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

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.

'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

I think you are right. I had exactly this idea for quite some time already. In quantum mechanics the 'position space' does not play any special role. One can represent wave functions in any convenient basis (of eigenvectors of a maximal set of mutually commuting observables), e.g., in the momentum basis. Obviously our human senses (e.g., vision) map the world for us in the 'position representation'. Why it is so? I think that humans (as a species) found through natural selection and evolution that this representation is best suited for our survival. I can imagine some living organisms whose survival depends more on the velocity of surrounding objects rather than on the distance to them. It is quite possible that such organism would have a "velocity" or "momentum" vision rather than "position" vision.

However you should be also aware of the fact that denying the special role of the "position space" go against many popular physical theories. For example, the basic objects of quantum field theory - quantum fields - are formulated as operator functions in the position space. General relativity considers curvature of the "position space" rather than "momentum space". So, it is fun to think about how modern physics should be reformulated so that "position space" does not play any special role there.

Math Is Hard
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note: This thread already existed in the Philosophy forum so I have moved it over from Quantum Physics. (We don't allow double-posts).

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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.

'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