Gravity is not a force – free-fall parabolas are straight lines in spacetime(timhutton.github.io) |
Gravity is not a force – free-fall parabolas are straight lines in spacetime(timhutton.github.io) |
It's not a fundamental problem, nobody has abandoned Maxwell's equations for EM except for the most specific cases, but it's a similar case.
There's probably a better explanation than just "distortion of space time" which is a great way of viewing it, but it's a bit of a stretch (pun intended)
F means force. Gravity is a type of acceleration, not a force without being multiplied by a mass!
I tried to explain it with words, but I guess the images are worth more than I could write..
By definition, the world line of a stable orbit would be a line in curved spacetime.
Likewise I guess for the 1D gravity well case, where a sine wave would become a straight line in spacetime.
[0] https://www.youtube.com/watch?v=XRr1kaXKBsU&t=504 (Veritasium on Youtube: Why Gravity is NOT a Force @ 8:24)
but the real question is: can you counter your own arguments? Because that's where absolutely fascinating science happens.
(also nice engineering on the physical "space time stretcher" he built)
I understood it rationally before, but only with this video it also feels right.
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?
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.
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.
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.
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.
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.
https://www.audible.com/pd/Black-Holes-Tides-and-Curved-Spac...
I want left to be 0 frame acceleration and left to be backwards in time. I kind of also want the graphs to be reverse order too, but I get why it's all presented this way. :)
I won't push my luck by pretending to understand how this changes when your spatial velocity is nontrivial (intuitively I feel like it should not even possible to differentiate between spatial and temporal components except relative to your own reference frame, but I could easily be wrong there). But in the case you describe it seems pretty clear.
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?
In f = m * a, for objects falling from sky, it will be f = m * g where g is gravity, m is mass & f is force
Sorry, I think I am missing the point of the article.
Another good video to visualize GR is this by ScienceClic: https://www.youtube.com/watch?v=wrwgIjBUYVc
How is gravity like a force at all, even in Newtonian physics? It seems like mismatched units. Gravity is an acceleration, not a force. F=ma, right? So if gravity were a force, it would produce an acceleration that was dependent on the mass, and it doesn't, so it seems to me like the only sense in which gravity is a force is if you define force as "something you can't see that makes things move", which is a pretty useless definition.
For two different objects at the same point in the same gravitational field, the difference in gravitational force due to their differing mass exactly cancels out the difference in acceleration due to their differing mass, so they both accelerate at the same rate.
My point is that it really seems like "gravity" is not a force, it's an acceleration, but there is something you could call "force due to gravity" that you reverse-engineer from the known acceleration, and that means you need to multiply by the mass. Clearly different masses will just cancel, so the resulting acceleration is the same.
I'm fine with saying "force due to gravity" or even "gravitational force". Which is what you're describing in your first sentence, and I have no disagreement with that. "Force of gravity" starts to sound a little off, and I bet if I ask "what is gravity at Earth's surface?" I'll get back "9.8 m/s^2", which is an acceleration not a force.
Since gravity acts in a magnitude directly proportional to the mass being acted upon, it just so happens that it manifests as an acceleration since the mass cancels out, unlike EM where acceleration due to charge does not cancel out the mass.
An artifact of rotating coordinate frames in one, the curvature of spacetime in the other
I'd be very sad if we had to lose that and deal with gravitons.
https://www.diffen.com/difference/Centrifugal_Force_vs_Centr...
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.
- when you stand on the ground you are the subject of 2 forces: gravitational force m * g and the opposite reaction force of the ground surface, they cancel each other so you stand still
- when you free fall your acceleration is g and the gravitational force is m * g, this is according to Newton's 2nd law
when you hit the ground depending on your velocity and... deformation, the force of impact will be different because you will de-accelerate to 0 or even bounce back very quickly much faster than g. It's gonna be much stronger than g * m
I don't see how. A "force between two bodies with a magnitude proportional to the product of their masses and inversely proportional to the square of the displacement between them" seems no different in principle from a "force between two bodies with a magnitude proportional to the product of their electric charges and the inversely proportional to the square of the displacement between them".
My point is that it really seems like "gravity" is not a force, it's an acceleration, but there is something you could call "force due to gravity" that you reverse-engineer from the known acceleration, and that means you need to multiply by the mass. Clearly different masses will just cancel, so the resulting acceleration is the same.
We're talking Newtonian physics, a model of the world where an acceleration is the result of an unbalanced force applied to a mass. You don't have to "reverse-engineer it from the known acceleration", you can calculate it as Gm₁m₂/r².
I'm fine with saying "force due to gravity" or even "gravitational force". Which is what you're describing in your first sentence, and I have no disagreement with that. "Force of gravity" starts to sound a little off, and I bet if I ask "what is gravity at Earth's surface?" I'll get back "9.8 m/s^2", which is an acceleration not a force.
You can equally describe the magnitude of the gravitational field as 9.8 Nkg⁻¹.
So... you can't get away from it. That's what I said isn't 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.
No. You are always traveling at a constant velocity through spacetime.
[0] Spacetime: https://en.wikipedia.org/wiki/Spacetime
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.
> 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...
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.
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?
dist^2 = (c * seconds)^2 - meters^2
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.
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.
Using quotes since terms are more metaphorical than exact.
Because they're following different straight lines in spacetime. Roughly speaking, if you pick a point in space and a particular direction in space from that point, there is a continuous infinity of possible straight lines in spacetime that point in that direction in space. One endpoint of that continuous infinity is the worldline of a light ray. The ball's path is somewhere in the middle of that continuous infinity.
From the reference of the outside observer the light emitted at the event horizon will forever try to leave it, but as spacetime itself casdades into the hole at the speed of light (at the horizon) this light will get redshifted until you can't see it anymore. This doesn't mean that the light you shoot into the hole never reaches the singularity. It just means that the light emitted at the event horizon will struggle forever to get out of the insane warp. Think about this: if you're walking on a conveyor belt with a constant speed `n` in the opposite direction and the belt itself is moving with a constant speed `n` you'll never make progress. This is what happens at the event horizon.
Light beams are not reversible. If you use a mirror they won't travel back in time, they will just change course. They will never go back in time.
Because light is much faster. Throw a ball at the speed of light and you will see exactly the same path.
Lets say you shoot rifles with different calibers. Each time the bullet takes one second to hit the ground but the faster bullets travel longer distances. Light is so fast it escapes from the planet but if the planet were big enough even light would hit the ground like a bullet.
The line is only straight in spacetime, not in space.
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.
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.
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.
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.
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.
—Kurt Vonnegut, Slaughterhouse-Five
The best way to picture it is via Minkowski diagrams, you can find some neat visualizations in the wikipedia article: https://en.wikipedia.org/wiki/Relativity_of_simultaneity
Simply picture an extended object in the x direction, Lorentz transformations are going to rotate it slightly in the time direction causing it to become extended in the time direction.
[1] If you take it to the extreme you may consider that different parts of your body move with respect to each other and thus they are not in the same reference frame. In which case, not even with respect to yourself are totally "flat" in the time direction.
299,792,458m is for the distance traveled by light in one second. The -1m is for the distance between your feet.
That's just another way of describing the total time you exist.
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
Probably not, because "the sun" appears in your response. If you're watching a ball move on Earth, the sun is an irrelevant variable.
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.
So you can change your acceleration through the time dimension of spacetime, by dint of changing your acceleration in the spatial ones.
But because massive objects also cannot move as fast as photons, we're probably both saying the same thing from two different perspectives.
I suspect that the answer is that this is a false comparison.
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.
Also, like everything else in physics: it depends how you observe it.
For instance, electromagnetism comes from the curvature of a U(1) bundle over space time, the (local) U(1) symmetry yields electromagnetic interactions. For gravity the symmetry is the (local) Pointcaré (SO(1,3) + translations) symmetry and curvature of spacetime itself.
Also gravity on Earth (weak gravitational field) is mostly curvature of time, namely the spacelike curvature can be ignored, and the g_{00} component of the metric can be seen a a gravitational potential. see p 80 of this:
Why does the existence of a transformation that makes movement under a supposed force actually follow a straight line mean it's not really a force? For the other forces (e.g. electromagnetism) can we say that there's _no way_ to exhibit a transformation that causes charged particles travel on "straight" lines?
Not that I'm afraid of math, I just don't feel like I need to see equations when it's a concept that is being explained rather than how to numerically calculate something. Math helps me as much as a code implementation does to explain the concept of a variable: I can observe its behavior but it doesn't necessarily teach me the concept.
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.
Are they incompatible viewpoints, or just different perspectives on the same thing? (E.g. are gravitons hypothesized to disappear depending on frame of reference?)
I'm assuming they're incompatible (that we need the theory of everything [2] to reconcile them) but would love to know if there's something I'm missing.
Interestingly the Yang-Mills equations (used in quantum mechanics) and the Einstein-Hilbert action (used in general relativity) are pretty much identical if you use general enough mathematics.
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.
I had never visualized it this way in my head before, and it all makes a lot more sense now. Highly recommend!
Reminded me of the arguments still going on about ‘whether this is true or not’ in the sense that the mathematics is painting this more accurate picture than what Newton’s math painted, but the math can’t explain most of the universe’s lack of observable mass/energy, so there might be some higher level of mathematics that describes a different but ‘more true’ state of events.
The inconsistency points towards an actual type of matter as opposed to systematic error.
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.
The surface of the Earth keeps you from actually falling in, and is therefore pushing you away or upwards from the center. This is the acceleration acting on your straight line path through curved spacetime. This is the deviation from your geodesic.
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
Light always travels in straight lines. Even when light is experiencing a gravitational lensing and looks to us from earth that it's bending around a star or whatever, from the perspective of the light beam itself, it's moving in a straight line. It's entire reference frame is bent compared to ours (relativity) but nonetheless the correct view is that the light is still moving 'straight' in it's own reference frame.
Also if the light wasn't moving straight that would mean it's changing direction, which is the same as an acceleration, and a beam of light traveling thru a gravitational field feels no acceleration, because it's not accelerating. Again from this view you can say light is moving straight and experiencing no acceleration, just like an object in free-fall doesn't 'feel' any acceleration, even though they are accelerating from the perspective of some other reference frame other than it's own.
You could have both a deviation (i.e tangential acceleration) and a constant speed.
One bearded sage concluded: there's no motion.
Without a word, another walked before him.
He couldn’t answer better; all adored him
And all agreed that he disproved that notion.
But one can see it all in a different light,
For me, another funny thought comes into play:
We watch the sun move all throughout the day
And yet the stubborn Galileo had it right.
Both are right, in short. We observe parabolas and we are right counting on them - we have great successful experience using these prediction. GR theory predicts lines, they are right too, but in different context.
Play with the accelaration to see some spooky seemingly faster-than-light movement.
The title says "gravity is not a force". In the article's perspective, why does a kitchen scale report a higher number when I place an object on it?
(In my perspective there is gravitational attraction between the object on the scale and the rest of the Earth, and the the scale, assuming it is "level" (set perpendicular to the direction of gravitation toward the center of the Earth) reports the magnitude of that attraction.)
If gravity isn't a force, then when the object and Earth are not in freefall or moving, what does the kitchen scale measure?
https://www.youtube.com/watch?v=cb_PCuv0vcY&feature=emb_logo
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?
The indicator that gravity is special is the fact that 'inertial mass' and 'gravitational mass' are the same thing.
That's undecidable and gravity is not special in that way
https://physics.stackexchange.com/questions/390540/what-is-t...
> the gravitational field and acceleration are inductive pairs (similar to the electromagnetic field and electric current.)
Light is without mass, but not without energy. That energy causes what you could describe as "propulsion". Even the slightest bit of propulsion in the emptiness of space will cause matter to move around.
It's like light being a big ladle. And using that ladle to spin the water + tiny floating objects in a bath. They will all affect one another until the heat death of the bath occurs and all life grinds to a halt.
Could this be named more correctly: Gravity is not a force – free-fall hyperbolas are straight lines in spacetime (timhutton.github.io) ?
- 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.
I'm trying to understand what is meant by this. When I drop an item on the floor it goes there in a straight line, not a parabola. Same if I drop something from a helicopter. Obviously I'm missing something here. Can someone with more insight ELI5 this to me please?
That could be a physical dimension, such as throwing a ball to your friend across the room and plotting x vs y. Or even plotting the height of the ball against time.
consider the x-axis of this image the distance between you and your friend, or time.
However, that concept is not available in arbitrary manifolds, you need additional structure: The covariant connection, which allows you to parallel transport velocity vectors, enabling you to define the concept of straight lines (autoparallels, which will be geodesics if the connection is 'metric').
According to general relativity, gravity hooks into that. So from that perspective, the gravitational force on a test particle will be a consequence of (the generalization of) the first law instead of the second one, making it into a pseudo-force like the Coriolis force.
but if you introduce a derivative which is covariant under diffeomorphisms and u(1) transformations
D = d + \omega + A
you see that gravitation (connection \omega) enters on a somewhat same footing as the electromagnetic potential (A). there are nuances ofc, but the view (force/curvature) depends from where you're looking.
also in real life particles don't real exist... they're excitations in a field
1) it still somehow works like other fundamental forces since it derives from asking invariance under a local symmetry group
2) it is different from other forces since the symmetry group associated to it is directly symmetries of space-time (rather than some internal U(1) vector bundle like maxwell or SU(3) nuclear strong force)
3) in weak fields like on earth it mostly reduces to a conservative force driven by a gravitation potential (what you experience while climbing a mountain)
3 bis) like (mostly) anything in physics there is a duality i.e. there are regimes where you can consider it as a force, and there are regimes where you cant.
read the textbook, i know it's a 1000 pages but it's a great introduction :)
Also in the paper:
"In a certain sense the main effect of curvature (or gravity) is that initially paralleltrajectories of freely falling non-interacting particles(dust, pebbles,. . . ) do not remainparallel, i.e. that gravity is an attractive force that has the tendency to focus matter."
Maybe don't immediately look for ways to discredit someone's contribution to the discourse without examining all of the content they have shared?
Like Sean Carroll said in the Veritassium video about the "many worlds" [1], there's no such such thing as "pressure", it is just the interaction of fluid molecules. For practical purposes though, it is best described as a scalar called "pressure".
"best described as not a force" is not the same statement as "is not a force".
In physics and mathematics there can be multiple different, complementarity descriptions of the same thing. In fact, if you can reach the same result by two very different routes that seems to make it more robust.
A simple example to understand how perspective can alter reality is to imagine being a point floating in a 3-D space where you are able to see the X-Y-Z axes. Now, imagine tracing (0,0,0) when you are at (500,500,500). Trivial.
Now, trace (0,0,10^100). That is a huge Z-line you would say. This is the side view.
Now, move to (0,0,10^100) from (500,500,500). This is the top view. What do you see?
Another example: When viewed from perpendicular to X-Y plane, a circular motion on X-Y plane looks properly circular.
When the same motion is viewed standing far away on the X-axis, the motion resembles an oscillation.
Same motion, different perspectives, seemingly different results.
Isn't gravity an acceleration, and weight a force? Otherwise gravity would accelerate heavier objects more slowly.
Gravity is the natural phenomena, or experimental observation, whereby bodies with mass appear to gravitate towards each other. One model and explanation of this phenomena is Newton's Law of Gravity used within the framework of Newton's dynamics (or laws of motion). The Law claims that gravity is a force, with a very specific formula we are all aware of.
If you ignore Newton's third law (about action-reaction pairs) for the gravitational phenomena of small bodies near a planet, and assume that the planet doesn't move at all, then we call the force on the small body its weight.
Now, returning to your question, in daily lingo, physicists use the word gravity to refer to the phenomena, the force law, or the weight. You have ascertain from context. In summary, gravity is a force is a perfectly valid and understandable statement within the slang of physics.
[0] with the exception of light, which is very light[1], but made of light particles rather than light particles.
[1] Homographs ahoy
F = - q * d\phi/dx
where q is the electric charge
now suppose you're in a gravitational potential \phi_g, the force is
F_g = - m * d\phi_g/dz
where m is the mass. as you can see it's like the newton equation, so yes looks like an acceleration :)
Weight is the force a body exerts on its support.
Force of gravity is a force exerted by each body in a system onto every other body.
The 'two spheres in a box' experiment for testing the gravitational constant has no relative velocity at all, so how could 'curved space' describe the force between them?
This affects our understanding of forces: Accelerations live in the double tangent bundle, which gets split into a horizontal and vertical part by the connection. The horizontal part is the contribution by inertia, yielding pseudo-forces (including gravity according to GR). The vertical part is due to non-inertial forces.
How this can be connected to gravity I do not exactly know. I suppose the change in the refractive index of the water is akin to g_{00} component of the Riemann metric, since it produces a compensating change in the wave vector at that point. Whether you could imagine GR consistently in terms of changes in the local speed of light a.k.a. changes in the permittivity of free space, again, I do not know.
(Thanks for the effort, though, it might just be me, in the end I changed profession for a reason)
I was replying to the headline: 'umm, yes and no...'
However, when I've graduated I don't think I would ever call myself a physicist like yourself unless I actually went on to do research in physics as a career, which likely means following the traditional academic path of doing a PhD (since I'm not Freeman Dyson).
Sorry for the nitpick but such titles should be earned don't you think?
the key principle of general relativity is the equivalance principle: there is no (local) way to tell if you're being accelerated (in a spaceship for instance) or in a gravitational field. in other terms the inertial mass is the same as the gravitational mass.
this, and lorentz invariance, yields general relativity almost uniquely, so it's a very strong principle.
so yes, in some sense gravitation shift the notion of "inertial frame of reference"
At around the time of Newton, what we now call physics changed from being something based in an ontology—a theory of what the world was made of to explain why it worked a certain way—into something mathematised where the equations accurately predict the behaviour of the world but there is no ontology other than that the universe is a universe where those equations hold. Modern physics still fundamentally works this way (see Maxwell’s equations, quantum physics, etc). Compare to, for example, Descartes with his theory of corpuscles and (totally wrong) billiard ball mechanics, or just about any other ontology from before him.
Interestingly, I could only find one other reference to that phrase[1]:
One 18th century natural philosopher wrote that forces were incomprehensible but "time has domesticated them."
[1] Why do we study geometry https://www.dpmms.cam.ac.uk/~piers/F-I-G_opening_ppr.pdf
So, the definition of a force as something that causes an object to change its movement from a "straight line" comes to us from Newton's laws.
> Why does the existence of a transformation that makes movement under a supposed force actually follow a straight line mean it's not really a force?
It's not just the fact that the transformation exists that means we don't really consider gravity to be a force. It's that the transformation exists, and provides useful predictions about the universe that turn out to be backed by experiment.
Under the theory of general relativity gravity isn't a force, because the fundamental premises of general relativity assume that gravity is actually a distortion of spacetime caused by mass.
We say that "gravity" isn't a force simply because the predictions made by general relativity have been validated by a number of experimental observations—at least on the macro scale.
> For the other forces (e.g. electromagnetism) can we say that there's _no way_ to exhibit a transformation that causes charged particles travel on "straight" lines?
I'm certainly not an expert, so I can't really comment on this. My best guess is that there doesn't exist any such transformation that causes charged particles to travel on "straight" lines that makes experimental predictions as well as our current scientific theories.
That seems kinda odd. What exactly would provide this difference? How is magnetism different from gravity? Is it that gravity doesn't have a mass, but magnetic fields do?
However, there are a lot of parallels between electromagnetism and relativity! Quite often relativity effects are introduced with an EM analogy, e.g. gravitational waves (which have polarisation) and electromagnetic waves ie photons (which also have polarisation). Note though it really is an analogy - they are fundamentally different things in both reality and mathematical form.
String theory tries to do the same thing with other forces; so it's not clear whether there's such a transformation. Forces are technically simpler than embedding extra dimensions that there are no evidence for.
Gravity is peculiar in that there is only one type of charge and it's exactly equal to the inertia quantity. If you try to do something similar to the other forces, you'll get really complicated models, with hidden dimensions and things that don't interact the same way with them.
When you accelerate or decelerate in a vehicle, you feel it. But when you jump out of a plane and accelerate towards the ground, you don't feel a force.
Noticing this fact was a big part of what led Einstein to his equivalence principle and General Relativity.
It depends a bit how you define words like real.
The thing is, I watched the French version and I didn't know an English version existed, that's why I didn't post it here, French speakers are, I believe, a minority.
And BTW, the French channel has an 8 part explanation of the maths behind general relativity that is the best I have ever seen. It is on a level above most pop science video since it actually shows the equations, tensors, etc... but the explanations are actually quite accessible.
Matter continuously destroys spacetime at its location, sucking in the fabric of the universe.
The Universe isn't expanding; matter is shrinking. Light isn't redshifted on the way to us, it's just that our sensors are getting smaller relative to the unmodified wavelength of light.
Indeed; light is blue-shifted as its source is on its way to us (and is red-shifted as its source is on its way away from us).
Is there any way to distinguish these? Surely it depends on who's point of view you're looking from
The apple doesn't curve space-time as much as the earth does.
Because both terms of the equation affect one another, solving it is complicated but here, the result is that spacetime contracts to the center of the earth.
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.
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.
But some of these forces are not observed by other people who are watching; they arise as by-products of the fact that you are the one doing the measuring. For example, if you're falling in a lift, you won't observe the force that causes a ball to fall towards your feet; but I, standing on the ground outside the lift, will observe that actually you and the ball and the lift are subject to this force.
In fact there's an underlying reality which we can't directly observe but which we can infer from the paths of objects. That reality is a curved spacetime, not a flat one (as it appears to be). This curvature means that "straight line" is actually not quite what you're used to; things follow straight lines, but those straight lines don't look straight to us, because of the underlying space's curvature: we can't see the whole of spacetime, only small segments of it, so we can't see enough to get a proper sense of the curvature. But since our limited frames of reference have their own notion of "straight line" which is incompatible with that of the global spacetime, we observe a mysterious tendency of things to deviate from what we think is the straight line they should be following.
So gravity "is a force": it's a mysterious tendency of things to move, because we are limited in what we can see and our own observation frames are subtly incompatible with the global structure. But it's also "not a force": if we were somehow able to take a fully global view of the universe, there would be no mysterious movement, only a huge number of things moving at exactly the same speed in perfect straight lines through a curved spacetime. (Assuming General Relativity is 100% accurate.)
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.
Imagine a bowling ball and a marble at rest from your perspective, and an apparatus with a pair of pneumatic guns that eject pistons with the same precisely-calibrated amount of force. You arrange the guns so that they will hit the marble and the bowling ball at the same moment, and you trigger them together. The marble and the bowling ball are hit at the same time by the same amount of force. The marble, being much lighter takes off much faster than the bowling ball.
Now take the same marble and bowling ball to a place a mile above the moon (so that there is no confounding atmosphere to complicate things) and release them next to one another at the same moment.
If gravity is a force, then we should expect that the marble will fall much faster than the bowling ball, because the same force is acting on two different masses; the lighter mass should be accelerated more, just as it was when the source of the force was the pneumatic gun. F = ma, after all. If the force is the same and the mass is less, then the acceleration must be more.
That's not what happens, though. The marble and the bowling ball fall together at the same accelerating rate.
Gravity acts like an acceleration, not a force.
Lo these many years ago when I was an undergraduate physics student, my advisor told me that we should say "the force due to gravity", not "the force of gravity".
In every day colloquial speech it doesn't matter, of course.
Vi Hart has a nice explanation: https://www.youtube.com/watch?v=v-pyuaThp-c
So when light goes thru a gravitational field it doesn't change direction (EVEN though gravitational lensing is happening, from the perspective of an observer). If it did change direction that would be synonymous with an acceleration, and light never accelerates.
"A Slower Speed of Light" http://gamelab.mit.edu/games/a-slower-speed-of-light/
"Velocity Raptor" https://testtubegames.com/velocityraptor.html
PBS spacetime did an episode about this recently.
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.
No, this is not correct. The correct statement is that the concept of "elapsed time" does not apply to a photon; it only applies to timelike worldlines, not null worldlines.
To put it another way, if your statement were true, it would mean that the origin and destination events were the same point in spacetime. But they're not; they're distinct points in spacetime. Which means that, since the spacetime interval along the worldline is zero, you can't use the interval to distinguish points on the photon's worldline. And the concept of "elapsed time" requires that you be able to do that. So the concept of "elapsed time" can't be used for a photon.
So you are completely incorrect insofar as what you are saying is physically nonsense.
Both gravity and EM fields have energy which is what couples to the gravitational field. Neither of the fields has mass, though.
> If all matter reacted to EM fields the same way it would to gravitation, would that make EM fields no force either? Or put another way, gravitation act universally on all particles, while EM fields do not. That necessarily has consequences when it comes to relativity. However it seems odd to argue that general relativity would exclude gravitation from being a force. If it acted only on a subset of particles, it would likely be in the same position as EM fields, and suddenly become a force again?
This is very well thought. Indeed, the equivalence principle, the fact that gravity couples to everything in exactly the same way (and that includes gravity itself as per the previous clarification) lurks behind our ability to reinterpret gravity in a geometric fashion. After all, if something didn't interact with gravity in the same way as everything else we could establish an experiment to differentiate if a spaceship is accelerating or stationary under a gravitational field (see Einstein's mental experiment) by measuring how that thing behaves. And that same fact would stop us from interpreting gravity as curvature of spacetime itself.
To your last point, speaking of forces is probably antiquated anyway, although still in use partly for historical reasons partly abuse of terminology. Preferably we should use the term "interactions", after all some of the "forces" do not result in push or pull as we usually understand a force in Newtonian mechanics but in things like color change. Others, like the gravitational "force" can be expressed entirely as spacetime geometry. But discussing semantics is quite pointless so as long as everyone understands in what way the term "force" is an abuse of terminology it's OK to keep using it.
We can pretty much boil EM down to: like charges repel, unlike attract, strength is charge1*charge2/distance^2. What about magnetic field, photons, QFT etc?? None of this exhibits effects which could be described as stretching space-time either.
But we cannot do the same with gravity. An explanation like the above but for gravity (which is traditional Newtonian) leaves out many, now observed effects such as:
-> time dilation (GPS relies on this calculation) (measures time stretching and contracting)
-> gravitational waves (LIGO) (measures space stretching and contracting)
How do we _know_ any of this? People propose theories, those theories are then tested against experiment. AFAIK to date there is no experimental evidence suggesting EM stretches space, and no theory proposed that includes such an effect and correctly matches experimental data. That's the most holistic answer (but unfortunately one you just have to believe unless you have a lot of spare time!)
And now I'm wondering if it also applies to matter if matter is just an excitation of a quantum field.
1) the high-energy field is in deep crisis, unlike in Dyson era there is almost no new experimental data.
2) seeing people trying to get a temporary position looked pretty much like a pack of dog on a single bone with few left scraps of meat. for getting to the bone marrow (aka permanent pos) one basically had to kill all the other dogs then wait the bone crack open (i can tell you the resulting science is not always of high quality)
3) i wanted to do sth useful for mankind.
so yes i was not masochistic enough to become a career physicist, even if i am a respected expert in my field. also i don't think you can compare present day physics to Dyson era, science careers these days are more about social skills and PR.
so you're correct: i'm an aborted / half-backed physicist, who is highly p* of what the field has become, converted to computer sciences, just to realise my new field is as scientifically crooked as the first one.
i'll try to get it right next time :)
... at least this time i didn't get down voted too much on HN
So a photon, which has 0 mass is still bent by gravity. Everything that we've observed that moves through spacetime is bent by gravity. That's why we say that gravity is a warping of spacetime itself, where electromagnetism isn't.
If you tried to build the "general electromagnetic theory of relativity", then 0 charged particles wouldn't follow a straight line on a geodesic of spacetime. With gravity, everything follows a straight-line on the geodesic of a curved straight line, regardless of its mass.
As to why such a difference exists between gravity and electromagnetism, that's well above my pay grade.
The word “dimension” in this context is overloaded. We think of space being three dimensions but really it’s only one - velocity relative to a specific reference frame. Thinking of it this way, the word “spacetime” makes sense; it’s a two-dimensional system: “spatial velocity” (S) on one axis and “temporal velocity” (T) on another. Both velocities are always measured against a reference frame, and their sum is c (c=S+T).
This would mean that time travel is impossible not because of a “speed limit”, but because c is a dimensionless physical constant.
“So pushing just two atoms close to each other takes energy, as all their electrons need to go into unoccupied high-energy states. Trying to push all the table-atoms and finger-atoms together demands an awful lot of energy – more than your muscles can supply. You feel that, as resistance to your finger, which is why and how the table feels solid to your touch.“ https://theconversation.com/if-atoms-are-mostly-empty-space-...
How so? You can have different electric charge to inertial mass ratios, but that is not so for gravitational mass to inertial mass.
Also, what if you have a charge so high that the electrical-escape velocity exceeds the speed of light? A strange kind of black hole?
I ask these things because I do not understand why gravity is called "not a force", while electromagnetism is, when I see no real difference between how particles act.
The way that varies is always in proportion to the object's inertial mass though, which has the result that the path traced by an any object with the same starting position and velocity in a given gravitational field is going to be the same.
Contrast this with charge, which can vary independently of inertial mass. This has the result that the paths traced by objects with the same starting position and velocity in a given electrical field will vary.
This also means there is no fixed "electrical escape velocity". More massive objects with the same charge can escape with a lower velocity.
But let's just say they are the same, then gravity and "spacial" inertia are intertwined. Gravity is only special if intertia is also considered special. Inertia seems special because it's explainable in terms of motion in space. There might be other kinds of motion in other dimensions that could explain the randomness of quantum space.
* photons
* spherical, massless cows in a vacuum
"No, Mr Bond, I expect you to die."
Obligatory https://xkcd.com/123/
Forces are mathematical models, not fundamental properties of reality (we don't know what the fundamental properties of reality are).
Once again, it's largely down to your frame of reference.
So we're curving in towards the center of the mass of the Earth, but the reason we don't end up in the core of the Earth is because the surface stops us. The Earth is "pushing" us away from the center, and that's the acceleration. It's accelerating you off your straight line path, and this is the deviation from the geodesic.
What's confusing me here is the notion that when two objects collide, they accelerate into each other. Why and how is force constantly applied after the collision? My intuition is falling down here, and none of the resources I've looked at so far have explained why the acceleration happens.
Remember that spacetime = space + time dimensions. The object is always travelling through time, and the curvature of spacetime is converting some of that speed through time into speed through space. That's what you perceive as motion (caused by gravity).
Time and space are linked together. The faster you go through space, the "slower" you go through time (as in you experience it slower). This is very measurable and even used to alter timings for satellites GPS readings. You can take an atomic clock on a plane and age slower than someone who just stayed on the ground.
So the spacetime curvature is continuously converting some of your temporal motion into spatial motion, until that's stopped by the surface of the Earth which is constantly "accelerating" to stop you from going further.
As to why we always move through time, that's beyond my understanding at this point but it's a fundamental axiom of physics.
I don't really understand why, that was just the explanation Derek gave.
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.
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."
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.
A more energetic particle of the same mass will have a very slightly higher gravitational attraction.
[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.
In fact, the fact that heavy and light objects fall at the same speed is a profoundly special property of the gravitational interaction. No other fundamental force behaves this way: in an electric field, objects with more charge will accelerate more quickly than objects with less charge (and the same is true for the weak and strong forces).
In fact, the acceleration of an object or particle in a field is proportional to its field-specific charge divided by its inertial mass. The really interesting thing about the gravitational interaction is that the "charge" associated with the gravitational field is exactly equal to the inertial mass of that object, so all objects accelerate at the same rate because of the gravitational field.
This truly special property of the gravitational field had no explanation until Einstein's theory of general relativity, which discarded the idea that the gravitational field is a field at all, and described the motions of objects only in terms of rectilinear movement in a curved space-time (the reason why inertial mass curves space time is still unexplained though - it seems to simply be a property of the universe).
If you and others in the thread feel that these popular authorities are spreading misinformation or using inappropriate analogies, doesn't it behoove you to raise an objection with them directly? Or perhaps with the appropriate faculty committees at their institutions?
If they want to make money by getting "the unwashed laity" to buy their books, why should I stop them? I simply don't buy them myself. If other people want to get told comforting nonsense, that's their problem. Caveat lector.
> Or perhaps with the appropriate faculty committees at their institutions?
Which would be pointless and absurd, since, as I have already said, the claims in question are not being made in textbooks and peer-reviewed papers.
I suspect you are trolling.
You can win an internet argument anywhere, but if that's all you want to achieve here, then maybe stop trying to debate physics.
If I drop a ball above the glass, and we consider things from the frame of reference where the ball is stationary, which (neglecting air resistance) is an inertial reference frame. In this frame, the glass is accelerating ball-wards , because of the table pushing on it, and, this force is applied over a distance as the glass approaches the ball. So, yes, it seems that the KE of the glass should be increasing in the reference frame of the ball.
Hm, I'm confused.
I suppose if we consider a geodesic representing a periodic orbit around the earth, that the positions and velocities of various objects on earth will be in a cyclic pattern?
See Veritasium's video at 10m17s:
https://youtu.be/XRr1kaXKBsU?t=617
He addresses that basic science makes this confusing because there's a curvature term that is usually left out of acceleration equations which balances out when you're accelerating along your curvature (e.g. against gravity), instead of along your spatial coordinates.
Your explanation makes sense, and it sounds like I'd need to understand the maths behind relativity to be able to really understand how objects behave in spacetime.
Right, but if this were the case, a dumbbell would fall about twice as fast when its axis is perpendicular to the ground, than when it's parallel to the ground. Realizing this is not true from lived experience completes the thought experiment.
However, what you could expect to see is that dumbbells with different weights for the two parts would never fall horizontally, they would tend to reorient vertically, with the heavier end first. Not sure how likely it would be to have noticed that this is not the case from lived experience.
Let's say I put you in a spaceship and accelerate you to 50% the speed of light toward the sun. From an inertial viewer's perspective you are travelling toward the sun at half the speed of light and it takes you ~16 minutes to crash into the sun. But from your perspective it only took ~14 minutes to crash into the sun[0].
Repeat the experiment except I accelerate you to .99c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took ~1 minute to crash into the sun.
Repeat the experiment except I accelerate you to .999c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took 20 seconds to crash into the sun.
Repeat the experiment except I accelerate you to .9999c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took 6 seconds to crash into the sun.
Repeat the experiment except I accelerate you to .99999c. From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. But from your perspective it only took 2 seconds to crash into the sun.
See what's happening? As you approach the speed of light, the amount of time that elapses until you reach your destination approaches zero. So from an inertial observer's point of view, time has completely frozen for travelers approaching light speed.
[0] Using time dilation formula from this page: https://www.phy.olemiss.edu/HEP/QuarkNet/time.html
Yes, but you cannot extrapolate from this to say that the time lapse for a photon would be zero. A photon is not the limit of objects with mass going closer and closer to the speed of light, because "closer and closer to the speed of light" is frame-dependent, but a photon's speed being c is not. I can find an inertial frame in which each of your objects is at rest, and in that frame, you are the one who is "close to c" (in the opposite direction). But that doesn't mean your elapsed time approaches zero. By contrast, it is impossible to find any frame in which a photon is at rest. The two types of objects are fundamentally different.
In more technical language, the action of Lorentz transformations on photons is fundamentally different from their action on timelike objects. So it is simply not valid to view photons as some sort of limit "as speed approaches c" of timelike objects.
I don't believe that, and have never heard it before. There are many ways in which light actually behaves just like particles with mass traveling at speed c. It has to or conservation of momentum is violated.
I'm thinking of solar neutrinos which, for a while, we weren't sure if they were massless or not. We had to observe them experiencing a duration of time to conclude they were massive. If we didn't find that, maybe it was just an even shorter duration, not the absence of one and we would never be able to tell the difference.
Show me an actual textbook or peer-reviewed paper Tyson has written where he makes this claim. Pop science videos don't count. (Tyson is by no means the only one; Brian Greene is notorious for the same thing.)
You won't be able to because there aren't any. No scientist who talks about a photon "experiencing zero time" in informal contexts will try it in a textbook or paper. That's because they know that if they did, other scientists would call them out on it, so they confine such claims to contexts where there are no other experts so there's nobody to call bullshit.
Another point is that if this concept were actually scientifically useful, somebody would be using it in a textbook or peer-reviewed paper. The fact that nobody is is a huge clue that the concept is not scientifically useful. It's only useful for selling pop science books or getting views of pop science videos, where, again, there are no other experts around.
Photons put it all into the X, Y, and Z components, leaving nothing for the t component. They experience a change of position in space, but not in time. What's so hard to grasp about this?
Another point is that if this concept were actually scientifically useful, somebody would be using it in a textbook or peer-reviewed paper.
Seems that a fellow named Maxwell got a lot of mileage out of the concept, even if he didn't know what was really going on.
I mean the whole way looking at it seems wrong to me. There is no "rest of the world" in relativity. Assigning some objective vector to everybody doesn't work. These only make sense from some specific point of view.
By the question you asked now I'm assuming, you meant "but hey, without GR..", but even without GR, ignoring that the universe is expanding, assuming flat space time etc. If the universe consisted just of 3 bodies, 1 being you and 2 being rest of the world, then the way of thinking you described still doesn't make sense in context of relativity and may lead to some confusion (apart from it being, to me, incoherent in context of special relativity).
But maybe I'm missing something from your picture, I'm happy to read and learn.
You can certainly imagine a scenario where two objects measure their mutual distance as being constant in time. You can also imagine other scenarios, but I'm asking to imagine the scenario where two objects do measure their distance to be D and then measure it again and it's still D, and measure it again and again and it's still D. That's just the definition of standing still with respect of each other, and when you plot a space time diagram, their space curve is parallel (because their spacial distance doesn't change).
Special relativity doesn't make that scenario impossible. It doesn't force things to move. It just describes what happens when things do move (through spacetime).
GR I'm less familiar with.
No, Tyson's claim is not "basic theory at the high school level". It is a particular interpretation of a theory (Special Relativity) that does not work, for the reasons I gave.
> Photons put it all into the X, Y, and Z components, leaving nothing for the t component.
Wrong. The spacetime vector that describes a photon's trajectory does have a t component.
> Seems that a fellow named Maxwell got a lot of mileage out of the concept
Dude, if you think the concept Tyson described is the same as the concept that Maxwell got a lot of mileage out of, then you are the one who needs to learn more about "how it works".
Sounds interesting. Where can I read more about this t component?
However, this comment has significantly raised my estimate of the probability that you are just trolling.
Are you asking if there is a way to distinguish a timelike object from a lightlike object? Of course there is. The fact that, for something that has a very, very small invariant mass, it might be practically difficult does not change the fundamental principle.
Also note that the reason it was difficult, for example, to tell whether neutrinos have mass or not is that we can't just do the obvious and straightforward thing and find an inertial frame in which they are at rest (by, for example, taking a rocket and accelerating it in the direction of a neutrino to see if we can bring it to rest relative to the rocket). So we have to resort to indirect methods. But, again, that's a practical limitation that doesn't change the fundamental principle.
For neutrinos, even if we accelerated an rocket and somehow checked if a neutrino was at rest relative to it, we might find that it's not. That means we won't know if we need more speed or if it's impossible. I suppose it's a bit easier than that because we only have to accelerate the rocket fast enough that the neutrino's speed becomes measurably less than c, rather than 0. But still, what if we can't even get it to go fast enough for that? No way to prove that it's travelling at c, it seems.
I'd like to add that even photons have a nonzero upper bound to their possible rest mass. At least they used to. Is there any way, in principle, to show that it's exactly zero, and thus falls into this distinct category?
If you try what I described with a light ray, it will be moving away from you at c no matter how much you accelerate in its direction.
If you try it with a massive object, even a neutrino with a very, very tiny invariant mass, that will not be the case; its speed relative to you will decrease as you accelerate after it, eventually to zero.
There is no continuum between those two possibilities; they are distinct and discrete. The only continuum is in the latter case, where the final speed of the object relative to you will depend continuously on how long you accelerate.
> even if we accelerated an rocket and somehow checked if a neutrino was at rest relative to it, we might find that it's not. That means we won't know if we need more speed or if it's impossible
Yes, you will know, because you will know if the neutrino's speed relative to you has decreased or not. If it has, it's possible to bring it to rest relative to you. If it hasn't, it's not. See above.
> I suppose it's a bit easier than that because we only have to accelerate the rocket fast enough that the neutrino's speed becomes measurably less than c, rather than 0.
Exactly.
> But still, what if we can't even get it to go fast enough for that?
That's basically the position we are in now: we have no way of building a rocket or other device that can accelerate after a neutrino long enough to tell whether its speed relative to the rocket is measurably decreasing. So we have to resort to indirect measurements. But as I said before, that doesn't change the principle.
> even photons have a nonzero upper bound to their possible rest mass
Yes, because, as I said, practically speaking we can't run the obvious and straightforward experiment I described, to confirm that a photon moves away from you at c no matter how much you accelerate after it. So we have to resort to indirect measurements, like trying to measure its invariant mass by other means. But that doesn't change the principle.
> I'd like to add that even photons have a nonzero upper bound to their possible rest mass. At least they used to. Not sure what you're talking about, their momentum? No object with mass can reach the speed of light and we know they're travelling at that exact speed.
This turns out to be not pedantic but very important if you're guiding an ICBM. And when landing on the Moon, Apollo had to deal with irregularities in the Moon's gravity due to mass concentrations, called mascons.
(If you're interested in missile guidance, take a look at the book Inventing Accuracy. Among other things, it discusses some of the efforts to map the Earth's gravity field to increase missile accuracy for Trident and Minuteman missiles. I knew a physicist who worked on this.)
It wouldn't be an ellipse even if Earth were a point mass. The gravity of the Moon and Sun, the gravitational lumpiness in the sky, has the same effect as the gravitational lumpiness underground. The combined result may be no closer to an ellipse than it is to a parabola.
Source is a table in the first chapters of Fundamentals of Astrodynamics.
It's not a force. From the right frame of mind[0], it's just a straight line.
[0] Substituting for frame of reference.
ICBMs were never used to toss nukes at people.
Pretty sure their existence saved the world from WW3.
> Surely there's something else we could be doing instead?
The application most useful in everyway life is GPS.
So, moral of the story - we have to be not too pedantic.
I'm not a physicist, but that doesn't sound right. One example is that if you are inside of the sphere, at least some of the mass will be pulling you away from the point at its center. I think what you mean is that a point mass closely approximates a spherical mass, but the degree to which that is true becomes less and less the closer you get to the center. I don't think you have successfully contradicted what the person you responded to said.
Proving this is a classic problem in undergraduate physics.
If the mass is spherically symmetric, this will not be the case; all of the Newtonian forces from the masses further away from the center than you are will cancel out. This is called the "shell theorem", and it turns out to hold even in General Relativity.
For each point of any given distance, you can find a disk of points at the plane of the same distance whose gravitational pull will be equivalent to a single point at their center.
You do this for all distances x, and you will find an equivalent rod going from the attracted objected to the center of the sphere, of a non-uniform but symmetrical density.
We find that the density is linearly correlated to the area of the corresponding section, and we then take the closer half of the rod, multiply the density by 1/r^2, and find that it is constant!
For the far half of the rod, we cannot do this, so instead we divide it into two halves of equal pull, then divide those to halves and so on, and find that it this reduces to the equivalent of a point.
Now that we have two points in-line with the object, we find the point with the same total mass that exerts and equivalent force, and lo and behold it is at the center.
I'm sure there is a much simpler way to intuit it, though :)
Would it? Even of uniform density, the mass would not the at the core, only the center of mass would be. Most of the mass is actually closer to the surface. I'm no physicist, but I'd imagine that would have quite some impact[0] on any trajectory that crosses the surface.
And for any ball thrown at human speeds, I'd expect Earth's gravity would be much closer to a uniform gravitational field than one from a point mass.
[0] Pun not originally intended but I'm quite happy with it now.
In relativity, there is no such thing as a "uniform gravity field", if by that you mean a field where the "acceleration due to gravity" is the same everywhere. The closest you can come is the "gravity field" inside a rocket accelerating in a straight line in empty space, where the acceleration felt by the crew is constant. That kind of "gravity field" has an "acceleration due to gravity" that decreases linearly with height.
Look up the Bell Spaceship Paradox. In relativity, two spatially separated objects (or two ends of a spatially extended single object) that have the same proper acceleration in the same direction do not stay at rest relative to each other; they move apart, as seen in each of their own frames. This is different from the behavior predicted by Newtonian mechanics. In order to have the two objects (or two ends of a single extended object) remain at rest relative to each other, the one in front has to have a smaller proper acceleration than the one in back. (Rindler coordinates are often used to describe this case.)
Even if you consider the point mass to move because of the mutual attraction?
Assuming a uniform+spherical earth. And also a uniform+spherical ball I supposed.
Based on what I've seen over the years I've been around here, I'm quite certain that's a primary motivator for a non-trivial number of commenters here.
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.
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 :)
The rest get so perturbed by gravitational anomalies that they fall out of orbit after a few months or years--faster than low Earth orbit where there is atmospheric drag!
https://www.lpi.usra.edu/lunar/documents/NTRS/collection2/NA...
We don't, strictly speaking. The measurements you refer to aren't even measuring the speed of photons. They're measuring their rest mass.
> physicists would occasionally measure a new maximum possible rest-mass for photons. It would be very tiny, of course, but they couldn't say it's exactly zero.
Based on just those measurements, no. The most they can say is that the photon rest mass is zero to within some error bar, and the size of the error bar keeps getting smaller. (The current error bar, IIRC, is 10^-52 grams, or about 24 orders of magnitude smaller than the electron mass.)
However, we have a ton of indirect evidence that photons are massless; the most extensive body of such evidence is all the evidence for the gauge invariance of electromagnetism. If photons had a nonzero rest mass, that would break electromagnetic gauge invariance. So photons having a nonzero rest mass would be a huge issue for our current theories, in the way that neutrinos having a nonzero rest mass would not; there is no important symmetry coresponding to electromagnetic gauge invariance that is broken by neutrinos having a nonzero rest mass.
I don't think this quite works because of relativistic addition of velocities. Naively, it seems to. For example, if the object was travelling at 0.999999c relative to you (appears to be 1.0c according to your limited instruments), then you accelerate to 0.50c in its direction, you'd see its speed reduce to 0.50c (same 2s.f. instrument), which would clearly prove it's not massless. But velocities don't add like that relativistically and I think you'd still see it as travelling at 1.0c because it only decreased a tiny amount, below what you instrument can detect. If you use a more precise instrument or a faster rocket, you might measure it as 1.00000c but then you still won't know if it's exactly c or a smidgen less.
Maybe I've got my relativistic velocity addition wrong? But it still looks like the same measurement problem as trying to prove a classical object has a speed of exactly 0, which can't be done no matter how accurate our instruments are.
For the specific case you give, that depends on what accuracy you are assuming. The relativistic velocity addition would be:
v_new = (0.999999 - 0.5) / (1 - 0.999999 * 0.5) = 0.999997.
So if your accuracy is, say, 1 part in 100,000, you wouldn't be able to see the difference. But with an accuracy of 1 part in 500,000, you would, even though you wouldn't have been able to see the difference before the acceleration.
Also, suppose you accelerated for a second increment equal to the first; you would get
v_new = (0.999997 - 0.5) / (1 - 0.999999 * 0.5) = 0.999991.
And one more increment:
v_new = (0.999991 - 0.5) / (1 - 0.999999 * 0.5) = 0.999973.
As you can see, the differences in velocity grow fairly quickly for each equal increment of acceleration; the growth is not at all linear. And, as I said in my other post just now, for any given measurement accuracy, it would be simple to calculate how much acceleration you would need to be able to distinguish moving at exactly c from moving at 0.999999c (or any other speed less than c that you choose) to that accuracy.
Not indefinitely. Sure, if you accelerated for a short enough time in the direction of the neutrino, you might still be within your measurement error and so not have learned anything. But that just means you need to accelerate for a longer time. For any given measurement accuracy, you will be able to calculate how long you need to accelerate, by your clock, to definitely distinguish the two cases. Relativistic velocity addition does not change that fact. All it changes is the details of that calculation; yes, for a given measurement accuracy, you need to accelerate for a longer time, by your clock, to definitely distinguish the cases than you would if velocity addition were linear. But that doesn't mean relativistic velocity addition makes it impossible to distinguish the cases at all, ever. It doesn't.
Yes, it is certainly not intuitive. That's why Bell took the time to write a paper about it years ago.
This article might help:
https://www.physicsforums.com/insights/what-is-the-bell-spac...
Or equivalently, if you are inside a shell (sphere outside, hollow sphere inside) then the gravitational effect is zero. This can be explained by analogy with light which also follows the inverse square law--changing your position inside a hollow sphere does not change the fact that you see the sphere all around you. Same reason that there is no electrical field inside a hollow conductive object.
You can use this law to see what's the gravity fields as you move under ground and in other very symmetrical cases.
It doesn't break it at all. The meter above you can be treated as a hollow shell, which surprisingly has zero net pull, and the solid sphere below can be treated as a point mass just as before.
Just remember these two facts, each provable with a simple integral calculation, usually done in high school physics or freshman college physics: a uniform sphere has the same gravitational pull on an object as a point mass at it's center, and the net gravitational pull on an object inside a spherical shell is zero.
This all works under perfect spheres, uniform (at the spherical shell level at least) density... There are other cases it works, but this simple case is the basic idea.
A solid ball (filled sphere) is just a union of many shells (hollow spheres), so the theorem still applies.
en.wikipedia.org/wiki/Shell_theorem
No, it's stronger than that. It says that any spherically symmetric distribution of matter outside a certain radius exerts no "gravitational force" on anything inside that radius, whether there is matter inside that radius or not.
Then you are not inside the shell, you are on it. The shell theorem only applies if you are inside the shell.
> Would I not feel infinite acceleration towards the massive point on the shell that I was infinitely close to?
In General Relativity, matter is not viewed as point particles. It is viewed as a continuum, described by the stress-energy tensor. This is one of those cases where the difference shows up.
But as you get close to stuff, say two atoms, the electrostatic and other forces are far greater than the gravitational ones.