When/if the universe collapses in onto itself as described by the big crunch theory, would time slow down due to time dilation (relative to our experience) as all matter gets pushed together, or do I have this all backward and don't have a thorough enough understanding of either topic?
closed as unclear what you're asking by WillO, user191954, Jon Custer, ZeroTheHero, Kyle Kanos Oct 1 '18 at 10:13
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If you talk about gravitational time dilation then no, time doesn't slow down in a Big Crunch. The reason is that gravitational time dilation is not applicable in expanding or contracting space. It is applicable in a static space-time with a central mass instead where it depends on the potential difference of observers as was pointed out already.
You might however have the cosmological frequency-shift in your mind. We see far away objects like galaxies red-shifted due to the expansion of the universe (distances to us are increasing). For the same reason we see the duration of a far away super nova red-shifted which means it seems to happen slower compared to a super nova much closer to us. In contrast in a Big Crunch the universe contracts (distances to us are decreasing) and hence far away objects like super novae would appear to happen faster. So depending on the epoch of a universe things far away seem to speed up or to slow down, but this may not be confused with gravitational time dilation.
First, you are asking about GR time dilation. it is an actual difference in time elapsed between two events as measured by two observers situated at varying distances from gravitational mass.
GR time dilation is caused by gravitational potential (difference).
Now you are right, that as gravity would become dominant, and no other force could withstand its power (not even EM), you could talk about a big crunch, and gravity would crunch everything into a singularity.
The problem is, GR time dilation is caused by a difference between two places in space, that have different gravitational potential. The singularity itself would not be compared to anything else. So if you are inside the singularity (and everything is there), there is nothing to compare your time to. Even if you would have a clock in the singularity, what would you compare it to? There is nothing outside the singularity, so there is nothing to compare it to (where the gravitational potential would be different).
So time could slow down in the singularity, caused by gravity becoming dominant, like in a black hole, but when you are inside the singularity, you feel time passing normally. It is only when you try to compare your clock to another one, that is at another place, that has a different gravitational potential, when you see that your clock ticks differently. But in your case there is nothing to compare it to.
It seems to me you have it right so far, because a collapse due to gravity is a "falling-in" of matter at the ever-increasing speeds caused by the gravitational force, thus the time rates of matter will decrease at rates inversely proportional to the speeds of discrete matter objects. The fifth force time sets the rates of the passage of time by the speed of all matter regardless of position or direction of motion within the cosmos. The fourth force causes matter objects to speed up, which causes their time rates to run slower.