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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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  • $\begingroup$ Notice that if the speed of light is different from the beginning in that universe there is no need for momentum to increase by 1.1 as why will you want to compare with our universe because the energy and momentum of that universe is of its own with no relation to energy or momentum here in ours. $\endgroup$ – Tausif Hossain Aug 12 '18 at 3:22
  • $\begingroup$ The speed of light is unity as in one light second per second. It is not a physical constant that can change from one universe to another. In the equation, $c$ is simply a number that translates light seconds to meters by the definition of meter, so $c$ is a predefined number, not a physical constant. In light seconds per second $c=1$, in meters per second $c=299,792,458$ (a predefined whole number), etc. depending on your chosen units of length. So in natural units you can simply write $E=m$ for any universe with the same spacetime symmetry as ours. $\endgroup$ – safesphere Aug 12 '18 at 3:39
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    $\begingroup$ Possible duplicates: physics.stackexchange.com/q/291316/2451 and links therein. $\endgroup$ – Qmechanic Aug 12 '18 at 4:58
  • $\begingroup$ Hypothetically, if it was 10% slower, would energy contained in a given mass at rest simply be 10% less relative to our universe? $\endgroup$ – Scott Aug 15 '18 at 16:48
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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 $c$.

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  • $\begingroup$ What about a scenario where in the alternate universe, the speed of light were the same as ours, but what is observed requires a constant ...for example 1.1 or .9 next to c^2, would the math still work? $\endgroup$ – Scott Aug 16 '18 at 1:50
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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.

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