# Thought experiments about $c$ [closed]

Poincare had a brilliant thought experiment about what if everything in the universe doubled in size, would anybody notice any difference or even be able to measure anything that can be compared with previous measurements.

Similarly what if one morning one the great constants in physics; that is the speed of light suddenly increased to 150% of what it was; would there be observable differences?

## closed as off-topic by Carl Witthoft, CuriousOne, Daniel Griscom, ACuriousMind♦, John RennieJan 26 '16 at 6:42

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• If the speed of light was faster would this distort one's perception of time making detecting changes in speed suspect? Since the speed of light is so pervasive as concepts go it affects all other constants and their measurements. And why would Maxwell's equations fail? – 201044 Jan 25 '16 at 14:58
• I'm voting to close this question as off-topic because it's a dupe of a standard question in Halliday&Resnick ; sorry I can't find the duped entry on SE – Carl Witthoft Jan 25 '16 at 20:03
• Poincare died, unfortunately, before modern physics came into its own. We can't know what he would think today, knowing what we know. It's a pretty straight bet that he would stop putting up simplistic suggestions like that. – CuriousOne Jan 25 '16 at 20:45
• Possible duplicate of If everything in the universe doubled in size overnight, would it be noticeable? – ACuriousMind Jan 26 '16 at 4:34
• @CarlWitthoft: Found it $\uparrow$ – ACuriousMind Jan 26 '16 at 4:34

## 1 Answer

1) In view of the fact that we know how to measure the speed of light, it follows that a change in the speed of light would be detectable.

2) Any change in the speed of light would have to be accompanied by either a change in $\mu_0$, a change in $\epsilon_0$, or (far more drastically) a failure of Maxwell's equations, any of which would be easy to detect directly.

3) As for universes "like ours" where the speed of light is 150% greater, much depends on what meaning you attach to the phrase "like ours". It's easy to write down a simple Universe --- say Minkowski spacetime with a different constant in the metric --- in which the speed of light is anything you want it to be. If you want a Universe that is more like ours in more exquisite detail, then everything depends on which details you care about. Obviously it can't be exactly like ours.

• The phrase 'all possible worlds' has been analysed by many philosophers trying to think of consequences of their logical implications on 'other possible worlds'. Philosophers certainly use the concept of a 'world like ours', maybe that's one reason for friction between philosophy and science.. That's the point of thought experiments ; to use imprecise terminology and creativity to try to point out interesting avenues for more questions. – 201044 Jan 25 '16 at 15:04
• @201044: Your question about possible worlds is exactly of the same nature as: "Is there a figure that is like a triangle but has four sides?". The answer depends on whether you consider a rectangle to be "like a triangle". Does that strike you as a question with a definitive answer? – WillO Jan 25 '16 at 15:07
• Also depends on the dimensions of a figure ; a tetrahedron is 'like' a triangle and it has 4 sides ( this question was actually in the movie 'The Forbin Project'). Like I said the point of thought experiments is to use imprecise but USEFUL terminology and ideas to point out interesting possible avenues for further questioning.. – 201044 Jan 25 '16 at 15:11
• @201044: It's pretty bad practice to bring philosophy into the science classroom. Philosophers haven't made any significant progress in their own field since Plato took a wrong turn in a cave. Of course, the day philosophers turn around and go the right way, they have 2400 years of intellectual catch up to do... – CuriousOne Jan 25 '16 at 20:44
• @ CuriousOne; so you don't think philosophy or philosophical thought experiments have any effects in physics? – 201044 Jan 29 '16 at 3:44