Formulas of Shans: math behind “The Cosmic Mirror”.
When I was a freshman in college, I encountered the Theory of Relativity for the very first time. I was both amazed and a little stunned. Until that moment, I had always called Einstein a “genius” simply because that’s what everyone else did. But after delving into his ideas, I found myself exclaiming, “Son of a…! What else could you possibly call a mind like that?”
All of the wild and surprising ideas from this theory captivated my imagination. Yet one concept — the Cosmic Mirror — especially drew my attention. I began running thought experiments in my head, picturing various scenarios.
Wanting to be more precise and methodical, I ultimately translated those ideas into mathematics. As a result, I arrived at a simple and elegant formula that can be used to calculate “past-seeing” effects.
I don’t want to delve too deeply into the complexities of the theory of relativity. Instead, I’d like to offer a brief explanation of the Cosmic Mirror and how it can be used to glimpse the past.
The Cosmic Mirror: viewing the past through light.
Light as a carrier of the visual information.
When you see something, photons (light particles) reflecting off an object arrive in your eyes (or telescope). That’s how an actual observation works. The photons contain information about that object’s state at the time they reflected.
The idea here is that, so-called old photons — for instance, photons, reflected from Earth during the time of the dinosaurs — would still be traveling outward into space. In theory, if one could “catch” those ancient photons and bounce them back to Earth, we’d see snapshots of that bygone era.
What is a light year?
For the simplicity, in our experiments we’re going to use light year as a unit of distance: it represents how far light (or something with speed of light — ~300.000 km/s) travels over the course of one Earth year.
For example, if there’s a planet 20 light-years away, any potential inhabitants there would see Earth as it was 20 years in the past.
This is because the light reflected from our planet reaches them only in 20 years and before it reaches another 20 years pass in Earth. And there is always a delay of 20 years — the naturally occurring cosmic lag. :)
I’m writing this article in 2025, but from their perspective — looking at us through a telescope — they’d be witnessing the release of the iPod Nano back in 2005.
Somewhere out in the cosmos, there are photons journeying through space, preserving images from the time of Jesus.
When He was baptized, beams of light reflected off His face and radiated outward. If we could somehow “catch” those photons, we would see the face of Jesus as it appeared all those centuries ago.
What is The Cosmic Mirror?
It’s just a mirror…but with cosmic scales.
In theory, we can send a huge cosmic mirror far away into space — potentially many light-years from Earth — so that when ancient Earth photons eventually reach it, the mirror reflects them back home. Once these photons return, we’d effectively watch “live footage” of past events.
To intercept those photons, though, the mirror would need to travel faster than the photons themselves — i.e., faster than the speed of light. Today’s physics (special relativity) tells us this is not possible for any massive object.
Nevertheless, the concept serves as a thought experiment illustrating what would happen if such a mirror could be placed.
Formulas of Shans
So far, nothing I’ve mentioned is entirely new. The idea of seeing the past through a cosmic mirror wasn’t mine originally. However, I took the concept further by developing a mathematical framework around it.
First, let’s define the variables (believe me, it’s much simpler that it looks like):
• v : speed of the mirror.
• c : speed of light.
• y (year): the year the mirror is launched.
• S: distance from Earth to where the mirror will be placed (in light-years).
• n : how much the mirror’s speed is greater or less than c.
• p (past): the “oldest possible year” we can see from the reflected light.
• R: the year when those “images” actually arrive back on Earth.
Don’t worry if most of this seems unclear. Once we apply these ideas to real-world calculations, everything will become much clearer.
Now, let’s explore all three cases…
Case 1: speed of mirror = speed of light
If v = c, then p = y
Interpretation: If the mirror travels at the same speed as light, it can’t overtake photons that left Earth before the launch. Essentially, you would only be able to catch photons that left Earth after your mirror deployment year.
Result: The maximum past you can see — is the year of the launch of the mirror.
Case 2: speed of mirror < speed of light
If v < c, then p = y + S * n
Interpretation: Because the mirror is slower than light, it certainly can’t catch photons that left Earth in the deep past. In effect, you end up getting images from the future relative to the launch year (because the photons that left Earth even one year before your mirror set out will already be ahead of it).
Result: You will see the near future in the the distant future.
Case 3: speed of mirror > speed of light
If v > c, then p = y — S / n
Interpretation: If v were faster than c (which current physics rules out), you could intercept photons that had left Earth before year y. The faster beyond c you go, the deeper into the past you might “reach.”
Result: You will behold the ancient past!
For example, if n = 2, the mirror is moving at twice the speed of light. That means it can reach a point 20 light-years away in just 10 years. If we launch it in 2025, it arrives by 2035.
Meanwhile, the light that left Earth in 2015 also gets there in 2035 (covering 20 light-years in 20 years). As a result, we’d be able to see 2015 — effectively peering into the past. And the larger the value of n, the deeper into the past we can gaze!
Calculating Return Time (R)
After you intercept old photons, they need to come back to Earth. Typically, one might approximate:
R = p + 2S
In simplistic terms, the year of the captured scene, plus the round-trip time for the light to return.
For example, if you launch mirror (with speed of light) in 2025 to the point of 20 light years away, you will see the first pictures in 2065, because the mirror will reach that point in 2045 and the reflected light also needs 20 years to return to the Earth.
Technical limitations:
Speed-of-Light Limit
According to relativity, no massive object can reach or exceed c . This alone defeats the premise of overtaking photons that departed millions of years ago.
Signal Intensity Drop
Photons from ancient Earth (e.g., dinosaur times) are already extremely diluted; after traveling millions of years, their density (flux) would be incredibly small. By the time they reach the mirror, they would be even weaker.
Background Noise & Interference
Cosmic background radiation, starlight, cosmic dust scattering, and other noise sources are huge in comparison. Isolating the extremely tiny signal of “ancient Earth photons” would require unbelievably sensitive instruments, both at the mirror and back on Earth.
Spectral Shifts
Over millions of years of travel (and with the expansion of the universe), wavelengths may shift (redshift), potentially pushing what was once visible light into infrared or radio frequencies. A single “silvered” mirror wouldn’t suffice; you’d need specialized surfaces or a system capable of reflecting multiple wavelengths.
Enormous Time Delays
Even if (magically) a mirror was instantly placed at some distant point, light from, say, 65 million years ago would still need to return to Earth. That’s more tens of millions of years of waiting.
Mirror Size and Materials
Well, even if the laws of the physics were not a problem —to built a mirror orders of magnitude larger than any space telescope mirror we’ve ever built is almost an impossible task. The sheer scale (kilometers wide, if not bigger) poses unsolved engineering and material-science challenges.
Afterwords
Well, I’m neither physicist nor mathematician. (I’m a software engineer).
So, most probably, I missed a lot of details in the formulas. Yet, I found them useful for simple introduction purposes. Come on, give it a try and play with them, put some numbers and make some experiments :)
They mathematically illustrate what would theoretically happen if one could place a mirror at various speeds (below, at, or above c ).
This highlights the notion that light from the past is still “out there,” even if practically unreachable.
I tried to emphasize the speed-of-light limit and show how crucial it is to modern physics. No matter the contrivance, we can’t magically view dinosaurs in real-time without confronting these fundamental laws.
I hope I’ve managed to shed a bit of light on this complex topic. :) Thanks!
P.S
Always, plan your activities outside — under the sky. So your life history could be visible from the future :)
