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I'd like to add some details to Studiots posts in regards to the function of the metric. Though I will add the metric tensors. The tensors are useful for handling multiple unknowns. The main purpose of the metric is to define the coordinate changes. For example if you have Euclidean flat (Cartesian) coordinates the metric tensor takes the form. [math]dx^2=(dx^0)^2+(dx^1)^2+(dx^2)^2(dx^3)^2[/math] In Cartesian coordinates the metric takes the form [math]G_{\mu\nu}=\begin{pmatrix}g_{0,0}&g_{0,1}&g_{0,2}&g_{0,3}\\g_{1,0}&g_{1,1}&g_{1,2}&g_{1,3}\\g_{2,0}&g_{2,1}&g_{2,2}&g_{2,3}\\g_{3,0}&g_{3,1}&g_{3,2}&g_{3,3}\end{pmatrix}=\begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/math] Now as Studiot mentioned infinitisimals to see the metric tensor in differential form which is used to handle infinitisimals. [math]\frac{dx^\alpha}{dy^{\mu}}=\frac{dx^\beta}{dy^{\nu}}=\begin{pmatrix}\frac{dx^0}{dy^0}&\frac{dx^1}{dy^0}&\frac{dx^2}{dy^0}&\frac{dx^3}{dy^0}\\\frac{dx^0}{dy^1}&\frac{dx^1}{dy^1}&\frac{dx^2}{dy^1}&\frac{dx^3}{dy^1}\\\frac{dx^0}{dy^2}&\frac{dx^1}{dy^2}&\frac{dx^2}{dy^2}&\frac{dx^3}{dy^2}\\\frac{dx^0}{dy^3}&\frac{dx^1}{dy^3}&\frac{dx^2}{dy^3}&\frac{dx^3}{dy^3}\end{pmatrix}[/math] Now for Minkowskii metric the above will correspond to the following [math]ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/math] [math]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/math] Now when you have say spherical coordinates the metric changes. [math](x^0,x^1,x^2,x^3)=(\tau,r,\theta,\phi)[/math] [math]G_{a,b} =\begin{pmatrix}-1+\frac{2M}{r}& 0 & 0& 0 \\ 0 &1+\frac{2M}{r}^{-1}& 0 & 0 \\0 & 0& r^2 & 0 \\0 & 0 &0& r^2sin^2\theta\end{pmatrix}[/math] Now all the above simply described the metric changes. That is the primary purpose of the metric tensor.

Hello. I've read through this interesting thread and have some follow up questions. First; alternative approaches and analogies for explaining relativity (or science in general) are good*. The concepts of no universal "now", time dilation and length contraction are AFAIK central parts of understanding SR. Why are students asking about them to understand more a problem? Why does it help to remove those concepts? If I try to put my self into the role of a beginner, studying relativity: length contraction / time dilation is not a point of view, it is what actually happens according to the theory and its supporting experimental results. *) As long as such approaches and analogies are used within their respective area of applicability and not as replacement for models and math or contradict mainstream observations.

Has anyone ever claimed that? If anyone said that everyone were lying, I would consider them just as ridiculous as someone who claims that aliens walk among us and run the government. Volume of data is not the same thing as quality of evidence. A single data point could be compelling. But a gazillion bits of low quality data are no more useful than 10. You really think those are the only two possible explanations? Sorry, but no. Mundane explanations are based on known, existing phenomena (despite your attempts at ridicule and dismissing them out of hand [see what I did there?]). Any explanation based on aliens is inherently less plausible than any mundane explanation because it is not based on things that are known to exist. Your are being blinded by your faith, here. So, you are saying that either aliens only ever visit the USA, or the US Air Force has a lot more control than seems reasonable.

Go Andrew Yang!!!!! I mean. He get's a passionate voting response from me at least. I feel that he'd fair extremely well against Trump. He has very little baggage, he's straight forward, he's not boring to listen to speak, he's not an absolute a-hole, he has a very good grasp of economics, and even though a lot of what he mentions is a rather extreme idea to conservatives, his arguments are really well laid out. They're not mind boggling complex. Simple, and to the point. I'm not entirely optimistic of Universal Basic Income and how it'll work, but if he were president I wouldn't mind us trying and seeing how it went because it doesn't seem like we're throwing ourselves off a cliff without a plan other then "it sounds good and people applaud."

You have to apply some kind of simple logic to these UFO claims. I love a mystery, but I'm also well aware how people can hallucinate, at odd times, without any input from illicit drugs. Which is more likely, a hallucination, that is very real to the victim, or a visit from aliens ? Obviously, the answer is hallucination, so without any harder evidence, that should always come before the alien explanation. But personally, I think the very first go-to explanation for any UFO claim should be that the witnesses are lying, and/or that the person reporting second-hand what alleged witnesses said is lying. There's a huge amount of lying happening every day. Some people just can't help themselves, and those of us who are unused to their ways are often easily taken in. You often hear people discussing these claims asking " why would anyone make that up? " and that's the biggest weapon of the liar. They often throw in details that actually go against their claims, to make people think, "a liar wouldn't have said that " . They are devious buggers. The biggest logical argument against UFO claims though, is common sense. If we humans eventually got the technology to visit another world, that was inhabited by a more primitive civilisation, what would we do ? Creep around in secret, just appearing as a Will-O'-The-Wisp to one or two individuals? I don't think so. And of course, there is the glaring fact that as smart phones get better and better, and billions of people are carrying high quality video cameras with them, the UFO sightings seem to be getting fewer and fewer. When they should be all over the media, in HD video. So as I said, I love a good mystery, but not the obvious hoax kind. Rule out lying and hallucination, and produce some proper evidence, and I'm interested.

This is a blogging tactic. You opened a discussion here, not a blog, and now you're saying you aren't ready to talk?! People are showing up to your party and you haven't made the dip yet.

What is frition? Fiction? Don't worry about which section you are in, just hurry up and reveal how to time travel. I want to go back in time to see if a hadrosaur taste like chicken. Thanks!

As long as the externalised costs of fossil fuels are omitted from calculations of relative costs the alternatives will look more expensive than they actually are - or rather, not using alternatives appears cheaper than it actually is. A lot cheaper if credible estimates of Social Cost of Carbon around US$40 per ton of CO2 are anything near correct - doubling or tripling the cost of coal. I do see great potential in solar and wind with storage to take us a lot further than we are now without expecting it to reach a 100% threshold easily, especially were existing patterns of energy supply and use to remain unchanged. But I also see the way we use and distribute energy changing in ways that do moderate the impacts of variability of supply. Some regions would find it harder, but a large portion of the world's population do live in places that get lots of sunshine all year round. I see gas plant being relegated to backup to solar as a step forward - because that reduces overall emissions, a circumstance where it does not compete with solar but competes with batteries and hydro or demand response (reducing load by agreement). Relatively small amount of storage (compared to the amount needed to do it all) can change the mix from gas or other fossil fuel plant running every night to switching off for days at a time during sunny periods: I think batteries appear to be capable of doing a lot of that. Dedicated pumped hydro is only just getting started - like other elements, they tend not to happen until the need is there. ie wind and solar penetration grows and other options for moderating the variability and demand are not available. Once through hydo can also be adapted to more responsive variability. I am increasingly of the view that renewable Hydrogen, using excess solar and wind, is going play a big role; for one, it offers the best non-fossil fuel option for iron and steel smelting. But with respect to an RE heavy energy system, having gas plant that can transition to H2 offers another kind of storage and backup. I think that gas plant ought to be built to be H2 capable (a lot of it should be already) and thus able to utilise Solar and Wind during it's periods of abundance to make fuel for when it is not. On-site production and storage bypasses the need for economy wide H2 infrastructure and would not require the very high pressure storage (and related costs) that transporting - and transport fuel use - requires. Demand response - curtailing loads by agreement when demand is more than supply should not be underestimate either. As should opportunistic industrial batch processing, that can be flexibly scheduled; periods of overabundance of electricity, ie very cheap, is a huge opportunity. I would be very surprised if ways to exploit it aren't developed. Presuming industry cannot adapt seems shortsighted. They won't if the don't have to - which is why seeing governments and leaders accommodating that desire to not have to is so dismaying. If this all seems complicated compared to "just build lots of nuclear" - I think that underestimates how difficult "just build nuclear" actually is and overestimates our ability to manage complicated systems. Solar and wind and storage and efficiency and demand management and etc are forging ahead now because they are easier and cheaper. I see a lot of this happening despite a continuing absence of comprehensive, overarching planning, let alone appropriate pricing of emissions. I can't see nuclear happening at the scales needed without carbon pricing as well as high level of government planning and intervention. Whereas RE proceeds with projects with short build times, with changing course always an option; even legislated 100% RE commitments are never going to be truly binding and can be changed relatively quickly in response to emerging problems and constraints. I think a big nuclear approach requires a level of planning and commitment that cannot yet be achieved - and must wait on the Wall of Denial to come down and let the largest bloc of support for it come out from behind it.

“If the solar industry had to supply all of it” implies your analysis is based on 100% solar. Which is a ludicrous position. And? Is anyone suggesting otherwise? You don’t need 1000 coal or gas plants if 500 will cover the load. So you don’t have the same capital costs. No, it’s not like that. You said yourself that the plants are being used, so it’s a pretty bad analogy. Renewable energy is cheaper in many, many cases. That’s not politics. Overall cost of electricity in the US doesn’t seem to have been negatively impacted. 2013-2018 it went up ~5% https://www.statista.com/statistics/183700/us-average-retail-electricity-price-since-1990/ 5% is lower than inflation, so in terms of buying power, the cost went down http://www.in2013dollars.com/2013-dollars-in-2018?amount=100

FORCE ON A CURRENT CARRYING WIRE. ITS CALLED THE LORENZ FORCE. I honestly need to put it down? Can you not read or reference it yourself? I don't need to back up a WELL KNOWN CALCULATION STRANGE. grow up.

in the attached picture i attempt to show the force I'm working with. The idea is to exploit the force on AB. although the currents in the example DO NOT CREATE A CIRCUIT, they show the force im working with. IF, the circuit were to be closed with a wire from D to C, the total force on DC would cancel out the total force on AB. also, We find the magnetic field vector direction by using the right hand rule. Because the current vector is inline with the writing surface, the magnetic field vector is represented as an X for into the surface and O for the vectors outward direction. Magnetic fields at 90 angles from an ions velocity vector do something curly to its path, but still follow electric field lines. not talking about radiation. im talking about magnetic fields acting on currents in wires and free ions. change your drugs bro.