Global Definition and 413 Threads

Please see the derivation below that, if the metric is time-independent, then the integral over a sufficiently large 4D spacetime region of ##T^0_{\,0} \sqrt{-g}## is independent of time, where ##T^{\mu\nu}## is the energy-momentum tensor of a relevant collection of matter-energy fields. Thus, I...

I found some interesting discussions in this site (e.g: https://www.physicsforums.com/threads/smolin-lessons-from-einsteins-discovery.849464/; https://www.physicsforums.com/threads/relatismo-to-the-max.83885/) which are related to Lee Smolin's ideas that laws are not immutable and can therefore...

I have a likelihood function that has one global minima, but a lot of local ones too. I attach a figure with the likelihood function in 2D (it has two parameters). I have added a 3D view and a surface view of the likelihood function. I know there are many global optimizers that can be used to...

Hi Pfs, consider a pair of maximally entangled photons where the total momentum is null and the same thing for the total angular momentum. I suppose that this pair is like an universe: nothing outside the pair acts on it except maybe a device for the measurement of these two properties (no local...

It is known, that due to global warming, the average temperature on Earth over the past 100 years has increased by 1.2 degrees. At the same time, I heard that earlier the temperature of the Earth was 7 degrees higher than the current one. I do not deny the danger of global warming, because I...

https://bgr.com/science/mit-scientists-think-theyve-discovered-how-to-fully-reverse-climate-change/

Solar radiation-: it is em radiation emitted by son. it is short wave radiation. it comes in many forms. 1) visible light 2) radio waves 3) infrared 4) x rays 5) uv rays Global radiation-: it is sum of direct and diffuse radiation arriving at a ground. What are the differences between these two?

Physicists have proposed linking a global network of cesium clocks in a phase-coherent entangled state, for example in the article A Quantum Network of Clocks (arXiv:131045v1). My audience would like to know how better synchronization or more accurate timekeeping would lead to advances in our...

Methane and hydrogen sulfide are supposed to be heavier then air, thus why they remain in low lying areas. I am to believe that only when they begin to disintegrate, they rise into the atmosphere. So my question is, if these gases are already disintegrated, how can they be so formidable?

Gauge symmetry is highly confusing, partly because many definitions differ in the literature. Strictly speaking gauge symmetry should be called gauge redundancy since you are mapping multiple representations to the same physical state. What is your favourite definition of what "large" gauge...

Hi, searching on PF I found this old post Global simultaneity surfaces. I read the book "General Relativity for Mathematicians"- Sachs and Wu section 2.3 - Reference frames (see the page attached). They define a congruence of worldlines as 'proper time synchronizable' iff there exist a...

Consider the following theorem: Theorem: Let ##f## be a concave differentiable function and let ##g## be a concave function. Then: ##y \in argmax_{x} {f(x)+g(x)}## if and only if ##y \in argmax_{x} {f(y)+f'(y)(x-y)+g(x)}.## The intuition is that local maxima and global maxima coincide for...

I've no political agenda. This is strictly a math question about optimization. Those addressing it should do so strictly from a mathematical perspective. Thank you! If the world simply had one global currency, like Bitcoin, and everyone had an account, then the sum total of all accounts...

@Bystander @fresh_42 pasta is normally made from tetraploid wheat ( 4n = 4 sets of chromosomes, humans are diploid with 2 sets. ) Semolina and durum are names you will encounter for 4n wheat cultivars. 6n (hexaploid) wheat is so-called bread wheat or sometimes modern wheat. 4n wheat crops...

Hi, I know there is actually no way to set up a global coordinate chart on a 2-sphere (i.e. we cannot find a family of 2-parameter curves on a 2-sphere such that two nearby points on it have nearby coordinate values on ##\mathbb R^2## and the mapping is one-to-one). So, from a formal...

Hello, I am learning about functions and namespaces and I have a question about the keyword global. Variables defined inside a function are local variables and cannot be used outside of the function by the rest of the program (by using the return keyword, we can assign the value of a local...

Is it possible to create a two-seasonal global climate calendar as a statistical model of some physical property of Earth's upper air, independent from interacting factors such as topography, elevation, latitude, nearby water, ocean currents, vegetation and prevailing winds? The beginning of the...

I was teaching the basics of quantum states and was showing the students that an arbitrary state in a quantum two-level system could be written as ##|\psi\rangle = C_1 |+\rangle + C_2 |-\rangle = R_1 |+\rangle + R_2 e^{i \alpha} |-\rangle##, with {##C_i##} complex and {##R_i##} real. Then...

Hi, starting from this thread Principle of relativity for proper accelerating frame of reference I'm convincing myself of some misunderstanding about what a global inertial frame should actually be. In GR we take as definition of inertial frame (aka inertial coordinate system or inertial...

Hey ! :giggle: Let $f:\mathbb{R}^2\rightarrow \mathbb{R}^2$, $f(x,y)=\sin^2(x)\cdot \cos^2(y)$. - Show that $f$ has at $\left (\frac{\pi}{2}, 0\right )$ a strictly local maximum and that is also a global maximum. - Determine all points at which $f$ gets its global minimum. I have sone...

does this Beam, composed of three elements and 4 nodes(considering lateral deflections and slopes) has an 8x8 global stifness matrix and if so is the global matrix calculated the same way as a 6x6 stifness matrix for the same kind of beam but only with two elements and 3 nodes

How much will this phenomenon affect the Earth's rotation? Is it possible that the change in the Earth's rotation movement will significantly affect agricultural production on a global scale, for example?

The "Weak Signal Propagation Reporter" (WSPR) has been used in combination with other tracking methods by Richard Godfrey to refine the initial path of flight MH370 in March 2014. That flight disappeared in the Indian Ocean and two extensive underwater searches were unable to locate it. WSPR...

1.) The rule for the global ##SO(3)## transformation of the gauge vector field is ##A^i_{\mu} \to \omega_{ij}A^j_{\mu}## for ##\omega \in SO(3)##. The proof is by direct calculation. First, if ##A^i_{\mu} \to \omega_{ij}A^j_{\mu}## then ##F^i_{\mu \nu} \to \omega_{ij}F^j_{\mu\nu}##, so...

A recent thread Why Grid North doesn't agree with True North on maps had a lot of discussion on map projections. Here is a new contender for best way to project the globe in 2D. I am interested in their claim. "distances across oceans or across poles are both accurate and easy to measure."...

https://www.nature.com/articles/s41586-020-03173-9

Is it possible (read: reasonably easy) to find global minima of an nth degree polynomial of the general form $$a_nx^n + a_{n-1}x^{n-1} ... a_2x^2 +a_1x + a_0 = 0$$ It seems to have applications in computational chemistry as I have a "hunch" that polynomial regression could be used to somewhat...

Is anyone opting for online schooling, during this global pandemic ?

Is the phase factor in : ##e^{i\phi}\Psi(x)## a constant or a global phase factor called ?

I emphasize that I am not posing a rhetorical question, and am not trying to make a political statement (and would ask all respondents to steer clear of politics), but would genuinely appreciate knowing whether the report in question is considered valid by those in the field who are impartial...

Some students I mentor in the SE US have reported that their local PGRE has been cancelled, but additional info is hard to come by. They are trying to find out if it is still being offered on that date at other locations. What do y'all know? Anyone know of a location in the US where it is...

Temperature is often imagined as a scalar field varying over (physical) space. Yet temperature seems to be generally defined as the (reciprocal) rate of change (with fixed V,N) of the entropy of a system w.r.t. the energy of that system; a seemingly global property. Is this definition only for...

In page 9 it says: "It is interesting to note that Riemann does not speak of the “analytic continuation” of the function beyond the halfplane Re s > 1, but speaks rather of finding a formula for it which “remains valid for all s.” [...]. The view of analytic continuation in terms of chains of...

Usually it is just about the nasty oil, and goodness of electricity. Of the 100 solutions Project Drawdown has listed, some would not even be considered along with the more commonly known by the public at large https://www.drawdown.org/ From cultivation of rice ( number one crop of the world )...

Almost 90% of all humanity lives in the Northern hemisphere. Due to colonization, expansion, growth, war, water sources, etc. we have amassed our populations in specific areas around the Northern hemisphere. We continue to build at an unprecedented rate. Our buildings are growing wider, taller...

I'm a bit lost at how to exactly start this exercise... As far as I understand we need to first determine ##d\tau_E## and ##d\tau_S##. First question: Since we can neglect the Earth's movement, can I also neglect the movement of the satellite with respect to the far away observer? If so, I...

1) How do we determine a Lie group's global properties when the manifold that it represents is not immediately obvious? Allow me to give the definitions I am working with. A Lie group G is a differentiable manifold G which is also a group, such that the group...

I'm trying to do a fairly complete system analysis script in Octave that involves these steps: 1) Assign values to all fixed system parameters 2) Make various preliminary calculations based on system parameters 3) Solve a system of differential equations 4) Make various post-ODE solution...

https://link.springer.com/article/10.12942/lrr-2005-6 https://en.wikipedia.org/wiki/Exact_solutions_in_general_relativity http://www.numdam.org/article/SEDP_1989-1990____A15_0.pdf A moderator removed this off-topic discussion from another thread. Does anyone on the Physics Forums have...

I found this link off of a politically charged website (of the persuasion to deny that Global Warming exists), so I am apt to be skeptical. (The website is hosted at the Northern Marianna Islands, making me even more suspicious.)...

ESL: Since valuable discussions are being made and then threads closed, here is an input: Melting ice to liquid water, will gather around equator because of gravity @lomidrevo

I'm always struggling understand how to determine if a two variable function has global minima, I know that if I find a local minima and the function is convex than the local minima is also a global minima, in this case is really difficult to determine if the function is convex. Sorry if I...

As a start for discussion I'd like to make the following bold claim: Both the problems of enough usable energy and global warming can be resolved by implementing Maxwell's demon on a large scale. To justify this bold statement somewhat, I'd like to point to a (relatively) recent...

Here is the BBC article, I've read today. Conclusion from the original study: This sounds really alarming to me.

Are there any studies that explore what an affordable level of global health care potentially looks like? EG - Can the human race afford potable water and sewage for all humans? If so, can we then afford making aspirin available to all humans (if that were next)? If so ... Etc. At a macro...

A fusion reactors releases a lots of energy. Most of this energy will end up as thermal energy after it has been used by the consumers. Wouldn't this heat up the earth? People use the energy to run cookers, drive cars, light up houses, etc. This energy (99%?) will end up as thermal energy where...

Can anyone point to a refereed paper exploring the heat absorbed by melting around 500 GT of ie per year (Antarctic - 127 GT pa; Greenland 286 GT pa; sea ice, glaciers estim. 100 GT pa)? As latent heat of fusion is 333.55 KJoules per Kg, I reckon the heat absorbed per year is around 1.67 X 1023...

Homework Statement y=0.5x^3 - abs(1-3x), [-2,2] The Attempt at a Solution So i found the min value y(-2)=-11 and i found lokal min at x=sqrt2 There is a sharp max somewhere around x=0.3 but i cannot for the life of me find how to get that point. Also i wrote there is only 1 local min and...

We know that greenhouse gases are the biggest cause of global warming and that the Earth has gotten warmer and warmer over the past few decades. Question: Since not all locales produce greenhouse gases (namely, carbon dioxide) equally, are the effects of global warming distributed more to...