There is a real world, but our perceptions of that world are unique to each of us. For example, what I think of as a green leaf may look very different to what you think a green leaf looks like, but we can measure the light coming off of it and determine its wavelength objectively.
If you want another fun one, it takes a fraction of a second for our brain to perceive what we sense. As such, what we think of as the present is actually a tiny bit in the past, it's already happened.
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