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bio website math.mit.edu/~shor
location Cambridge, MA
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1d
comment Is assuming spacetime to have |2^N| points overkill?
When you quantize space and time, there will probably not be a continuum of points. Nobody truly understands a theory of quantum space-time yet, but there are good reasons for believing that such a theory exists.
Apr
8
comment Where can I find the list of the planetary motion equations?
The planetary motions aren't ellipses aligned with the $x$- and $y$-axes, so the equations are going to be quite a bit more complicated than that.
Apr
2
comment If quantum computing requires hundreds of digits of accuracy, how will it be possible?
If physics depends on the coordinates of the quantum state vector, it's not well-defined unless it also has some recipe for choosing which coordinates you should work in.
Apr
1
comment If quantum computing requires hundreds of digits of accuracy, how will it be possible?
You're operating under the same assumption as Leonid Levin: that the universe acts like a simulation of a quantum system on a classical computer which uses floating-point arithmetic. If this were true, probabilities wouldn't be guaranteed to add up to 1. I think we would have noticed. Physics shouldn't depend on which coordinates you pick to represent the quantum state vector.
Apr
1
comment If quantum computing requires hundreds of digits of accuracy, how will it be possible?
The factoring algorithm doesn't require the $2^n$-th root of unity. If you leave all the tiny phases out in the Fourier transform, the resulting transform is close enough that the factoring algorithm works fine. If you have 10 digits of accuracy in the unitary transformations for my algorithm, it will work fine, as long as you take fewer than $10^{10}$ steps. On the other hand, if you drop the unitarity condition on physics, it's not at all clear what happens. Presumably probabilities still add up to exactly 1; this is usually ensured by unitarity, so you need something to take its place.
Mar
31
comment If quantum computing requires hundreds of digits of accuracy, how will it be possible?
Beyond a certain number of decimal places, we don't know whether the evolution is unitary or not. If it's not, the hypotheses of our fault-tolerant threshold theorems are certainly not satisfied. But this doesn't mean the fault-tolerance protocols wouldn't work. I don't believe anybody has a concrete proposal for a kind of non-unitarity which would have to cause quantum computing to fail, and not cause any other observable changes in physics.
Mar
30
comment If quantum computing requires hundreds of digits of accuracy, how will it be possible?
The real question is whether the rules of the universe are exact unitary evolution or something else. If they're exact unitary evolution and you have locality of action (quantum field theories, including QED, satisfy these) then the fault-tolerant threshold theorem holds. If the universe has extra levels of weirdness under the quantum field theory, then it's not clear the hypotheses are satisfied.
Mar
30
revised If quantum computing requires hundreds of digits of accuracy, how will it be possible?
added 117 characters in body
Mar
30
revised If quantum computing requires hundreds of digits of accuracy, how will it be possible?
added 117 characters in body
Mar
30
answered If quantum computing requires hundreds of digits of accuracy, how will it be possible?
Mar
29
comment Where does a string tighten when you pull it?
If there is no friction, when you start pulling the string, you give it kinetic energy. Without friction to dissipate that energy, it starts moving and never stops. You will thus need to solve a differential equation which I don't know enough physics to write down, but it will depend on parameters you haven't given us like the elasticity of the string.
Mar
23
comment Do gravitational waves cause time dilatation?
Electromagnetic fields don't distort time; gravitational fields do.
Mar
20
revised Is it possible for a sound to be louder as you move away from it?
added 56 characters in body
Feb
27
comment Rigid body rolling quesion
That's correct.
Feb
27
comment Rigid body rolling quesion
That's the answer, then. If the cylinder rolls three inches, the relevant part of the rope is three inches shorter, and the box moves up six inches. So the box travels twice as far, and its velocity and acceleration are twice as large.
Feb
27
comment Rigid body rolling quesion
Is the rope being wrapped around the cylinder?
Feb
24
comment Reaction force of the ground beyond the equator
You're assuming that the Earth is perfectly spherical. That's not true.
Feb
24
comment Why does the bathroom become hot after a bath?
The water isn't heated, if I understand correctly. It's hot in India.
Feb
24
comment Why does the bathroom become hot after a bath?
Do you heat water before using it to bathe, or do you live in a warm climate so that you don't have to?
Jan
24
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