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Oct
17
revised Simpler derivation of Sackur-Tetrode equation
corrected spelling the surname of O. Sackur in the title; and some copy-editing
Oct
17
revised Relativity and “light years”
added tag [tag:metric-space], since the question is foremost about meaning and determination of distances
Oct
17
revised Relativity and “light years”
p.s. on the chronometric distance definition, in relativity.
Oct
17
answered Relativity and “light years”
Oct
16
answered Why collide a moving particle with a particle at rest, rather than two moving particles?
Oct
16
comment Constant Jerk Relativistic Rocket
user2096078: "What if jerk is [...] held constant in a relativistic rocket?" -- Then simply $$\mathbf a_{end}- \mathbf a_{init}=\mathbf j ~\tau[~{}_{init}, {}_{end}~],$$ where $\mathbf a$ is acceleration, $\mathbf j$ the constant jerk, and $\tau$ is duration, and it goes without saying that these are understood as "proper", i.e. referring to the rocket itself; not to incidental other participants. Relating these quantities to geometric relations between certain other participants (planets, stars) would certainly be a loftier goal; but perhaps not the topic of this OP question.
Oct
15
revised Quantum States, Hilbert Space and Time
corrected spelling the surname of D. Hilbert; cmp. https://en.wikipedia.org/wiki/Hilbert_space + some copy-editing
Oct
15
suggested approved edit on Quantum States, Hilbert Space and Time
Oct
15
revised Transitions in a time-dependent field: why shouldn't the field change rapidly?
(v3.141: minor copy-editing)
Oct
14
answered Transitions in a time-dependent field: why shouldn't the field change rapidly?
Oct
14
comment Is there a geometric interpretation of the spacetime interval?
Danu: "in cases such as this (obvious typo's), it is advised to implement an edit yourself. Please, feel welcome to do so in the future." -- Thanks; but suggesting an edit of another user's contribution requires at least 5 characters to be altered; at least at reputation levels I've reached so far. "As for the notation for the interval: Let's agree to disagree." -- Let's also recognize that at least we agree on spelling out the two (not necessarily distinct) arguments of any interval. Consequently we agree on never to seriously write expressions such as$$"{\rm d}s^2 ="~...,$$ don't we.
Oct
14
comment Is there a geometric interpretation of the spacetime interval?
Danu: Your answer, as it presently stands, still shows traces of the mistake that you had begun to correct yesterday (you're welcome, btw.). Namely: "Secondly, whenever $\Delta x^2_{1,2} := \vec x^2_1 - \vec x^2_2$ is larger than [...]". And your use of two integer indeces for denoting events (while being lousy style, IMHO) is still vastly superior to not making these two arguments explicit at all. And accompanying a down-vote with a (signed) comment, as silly as that comment may have been, still seems more reputable than an anonymous drive-by. (But it's also more memorable.)
Oct
12
comment Is there a geometric interpretation of the spacetime interval?
Timaeus: "you just seem to object to terminology that doesn't seem strange." -- I do find your terminology strangely detached from the foundational terminology that "All our well-substantiated space-time propositions amount to the determination of space-time coincidences {such as} encounters between two or more {...} material points". "A location is a 1d affine subspace with a timelike tangent." -- What's a "tangent", and how to determine whether that's "timelike"?? ...
Oct
12
comment Is there a geometric interpretation of the spacetime interval?
Timaeus: "the word event is standard terminology" -- Certainly. I am objecting to your using the word "location" instead of standard terminology. "take the past light cone of the latter event and the future light cone of the earlier event and intersect them" -- Alright; thereby we identify numerous events, all of which are space-like with respect to each other. Which pair among these events should be considered? (A pair with maximum separation?) "then select an appropriate direction (a time like direction, at random if needed) [...]" -- What's a "direction"?? ...
Oct
12
comment Is there a geometric interpretation of the spacetime interval?
@Danu: "Funny, different way of thinking about things. [ N. D. Mermin, AJP 66, 1077 (1998) ]" -- I'm curious whether this claims to add anything to Robb ("Geometry of Time and Space"), or even to Einstein; cmp. MTW Box 1.3. (So I plan to hit my local library later this week.)
Oct
12
comment Is there a geometric interpretation of the spacetime interval?
@Timaeus: "[...] get to that location too soon [...]" -- "Location"? Of an event?? Rather: any "material point" (or "principal identifiable point", or "participant") who (later) took part in the event under consideration. "spacelike separated events, in the frame where they are simultaneous" -- Whole events, having several participants, don't belong to only one frame. "the area is physically related to the clock readings on a radar time or radar distance measurement." -- The radar duration $T$, and hence the corresponding interval, does not depend on incidental clock readings.
Oct
11
revised Is there a geometric interpretation of the spacetime interval?
(v3.14159: introducing the five events as their names appear in the subsequent Cayley-Menger determinant.)
Oct
11
revised Why is $\ell$ in $\mathbf F = I~\ell \times \mathbf B$ taken as shortest distance?
formatting; added link to https://en.wikipedia.org/wiki/Lorentz_force#Force_on_a_current-carrying_wire
Oct
11
suggested approved edit on Why is $\ell$ in $\mathbf F = I~\ell \times \mathbf B$ taken as shortest distance?
Oct
10
revised Is there a geometric interpretation of the spacetime interval?
(v3.1415: more formatting; since s^2 requires a specific convention.)