Einstein says objects do not fall to the Earth?

[inertiaforce]

Ok thanks. My mistake lol.

 

[rajeshmarndi]

Now I understand, If I'm right ,that opposites ball when released hit the Earth surface at the same time because the curve path of the balls and that of the Earth collide at the same time, as time move on.

How is it possible for opposite sides of the Earth to be accelerating in different directions, without the Earth expanding?

Suppose you have two objects on the equator, a distance of 10 meters apart. As time moves on, those objects move north along lines of longitude. If there were no forces acting on those objects, they would be getting closer and closer together, until they collide at the North Pole. It requires a force to keep the two objects 10 meters apart as they move North.

I didn't understand "It requires a force to keep the two objects 10 meters apart as they move North." How does this correspondence to acceleration of Earth surface in different direction.

What is the source of Earth acceleration in all direction. I can think as Earth revolves around sun at constant velocity experience acceleration as it changes direction continuously. Also the Earth rotation on its axis.

 

[stevendaryl]

I didn't understand "It requires a force to keep the two objects 10 meters apart as they move North." How does this correspondence to acceleration of Earth surface in different direction.

Once again, picture two objects both moving straight north, starting at the equator. Do you see that the distance between them shrinks as they move North? To keep the distance between them from shrinking, you have to have a force pushing them apart. That force pushes one object to the west, and it pushes the other object to the east.

An analogous thing is happening to two points on the opposite sides of the Earth. It requires a force to keep those two points from getting closer together. The force has to keep the two points apart.

What is the source of Earth acceleration in all direction.

Pressure. The material that the Earth is made out of is under pressure, and that pressure exerts an outward force on all points on the surface of the Earth.

 

[Nugatory]

Interesting how people can be experts about gravity without being able to tell us the mechanism of gravity.

That's true about just about all of science; the same criticism can be levied at just about all of classical mechanics: We know that like charges repel and unlike charges attract, and we can describe the forces using Coulomb's law $F=Cq_1q_2/r^2$ but that's a description not an explanation of mechanism.

 

[rajeshmarndi]

Pressure. The material that the Earth is made out of is under pressure, and that pressure exerts an outward force on all points on the surface of the Earth.

What is the term referred to the above phenomenon.

So, the pressure of the material, which actually causes experiences of the weight?
But we studied, we feel weight because of Earth gravity. It seems gravity and weight are two different thing.

I understand due to gravity or due to curvature of space, as each points on Earth follow this curved path, they build internal pressure, which exert on our body and we feel it as weight.

But as commonly understand, our body is pulled to the Earth surface and it exert pressure on the surface, in return the surface exert equal opposite force on us.

 

[georgir]

Weight is still the same thing as in the classical explanation - the force which an object exerts on its support, equal and opposite to the "normal force". But you are right that in GR the "normal" comes first, as a result of the support's "pressure" or more generally just its tendency to keep a fixed distance from the Earth's center (or from the definition of "fixed support"), and that weight is then just its equal and opposite counter force.

Edit:
As to "What is the term referred to the above phenomenon.", can you say which phenomenon that is? Do you mean why the earth, or anybody for that matter, does not collapse under its own gravity? I guess the term would be "rigidity", until we move to the surface of a gas giant ;)

 

[rajeshmarndi]

As to "What is the term referred to the above phenomenon.", can you say which phenomenon that is?

stevendaryl said: ↑
"Pressure. The material that the Earth is made out of is under pressure, and that pressure exerts an outward force on all points on the surface of the Earth."

The above statement, where it says, "...The material that the Earth is made out of is under pressure..."

 

[stevendaryl]

What is the term referred to the above phenomenon.

So, the pressure of the material, which actually causes experiences of the weight?

Yes, you don't actually feel gravity when you stand on the ground. You feel the force of the ground pushing up against your feet.

But we studied, we feel weight because of Earth gravity. It seems gravity and weight are two different thing.

You can't feel gravity. If you were falling, you wouldn't feel any different than if you were floating in space (well, except for the air rushing past you). The only time you feel weight is when you are being prevented from falling, by the ground (or whatever is holding you up). As I said, what you feel as weight is an upward force preventing you from falling.

I understand due to gravity or due to curvature of space, as each points on Earth follow this curved path, they build internal pressure, which exert on our body and we feel it as weight.

But as commonly understand, our body is pulled to the Earth surface and it exert pressure on the surface, in return the surface exert equal opposite force on us.

Yes, that's the way that Newton viewed gravity.

 

[Wes Tausend]

According to this video, a bowling ball and a feather fall at the same rate because according to Einstein, they aren't falling:

https://testtube.com/dnews/which-falls-faster-a-feather-or-a-bowling-ball/?utm_source=FB&utm_medium=DNews&utm_campaign=DNewsSocial

What does this mean exactly? The Earth comes up to the ball and the feather?

Suppose two balls were "dropped" at the same time on opposite sides of the Earth. Which way would the Earth fall?

Since Newton came up short, gravity never attracts and nothing accelerates in a fall anymore. It just looks like it does. It's all because of Einsteins wonderful Equivalence principle, of which he used to look at gravity from a different perspective in a unique coordinate system.

Many years ago I developed a thought experiment that allows me to see how a rendition of the Equivalence principle works. Perhaps it will help others. A good thought experiment is even better than youtube, and is all we had back then anyway.

The trick is to temporarily imagine Earth expanding as stevendaryl briefly mentioned earlier. In this imaginary case, the surface of an enlarging model Earth rises to meet the surfaces of the bowling ball and feather "simultaneously".

The easiest way to visualize this comprehensive thought experiment is to imagine we have a large, sealed bell jar that we may began to evacuate of air. The internal experiment must also take place in a gravity-free area of space, or free-fall (the same thing).

In this bell jar we place several soap bubbles. For PeroK's 2-ball thought experiment, somewhat towards the center, we place a large soap bubble we will call earth. Above(?) it we place a smaller bubble we call ball 1. Below "earth" we place another similar sized small bubble we call ball 2. Now we began to evacuate the chamber by opening a valve that is hose-connected to an indefinitely large tank that already contains a near vacuum. We have a well equipped lab. When the air leaves the chamber, the Earth body and two smaller balls will all began to enlarge, or swell, because the air pressure on the outside of the bubbles reduces. If we keep opening the valve further all the time, the bubble expansion will accelerate. If we open the valve slightly, then leave the setting, the expansion will only represent an undetectable steady inertial movement. We will choose the former for our acceleration experiment.

Now imagine the bubbles want to maintain their center-to-center distances, i.e. remain at rest. In this case the surface of the large Earth bubble will expand into the space that the surfaces of the smaller bubbles also wish to expand and occupy. The surface of model Earth will rise to hit the balls at the same time the swelling balls have a small "enlargement gravity" of their own. This is classic Equivalence principle. There is a catch, but I won't say for now and chance breaking this Lawrence Welk spell.

For inertiaforce's thought experiment, one can carry the thought experiment a bit further and imagine that beside one of the other normal balls (ball 1) there is a tiny bubble. This delicate little guy can be the feather. If the surfaces of the feather and ball 1 are equally distant from the surface of earth, they will strike Earth simultaneously (or Earth will strike them). Now it is important that both small bubble surfaces, not the centers, be equi-distant from the surface of earth. Otherwise one can imagine that the larger "heavy" ball has a head start to make contact. The ball and the feather also do one other thing that is remarkably like gravity. They both seem to "fall" towards Earth's center and towards one another at the same time. If the ball and feather are in close proximity compared to their relative distance from earth, they may even make "swelling" contact before contacting the surface of our model earth. Besides "falling" towards the center of model earth, they also seem to move closer together on their own, which is in keeping with properties of all material objects, which of course have a small amount of gravity of their own. Ignoring ball 2, these three bodies seek not the center of earth, but a common center.

One other Equivalence thought coincidence, that is remarkable, results when we place a special small bubble on the surface of our Earth bubble. This precious bubble can be our human observer. This flat-footed human bubble must enlarge in our vacuum chamber also. So the relative comparative size of this "human" and that of model Earth never change, ala Poincaré. We could even grant him/her a bubble for a yardstick, but our oblivious human observer still has no way to measure that he/she is part of a slow bang process. But yet the human bubble experiences a mysterious acceleration that he/she interprets as gravity. As we, the real humans, safely watch the chamber from our assigned privilaged rest outside our little bell-jar universe model, we will see that as the model Earth bubble expands, the small human bubble actually squashes a bit as he/she rides the accelerating surface of the Earth bubble. This equivalent compression is so true in our real world, over many years I have permanently become nearly an inch shorter from the perpetual stress of standing, and I, like all of us, am always longer when I lie down.

And that is my shortest condensed rendition of the Equivalence principle. I think Poincaré would have particularily liked it.

P.S.
Earlier I mentioned a catch to this ancient thought experiment though. If we really evacuated a chamber, the air between the bubbles would expand also. That means the bubbles would be drawn apart in expanding space and perhaps never make contact. It seemed a story spoiler to openly mention this too soon. I'm sorry if it nagged at some of you throughout.

Wes
...

 

[A.T.]

The trick is to temporarily imagine Earth expanding as stevendaryl briefly mentioned earlier.

Stevendaryl said nothing about the "Earth expanding", which is exactly the wrong way to explain this, and leads people to conclude that GR is a bunch of nonsense.

He says that the surface accelerates away from the center. But that doesn't imply movement away from the center (expansion). He also gives a much better analogy:

Think of spacetime as the surface of a globe, and think of the time axis as being measured North-South, while spatial distances are measured East-West. Suppose you have two objects on the equator, a distance of 10 meters apart. As time moves on, those objects move north along lines of longitude. If there were no forces acting on those objects, they would be getting closer and closer together, until they collide at the North Pole. It requires a force to keep the two objects 10 meters apart as they move North.

 

[PeroK]

Here's a thought experiment:

We take two balls at a large distance apart in space. They are at rest. So, we have a rest frame.

We introduce the Earth close to one ball (the second ball is so far that the Earth's gravity is negligible).

If the Earth moved to the first ball, then that ball would remain at rest in the inertial frame we have established.

But, in this inertial frame, the first ball would move to the Earth.

We could also establish an inertial frame in which the Earth is at rest and then bring a ball near the Earth. The Earth would effectively remain at rest.

Isn't it obvious that the Earth has a massive influence (whatever your theory of gravitation) on a ball; whereas, the ball has almost no influence on the Earth?

 

[Wes Tausend]

Stevendaryl said nothing about the "Earth expanding", which is exactly the wrong way to explain this, and leads people to conclude that GR is a bunch of nonsense.

He says that the surface accelerates away from the center. But that doesn't imply movement away from the center (expansion). He also gives a much better analogy:

I agree Stevendaryl does a good job explaining an aspect of gravity.

I think you have the wrong post from Stevendaryl. I quote the one that I referenced below.

There is a sense in which it is correct to say that the surface of the Earth is accelerating upward: there is an upward force on the surface of the Earth, and this force causes the surface to accelerate upward relative to a freefall path (or geodesic). All parts of the Earth are accelerating upward, in this sense (I wouldn't call it "falling" upward, falling means traveling in the absence of any forces holding you up, and that is not the case with the surface of the Earth; the surface of the Earth is held up by contact forces from the rocks below). This notion of acceleration, relative to a geodesic, or freefall path, is local, so different spots on the Earth are accelerating in different directions.

How is it possible for opposite sides of the Earth to be accelerating in different directions, without the Earth expanding? I think it's helpful to think of a lower-dimensional analog. Think of spacetime as the surface of a globe, and think of the time axis as being measured North-South, while spatial distances are measured East-West. Suppose you have two objects on the equator, a distance of 10 meters apart. As time moves on, those objects move north along lines of longitude. If there were no forces acting on those objects, they would be getting closer and closer together, until they collide at the North Pole. It requires a force to keep the two objects 10 meters apart as they move North.

Stevendaryl was clear that Earth is not expanding and is trying to avoid a scenario where it could be. I merely pointed out why it is a good thought experiment to think of it temporarily that way. I think most people know the difference beween reality and a thought experiment, so no one need be "mislead", or think GR non-sense. The bubble thought experiment, if carried to conclusion will stall.

Otherwise the bubble expansion idea is a very, very good approximatization of exactly how the Equivalence principle works, a valuable tool and I'm surprised and hurt you can't see that. It is very similar to Einsteins rendition of a "chest drawn up by a cable", along the lines of Poincaré's thoughts, and can be carried far further than I did. On the other hand, If there is some serious flaw to the chest or bubble equivalence idea, I need to hear it.

Wes
...

 

[A.T.]

...inertial frame ... whatever your theory of gravitation...

But the definition of inertial frame depends on which theory of gravitation you use. In GR "inertial frames" are just local approximations and there are no valid global inertial frames, when gravity sources are around.

...then that ball would remain at rest in the inertial frame we have established...

In GR the free falling ball does remain at rest in an local inertial frame, and so does the center of the Earth.

 

[A.T.]

I think most people know the difference beween reality and a thought experiment, so no one need be "mislead", or think GR non-sense.

Unfortunately I have seen many concluding that GR is nonsense after being exposed to such non-sequitur explanations, and I cannot even blame them. We know the Earth doesn't expand, so assuming that it does explains nothing.

 

[PeterDonis]

If the Earth moved to the first ball, then that ball would remain at rest in the inertial frame we have established.

No, it wouldn't. Moving the Earth close to the first ball curves spacetime, so the "inertial frame" you established is no longer a valid inertial frame.

We could also establish an inertial frame in which the Earth is at rest

No, you can't. There is no valid inertial frame that covers the entire Earth. The best you can do is construct a local inertial frame at the center of the Earth, but this frame will only cover a small region around the center; it will certainly not extend all the way to the surface and beyond.

You could also construct a local inertial frame in which the surface of the Earth at a particular point (say, just beneath a ball that is falling) was momentarily at rest. But the "momentarily" is crucial: the surface of the Earth will not stay at rest in such a frame. It will accelerate upward, while the falling ball will move at a constant speed. So again, there is no inertial frame in which the surface of the Earth at any point is at rest (for more than a single instant).

 

[PeroK]

But the definition of inertial frame depends on which theory of gravitation you use. In GR "inertial frames" are just local approximations and there are no valid global inertial frames, when gravity sources are around.

In GR the free falling ball does remain at rest in an local inertial frame, and so does the center of the Earth.

Thanks for this explanation. I'm still teaching myself SR and I haven't taken the leap to GR yet. But, it seems odd that one can't take an experimental view of what is happening from outside the system. E.g. from outside the solar system, from my naive perspective, one should be able experimentally to conclude that the Earth orbits the sun and not vice versa.

Kepler was a pure observationist for example. He had no knowledge of Newton's or Einstein's or any theory of gravity. He concluded by observation alone that the planets orbited the sun. That might be theoretically invalid from the GR perspective. But, how can it be observationally or experimentally invalid? If that is what you are saying. "And yet it moves"!

 

[PeterDonis]

from my naive perspective, one should be able experimentally to conclude that the Earth orbits the sun and not vice versa.

More precisely, the solar system, to a very good approximation, can be described as an isolated system of matter surrounded by empty space, with a definite center of mass, and that the object whose trajectory is closest by far to the trajectory of that center of mass is the Sun. We describe this informally as the planets orbiting the Sun (though a more precise description would be that the planets and the Sun all orbit their common center of mass).

But to say that the Earth orbits the Sun "and not vice versa" is to assert a preference for a certain system of coordinates (one centered on the Sun--or on the common center of mass), which is not, in principle, valid. Certain coordinates may be more useful than others, because the description of the solar system looks a lot simpler in terms of them, but that doesn't make other coordinates invalid; it just makes them less useful for certain purposes--but not for others. Try describing your route to the grocery store, or the path of an airplane flying from New York to London--or even the trajectories of the Apollo missions to and from the Moon--using coordinates centered on the Sun. In Earth-centered coordinates, the Sun does "orbit" the Earth; even our common language still says the Sun "rises" and "sets", instead of that the Earth turns to make the Sun visible or not visible from our location. Different coordinates are useful for different purposes.

He concluded by observation alone that the planets orbited the sun.

Actually, he concluded by observation alone that a description of the solar system that had the planets orbiting the Sun was a simpler way to account for the data. So he was really just discovering what I said above, that the physics of the planets and the Sun looks simpler in coordinates centered on the Sun (or, more precisely, on the solar system's center of mass).

 

[Wes Tausend]

Unfortunately I have seen many concluding that GR is nonsense after being exposed to such non-sequitur explanations, and I cannot even blame them. We know the Earth doesn't expand, so assuming that it does explains nothing.

Then you know more than Poincaré. He wasn't so absolutely sure we would be able to know. Poincaré eventually came within an inch of solving SR before Einstein and I admire him too.

If it makes you more comfortable, we could easily assume Earth does not expand for the explanation and that would be very conventional and along the lines of how Einstein personally developed the relativities. In GR he basically assumed that the vacuum of space was "vacuumed in" (curved) by the resting firmament of steady state matter. To explain thusly, one can nearly imagine the particles, the field lines, of nothingness being vacuumed by earth, very much faster as nothingness approaches the vortex ever closer. And that stretching vortex, causing a far reaching drift of nothingness towards earth, thereby drawing the moon close and keeping it in orbit, corraled in an invisible funnel cloud. Or a meteor rolling right over the edge straight on. Pretty much like the bowling ball stretching the blanket close to large mass. :)

Wes
...

 

[A.T.]

Pretty much like the bowling ball stretching the blanket close to large mass.

From bad analogy to the worst analogy.

 

[PeroK]

More precisely, the solar system, to a very good approximation, can be described as an isolated system of matter surrounded by empty space, with a definite center of mass, and that the object whose trajectory is closest by far to the trajectory of that center of mass is the Sun. We describe this informally as the planets orbiting the Sun (though a more precise description would be that the planets and the Sun all orbit their common center of mass). ...

I understand all your arguments about being free to choose any coordinate system. If you are saying: whatever the theory, whatever the experiment, you can always choose whatever coordinate system you like, then I'd agree with that.

I was trying to argue that, experimentally, you could show that the Earth has a bigger influence on the "motion" of a ball than the ball has on the Earth. And that the sun has a bigger influence on the motion of the planets than the Earth does (take the Earth out of the Solar system and would Jupiter even notice?). Yes, there would be a perturbation, but not much more I imagine.

It seems strange to say: it's equally valid to view the Sun as orbiting the Earth and Mars orbiting the Sun. But, then, why does a massive object in one case orbit the small object, but in the other case the smaller object orbits the larger one. I can't see a theoretical explanation for that.

Maybe this way of thinking has no scientific value. But, anyway, here's my question:

If the Sun is orbiting the Earth and Mars is orbitting the Sun, how do you explain that using classical physics? Without resorting to a model whereby both planets are "actually" orbitting the Sun? In order to explain this, you have to put the Sun at the centre, I thought?

 

[A.T.]

If the Sun is orbiting the Earth and Mars is orbitting the Sun, how do you explain that using classical physics?

In non-inertial frames there are inertial forces, additionally to Newtonian gravity. That is why the description from the inertial frame of the common center of mass is simpler, because it involves only Newtonian gravity.

 

[PeterDonis]

I was trying to argue that, experimentally, you could show that the Earth has a bigger influence on the "motion" of a ball than the ball has on the Earth.

"Bigger" here is coordinate-dependent (because "motion" is), so there will be no invariant way to show this. You will always be able to adopt a reference frame in which the ball is at rest and the Earth is moving. There's no measurement that can show that the ball is what is "really" moving.

It seems strange to say: it's equally valid to view the Sun as orbiting the Earth and Mars orbiting the Sun.

That's not what I said. I said it's equally valid (in principle) to adopt coordinates centered on the Sun, or coordinates centered on the Earth. Neither of those will result in the Sun orbiting the Earth but Mars orbiting the Sun. In coordinates centered on the Earth, the Sun orbits the Earth in a relatively simple trajectory, and Mars orbits the Earth in a much more complicated trajectory, with loops in it.

If the Sun is orbiting the Earth and Mars is orbitting the Sun, how do you explain that using classical physics?

You don't. Nobody ever proposed a model like this. The model that was used for many centuries before Copernicus and Kepler had everything orbiting the Earth. I would advise you to do some research into what that model actually said. It was nowhere near as naive and simplistic as you appear to believe.

 

[PeroK]

"Bigger" here is coordinate-dependent (because "motion" is), so there will be no invariant way to show this. You will always be able to adopt a reference frame in which the ball is at rest and the Earth is moving. There's no measurement that can show that the ball is what is "really" moving.

Some final questions.

In classical physics: I thought that Foucault's Pendulum and the Coriolis effect (for example) showed that the Earth is spinning (every 24 hours) and not that the Sun is orbiting the Earth every 24 hours. Is that not the case? Is there no experiment - in classical physics - that shows that the Earth is spinning?

In GR: is it not possible to conduct an experiment to show that the Earth orbits the Sun every year and not that the Sun orbits the Earth every day? It seems to me that the curvature of spacetime would be different in these two cases. Can the absolute curvature of spacetime not be measured?

I understand the idea about relativity of observations and motion. And I know that you can't detect absolute motion. But, I thought you could detect absolute acceleration? And an accelerating reference frame is equivalent to a gravitational field? But, is it impossible to measure the curvature of spacetime?

Final thought: a ball in local inertial motion starts a long way from a massive body and gradually gets closer to it. The ball gradually sees everything else "accelerate" until it collides with the massive body. Meanwhile, an observer on the massive body sees no significant changes to its motion.

This does not seem to me like a symmetric situation. The ball saw the rest of the universe "accelerate" and the massive object didn't. But, there is no experiment that shows that the ball entered a large gravitational field, while the massive object was the source of the gravitational field? I know they are both in "free fall", but it seems that their obseravtions are asymmetric.

I find it strange that you can't detect this asymmetry. The massive object is in massively curved spacetime all along, whereas the ball experiences increasingly curved spacetime.

 

[A.T.]

In classical physics: I thought that Foucault's Pendulum and the Coriolis effect (for example) showed that the Earth is spinning (every 24 hours) and not that the Sun is orbiting the Earth every 24 hours. Is that not the case? Is there no experiment - in classical physics - that shows that the Earth is spinning?

It shows that it's simpler to describe the Earth as spinning, because that eliminates the Coriolis and other effects related to a frame where the Earth doesn't spin.

In GR: is it not possible to conduct an experiment to show that the Earth orbits the Sun every year and not that the Sun orbits the Earth every day? It seems to me that the curvature of spacetime would be different in these two cases. Can the absolute curvature of spacetime not be measured?

The absolute curvature of space time is related to tidal effects, which are indeed frame invariant. And yes, of course it would be different.

I understand the idea about relativity of observations and motion. And I know that you can't detect absolute motion. But, I thought you could detect absolute acceleration?

You can detect proper acceleration, but gravity doesn't cause proper acceleration.

This does not seem to me like a symmetric situation. The ball saw the rest of the universe "accelerate" and the massive object didn't.

It's not symmetric because you introduced a third object: the rest of universe.

The massive object is in massively curved spacetime all along, whereas the ball experiences increasingly curved spacetime.

That is correct, if the ball is big enough it will be stretched by tidal forces, while the planet wont' be. But that doesn't imply anything about which of them is actually moving, beyond simplicity of calculations.

 

[PeroK]

It shows that it's simpler to describe the Earth as spinning, because that eliminates the Coriolis and other effects related to a frame where the Earth doesn't spin.

Thanks. I think I understand all this, but perhaps I'm looking for conclusions that modern physics, in general, does not like to draw.

 

[rajeshmarndi]

When we throw a ball up, it decelerates and ultimately comes to rest and then accelerates towards the surface. Is it the ball actually travel in curve path at constant velocity but since we see the ball always vertically above us, we don't see the ball path which is curve [Edited: and therefore we don't observe constant velocity of the ball either]. Just like in a half ellipse , we move ahead in time along the minor axis of the half ellipse from one end and the thrown ball(vertically above us) moving along the curve of the half ellipse and the ball meet with us at the other end of the minor axis.

 

[PeterDonis]

I thought that Foucault's Pendulum and the Coriolis effect (for example) showed that the Earth is spinning (every 24 hours)

The Foucault Pendulum shows that the Earth is spinning relative to the pendulum. The Coriolis effect is a coordinate effect, and can be eliminated, as A.T. pointed out, by choosing different coordinates.

and not that the Sun is orbiting the Earth every 24 hours

The Foucault pendulum and the Coriolis effect are separate sets of observations from the observation of the relative motion of the Sun and the Earth, so they have to be considered separately. (For example, the period of relative rotation of the Earth and the Foucault pendulum is not 24 hours; it's 23 hours, 56 minutes, and some number of seconds that I can't remember right now.)

is it not possible to conduct an experiment to show that the Earth orbits the Sun every year and not that the Sun orbits the Earth every day? It seems to me that the curvature of spacetime would be different in these two cases.

of course it would be different.

The situation that exists in our actual solar system can be described both ways, and the curvature of spacetime is the same. Of course if the relative masses of the Earth and the Sun were different, the curvature of spacetime would be different, but then experiments would show a lot of other differences as well. Given the experimental results we actually have, there is no experiment we can do that shows that the Earth "really" orbits the Sun; the best we can show is where the center of mass of the solar system is, and that the simplest description of the motion of the Sun and planets is given in a frame centered on that center of mass.

 

[PeterDonis]

When we throw a ball up, it decelerates and ultimately comes to rest and then accelerates towards the surface.

In a frame in which the surface is at rest, yes. But this is coordinate acceleration, not proper acceleration. An accelerometer attached to the ball will read zero, and an accelerometer attached to the surface will read nonzero, so the surface is what is accelerated in the sense of proper acceleration.

Is it the ball actually travel in curve path at constant velocity but since we see the ball always vertically above us, we don't see the ball path which is curve

No, it's that whether or not the ball's path is "curved" or not, in a coordinate sense, depends on the coordinates you pick; it's curved in coordinates in which the surface is at rest, but it's straight in coordinates in which the ball is at rest. If you want an invariant sense of "curved", then you have to define a path as "curved" if it has nonzero proper acceleration, and "straight" if it has zero proper acceleration; as above, that means the ball's path is straight and the surface's path is curved.

 

[A.T.]

Of course if the relative masses of the Earth and the Sun were different, the curvature of spacetime would be different

Yeah, that's how I meant it.

 

[inertiaforce]

Guys, take a look at this video. Brian Greene is also saying that Einstein's view was that the Earth rushes up and hits you. You do not fall to the earth. Watch this video from 9:30 to 15:00:

 

[A.T.]

Brian Greene is also saying that Einstein's view was that the Earth rushes up and hits you.

That is not just Einstein's view, but every free faller's view. Even in classical Newtonian mechanics you can view things from the free falling frame, where the Earth is moving, while the free falling object is still.

You do not fall to the earth.

See my earlier comments on the ambiguity of pop-sci language, aimed at a mass audience:
https://www.physicsforums.com/threa...do-not-fall-to-the-earth.781200/#post-4909705

 

[inertiaforce]

That is not just Einstein's view, but every free faller's view. Even in classical Newtonian mechanics you can view things from the free falling frame, where the Earth is moving, while the free falling object is still.See my earlier comments on the ambiguity of pop-sci language, aimed at a mass audience:
https://www.physicsforums.com/threads/einstein-says-objects-do-not-fall-to-the-earth.781200/#post-4909705[/QUOTE]

Thanks for your reference A.T. I agree with you. "Falling" appears to be an ambiguous term.

 

[Dale]

Note that while "falling" is ambiguous, "free-fall" and "free-falling" are not. They refer to the inertial object and the ground rushes up to meet the inertial object precisely because the ground is not free-falling and the inertial object is.

When Brian Greene uses the unambiguous scientific term he uses it correctly (at least in the brief clip I watched).

 

[A.T.]

Note that while "falling" is ambiguous, "free-fall" and "free-falling" are not. They refer to the inertial object and the ground rushes up ...

To me "rushing up" is ambiguous too. It could mean movement, which is relative. So even in classical mechanics the Earth can be "rushing up" in some frame.

 

[CKH]

But to say that the Earth orbits the Sun "and not vice versa" is to assert a preference for a certain system of coordinates (one centered on the Sun--or on the common center of mass), which is not, in principle, valid. Certain coordinates may be more useful than others, because the description of the solar system looks a lot simpler in terms of them, but that doesn't make other coordinates invalid; it just makes them less useful for certain purposes--but not for others.

But the choice is more than just a preference for a certain system of coordinates. The laws of motion are stated for an inertial frame. If you choose a non-inertial frame and incorrectly apply these laws of motion to that frame, fictitious force fields appear. These fields don't actually exist. They are the result of misapplication of physical law.

For example, if you contend that the Earth is stationary (that it is at rest in an inertial frame) and that the universe revolves around the earth, you need fictitious force fields (pseudo centrifugal and coriolis forces) to explain this. This is just a mistake in the application of physical law. The conclusion that the universe revolves around the Earth is untenable.

The choice of coordinates is not arbitrary when you apply physical laws that are expressed for an inertial frame. To apply the laws you must choose an inertial frame.

So long as you know how two coordinate systems are related, you can transform physical events from one system to another, no physics is involved in this, it is just math.

 

[A.T.]

But the choice is more than just a preference for a certain system of coordinates.
...
So long as you know how two coordinate systems are related, you can transform physical events from one system to another, no physics is involved in this, it is just math.

So, it is just a preference for a certain system of coordinates. For example a preference based on the simpler math in those coordinates.

 

[DrGreg]

But the choice is more than just a preference for a certain system of coordinates. The laws of motion are stated for an inertial frame. If you choose a non-inertial frame and incorrectly apply these laws of motion to that frame, fictitious force fields appear. These fields don't actually exist. They are the result of misapplication of physical law.

For example, if you contend that the Earth is stationary (that it is at rest in an inertial frame) and that the universe revolves around the earth, you need fictitious force fields (pseudo centrifugal and coriolis forces) to explain this. This is just a mistake in the application of physical law. The conclusion that the universe revolves around the Earth is untenable.

The choice of coordinates is not arbitrary when you apply physical laws that are expressed for an inertial frame. To apply the laws you must choose an inertial frame.

So long as you know how two coordinate systems are related, you can transform physical events from one system to another, no physics is involved in this, it is just math.

All this would be correct within Special Relativity.

In General Relativity there are no such things as truly inertial frames. However in a small enough region, where the tidal effects of gravity are negligible, you can find a locally-approximately-inertial frame.

 

[jerromyjon]

you can find a locally-approximately-inertial frame.

"Near Earth Objectivity"?

 

[Dale]

The choice of coordinates is not arbitrary when you apply physical laws that are expressed for an inertial frame. To apply the laws you must choose an inertial frame.

I mostly agree with that, but I would say "The choice of coordinates is not arbitrary when you apply THOSE physical laws that are expressed for an inertial frame. To apply THOSE laws you must choose an inertial frame."

Not all physical laws are expressed in terms of an inertial frame. For instance, the EFE is expressed in terms of tensors, and Lagrangian mechanics is expressed in terms of generalized coordinates. So you need to know for each specific physical law you are using whether or not the choice of coordinates is arbitrary. If the choice is not arbitrary for that specific law then, as you said, you cannot use a non-inertial frame with that law.

 

[DrGreg]

you can find a locally-approximately-inertial frame.

"Near Earth Objectivity"?

I don't understand what that means.

 

[jerromyjon]

Objective permanence for the agoraphobic. Look up at the sky and see through the manifolds... kind of like a joke I guess. I wasn't sure what to think it meant but in my endeavors I finally envisioned a manifold in spacetime so its all good.

 

[CKH]

Not all physical laws are expressed in terms of an inertial frame. For instance, the EFE is expressed in terms of tensors, and Lagrangian mechanics is expressed in terms of generalized coordinates. So you need to know for each specific physical law you are using whether or not the choice of coordinates is arbitrary. If the choice is not arbitrary for that specific law then, as you said, you cannot use a non-inertial frame with that law.

I rather expected that when I posted. Unfortunately I'm not up to speed on those subjects (tensors, Lagrangian mechanics and generalized coordinates) nor the physical law that uses them. So I cannot appreciate yet how physical law can be stated independently of any background conditions in which the law is said to apply.

.

 

[CKH]

So, it is just a preference for a certain system of coordinates. For example a preference based on the simpler math in those coordinates.

I don't see how you can say that. What I'm talking about is how a physical law is stated. If it's stated for an inertial frame (which is not unusual) then you cannot apply it directly to a non-inertial frame. That is not a matter of preference, it is a requirement. You may have some freedom to choose a particular inertial frame but you have no freedom to apply the law to non-inertial frames.

Take for example :

This law cannot be applied to non-inertial frames, it's not just a matter of convenience.

 

[CKH]

In General Relativity there are no such things as truly inertial frames. However in a small enough region, where the tidal effects of gravity are negligible, you can find a locally-approximately-inertial frame.

Is there a name for that beast? Apparently by definition an "Inertial frame" is global (over all time and space) rectilinear motion. Therefore we cannot say that the space station is at rest in any inertial frame. However, the motion of the space station is inertial in that it has nearly 0 proper acceleration.

How do we properly express this in physics? Do we say "local inertial frame" perhaps "local inertial space" or perhaps "momentarily comoving inertial rest frame". Momentary isn't particularly satisfying because whatever we name this frame it retains it's inertial motion (in the sense of 0 proper acceleration) over time. Can we call it's worldline an "inertial path"?

 

[A.T.]

...If it's stated for an inertial frame...

Here is where the preference comes in. We prefer to state the laws for inertial frames, because that is simpler.

 

[A.T.]

Apparently by definition an "Inertial frame" is global (over all time and space) rectilinear motion.

Not in curved space time. There it only applies to a small region approximately.

Therefore we cannot say that the space station is at rest in any inertial frame.

For one small object that creates only negligible gravity itself you can say this. Build the space-station bigger, and some parts will experience non-zero proper acceleration, so it its not entirely inertial. And when you have two massive celestial bodies, there is no way you can define global inertial coordinates, that have zero proper acceleration everywhere.

 

[CKH]

Here is where the preference comes in. We prefer to state the laws for inertial frames, because that is simpler.

OK. I'm curious about what the alternative might be. How would you express the physical law below for any arbitrary frame? Or does each frame have it's own different physical laws? The latter concept is not an attractive approach to defining physical law.

Whenever you mistreat a non-inertial frame as inertial and apply the above physical law, fields appear that are not real, that is they have no existence independently from that frame.

Re global inertial frame:

Not in curved space time. There it only applies to a small region approximately.

Right. So the strict definition of an "inertial frame" is something that only exists in principle. As I mentioned we need a term for "local inertial frame". Is that the term that is standard? For the space station there is an instantaneous local inertial frame, but there is also is also continuous inertial motion. If you consider the worldline of the space station, a small region of space around the worldline is "continuously inertial" in that proper acceleration approaches 0. Does such a worldline have a name? E.g. inertial path, geodesic path in spacetime?

 

[A.T.]

The latter concept is not an attractive approach

Hence we prefer not to use it

Does such a worldline have a name? E.g. inertial path, geodesic path in spacetime?

That’s how I would call it.

 

[Dale]

I rather expected that when I posted. Unfortunately I'm not up to speed on those subjects (tensors, Lagrangian mechanics and generalized coordinates) nor the physical law that uses them. So I cannot appreciate yet how physical law can be stated independently of any background conditions in which the law is said to apply.

.

No problem. This way at least you are aware of their existence, if not their mechanics.

Your point is correct, just not universally applicable. For laws expressed in terms of inertial frames you certainly do not have the option to use them in a non inertial frame as is.

For laws expressed in a covariant form or in terms of generalized coordinates the above doesn't apply. Luckily, most laws of physics have a known formulation or generalization in one of these types of structures.

 

[CKH]

Hence we prefer not to use it

You did not address my question directly. You claim that we just "prefer" to describe this physical law in an inertial frame. So what is an alternative expression of the physical law?

Perhaps you would say, "instead of using an inertial frame for this physical law, I will define a more complicated physical law for a frame fixed to the surface of the earth"?

How would you do that? I.e. how would you derive an equation for the corresponding physical law of inertia in this frame?

Do you believe that fictitious forces should be considered as having physical existence? (To me that's like believing "my shadow has an independent existence" or "when I turn my head it is equally valid to say my head is still, but my body twisted and caused the entire universe to accelerate, rotate about my head and then stop again".)