In quantum mechanics, a free particle is described by a continuous superposition of wavefunctions, which can be done equivalently in real or momentum space. We can look at a particle's probability distribution in real space, take its Fourier transform, and obtain the particle's distribution in momentum space. We can invert the process and obtain the distribution in real space from the momentum distribution. This got me thinking about how we map the world around us - eyesight.(adsbygoogle = window.adsbygoogle || []).push({});

'Eyesight' is essentially a mapping of bodies in 'real' space. If this mapping were done of quantum particles like free electrons (i.e., if we had these tiny cockroach eyes, but probably far smaller), we could imagine taking the Fourier transform of the observed (collapsed) position distributions and obtain the corresponding (very wide) momentum distributions. But - since they are both observables, and equivalent ways of describing the same quantum state - why not map the (collapsed) momentum distribution directly, with little 'momentum eyes'?

Ultimately, I am wondering if what we call *real space* is simply one of a few ways of *mapping* the world around which we could have adapted. Could we imagine *seeing* the world around us in a 3D momentum space instead of our 3D real space?

It's a weird idea, and maybe just a bad display of ignorance - but it would be kind of neat if 'real' space were just one of two *equivalent* mappings of the world around us. We could imagine funny little creatures 'seeing' things in momentum space, collapsing wavefunctions in k-space instead of real space. Considering that so much of what we consider 'real' is nothing more than a convenient mental representation of the world, I wonder if 'real space' could be another.

Thank you

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# Is 'real space' merely a convenient mental representation?

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