Also light has energy which is mass in Relativistic thinking, and is moved by (and moves other things by) gravity which is due to it's energy (same as mass).

This is confusing because people think of "mass" as the things photons don't have and matter does (which is true if we mean intrinsic mass), but also think of "mass" as the thing which effects/is affected by gravity and makes objects resist acceleration, when that's actually the relativistic mass (= energy).

A photon is a quantum mechanical particle, which is a thingie which behaves kinda like a classical particle and kinda like a classical wave but not exactly like either.

However the key thing about quantum mechanics is that stuff is quantized... like particles are. So we call them particles. There is no misconception in doing so.

What you said was quite correct.

I'm not sure what they were saying. I think maybe they meant to reply to justthinkit who was actually proposing an alternative?

No. Gravity is determined by the stress-energy tensor, and the energy component is total energy, aka relativistic mass (literally, they're the same thing). Relativistic mass is the gravitational mass is also the inertial mass.

A proton's mass -- the ratio between its acceleration and the force exerted by an electric field -- is much higher than the intrinsic mass of the quarks that make it up. It's the kinetic energy of those quarks held together by the Strong Nuclear Force that gives a proton 90% of its mass. The Higgs Field only explains that last 10%.

Similarly the gravity of the sun is far greater than just the intrinsic mass of the quarks and electrons inside it. It's the sum of all energy in the sun.

If you an accelerate an object it gains energy, and therefore (E=mc^2) relativistic mass, and also therefore increased gravity.

Oh, and yes, this means photons have gravity. Not are affected by gravity (though of course they are) but exert it.

A black hole of one solar mass will take 10^67 years to evaporate from Hawking Radiation -- and this time is proportional to the cube of the mass, so think about those SMBHs out there with billions of solar masses. That's a mind-bogglingly long time. You might think it's a long time waiting in line at the Department of Transportation, but that's peanuts compared to black hole evaporation...

And that's only after the CMBR has been red-shifted into near non-existence since until then the black hole is absorbing more energy than it is losing.

Though there are in theory primordial black holes (ones created in the moments after the Big Bang) that would have a lifespan measured merely in billions of years.

"Beware of he who would deny you access to information, for in his heart he dreams himself your master".

                Commissioner Pravin Lal, "U.N. Declaration of Rights"

What I really love about this quote, aside from it being amazingly insightful, is that it always seemed to turn up just after I'd gotten done refusing to share some piece of tech I'd developed with one of my "allies" because I wanted to have every advantage when I inevitably steamrolled them. It's like Commisioner Lal knew me, man.

Spoken like someone who doesn't understand and hasn't even really thought about mental illness.

Hint: The thing you think gives you "complete control" is the thing affected by the disease.

If a tree falls in the woods and no-one is there to hear it, is the next tree to fall guilty of plagiarism?

A household barely on the poverty line in USA is richer than 80% of the world! About 10% of the world, [globalissues.org] or 700 million people or twice the population of USA, lives in less than $365 a year! Again these dollar figures are not the foreign exchange rate based dollars. These are "purchase power parity" dollars. Which means the $365 buys in the poor country, what $365 would buy in the USA.

The poverty line in the USA is (intended to be) defined such that the household barely on it is barely able to supply basic needs - food, clothing, shelter, medical attention, education, sanitation - with the products available for sale in the USA. I think that's a more meaningful statement than comparing "purchase power parity" for hypothetical identical products available for sale in the other countries. I say that for a couple reasons:

First, as others have pointed out, the products available for sale in other countries tend to fulfill the same basic needs with inferior, cheaper products (even in purchase power parity-adjusted dollars). This means there are people with lower "purchasing power" who are better able to fulfill their basic needs. For the purchasing power parity to be truly meaningful, the most appropriate products have to be available in both marketplaces.

Second, I suspect these dollar figures are skewed by people who get their basic needs fulfilled outside of the marketplace. There are communities of subsistence farmers who make little to no money but are able to feed themselves, create their own clothes, and/or construct their own shelter without money. I wouldn't recommend this exactly - they're incredibly vulnerable to droughts and other disasters - but you'd be overstating it if you claimed one cannot survive in this way or that these things have no value, as I suspect those World Bank figures are implicitly doing.

Okay, but don't complain about a fact that even in a world where the military was managed and utilized ideally would still be true.

Thanks. Last time I related that story, someone just couldn't believe that a class was harder with Maple doing the grunt work. They assumed I just hadn't taken much math so it was the hardest by default. Then tried to impress me with their standard engineering math curriculum.

Well then you have a problem because while it may be argued that the ends justify the means, that argument falls apart when the means contradict and thus prevent the ends.

All-out-war is over because the political goals of war have changed. You simply cannot fight a war of "liberation" without respecting the civilians. And this was self-evident in the years of complete and utter failure in Iraq. Sure, we didn't engage in "all out war" against a poorly understood collage of insurgent forces because that's a completely ineffective way to fight an insurgency unless you're willing to go the Roman or Mao Tse Tung route and use genocide. Which would have resulted in us "winning" for a definition of "winning" completely different than what we started with. The warfare equivalent of flipping the chessboard. Good job. You "won". Slow clap.

So instead we tied our soldiers' hands with rules of engagement while simultaneously maintaining a flippant attitude toward colateral damage -- enough to "look nice in the papers" back home, but definitely not the ones in Iraq. This was because the people in charge, like you, really would have rather engaged in all-out war but knew they couldn't because of politics at home.

The result was unsurprisingly ineffective as the ranks of insurgents swelled with angry former-civilians (many of whom were former-army, but don't get me started on that).

A lot of people credit The Surge with turning Iraq around, but while a component it was actually the least important part of what changed. Petraeus' real genius was in not only using force even more judiciously than before -- the opposite of what you would do -- but also in fully engaging the civilian population. He didn't treat them as though they were basically the enemy that he couldn't shoot because it looked bad on CNN. He treated them as if they were already allies that required help. He took "winning hearts and minds" seriously, and it worked. When the area of Iraq Petraeus was in charge of stabilized like none of the rest of Iraq had, they put him in charge of the lot so his demonstrably effective (and not coincidently completely unlike your) strategy could benefit everywhere. And it did. Only in the environment created by this new strategy could the additional troops put in have been effective.

You know what the REALLY sad part is? The part that really causes comments like yours make the bile swell up in my throat?

It's that when we began in Afghanistan, the people did support us. Unlike the Iraqi people who felt betrayed by us after Desert Storm, the Afghan people still thought of us as the folks who helped them kick out the Russians. With no love lost for the Taliban, they were actually on our side. At first.

Thanks to years of idiotic management, that flippant attitude towards collateral damage you embody, and years of neglect due to being focused on Iraq, we lost both literal and figurative ground in Afghanistan. We squandered our advantage. Pissed it away. Turned the people against us.

And then some dweeb comes along and says the people "will never support us". As if it was always this way. As if it's their fault, instead of ours. Gee, maybe we should just stop worrying about killing them. That would probably fix it.

So fucking sad.

To make it clear how big a difference it is, let's look at the ratio of the mass of the body in question to the mass of the rest of the objects in its orbit (discounting direct satellites).

Of the planets Neptune happens to have the lowest such ratio. It outmasses everything else in its orbit by a factor of over 10,000.

Meanwhile Pluto is outmassed by the other objects in its orbit by more than a factor of ten. It is less than 10% of the mass in its orbit.

That's a five order of magnitude difference. "Clearing the orbit" isn't precisely defined... and it doesn't need to be. You don't need a precise definition of where exactly on the beach the ocean begins to know that Asia and North America are separated by the Pacific Ocean.

And I suspect that such a large distinction isn't a cosmic accident, and that other star systems of sufficient age will show a similar trend. Unfortunately it's going to be a long time before we can test this hypothesis.

The sun will become a white dwarf, which is a post-stellar remnant made of electron-degenerate matter (where the electromagnetic repulsion is not sufficient to hold electrons apart against gravity, and instead they're held apart by the Pauli Exclusion Principle) about the size of the earth. Before that, when it ends its Red Giant phase, it will shed much of its mass in novas. Which are gentle events only in comparison to a supernova. "Explosion" is quite fair. Certainly nobody in the solar system watching would say, Crocodile Dundee style, "That's not an explosion..."

The most difficult math course I ever took was my first college math course, Calc II with Maple. Why yes, use of the symbolic calculus program Maple was so important to the class it was in the name. We took our tests at a workstation with Maple on it.

When my adviser suggested I take this version instead of normal Calc II, I didn't hesitate because I naively assumed this would make the class easier.

Turns out that when you remove the time it takes to do the actual mechanics of taking integrals and derivatives, you can instead focus on problems where the difficulty is figuring out how to set up that integral and derivative. Which is much harder than following some rules by rote.

That's why Feynman Diagrams were such a big deal -- they actually allowed physicists to figure out how they should be applying the equations of quantum mechanics to a specific problem. It let them figure out what to calculate. How wasn't the challenge.

I don't know, exactly. I'm assuming it's the same Aristotlean Physics Kook from quite some time ago with a new nick. They had a pretty extensive blog about how Newtonian mechanics was wrong and Aristotlean motion was obviously correct. Seemed like a bit much for just a troll. So, instead, I think it's your run of the mill Internet Crackpot who never studied any physics, came across one puzzling question, decided ignorance + a question + their genius = proving everyone else wrong. The rest is history and irrational slashdot posts.