Why are quantum fluctuations amplified when viewed on a smaller scale?

[Mukilab]

Why are quantum fluctuations amplified when viewed on a smaller scale?

I read about this in 'elegant universe' but the book never answered my question.

 

[A. Neumaier]

Why are quantum fluctuations amplified when viewed on a smaller scale?

I read about this in 'elegant universe' but the book never answered my question.

All fluctuations look big when viewed at small scales. For an ant, a newly ploughed field is full of rugged hills, while for us, seen from far, it looks very uniform.

 

[Mukilab]

The way the book explained it, it sounded like the waves actually became more energetic when viewed on a smaller scale.

 

[A. Neumaier]

The way the book explained it, it sounded like the waves actually became more energetic when viewed on a smaller scale.

This is a misunderstanding. On smaller scales, waves have a smaller wavelength lambda, hence a larger frequency omega = 2 pi/lambda, and hence are resolvable only with larger energies of the order of E = omega hbar.

This is why one needs huge accelerators to discover news at the smallest scales.

 

[Mukilab]

This is a misunderstanding. On smaller scales, waves have a smaller wavelength lambda, hence a larger frequency omega = 2 pi/lambda, and hence are resolvable only with larger energies of the order of E = omega hbar.

This is why one needs huge accelerators to discover news at the smallest scales.

So was the book incorrect?

Would the increase in frequency be larger than the decrease in wavelength, creating a need for more energy overall?

 

[A. Neumaier]

So was the book incorrect?

Books for laymen are often inaccurate, bordering sometimes on incorrectness.
To get a correct view of things, one shouldn't rely too much on a single source.

Would the increase in frequency be larger than the decrease in wavelength, creating a need for more energy overall?

Frequency and wavelength are inverse proportional, so this question doesn't make sense.

The energy is needed to reduce the uncertainty to a level where one can distinguish the small scales.