alancalvitti
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 Feb 4 comment If you are on Earth, are your mass and weight the same? Btw, a consequence of treating the radian as dimensionles is that it breaks symmetry b/w translational vs rotational motion: torque has units of work rather than force. This has been pointed out as a limitation in metrology research. Feb 4 comment If you are on Earth, are your mass and weight the same? Your post also mentions that historically " ... distinction was not always recognized". Historically, fractional calculus is a latecomer as well. Jan 31 comment If you are on Earth, are your mass and weight the same? Agree on math vs phy, but still, $e^i$ makes physical sense as unit rotation (1 rad); the imaginary unit isn't factored out. Jan 31 comment If you are on Earth, are your mass and weight the same? @dmckee, see this commment by Arkamis: " In materials engineering, it is not unheard of to have units of $MPa(m)^{1/2}$..." here: math.stackexchange.com/questions/567172/…. If some fractional units are useful, why not transcendentals at some point - isn't that the story of generalization in math? Jan 29 comment Fundamental question about dimensional analysis @MarkEichenlaub, you're right that exponentiation is a limit and it started in analysis, but categorically, an exponential $A^B$ is the set of functions from $B$ to $A$. Jan 29 comment If you are on Earth, are your mass and weight the same? @dmckee, ok, so only transcendental functions of ratios are acceptable. In following up on your link, found the paper by Matta ea J Chem Edu 2011 that describes it. Same paper also shows the Taylor expansion explanation is flawed btw. Jan 29 comment If you are on Earth, are your mass and weight the same? @dmckee Re unit analysis, since distinct units can be multiplied, their logarithms can be added. Re "same rules"? "spin is an intrinsic property of a particle, unrelated to any sort of motion in space and fundamentally different from orbital angular momentum" > en.wikipedia.org/wiki/Angular_momentum. So even if OAM and SAM share the same units (multiple of hbar, with SAM limited to +/-hbar, while OAM can take unbounded integer multiples of hbar), they are differen types of motion. Jan 28 comment If you are on Earth, are your mass and weight the same? @dmckee, "Things of a different kind can never be the same", can you define different and same objectively, eg Spin (SAM) and Orbital Angular Momentum (OAM) are distinguishable yet both measured in angular momentum units afaik. Jan 16 comment What experiment would disprove string theory? The hidden puppet strings of Brian Greene: The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next (2007) + Bankrupting Physics: How Today's Top Scientists are Gambling Away Their Credibility (2013) + Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth (2014) Dec 6 awarded Commentator Dec 6 comment A mirror flips left and right, but not up and down @user4577, "one-eyed" camera still sees left-right flip. Dec 6 comment Can I compute the mass of a coin based on the sound of its fall? What if it falls on a carpet or sand, not making much noise? Dec 6 comment What is Optimal Control Theory and Controllability Theory? Have you tried Wikipedia? Optimal control means optimizing a system, but the other term is "control theory", whereas "Controllability" is complementary to "observability". Feb 24 answered What is the meaning of phase difference? Feb 20 comment What happens if object is thrown in empty space? You write "in empty space" but is there a gravitational potential? Feb 19 comment Could a universe with purely Newtonian mechanics exist? @JoeZeng, how do you plan on deciding one way or the other without access to such a universe? Feb 19 comment Could a universe with purely Newtonian mechanics exist? @MichaelBrown sure, in fantasyland Feb 18 comment Could a universe with purely Newtonian mechanics exist? Then the answer is no, because some things move fast, and some things are massive, and Newtonian mechanics could not account for observations like precession of Mercury, gravitational lensing, the accuracy of GPS and many others. Feb 18 comment What's the basic difference between heat and temperature? For one thing, heat and temperature have distinct units of measurement, the former being expressed in SI units of Joules, resp. Kelvin. Think of heat as an extensive quantity and temperature as intensive quantity. Feb 18 comment In mechanics, is shock really better expressed as jerk instead of acceleration? @Sankaran, re: "or a very sharp gaussian" - why Gaussian? how do you know that it's exponential for example?