How do we know this is real life? The short answer is: we don't. We can never prove that we're not all hallucinating, or simply living in a computer simulation. But that doesn't mean that we believe that we are.
There are two aspects to the question. The first is, "How do we know that the stuff we see around us is the real stuff of which the universe is made?" That's the worry about the holographic principle, for example -- maybe the three-dimensional space we seem to live in is actually a projection of some underlying two-dimensional reality.
The answer to that is that the world we see with our senses is certainly not the "fundamental" world, whatever that is. In quantum mechanics, for example, we describe the world using wave functions, not objects and forces and spacetime. The world we see emerges out of some underlying description that might look completely different.
The good news is: that's okay. It doesn't mean that the world we see is an "illusion," any more than the air around us becomes an illusion when we first realize that it's made of atoms and molecules. Just because there is an underlying reality doesn't disqualify the immediate reality from being "real." In that sense, it just doesn't matter whether the world is, for example, a hologram; our evident world is still just as real.
The other aspect is, "How do we know we're not being completely fooled?" In other words, forgetting about whether there is a deeper level of reality, how do we know whether the world we see represents reality at all? How do we know, for example, that our memories of the past are accurate? Maybe we are just brains living in vats, or maybe the whole universe was created last Thursday.
We can never rule out such scenarios on the basis of experimental science. They are conceivably true! But so what? Believing in them doesn't help us understand any features of our universe, and puts us in a position where we have no right to rely on anything that we did think is true. There is, in short, no actual evidence for any of these hyper-skeptical scenarios. In that case, there's not too much reason to worry about them.
The smart thing to do is to take reality as basically real, and work hard to develop the best scientific theories we can muster in order to describe it.
“If you asked anyone twenty years ago how many dimensions our world has, most of us would answer 'three spatial dimensions plus time.' The holographic principle would mean that this is actually a matter of perspective.” Craig Hogan to Motherboard
The theorysuggests that the entire universe can be seen as a two dimensional information on the cosmological horizon, such that the three dimensions we observe are an effective description only at macroscopic scales and at low energies.
The Nature of Space and Time: Is Space Digital?
Space may not be smooth and continuous. Instead it may be digital, composed of tiny bits. Physicists have assumed that these bits are far too small to measure with current technology. Yet one scientist... Scientific American, 2014
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