Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Does time expand along with space?

  1. Apr 12, 2015 #1
    Sorry to go on about this topic. I'll get it out of my system soon!

    The flat FRW metric is given by:
    $$ds^2=-c^2dt^2+a(t)^2dr^2$$
    If we take ##dt=0## then we get:
    $$ds=a(t)\ dr$$
    The proper distance between co-moving points scales with ##a(t)##. Thus we find that space expands.

    If we take ##ds=0## to find the null geodesic followed by a light beam we get:
    $$c\ dt=a(t)\ dr$$
    Surely this implies that cosmological time intervals expand in the same way as space intervals?
     
  2. jcsd
  3. Apr 12, 2015 #2

    wabbit

    User Avatar
    Gold Member

    This implies ## dt=\frac{c}{a(t)}dr ##, which is a useful relation but says nothing of "time expansion".
    If ##\tau## is the proper time of a comoving observer, and ##\delta## the distance in his reference frame to another comoving object situated at comoving distance ##r##,
    ##\quad\tau=t## (no time expansion)
    ##\quad\delta=a(t)r## ("space expansion")

    But you may be referring to the time dilation effect when this observer looks at a comoving source. Light emitted by that source at ##t## and ##t+dt## is received at ##t'## and ##t'+\frac{dt}{a(t)}## because the second pulse was emitted from a more distant source than the first - this is actually the same thing as the redshift ot a distant source due to expansion.
     
    Last edited: Apr 12, 2015
  4. Apr 12, 2015 #3

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    No, it implies that the wavelength of light expands with ##a(t)##--i.e., that the light gets redshifted as the universe expands, as wabbit said.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Does time expand along with space?
  1. Does Space Expand? (Replies: 176)

  2. How does Time expand? (Replies: 12)

Loading...