Without a doubt the strongest evidence for vast time is distant star light. Unlike most dating methods it strait forward in the formula is t = d /c where t = time, d = distance and c = the speed of light. It really only requires two assumptions. One is that the distances are real and other is that the speed of light is constant. This simplicity has made it the toughest claim of vast time for Young Earth Creationists to deal with. However there have been Young Earth Creationists several theories to deal with this. I will deal with each of these briefly in this posting and the each of them in turn in more detail in separate posts
Light created in transit.
This is the idea that God created the star light already in transit from the stars on day four of the creation week without having to cover the distances. The main argument against this idea is that it make most of what we see in the universe distance greater than 6500 light years a fiction that never happened. This put God’s honesty in to question since most we see of God’s creation 99.999975% by distance would be fictitious.
The distances are wrong.
This questions if the distances are being measured accurately since you can not use a ruler to do it. The basic method of measurement which is stellar parallax is based on geometry and would be quite accurate but it only works up to about 100 Light years, so go further required other forms of measurement. This idea suggested that the other forms of measurement may not be accurate. However the assumptions behind using Cepheid stars and galactic redshift are reasonable enough that they are probably off by no more than a factor of 10 not the factor of 2,200,000 needed by this claim.
Decay of the speed of light.
This is the idea that the speed of light had decreased sine creation, maybe starting with the fall. It was based on the some old measurements of the speed of light, most of which are highly inaccurate and the oldest of which has been recalculated showing an error in the original calculation with the corrected value within the margin of error of the accepted value for the speed of light. While it still has its supporters it has fallen out of favor.
This is in general the basic idea proposed by Russell Humphreys and John Hartnet. While there different versions of this idea it proposed that the Earth experienced one or two pariods of time dilation (slowed down time) usually durring the first four days of the creation week and durring the Flood. When using General Reletivity this aproach has the most appologetic value since it requiers no new physics and it has the advantage being expandable to a general Young Earth cosmology.
There other theories that have been proposed but they never caught on. These four will be elaborated on it future postings.