101–110 of 250 posts
Earlier quoted context omitted.
> continuity of spacetime is a convenient approximation I disagree, and there's no evidence for this. This is computer science leaking out; physics has no formulation of spacetime in discrete terms, and indeed, all of physics presumes continuity. In QM, the space of wavefns is infinite-dim continuous, and if wasnt, QM wouldnt be linear. Cognition is discrete, but the world is continuous.
Its 99 years since Einstein published the paper on the photoelectric effect whith had far-reaching consequences. [1] And 93 years since the first Solvay Conference. [2] [1] https://en.wikipedia.org/wiki/History_of_quantum_mechanics [2] https://en.wikipedia.org/wiki/Solvay_Conference
Earlier quoted context omitted.
> continuity of spacetime is a convenient approximation I disagree, and there's no evidence for this. This is computer science leaking out; physics has no formulation of spacetime in discrete terms, and indeed, all of physics presumes continuity. In QM, the space of wavefns is infinite-dim continuous, and if wasnt, QM wouldnt be linear. Cognition is discrete, but the world is continuous.
But isn't the whole point of QM is that this assumption doesn't hold in some scale? I mean it's literally in the name. Care to explain? :)
OK, I do not understand prof.Dyson's argument at all. "This does not mean that an electric field-strength can be measured with the square-root of a calorimeter. It means that an electric field-strength is an abstract quantity, incommensurable with any quantities that we can measure directly." Electric field-strength is measurable no less directly than energy, it is a force experienced by a unit charge placed within t…
You can make the electric field disappear by choosing the right gauge. Same goes for the magnetic field (can't make both disappear together though). The vector potential, in that sense, can be regarded as a more fundamental description of the electromagnetic field. It can't be observed directly though, but electric and magnetic field strengths are manifestations of the vector potential, they are not fundamental in th…
What? No you can't. The fields are invariant under gauge transformations.
My proudest moment in high school was getting a 5/5 on the calculus based AP Physics C exams at 15 with no calculus and only rudimentary algebra knowledge at the time. That experience permanently colored my thinking, and made me much more open to practicing thorough visual imagination as a way to solve problems. I found that practice useful all the way through my EE degree's vector fields courses a decade later. I th…
The originally published equations were "20 or so" because one equation was written for each scalar component. Rewriting the equations in vector form reduces the number to the modern number. Moreover, the original equations are the complete system. The variant with 4 equations is the simplified variant for vacuum, which is mostly useless, except for the purpose of studying the propagation of electromagnetic radiation…
> Rewriting the equations in vector form reduces the number to the modern number.
And if you use the differential form or 4d tensor notation they get reduced to 1 equation. Of course, for a lot of practical problems this is not very useful and it's better to work with the 3d vector form.
> The variant with 4 equations is the simplified variant for vacuum, which is mostly useless, except for the purpose of studying the propagation of electromagnetic radiation in vacuum.
> Instead of learning a large number of simplified variants of the Maxwell equations with limited applicability, it would have been much better if a manual would present since the beginning the only complete variant that is always true, which must be in integral form, as initially published by Maxwell.
Here I have to strongly disagree. The version of Maxwell's equations that is fundamental and exactly correct [1] is the vacuum version. The ones with magnetization and displacement vectors are only approximations where you assume continuous materials that respond to fields in simple way. In truth, materials are made of atoms and are mostly vacuum: there is no actual displacement vector if you look close enough.
Also the vacuum Maxwell equations are useful in many scenarios. For instance, that's how you compute the energy levels of Hydrogen atom or how you derive QED. Also, you have to start from them to derive the macroscopic versions with magnetization and displacement that you seem to like.
[1] Well, up to non-linear quantum mechanic effects.
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All the people who use thinks like the word "information" in this context are confusing thermodynamic, logical, probabilistic, (+ many others) and equivocating. "Information" is not a physical quantity, and there cant be a "volume" of it. Nor does this have anything to do with real numbers. It is impossible for there to be any system extended in space and time to "zoom infinitely" into a continuous range and hence re…
Some people would disagree with dismissing information as non physical. For instance: https://scottaaronson.blog/?p=3327 The argument there would be that stuffing an extra bit of information in an information saturated volume would make it collapse into a black hole.
For example in E = 1/2mv^2, a particle has kinetic energy in virtue of being matter in motion -- it is motion and matter which are basic. Energy is just a system of accounting which tracks motion in the aggregate over time (with kinetic/potential just being the future/past in the accounting) hence why energy conservation is just a temporal invarience.
When making arguments about the physical properties reality has (eg., whether aspects are continuous) you need to be exceptionally clear what your terms mean, and terminology in physics isnt designed for this.
There are no "information saturated volumes", this is a series of abstractions piled on top of each other.
All the words in this area have quite complex formal definitions that are have quite difficult to unpack semantics, you cannot just go around saying "saturated volumes" -- it is this sort of language which breeds cranks, and pop sci does it with abandon.
This entire discussion is a matter of several PhDs, and to be done only well by people with PhDs in the matter (philosophy of physics), or equivalent research. It's not possible to scrap fragaments of what compusci bloggers say and derive much that's likely to be actually correct.
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yes, i thought that was too obvious to be worth saying, but i'm glad you've said it so the knuckle-dragging contingent don't think i'm endorsing their untutored 'theories' for that matter i use the aristotelian paradigm of physics when i expect my bed to stop moving when i stop pushing it across the floor; i don't bother with calculating the deceleration due to the friction coefficient with the floor
Sorry, I think the first part of your original comment was a bit confusing. Upon rereading: the second part already made it clear that this is what you meant.
My proudest moment in high school was getting a 5/5 on the calculus based AP Physics C exams at 15 with no calculus and only rudimentary algebra knowledge at the time. That experience permanently colored my thinking, and made me much more open to practicing thorough visual imagination as a way to solve problems. I found that practice useful all the way through my EE degree's vector fields courses a decade later. I th…
> continuity of spacetime is a convenient approximation I disagree, and there's no evidence for this. This is computer science leaking out; physics has no formulation of spacetime in discrete terms, and indeed, all of physics presumes continuity. In QM, the space of wavefns is infinite-dim continuous, and if wasnt, QM wouldnt be linear. Cognition is discrete, but the world is continuous.
Planck constant would like to have a word with you. But it is true that CS shines a light on the matter of mapping the infinite into bounded spaces.
This matter of ‘cognition’ is the entire matter (npi) of contention. What is the actual relationship between number and perceived phenomena? What is the deeper meaning of the concordance of mathematics and physics? Where do these magical constants come from and what does it all mean?
It seems we bring the ‘world’ into being by partitioning. See Genesis 1 for details.
> the world is continuous
Reality is actually a unified undivided unity without form and timeless & eternal - that is all we can say with certainty. The “world” is our perception of this reality. Our cognitive machinary is discreet, and a mapping of this reality into metric & temporal spaces of the mind.