We know certain astronomical events in our neighborhood occur within a specific time interval,for example a solar flare, a nova, etc. Does the time interval of these 'standard metronomes' change if they are further away (millions of light years?)
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$\begingroup$ An important fact about things million of years away is that they are moving relative to us, so experience relativeistic time dilation. There is a standard clock to use, the rate of decay of nickle56 as this causes the brightness of supernovae to change at a regular rate. As far as I recall, the predictions of relativity are supported by these observations, that is, there is time dilation for objects moving at high velocity, but not for merely being in a different place, I'll try to find where I read this. $\endgroup$– James KCommented Apr 12, 2023 at 15:10
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Yes, there are two good examples that I know of that have been used to show that a natural phenomenon appears to show time dilation that is consistent with the redshift that they are observed at.
Type Ia supernovae have decay light curve widths that are reasonably standardised (there is some dispersion). However, when the widths of distant supernova light curves are observed, they appear to be dilated by a factor $(1+z)$, where $z$ is the redshift (e.g., Blondin et al. 2008).
Another piece of evidence comes from Gamma Ray bursts under the assumption that they should have (statistically) a similar mean duration at any point in the universe. Zhang et al. (2013) find that the duration of "long" GRBs at known redshifts (and measured in the same rest-frame energy) varies as $(1+z)^{0.94±0.26}$, consistent with cosmological time dilation. See also Littlejohns & Butler 2014.
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$\begingroup$ Thank you for your reply. So my naive interpretation of these data is that the rate of time passage is due only to relativistic time dilation (due to motion) and there is no other phenomenon. For example, if the duration of long GRBs was different than the time dilation predicted by their redshift, then we would have to say that time passage was intrinsically different at some time in the past. Because time passage is therefore constant across the age of the universe, we can then state the corollary, the speed of light is constant across all space AND time. $\endgroup$ Commented Apr 13, 2023 at 0:33
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$\begingroup$ @aquagremlin if the amount of time dilation was a factor of 1 (i.e. independent of redshift), then it would be evidence for the so-called "tired light" explanation of the redshift. It isn't. Interpretation for dilation of $(1+z)^\alpha$ where $\alpha \neq 1$ could be that the nature of these events has changed over cosmic time. The speed of light is defined to be constant, it is meaningless to discuss a change in the speed of light; only dimesnsionless constants can show evidence for variation. $\endgroup$– ProfRobCommented Apr 13, 2023 at 8:17