Does every past state of the Earth currently "travel" through the universe?

Question

So I just read this question.
The 27 year old user asks if it would be possible to see his own birth if he would be 27 lightyears away from the earth and the answer states Yes, if you could magically be transported 27 lightyears away, or had a mirror strategically placed 13.5 lightyears away, you could see yourself being born.

My question that came to my mind is: Does this mean that every past "state" of the Earth (and possibly every other object in the universe) currently travel as light through the universe?

Answer 1

The simple answer is no, or, more precisely, the arguments that you cite give no weight to the idea that past states "travel" through the Universe.

Let's look at the 13.5 light year away mirror. Yes, in theory you could see your own birth through it, if you could overcome all the optical resolution problems associated with such an undertaking.

But this is no more supportive of the idea of a time travelling state than is MPEG file containing footage of your birth that is uploaded to the internet and emailed to you on your 27th birthday from the "see-my-birth.com" website that was (hypothetically of course!) set up by some entrepreneur who asked the same question as you do 27 years beforehand and who saw dollar signs rather than Ricci and Einstein tensors in the question. Or, in terms that the older of us can more relate to: you are told in your childhood that you will get to see your own birth on your 27th birthday. On your 27th birthday you open a box that you've never been allowed to open, and in it is a video disk bearing the footage: so you curl up in front of the fire with your computer, make yourself comfortable and watch your own birth.

What this example shows is that you are not accessing the state of the universe for the second time, but simply an "imprint" of it, i.e. some aspect (in this case video disk or telescope image) of the present (on your 27th birthday) state of the World around you that has been selected by the former event. Whether it be video disk or telescope image you watch, in principle there is no difference, at least from the standpoint you must take to sensibly answer your question.

Now let's address the magical transport through 27 light years to a point where you could witness your own birth from afar. This is tantamount to faster than light travel, which implies violation of causality (see my answer here) and the possibility of time travel (see the Tachyonic Antitelephone allegory, formulated by Einstein and Tolman in 1907 and 1917, resepectively). Since there is no experimental support for either of these last two notions, contrapositively we believe the 27 light year displacement to be impossible. So we can't use it in any physical argument.

Answer 2

One can rationally ask what one could possibly see from 27 light-years away. Assuming that spacetime is neither grainy nor foggy (something that it very possibly is), it's mostly a matter of the size of the telescope and how well the scene is lit. One square meter of ground on Earth (roughly the area of a human sized "pixel", if we are generous and account for an obese population...) reflects approx. $10^{22}$ photons per second into the $2\pi$ solid angle above it. How much actual area is that? Well, it's

$A=2\pi\times(27)^2 ly^2\approx4600 ly^2$.

A light-year, on the other hand, is

$1ly\approx 365 d/y\times 24 h/d \times3600s/h \times 300000km/s\approx9.46\times 10^{12}km$.

If we substitute that into our estimate for the illuminated area, then we find that our $10^{22}$ photons/s get distributed over roughly $A=4\times 10^{29} km^2$. This means that, on average, each square meter size "pixel" on Earth produces one possible photon detection event every $400000s$ in a $1 km^2$ telescope at this distance. That's about once in five days...

So unless we want to stand very still for the duration of months or years, we need to assume that the telescope looking at us has millions of $km^2$ in optical aperture, just so that it can collect enough photons to pick us out from the background. To have enough photons to shoot an identifiable movie of a birth would take several orders of magnitude more than that. One really starts to wonder who will pay for a scientific instrument of maybe a hundred million square kilometers (roughly half the diameter of Earth, I believe) or more, does one not?

PS: This is just for sensitivity, the actual, diffraction limited optical aperture for this kind of resolution would probably have to be the size of the solar system.