# Kind of newbie question about gravity

1. Nov 18, 2014

### 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.

2. Nov 18, 2014

### Orodruin

Staff Emeritus
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.

3. Nov 19, 2014

### A.T.

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

This videos deal with the local effect.

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:

4. Nov 19, 2014

### Wes Tausend

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 earths 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
...

5. Nov 20, 2014

### 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 gotta do the math at some point.

6. Nov 20, 2014

### 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.

Last edited: Nov 20, 2014
7. Nov 20, 2014

### Staff: Mentor

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.

8. Nov 20, 2014

### A.T.

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):

9. Nov 22, 2014

### 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.. wich means towards the body that's curving the spacetime (Earth). Is this more or less accurate?

Thanks!

10. Nov 23, 2014

### Staff: Mentor

It influences every body, accelerated or not.

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.

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.

11. Nov 23, 2014

### rajeshmarndi

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

12. Nov 23, 2014

### Staff: Mentor

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

13. Nov 23, 2014

### Wes Tausend

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
...

14. Nov 23, 2014

### Staff: Mentor

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

This is incorrect as well.

15. Nov 23, 2014

### Wes Tausend

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
...

16. Nov 23, 2014

### A.T.

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.

17. Nov 27, 2014

### Staff: Mentor

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

18. Nov 27, 2014

### harrylin

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.
Yes indeed. However:
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.

19. Nov 27, 2014

### A.T.

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

20. Nov 27, 2014

### Staff: Mentor

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

21. Nov 27, 2014

### harrylin

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 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!

22. Nov 27, 2014

### A.T.

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).

Last edited: Nov 27, 2014
23. Nov 27, 2014

### Staff: Mentor

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/Gravitation-Spacetime-Hans-C-Ohanian/dp/1107012945

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

Thanks
Bill

Last edited by a moderator: May 7, 2017
24. Nov 27, 2014

### Staff: Mentor

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 wont 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/Mechanics-Third-Edition-Theoretical-Physics/dp/0750628960
'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

Last edited by a moderator: May 7, 2017
25. Nov 27, 2014

### harrylin

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 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 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: