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Velocity in 4th dimension

  1. Jan 24, 2012 #1
    How is it like to travel at the speed of light in the 4th dimension?
    and according to general relativity, the 4th dimension is time, what does that mean ?....and why? :rolleyes:
     
  2. jcsd
  3. Jan 24, 2012 #2

    phinds

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    You cannot travel at the speed of light unless you are a photon in which case you would not be self-aware, so there is no answer to that part of your question.

    As to traveling in 4D space-time, you are doing in time right now, 1 second per second. Your "speed" depends on what reference point you chooose.
     
  4. Jan 24, 2012 #3
    Thinking about time as a fourth dimension means that it morphs into space and space into it. Different observers may see them differently.

    So space and time vary with velocity which is not expected in Newtonian physics. It turns out that space and time are not fixed and immutable, but the speed of light IS fixed, also unlike Newtonian physics where forces act instantaneously. The formula for the addition of two velocities is only approximately v1 plus v2 that we typically learn is early school. You can read about that here:

    http://en.wikipedia.org/wiki/Addition_of_Velocities_Formula


    As you approach the speed of light, your time as observed by an outside inertial observer appears to run slower than theirs....you see it locally as passing normally. You observe space in front contracted, so the distance you need to travel is foreshortened, but an outside inertial observer is unaware of your observation change from theirs. Different observers in different frames of reference see different things.....there is no 'absolute' reality.

    There is no intuitive reason for all this: if it were 'obvious' it would not have taken an Einstein to realize what's happending. But once it was understood the speed of light is very fast, but finite, a number of pieces fall into place. So with relativity, and separately quantum mechanics, we need some new ways of thinking, some new mathematics and a new perspective because what we observe macroscopically and at slow speed is not how nature behaves at high speed or microscopically. Our senses are just not attuned to those phenomena.
     
  5. Jan 25, 2012 #4

    This is obviously very difficult to picture. One analogy that may help the imagination perhaps is that of the quote by Yeats: "How can we separate the dance from the dance?"

    If we conceive of time as a measure of relative movement (ie, the pacing of any given movement with respect to a standard movement generated by an apparatus we call a clock) then spacetime as a 4-dimensional theatre takes that question one step further to "How can we separate the dancer and the dance from the space they occupy?". The physical answer is that we simply can't, neither the dancer (matter) nor the dance (relative movement, which implies time) can exist independently of the space they occupy or 'consume' so to speak.

    IH
     
    Last edited: Jan 25, 2012
  6. Jan 27, 2012 #5
    It's an utterly CRAZY idea...but it works!!!! So far, we have no better description.
     
  7. Jan 27, 2012 #6
    Electrons and protons and neutrons are not self-aware either. And guess what we are made of a very large collection of them.

    What has this whole self-aware thing to do with physics?
     
  8. Jan 27, 2012 #7
    If [itex]x^4 = ct[/itex] then [itex]dx^4 / dt = c[/itex], which is the speed of light signals. This is not a velocity.

    According to general relativity the 4th dimension does not need to to be time.
     
  9. Jan 27, 2012 #8

    Matterwave

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    I think it's because the OP said "How is it like?" suggesting that he wants to know what it would feel like...
     
  10. Jan 28, 2012 #9
    In Hermann Weyl's concept the universe is 4-dimensional populated by 4-dimensional objects, including the physical bodies of the observers. So, with this model there is no motion at all of the physical bodies (not even motion along the 4th dimension).

    But, every observer's consciousness moves along his respective 4th dimension at the speed of light, c. However, there doesn't seem to be a consensus among physicists about this concept, and on this forum such a concept is considered speculation and therefore not an appropriate topic.
     
  11. Jan 28, 2012 #10
    Unless the universe is 4-dimensional. But, this is not an appropriate topic for this forum.
     
  12. Jan 28, 2012 #11

    DaveC426913

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    Perhaps a poor choice of words, but it is perfectly valid thought experiment to ask what an electron or proton would "experience" moving at .5c. The fact that they have no awareness does not mean we cannot meaningfully ask and answer what happens to them.


    Contrarily, we cannot do this with photons. Photons, since they travel at c, do not have a valid reference frame at all. It is nonsensical to ask what a photon experiences.
     
  13. Jan 28, 2012 #12
    The the sequence of space-time diagrams in the sketch below depicts the situation for an observer moving at ever greater relativistic speeds. You can see that if a photon was "self aware", his total world line would be experienced simultaneously, evidently becoming unintelligible. His X1 and X4 axes have become colinear. Thus, his X1 component of his instaneous 3-D cross-section view of the 4-D universe is colinear with the 4th dimension. Of course this kind of discussion is not appropriate for this forum.
    Approach_LightSpeed_C.jpg
     
    Last edited: Jan 28, 2012
  14. Jan 28, 2012 #13
    It means it is one of the measurements people take when making certain observations of spacetime.

    Length and time, simple as that. There is of course a unique relationship between these two measurements which is apparent in the interval equation..thing. :)

    Trying to bridge that to an answer of what it "feels" like;
    The above is true from any inertial perspective, from great big to nearly the smallest. Even a rock "ages" in the sense that its composition changes at regular Intervals.

    This is important, the regular intervals in the changing of the rocks composition (radiocarbon dating) are assumed to be purely timelike, that is the time measurement is assumed to be a measurement of just time and not distance, as would be the case if the rock traveled at relativistic speeds compared to the archeologist that dates the rock)

    By whatever blessing this changing of composition along a purely timelike interval can amount to a point of self awareness. Where there is consciousness "along" that purely timelike interval, the 4th dimension time.

    So time "feels" like when you're not unconscious :smile:, which is far from being measurable as an observation with rulers & clocks and is a different field of study all together.

    lol Naty1 "our" best description of time as a dimension is not "Thinking about time as a fourth dimension means that it morphs into space and space into it." Infact I think that's one of the difficulties in understanding time as a dimension; it's relationship with length. Unless "morphs" has some loaded definition I don't know of.
     
    Last edited: Jan 28, 2012
  15. Jan 28, 2012 #14
    And again what on Earth has self-awareness to do with it?
     
  16. Jan 28, 2012 #15
    What is "it" that self awareness has nothing to do with?
     
  17. Jan 28, 2012 #16
    The world line.
     
  18. Jan 28, 2012 #17

    DaveC426913

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    This question was answered in post 11.

    Read it. Embrace it. Move on.
     
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