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I've recently come across theories involving variable speed of light as a solution for the Horizon problem as well as for Dark Energy's accelerating expansion of space.

In a discussion with a friend, the idea that a significantly decreased speed of light would make objects appear more distant (the light takes longer to travel to the observer) was presented. I'm not so sure about this, I think objects would appear the same size and shape because they're coming from the same direction as before, only redshifted due to the loss in energy. We also thought about if light experiencing more curvature than before due to being within the gravitational field of large celestial bodies would make them appear in different locations relative to where we currently observe them. Also, perhaps everything would appear a little dimmer, as the light is hitting our eyes with less energy.

In a theoretical alternate reality where the speed of light is half of our measured $c$, and that other constants depending on $c$ have changed proportionally, what visual differences might a human observer from our present reality see, and why? Are the ideas presented above realistic at all or way off? Please note that I'm not interested in a discussion on the validity of the theory above, only what theoretical effects a slower speed of light may have on optics.

If possible, I would greatly appreciate being pointed to resources with formulas for calculating these effects - I have some interest in writing a renderer capable of simulating them.

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    $\begingroup$ en.wikipedia.org/wiki/A_Slower_Speed_of_Light $\endgroup$
    – Kyle Kanos
    Nov 23, 2019 at 1:22
  • $\begingroup$ @KyleKanos I may be wrong in my understanding, but that game seems like it simulates an observer going close to the speed of light, instead of the perceived constant c actually changing, despite the name. Are they functionally not different? $\endgroup$
    – Klaycon
    Nov 23, 2019 at 2:03
  • $\begingroup$ Perception of distance has little to do with the time it takes for light to reach our eyes. For any practical scenario, this time would be on the order of nanoseconds, so it's unlikely we can even detect such small time variations. The perception of distance arises from perspective and angles. $\endgroup$
    – Tob Ernack
    Nov 23, 2019 at 5:24
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    $\begingroup$ You can't detect a change in a dimensionful universal parameter like $c$. See physics.stackexchange.com/q/78684 . Note that warning tag in the section of the WP article you linked to. It's kook stuff. $\endgroup$
    – user4552
    Nov 23, 2019 at 15:34
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    $\begingroup$ “it goes without saying those dimensionless constants derived from c have also changed” It doesn’t go without saying. It is critical to state clearly and explicitly in your question. If you intend for a dimensionless constant to change then you need to specify which constant and how much. Otherwise there is no way to ensure that everyone is understanding your question as you intend it. I certainly did not see that was your intention $\endgroup$
    – Dale
    Nov 23, 2019 at 22:24

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The speed of light is a dimensionful constant and, as such, it is impossible to talk about changes to the speed of light without being dead clear about what you do want to keep constant.

Your question doesn't really give any meaningful benchmarks for this, so to some extent your question is completely unanswerable.

On the other hand, your emphasis on what it would visually look like to a human does supply an answer to this: define some characteristic speed $v_\mathrm{human}$ that describes your observer's motions, and set that as a constant. (In other words: when the speed of light gets slower, does your observer also move slower? Presumably that's not something you want, which points in the direction I've just mentioned. However, it's important to note that it's in direct conflict with your statement that "it goes without saying those dimensionless constants derived from c have also changed", from this comment, because there is no guarantee that the physics that sets $v_\mathrm{human}$ is independent of $c$. This is why your question is ill-posed and not really about physics, but that's neither here nor there.)

The problem posed in that form asks what the world would look like if $c/v_\mathrm{human}$ were smaller, or if $v_\mathrm{human}/c$ were bigger. (Note that the two are completely equivalent, and there is no way to tell them apart.) This problem has been completely solved, and its solution exists:

with the latter being the essentials of the back-end for the former. If all you want is the mathematics, so that you can re-implement the code yourself elsewhere, the place to turn to is the sister publication,

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  • $\begingroup$ I appreciate this answer. I think I've realized a source of this question's issues - I was implicitly seeking an answer from the perspective of the VSL theory yet trying to frame it in vague terms of physical accuracy under currently accepted theories, which I can see now are fully incompatible. Should I edit my question to make this explicit or ask a new one? $\endgroup$
    – Klaycon
    Nov 25, 2019 at 16:44
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    $\begingroup$ @Klaycon I'm unlikely to update this answer either way. $\endgroup$ Nov 25, 2019 at 16:45

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