To add some back of the napkin calculations to this:
Angular resolution of the earth at 66 million light years away would be approximately 2e-17 radians. Using the Raleigh Criterion [0] for lens size for the visible light spectrum (700nm for the best case scenario), you would need a lens with a diameter of about 4e10 meters. That's about the radius of Mercury's orbit around the sun.
If you want to see dinosaurs, say 1m resolution, that's about 1.5e-24 radians at 66M light years, needing a lens of diameter 5E17. The entire solar system has a diameter of ~3e14. So even if your lens was the size of the solar system you'd still be off by a factor of 1000 trying to resolve the dinosaurs.
At these scales you start running into some pretty fundamental engineering and physics problems with building a telescope this big.
Warning: this math may not be totally right, I'm just procrastinating some PDE homework right now, but the scales should be roughly correct.
The problem would be the amount of signal you can collect. Might be interesting to do a calculation of the number of photons that would be detectable at that distance per unit solid angle to figure out roughly how big the mirrors would have to be to capture an image in a reasonable amount of time.
> So even if your lens was the size of the solar system you'd still be off by a factor of 1000 trying to resolve the dinosaurs.
What's the effective size of a gravity lens? You know, the kind where you park a satellite out at 550 AU and image whatever's directly on the opposite side of Sol (or an equivalent distance in proportion to some remote star's gravity).
The idea of using sun's gravitational lensing effect as a telescope has been proposed seriously (https://en.wikipedia.org/wiki/Solar_gravitational_lens). this has much smaller resolution then what you mention but perhaps can be used to witness other planets in ours and nearby galaxies in our cluster.
I’m imagining an advanced civilization with a telescope capable of doing observing dinosaurs, but only ones being thinks that it an interesting use of the telescope. So they work super hard and get exactly one Earth day’s worth of observing time to look at dinosaurs w/ no possible rescheduling. When the day finally comes… clouds.
This is admittedly a bit over my head, but does that mean it is technically possible that an image of earth could be captured from the distance needed to see Pangaea?
Thinking about this has sparked a bunch of questions I hadn't thought of before. For instance, does information encoded with light degrade over long distances in a vacuum? If not, it does seem like a mega-lens could potentially capture such an image right?
Under this perfect assumption you end up having a problem with the red shift caused by the expansion of the universe (which I didn't account for above) that lengthens the wavelength of the light you want to see, requiring an even larger lens.
On the lens side of things, as far as I'm aware (not a physicist, math PhD student who is just generally into this sort of thing) there isn't anything fundamental preventing you from collecting this light and building the lens, but from our current understanding of materials science I'm fairly confident it's currently impossible to construct a structure that will stay together that large.
That being said there may be ways around this problem, like I said not a physicist or engineer, but you are right that from an information theoretical perspective if you ignore dust and other things in the way then yes all the information is still there.
> Under this perfect assumption you end up having a problem with the red shift caused by the expansion of the universe (which I didn't account for above) that lengthens the wavelength of the light you want to see, requiring an even larger lens.
Redshift does not come into play at the 'small' scale of our galaxy since the Milky Way is a gravitationally bound system that does not itself expand with the Universe. Even within our local group (eg from Andromeda) it is not an issue since the local group is also gravitationally bound. Redshift only becomes an issue at much larger scales, if you are in another galaxy outside our local group.
Angular resolution of the earth at 66 million light years away would be approximately 2e-17 radians. Using the Raleigh Criterion [0] for lens size for the visible light spectrum (700nm for the best case scenario), you would need a lens with a diameter of about 4e10 meters. That's about the radius of Mercury's orbit around the sun.
If you want to see dinosaurs, say 1m resolution, that's about 1.5e-24 radians at 66M light years, needing a lens of diameter 5E17. The entire solar system has a diameter of ~3e14. So even if your lens was the size of the solar system you'd still be off by a factor of 1000 trying to resolve the dinosaurs.
At these scales you start running into some pretty fundamental engineering and physics problems with building a telescope this big.
Warning: this math may not be totally right, I'm just procrastinating some PDE homework right now, but the scales should be roughly correct.
[0] https://en.wikipedia.org/wiki/Angular_resolution#The_Rayleig...