnalls, dimension can also mean attribute or feature.
    Here is one opinion that has more credibility than mine.

    Einstein's Theory of Relativity, Max Born, pg 307
    "Thus Minkowski's transformation u=ict is to be valued only as a mathematical artifice which illuminates certain formal analogies between space coordinates and time
    coordinates without however, allowing them to be interchanged."
  17. May 4, 2009 #16
    You quote an opinion with "more credibility" than yours. What is your "less credible" opinion?

  18. May 5, 2009 #17
    It's the same, but he wrote a book and I didn't.
  19. May 5, 2009 #18
    Lets say I have lump of lead that has a mass (m) of 1000 gms and a lump of steel that has a volume (v) of 400 cm3 and a density(p) of 8 gms/cm3. How much more does the lead weigh than the steel? The answer is:

    diff = m - v*p = 1000 - (100*8) = 200gms

    Have I turned volume into mass by using a minus sign? No I have not. I have used a density (p) figure to mathematically convert the volume to mass but that in no way implies that volume and mass are the same thing.

    Lets also say 1 took a journey of distance (d) = 300 miles and another journey that took time (t) of 3 hrs at a speed (v) of 60 mph. How much longer was the first journey than the second? Again the answer is:

    diff = d - t*v = 300 - (3*60) = 120 miles.

    Again, I have not turned time into distance by using a minus sign. I have done it by using velocity to mathematically convert time units into distance units.

    The same is true for the invariant interval in relativity:

    S^2 = x^2 - (c*t)^2

    (I have used the 2D version for simplicity here.)

    The time has not been converted into distance by the minus sign. The time has simply been converted into units of distance by multiply by a velocity (c) and there is no physical implication of time turning into distance, anymore than there is any physical implication of volume turning into mass in my first example.

    Sorry to labour the point, but some people really believe that time turns into distance and vice versa in the context of below the event horizon of a black hole and it the source of much confusion.

    Basically the invariant interval finds the difference between how far a particle travels, compared to how far a photon would travel at the speed of light (c) in the same time. If the difference by subtraction is zero, then the particle is a photon. If the particle travels less distance then it must be a particle with mass travelling at less than the speed of light. If the particle travels further then it must be a purely hypothetical particle that is travelling at greater than the speed of light. Nothing mystical at all.
    Last edited: May 5, 2009
  20. May 5, 2009 #19


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    What is a "literal interpretation"? What would be the difference between being "treated as a dimension" and being "literally" a dimension? The definition of a "dimension" is itself purely mathematical.
  21. May 5, 2009 #20


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    Coordinate time in Schwarzschild coordinates does turn into a spacelike dimension and the radial coordinate turns into a timelike dimension below the event horizon. Of course this is just a quirk of Schwarzschild coordinates rather than something of physical significance.
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