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I know we can't move at the speed of light, but if we were to travel on a photon how fast would we see other photons going? The speed of light is constant... So do photons see other photons moving at the speed of light?

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    $\begingroup$ I know there are no giraffes on the moon, but if there were giraffes on the moon, what would their names be? $\endgroup$
    – WillO
    Commented Oct 11, 2021 at 21:08

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According to Special Relativity, an object moving with speed c in one frame of reference moves with speed c in all frames of reference.

The immediate consequence is this: a photon has no frame of reference.

To appreciate this fully, consider that, no matter what speed you travel with respect to something else, you are at rest with respect to yourself.

But, and again, according to SR, if you were to have speed c in any frame of reference, there would be no frame of reference in which you were at rest with respect to yourself.

The bottom line is that asking a question along the lines of your question presumes that there exists a frame of reference that moves with speed c in which observations can be made.

But, there isn't!

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The frame of reference of something moving at the speed of light is not well-defined within special relativity. A photon does not see anything, it just is. For a mathematical argument, look at the relativistic factor $\gamma$, which appears in relativistic equations:

$$\gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}.$$

If you set $v$ equal to $c$, this expression is equivalent to a division by zero.

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