Do objects fall towards the center of the of the Earth because space is curved that way or because the object moves to a position where time passes more slowly.
This is going to be an unsatisfying answer, but it is best to try an not visualize is as a slope, or to even visualize it anyway as us humans really can’t think in 4D.
While analogies fail here the best way I can think of to describe it, which will also sound the most absurd is that the objects are not falling, but the that actually the earth runs into them and pushes them away from their preferred path in spacetime.
While there are other analogies and though experiments that will work, I found this model the easiest because it helps preserve the concept that a falling object, or a tossed ball, bullet or anything else on a ballistic path is actually as close to an inertial frame as you can get.
This helps map to some useful functions within Classic physics without having a crisis of faith when you run into issues assuming that the “accelerated frame” which is actually the weighted stationary frame should be the one where F=ma is true as an example.
While F=ma is still an extremely useful approximation in our 9.80665 m/s^2 standard gravity, it will become more problematic once you try to work with post-newtonian methods that work in an simpler euclidian math domain.
but remember that all visualizations of spacetime are “artists conceptions” and not indicative of the actual effects. Once you can let go of the desire to visualize the effects the math really starts to make more sense and it is far easier to calculate and predict effects.
TLDR, a falling object in a gravitational field is still closely following it’s frame’s geodesic, is is not correct to view it as falling, it is more correct to think of the massive body that is causing the curvature as running into it, as it is the divergence from the geodesic that causes the fictional force of gravity. But both of these analogies are just thought experiments and not descriptive of the fundamental realities which we humans lack the ability to visualize directly.
Username / OP combo!
I thought it was because things move towards the center of the gravitational mass?
Physics just tells you what things do. It doesn’t tell us why they do them. Any model we develop is going to be just that-- a model. If it works in describing things, and helps us predict other things, that’s all that matters. But don’t get too hung up on the model itself.
Two problems with that statement. One, gravity only points towards the center of mass for spherically-symmetric masses (or when you’re far enough away from a mass that it might as well be spherically symmetric). But one can very easily envision situations where that won’t apply. For instance, suppose you had something shaped like a dumbbell, with two equal massive spheres held apart by a long, lightweight bar: The center of mass will be in the middle of the bar, but objects will still be attracted to one bar or the other.
The other problem is that gravity doesn’t make things move down at all. It makes things accelerate down, because force is proportional to acceleration, not velocity. If you throw a ball straight up in the air and then catch it again, the ball is falling (i.e., accelerating downward) right from the moment it leaves your hand, even though it’s initially moving upwards.
To the OP, it’s an interesting question. It is in general the case that objects fall towards the places where time will pass more slowly. And you probably could mathematically re-cast General Relativity in those terms, while still being exactly mathematically equivalent to the theory we know. But I can say that I, personally, have never seen it actually cast that way.
And of course, since nobody else has mentioned it, your username happens to be rather apt for this thread.
the force between two objects is F = GMm/R2.
R is the distance between their centers of mass.
What am I missing here, Chronos?
What you’re missing is that that equation is only for spherically-symmetric mass distributions. For other mass distributions, you have to break it up into pieces that are spherically-symmetric, find the force from each, and add them up (which, for complicated distributions, will generally require calculus, which is why Newton went and invented it).
uh…
And it should be noted that even the Earth (and other celestial bodies) are not perfectly symmetric. They have both ellipsoidal and irregular shapes due to rotational movement and tidal bulges, as well as mass concentrations (MASCONS in geophysics jargon) where denser materials have welled up and solidified in the core or have impacted and flowed into the crust, forming a volume of higher than average density. This doesn’t really affect terrestrial objects to a significant degree, but it definitely affects the trajectories of ballistic objects in long term orbits or requring high precision.
In answer to the o.p., the former speculation (that the curvature of spacetime is responsible for the acceleration effects of gravity) bit that is hardly a complete answer as it begs the question of what this “spacetime” business is all about, the answer to which is really complicated but fundamentally we just don’t know. It is just the way gravity works, and while we can describe that with hig precision under most conditions, we can’t answer the questio “Why?” to the satisfaction of an eight year old.
I hope that makes everything as clear as a planetary nebula.
Stranger
Logically, it seems to me that gravity could not be expressed as an effect of time dilation because the force would become repulsive. If you look at a small spherical body tangentiallly approaching a large spherical body, the side facing the large body would be moving into a slower frame of reference than the side away from the large body. Since v=d/t, the facing side would be moving faster than the far side, so one would expect the smaller body to tend to curve away from the larger body, which is the opposite of what we see happening. In almost all cases, the difference is way too small to even think about measuring. Time dilation seems to be a side-effect of gravity, not its impetus.
That is an approximation and a very very useful one, but as the OP referenced curved spacetime, you have to be careful.
Remember that although he himself called it “Absurd” Newton assume that Gravitation was instantaneous no matter what the distance was between objects. As soon as you move into a model where Gravity is constrained by the speed of light that model will cause issues if you assume it is descriptive of the actual interactions.
First once you move to relativity, like centrifugal force, Gravity is a “Fictional Force” or an “Apparent Force” that is observed purely due to your frame of reference.
While I did create a silly PIT thread about this recently the implications are huge when trying to understand the fundamentals at work under the currently accepted theories.
While still extremely useful for most use cases, Physicists are very careful to call these “approximations” when developing Post-Newtonian simplifications. But as the Earth and other objects actually experience this force under the apparent location of a body and not the actual instantaneous location like assumed under Newtonian Mechanics it will result in serious issues with the conservation of momentum.
As an example the Earth actually reacts to the the apparent position of the Sun, or the location the sun was more than 8 min ago (due to the speed of light).
If you assume this to be an absolute truth and not an approximation even a rotating body with anything but universal density would actually experience a breaking effect as it is pulled backwards by the delayed previous position of the body. And in cases like the Earth Moon system the orbits would slow down and degrade over time.
While it is commonly claimed that relativistic corrections are not required this does not match with the practical requirements to work under limited payload sizes and while they have been selective all lunar and planetary NASA missions have leveraged relativistic corrections post 1968. Voyager as an example would have lacked the fuel to accomplish the “Grand Tour” without these adjustments.
Obviously this isn’t true for all need but here is a link to the math for the "Double-Precision Orbit Determination Program (DPODP) from JPL. This project was started less than 5 years after the US’s first space flight, and as soon as they could buy a Computer that would enable it. It was actually one of the largest computer programs of the era and was given priority over other computing efforts at JPL.
Note that once laser cooled atomic clocks were developed the limitations of the Newtonian model were causing issues for even astronomical Observations, but due to a simple to use coordinate model it was hard to move to a relativistic corrected method for more general purpose needs, but the IAU was already attempting to do so and they had formalized the model in 1991 to do so.
They officially completed the move to a relativistic corrected model in 2000.
http://iers-conventions.obspm.fr/2010/2010_official/chapter10/tn36_c10.pdf
Because JPL calculates the ephemeris there are still a massive number of use cases where the lack of precision is acceptable and the JPL produced data protects efforts from needing to directly consider the relativistic implications.
But is is important to realize that these simplified, and typically good enough Newtonian approximations are approximations.
As the speed of light or causality is far easier to conceptualize I think that people tend to forget that Newtonian gravity has to be instantaneous on a universe scale to be accurate enough to use in low precision models. But Chronos’ statements are constant with the very useful approximation while also avoiding wording which will ignore the more recent, experimentally validated models that are more accurate and a step closer to the fundamental realities.
Note that confusion here is expected, and without a unifying theory there will be differing needs, useless and claims. I personally find the habit of adding “approximation” to any phrase that includes “Newtonian” helps avoid the cognitive dissonance caused by the human tendency to confuse useful with being the best current descriptive understanding.
While unimportant for most intra-solar system needs, rotation greatly complicates this and even most people working directly in GR tend to simplify. But it may be helpful to mention the Lense–Thirring precession, where rotation of a body actually causes precession due to frame dragging. Topology may be global, but movement of massive bodies actually changes the connectivity for themselves and others.
I should note that it is particularly difficult, because some of the most favored but yet untested theoretical models like string theory really need to find invariance in these Einsteinian models to be valid, and the champions for these models may make statements that may not clarify this distinction. While I will be excited if any of these ideas are eventually found to be a more accurate replacement or find issues with the SR/GR models, they often fail to make a clear distinction between what has been experimentally verified and what the end state would be if their claims are found to be more valid.
By all means, use the simplest method available, but remember that some of these ideas have been superseded and are tools of convenience and not descriptive under the currently best tested theories. It would be wasteful and confusing to resort to more complicated models, and so to avoid the inevitable responses I need to clarify that the utility of the Newtonian models is not in question, and the the post-Newtonian method can gain most of the relevant needed corrections without resorting to 4D, non-euclidian GR calculations.
If you look at the NASA SPICE toolkit comments they will call out the most common cases where the Newtonian model approximations are good enough or when they are problematic for common use cases.
And you don’t even have to only imagine how gravity works on non-perfect spheres–deflections in Earth’s gravity can be measured near objects as small as a mountain with tools available in the 1700s.
Now that there have been some serious answers, let me add: “Gravity is only a theory, you know!” :rolleyes:
The attractive force of gravity is a “fictional force” and not even a “force” in the theory of relativity.
It is more correct to think of the path of the orbiting body as traveling in the geodesic, and it only ends up running into the spherical body if the actual geometry of that geodesic happens to intersect that body.
The IIS, or a tossed baseball is following a geodesic, and is actually following a “straighter” path than I am sitting on this chair.
The perceived force or acceleration is purely an artifact of your frame of reference.
While the theories of gravitation are not complete I hope that this response helps clarify.
Try considering that there is no acceleration or unbalanced force and it is purely a geometry of the spacetime manifold that changes and the orbiting body is traveling at a constant speed and following the geodesic.
It may seem absurd but this is why it is more correct to think of the earth running into the apple than the apple accelerating towards the earth but this is at a point where analogies will fail.
There it is! That’s the sentence I needed, the veil has been lifted on that for me, thankyou!
mc
It is a bit complicated to explain, but the form of the curvature of spacetime outside an object like the Earth and the tendency of objects to move towards positions where the gravitational time dilation effect is increased are one in the same.
I want to call out the book Gravitation which Stranger On A Train linked to here.
The book is developed into two tracks, and the first track is easily workable by just stopping and leveraging tools like khan academy when you run into math that you have forgot or need to learn. The second track takes significantly more effort as the resources are scarcer for autodidact pursuit but the first track will show you the beauty of what is understood and the mathematics you learn are very applicable to many technologies that are becoming commonly used in the computing industry.
If you are curious about this subject I highly encourage you to purchase that book and set aside time to work on it. While it will still be a challenge to describe or visualize, which will never change no matter how much schooling you have, it is well worth the effort.
While you may lack the depth required to produce new work, it will allow you to read and understand papers related to the subject at a depth that was impossible before the rise of the internet through self study.
Realize is is actually two graduate level textbooks in one, but that you can dabble in the second track when needed, while in context of the easier to learn sections of the first.
There is a reason even Mitch in “Real Genius” is using it as a pillow, is is the book to read.
I’m not knowledgeable enough to explain any of the above stuff, but I think this is a cool and applicable thing: a gravity map of the Earth, showing why stuff doesn’t fall OR accelerate towards the CENTER of this lump.
I totally missed that-- I’m going to have to keep an eye out for it the next time I see that movie.
Mitch must like his pillows awfully thick, though: MTW is bulkier even than a CRC.