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I like physics because it explains how stuff works.


Jul
22
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
Thinking about this more, I think my argument falls into the category of "not even wrong". It doesn't make any predictions.
Jul
20
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
Let us continue this discussion in chat.
Jul
20
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
@Jimself, momentum is conserved in your example only if the distance between two pixels is the order of one unit. But what if the distance between two pixels is 10 units?
Jul
20
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
@MengCheng, I don't see it. Please explain more.
Jul
20
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
@Jimself, I didn't mean Noether's Theorem isn't true. I meant that one can't apply Noether's Theorem for small scales, because the picture created by the pixels is more dependent on the choice of coordinates.
Jul
20
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
@MengCheng I don't see from your comment how my argument doesn't make sense. I wasn't talking about general non-commuting operators.
Jul
20
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
@Jimself, yes, this is what I'm saying and it's consistent with observation: It is well-known that Newtonian Mechanics is true on larger scales but it ceases to be true on smaller scales. My argument is that the reason for this is because on smaller scales, reality becomes pixelated and Noether's Theorem is no longer an accurate description of reality.
Jul
20
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
@Jimself, I don't understand your question.
Jul
20
revised Does Digital Physics imply Heisenberg's Uncertainty Principle?
added phrase
Jul
20
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
@Jimself, I mean that when one normally views a computer screen, it looks as if it is continuous and it appears to have spatial translation symmetry. When one stares at the pixels of the computer screen, it looks discrete and one sees that it lacks spatial translation symmetry.
Jul
20
comment Does Digital Physics imply Heisenberg's Uncertainty Principle?
@Qmechanic, thank you, I actually read your post before I posted this.
Jul
20
asked Does Digital Physics imply Heisenberg's Uncertainty Principle?
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Apr
2
comment If quantum computing requires hundreds of digits of accuracy, how will it be possible?
So the heart of this debate seems to be whether our universe is discrete or continuous.
Apr
1
comment If quantum computing requires hundreds of digits of accuracy, how will it be possible?
There are two possibilities: 1) physics depends on the coordinates. 2) Physics doesn't depend on the coordinates. Certainly, all of the experiments of modern physics show that possibility 2) holds. But at the same time, all of the experiments of modern physics have only been shown to be true to around 10 decimal places. So it seems to me that assuming that possibility 2) is true for more than 10 decimal places is a hasty generalization.
Apr
1
comment If quantum computing requires hundreds of digits of accuracy, how will it be possible?
But what if you run your algorithm to 10 digits of accuracy on a 200-qubit machine where all of the coefficients in the state-vector are initialized to $1/2^{100}$? Then you will get zero for the state-vector in the end. This is what I was talking about in my question. This seems to me to be a big problem.
Apr
1
comment If quantum computing requires hundreds of digits of accuracy, how will it be possible?
But if QM is unitary only up to say 10 digits, how could QC work with your factoring algorithm, which requires computing the $2^n$-th root of unity in the Fourier Transform part, and the state-vector has dimension the order of $2^n$? Ten digits of accuracy is too coarse for your algorithm to work.