Compact Precision Scale: Fill & Download for Free

There are many, many pieces of evidence—GPB was definitely not the first! (And by the way, we never "prove" things in science; we can show that theories are (in)compatible with data). There is already an excellent Wikipedia article on Tests of General Relativity (http://en.wikipedia.org/wiki/Tests_of_general_relativity), some of which I repeat below:The perihelion precession of Mercury, which was one of Einstein's litmus test for the theory (measured earlier, calculated by Einstein in 1915 and found in agreement with measurement—a postdiction)Deflection of light by the Sun (measured in 1919 by Eddington's expedition, argued as to the precision of his claims, but measured with much greater precision in the era of satellites and radar)Gravitational redshift of light (measured by Pound and Rebka in 1959)Other so-called "post-Newtonian parameters" measured in the solar system by various satellites (not their primary missions, e.g. the Cassini mission's measurement of the Shapiro delay)Global Positioning System, as mentioned in another answer, requires GR correctionsGeodetic precession as measured by many satellites, perhaps most famously by GPB (and Lense-Thirring precession, but only a 10-20% measurement)Tests of the equivalence principle(s) by various lunar Laser ranging experiments, most precisely by the Apache Point Observatory LL Operation (APOLLO).Several compact binary systems testing the so-called "post-Keplerian parameters", most famously the Hulse-Taylor pulsar binary which led to the 1993 Nobel prize. This system (and others) exhibits an inspiral rate which is predicted by GR due to energy loss due to emission of gravitational radiation.[1]Many cosmological tests—most if not all results in cosmology require GR (or some theory that looks like GR in some region of parameter space). This includes, most famously, the Cosmic Microwave Background power spectrum, but also things like the galaxy power spectrum.To be fair, most of these tests are in the weak-field regime. This means that we know (to very good precision) that GR works excellently for cosmological scales, solar system scales, even all the way down to compact binary system scales (though still with [math]v/c \ll 1[/math]). One reason may be that most (reasonable) theories of gravity look like GR (quantitatively) in these regimes, and we simply haven't probed scales outside of the regime of validity of GR. This reasoning is behind ongoing investigations into possible corrections to general relativity.[1] In my book, this is the only "dynamical" test on the list because radiative degrees of freedom are important.

No, it will not.Even galaxies with much larger supermassive black holes are stable over cosmological time scales. The supermassive black hole in our own Milky Way is relatively small, only about 4 million suns in mass, as opposed to the very large supermassive black holes that weigh as much as several billion suns.The gravity of a black hole is no different from the gravity of any other object of the same mass; our own Milky Way’s supermassive black hole has the same gravity, say, 100 light years from it as a compact globular cluster of 4 million stars. You wouldn’t expect the Milky Way to “collapse” into one its own globular clusters that weighs less than one one hundred thousandths the Milky Way itself, would you? So why would it collapse into a black hole of the same mass and same gravity?The only thing that makes black holes in this regard is that because they are very compact, you can get very close to them, and when you are very close to them, gravity is very strong. But black holes are very inefficient eaters. To get very close to them, you have to aim very precisely. And even then, as a result of “falling” in the black hole’s gravitational field, you attain a huge velocity. So unless you happen to “hit” the event horizon precisely, you’ll just fly by the black hole in a rapid hyperbolic trajectory and emerge on the other side.No, the future of the Milky Way is very different. A few billion years from now, it will merge with the similar-sized (maybe a little larger) Andromeda galaxy. Over the course of many billions of years to come, this merged galaxy will merge with other members of the Local Group. Eventually, there will be one gigantic, but dying elliptical galaxy with a diminishing number of still active stars, in a rapidly expanding cosmos in which other galaxies, not gravitationally bound to this one, will recede away at an ever higher speed.Ultimately, in the very distant future, there will be this remaining elliptical galaxy, a few freshly escape stray stars or clusters nearby, and otherwise emptiness. But no collapse.I thank my generous supporters on Patreon. If you like my answers, please consider joining them.

Just to add some color commentary, yeah, there are systems of units that seem funny from an everyday perspective. Making speed dimensionless seems funny. After all, speed is measured in units of distance per time, right?Right. Making speed dimensionless simply provides a conversion factor between units of distance and units of time.If that sounds terribly strange, it shouldn’t. You probably have some experience with the concept. Suppose you’re walking around a city that’s new to you. You stop a stranger and ask how far to the nearest train station. The stranger responds: “It’s about 5 minutes that way.”That’s not an incomprehensible answer to you. You probably understand that to mean that if you walk for five minutes that way, you’ll get to the nearest train station.Granted, this isn’t a perfectly precise answer. The person who gave the directions probably assumed that you walk at a certain speed. You have a separate understanding of your own walking speed. Hopefully those two speeds are close. To the extent they’re not, maybe the whole thing can be glossed over by the hedge “approximately five minutes.”But the speed of light is known to everyone, and in fact it’s measured the same by any observer, regardless of their relative motion. So setting the speed of light equal to 1 just means that you can say “walk about 1 second that way” instead of saying “walk about 300,000 kilometers that way.”There’s a more practical reason for setting [math]c=1[/math]. It’s probably less interesting.If you’re a theoretical physicist going around doing theoretical physics things, your formulas are probably going to have a lot of [math]c[/math]'s piling up. If you keep turning your formula crank, the [math]c[/math]'s are going to get annoying. And in fact, they add nothing fundamental to the equation. After all, it’s just a choice of unit.So setting [math]c=1[/math] just lets you clean your formulas up a little.BTW, same deal with other constants. The universal gravitational constant, [math]G[/math] has units of (distance)^3 / (mass)(time)^2. If you already set [math]c=1[/math], then units of distance are units of time, so [math]G[/math] takes the units distance/mass. Setting [math]G=1[/math] just means you can measure distance in units of mass. I.e., you can say “drive 1 gram that way.”In case that seems strange, the physical interpretation of setting [math]G=1[/math] is that you associate a mass with the radius of a black hole having the same mass. So even if you didn’t know the numerical order of magnitude of [math]G[/math], you could intuit that a normal, human-scale distance like a kilometer is going to translate to a pretty huge mass by human scales. Or that human-scale masses like a kilogram are going to translate to pretty small distances.Final observation: why are these called natural units? I’m not sure if this is historically the correct answer, but I’ve always interpreted it to be because we’re setting units based on unambiguous natural phenomena.Contrast that with more common units, like meters, seconds, and grams. Why is 1 meter “the” special distance? There are historical reasons, but there’s nothing special that happens in terms of physics. One meter isn’t some magical scale at which interesting things start to happen.On the other hand, the speed of light is a naturally distinguished speed. It’s the top speed. A black hole is a naturally distinguished structure. It’s the most compact structure of a given mass.Thus, natural units.