Although I understand that the universe is approximately 12 billion light years wide, and that may mean that it took the light photons 12 billion years at 186,000 miles per second to reach the distance they did:
If you could travel at the speed of light for a time of 10 earth years, then, when you returned to the earth after 10 of its years, you have aged much less than 10 years. My question is, since a light year as it pertains to the light itself, is different or shorter than an earth year, if these comparisons can be concise and relevant? To us the universe seems to be 12 billion years old but to the photon or (if possible in theory) the human that traveled the 12 billion light years the universe would not be 12 billion years old but it would be much less. This seems to be a paradox to me.
For earth the universe is calculated to be 12 billion years old but for the light speed traveler it would seem to calculate a much younger universe. How do I reconcile this paradox Or is my assumptions wrong?
Best Answer
I'm going to first address some misconceptions you seem to have and then I will get to answering your question. Now, as stated in the comments, @Pulsar did a very thorough job of answering this question in another post. But I read through that answer and it's a bit technical. I already knew the stuff, so it made sense to me, but I can see how someone unfamiliar with the material might find that to be more like science gobbledegook than a clear and helpful explanation.
So first things first, we think the universe is about 13.8 billion years old. Second, the universe is expanding, which means the size of the observable universe has expanded to larger than the distance light travels in that time. The diameter of the observable universe is thought to be about 93 billion light years and no light from us will ever reach this edge again (if we're right in our model of the universe).
Next, I'll get slightly more technical. A light year can not be shorter, longer, or the same length as an Earth year. One is a unit of distance, the other is a unit of time. That is like saying a metre is shorter than an hour. A light year has a rigidly defined distance length. Furthermore, a photon has no reference frame in which to define a length or a time. There is no light year that pertains to light itself.
Okay now, let's get even more technical. The universe is expanding. We know this. Because of the expansion and because of this wonderful and not at all magical thing called the Cosmic Microwave Background (CMB), we can identify a frame of reference of the universe that is at rest with respect to what we assume is the stationary background of spacetime (once you factor out the expansion). We call this the comoving frame. Anything at rest in the comoving frame sees the CMB as the same from all directions and the only reason things in the comoving frame move away from each other is because of expansion. The reason we like this frame is because it is a universally discoverable frame. Aliens from a distant galaxy would be able to find this frame and agree on what observers in it would see. Having said that, the age of the universe is calculated in this frame. The detailed calculations are all in @Pulsar's post, but when we say the universe is 13.8 billion years old, we have figured out the number of Earth years in the comoving frame since the Big Bang era began. That means that no matter who is trying to find out the age of the universe, they'll be able to find the comoving frame and figure out the age in that frame and get the same value.