cianfa72's latest activity
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cianfa72 reacted to jbergman's post in the thread Undergrad Spacetime coordinate smoothness requirement with
Agree.
Polar coordinates are not a valid chart for an open set ##U## containing the origin since the transition function with the identity... -
cianfa72 reacted to PeterDonis's post in the thread Undergrad About spacetime coordinate systems with
Like.
No, it isn't. The proper acceleration is a direct observable; you don't even have to know the overall mass distribution to measure it... -
cianfa72 reacted to martinbn's post in the thread Graduate Trivial fiber bundle vs product space with Like.
I am starting to think that the question of the thread is not about fibler bundles, but whether isomorphic objects are to be considered...
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cianfa72 replied to the thread Graduate Trivial fiber bundle vs product space.Let me try to recap my understanding about this. In the context of category theory, given two objects ##X_1## and ##X_2## of a given...
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cianfa72 reacted to mathwonk's post in the thread Graduate Trivial fiber bundle vs product space with Like.
It seems indeed this is the usual meaning of trivial, i.e. equivalent to a product, but without a choice of trivialization. I was...
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cianfa72 replied to the thread Graduate Trivial fiber bundle vs product space.As far as I can understand, your point is that a trivial bundle includes two pieces of information: a trivializable bundle plus a...
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cianfa72 replied to the thread Graduate Trivial fiber bundle vs product space.You mean, take a topological space ##B## that is homeomorphic to the Cartesian product ##A \times F##. The choice of the homeomorphism...
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cianfa72 reacted to lavinia's post in the thread Graduate Trivial fiber bundle vs product space with Like.
A choice of a product decomposition of a topological space that is homeomorphic to a Cartesian product AxF naturally supplies a...
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cianfa72 replied to the thread Graduate Trivial fiber bundle vs product space.Yes, but for the case of product bundle the projection mapping is canonically/naturally given by the structure of the product (it is one...
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cianfa72 reacted to etotheipi's post in the thread Graduate Meaning of potential energy in external fields with Like.
Though I don't think this is an approximation, but rather bending the rules to make things simpler. The following is from Morin Once...
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cianfa72 replied to the thread Undergrad Why is thermal energy treated differently than other kinds of energy?.Ok, you are assuming the inertial rest frame of the table. By Newton 3rd law, the book acts with a force on the table, so there must be...
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cianfa72 replied to the thread Undergrad Why is thermal energy treated differently than other kinds of energy?.You mean the table doesn't move w.r.t. the rest frame of "book + table" system's Center-of-Mass.
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cianfa72 replied to the thread Undergrad Why is thermal energy treated differently than other kinds of energy?.Yes, for instance in the rest frame of the "Earth + object" system's Center-of-Mass, the kinetic energy is basically associated to the...
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cianfa72 reacted to kuruman's post in the thread Undergrad Why is thermal energy treated differently than other kinds of energy? with Like.
Sure, but note that mechanical energy is the sum of kinetic plus potential energy. Therefore, in my expression, it is implied that...
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cianfa72 replied to the thread Undergrad Why is thermal energy treated differently than other kinds of energy?.I'd like to point out that the increase in mechanical energy associated with lifting an object up, goes into the potential energy of the...