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taeto last won the day on August 1 2018
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Infinitesimals and limits are the same thing
taeto replied to dasnulium's topic in Analysis and Calculus
Thanks for the useful link! Regarding an "original theory", such a one would have a theorem like \( dy = \frac{dy}{dx}dx,\) which means that you can do arithmetic with an "infinitesimal" \(dx\), assumed nonzero. In contemporary mathematics the same expression is still a theorem, but it stands for something entirely different; both \(x\) and \(y\) are functions that have differentials \(dx\) and \(dy\) respectively, with \(\frac{dy}{dx}\) being their derivative. None of the latter functions represent anything "infinitely small", indeed the range of either differential can easily be unbounded. In that sense the "theories" somehow should not be considered comparable, because they speak of completely different things. On the other hand, they might be, at least partially, "isomorphic", by being able to show theorems that have an identical outward appearance. I am definitely interested in any small nuances which would make a proposed "original theory" make a different prediction than what we would expect today. 
Infinitesimals and limits are the same thing
taeto replied to dasnulium's topic in Analysis and Calculus
I have read somewhere that Cauchy tried to use the "original theory" in an argument, but ended up with a wrong result. I will look for the reference, though maybe someone knows already?! 
Problem with Newton's law of universal gravitation
taeto replied to Harald Linke's topic in Classical Physics
Absolutely not. Clearly 150kg is the combined mass of the two objects . 
Approaching the question from the mathematical side (and being somewhat naive about the physics), the question isn't necessarily so much about the finiteness of time, but rather whether time has an actual "beginning". Assuming that time will proceed forever after (I have not seen anybody opposed to that assumption), there could be three distinct possibilities: (1) time progresses as \(t \in (\infty,\infty)\), or (2) as \( t \in (0,\infty)\), or (3) as \( t \in [0,\infty],\) where \(0\) is a 'starting point' for the existence of time. Possibilities (1) and (2) are homeomorphic, in particular, for every time, there was a time prior to it. The only difference being that the progression of time would appear faster in (2) as in (1). Possibility (3) would be similar to the familiar picture of BB in a spacetime with only one space dimension, where BB represents the North Pole of the globe and the time represents moving south along laterals such that space is represented by ever increasing circles. It also means that there were times for which there was no time that was 1 second previously. Does this seem the most reasonable idea of the 'beginning' of time? Oh, and if my intuition is worth much, then I do not see much chance of making any determination of either possibility by physical measurement. But feel free to disagree.

I am not sure what your "it" stands for. In the turtle picture, a turtle is supposed to stand on a lower turtle. I am trying to suggest that a segment of time does not have to stand on any previous segment of time necessarily. Viewed in isolation it could conceivably be the initial segment of time that exists, or it might have any amount of time preceding it. Which is why I would hesitate to entertain the turtle analogy when it comes to time progression. If you mean to point to different possible choices of inertial frame of reference, then the question of finiteness of time appears to be frame independent. I.e. if an amount of time is finite in any frame then it would also measure finite as seen from any other frame, even when the precise length of time measures different.

For the turtles to do proper support, there cannot be a bottom turtle, unless it gets provided with something else to stand on. It doesn't seem that a time measuring device must have a similar property. Either there is a first second (say, after BB), or there isn't one, it doesn't appear to make a big difference to what comes after.

We would get here in a finite amount of time from any previous point in time, there is nothing problematic about that

Something wrong with this Theory of Quantum Gravity?
taeto replied to Atom22's topic in Modern and Theoretical Physics
Who? Romeo D. Matshaba, the author? 
Something wrong with this Theory of Quantum Gravity?
taeto replied to Atom22's topic in Modern and Theoretical Physics
I answer the OP's question, only to get a downvote. Not that I care a lot. But seriously, in a forum is it really supposed to be better rewarded not to answer questions? Possibly not as familiar as you are. But the transfer principle immediately allows me to ascertain that the limit p in (2) is identically equal to 0. I did not say that (2) does not make sense. What I said was that it only makes sense if p is 0. 
Something wrong with this Theory of Quantum Gravity?
taeto replied to Atom22's topic in Modern and Theoretical Physics
It is de Broglie, not De Broglie. You say that you understand the explanation in the paper. Do you know how the de Broglie wavelength of a particle is defined at all? These are correct. But if you check again with the paper, it says something completely different. 
Something wrong with this Theory of Quantum Gravity?
taeto replied to Atom22's topic in Modern and Theoretical Physics
Correct. Gravity is a concept. The gravitational constant is a quantity, and it is not measured in meters. 
Something wrong with this Theory of Quantum Gravity?
taeto replied to Atom22's topic in Modern and Theoretical Physics
I am not sure that saying that all the mistakes are just "innocent typos" gives evidence in favor of the article likely having been reviewed. And we can throw in that the author's name is duplicate. No journal would allow that. The first line of the abstract states that we can "view gravity as the de Broglie wavelength of quantum mechanics". A few problems here. Gravity is not a physical quantity, and certainly not a length. And QM does not possess a de Broglie wavelength. The second to third line of the abstract is just nonsense as well. But you want equations. Equation (1) is nonsense. The LHS is a number, and the RHS is either undefined or a binary operator, which is anyone's guess so long as it is not defined. Thereafter, the quaternions do not have the properties that are claimed here. There is no "familiar Clifford space" either. The concept that is familiar is Clifford algebra. Equation (2) makes no sense unless p is identically zero. In the subsequent displayed equation, the "p_i" is not even defined. In the next displayed equation, there is no referent to the symbol "n". Right after that, there is division by zero; N=1/p. After that everything is mostly word salad and nosensical expressions. But tell me one single thing, somewhere in this paper, that you are convinced that it is actually correct, please? 
Something wrong with this Theory of Quantum Gravity?
taeto replied to Atom22's topic in Modern and Theoretical Physics
It is unlikely that the version that you link to has been peer reviewed, seeing how it is full of mistakes of all kinds. 
I suspect you are supposed to see that G is abelian. That certainly helps for showing normality.

Where are you stuck, showing that H is a subgroup or showing that H is normal?