Regarding $E=mc^2$, in a hypothetical parallel universe. If in that universe the speed of light squared were let’s say 10% slower, would everything still work but just slightly different? Or would an extra constant of 1.1 need to be added to make momentum equations match up? I heard that both momentum and energy must be conserved. My reasoning so far seems circular and I am having trouble getting a clear picture of this.
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Notice that Physics is understanding our universe with models that agree with observations. Consider the example that without even considering the value of the speed of light we know that relativistic momentum is given by $$p=\frac{m_0 v}{\sqrt{1-\frac{v^2}{c^2}}}$$ It doesn’t matter what the value of $c$ is(to maybe $10%$ lower to even being a $100km/h$, where being $100km/h$ would have quite drastic effects so this is a good read that focuses on the details of the scenario).
Hence, the laws we know would still hold and so would other laws of physics and other equations as the in-built structure of the equations are not dependent on the value of $c$.
Tausif Hossain
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A change in the speed of light would not change such a universe.
The requirement that the theory of special relativity makes is that the speed of light must be constant in any given inertial reference frame. A change in its value would only lead to a different system of units. As an example, in theoretical physics it's very common (I'd say theoretical physicists always do) to set the value of the speed of light equal to one $c = 1$ in order to simplify the notation.
mr. Merlo
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