Kind of newbie question about gravity

[Tiago]

Hi,

We know from Einstein's GR that gravity bends spacetime and that curvature effect makes other masses "fall" down that curvature and orbit around it. But I can't understand how that affects everyday life, like why are we attracted to the Earth, no matter where we are. A guy in the north pole is attracted to the Earth as much as someone in the south pole and we now know that gravity is not an attraction force. So how can we illustrate that effect? I've seen those videos where they show a planet causing a bump in the spacetime and all the planets orbiting around it, falling to that curve, without ever reaching it. But how does that explain that we are attracted to the Earth, no matter where in the planet we are? I'm sorry if this is a stupid question, but I'd really like to understand it.

Thanks in advanced!

 

[Orodruin]

The rubber sheet analogy is a bit misleading in that space-time is represented by a two-dimensional rubber sheet (with only spatial directions), when it is in fact four-dimensional. In the GR setting, anyone standing still on the Earth surface is in an accelerated frame, accelerating outward with an acceleration of 9.8 m/s^2. What stops these people from being in a locally inertial frame is the fact that the Earth is in the way and ultimately that the Earth constituents are repelling each other due to pressure.

To get back to the rubber sheet, imagine the Earth as a two-dimensional object instead. The best analogy possible with this setup is to imagine the Earth as a circle on the rubber sheet. On both sides of the circle, the sheet is tilted towards the circle and things therefore tend to move in that direction.

 

[A.T.]

I've seen those videos where they show a planet causing a bump in the spacetime and all the planets orbiting around it, falling to that curve, without ever reaching it. But how does that explain that we are attracted to the Earth, no matter where in the planet we are?

It doesn't explain that. It's a flawed analogy confusing space-time with a potential well. See:
http://en.wikipedia.org/wiki/Gravity_well#Gravity_wells_and_general_relativity

But I can't understand how that affects everyday life, like why are we attracted to the Earth,

This videos deal with the local effect.

A guy in the north pole is attracted to the Earth as much as someone in the south pole and we now know that gravity is not an attraction force.

At the end of the second video above you see a space-time cone, that gets thinner, as it gets further away from the Earth. On the other side of the Earth you have symmetrically the same thing, Here is an interactive diagram that shows space-time along a radial line for both sides of the planet:

http://www.adamtoons.de/physics/gravitation.swf

 

[Wes Tausend]

Hi,

We know from Einstein's GR that gravity bends spacetime and that curvature effect makes other masses "fall" down that curvature and orbit around it. But I can't understand how that affects everyday life, like why are we attracted to the Earth, no matter where we are. A guy in the north pole is attracted to the Earth as much as someone in the south pole and we now know that gravity is not an attraction force. So how can we illustrate that effect? I've seen those videos where they show a planet causing a bump in the spacetime and all the planets orbiting around it, falling to that curve, without ever reaching it. But how does that explain that we are attracted to the Earth, no matter where in the planet we are? I'm sorry if this is a stupid question, but I'd really like to understand it.

Thanks in advanced!

Tiago,

No question is stupid here. Sometimes Nature's answers seem a little strange.

Sometimes the explanations can get complicated and even more confusing for a newby. Einstein started with a quite simple assumption when he started looking at properties of gravity. I urge you to also read Einstein's parallel link I just gave. Einstein had a gentle way to explain things to us lesser mortals and is probably best at it.

Einstein did a thought experiment. He assumed that, if a pair of scientists were enclosed within a chest in a gravity-free (same as free-fall) area, that was drawn up by a "rope" at the same acceleration rate as Earth's gravitational field (that of 9.8 m/s²), they would not be able to tell the difference between a gravitational field or ordinary inertia which would form a sort of artificial field. The would feel the same body weight as they had on earth. Or another way to look at it is sitting in a hotrod that takes off in a drag race and being thrown back in the seat from the acceleration. In the hotrod, they are called "G's" for a reason (G's for Gravity).

Einstein supposed that the scientists in the accelerating chest could "drop" an object from their lab table and it would seem to fall to the floor. In reality, it would coast in space at the exact momentary speed it was going when released from table-top acceleration... and the still accelerating, ever quicker rising floor would be drawn up to meet and strike the coasting object, so it gives us another intepretation of the word, "falling". The scientists would not be able to tell the difference between that observation of the coasting object and gravitational "free-fall" of the object. Einstein called this interesting phenomenon the Equivalence principle. Inertia is observed to be equivalent to gravity under these limited conditions and no "attraction" is required. Behold! Newtons apple does not fall... the ground effectively rises to strike the apple. Einstein built his entire gravity-included theory, General Relativity (GR), partly from this simple principle, plus including his previous Special Relativity (SR) theory on light (matter vs energy, E=mc²). No wonder the blackboards become filled with equations!

Were we to think of thee pair of scientists split between the north and south pole on earth, we could think of them as each being in a drawn chest (I prefer elevator) and being pulled apart at an ever increasing speed. Although the "accelerating" scientists appear to be moving faster and faster in opposite directions to an outside observer, each feels exactly as though they are standing still in the field of Earth's gravity.

Only were the scientists to look out, would they see the other elevator getting smaller and smaller in the distance, and then be inspired to assume they are really being drawn apart. There arises a caveat to this imagineering and Einstein addressed it. He said that in the single chest, "In course of time their velocity will reach unheard-of values—provided that we are viewing all this from another reference-body which is not being pulled with a rope." By this, I assume he concerned himself with the limiting speed of light, so the simplified thought experiment, if fully carried out, does take much more complicated geometry to fulfill his General Theory, and yet remain consistant with his electromagnetic light theory.

This same elevator "thought experiment" can be used to easily visualize how gravity curves light, but this post is long enough for now. I hope this helps. Feel free to ask more questions, especially if Einsteins thought experiment does not make sense the way I explained it.

Wes
...

 

[jambaugh]

Here is an analogy which might help. You and I stand on the equator of a small spherical planet and begin walking north. Suppose we are separated by some kilometers but have radio ranging equipment to measure our distance from each other and to communicate. Initially we are moving parallel but soon we notice that our direction of motion is turning toward one another and the distance between us is decreasing. We wonder at the mysterious "gravitational" force that is causing our paths to turn as we both walk northward. The actual cause of our surprise is that our intuition is based on a flat world mindset and we have neglected the fact that the surface on which we travel is curved.

The problem with this and any such analog is that we are embedding curved surfaces in an Euclidean space while we cannot do that with the true pseudo-Euclidean space-time. The analogy will break down at some point if you try to match up all the pieces. But what you can do is sit down and work out the quantitative equations for the motion of paths in say this curved example and then generalize the math to other indefinite spaces. You got to do the math at some point.

 

[s_luke52]

Think of spacetime as having an elasticity. The greater it is deformed by the matter which exists in it the greater it is displaced from its relativistic rest position; the greater it pushes back and exerts inward pressure toward the matter.

Instead of referring to the deformation of spacetime I think it is easier conceptually to think of the state of displacement of spacetime. For conceptual purposes, consider spacetime to be a supersolid displaced by the Earth. The supersolid spacetime displaced by the Earth pushes back and exerts inward pressure toward the Earth.

Displaced spacetime pushing back and exerting inward pressure toward matter is gravity.

The state of displacement of spacetime is gravity.

 

[Nugatory]

Think of spacetime as having an elasticity. The greater it is deformed by the matter which exists in it the greater it is displaced from its relativistic rest position; the greater it pushes back and exerts inward pressure toward the matter.

If thinking about it that way helps you understand... great. But as with any metaphor/analogy you have to be careful not to take it too seriously as an explanation. Yours isn't necessarily worse than the popular but totally bogus misleading "rubber sheet" analogy, but it's still misleading in several ways. Consider:
- If I measure the pressure on an object on the surface of the earth, I won't see a downwards pressure from "displaced spacetime". I'll see an upwards pressure from the Earth underneath it.
- If we open a trapdoor under the object the object will experience no "pressure" whatsoever, and indeed will behave exactly as if it is floating free in empty space far from any gravitational source (until it and the ground collide).

Einstein's epiphany, and the key to understanding general relativity, is that the real physical phenomenon here is the one that our instruments can detect - and that's the force of the Earth pushing up on the object.

 

[A.T.]

what is the Earth exerting a measurable upward pressure against?

The surface exerts an upwards force on objects resting on the surface, which is not opposed by any other force. That's why these objects experience an upwards proper acceleration, which can be measured with an accelerometer.

See for example the green apple hanging on the branch. The branch exerts an unbalanced upwards force on the apple (in Einsteins model):

 

[Tiago]

I wanted to thank everyone who replied to my initial post! It was incredibly educating. I actually understood, at least the concept of einstein's gravity. The curvature of spacetime influences every accelerated body. If it only existed space and a single body with some degree of acceleration, it would float on a straight line forever. But that same body on Earth will float towards the curvature of space time.. which means towards the body that's curving the spacetime (Earth). Is this more or less accurate?

Thanks!

 

[PeterDonis]

The curvature of spacetime influences every accelerated body.

It influences every body, accelerated or not.

If it only existed space and a single body with some degree of acceleration, it would float on a straight line forever.

If the body were accelerated (i.e., feeling a force), it would not "float on a straight line"; its worldline would be curved, and it would not be "floating" because it would be feeling weight.

that same body on Earth will float towards the curvature of space time.. which means towards the body that's curving the spacetime (Earth).

Freely falling (i.e., unaccelerated) bodies will do this, yes. Accelerated bodies may not; for example, rockets can launch objects from Earth's surface into orbit, by accelerating them.

 

[rajeshmarndi]

The surface exerts an upwards force on objects resting on the surface, which is not opposed by any other force. That's why these objects experience an upwards proper acceleration, which can be measured with an accelerometer.

You mean, just like an elevator accelerates up, the surface of the Earth too accelerates up. Isn't then the Earth surface expanding?

 

[PeterDonis]

Isn't then the Earth surface expanding?

No, because in a curved spacetime, the surface can be accelerating upward (i.e., feeling an upward force) without moving upward (i.e., expanding).

 

[Wes Tausend]

You mean, just like an elevator accelerates up, the surface of the Earth too accelerates up. Isn't then the Earth surface expanding?

No. The Equivalence effect is considered to be an apparent phenomenon. As Einstein stated, the elevator would reach "unheard of speed". Energy, not matter, is assigned a privilaged frame of motion (C) in contemporary physics. Energy and matter are not considered to be interchangeable in examples of velocity.

Wes
...

 

[PeterDonis]

Energy, not matter, is assigned a privilaged frame of motion (C) in contemporary physics.

Huh? Where are you getting this from? There are no "privileged frames of motion" in relativity, period.

Energy and matter are not considered to be interchangeable in examples of velocity.

This is incorrect as well.

 

[Wes Tausend]

Wes Said: Energy, not matter, is assigned a privilaged frame of motion (C) in contemporary physics

Huh? Where are you getting this from? There are no "privileged frames of motion" in relativity, period.

Wes said: Energy and matter are not considered to be interchangeable in examples of velocity

This is incorrect as well.

Peter,

I do appreciate your attention on this.

I got my perception from a FAQ that I thought infers this:
"A rest frame of some object is a reference frame in which the object's velocity is zero. One of the key axioms of special relativity is that light moves at c in all reference frames. The rest frame of a photon would require the photon to be at rest (velocity=0) and moving at c (velocity=299792458 m/s). That of course is contradictory. In other words, the concept doesn't make sense."

The sentence that in part that says "light moves at c in all reference frames", made me think light always enjoys a privilaged frame of motion.

The remark about the non- interchangeable velocity exception follows, also based on, "Energy and matter are constant and interchangeable throughout the universe."

The idea that the FAQ argument "does not make sense" to ones intuition does not seem like a good science argument actually. I'm curious if the reason is just that current math is fouled up if a photon can be assigned rest?

This wanders off topic. Should I start a different thread concerned with my misunderstanding? I am curious about this apparent imbedded misconception on my part. I've never gotten to learn relativity in a live classroom setting , so I hope you forgive me. Any enlightenment you can shed on this will most appreciated. Thanks.

Wes
...

 

[A.T.]

You mean, just like an elevator accelerates up, the surface of the Earth too accelerates up. Isn't then the Earth surface expanding?

No read this:
https://www.physicsforums.com/threa...-fall-to-the-earth.781200/page-2#post-4913216

In curved space time, proper acceleration away from a point doesn't imply movement away from that point. Note that in even in classical mechanics, acceleration towards a point doesn't imply moment towards that point (e.g. uniform circular motion). Curved space time allows this for the opposite direction too.

 

[bhobba]

A rest frame of some object is a reference frame in which the object's velocity is zero

That's right. But you need to get the terminology straight.

A frame is a conventional standard of rest in which experiments can be conducted. A frame attached to the Earth will see the stars rotate. If you arrange your frame to rotate with the Earth they will be stationary.

A frame where free particles move with constant velocity is called inertial. Without going into the details (you will find it in Landau - Mechanics) this follows from the fact such a frame is isotropic in direction (ie all directions are equivalent), homogeneous in space and time (all point of space and instants in time are equivalent).

Special Relativity only applies to inertial frames. In fact SR basically follows from those symmetry properties which is a very striking and deep insight indicative of much of modern physics - symmetry is its rock bottom essence - in fact this was one of Einstein's greatest insights:
http://www.pnas.org/content/93/25/14256.full

A frame attached to the Earth is not inertial - although for most purposes it can be considered to be one. However if you imagine you are in a freely falling elevator then that would be inertial - let go of an object and it stays put.

That is the sense the surface of the Earth is considered accelerating upwards - that's what happening in an inertial frame.

Thanks
Bill

 

[harrylin]

[..] you need to get the terminology straight.
[..]
Special Relativity only applies to inertial frames.

Just a precision: the laws of special relativity apply to inertial frames only, but special relativity works with frames in all forms of motion, by mapping to them from inertial frames.

A frame attached to the Earth is not inertial - although for most purposes it can be considered to be one.

Yes indeed. However:

However if you imagine you are in a freely falling elevator then that would be inertial - let go of an object and it stays put. [..]

Caution here! According to the definition used by for example Einstein in his publications as well as Moller in his textbook, an object that falls in a gravitational field is not inertial but in free fall. Motion that is not affected by any field or contact forces is inertial. So, if you imagine that you are not falling down but the Earth is falling upward, then you can pretend to be at rest in an inertial frame.

Regretfully many people nowadays use terminology that is incompatible with the terminology that was used with Einstein's GR, and that causes unnecessary confusion.

 

[A.T.]

...an object that falls in a gravitational field is not inertial but in free fall...

Which is locally equivalent.

Regretfully many people nowadays use terminology that is incompatible with the terminology that was used ...

Or maybe the problem is people who even nowadays insist on using some terminology that was once used?

 

[bhobba]

Regretfully many people nowadays use terminology that is incompatible with the terminology that was used with Einstein's GR, and that causes unnecessary confusion.

Yes - but things have moved on since Einstein's time after criticisms by Kretschmann etc - it is now understood a lot better.

My bible is Wald - and yes I have taken a few liberties (eg I neglected the bug-bear of tidal forces) - but gee - I was answering a beginners question :D:D:D:D:D:D:D

Thanks
Bill

 

[harrylin]

Yes - but things have moved on since Einstein's time after criticisms by Kretschmann etc - it is now understood a lot better. [..]

Recently I myself presented criticism of Einstein's theory (incl. Moller) on this forum; this is something else. From the start one had the choice of such descriptors as "inertial", free-fall" and "geodesic", each with its particular meaning that helps sharp thinking.
How can unnecessarily obscuring a commonly used meaning be helpful for better understanding? I would appreciate it if you can give a link to a convincing advocacy (by Kretschmann?) of that.

I can imagine several reasons for unnecessarily modifying an existing definition that has not fallen in disuse, such that its proper meaning effectively disappears:
- confused misinterpretation (like happened with Billion in the USA)
- acceptance of misinterpretation for harmonization (like happened next with Billion in the UK, as imposed by Tony Blair)
- Newspeak (that is, purposeful thought sabotage as explained by George Orwell)

I was answering a beginners question :D:D:D:D:D:D:D

I appreciate that. :)
However, beginners should be more familiar with its meaning as they know from classical mechanics. I recall how confusing early discussions on this newsgroup about GR were for me, due to this alteration of meaning.

Thank you too!

 

[A.T.]

However, beginners should be more familiar with its meaning as they know from classical mechanics. I recall how confusing early discussions on this newsgroup about GR were for me, due to this alteration of meaning.

There is no alteration of meaning of "inertial movement" between classical mechanics and GR. In both contexts it means that the sum of external interaction forces is zero. What changed is that gravity is not modeled as an interaction force anymore, but as a coordinate effect (inertial force).

 

[bhobba]

How can unnecessarily obscuring a commonly used meaning be helpful for better understanding? I would appreciate it if you can give a link to a convincing advocacy (by Kretschmann?) of that.

I think you misinterpreted what I wrote. I didn't claim Kretschmann advocated the view I presented in my post, which is a simplification.

That said I don't think I obscured any commonly used meanings of anything.

I claimed things have moved on since Einstens time because of criticisms by people like Kretschmann.

Specifically Kretschmann, pointed out, correctly, the principle of general covarience that Einstein used was vacuous and is now replaced with the principle of invariance.

If you want to investigate the issue further the book to get is Gravitation and Space-Time by Ohanian:
https://www.amazon.com/dp/1107012945/?tag=pfamazon01-20

He also presents a very important development based not on geometry but on the most reasonable generalisation of Maxwell's equations.

Thanks
Bill

 

[bhobba]

There is no alteration of meaning of "inertial movement" between classical mechanics and GR. In both contexts it means that the sum of external interaction forces is zero. What changed is that gravity is not modeled as an interaction force anymore, but as s coordinate effect (inertial force).

That's true.

But even more important is the correct development given in Landau - and of course he is not the only one. An inertial frame is often defined as one where free particles move with constant velocity - but a careful analysis shows its vacuous. And the definition based on no nett external forces is, while also correct, basically tautological. The issue dates to Newtons first law, which follows from his second law which is merely a definition. Newtons laws is basically a prescription - get thee to the forces. The approach of Landau is much better - but I won't say any more - not only because it's way off topic - but because exposure to that masterpiece you must experience for yourself:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20
'If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages.'

Thanks
Bill

 

[harrylin]

There is no alteration of meaning of "inertial movement" between classical mechanics and GR. In both contexts it means that the sum of external interaction forces is zero. What changed is that gravity is not modeled as an interaction force anymore, but as a coordinate effect (inertial force).

Assuming that you mean with "GR" Einstein's theory of gravitation, that is certainly correct: I found no inconsistency of definition of inertial motion in the literature at hand on classical mechanics, SR and GR. The meaning of "inertial" in Einstein's theory as expressed in his own papers as well as in GR textbooks by Moller and by Adler et al, is quite the same as in classical mechanics and special relativity. As I briefly explained, the meaning according to Bill is incompatible with that meaning.
I won't comment further in this thread.

I think you misinterpreted what I wrote. I didn't claim Kretschmann advocated the view I presented in my post, which is a simplification. That said I don't think I obscured any commonly used meanings of anything.

I was not sure if you mentioned Kretschmann concerning theory, or concerning definitions - that's why I clarified that Einstein's theory isn't the issue here. And I certainly won't accuse you of personally obscuring anything - instead, I appreciate your sincere efforts to be helpful on this forum (in particular concerning QM)!

I claimed things have moved on since Einstens time because of criticisms by people like Kretschmann.
Specifically Kretschmann, pointed out, correctly, the principle of general covarience that Einstein used was vacuous and is now replaced with the principle of invariance. [..]

I think that you refer here in fact to his "general principle of relativity" - and with a quick search I found the 1993 review by Norton, "General covariance and the foundations of general relativity: eight decades of dispute". That relates to the subject of my criticism some days ago, somewhat following Builder. The plain rejection of that principle results in a GR (effectively without GR!) that is less different from SR than the theory that Einstein had in mind.

Consequently, I remain riddled as to the motivation for the change in meaning of "inertial" in (I suppose) many textbooks. I suspect that it originates from John Doe's interpretation, and so I would like to know:

- who was this John Doe
- what was his (or her) argument

Earlier you mentioned Wald; perhaps he mentions this John Doe?
As this is indeed going totally off-topic, I'll reply your answer in a PM.

Thanks!

 

[bhobba]

Consequently, I remain riddled as to the motivation for the change in meaning of "inertial" in

I presume you are concerned with the definition based on symmetry.

Its the more advanced view that avoids issues with other definitions such as a frame where free particles move with constant velocity - and its pretty well standard these days eg:
http://en.wikipedia.org/wiki/Inertial_frame_of_reference

If that isn't it can you please clarify?

Who originated it? Blowed if I know. I first came across it in Landau - but if I was to guess I would say Wigner - he constantly stressed the importance of symmetry, and some of his greatest discoveries were based on it:
https://www.amazon.com/dp/0918024161/?tag=pfamazon01-20

Regarding Kretschman you will only find advanced discussion of it on the internet - get the book by Ohanian to get to grips with it.

Thanks
Bill

 

[harrylin]

I presume you are concerned with the definition based on symmetry.

Its the more advanced view that avoids issues with other definitions such as a frame where free particles move with constant velocity - and its pretty well standard these days eg:
http://en.wikipedia.org/wiki/Inertial_frame_of_reference [..]

I see on your profile page no possibility to send PM's to you. Thus I'll post one more time here.

That definition of Landau certainly deviates from the definition of others. Funny enough, as also indicated on the wiki Talk page, even his definition is similarly incompatible with yours - I can add Landau to my list in post #18.

However, that same Talk page does give a lead: apparently you are following the definition of Misner et al.

Thanks!

PS suddenly I can send you PM's; I'm still getting used to the new software.

 

[Tiago]

Thank you all for you precious help on my newbie question. I do have a follow up question though...

If Einstein is right and gravity is not pulling us to the Earth and it is in fact the Earth that is actually moving and keeping us stuck to it (like going up on a super fast elevator), then why do lighter things such as feathers take longer to reach the ground (or for the ground to reach them) than heavier things? I always thought that, of course, the air caused the necessary resistance to differentiate how objects fall, but that was when I thought that objects actually fell... If it's the ground that's meeting the objects, how come they are not reached by the ground at the same time? Why is the air resistance even important since they are not falling? I know there is a very simple answer, but in light of these Einstein theories I've been reading, I'm failing to make sense of it :)

Thanks!

 

[A.T.]

If Einstein is right and gravity is not pulling us to the Earth and it is in fact the Earth that is actually moving and keeping us stuck to it (like going up on a super fast elevator)

You seem still very confused about the difference of movement and acceleration.

then why do lighter things such as feathers take longer to reach the ground (or for the ground to reach them) than heavier things?

Because that's exactly what would happen in an accelerating rocket in space too. The floor pushes the air, which pushes the objects, so their aerodynamics becomes relevant.

 

[Tiago]

You seem still very confused about the difference of movement and acceleration.

Because that's exactly what would happen in an accelerating rocket in space too. The floor pushes the air, which pushes the objects, so their aerodynamics becomes relevant.

You're absolutely right when you say I was confusing the two terms. What I wanted to say is that traveling in an elevator that is going up at a superspeed should hold a similar effect as standing still on Earth, because the Earth is moving. There is a question about acceleration that comes to my mind. Why do objects accelerate in a free fall until they hit the ground? It's actually the ground that's meeting them...

Your response about the floor pushing the air makes sense, thanks for sharing! :)

 

[A.T.]

You're absolutely right when you say I was confusing the two terms.

You still are confusing them it seems:

What I wanted to say is that traveling in an elevator that is going up at a superspeed should hold a similar effect as standing still on Earth, because the Earth is moving.

Moving at superspeed has no gravitational effect at all. Neither in the elevator, nor on the Earth. Movement is just a function of the chosen reference frame. What has an effect is the frame invariant proper acceleration, which is expierenced by both: the Earth's surface and a rocket in space with engines on.

 

[Tiago]

You still are confusing them it seems:Moving at superspeed has no gravitational effect at all. Neither in the elevator, nor on the Earth. Movement is just a function of the chosen reference frame. What has an effect is the frame invariant proper acceleration, which is expierenced by both: the Earth's surface and a rocket in space with engines on.

Ok, so, from common knowledge, I'll say acceleration is an increase in velocity (movement speed) at a certain rate. I'm guessing that, with gravitational fields, we can ilustrate this with someone jumping of a building. The velocity the subject falling down is increasing until it hits the ground. But if the ground is meeting the person (and not the other way around), why is there an acceleration? Why isn't the person falling at the same speed from beginning to end? I think I'm also confusing some concepts here, but not sure what they are :) Probably, the most confusing is understanding GR (wich is easy at a planetary level), but how it makes us stuck to the ground and how we are not being pulled, but instead it's the ground that's pushing us...

 

[A.T.]

Ok, so, from common knowledge, I'll say acceleration is an increase in velocity (movement speed) at a certain rate.

That is coordinate acceleration, a function of the chosen reference frame, which is arbitrary. The physically relevant acceleration is proper acceleration, that an accelerometer measures.

I'm guessing that, with gravitational fields, we can ilustrate this with someone jumping of a building. The velocity the subject falling down is increasing until it hits the ground.

In the frame of the ground, which is an arbitrary choice of coordinates. In the frame of the subject the velocity of the Earth is increasing.

But if the ground is meeting the person (and not the other way around),

That distinction is arbitrary, just like the choice of coordinates.

why is there an acceleration?

The person in free fall doesn't experience any proper acceleration. The Earh's surface experiences proper acceleration upwards, because of electromagnetic repulsion from layers below,

Why isn't the person falling at the same speed from beginning to end?

There are frames where it is.

I think I'm also confusing some concepts here, but not sure what they are

velocity vs. coordiante acceleration vs, proper acceleration, also frame dependent vs frame invariant quantities,

 

[Tiago]

That is coordinate acceleration, a function of the chosen reference frame, which is arbitrary. The physically relevant acceleration is proper acceleration, that an accelerometer measures.

In the frame of the ground, which is an arbitrary choice of coordinates. In the frame of the subject the velocity of the Earth is increasing.That distinction is arbitrary, just like the choice of coordinates.

The person in free fall doesn't experience any proper acceleration. The Earh's surface experiences proper acceleration upwards, because of electromagnetic repulsion from layers below,There are frames where it is.velocity vs. coordiante acceleration vs, proper acceleration, also frame dependent vs frame invariant quantities,

Fantastic help! :) Will start reading on those concepts. Sorry if my questions seem so basic, but I'm really a newbie at these subjects.

 

[A.T.]

Fantastic help! :) Will start reading on those concepts. Sorry if my questions seem so basic, but I'm really a newbie at these subjects.

No problem. You're welcome. Some further comments:

Probably, the most confusing is understanding GR (wich is easy at a planetary level),

I doubt that you actually understand GR on the planetary level, if you don't on the local level. You probablly think about balls rolling on a rubber sheet, which is a very wrong analogy. See:
https://www.physicsforums.com/threa...visualization-of-gravity.726837/#post-4597121
http://en.wikipedia.org/wiki/Gravity_well#Gravity_wells_and_general_relativity

Here are some better analogies:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.relativitet.se/spacetime1.html
http://www.adamtoons.de/physics/gravitation.swf

but how it makes us stuck to the ground and how we are not being pulled, but instead it's the ground that's pushing us.

See the video below again. Instead of ground pushing you have the branch pulling, but otherwise it explains exactly that: The apple is not pulled by the Earth.

 

[Tiago]

I understand what you're saying about the rolling balls on rubber sheet, but have you seen the Elegant Universe by Brian Greene? He actually explains the GR, not quite like rolling balls on a rubber sheet but he does say that the distortion of spacetime caused by the presence of a large mass (such as the sun) makes it so that other planets don't move in straight lines, but rather follow the natural path of the warped / distorted spacetime. This is, at least, the explanation that I've accepted as correct in my limited knowledge on the matter. I find this is much easier to understand at a planetary level than on a local level. Because on a planetary level we're just talking about warped spacetime and masses following those distorted paths, and on a local level the rules are different. What I'm probably confused about are two concepts such as feeling gravity (acceleration of the ground underneath our feet) and knowing it exists even though I'm in free fall. If I fall of a building I can't go on a straight line because the Earth's presence is distorting the spacetime or because it accelerated to "get me"? Does this even make sense?

Thanks

 

[A.T.]

I find this is much easier to understand at a planetary level than on a local level. Because on a planetary level we're just talking about warped space-time and masses following those distorted paths, and on a local level the rules are different.

The rules are the same. You probably just misunderstood a (potentially misleading) pop-sci explanation of the plantary level, which confuses paths in space with paths in space-time. A correct GR explanation of orbits (or anything with more than 1 spatial dimension) cannot be easily visualized in one diagram.

 

[PeterDonis]

the distortion of spacetime caused by the presence of a large mass (such as the sun) makes it so that other planets don't move in straight lines, but rather follow the natural path of the warped / distorted spacetime

Brian Greene has a way of explaining physics that, while it isn't exactly wrong, tends to easily generate misconceptions (and those often lead to threads here on PF...). In this case, the misconception is stated explicitly: "planets don't move in straight lines" is wrong. The paths of planets are straight lines--in curved spacetime. More precisely, they are geodesics, which are the equivalent of straight lines in a curved manifold. (The "straight lines" Greene was probably referring to are straight lines in a hypothetical flat "background", but that background doesn't exist and there's no way to actually physically measure these hypothetical "straight lines", so thinking about them only causes confusion.)

If I fall of a building I can't go on a straight line because the Earth's presence is distorting the spacetime or because it accelerated to "get me"?

If you fall off a building, you are moving in a straight line--more precisely, as above, a geodesic in the curved spacetime around the Earth. The Earth's surface accelerates upward to "get" you.

The reason this view is preferable is that it gives an easy way of telling what is moving in a "straight line" and what isn't: test for weightlessness. When you fall off the building, you are (ignoring air resistance) weightless. The Earth's surface is not. So you are the one moving in a straight line.

 

[Tiago]

Brian Greene has a way of explaining physics that, while it isn't exactly wrong, tends to easily generate misconceptions (and those often lead to threads here on PF...). In this case, the misconception is stated explicitly: "planets don't move in straight lines" is wrong. The paths of planets are straight lines--in curved spacetime. More precisely, they are geodesics, which are the equivalent of straight lines in a curved manifold. (The "straight lines" Greene was probably referring to are straight lines in a hypothetical flat "background", but that background doesn't exist and there's no way to actually physically measure these hypothetical "straight lines", so thinking about them only causes confusion.)
If you fall off a building, you are moving in a straight line--more precisely, as above, a geodesic in the curved spacetime around the Earth. The Earth's surface accelerates upward to "get" you.

The reason this view is preferable is that it gives an easy way of telling what is moving in a "straight line" and what isn't: test for weightlessness. When you fall off the building, you are (ignoring air resistance) weightless. The Earth's surface is not. So you are the one moving in a straight line.

Of course I probably understand the idea behind what Brian Greene explained, but not the complexity of its concepts. And it's good that I don't, cause I'm not a physicist, I'm merely someone that admires physics, live fascinated by it and largely because of enthusiasts like Brian Greene that make these subjects easy to follow for someone not linked to the field. Of course, like you said, that probably causes a lot of misconceptions and you guys have to deal with newbies with dumb questions :)

Anyway, I'm going to take advantage of my newbie position and insist on this stupid question. I understand that the Earth's surface accelerates to get whoever is in freefall with no proper acceleration (did I get this right?), but this is due to the Earth's own rotating movement (or acceleration, this I didn't get). But if everyone on the planet suddenly jumped of a building, how can the planet accelerate in every direction to get everyone? This is confusing and I'm asking this, probably without the basic knowledge to understand your explanation, but I'll risk it anyway :)

Thanks!

 

[A.T.]

I understand that the Earth's surface accelerates

Yes proper acceleration of 1g upwards, as an accelerometer placed on a table will confirm.

to get

It doesn't accelerate to get anyone. It accelerates just to stay in place, at a constant distance from the center. Remember that this is proper acceleration, not a change in velocity (coordinate acceleration).

whoever is in freefall with no proper acceleration

Yes, free fall = zero proper acceleration.

but this is due to the Earth's own rotating movement

No. The Earths rotation has nothing to do with it. A non-rotating planet would have gravity as well.

how can the planet accelerate in every direction to get everyone?

Proper acceleration away from the center doesn’t imply movement away from the center. Even in classical mechanics you can accelerate towards a center without getting closer to it (uniform circular motion). In curved space-time you can also accelerate away from a point without getting further away from it (without any rotation). Again, remember that the relevant acceleration is proper acceleration, not coordinate acceleration.

Do you understand the apple animation posted above (post #35)? When the green apple hangs on the branch, it has only an upwards force on it, so it has upwards proper acceleration. Proper acceleration upwards just says it has a curved (non-geodesic) path in space time. It says nothing about moving upwards.

To see what happens with an apple on the opposite side of the Earth, at the same time, have a look at this link, which shows both sides and the inside:
http://www.adamtoons.de/physics/gravitation.swf

 

[PeterDonis]

I understand that the Earth's surface accelerates to get whoever is in freefall with no proper acceleration (did I get this right?),

Locally, yes, you can view it this way: with respect to a local inertial frame in which the free-falling apple is at rest, the Earth accelerates upward (where here we mean "accelerates" in the Newtonian sense of the second derivative of position with respect to time) and hits the apple.

But this doesn't work globally, because spacetime around the Earth is curved, not flat. The curvature means the local inertial frames at different points on the Earth do not "line up" the way they would in flat spacetime (i.e., far out in empty space away from all gravitating bodies). So there is no single global inertial frame in which an apple falling in England and an apple falling in Australia are both at rest. So we can't view the Earth surface as globally accelerating (in the above Newtonian sense) in all directions at once, because that view of "acceleration" only works in an inertial frame.

GR solves this problem by not requiring global inertial frames; if we want to view things globally, we can use a system of coordinates centered on the Earth just fine. But these coordinates will not be an inertial frame--obviously, because free-falling objects, like falling apples and orbiting spacecraft , are not either at rest or moving in a straight line at a constant speed in this frame. GR also uses a different definition of acceleration, called "proper acceleration", which, as A. T. said, is just the reading on an accelerometer attached to the object. The advantage of this definition is that it is frame-independent; the reading on a given accelerometer attached to a given object is the same no matter what coordinates we use. But, as A. T. pointed out, this definition breaks the link between acceleration and motion: the Earth's surface can perfectly well be accelerating in all directions at once in this sense.

 

[Tiago]

I think what makes it confusing (at least for me) is understanding the principle of equivalence. Of course it's easy to understand why a person would feel an artificial gravitational field if traveling upwards on a rocket in empty space. I would feel the force of the acceleration of the rocket pushing me down and that would create an artificial sensation of gravity (assuming it's accelerating at 9.8m/s2). This is easy to understand because it's intuitive. But how do you transfer this principle to a circular surface such as a planet? If I was in a circular rocket accelerating in space, we all would feel the push downwards just the same. If we could imagine the rocket to be circular and have several floors, wouldn't we all feel the push the same direction? If it would work like the Earth, we would be pushed to the center of the rocket, right?

 

[A.T.]

But how do you transfer this principle to a circular surface such as a planet?

You have gravity in the rocket, because it follows a curved path in space time. The same is true for every part of the surface.

If it would work like the Earth

It's not like the Earth because the rocket in in flat space-time, so you cannot have outwards proper acceleration at each part.

 

[Tiago]

Is this video accurate on ilustrating GR?

 

[A.T.]

Is this video accurate on ilustrating GR?

It's not clear which aspect of GR is tries to illustrate. The distorted 3D grids might be an attempt to illustrate the purely spatial distortion (without the time dimension), but that cannot explain gravity (you need the time dimension for that).

And even for the spatial part it is wrong, because the distorted 3D grid still encompasses the same total volume an undisturbed grid would (within the same boundary). But the key feature of curved space is that there is more volume inside a boundary that you would expect based on Euclidean geometry. You cannot visualize this by shifting nodes around in an 3D grid. What you can do is:

- Reduce 3D space to a 2D surface with a dent, which has more surface area than a flat plane would, which corresponds to the extra volume the 3D space actually has.

- Use sector models: http://www.spacetimetravel.org/sectormodels1/sectormodels1_en_w.pdf

 

[jbriggs444]

The distorted 3d grid has more proportionally more coordinate volume assigned to the Earth than would otherwise be the case. That is, if the Earth occupies more volume, it covers more grid lines in the chart, so the grid lines have to be bent toward the earth. That part makes a certain amount of sense.

Beyond that, I won't try to defend the depiction.

 

[A.T.]

The distorted 3d grid has more proportionally more coordinate volume assigned to the Earth than would otherwise be the case. That is, if the Earth occupies more volume, it covers more grid lines in the chart, so the grid lines have to be bent toward the earth. That part makes a certain amount of sense.

Distorting the 3d grid merely shifts volume around, between the coordinate cells. It doesn't add to total volume as the actual spatial distortion does.

 

[Tiago]

I'm going to risk bringing a different subject that I think relates to everything we've been talking about. Of course, before Einstein, gravity according to Newton was much easier to understand. And in some websites, people will still say that gravity is a force that pulls to the center of the Earth. And that gravity is the attraction between bodies (which, of course, can't be true, since Einstein proved light is also bent by gravity). I think, besides Einstein's equations were more accurate than Newton's, his model to understand gravity is not as intuitive.

What I understand: the presence of mass bends spacetime, making planets and asteroids and whatever move through straight lines that are curved by the presence of bigger masses. This is an easy idea to understand, though it needs simplification to illustrate. At a local level (on Earth), if someone jumps of a building, the body will follow a straight line the same as if it were in space. But the straight line is bent towards the Earth, so it follows that path.

What I don't understand: how is the above compatible with "the ground meeting the body and not the body meeting the ground"? Is the fact that the planet is moving what creates our own feeling of weight?

thanks

 

[bhobba]

What I don't understand: how is the above compatible with "the ground meeting the body and not the body meeting the ground"? Is the fact that the planet is moving what creates our own feeling of weight?

In GR the gravitational force is simply an artefact of your coordinate system. The most natural coordinate system is a small freely falling one. In that frame there is no gravitational field, it is locally inertial, and the Earth comes towards you.

Their are a number of routes to GR. One is simply to take the above observation to its logical conclusion. When you 'stitch' all these small internal frames together you get curved space-time.

Thanks
Bill

 

[Nugatory]

What I don't understand: how is the above compatible with "the ground meeting the body and not the body meeting the ground"? Is the fact that the planet is moving what creates our own feeling of weight?

Suppose that you and I are both standing at the equator, one kilometer apart. We both start walking due north. We smack into one another at the north pole. Did you meet me or did I meet you? We can think about it either way, and they're both right - the actual physical phenomenon we're observing is that the distance between us shrank from one kilometer to zero, and that is described equally well by the "I met you" picture and the "you met me" picture.