Linear size of everything in the Universe has been doubled overnight

[Monsterboy]

Homework Statement

Suppose you are told that the linear size of everything in the universe has been doubled overnight. Can you test this statement by measuring sizes with a meter stick ? Can you test it by the fact that the speed of light is a universal constant and has not changed ? What will happen if all the clocks in the universe also start running at half the speed ?

Relevant Equations

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I found this question in a textbook, not sure if this question has been asked before. Not sure if the author just wanted to make the reader think or he had anything specific in mind that he wanted the readers to understand.

Most of the people immediately conclude that the speed of light doesn't change and that's how we figure it out. But if the linear size of everything changes does that include the wavelength of light ? If the wavelength is also doubled, can the speed of light remain the same or doubled ?

 

[DaveE]

c = νλ. If c is constant (hint: yes) then if the wavelength (λ) is doubled, then the frequency (ν) will be halved. Although, it's not obvious to me that anything changes with the photons, they may just have a greater distance to travel. It's hard to answer this sort of physically unrealizable scenario.

With expansion of the universe, we observe that the wavelength increases (google: red shift).

I think the bottom line is that we never observe any change in c in the real world, and c = νλ is more of a definition of speed, wavelength and frequency than an observation.

 

[haruspex]

I consider the question unanswerable because it needs to specify what doesn't change. E.g., either c or time changes, but which? Does G change, or masses or time? If we keep G and c constant then masses must increase in proportion to distance...

 

[Leonard Hofstader]

According to the 2018 definitions of fundamental units, length is defined as the distance traveled by light in 1/299,792,458 seconds. Hence, even if the linear size of everything is doubled, light still covers the same distance in 299,792,458 seconds. Therefore, at the end of the day, the lengths will remain same as the definition of metre is unchanged.

However, now if all the clocks of the universe start running with half the speed, then the definition of time will practically change. As we say that 1 second is the duration in which a stable ground state hyperfine transition frequency of Cs 133 emits frequency of 9192631770Hz, but when this duration is measured, the value differs.

That is, the ideal duration of the frequency has not changed yet the equipment through which it is measured has changed, hence the ultimate value differs. This will also have an effect on the definitions of length as it is ultimately based on m/s i.e. second, which is defined through the hyperfine transition frequency in Cs 133.

This is however my opinion and I encourage any counterpoints.