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  1. #1951
    But is the big bang the reason that space expands? As I understand it, space expands uniformly and constantly throughout the universe. EM and gravity serve to hold things together (atoms, molecules, galaxies etc), but what is it that drives the expansion of space? Is it momentum originating from the big bang?
    Quote Originally Posted by wufwugy View Post
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  2. #1952
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    Dunno. The Big Bang is the reason stuff is moving apart. It's not explaining why the space between the stuff is expanding.
    As of yet, I don't know of any accepted model for why space is expanding.
    We're still just calling it dark energy so we can sound smart and a little bit mysterious.
  3. #1953
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    Universe is expanding cause of dark energy, aka we have no clue. Btw Fred Hoyle came up with the term Big Bang, since he thought the idea of an exploding universe was silly.
    Our brains have just one scale, and we resize our experiences to fit.

  4. #1954
  5. #1955
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    Quote Originally Posted by CoccoBill View Post
    Universe is expanding cause of dark energy, aka we have no clue. Btw Fred Hoyle came up with the term Big Bang, since he thought the idea of an exploding universe was silly.
    Huh? I thought it was Geoge Lemaitre.

    ***
    Got it

    On George Lemaitre's contribution:
    Lemaître was then invited to London to participate in a meeting of the British Association on the relation between the physical universe and spirituality. There he proposed that the universe expanded from an initial point, which he called the "Primeval Atom".

    On Fred Hoyle's contribution:
    In 1949, Hoyle began a popular and often repeated series of BBC radio broadcasts on astronomy, with versions being broadcast in the United States as well as in a book “The Nature of the Universe”. It was in the last of these radio lectures that Hoyle coined the phrase "Big Bang" for the creation of the universe, although many people believe he actually intended it as a scornful description of a theory which he did not himself accept.
  6. #1956
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    Quote Originally Posted by OngBonga View Post
    Pretty good explanation for why the "many interpretations" theory is (very very probably) a load of bollocks.

    Also, who's to say if that theory is viable that there are an infinite number of alternative universes? Why not simply approaching infinity (but finite at any given point in time)?

    On an unrelated sbuject, here's something that blows my mind...

    Imagine first a "table" with edges that bounce balls perfectly elastically, ie no energy is lost... all energy and momentum is conserved.
    Take two balls, ball A, which has a mass of x, and ball B, which has a mass of 16x. Now roll them towards each other at the same velocity. When they hit each other, ball A will bounce off ball B, because B is much larger. Ball A will then hit the edge of the "table" (losing no momentum), and then bounce right back at ball B and hit it again.
    The question is, how many times does ball A bounce off ball B before ball B loses its energy and starts to move backwards?
    The answer is 3.
    Now scale the big ball up x100.
    Now the answer is 31.
    Scale up x100 again
    314
    and again
    3141
    next
    31415
    then
    314159
    and then
    3141592

    And on and on... so long as we're scaling up x100 from an intial ratio of 16:1 then we get the digits of pi. This works all the way.

    Where the fuck is pi coming from here? This has nothing to do with circles, it would happen with cubes, under the same conditons, ie conservation of energy and momentum, which means no friction.

    THAT shit blows my mind, not thought experiments about the improbability of many worlds.


    Satisfying.
  7. #1957
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    How many years, do you reckon, till we figure out the source code for our simulation?
    Our brains have just one scale, and we resize our experiences to fit.

  8. #1958
    Quote Originally Posted by MadMojoMonkey View Post


    Satisfying.
    Yep I saw that too. Bastard made me wait for the explanation. It was nice to see where the circles came from.

    Now where the fuck does pi come from in the "inverse square" infinite sum?
    If you're not sure what I'm getting at...
    1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36... the solution to this infinite sum is pi^2/6

    Oh, and if ever you want to really troll the shit out of stupid people on youtube...
    ​Read more
    Quote Originally Posted by wufwugy View Post
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  9. #1959
    Quote Originally Posted by CoccoBill View Post
    How many years, do you reckon, till we figure out the source code for our simulation?
    We already figured it out. It's pi. Clever bastards made sure we could never hack it because we can only ever approximate it in "reality".

    Fucking genius.
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  10. #1960
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    Quote Originally Posted by OngBonga View Post
    Yep I saw that too. Bastard made me wait for the explanation. It was nice to see where the circles came from.
    I already told you the explanation.
    https://www.flopturnriver.com/pokerf...60#post2289460

    He just provided epic animations to go along with it. Also, uses the words phase space, which I didn't, but that's what I was using.
    You see the sqrt(mass)*velocity terms in my answer, there... the same as he uses for his axes labels' in the phase space.
  11. #1961
    Your post does seem to make a little more sense to me now with the benefit of his animation. Well done for being correct!
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  12. #1962
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    Not a question, just awesome.
    Our brains have just one scale, and we resize our experiences to fit.

  13. #1963
    Planets have to be much smaller if drawn to scale, or not?
  14. #1964
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    "bodies x20 larger" so yeah, way smaller.

    That should give some perspective about distances and how unlikely it is that we'll ever travel anywhere outside the solar system.
    Our brains have just one scale, and we resize our experiences to fit.

  15. #1965
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    Quote Originally Posted by CoccoBill View Post
    "bodies x20 larger" so yeah, way smaller.

    That should give some perspective about distances and how unlikely it is that we'll ever travel anywhere outside the solar system.
    The Voyager Probe has already left the solar system.
    If we can have a sustained human biosystem in a spacecraft, then traveling between stars is viable. Time scales are long, but relativity helps if you can get a spacecraft up to a decent fraction of the speed of light. Even small accelerations acting over long time scales can do this. It would still be a years-long journey to the closest star.

    There's a practical design for a spacecraft that accelerates off the shock waves of nuclear bombs dropped out it's back side. It could probably launch a small town into orbit.

    The designs for that craft are decades old, and it was intended to be made with materials available at the time.
    https://en.wikipedia.org/wiki/Projec...ar_propulsion)
  16. #1966
    Why can't they use magnets as a method of propulsion?

    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  17. #1967
    How much would you need to scale that up to get nuclear comparable energies?
    Quote Originally Posted by wufwugy View Post
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  18. #1968
    I already know what's wrong with this idea. The magnet will be destroyed.
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  19. #1969
    Quote Originally Posted by MadMojoMonkey View Post
    There's a practical design for a spacecraft that accelerates off the shock waves of nuclear bombs dropped out it's back side. It could probably launch a small town into orbit.
    I believe that's referred to as the 'fart propulsion' method.
  20. #1970
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    Quote Originally Posted by OngBonga View Post
    Why can't they use magnets as a method of propulsion?
    how many balls would you need?
    The strengh of a hero is defined by the weakness of his villains.
  21. #1971
    Quote Originally Posted by oskar View Post
    how many balls would you need?
    Well, eight small balls and a two poxy neodymium magnets and we can probably take someone's eye out. Scale that up so the balls and magnet are much bigger, and there's 20 magnets instead of 2, and I think we'll probably vapourise some metal.
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  22. #1972
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    The problem with a Gauss Gun is that the stored energy of the system is in the geometry of the setup and that geometry changes to give thrust, but then you have to put in an equal amount of energy to reload the thing.
    It's not the same as a bullet with a lot of stored chemical energy in the gunpowder in its casing.
    It's not the same as carrying fuel that releases energy.
  23. #1973
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    Quote Originally Posted by OngBonga View Post
    I already know what's wrong with this idea. The magnet will be destroyed.
    Pretty much. Strong rare Earth magnets are brittle.
    I don't see why you couldn't use a toroidal magnet and put a steel rod down the center to transmit the force, though.
    A cylinder with a hole through it from N to S, and a rod stuck through that hole so it's not too snug a fit.
    The magnetic field is slightly less, but the magnet is removed from the shock path.
  24. #1974
    ...then you have to put in an equal amount of energy to reload the thing.
    Forgetting the flaw of how brittle the set up is, can chemical energy not be used to reload? For example, a tool could be made that is designed to remove the trigger ball, and this tool can run on electricity, which ultimately comes from chemical energy.
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  25. #1975
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    Quote Originally Posted by OngBonga View Post
    Forgetting the flaw of how brittle the set up is, can chemical energy not be used to reload? For example, a tool could be made that is designed to remove the trigger ball, and this tool can run on electricity, which ultimately comes from chemical energy.
    Maybe. The question would be, "Do we 'waste' less energy using this chemical process to reload the Gauss Gun than we would to use this chemical process to fire a bullet?"

    The 2nd Law of Thermo makes this difficult. Every time we try to change energy from being stored in 1 way to being stored in another way, we tend to lose some of it in the form of entropy. Heat, light, sound, plastic deformations, etc. all tend to be energy sinks from which it is difficult to recover that energy.

    It's theoretically possible to make something that uses chemical reactions to reload the firing ball to its original position and add a new bullet ball. It's even possible this would be more efficient than firing bullets using gunpowder. It's not too likely it would be more portable, though.
    Also worth noting that the faster a reaction tries to move energy from 1 form to another, the more lossy it is.
    Maybe if we only try to reload it really slowly, we can remove enough losses to make it efficient.

    IDK, though... seems like if you're carrying around the chemical energy to reload, then why not just use that chemical energy to fire in the first place?
  26. #1976
    Are there any easy tests you know of to differentiate between borosilicate and soda lime glass? Preferably non-destructive. Density and refraction are two methods to consider, but I'm not sure where to start. Density is easy in theory, but I don't have accurate enough scales, nor accurate enough means of measuring water displacement, to give a reliable measurement.

    I ask because some guy bought ten watch glasses, then returned them, claiming they are soda lime, not borosilicate. He only returned nine, so I suspect he only wanted one and is on the blag. No one else is selling them on ebay in the UK, while buying overseas incurs a hefty shipping fee. I only sell them in packs of ten.

    I'm currently baking one at 150 degrees C, and will be submerging the hot glass in cold water. Soda lime will certainly break,while borosilicate shouldn't. However, these watch glasses are not the only thing I want to test, and I don't want too much breakage.
    Quote Originally Posted by wufwugy View Post
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  27. #1977
    It didn't shatter.
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  28. #1978
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    I realize that gravity doesn't just suddenly stop when you leave Earth's athmosphere, and you'll actually fall back down, so how far would you have to go to not fall back down? And when you're there, where would you fall? Saturn? Sun? Or just float there for an eternity.
    Our brains have just one scale, and we resize our experiences to fit.

  29. #1979
    It depends on your orientation to the Earth, and your velocity. The Moon doesn't fall because its tangential velocity is equal to the rate at which it falls towards Earth. If it slowed down, it would fall towards Earth, rather than around it.

    If you have zero velocity relative to Earth, then I would guess that it depends how close you are to another gravity source. In a hypothetical universe containing just the Earth, there is no distance you can go to escape the Earth's gravity, so you will fall from light years away, assuming zero relative velocity. In the real universe, it depends on what the locally dominant gravity source is.
    Last edited by OngBonga; 02-14-2019 at 11:31 AM.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  30. #1980
    This thread should be renamed to "Ask a monkey a physics question and ong will guess the answer before monkey posts".

    I suppose it's a bit of a mouthful.
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  31. #1981
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    https://www.physicsclassroom.com/cla...al-Gravitation

    I believe this is what you're looking for. You just need to plug in the numbers... in a theoretical scenario where both you, the earth and the sun are on a plain and not moving you'd just have to figure out at what point the sun's gravitational force > earths gravitational force.
    The strengh of a hero is defined by the weakness of his villains.
  32. #1982
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    Quote Originally Posted by OngBonga View Post
    Are there any easy tests you know of to differentiate between borosilicate and soda lime glass? Preferably non-destructive.
    For the refraction, go to a hardware store and buy some Mineral Oil. It should have about the same index of refraction as the borosilicate glass, and if you submerge the glass in it, it will disappear.
    I do this in my office using Glycerol (or Glycerine - same chemical), but I'm not sure if it's better or worse than mineral oil, and I've never compared different kinds of glass to see if one disappears more convincingly than the other.
    It's worth a shot, though, as mineral oil is cheap and has other uses (treating wood cutting boards, for example).

    I've found some google hits that suggest doing a flame test, but that would require chipping off pieces of the glass to burn them, and I know you don't want to do that.

    I've sent an email to the chemistry dept. glass blower to ask if he has any suggestions. Hopefully he'll get back to me by early next week. His position is not full time, so he's not in every day.
  33. #1983
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    Quote Originally Posted by CoccoBill View Post
    I realize that gravity doesn't just suddenly stop when you leave Earth's athmosphere, and you'll actually fall back down, so how far would you have to go to not fall back down? And when you're there, where would you fall? Saturn? Sun? Or just float there for an eternity.
    It's really complicated.
    If you're anywhere in the universe and your relative speed to Earth is above the escape vleocity (really a speed), then it doesn't matter what direction you're going, you'll never be trapped in Earth's gravity. This assumes you can move through the Earth with no friction. Also assumes you and the Earth are the only things in the universe, but what's a little simplifying model among friends?

    Sphere of Influence is more along the lines of what you're asking, but it's, again, more complicated than a single number I can throw at you to answer the question.
    Roughly speaking, with a lot of hand-waving and assumptions made, the SOI of the Earth is about 575,000 miles. If you're outside of that, you're in orbit around the sun, unless you happen to be close enough to another planet as it swings past you in its own orbit.

    If you move beyond the sun's SOI, then you're in orbit around Sagitarius A*, the Black Hole at the center of the Milky Way.

    If you move beyond that, you're in orbit around the gravitational center of the Local Group. The Local Group is the Milky Way, Andromeda and about 50 other, smaller galaxies "nearby."

    If you move beyond that, you're in orbit around The grav. center of the Virgo Supercluster (of galaxies).

    Keep going and it's the Pisces-Cetus Supercluster Complex.

    Further still and it's the Laniakea supercluster (I know... we kinda ran out of names for obscenely big objects in the universe after galactic supercluster, but we keep finding bigger structures anyway). The Laniakea supercluster is in orbit about what's called "The Great Attractor" because we have no idea what it is, but we're in orbit around it so it must be pretty great and also attractive.



    ...and now you know all the different names for a duck, but you still know nothing about ducks.
  34. #1984
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    Quote Originally Posted by OngBonga View Post
    The Moon doesn't fall because its tangential velocity is equal to the rate at which it falls towards Earth. If it slowed down, it would fall towards Earth, rather than around it.
    Not really, no.
    The moon is falling away from the Earth at a rate of a couple-few inches per year.

    Lots of objects have non-circular orbits.
  35. #1985
    Quote Originally Posted by mojo
    I've sent an email to the chemistry dept. glass blower to ask if he has any suggestions. Hopefully he'll get back to me by early next week. His position is not full time, so he's not in every day.
    Thanks.

    As for the Moon's drift, well this demonstrates my point... that it depends on relative velocity. Why is the Moon drifting away? As I understand it, it's because of tidal forces... gravitational drag, caused by the Moon, gradually slows down the rotation of Earth on its axis. This, in turn, causes the Moon's orbital velocity to increase... conservation of angular momentum. So the Moon drifting away demonstrates both that relative velocity is a crucial factor, and that gravity is not something that suddenly loses influence. The Moon is clearly within the Earth's gravitational field, yet it is moving away. In a universe with just Earth, there is no constant velocity that will result in escape. Even light will orbit Earth.

    Lots of objects have non-circular orbits.
    If by "lots of", you mean "everything", then yeah. The Moon is still "falling around" Earth, in a simplified sense. It's just it's falling faster (and closer) sometimes than it is at others.
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  36. #1986
    Orbits aren't circular or elliptical, anyway.

    *invokes GR*

    Orbits are straight lines through time that appear elliptical in space from our frame our reference.
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  37. #1987
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    If the moon slowed down, it would fall slightly more toward the Earth (for a bit), and so long as it didn't slow enough to hit the Earth, it would fall to its perigee (closest point in orbit around Earth) and then start moving away from Earth. It would continue to rise until it got to its apogee (furthest point in orbit around Earth), then start falling again.

    This is true for all elliptical orbits, but the words get changed/generalized to periapse and apoapse, which don't roll off the tongue as well, and spell check doesn't even recognize them.
    Those are the general words that always apply, even to objects around the Earth or Sun. For the Sun, the words are perihelion and aphelion, which are recognized by spell check... so that's interesting in a not at all physics kind of way.

    ***
    Sagitarius A* is not a typo or indicative of a missing footnote, it's read, "Sagitarius A-star" with the emphasis on A, so it doesn't sound like, "Sagitarius, a star."

    ***
    The glass blower responded quickly, but unfortunately, he recommends the flame test to be certain. He also said he can often tell by looking at a glass piece, so I asked if it's possible to describe what he's looking for or if it's more of a feel thing. We'll see.
  38. #1988
    The glass blower responded quickly, but unfortunately, he recommends the flame test to be certain.
    Cheers. Perhaps I'll stick with my thermal shock test, since it only destroys it if it's practically worthless.
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  39. #1989
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    Quote Originally Posted by OngBonga View Post
    In a universe with just Earth, there is no constant velocity that will result in escape. Even light will orbit Earth.
    Oooohhhh.... you were doing OK, there for a minute.
    ANY constant velocity results in escape. If I'm going 10^-[big] m/s in any direction without changing speed ever, then I am not in orbit around anything.

    The Earth is a tiny little rock. Nothing to Jupiter, which is nothing to the sun.
    Of course you can escape it. It's not a black hole whose event horizon you're inside. Those are the only things that cannot be escaped, and only from the inside. You can be in orbit outside a black hole. You can have an unbound hyperbolic path that sends you ripping off to infinity, ever slowing, but never enough to stop you.
  40. #1990
    ANY constant velocity results in escape. If I'm going 10^-[big] m/s in any direction without changing speed ever, then I am not in orbit around anything.
    Are you sure about this? An orbit is a straight line through curved space. It is a constant velocity. If you're not orbiting anything, you must be constantly accelerating.
    Quote Originally Posted by wufwugy View Post
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  41. #1991
    The Earth is a tiny little rock. Nothing to Jupiter, which is nothing to the sun.
    Yeah but I was talking about a hypothetical universe with just the Earth. The only reason you can escape the Earth's gravitational influence is because there are bigger things out there.

    And even then, strictly speaking, you never really do escape the Earth's gravity. It just becomes more and more negligible.
    Quote Originally Posted by wufwugy View Post
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  42. #1992
    ANY constant velocity results in escape. If I'm going 10^-[big] m/s in any direction without changing speed ever, then I am not in orbit around anything.
    I note you went from "velocity" to "speed". The problem with saying the Moon is accelerating is that you're observing this acceleration from Earth, not the Moon. Is the Earth accelerating as it moves along its elliptical orbit around the Sun? Well, sure, if we put the Sun in the centre of our model. But if we put the Earth at the centre, it's everything else that accelerates.

    Acceleration due to gravity is not a true acceleration. It's an observed one from another frame of reference. Something that is in freefall (such as a body in orbit) is not accelerating, it is moving at a constant velocity.
    Quote Originally Posted by wufwugy View Post
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  43. #1993
    Here's a thought experiment...
    We're in a huge vacuum chamber. We throw a ball upwards at an angle of 45 degrees. It slows down as it reaches its apex, then begins to speed up as it falls, before hitting the ground.
    Did the ball accelerate after we let it go? No, it moved at a constant velocity until it hit the floor. The path it took was a straight line through curved space. That's how much space is curved at the surface of Earth.
    Quote Originally Posted by wufwugy View Post
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  44. #1994
    One more...

    I've been thinking more about elliptical orbits.

    As the Moon moves around the Earth, it appears to accelerate relative to Earth. What is actually happening is kinetic energy is being transferred to potential energy as it approaches apogee, and then potential energy is in turn transferred to kinetic energy as it approaches perigee. However, the total energy in the system is constant. So where is the acceleration? Acceleration is a measure of the change in net forces acting upon a body. If these forces remain in balance, then how can it be said to be accelerating?
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  45. #1995
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    Quote Originally Posted by OngBonga View Post
    Are you sure about this? An orbit is a straight line through curved space. It is a constant velocity.
    Well, you're jumping from a Newtonian model to a Relativistic model. The explanations are different, but in this context, no less descriptive. If we're talking orbits about black holes that have periapses close enough to experience significant frame dragging, then we're not equipped with Newtonian mechanics. Aside from those exotic cases, though, the Newtonian model is fine to help picture what's going on.

    Please recognize that my original answer was to CoccoBill in the context of Newtonian mechanics. His Phrasing "fall back down" invokes the Newtonian model, and not the relativistic model in which we're more likely to say, "There's no such thing as down."

    It's worth being more careful on my part to point out which model I'm assuming, too.

    Quote Originally Posted by OngBonga View Post
    If you're not orbiting anything, you must be constantly accelerating.
    I'm not super hot on Relativity, but I think I know what you mean.

    If I was otherwise accelerating, I could fire some thrusters to counter that acceleration, such that I'm no longer accelerating. Which means I've pinned myself down to a geodesic.

    Is that right? If so, I agree... as long as we're talking about photons.
    Last edited by MadMojoMonkey; 02-15-2019 at 01:01 PM.
  46. #1996
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    Quote Originally Posted by OngBonga View Post
    Yeah but I was talking about a hypothetical universe with just the Earth. The only reason you can escape the Earth's gravitational influence is because there are bigger things out there.

    And even then, strictly speaking, you never really do escape the Earth's gravity. It just becomes more and more negligible.
    If unbound paths in the Earth's gravitational field are still being called orbits (which they sometimes are since they're still solutions to the same equation, just with non-negative total energy in the system), then it's moot.
    There are 2 things in the universe. Assuming that gravity waves have had time to communicate the curvature in spacetime caused by each other, they are affecting each other gravitationally, and we've defined that as an orbit, no matter what motions these bodies have relative to each other.
    That's fine so long as we keep in mind that orbit no longer means "bound to" nor does it mean "going around each other over and over again." In this context, an orbit may only pass periapse 1 time and then proceed off to apoapse at infinity.

    It is aboslutely a thing that gravity extends infinitely, but also a thing that it gets weaker the further from its source. If the relative speed is above a threshold, the objects will have a single closest approach, then speed away from each other forever. Always slowing down, but never enough to stop, even over infinite time and space.
  47. #1997
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    Quote Originally Posted by OngBonga View Post
    I note you went from "velocity" to "speed".
    Not really. I simply decoupled the direction and magnitude of the velocity to talk about them individually.
    "In any direction without changing speed ever" is just a re-phrasing of "constant velocity."

    Quote Originally Posted by OngBonga View Post
    The problem with saying the Moon is accelerating is that you're observing this acceleration from Earth, not the Moon. Is the Earth accelerating as it moves along its elliptical orbit around the Sun? Well, sure, if we put the Sun in the centre of our model. But if we put the Earth at the centre, it's everything else that accelerates.
    Whether or not an object is accelerating is unambiguous. All observers can answer this question about a given object at a given time and all observers will agree on the answer, once relativistic effects are accounted for. In other words, absolute acceleration is a physical property.
    Compare to, absolute position is not a physical property. However, relative position is. I.e. the spacetime interval between 2 objects is invariant.

    If you choose a non-inertial reference frame (by saying the Earth is the center), then you can't rely on the statements of physics which begin, "In an inertial reference frame..." You need to pull out the big guns to deal with that, and let me tell you that dealing with an accelerating reference frame is not my idea of a good time.

    Quote Originally Posted by OngBonga View Post
    Acceleration due to gravity is not a true acceleration. It's an observed one from another frame of reference. Something that is in freefall (such as a body in orbit) is not accelerating, it is moving at a constant velocity.
    Acceleration due to gravity is indistinguishable from acceleration due to application of a force. There is no experiment which could tell you whether you're in a closed room being constantly lifted at g by a "hand of God" or simply in a closed room somewhere near the surface of the Earth.

    Light travels in logically straight lines through curved space.
    Massive objects do accelerate in their orbits.

    All observers can measure the relative velocity of 2 bodies in orbit about each other at various times and confirm that the relative speed has changed (for non-circular orbits), indicating acceleration.

    Force is invariant. Mass is invariant. Therefore F/m is invariant and F/m = a.
    If any observer (after minding their p's and q's, relativistically speaking) observes acceleration, than all observers will.
    For not-too-massive objects like the Earth and Moon, which have low relative velocities, the Newtonian approximation is many orders of magnitude more significant than the relativistic correction. Ergo massive bodies are shown to accelerate to some observers who have minded their p's and q's w.r.t. Einstein's Relativity, and therefore all observers will observe the same if they are also careful in their math.
  48. #1998
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    Quote Originally Posted by OngBonga View Post
    Here's a thought experiment...
    We're in a huge vacuum chamber. We throw a ball upwards at an angle of 45 degrees. It slows down as it reaches its apex, then begins to speed up as it falls, before hitting the ground.
    Did the ball accelerate after we let it go? No, it moved at a constant velocity until it hit the floor. The path it took was a straight line through curved space. That's how much space is curved at the surface of Earth.
    I've answered this. The ball accelerates, unless it's massless. Do the same experiment with a photon and it'll take the straight line path through curved spacetime.

    ***

    If I have an electric dipole - like that produced by any battery - the Electric field lines originate at the positive end and terminate at the negative end.
    If I place a proton somewhere in that electric field, the moment I release it, it begins to accelerate in the direction of the electric field, according to
    F = qE = ma
    where q is the charge of the proton, E is the vector electric field, m is the mass of the proton and a is the acceleration.

    Now... since these Electric field lines are curved, the proton moves off the field line that first accelerated it, due to its inertial mass. It always experiences a force in the direction of the Electric field, but it now has momentum. Since the momentum doesn't HAVE to be aligned with the Electric field, there's no rule that says an object has to move along the field lines. In fact, it says only massless (charged) objects would move exactly along the field lines.

    This is directly analogous to the way massive bodies move along geodesics.

    Note that I invoked a dipole for the easy reference to a battery, and because the electric field of a dipole is curved. You can use any electric field which isn't well described as a "constant field" and this all holds true. In the special case where the field is constant, like between the plates of a capacitor, the physics is the same, but a convincing example is harder to describe.
  49. #1999
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    Quote Originally Posted by OngBonga View Post
    As the Moon moves around the Earth, it appears to accelerate relative to Earth. What is actually happening is kinetic energy is being transferred to potential energy as it approaches apogee, and then potential energy is in turn transferred to kinetic energy as it approaches perigee.
    @bold: that's acceleration - change in kinetic energy. Technically acceleration doesn't imply change in KE, but change in KE always implies acceleration.

    Quote Originally Posted by OngBonga View Post
    However, the total energy in the system is constant.
    The total energy being constant does not imply absence of forces. All (undamped) oscillating systems have constant total energy, but they wouldn't oscillate if not for the application of a conserved restoring force - a force applied by the conservation of Energy.

    Quote Originally Posted by OngBonga View Post
    So where is the acceleration? [...] If these forces remain in balance, then how can it be said to be accelerating?
    The bodies express force proportional to the inverse square of the distance between their centers. That distance changes, so the force changes.
    F = GmM/r^2
    where G is Newton's gravitational constant, m is one of the masses of the orbiting bodies, M is the mass of the other orbiting body, and r^2 is the distance between their centers.

    The accelerations are F = ma and F = Ma for each body, respectively.

    For mass m,
    F = GmM/r^2 = ma
    a = GM/r^2

    For mass M
    F = GmM/r^2 = Ma
    a = Gm/r^2

    Quote Originally Posted by OngBonga View Post
    Acceleration is a measure of the change in net forces acting upon a body.
    a = dF/dm isn't a form of that statement I've come across before, but the math says it's equivalent to F = ma, so I'll accept it.

    Here's a powerful and broadly true statement about the relationship between potential energy and force.
    F(x,y,z) = -(dU/dx + dU/dy + dU/dz)
    The force is the negative of the gradient of the potential function.
    The gradient is a slope map of (whatever, really, but in this case) the potential function U. To find it, you take the first partial derivatives of the potential function w.r.t. all your coordinate axes and you add them up, then flip the sign.

    Let's look at a simple example.
    If you have a topographical map, then the curves on the map represent lines of equipotential gravitational potential energy.
    The gradient of that map would add an arrow at every point on the map. Each arrow would point whatever direction is most uphill at that point, and each arrow's magnitude would be indicative of the steepness of the slope at that point.
    OK. We have a map of some hills and all the arrows point uphill.
    It's worth noting that all of the arrows are perpendicular to the equipotential line that passes through their point of origin. This makes sense. If I move along an equipotential line, I do not gain or lose any potential energy, so the max or min gain/loss would be perpendicular to that. Otherwise some portion of my direction is parallel to it, not contributing to the change.

    If we place a ball somewhere on that map, in which direction will it accelerate? Downhill, right?
    Well, downhill is the exact opposite direction of the gradient vector map, so that's the direction the math says the force will be, and experience tells us that's the same direction the ball will roll. Experiences tells us that balls accelerate more on steeper hills than shallow hills, and the math agrees, too.
    Excellent!

    So when looking at anything moving within a potential energy function, if it is not following exactly along an equipotential line, then it is experiencing an acceleration.
  50. #2000
    Aside from those exotic cases, though, the Newtonian model is fine to help picture what's going on.

    Not really. Newtonian mechanics is just an excellent approximation, but it's a flawed understanding of what's really happening.


    Please recognize that my original answer was to CoccoBill in the context of Newtonian mechanics. His Phrasing "fall back down" invokes the Newtonian model

    Fair enough, but it's more or less a reflex for me to shift my thought process from Newton to Einstein, simply because Einstein had a much better understanding of the causes of gravity than Newton did.




    Is that right? If so, I agree... as long as we're talking about photons.

    I'm talking about anything. Something in freefall is not subject to any forces other than gravity, which is an inertial force, that is one that emerges as a result of frame of reference. An orbit is freefall.


    In this context, an orbit may only pass periapse 1 time and then proceed off to apoapse at infinity.

    I don't agree. If there are two objects in the universe, they orbit each other. That orbit might be ridiculously huge, but it's an orbit. Something moving away from Earth will give up kinetic energy and gain potential energy. This is simply inevitable.


    In other words, absolute acceleration is a physical property.

    I need to think more about this.


    and let me tell you that dealing with an accelerating reference frame is not my idea of a good time.

    Sounds like a party to me.


    Acceleration due to gravity is indistinguishable from acceleration due to application of a force.

    I'm coming back to this point, because you're right.


    Mass is invariant.

    Not true. Mass changes depending on motion, and motion is relative. Therefore, we will disagree on the mass of an object from different frames of reference.


    @bold: that's acceleration - change in kinetic energy. Technically acceleration doesn't imply change in KE, but change in KE always implies acceleration.

    I'm not so sure. If KE is changing into PE, with no net loss of energy to the system, then no acceleration happened. Why? Because KE and PE are the same thing. If I throw a ball and then run alongside it, does the ball have kinetic energy from my frame of reference? If I catch it, it doesn't exert the same force on my hand compared to someone who catches it from a standing position. From two different frames of reference, we disagree on the amount of kinetic energy an object has, but we'll never disagree on its KE + PE.

    This is rather like electricity and magnetism. If you move with the same velocity as an electron flowing along a wire, you won't observe an electric flow, you'll observe a magnetic field.

    The total energy being constant does not imply absence of forces.
    No, but it does imply no net change in force.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  51. #2001
    Acceleration due to gravity is indistinguishable from acceleration due to application of a force.
    Gravity is also indistinguishable from the G-force we feel in a car when it turns or brakes sharply. But that force is inertial... it only emerges because things with mass resist a change in state of motion. When we're in a car, as the car turns right, we feel motion towards the left. But we're actually moving in a straight line while the car moves right. That motion to the left is an illusion.

    We do accelerate, because we don't continue along our straight line. But the Moon does continue along its path.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  52. #2002
    I skipped over some simply because it's beyond my understanding. I'll read your posts again and might come back to what I missed out if I can get to grips with what you're saying.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  53. #2003
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    I feel like I'm following a little bit here and there. So to put it simply, that guy floating out into space in Gravity would fall into (an orbit around) the Sun, unless by freak accident he happened to bang into the Moon or Jupiter, with these being dependent on the trajectory. Now, intuitively I'd think it's far more likely to either a) get sucked into something or b) get thrown out, but seeing all of them planets and moons on fairly stable orbits, would it be more likely to end up on collision course/get thrown out of the Solar system or end up eternally encircling something? And why is this? Like how precise do the velocities need to be for satellites and the ISS to remain up there, and not fling out or crash down?
    Our brains have just one scale, and we resize our experiences to fit.

  54. #2004
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    Quote Originally Posted by CoccoBill View Post
    I feel like I'm following a little bit here and there. So to put it simply, that guy floating out into space in Gravity would fall into (an orbit around) the Sun, unless by freak accident he happened to bang into the Moon or Jupiter, with these being dependent on the trajectory.
    Yep.

    Quote Originally Posted by CoccoBill View Post
    Now, intuitively I'd think it's far more likely to either a) get sucked into something or b) get thrown out, but seeing all of them planets and moons on fairly stable orbits, would it be more likely to end up on collision course/get thrown out of the Solar system or end up eternally encircling something? And why is this?
    It's really hard to say. The initial trajectory makes all the difference. As packed as the solar system is, it's still mostly empty, and generally in a plane called the ecliptic plane. An orbit exists in a plane. All the planets' planes are within about 7 degrees of making a single flat plane. Pluto is about 17 degrees off from Earth. If your initial trajectory isn't near that plane, then it's really unlikely you'll hit anything.

    The typical way things go is that in the early stages of planet formation, bigger bodies tend to interact with smaller bodies such that the bigger body moves into a closer orbit and the smaller body gets flung out. That is probably due to these bodies forming out of the same swirling mass of gas and dust in the pre-solar nebula. When you impose a random trajectory on this, I think it all evens out as to what possible interactions there are.

    Whether or not you'll escape the Earth is a matter of whether or not your speed is greater than the escape velocity for Earth. This is also true for the Sun, but it's a new relative speed and a new escape velocity. Then again for Sagitarius A*.


    Quote Originally Posted by CoccoBill View Post
    Like how precise do the velocities need to be for satellites and the ISS to remain up there, and not fling out or crash down?
    Orbits are weird.
  55. #2005
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    Quote Originally Posted by OngBonga View Post
    Not really. Newtonian mechanics is just an excellent approximation, but it's a flawed understanding of what's really happening.
    Fine, but I kinda suck at GR.

    Quote Originally Posted by OngBonga View Post
    I'm talking about anything. Something in freefall is not subject to any forces other than gravity, which is an inertial force, that is one that emerges as a result of frame of reference. An orbit is freefall.
    It's still a force and it still changes the velocity w.r.t. whatever it is you're orbiting about.
    Just because you can't measure the difference inside the closed box, doesn't mean you can't measure the difference outside the closed box.

    Quote Originally Posted by OngBonga View Post
    I don't agree. If there are two objects in the universe, they orbit each other. That orbit might be ridiculously huge, but it's an orbit. Something moving away from Earth will give up kinetic energy and gain potential energy. This is simply inevitable.
    A thousand times no, dude.
    If the total energy in the system is negative, then the system is bound. If it is non-negative, it is unbound.
    Escape velocity, man. I thought you got that much.

    Let's dig it, then:
    Empty universe. Just mass M in it. Just M and you, m, all the way out at infinity, with no speed at all relative to M.
    That's the initial condition.
    What's your speed as you fall toward M?
    Go.

    The force accelerating you toward M is
    F = GMm/r^2

    Your initial speed at r_inf is
    v_0 = 0 m/s

    The Work-Energy Theorem says that the work done on an isolated system is equal to the change in energy. In this case, the work done is 0 J, as there is no outside agency aside from the internal energy in the system, whatever it is. This is a purely mechanical system, i.e. there's no pressure changes, no entropy, no chemical changes, no heat, no sound, blah, blah... just Grav. PE and the KE of the relative motion.

    delta_W = delta_KE + delta_PE = 0 J

    Good, we've proved that KE + PE is constant, and that means the total Energy is constant.
    We can further state
    delta_KE = -delta_PE


    We can apply the same Work-Energy theorem on the isolated system of just the PE and state
    delta_W = delta_PE
    but delta_W is the change in work, or the work acquired by moving an object parallel to a force.
    delta_W = F*dr
    (technically that's a dot product, but since in our case the motion is always exactly parallel to the force, we can straight multiply)

    Integrate both sides
    W = PE = integral(GMm/r^2 dr)

    Good to go.

    KE = -integral(GMm/r^2 dr) r = inf to r_0

    where r_0 is the distance between M and m.

    KE = -GMm * integral(1/r^2 dr) r = inf to r_0
    KE = -GMm * integral(r^-2 dr) r = inf to r_0
    KE = -GMm * [-1/r] | r = inf to r_0
    KE = -GMm * (-1/r_0 - -1/inf) = -GMm * (-1/r_0 + 0)

    KE = GMm/r_0

    A familiar gem, and not too bad to get there from first principles.

    KE = 1/2 m |v|^2 = GMm/r_0
    |v|^2 = 2GM/r_0
    |v| = sqrt(2GM/r_0)

    We've answered the question. That may not be as familiar to you, but that is the equation for escape velocity.

    OK. Now. If starting at infinity distance and approaching to any finite distance r_0 gets you up to v_escape, then moving in exactly the opposite direction at v_escape is enough to barely make it back to infinity. If you go any faster at all, then you are only escaping to infinity even faster. The only part of v_escape that's even relevant is that it is finite.

    Not all orbits are closed. QED

    If we open this problem to allow all possible initial positions and velocities, then all the possible solutions are conic sections. Circles and ellipses, yes, but also parabolas and hyperbolas. The parabolas are the ones that are just exactly at v_escape for all r_0. The hyperbolas are the ones going above v_escape at all r_0. The circles and ellipses are the ones going below v_escape for all r_0.


    Quote Originally Posted by OngBonga View Post
    I need to think more about this.
    We could flip the prior problem around and talk about how you're sitting still while M starts at inf distance away. It's the same problem. Then of course, we don't see you accelerating, but M accelerating, and in order to understand acceleration, we have to know what it's in relation to.
    Since position, x, isn't absolute, then dx/dt and d^2x/dt^2 aren't either.

    It's probably incorrect language on my part, but look at it from the F = ma ; F/m = a perspective.
    Force and mass need to be understood relativistically, but once they are, all observers agree on the force and rest mass experiencing the acceleration... so they must ultimately agree on the acceleration. All Einstein really talked about was F/m if you read the way he did his own math.

    Quote Originally Posted by OngBonga View Post
    Not true. Mass changes depending on motion, and motion is relative. Therefore, we will disagree on the mass of an object from different frames of reference.
    I should have said rest mass. Once relativity is accounted for, all observers agree on rest mass.

    Quote Originally Posted by OngBonga View Post
    I'm not so sure. If KE is changing into PE, with no net loss of energy to the system, then no acceleration happened. Why? Because KE and PE are the same thing.
    F = -grad(PE)
    This is a hugely broad-sweeping statement that holds in all cases. For every potential energy function, an object interacting with it experiences a force of minus the gradient of the potential. Nothing to do with KE, there.

    That PE may turn into KE, but there are all kinds of other forms of energy when we move beyond a purely mechanical system.

    Within a purely mechanical system with no losses, KE = -PE and the only way KE can change is if m changes or v changes. When we assert that m is constant, then v is the only variable that can change. a = dv/dt. If v is changing, a is happening.

    Quote Originally Posted by OngBonga View Post
    If I throw a ball and then run alongside it, does the ball have kinetic energy from my frame of reference? If I catch it, it doesn't exert the same force on my hand compared to someone who catches it from a standing position. From two different frames of reference, we disagree on the amount of kinetic energy an object has, but we'll never disagree on its KE + PE.
    Yes. It has KE.
    No. The force is different. You're in a moving frame w.r.t. the other person, and applying the Galilean frame transformations is plenty enough for you to agree.

    You don't agree on its KE + PE, because you agree on its PE, but differ on its KE. You agree that KE + PE = const., but you observe different E_tot as a constant.
    They observe only velocity in the up-down direction. You also observe additional motion in the not-up-down direction, so you observe greater velocity.
    All of this is assuming you move a constant velocity w.r.t. the line traced out by the ball's trajectory.

    Quote Originally Posted by OngBonga View Post
    This is rather like electricity and magnetism. If you move with the same velocity as an electron flowing along a wire, you won't observe an electric flow, you'll observe a magnetic field.
    I know what you mean, but no. The equations which describe how energy is stored in a magnetic field and electric field are different in form from the equations that describe how energy is stored as potential and kinetic energy. You can't just draw this parallel with any 2 forms of energy.

    FYI
    By invoking a wire, there is no reference frame in which there are no moving charges.
    Whether you see electrons flowing against a stationary background of cations or you see electrons sitting still while a stream of cations flow past in the opposite direction, the conventional current is the same. There is always a magnetic field, and its orientation (direction it rotates around the wire) is agreed upon by all observers.
    I.e. you will either see electrons going one way or protons going the other way, which is equivalent in E&M equations.
    (obv. you could see inf possibilities of both moving, but the relative speed is the same, once relativity is taken into account.)

    Quote Originally Posted by OngBonga View Post
    No, but it does imply no net change in force.
    dF/dx = 0 at apoapse and periapse... so even a broken clock..?
    Last edited by MadMojoMonkey; 02-15-2019 at 10:10 PM.
  56. #2006
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    Quote Originally Posted by OngBonga View Post
    Gravity is also indistinguishable from the G-force we feel in a car when it turns or brakes sharply. But that force is inertial... it only emerges because things with mass resist a change in state of motion. When we're in a car, as the car turns right, we feel motion towards the left. But we're actually moving in a straight line while the car moves right. That motion to the left is an illusion.
    It's not a illusion, per se. That statement presumes a moral superiority of inertial reference frames. If you're spinning, then who are we to say what you observe is an illusion? It's ego-stroking talk, IMO.

    Non-inertial reference frames are no less real than inertial reference frames. They're just generally harder to work with mathematically.

    Quote Originally Posted by OngBonga View Post
    We do accelerate, because we don't continue along our straight line. But the Moon does continue along its path.
    I hope my wall of text has at least made you question this more.
    The moon is not at constant distance from the Earth.
    It's changing it's PE -> it's changing it's KE-> it's changing it's |v| -> it's accelerating.
  57. #2007
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    Quote Originally Posted by MadMojoMonkey View Post
    It's really hard to say. The initial trajectory makes all the difference. As packed as the solar system is, it's still mostly empty, and generally in a plane called the ecliptic plane. An orbit exists in a plane. All the planets' planes are within about 7 degrees of making a single flat plane. Pluto is about 17 degrees off from Earth. If your initial trajectory isn't near that plane, then it's really unlikely you'll hit anything.
    I guess I could google it but why is that? The Sun is spinning and we're (we as in planets) all dragged around perpendicular to the spinning axis like Saturn's rings? Kind of like the Milky Way is flat, dragged around the SMBH in the middle, though not quite as flat as we had previously thought, and Brian Cox says the universe is flat. Like wtf?

    Quote Originally Posted by MadMojoMonkey View Post
    The typical way things go is that in the early stages of planet formation, bigger bodies tend to interact with smaller bodies such that the bigger body moves into a closer orbit and the smaller body gets flung out. That is probably due to these bodies forming out of the same swirling mass of gas and dust in the pre-solar nebula. When you impose a random trajectory on this, I think it all evens out as to what possible interactions there are.
    Ok I see, some survivorship bias on my part. Seems obvious now that you spell it out.

    Quote Originally Posted by MadMojoMonkey View Post
    Whether or not you'll escape the Earth is a matter of whether or not your speed is greater than the escape velocity for Earth. This is also true for the Sun, but it's a new relative speed and a new escape velocity. Then again for Sagitarius A*.
    Gotcha.

    Quote Originally Posted by MadMojoMonkey View Post
    Those trajectories make me angry.
    Our brains have just one scale, and we resize our experiences to fit.

  58. #2008
    Escape velocity, man.
    But the problem with escape velocity is that you'll need to constantly accelerate in order to maintain escape velocity. Something moving away from the Earth (or whatever big M is in this universe) is constantly losing kinetic energy and gaining potential energy. How do we maintain escape velocity?

    I really don't see how an object that loses kinetic energy can continue along a straight line. And if it moves along a curved path, then how is it not ultimately a closed orbit? What happens when kinetic energy is zero?

    The only way I can picture this is to imagine something that is losing a constant percentage of its KE, but never reaching zero. Maybe this can happen, idk. How much does escape velocity change over distance?

    I hope my wall of text has at least made you question this more. The moon is not at constant distance from the Earth.
    It's changing it's PE -> it's changing it's KE-> it's changing it's |v| -> it's accelerating.
    I'm still not satisfied with this. I feel like "acceleration" in the context you're explaining it is Newtonian, not Einsteinian. Newton would say the Moon changes velocity, but Einstein would say that it moves at a constant speed in a straight line through curved space. If something is moving at a constant speed in a straight line, it is not accelerating.

    Acceleration depends on frame of reference. One person observes acceleration while another person doesn't. So who is right?
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  59. #2009
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    Quote Originally Posted by CoccoBill View Post
    I guess I could google it but why is that? The Sun is spinning and we're (we as in planets) all dragged around perpendicular to the spinning axis like Saturn's rings? Kind of like the Milky Way is flat, dragged around the SMBH in the middle, though not quite as flat as we had previously thought,
    Everything I'm about to say is hypothetical. We can only conjecture and model the history of the solar system.

    The pre-solar nebula that collapsed into the solar system was a vast cloud of dust and stuff. The majority of these are mostly Hydrogen with a smattering of Helium and Lithium, but ours was different. The presence of atoms which are not those elements means that our pre-solar nebula was contributed to by the death of another star. It may have been more than 1. The shock wave of a nearby supernova is thought to have triggered a wave of gravitational collapses that formed 1k - 10k stars, similar to what we see in the Orion nebula. The sun was one of those. That cluster interacted and broke apart within a few hundred million years of the formation.

    The original nebula was vast compared to the size of the solar system. It was composed of stuff with mostly random motions, but taken all together, non-0 Angular Momentum. As the nebula collapses toward a gravitational center, all the random momenta keep interacting and tending toward the mean. Particles moving against the mean tend to interact with particles moving with the mean such that both lose net angular momentum. (When + interacts with -, they tend toward 0.) This tends to cause the collapsing nebula to more and more spin in the same way, sending a lot of stuff to the center.

    As it collapses, it draws in material from all directions, but the stuff not moving in an orbit that is both around the center of mass and the axis of rotation gets drawn in more directly. As those particles interact, they tend toward a disk with a ball at the center.

    I think that's pretty close to your answer.

    As it forms, less than 1% of the total mass will remain in the disk, and that disk will eventually be the planets, asteroids, comets, etc. The bulge at the center will eventually collapse until the pressure at the core begins fusion and it becomes the Sun.

    Quote Originally Posted by CoccoBill View Post
    and Brian Cox says the universe is flat. Like wtf?
    Brian: Look at this table, it's flat, right? Just draw a triangle and measure the angles, and if they add up to 180 degrees, then flat. Imagine a globe, the angles don't add up to 180. Or a saddle. OK? The universe is flat. Moving on.
    Joe: It's flat? but how thick is it?
    Brain: What? Moving on.

    I was laughing at that, because it was a complete failure of communication on Brian's part.

    Here's a Minute Physics that does pretty good as a primer.

    Quote Originally Posted by CoccoBill View Post
    Those trajectories make me angry.
    I feel you, brother.
  60. #2010
    I've just watched a thing about electromagnetism in the context of frame of reference, and found it incredibly hard to follow it. What I learned was the electrical energy does not flow along a wire, rather it flows in the space around the wire. All the wire does is create a closed loop, initiating the flow of energy.

    I do not understand it at all. But it does kind of make sense, because if energy flows along the wire, alternating current wouldn't power our devices.

    Electromagnetism is a bigger beast than gravity.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  61. #2011
    Is this guy talking out of his arse?

    Basically, he claims that if gravity were responsible for an object falling to Earth, such as an apple dropped from arm height, it would take 21 minutes for the apple to fall to the ground. He claims it is electromagnetism that causes it to happen in a second or whatever. Is this true?

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  62. #2012
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    Quote Originally Posted by OngBonga View Post
    But the problem with escape velocity is that you'll need to constantly accelerate in order to maintain escape velocity. Something moving away from the Earth (or whatever big M is in this universe) is constantly losing kinetic energy and gaining potential energy. How do we maintain escape velocity?

    [...]

    The only way I can picture this is to imagine something that is losing a constant percentage of its KE, but never reaching zero. Maybe this can happen, idk. How much does escape velocity change over distance?
    The escape velocity is how fast you'd be going to just barely make it to infinity in an infinite amount of time. The exact value of the escape velocity is a function of the distance between the 2 bodies' centers. Its rate of dropoff exactly corresponds to your speed's dropoff as you decelerate, moving off to infinity. This is by design. This was the way we derived it. One of our initial assumptions was, "assume no accelerations except for gravity." In so doing, we define the line where any speed less than that cannot reach infinity, even given infinite time - the closed orbits. Any speed greater that that will reach infinity, given an infinite amount of time - the open orbits. The only acceleration in any of this is gravity. If your speed, given your distance, is ever greater than escape velocity, then gravity is definitely not enough to stop you, ever. It can just barely stop you if you're at escape velocity, so anything more than that, and it just can't. The energy in the system is positive. It is not bound.

    What I left unsaid, and could have really been more rigorous with, mathematically, is to set our starting distance to r_i and then take the limit as r_i goes to infinity. In avoiding that, it was hidden that it would take an infinite amount of time for 2 objects separated by an infinite distance to reach a separation distance that is finite.

    Had we set the problem up like that, we could ask, given some initial, finite velocity and some initial, finite separation distance, at what separation distance is apoapsis? When we do so, we see that for certain configurations, we find the apoapsis is infinitely large.

    The bodies are moving perpendicular to the (geodesics?) Potential Energy they form in spacetime, at least a little bit (in this case, entirely), therefore they are accelerating due to gravity. Whether you model that as curvature in spacetime or Newton's action at a distance, the result is the same.

    Quote Originally Posted by OngBonga View Post
    I really don't see how an object that loses kinetic energy can continue along a straight line. And if it moves along a curved path, then how is it not ultimately a closed orbit? What happens when kinetic energy is zero?
    A mass on a spring is a 1-D oscillator, a purely mechanical system. You can orient one to oscillate along a geodesic (horizontal), if you like, so that you isolate all forces and energy changes to the action of the spring. When KE = 0, the PE = E_spring, max = E_tot. These are the endpoints, where it turns around. Compare to periapsis and apoapsis.

    Note that for perfectly circular orbits, where the periapsis and apoapsis become ambiguous, there is no relative acceleration. The bodies remain at constant distance, and do move exactly along geodesics. (I think. A geodesic is an equipotential surface in spacetime?)

    I will help a bit by at reading the wikipedia pages on orbits and escape velocity. If nothing else, there are some lovely drawings showing how the parabolic and hyperbolic orbits look on a "curved sheet" drawing of GR spacetime.

    Quote Originally Posted by OngBonga View Post
    I'm still not satisfied with this. I feel like "acceleration" in the context you're explaining it is Newtonian, not Einsteinian. Newton would say the Moon changes velocity, but Einstein would say that it moves at a constant speed in a straight line through curved space. If something is moving at a constant speed in a straight line, it is not accelerating.

    Acceleration depends on frame of reference. One person observes acceleration while another person doesn't. So who is right?
    It's important that we're talking about the relative acceleration between 2 bodies, not the absolute acceleration of either body.
    I think it clarifies things to say we're talking about the rate of change in the spacetime interval being non-constant...
    That is, we're really talking about "the 2nd derivative of the set of spacetime intervals describing the evolving events of these 2 bodies w.r.t. time."
    Replace Cartesian space with GR spacetime. Replace the model of absolute position, x, with the model of a spacetime interval between 2 events, delta_s. Where an event is just a broad-sweeping word to mean "a something in spacetime."

    Classical acceleration is now GR acceleration.
    d^2x/dt^2 becomes d^2(delta_s)/dt^2


    I really don't think Einstein said that. For circular orbits, maybe. For light, definitely.
    Last edited by MadMojoMonkey; 02-17-2019 at 12:38 PM.
  63. #2013
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    re: video

    The Equivalence Principle says the acceleration of gravity is indistinguishable from acceleration by the application of any other force. It asserts that gravitational mass is equal to inertial mass. He's saying it was implicit in Newton's Law of Gravity.

    Einstein's pointing out that

    m a = G M m / r^2

    is really, really saying

    m_inertial a = G M_grav m_grav / r^2

    and that's of no use whatsoever without the implicit statement that m_inertial = m_grav for all mass.
    Since the data holds that Newton's Law is purty durn good, let's make this an axiom.


    The interpretation that it says, "In a closed room, you can't tell the difference between being at rest in a gravitational field and being accelerated by a hand of God at commensurate rate." is just that - an interpretation meant to try to explain the consequences of the statement to someone who is not as hot with physics as Einstein.


    In the video, at 2:20 when introducing the EP, he kinda misses the fundamental caveat, "in a closed room," and mistakes a dumbed-down interpretation of the EP as its definition.

    He then goes on to say that the EP therefore says that the surface of the Earth is accelerating up through spacetime to reach stationary objects.
    This is silly. We're not in a closed room. We have satellites and we know about planets and stars and orbits. We can tell the difference between a flat Earth accelerated by a hand of God and a spherical Earth with mass distorting spacetime.

    As far as I can tell, this is the premise that he takes for the rest of the video, but I only quickly scanned past that up to about halfway, since it seems he's jumped off that cliff and bouncing off rocks on the way down.
  64. #2014
    I really don't think Einstein said that. For circular orbits, maybe. For light, definitely.
    Let's look at this another way. Let's imagine we're on a trampoline in a vacuum chamber. When we bounce up, we will reach an apex before falling down again. Will we feel this acceleration? No, the only reason we determine we have accelerated is because we observe our curved path relative to the ground. The only time we actually feel an acceleration is when we hit the trampoline. If we close our eyes after we bounce up, there is no way for us to tell when we reach apex and begin falling again. Only when we hit the trampoline can we be certain we have accelerated. So, from our frame of reference, we moved in a straight line at a constant speed, since we experienced no force.

    I have to admit, I strongly suspect I'm wrong about orbits, that you are right about escape velocity. I read that wiki page, and it does seem to correlate with this comment of mine...

    The only way I can picture this is to imagine something that is losing a constant percentage of its KE, but never reaching zero.
    But when it comes to gravitational acceleration, I'm still of the opinion this is not a true acceleration, that it only appears so as a consequence of curvature. The Moon moves in a straight line at a constant speed, just like we do when we jump on a trampoline in a vacuum chamber (at least until we hit the trampoline again). For us to truly accelerate, we must feel a force, energy must be added (or removed) from the system.

    This is how I interpret GR.
    Last edited by OngBonga; 02-17-2019 at 01:51 PM.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  65. #2015
    re: video
    He really confused me when he started talking about electromagnetism doing the work that we assume gravity does. I've concluded he's talking out of his arse, much like I do, except I don't go making youtube videos sharing my ideas, I just talk shit in obscure corners of the internet.
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  66. #2016
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    Quote Originally Posted by OngBonga View Post
    This is how I interpret GR.
    I have not been talking about absolute acceleration any of this time. Whether or not you feel anything, or any object under consideration feels anything, is irrelevant. I'm talking about the distance between 2 objects changing over time. Specifically, the spacetime interval between 2 objects changing over time.

    Quote Originally Posted by OngBonga View Post
    I have to admit, I strongly suspect I'm wrong about orbits, that you are right about escape velocity. I read that wiki page, and it does seem to correlate with this comment of mine...
    That statement is spot on. Sorry to catch it so late.
  67. #2017
    I'm talking about the distance between 2 objects changing over time. Specifically, the spacetime interval between 2 objects changing over time.
    Fair enough, but I feel this is a loose definition of acceleration. For me, an acceleration is a deviation from a straight line at a constant speed (constant velocity). Simply observing distance changing is not enough, since distance is relative. What you observe as changing distance, someone else might observe as constant. But all observers should agree if a force (real, not inertial) is being applied to an object or not, at least if we all agree gravity is an inertial force.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  68. #2018
    I'm unconvinced by my own argument. I'm not sure one observer can see changing distance while another sees constant. You were saying about non-inertial frames of reference not being much fun?
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  69. #2019
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    Awesome fucking movie.

    As this is sort of our unofficial sciency stuff thread, I'm dropping it here



    And don't hate on Elon.
    My dream... is to fly... over the rainbow... so high...


    Cogito ergo sum

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  70. #2020
    If entropy is governed by probability, then does than mean there's a non-zero chance that the "heat death" of the universe won't happen? And if that's the case, does that mean that, given an infinite amount of time, it definitely won't happen?
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  71. #2021
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    Quote Originally Posted by OngBonga View Post
    If entropy is governed by probability, then does than mean there's a non-zero chance that the "heat death" of the universe won't happen? And if that's the case, does that mean that, given an infinite amount of time, it definitely won't happen?
    IDK, but I heard a cool interpretation of the Heat Death still jumbling through random configurations and that since there is no known timeline that changes this, the long-term certainty of a Boltzmann brain randomly existing approaches 100%.
  72. #2022
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    I don't understand geodesics at all. Please disregard as (probably) incoherent nonsense my prior statements on GR geodesics.
    If there's anything I've said that isn't terrible, it was by chance.
  73. #2023
    Personally I'm not a big fan of randomness in nature. I strongly believe that, if all initial conditions are known, then randomness disappears, to be replaced with certainty.

    But I also don't like the idea of entropy causing the heat death of the universe. There's a conflict here, but solving it is way beyond my grasp.
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  74. #2024
    Quote Originally Posted by MadMojoMonkey View Post
    I don't understand geodesics at all.
    I don't pretend to, other than to simply say they represent straight lines in curved space.
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  75. #2025
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    The general theory of relativity, published 100+ years ago, is supported again

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    Cogito ergo sum

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