16 ms·
I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how
by Smaug123 6y ago
I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?"
I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong answer out there, please correct me.
Intuitive answer: the curve is indeed very gentle, and (e.g.) light will be deflected only very slightly by the curvature; but the ball is moving for a couple of seconds, and that's an eternity. On human scales, the time dimension is much "bigger" than the space dimensions (we're quite big in the time dimension and quite small in the spatial dimensions); the ball moves only a small distance through space but a very large distance through time, amounting to a big distance in spacetime, and so the slight curvature has a bigger effect than you might expect.
- atoav 6y agoThis is in tune with what happens when you change the timescale in a game engine with proper physics.
- grenoire 6y agoI think this is more of an integration method error than an analogous case.
- hunterloftis 6y agoI'm not aware of any game engines that simulate general relativity / 4D spacetime. I think what you may be noticing is that, as you reduce the tick frequency of a newtonian physics simulation, parabolas become less accurate as integration error accumulates.
- Agentlien 6y agoAlong those lines: during my university years, this is what I saw in my homemade engine before I had a good understanding of numerical stability.
- pishpash 6y agoThat's too bad, such a simulator would be great for intuition.
- pdkl95 6y agoWhile we are (unfortunately) lacking general relativity simulators, a few special* relativity simulators exist: "A Slower Speed of Light" http://gamelab.mit.edu/games/a-slower-speed-of-light/ http://gamelab.mit.edu/games/a-slower-speed-of-light/ "Velocity Raptor" https://testtubegames.com/velocityraptor.html https://testtubegames.com/velocityraptor.html
- paulpauper 6y ago>I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?" Air resistance, wind, and horizonal acceleration. Over long vertical distances, these perturbations in the x-axis cause an arc. Nothing to do with general relativity.
- Smaug123 6y agoI assert that if you throw a ball upwards in a vacuum chamber on Earth, it will in fact still fly in a parabola.
- Koshkin 6y agoWhich is one reason scientists used to think that vacuum doesn’t exist.
- vikramkr 6y agoWhen you're tossing a ball into the air by hand, gravity is going to have a far more dominant effect on things than air resistance and friction. Things still fall on the moon...
- Koshkin 6y agoDepends on the density of the ball, of course.
- manigandham 6y agoThere wouldn't be an arc at all without gravity/relativity because the ball wouldn't return.
- Koshkin 6y agoTo be fair, you could make it return by using other forces of nature, e.g. by blowing said air from above.
- mrfusion 6y agoAre we flat in the time dimension? Or what is our time size?
- Retric 6y agoIt’s something of a philosophical question. We tend to think of distant galaxy’s as if we are viewing them via some FTL means with a single consistent now. NASA for example tracks distant Mars probes like that rather than marking timing based on when the signal was received. Alternatively, you can think of everything that could impact you as something of a now light cone. The second view has the universe existing as a 3D surface in 4D space time which means objects have a temporal width for each observer. That can be a really useful mathematical model. PS: Edited the above several times for clarity.
- aspenmayer 6y agoI’m reminded of the film Donnie Darko, but I won’t say more as to not spoil anything for anyone.
- ithkuil 6y ago"All tragedies are finished by a death, all comedies by a marriage." —Lord Byron
- AgentME 6y ago>Or what is our time size? That's just another way of describing the total time you exist.
- shawnz 6y agoYour size in X, Y, Z isn't equal to the total distance you've traveled, so why would your size in t be the total time you've traveled?
- deleted 6y ago[deleted]
- vbezhenar 6y agoAre we moving through time with constant speed? Or we're constantly accelerating through time?
- Smaug123 6y agoUnder special relativity, everyone and everything moves at a constant speed `c` through spacetime. If you feel like you're not moving, it's because all your speed is being put towards travelling faster through time. Conversely, if you manage to move very fast through space, the world around you will appear to speed up, because you've had to trade off some of your forward travel through time so as to travel in space; the rest of the world is moving forward in time faster than you are. So you can change your acceleration through the time dimension of spacetime, by dint of changing your acceleration in the spatial ones.
- ithkuil 6y agoAnd at the same time, in your new frame of reference, you're still moving at exactly c through the time and 0 through space. But your time axis is no longer parallel with the time axis of the rest of the world.
- comboy 6y agoAxes being parallel by whose point of view?
- Dylan16807 6y agoEveryone's.
- comboy 6y agoRelativity.
- Dylan16807 6y ago
- mytailorisrich 6y ago> the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola? I suspect that the answer is that this is a false comparison.
- Smaug123 6y agoCould you elaborate on why it's false?
- sohkamyung 6y agoOff topic, but in reality, the trajectory of a ball thrown on Earth is not a parabola, but an ellipse [1]: > under the laws of gravity, a parabola is an impossible shape for an object that's gravitationally bound to the Earth. The math simply doesn't work out. If we could design a precise enough experiment, we'd measure that projectiles on Earth make tiny deviations from the predicted parabolic path we all derived in class: microscopic on the scale of a human, but still significant. Instead, objects thrown on Earth trace out an elliptical orbit similar to the Moon. [1] https://www.forbes.com/sites/startswithabang/2020/03/12/we-all-learned-physics-biggest-myth-that-projectiles-make-a-parabola/ https://www.forbes.com/sites/startswithabang/2020/03/12/we-a...
- Smaug123 6y agoGood point; this becomes more obvious if you imagine throwing the ball up and then immediately collapsing all the mass of the Earth into a single point at the centre. What path does the ball follow now? It's probably following a path we would more usually call an "orbit", and it sure looks a lot like an ellipse. Now just put the mass of the Earth back where it was, and notice that the ball hits the ground before it can trace out very much of its orbit.
- est31 6y agoDespite both being conic sections, cutting up an ellipse won't yield you parabolas. An ellipse has two focal points to which the sum of the distances is constant, while a parabola has a focal point and a directrix line to which the difference of the distances is constantly 0. Two different things.
- Koshkin 6y agoIsn’t a conic section made by cutting up, well, a cone?
- srtjstjsj 6y agoMore symmetrically, Every comic section has one focus and one directrix (and a semi-major axis for scale), eccentricity is the ratio of distance. Ellipse has eccentricity less than 1, and a parabola has eccentricity equal to 1.
- dreamcompiler 6y agoI think of it as being because the ball has mass and photons don't. So Newton's Gm1m2/r^2 = 0 for photons, and you have to use Einstein to measure the "force" on a photon. But because massive objects also cannot move as fast as photons, we're probably both saying the same thing from two different perspectives.
- sixo 6y agoCurvature due to gravity does not depend on mass, which is kind of hinted at when mass cancels in F=ma for that force.
- dreamcompiler 6y agoCurvature due to gravity depends entirely on mass. No mass = no spacetime curvature. In this case, the mass of the Earth is causing the curvature.
- smallnamespace 6y agoSlight correction: curvature depends on the stress-energy tensor, of which energy is a component. A more energetic particle of the same mass will have a very slightly higher gravitational attraction.
- dreamcompiler 6y agoYes indeed. Thanks.
- thewakalix 6y agoThe curvature depends on the mass of the earth, but it _doesn't_ depend on the mass of the photon/ball.
- dreamcompiler 6y agoThe curvature does indeed depend on the ball's mass. The contribution to spacetime curvature the ball's mass brings to the table is extremely small compared to that of the earth, and the contribution that comes from the (massless) photon's energy[0] is smaller still, but they both influence the spacetime curvature. [0] Photons bend spacetime according to GR, although as far as I know this has not been proven experimentally. We'll probably need a theory of quantum gravity to be sure.
- phkahler 6y agoI've always wanted to know why a ball doesn't follow a beam of light if they are both following straight lines in spacetime. But even more important, if light beams are reversible under relativity (reflected off a mirror they will backtrack the same path) then light can not enter a black hole because its reversed path could allow it a way out. But then there's that whole thing of objects falling in appear to slow and stop as they approach the event horizon, so maybe light doesnt enter after all. My conclusion is that you cant really understand it without serious study of under someone who already gets it.
- umvi 6y agoThe difference is that light travels through space, but not time (similar to how a vertical line does not travel the x axis, only the y axis). The ball travels through both space and time. The faster you go, the less you travel through time. Thus, if the ball were travelling at the speed of light, it would not travel through time either and would follow the same path as light.
- pdonis 6y ago> The difference is that light travels through space, but not time This is a common pop science statement, but it's not correct. A correct statement is that the concept of "speed through spacetime", which is what has to be split into "speed through space" and "speed through time" in the pop science statement, does not apply to a light ray. In more technical language, the tangent vector to the light ray's worldline is not a unit vector, it's a null vector, and the concept of "speed through spacetime" only makes sense for a worldline whose tangent vector is a unit vector.
- CamperBob2 6y agoI wouldn't say it's incorrect at all. From the point of view of a photon, no time elapses between its the origin and destination endpoints.
- pdonis 6y ago
- wch 6y agoOn human scales, the time dimension is much "bigger" than the space dimensions... This is really interesting, and it made me wonder how to convert between space and time. I mean, one meter up is equivalent in magnitude to one meter forward, is equivalent to one meter to the right. Is _c_ the conversion between space and time? In other words, is 300 million meters equivalent in magnitude to one second of time?
- lostmsu 6y agoThis is right, yes. The distance (aka interval) formula for the flat 4D spacetime is dist^2 = (c * seconds)^2 - meters^2 So to compensate increase in 1 second you indeed need _c_ ~= 3e8 meters.
- Misdicorl 6y agoCorrect, the speed of light is the conversion factor
- scotty79 6y agoOr a meter is equivalent to the time that light needs to travel 1 meter.
- edem 6y agoIt is bigger only because you travel slowly in the spacial dimensions. You always travel thorugh spacetime with a constant speed (the speed of light). What happens is that you're usually going with 460 m/s (as Earth revolves around the Sun) and this is not really comparable to your `t` speed in the x/y/z/t coordinate system. So when you are still your speed is something like 230/230/0/299.791.998.
- abetusk 6y agoSo if light were traveling through "slow glass" where it's speed through the medium was significantly slowed down, we would see it go in a parabola like the ball?
- colechristensen 6y agoFor example, one of the first observational confirmations of relativity was being able to observe starlight near the sun during an eclipse being slightly out of place because it had been bent by the sun’s gravity.
- thaumasiotes 6y ago> we would see it go in a parabola like the ball? That is a valid path for the light to follow, hypothetically. But if that's what the light was doing, you wouldn't see it. You can only see things when light enters your eyes.
- herodoturtle 6y agoI never studied this stuff, so the genius of your intuitive explanation is appreciated. My intuitive response to your intuitive explanation: This ball is moving through spacetime relative to the earth, which is in turn also moving through spacetime relative to the sun - and so light is being deflected off of this ball at each point in its position in spacetime relative to the sun for much longer than light is being deflected off of this ball at each point in its position in spacetime relative to the earth - have I got that right? Light is a hitman Perpetual driveby shooter Never missing As we dance through the night
- p1mrx 6y ago> have I got that right? Probably not, because "the sun" appears in your response. If you're watching a ball move on Earth, the sun is an irrelevant variable.
- pdonis 6y ago> Intuitive answer Your answer is basically the one given in an early chapter of Misner, Thorne, and Wheeler, which is one of the classic General Relativity textbooks.
- gpsx 6y agoIt is much easier to think in two dimensions than three. If you picture the ball following a parabolic trajectory in space then you are really thinking in three dimensions here. It might be easier to think of throwing the ball straight up, after which it eventually falls straight back down. NOW plot this in two dimensions with one of the dimensions being time. As the original comment says, the scaling of the time dimension in seconds is not a good comparison to meters. Physicist like units where the speed of light is 1 (one). In these units, in our two dimensional space-time graph, the ball travels a very far distance while the change in our space dimension is still small. It is very close to straight line.
- ummonk 6y agoGreat answer! It’s also why I despise the popular portrayal of space time curvature. It looks at space in isolation rather than space time as a whole, and provides no intuition as to why objects traveling at different speeds follow different trajectories. FWIW I think that in general it is better to just teach people that gravity is an acceleration in classical spacetime (as opposed to a force or curvature). It is simply too hard to create intuition for laymen around minkowskian spacetime, and even harder for curved minkowskian spacetime.
- lopmotr 6y agoI think treating gravity as an acceleration is too abstract for many high-school students. For all the on-the-Earth problems, you'd have to analyze them in an accelerating reference frame. That means Newton's laws and the equations of motion don't apply. You'd have to use special linear acceleration equations. An inertial reference frame is simpler and more general. Gravity fits that OK if you consider it to be a force distributed in proportion to mass.
- m3kw9 6y agoWhen you throw a ball up and down in a moving car the ball is also parabola. You don’t need theory of general relativity to explain it.
- raducu 6y agoSo, do gravitons exist or not?
- lovegoblin 6y agoUnknown. They are only hypothetical.
- raducu 6y agoMy point was -- if gravity is not a force, it does not require a force carrier so there is no point for gravitons to exist.
- js8 6y agoHm, I think visualizing this would be a nice topic for a 3Blue1Brown's video or something..
- edem 6y agoThink about this. You're always travelling through spacetime with a constant speed (the speed of causality == the speed of light). This is your 4 vector because it has 4 components: x, y, z, t. Therefore the faster you go in one dimension (say, x), the slower you go in the other dimensions. The dimension that's affected the most by the warping of spacetime is time (t) in most cases, because you're moving much slower in the other 3. As you go faster your path becomes less warped. This is why the faster your ball is, the less curved its path look like. This also explains why objects with zero x/y/z speed fall straight towards the object that causes the warping: only t remains from your 4 vector so you're essentially moving through spacetime with the speed of causality (light) --> you fall straight down.
- Manishearth 6y agoSo this is the core problem with all of the general relativity materials that model it as a rubber sheet causing curvature in spacetime. They always model it with focus on _spatial_ curvature: which is totally able to model an orbit or a hyperbolic trajectory as a geodesic, but it totally cannot model "throwing a ball up" since the geodesic for throwing a ball up is just a straight line. The important thing is that gravitation is a distortion in space-_time_, which is way trickier to model as a rubber sheet because you end up with one dimension of space and one of time. If you distort _those_ (also, they don't distort quite like a ball-in-a-rubber-sheet), you can get the results of a ball being thrown up. It's also possible to visualize this for 2 spatial dimensions with a distorted 3d space, but tricky.
- newobj 6y agoThis is maybe one of those most disturbing things I've ever read. I'm going to be thinking about this for a WHILE.