At $t_0$, we have a ruler which has two tick marks (one at each end) with one labeled "$0$" and the other labeled "$L$" (it is $L$ units long). Suppose at that time we also have two point objects which are a certain distance apart. Suppose that, by $t_1 > t_0$, space has uniformly expanded so that the two point objects are twice as far apart. Would the ruler also have expanded, by $t_1$, so that the two tick marks are now twice as far apart, since the space that the ruler occupied doubled, or would the distance between the two tick marks stay the same, because of the forces holding the ruler material together? In the former case, length $L$, as measured by the tick marks on this ruler, means something different at the two different times, since the ruler has expanded between those times.

If the answer is that the ruler would have expanded, then, I have a follow-up question: if at $t_0$, the speed of light is measured to be $nL/sec$, by the ruler as it is at $t_0$, then, at $t_1$, is the speed of light still measured to be $nL/sec$, by this ruler as it is at $t_1$ (expanded), even though $L$ means something different at $t_1$ than it does at $t_0$?


1 Answer 1


If the ruler is a simple physical object, held together by chemical bonds, it will not expand, at least if the space is expanding slowly enough. The distance between atoms is determined only be the strength of electromagnetic interactions and the masses of the elementary particles. The expansion of spacetime may generate an additional force, affecting the distance between atoms, but in our universe it is negligible and approximately constant. Thus stretching of the space will not significantly affect the ruler's length.

  • $\begingroup$ so, if you measure the speed of light with the same ruler, at different times, in an expanding universe you will get, approximately, the same result? $\endgroup$ Sep 21, 2019 at 9:20
  • $\begingroup$ To measure the spead of light you need a ruler and a clock, but assuming you have both, yes, you'll always get the same result. $\endgroup$ Sep 21, 2019 at 11:42
  • $\begingroup$ Thank you! And, in this case, since the ruler is not expanding, I am using proper, not comoving, coordinates? If I used comoving coordinates, would the speed of light change since the coordinate system is expanding with space, but time is not? $\endgroup$ Sep 21, 2019 at 17:20
  • $\begingroup$ I don't really know what you mean by 'proper coordinates'. I don't also know what really is your procedure of measuring the speed of light. If you'd described it (in a question), the comments are not the right place for that, I may be able to tell. $\endgroup$ Sep 22, 2019 at 8:20

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