I notice an apparent asymmetry between the two processes of closing a question or voting for reopening. In the former case, a reason for the vote must be given. In the latter, it is not possible to explain the reason. What is the rationale for such difference? Wouldn't be better to know why there...
sometimes I don't understand. Can you really call some dimension time if it has the matching signature as that of time in the metric, when it has no causal consequences
From what I can understand, different phase spaces get related by a new set of symmetries in Itzhak Bars theory, but there isn't any indication on what motion is like in the underlying 2T theory, as in, are we expecting some gauge fields to spontaneously evolve into other gauge fields thus one dynamical system and another dynamical system are actually the same system at different coordinates of the 2nd time axis?
but if that is the case, then changing say electromagnetic fields will have instant consequence to gravitational fields some place away
snowing - the ground has some white banks and some dusts is dropping persistently - is this snowing? but the air temperature here indicated on web is 2 degrees Celsius now.
What is the causal structure of the underlying 2T theory. Yes I knew by fixing gauges in different ways you effectively singled out a time direction and the remaining spatial dimensions become different theories like massless and massive relativistic particles with their corresponding gauge symmetries such that unitarity is observed, and hence there is no causality violation
> 3 If one considers gauging Sp(2n), instead of Sp(2), then one finds that the system describes n particles with 2n times in (d + 2n − 2, 2n) dimensions [26]. After partial gauge fixing and solving a subset of the Sp(2n) constraints such a system reduces to the n-time n-particle theories in (d + n − 2, n) dimensions discussed in [27]. Fully solving all constraints one obtains n particles each in (d − 1, 1) dimensions, but each using a different timelike coordinate as embedded in the higher dimensions. So, to describe a single particle (and the associated field theory, i.e. a 1T
My question is how to prove that the the heat capacity of system is equals to the sum of the heat capacities of the object of at same temperature difference
The heat capacity of a system tells you the change in internal energy for a given change in temperature. So to answer your question we have to look at the temperature and energy of a pair of systems separately and to together.
The first one is easy. If the 2 systems are in thermal equilibrium t...
@CaptainBohemian Not physically, but on the conference?
@RyanUnger Speaking of Outer Worlds, I was saving up for No Man's Sky a couple years back. I ditched it at the last moment and bought Overwatch instead. Turned out to be the best trade deal in the history of trade deals, maybe ever.
@NiharKarve The funny thing is, for my tastes, Overwatch basically got worse over time, whereas No Man's Sky went from a total flop to an actual good game.
@JMac Yeah, I can see that. But I was hyped for the multiplayer in NMS, and while Overwatch was kinda unbalanced in 2018-19, I think it's pretty good right now
I personally waited till like 2019 to buy NMS, so I definitely didn't get screwed over by a lack of features. A big problem I have with OW and similar class/character based games is that I feel like I need to play them too often to keep up with the meta. I can't just jump back in after half a year and like enjoy myself, because I have no idea what changes have happened to skills/characters, let alone new ones, and don't want to do a ton of research just to get back into a game.
Seems iffy to start taking time derivatives of the momenta in the action like that also, even more so the way one is playing with coordinates, velocities and momenta simultaneously
@NiharKarve Yeah but chess also has like hundreds of years of meta development and a learning curve that I don't think I want to deal with lol. Right now I've just been playing the crap out of Rock Band and Guitar Hero anyways; which is definitely easy to get back into because I played it so much in high school.
Yeah the only thing that kinda worries me is that I seem to be trying to get as many of the fake plastic guitars as I can, almost like some sort of addiction at this point. Going into this weekend I had 2, and if a second kijiji deal goes down today, I'm going to be up to 6 lol
So... in trying to figure out how crazy unconstrained two time physics is (that is, it do not obey some constraints that ensures it to reduce to one time physics and other string theory stuff) by looking up how the ultrahyperbolic equation is solved link.springer.com/chapter/10.1007/978-1-4612-5406-5_8
I got an interesting conclusion: The general "dynamics" of two time physics do not resemble even remotely in any way to our real world that is think in terms of worldlines
Basically, having each particle to be constrained to only one time variable, or having CTC is relatively tame
The general case, which all two time physics researches ruled out because it do not resemble our world, is some weird n dimensional manifold of points that points within the same family of hyperplanes are somehow correlated and constrained in some complicated way (namely obey the radon transform and some mean value theorem like thing called Asgeirsson theorem) in an indeterministic fashion, meaning the directionality and linear character of time just breaks down completely
since I don't know how many features like autocompletion or fine control over the compilation process Overleaf offers I can't tell you whether it's lacking anything TeXstudio offers
> As you see, the signature is 10+2. Such a theory has two times. It's clear that the conventional physical interpretation of dynamical theories is impossible if there are two time coordinates. After all, if there were at least two large time coordinates, there would exist a two-dimensional "Euclidean" plane with purely time-like directions.
That is some stationary particle with some weird evolution, which the next paragraph in the blog said can move along a CTC
> In general, you don't want this term to identically vanish. That means that the non-constancy of W has to be crucial for the theory to be physically non-trivial. I feel that the variations of the fields in the direction along the gradient of W (and one more?) are kind of (identically) unphysical which makes the whole construction less meaningful and important.
I like that idea of a symmetry between phase spaces, but a lot of things felt forced as more and more constraints are added after equation 2 as if the whole aim is to constrain the 2T theory in such a way it can reduce into 1T theories with the desires qualities
but I may be not suitable to comment, as I don't fully understood how to read that 2T action yet other than the footnote said basically each particle travel along a worldline parametrised by one of the time dimensions
Including the time derivative of the momentum in the action really seems to be breaking the first order nature of the action, seems really like you've snuck in treating the second derivatives as independent variables in doing that simple step
IF I understood correctly, Bar's 2T structure is basically a lot of 1T structures related by symmetries, inserted in some not well justified way
Interestingly, I read some other paper where the authors explored 2T physics in a more general setting (subjected to the constraint of no CTCs) found that in general, many 2T theories will actually end up with each particle having their own worldlines in the 2T plane
From a Lagrangian perspective, it's basically like you did integration by parts so that accelerations are now in the action, and because you are talking about symmetry transformations you HAVE to treat accelerations as independent variables in the Lagrangian that are transformed by the symmetry transformation, but this is so ridiculous because on the one hand you're trying to maximally exploit the symmetry,
on the other hand you've literally ignored third derivatives for every field in your theory for zero reason
If you start talking about symmetry transformations on time-derivatives of momenta, the time derivatives of the momenta should be independent variables in the 'action' i.e. 2nd derivatives, but the whole point of going to the Hamiltonian formalism was to bring a 2nd order theory down to a 1st order theory, and treating accelerations as independent variables is just ignored (c.f. 'jerk' conversations)
It's interesting but I don't know if it makes sense, it's definitely an interesting idea to try see if this $\mathrm{sp}(2)$ thing is right
Both definitions are fine as long as you're careful with signs.
Here's a derivation of your gravitational potential energy using the idea of the negative work done "by the field." (Note the initial negative sign.)
$$U(r)=-W_\text{by field}=-\int\vec{F}_\text{field}\cdot d\vec{s}=-\int_{r=\inft...
What is the relation between the vectors ds and dr there?
It is the line element for an infinitesimal displacement in space, in Cartesian coordinates it reads as $d \vec{s} = dx \hat{i} + dy \hat{j} + dz \hat{k}$, in spherical coordinates it reads as $d \vec{s} = dr \hat{r} + r d \theta \hat{\theta} + r \sin \theta d \hat{\phi}$, you'd want to use spherical coordinates as the vector $\vec{F}$ is given in spherical coordinates, note $\hat{r} \cdot d \vec{s} = dr$ as is written in the answer
I am confused with the initial negative sign for the work done by the field. If the force and displacement are in the same direction, then what's the negative sign for?
Both definitions are fine as long as you're careful with signs.
Here's a derivation of your gravitational potential energy using the idea of the negative work done "by the field." (Note the initial negative sign.)
$$U(r)=-W_\text{by field}=-\int\vec{F}_\text{field}\cdot d\vec{s}=-\int_{r=\inft...
