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bio website math.stackexchange.com/users/…
location Champaign, IL
age 35
visits member for 3 years, 2 months
seen Apr 13 at 22:15

Amateur mathematician, professional software engineer. Interested in all kinds of math, becoming a better mathematician, and helping others do the same.

email: jdb1729 (at) gmail.com

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Mar
10
comment Knotted token-ring network
Literally tied in a knot. Simplest case would be a trefoil: en.wikipedia.org/wiki/Trefoil_knot However I realize now my assumptions are very vague so I would like to rephrase this as a soft question (but I am not allowed to delete as it has already been answered). I guess what I really want to know is whether "knottedness" is measurable locally, in some way analagous to how we can measure "coiledness" or rotation rate.
Mar
10
comment Paradoxical interaction between a massive charged sphere and a point charge
If it is correct to include the electric potential energy in the mass term of the gravitational force, isn't it also correct to include the (negative) gravitational potential energy? If so, doesn't this mean that by the same logic two neutral point masses can be placed so close together that their total mass-energy is zero or even negative, causing a repulsive gravitational force on another distant object?
Mar
9
awarded  Commentator
Mar
9
comment Knotted token-ring network
I know the question is obtuse and I appreciate your effort and patience. I am thinking of the electron packet as a DC current through e.g. a copper wire. Measuring its resistance gives the same information as the case of a photon in free space. Measuring the magnetic field at some points a distance away from a node gives additional information (the winding number of the path?). But the electric field is everywhere absent because the current-carrying wire is neutral.
Mar
9
comment Knotted token-ring network
Where and when to measure? We already know the topology of the network is a loop but we need to know the topology of the volume outside the network.
Mar
9
comment Knotted token-ring network
Sure, if the packet is an electron instead of a photon then the loop has a current and we can measure a magnetic field somewhere. I guess this would tell us something about how coiled up it is but is there any information about the knot?
Mar
9
comment Knotted token-ring network
Because of special relativity. See en.wikipedia.org/wiki/Ehrenfest_paradox
Mar
9
asked Knotted token-ring network
Mar
9
comment Paradoxical interaction between a massive charged sphere and a point charge
Georg, the phrase I used "binding energy" may be wrong, what I have in mind is electric potential energy as defined here en.wikipedia.org/wiki/…
Mar
8
awarded  Promoter
Mar
8
awarded  Student
Mar
2
comment Paradoxical interaction between a massive charged sphere and a point charge
Justin, I feel like it must be wrong for some reason because it is seemingly impossible to verify and the results are counterintuitive. For example, maybe binding energy doesn't affect gravitational mass, or maybe total binding energy doesn't grow quadratically with charge in the limit, or maybe the initial conditions (so much charge in one place) are impossible to realize for some other reason. But what is the best reason?
Mar
2
awarded  Supporter
Mar
2
revised Can a car get better mileage driving over hills?
clarify perfectly
Mar
2
revised Can a car get better mileage driving over hills?
edited tags
Mar
2
revised Can a car get better mileage driving over hills?
driving where
Mar
2
asked Can a car get better mileage driving over hills?
Mar
2
comment Paradoxical interaction between a massive charged sphere and a point charge
Just because electrons are supposed to repel each other and gravity is supposed to be a weak force. I wonder if there is another argument that gives a different answer?
Mar
2
awarded  Editor
Mar
2
revised Paradoxical interaction between a massive charged sphere and a point charge
more precise