[HN Gopher] Gravity is not a force - free-fall parabolas are str...
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Gravity is not a force - free-fall parabolas are straight lines in
spacetime
Author : tim_hutton
Score : 115 points
Date : 2020-10-18 21:07 UTC (1 hours ago)
(HTM) web link (timhutton.github.io)
(TXT) w3m dump (timhutton.github.io)
| mycommenthe wrote:
| if there is no force as gravity why does the curvature shape
| cause movement? why foes curve imply a movement at all?
| pininja wrote:
| The video for this page provides great context
| https://youtu.be/XRr1kaXKBsU
| c06n wrote:
| I do not understand how you can have acceleration without
| changing position (at 10:06). Acceleration is the derivative of
| speed, which is the derivative of position change. If the
| position change is zero, how can the acceleration be non-zero?
| saagarjha wrote:
| If you watch a bit more, there's another term that is added.
| Smaug123 wrote:
| Position is not an absolute notion: you need to answer
| "position with respect to what?".
|
| If the thing you're measuring position against is _also_
| accelerating, then you need to apply some acceleration of
| your own to stay still with respect to it.
|
| The terms you want to look up are "proper acceleration" and
| "coordinate acceleration". The curvature of spacetime means
| the thing I'm measuring position against is moving relative
| to me (c.f. the example of two people walking in parallel
| across the Earth, nevertheless eventually meeting: the
| curvature means that even though neither of them is measuring
| an acceleration, nevertheless they are accelerating towards
| each other), so I need to have some internal ("proper")
| acceleration of my own to counteract the fact that our
| geodesics are moving away from each other.
| umvi wrote:
| Great Veritasium video.
|
| So some flat earth arguments are actually correct if general
| relativity is correct, namely that gravity is an illusion and
| that the real reason we are stuck to the earth is that the
| earth is accelerating toward us at 9.8 m/s^2
| vbezhenar wrote:
| I don't understand it. How can it accelerate towards anyone
| on its surface? Where does it get energy to accelerate? We
| generally need to burn fuel to accelerate something in the
| space.
| nobody9999 wrote:
| My understanding of General Relativity[1] is that mass
| distorts space-time, so an object traveling in a "straight
| line" through distorted space-time will curve with that
| distortion.
|
| If the object's velocity isn't enough to traverse the
| curved space-time, it will move toward the center of the
| mass generating the distortion and fall out of the sky.
|
| If the object is traveling quickly enough, it can continue
| traversing the distorted space-time and orbit that mass.
|
| If the object is traveling even more quickly, it will
| traverse the distorted space-time and continue on without
| orbiting the mass.
|
| In all three cases, from the perspective of the object
| traversing the distorted space-time, it continues to travel
| in a straight line, as it's the space-time that's
| distorted.
|
| A (flawed) analogy would be riding a bicycle between the
| peaks of two identically sized hills. Starting at the top
| of the first hill, you coast down increasing your velocity.
|
| Once you reach the bottom of the first hill and head up the
| second, your velocity decreases.
|
| If your velocity at the bottom of the first hill is too
| small, you'll go up the second hill and as your velocity
| reaches zero, you roll back toward the bottom of the hill.
|
| You will pick up velocity and then roll back up the first
| hill, then down again, then back up the second, etc. until
| you end up stopped at the bottom of the hill. This is akin
| to falling to the center of the distorting mass.
|
| If your velocity is high enough to carry you back up to the
| top of the second hill and then stop, you'll roll back down
| and get to the bottom with the same velocity you had coming
| down the first hill. You'll then oscillate between the tops
| of both hills. This is akin to orbiting the mass.
|
| If your velocity at the bottom of the first hill is enough
| to carry you _past_ the top of the second hill, you 'll
| just keep going after reaching the top of the second hill.
| That's akin to flying by the mass.
|
| It's a flawed analogy, because in a curved space-time the
| directional portion of the motion vector doesn't change.
|
| As John Wheeler[0] simplified it: "Mass tells space-time
| how to curve, and space-time tells mass how to move."
|
| [0] https://en.wikipedia.org/wiki/John_Archibald_Wheeler
|
| [1] https://en.wikipedia.org/wiki/General_relativity
| umvi wrote:
| "in curved spacetime, an object needs to accelerate just to
| stay still"
|
| I don't really understand why, that was just the
| explanation Derek gave.
| Smaug123 wrote:
| This amounts to a confusion over notation: "proper
| acceleration" (e.g. as measured by an accelerometer) vs
| "coordinate acceleration" (the acceleration an observer
| observes an object to be undergoing).
|
| The acceleration an observer sees you undergoing is the
| same as the inherent "proper" acceleration you're
| undergoing, minus the acceleration of their coordinate
| frame with respect to yours. For me to stay still with
| respect to you, if you're in a frame that is accelerating
| away from me, I need some proper acceleration to catch up
| and counteract the fact that our frames are diverging.
| But if spacetime is curved, your frame _probably is_
| accelerating relative to mine - c.f. the example on the
| Earth 's surface, where our frames inexorably accelerate
| towards each other as we move parallel to each other. So
| for me to stay still with respect to you, I need to have
| some proper acceleration to balance out the coordinate
| acceleration derived from the fact that our frames are
| moving in a curved space.
| avmich wrote:
| A pretty good model. Thank you.
|
| The model shown is for 1D space and 1D time, and this 2D
| spacetime is curved, remaining 2D. Can you though show us a 3D
| model of curved 2D spacetime? Maybe as a rotatable, scaleable 3D
| scene, where more complex phenomena, like planetary motion around
| a star, would be possible to show?
| GuB-42 wrote:
| My enlightening moment about general relativity: apples do not
| fall on the ground, instead, the earth is inflating, and the
| inflation of the earth is accelerating at 9.8 m/s^2. Eventually,
| the ground catches the apple.
|
| Of course, you are going to tell me that the earth is not
| inflating, obviously, because it is still the same size after so
| many years.
|
| But here is the trick: the earth is inflating at the same rate as
| spacetime contracts. If the earth didn't inflate, the contraction
| of spacetime would have collapsed it into a black hole.
|
| Note: It is related to Einstein's elevator thought experiment.
| Here, the inflating earth replaces the rocket powered elevator.
|
| Note 2: If the idea of an inflating earth bothers you, I suggest
| you start considering that the earth is flat, seriously! Flat
| Earthers took Einstein's thought experiment quite literally and
| consider the Earth to be a disk that is continuously accelerated
| upwards. And in fact, if free fall trajectories were parabolic,
| that would be the correct explanations. In reality, because the
| earth is not flat, free fall trajectories are elliptic, though it
| is only apparent on a large scale.
| crazygringo wrote:
| I'm curious, how does the "gravity is not a force" viewpoint
| relate to the hypothesized graviton particle [1]?
|
| Are they incompatible viewpoints, or just different perspectives
| on the same thing?
|
| [1] https://en.wikipedia.org/wiki/Graviton
| xixixao wrote:
| You might enjoy my special relativity interactive illustration:
| https://xixixao.github.io/cheetah-paradox/
|
| Play with the accelaration to see some spooky seemingly faster-
| than-light movement.
| TheRealPomax wrote:
| someone watched verotasium...
| didibus wrote:
| I'm a bit confused, how does a 2D graph with a curved X axis
| work?
|
| Does this just mean to say that if we saw things distorted with
| an outward curve, then something that is moving in a curve would
| look to be moving in a straight line?
|
| And what's the point of such an observation?
| aeternum wrote:
| The polar or cylindrical coordinate systems are examples of
| graphs that can be though of as having a curved x-axis.
| [deleted]
| layoutIfNeeded wrote:
| How would periodic "free-fall" motion look in this setup? E.g. a
| point mass orbiting around a body, or a point mass oscillating
| back and forth in a 1D gravity well.
| jdmichal wrote:
| In the left-hand image, an orbit would be a horizontal line,
| because it's a constant distance. So it's a mirror of the time
| axis, but translated upwards in space. It would be exactly the
| same axis-mirroring translation in the other images. So,
| importantly, it would _not_ be a line in the right-hand image.
| bweitzman wrote:
| The concept of a constant distance orbit doesn't make much
| sense in 1D. A horizontal line in this model wouldn't
| indicate an orbit, but rather a completely stationary object.
| It would then make sense for the world line to curved because
| it must be accelerating in order to resist the attraction of
| the body it's near.
|
| By definition, the world line of a stable orbit would be a
| line in curved spacetime.
| xaedes wrote:
| This has some visualizations of space time curvature where you
| can get a sense of the lines particles take in different
| circumstances: http://www.relativitet.se/Webtheses/lic.pdf
|
| I tried to explain it with words, but I guess the images are
| worth more than I could write..
| tim_hutton wrote:
| With two space dimensions and one time dimension (2+1), an
| orbit in Newtonian physics is a helix. In general relativity
| that same helical path would be a straight line in an
| interestingly curved spacetime.
|
| Likewise I guess for the 1D gravity well case, where a sine
| wave would become a straight line in spacetime.
| frutiger wrote:
| True gravitational force is something that can't be transformed
| away by an arbitrary choice of frame (even an accelerating one).
|
| As a brief example, consider two objects in downwards free fall
| toward the centre of some massive object. Since they head towards
| the centre, in a free falling frame the two objects actually get
| closer to each other until they collide as they reach the centre.
|
| This is known as the tidal effect of gravity and is the actual
| physical content of general relativity. This effect can be shown
| to be obtained by an appropriate curvature of spacetime which
| itself can be shown to be related to the stress-energy of matter
| inhabiting spacetime.
| freshhawk wrote:
| "If you and a friend started walking straight north, both at
| the equator but a long distance apart, you would gradually get
| closer to each other until you collided at the north pole."
|
| I always thought that was a nice way to drop one dimension down
| to get the intuition. To the metaphorical 2D ant they see two
| friends attracted to/falling towards each other, but they are
| going in a straight line on a curved surface and there are no
| forces at play.
| didibus wrote:
| I'm super layman in all this, but I think the word force here
| refers to the Newton's force. Which experimentally was shown to
| not properly predict the effect of gravity, where as seeing
| gravity as a distortion of spacetime instead of as a
| acceleration force applied to the objects, did predict
| accurately the trajectory in experiments.
|
| You can call both a force in the generic dictionary definition
| of force. Because obviously it's crazy that something can be so
| powerful as to distort spacetime itself. But gravity wouldn't
| be a force in the Newton sense of being something that affects
| the acceleration of an object.
| rokobobo wrote:
| It's been some time since I studied these things, but I believe
| the post was trying to illustrate that the geodesic lines in
| spacetime created by Earth's gravity field can be visualized as
| straight lines after a nonlinear change of the coordinates
| system. [1] To simplify, these are the lines along which
| particles move when no outside force is exerted on them--again,
| considering gravity to be a distortion of spacetime and not a
| force, very much like the well-known metaphor of steel ball on
| a rubber sheet, which would curve marbles towards the "well"
| it's created in the sheet. But you're right that once the
| marbles and the steel ball get to a point where one of the
| gravitational fields cannot be ignored, this framework becomes
| less useful.
|
| [1] https://en.wikipedia.org/wiki/Geodesic
| dreamcompiler wrote:
| I take your point, but I think the author's main point was that
| because objects in free-fall merely follow spacetime geodesics,
| it makes calling gravity a "force" a little bogus, at least
| compared to the other forces. Tidal effects don't change that;
| tidal effects mean the spacetime curvature "over here" is
| different than the spacetime curvature "over there", which
| means the principle of equivalence isn't true in a global
| sense. But objects still follow spacetime geodesics, which is a
| concept that's hard to reconcile with the notion of a "force."
| shireboy wrote:
| I saw this and the related Veritasium video, but am still
| scratching my head about something. Does this mean that away from
| all gravity a body does not experience any time? ie a person on a
| spacecraft stopped in intergalactic space would not age relative
| to persons on planets?
| willis936 wrote:
| It's not that the absence of gravitational fields slows time up
| relative to observers in more massive reference frames, it's
| that the presence of gravitational fields speeds up time
| relative to observers in other reference frames.
|
| You would age about the same as you would in microgravity. You
| could get closer and closer approximations by going into Earth
| orbit, solar orbit, and galactic orbit. Each approximation has
| less gravity, so time would pass slightly slower relative to an
| Earthly observer at each step, but the effect diminishes.
| chrisseaton wrote:
| How do you get away from all gravity? Aren't you subject to
| gravity from all other matter in the universe at all times?
| nobody9999 wrote:
| >How do you get away from all gravity? Aren't you subject to
| gravity from all other matter in the universe at all times?
|
| Yes. But the effect of the distortion of space-time that we
| call "gravity" is subject to the inverse square law[0].
|
| This means that, as Newton described: "The gravitational
| attraction force between two point masses is directly
| proportional to the product of their masses and inversely
| proportional to the square of their separation distance. The
| force is always attractive and acts along the line joining
| them"
|
| As such, while objects are affected by the distortion of
| space-time, the effect is diminished (but not eliminated) by
| increased distance from the mass that's distorting space-
| time.
|
| Or at least that's how I understand it.
|
| [0] https://en.wikipedia.org/wiki/Inverse-square_law
| chrisseaton wrote:
| > but not eliminated
|
| So... you can't get away from it. That's what I said isn't
| it?
| nobody9999 wrote:
| Yes, you did. However, it depends on how you define
| "getting away" from it.
|
| At some point, the effect is so small that it either
| can't be measured or even if it can, the effect is so
| small that any impact is irrelevant in practical terms.
|
| If that's the case, you're _effectively_ "getting away"
| from it.
|
| I guess it's a matter of perspective.
| montagg wrote:
| I believe (from my limited knowledge from _Interstellar_ ) that
| it's the opposite: higher gravity environments move slower
| relative to lower gravity environments, which enabled the "go
| down to high gravity planet for a couple hours and come back
| and it's ten years later" plot point in the movie. So if you're
| in intergalactic space, time is actually passing very quickly
| in the higher gravity environment of a galaxy.
|
| But a person's experience should always be the same, no matter
| what reference they are in. They will perceive time as passing
| at the same rate in all environments, but it will be different
| from people in other environments.
|
| Caveat: IANA physicist, and this is not physics advice.
| kubanczyk wrote:
| > So if you're in intergalactic space, time is actually
| passing very quickly in the higher gravity environment of a
| galaxy.
|
| Not "very". Look up the actual equation, it's a really easy
| one. AFAIR for a standard stellar black hole, you'd need to
| be within _meters_ from the event horizon to get any
| substantial time difference.
|
| Thus the implication that Interstellar's Gargantua was an
| SMBH, i.e. probably the center of it's galaxy.
| umvi wrote:
| I don't think that is quite right. If you travelled near the
| speed of light and then slowed down again it would look (from
| your perspective) like you jumped 10 years into the future.
| So high gravity environments "moving slower" shouldn't result
| in a jump to the future upon exit.
|
| Instead I think what is happening is that massive objects
| actually stretch the fabric of spacetime somehow so that the
| closer you are to the object, the slower you travel through
| both space and time. And the more massive the object, the
| more stretched space and time become as you get closer to it.
|
| Hence if you go near a very massive object, from an outside
| observer it looks like you are frozen in time because time is
| so stretched it takes forever for you to move through it.
|
| As you mentioned though, from any given frame of reference
| time will always feel the same. 1 second will always feel
| like 1 second.
| vecter wrote:
| _> the slower you travel through both space and time_
|
| No. You are always traveling at a constant velocity through
| spacetime.
|
| [0] Spacetime: https://en.wikipedia.org/wiki/Spacetime
| a3w wrote:
| Somewhere I read that a free fall parabola does not even take
| into account earth's curvature. Although I cannot remember, what
| kind of function describes the reference system specific ``path,
| as a function of time''.
|
| Could this be named more correctly: Gravity is not a force -
| free-fall hyperbolas are straight lines in spacetime
| (timhutton.github.io) ?
| kubanczyk wrote:
| The planet's curvature is not very relevant to the article,
| but, yes, if an object is in a free fall at a slow speed (I
| mean non-orbital) its trajectory is:
|
| - parabola if you assume flat&infinite ground,
|
| - ellipsis if you assume a spherical planet (an ellipsis is
| crossing the planet's surface).
|
| This is Newton, not GR.
| dreamcompiler wrote:
| Yep. Orbits are always conic sections. Which sometimes
| inconveniently intersect with the surface of the thing being
| orbited.
| j1vms wrote:
| Gravity is not a force. The surface of the Earth is moving up to
| the object in free-fall at an acceleration of 9.8 m/s^2. The
| force pushing the surface, and the pressurized atmospheric shell,
| upward is a result of the processes occurring within the Earth
| (likely, in particular, those within the the core).
| colordrops wrote:
| How is it not a force though? Regardless of curvature, a starts
| moving if you let it go without applying any force. Curvature
| alone can't account for that could it?
| doomrobo wrote:
| When you are at rest on the surface of the earth, you're
| actually accelerating. I barely understand it but veritasium
| explains it in the newest vid
|
| https://youtu.be/XRr1kaXKBsU
| saagarjha wrote:
| In general, it is convenient to assume that forces exist.
| However, the model presented here shows that you can instead
| dispense of the need for there to be a force and show that the
| apparent acceleration is just the object moving along its
| curved path in spacetime. You could consider it as if the
| curvature itself making it look like there are forces.
| tim_hutton wrote:
| An object at rest is still travelling through time. In fact it
| continues to travel at the same speed through spacetime when
| you let it go. It's just that spacetime is distorted such that
| the straight line takes it across space too, as seen in the
| inertial frame on the right.
| gilgoomesh wrote:
| The falling object doesn't accelerate. You, standing on the
| ground are the one that's accelerating. You see the object as
| accelerating but that's an illusion due to frames of reference.
|
| As evidence: which object feels a force on it?
|
| You can feel the force the ground continually pushes up at you.
| The ground is accelerating you up. The falling object is
| completely idle in its inertial frame and feels nothing.
| Smaug123 wrote:
| 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.
| mytailorisrich wrote:
| > _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 wrote:
| Could you elaborate on why it's false?
| sohkamyung wrote:
| Off 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-a...
| Smaug123 wrote:
| Good 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 wrote:
| Despite 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.
| dmurray wrote:
| A good point to make, but if one is going to be that pedantic
| one shouldn't call it "impossible". A parabola is _possible_
| with the right wind, air resistance, gravity from nearby
| mountains, etc, and in practice those have a larger impact on
| almost any suborbital projectile than the difference that
| turns the trajectory from a parabola to an elliptical arc.
| saagarjha wrote:
| Speak for yourself. _My_ balls reach escape velocity and then
| make corrections to assume e=1.
| fouronnes3 wrote:
| It's a parabola in a uniform gravity field, an ellipse in a
| circular gravity field coming from a point mass.
|
| So if you want to be _really_ pedantic, it 's never an
| ellipse because the Earth is not a point mass. It would be
| equivalent to a point mass if the Earth were a perfect sphere
| of uniform density, but it isn't. In reality it's a potato
| like mass blob that's approximated by what geodesists call
| the "geoid". So in order of approximations the path of a ball
| thrown on earth is a parabola -> ellipse -> numerical
| integration of 6-dof initial conditions and spherical
| harmonics approximation of the earth gravity field.
| centimeter wrote:
| > it's never an ellipse because the Earth is not a point
| mass.
|
| At least classically, a sphere is indistinguishable
| (gravitationally) from a point mass while you're outside
| it. The earth is pretty sphere-ish, locally speaking.
| libraryofbabel wrote:
| > The earth is pretty sphere-ish, locally speaking.
|
| Kinda. There are mountains, they have their own
| gravitational attraction, and it can be measured... even
| in the 18th century!
| https://en.m.wikipedia.org/wiki/Schiehallion_experiment
|
| It all depends on how pedantic one wants to be :)
| perl4ever wrote:
| The first time I heard of the concept, it wasn't actually
| that, it was how in the 60s, they had to correct for
| mascons in the moon while orbiting.
| Tyr42 wrote:
| And a ball thrown in the air follows a parabola, locally
| speaking. At least, you're better off correcting for air
| resistance before you sub in the ellipse equation.
| avmich wrote:
| Spherical mass can be replaced with a point mass. Earth
| however is not spherical (biggest deviation is polar
| flattening). And even then, Einstein's model, unlike
| Newton's, says it's not an ellipse even for a point mass.
|
| So, moral of the story - we have to be not too pedantic.
| dreamcompiler wrote:
| I 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 wrote:
| Curvature due to gravity does not depend on mass, which is
| kind of hinted at when mass cancels in F=ma for that force.
| phkahler wrote:
| I'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.
| jeremyjh wrote:
| Light is moving so much faster. In the same two seconds it
| crosses a much larger distance in space.
|
| The line is only straight in spacetime, not in space.
| Ancapistani wrote:
| If I'm understanding, a theoretical ball thrown at 1c would
| follow the same path as a photon?
| Smaug123 wrote:
| Yes, although you can't actually get anything with mass
| to travel at 1c (subject to our current understanding of
| physics).
| maxcan wrote:
| They both follow straight lines but unless you have a really
| really really strong arm, the baseball is "moving" across far
| more time than the ray of light. So if it "experiences" much
| more gravitational effect from the larger swath of space time
| it covers.
|
| Using quotes since terms are more metaphorical than exact.
| umvi wrote:
| The 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.
| atoav wrote:
| This is in tune with what happens when you change the timescale
| in a game engine with proper physics.
| grenoire wrote:
| I think this is more of an integration method error than an
| analogous case.
| paulpauper wrote:
| >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.
| vikramkr wrote:
| When 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...
| Smaug123 wrote:
| I assert that if you throw a ball upwards in a vacuum chamber
| on Earth, it will in fact still fly in a parabola.
| mrfusion wrote:
| Are we flat in the time dimension? Or what is our time size?
| Retric wrote:
| It'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 wrote:
| I'm reminded of the film _Donnie Darko_ , but I won't say
| more as to not spoil anything for anyone.
| ithkuil wrote:
| "All tragedies are finished by a death, all comedies by a
| marriage." --Lord Byron
| vbezhenar wrote:
| Are we moving through time with constant speed? Or we're
| constantly accelerating through time?
| Smaug123 wrote:
| Under 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 wrote:
| And 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 wrote:
| Axes being parallel by whose point of view?
| moron4hire wrote:
| I've always intuitively understood this to be the reason
| why it would take infinite force to achieve light speed for
| a massive object. When we apply a physical force, it is
| applied in the spatial axes, so it is always perpendicular
| to the time axis. Acceleration is just rotating some
| magnitude of your fixed velocity vector out of the time
| axis and into the spatial axes. When your spatial velocity
| is apparently zero, then the component of force that is
| perpendicular to your velocity is large, so you achieve a
| large deflection. But as you rotate velocity out of time
| and into space, it becomes more perpendicular to time, so
| any force applied perpendicularly to time has a smaller
| component perpendicular to one's velocity.
|
| This is also why you can't travel backwards in time through
| just acceleration. There is no way to impart a force
| perpendicular to your velocity vector when it is already
| perpendicular to time, giving you no way to rotate the
| vector to have a component that points backward in time.
|
| So I've always wondered, whether general relativity allows
| for forces parallel to time, and we just don't know of any
| mechanism to actually do so, or if it does not cover such
| cases because we have no mechanism, or if it disallows it
| entirely.
| cylon13 wrote:
| We're moving through spacetime with a constant speed, so the
| faster you move through space, the slower you move through
| time.
| Ancapistani wrote:
| I still don't understand the graphs at the link, but this
| intuitively makes sense to me. Thank you - I now have a
| new, apparently accurate mental model of relativity.
| [deleted]
| nimish wrote:
| Gravity is a force in the same way the centrifugal force is a
| force
|
| An artifact of rotating coordinate frames in one, the curvature
| of spacetime in the other
| tiffanyh wrote:
| I think you mean _centripetal_ force.
|
| https://www.diffen.com/difference/Centrifugal_Force_vs_Centr...
| nimish wrote:
| No I mean centrifugal. It's a fictitious force, an artifact
| of choosing a rotating non inertial coordinate frame.
|
| Gravity arises similarly, by being in a non inertial frame
| induced by mass energy
|
| https://en.m.wikipedia.org/wiki/Fictitious_force
|
| This was the key insight behind Einstein attempting to get
| general relativity working.
| willswire wrote:
| Veritasium just put out a great video on this:
| https://www.youtube.com/watch?v=XRr1kaXKBsU
| avmich wrote:
| A great video :) . Makes you wish he'd include more
| explanations of mathematical details...
| ars wrote:
| Would not an electron and a positron trace out an identical
| line/parabola?
|
| Would that mean electromagnetism is not a force either?
|
| What is the difference between the two that makes one a force and
| one not a force?
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