Does time expand with space? (or contract) Einstein's big revelation was that time and space are inseparable components of the same fabric. Physical observation tells us that distant galaxies are moving away from us at an accelerated rate, and because of the difficulty (impossibility?) of defining a coordinate system where things have well defined coordinates while also moving away from each other without changing the metric on the space, we interpret this to mean that space itself is expanding. 
Because space and time are so directly intertwined is it possible that time too is expanding? Or perhaps it could be contracting? 
 A: The simple answer is that no, time is not expanding or contracting.
The complicated answer is that when we're describing the universe we start with the assumption that time isn't expanding or contracting. That is, we choose our coordinate system to make the time dimension non-changing.
You don't say whether you're at school or college or whatever, but I'm guessing you've heard of Pythagoras' theorem for calculating the distance, $s$, between two points $(0, 0, 0)$ and $(x, y, z)$:
$$ s^2 = x^2 + y^2 + z^2 $$
Well in special relativity we have to include time in the equation to get a spacetime distance:
$$ ds^2 = -dt^2 + dx^2 + dy^2 + dz^2 $$
and in general relativity the equation becomes even more complicated because we have to multiply the $dt^2$, $dx^2$, etc by factors determined by a quantity called the metric, and usually denoted by $g$:
$$ ds^2 = g_{00}dt^2 + g_{11}dx^2 + g_{22}dy^2 + ... etc $$
where the $... etc$ can include cross terms like $g_{01}dtdx$, so it can all get very hairy. To be able to do the calculations we normally look for ways to simplify the expression, and in the particular case of the expanding universe we assume that the equation has the form:
$$ ds^2 = -dt^2 + a(t)^2 d\Sigma^2 $$
where the $d\Sigma$ includes all the spatial terms. The function $a(t)$ is a scale factor i.e. it scales up or down the contribution from the $dx$, $dy$ and $dz$, and it's a function of time so the scale factor changes with time. And this is where we get the expanding universe. It's because when you solve the Einstein equations for a homogenous isotropic universe you can calculate $a(t)$ and you find it increases with time, and that's what we mean by the expansion.
However the $dt$ term is not scaled, so time is not expanding (or contracting).
A: How could someone inside the spacetime measure the expansion of the time dimension they participate in?  It could expand all day long but to the interior time is constantly flowing.
A: Since what science tells us is that spacetime expanded away in all dirctions from the singularity, then its logical to assume that it still continues to be emitting if you will, from matter to this day. But since all the matter has spread out it maybe said that all massive bodies including subatomic particles, (except massless ones) emit spacetime. This explains time dilation where gravity is present since gravity slows the emission of spacetime only to speed up again as light through glass. I believe that spacetime is emitted from all matter at the speed of light and therefore its this emission that carries all massless particle such as photons. In otherwords photons have no mass and when emitted out of say electron the spacetime expanding from the electron picks up and carries the photon at the speed of light. Though this is just a theory.
A: I'm neither a cosmologist or a physicist, but everything I have learnt about gravity, energy, momentum photons and universal expansion over around 15 years of spare time study, tells me that the dilation of length as the universe expands must be accompanied by the contraction of time.
I believe time contracts by the same percentage in a second as length contracts in a metre. In doing so, the rate of increase in energy wrt distance is equal to its rate of decrease in momentum wrt time and there is no net force and therefore no work being done as the universe expands, due to the expansion.
This is almost the exact opposite of the effect of gravity.
When we make observations of cosmological red-shift, we see a length dilation that meets our expectations, and there doesn't appear to be any time contraction. But don't forget that time must contract c times more slowly than length dilates, i.e. as proposed above it contracts the same amount in a second, which is c metres of travel, as length dilates in a metre. It's virtually insignificant in relation to length dilation.
If I'm right, then what we observe is the net effect of time dilation and length contraction due to gravity, combined with time contraction and length dilation due to universal expansion.
In regions of higher mass density, within galaxies,  gravity dominates, and the effect of expansion just makes gravity appear weaker than it really is. In intergalactic space, the effect of expansion is dominant. So when we look at a photon that's been on a relatively short journey, it doesn't seem to have been affected by expansion, but one that's been on an intergalactic journey does.
