General Relativity & External Forces: 2 Cases Examined

[Bob Walance]

TL;DR Summary

General Relativity and forces - two separate cases

It seems that there are two distinct gravitational cases to consider:

a) Object with no external contact with any type of stuff (e.g., a person in free-fall in a vacuum)
b) Object WITH external contact (e.g., a person standing on the ground)

I've enjoyed reading and listening to various discussions on General Relativity but these two cases are not clearly discussed. I believe that this is very important since - if I understand the basics properly - in the first case there are ZERO net external forces on the Object whereas in the second case there is a net external force on that Object..

It would be wonderful to get opinions on this - especially from those who teach GR.

Bob

 

[Nugatory]

in the first case there are ZERO net external forces on the Object whereas in the second case there is a net external force on that Object..

Yes and yes.

 

[pervect]

Summary:: General Relativity and forces - two separate cases

It seems that there are two distinct gravitational cases to consider:

a) Object with no external contact with any type of stuff (e.g., a person in free-fall in a vacuum)
b) Object WITH external contact (e.g., a person standing on the ground)

I've enjoyed reading and listening to various discussions on General Relativity but these two cases are not clearly discussed. I believe that this is very important since - if I understand the basics properly - in the first case there are ZERO net external forces on the Object whereas in the second case there is a net external force on that Object..

It would be wonderful to get opinions on this - especially from those who teach GR.

Bob

This is basically a good way of looking at things from the GR perspective, though we have to extend the notion of "not touching things" to the notion of "not interacting with any fields other than gravity".

For instance, a charged particle in an electric field will accelerate, though it's not really touching anything.

Confusion typically arises around the issue "why does a charged particle in an electric field accelerate, while a massive particle in a gravitational field does not". Hopefully there's no need to rehash those ol oints, though.

 

[Bob Walance]

This is basically a good way of looking at things from the GR perspective, though we have to extend the notion of "not touching things" to the notion of "not interacting with any fields other than gravity".

For instance, a charged particle in an electric field will accelerate, though it's not really touching anything.

Confusion typically arises around the issue "why does a charged particle in an electric field accelerate, while a massive particle in a gravitational field does not". Hopefully there's no need to rehash those ol oints, though.

Yes, in the electron-in-a-field case there is an exchange of photons or virtual photons. To me, that's easy to accept.

In the gravitational case, the force that arises from contact is baffling to me. I guess I'll have to wait for the likes of Maldacena, Susskind and others to fill that void in my head. It seems like they are focused on entanglement and the breaking of entanglement between virtual particles in the quantum "foam". It's a good time to be alive and have internet access.

 

[PeterDonis]

in the electron-in-a-field case there is an exchange of photons or virtual photons

We are not talking about quantum physics here. We are talking about classical physics. GR is a classical theory. In GR, electromagnetism is just classical electromagnetism; there are no photons.

In the gravitational case, the force that arises from contact is baffling to me.

There is no gravitational force arising from contact. The contact force between you and the Earth when you are standing on the Earth's surface is a non-gravitational force; in GR, those are the only kinds of forces since gravity itself is not a force in GR. Since it is the only force acting on you, you feel weight--in GR terms, you have nonzero proper acceleration--and do not follow the free-fall path you would follow if you were not subject to any forces.

 

[Dale]

Summary:: General Relativity and forces - two separate cases

if I understand the basics properly - in the first case there are ZERO net external forces on the Object whereas in the second case there is a net external force on that Object.

Yes. A simple test is to consider the reading of an attached accelerometer. If the accelerometer reads 0 then the net force is 0. If the accelerometer reads non-zero then there is a non-zero net force.

 

[Bob Walance]

Yes. A simple test is to consider the reading of an attached accelerometer. If the accelerometer reads 0 then the net force is 0. If the accelerometer reads non-zero then there is a non-zero net force.

Yes indeed! I built a simple accelerometer with rubber bands suspending a mass to demonstrate this concept. Brian Greene uses a bottle of water with holes in it. It's fun to watch.

The issue - from my experiences - is that the two cases I've described are NOT discussed in a way that makes it easy for the reader to understand. The closest I've seen is in 'Gravitation' by Misner/Thorne/Wheeler.

While I've read and watched numerous interpretations of the Equivalence Principle, explaining when an object experiences external forces - and when not - has never been presented in a succinct and easy-to-understand way. If you know of any sources that do this I would really like to know, too.

 

[PeterDonis]

the two cases I've described are NOT discussed in a way that makes it easy for the reader to understand

What are you finding difficult to understand? So far the only thing you've mentioned amounts to the fact that nonzero proper acceleration is different from zero proper acceleration. Which is true, but where do you want to go from there?

While I've read and watched numerous interpretations of the Equivalence Principle, explaining when an object experiences external forces - and when not - has never been presented in a succinct and easy-to-understand way.

It seems like you already grasp the key distinction, since you correctly state it in the OP, so I'm having trouble understanding what is missing.

 

[Bob Walance]

What are you finding difficult to understand? So far the only thing you've mentioned amounts to the fact that nonzero proper acceleration is different from zero proper acceleration. Which is true, but where do you want to go from there?

It seems like you already grasp the key distinction, since you correctly state it in the OP, so I'm having trouble understanding what is missing.

Yes, I believe that I do understand the two cases and have for a while, but it took me quite a long time to see it. Why not make it easy for us regular people who aren't physics majors?

The point of this post is that, in my opinion, the two case are not clearly talked about. Sean Carroll recently did a video on gravity. I watched carefully hoping to see these two scenarios juxtaposed. All the information was there, but someone learning from scratch would have a hard time visualizing it (again, this is my opinion only).

Perhaps someday I'll have a chance to discuss this with Prof. Carroll. I'm not too far from Cal Tech. It would give me an opportunity to practice my kowtowing. :-)

 

[Dale]

I watched carefully hoping to see these two scenarios juxtaposed.

I guess I don’t see why you think these two scenarios are so critical that they should be presented. What principle do you think they demonstrate?

I think that it would be more important to compare two scenarios with gravity vs with acceleration rather than to compare a scenario with contact vs one without. A gravity vs acceleration comparison teaches you something insightful about the nature of gravity: it is an inertial force.

I don’t see a similar insight from a contact vs non contact comparison. What physical principle do you see it teaching?

 

[Bob Walance]

I don’t see a similar insight from a contact vs non contact comparison. What physical principle do you see it teaching?

Eqivalence.

It's difficult to describe to someone that the moon is the exact same inertial state as that person if they were to jump up off the ground, and then also trying to convince that person that when land they will be non-inertial AND the direction of the force on their body is pointing away from the center of Earth.

I really think that having a reputable source describing this (like a college textbook) would go a long way in explaining the basic concepts of GR - especially for those of us that were initially taught gravity using the Newtonian model.

 

[Dale]

Eqivalence.

I don’t see it at all. How does a comparison of a contact vs a non contact room teach the equivalence principle? For equivalence I would think you would want the same situation in gravity and under acceleration.

I agree that this comparison is not made, but I think that the reason is that it serves no obvious pedagogical purpose. Physics teachers don’t teach scenarios, they teach physical principles. Examples are chosen only insofar as they illustrate a principle clearly and effectively.

 

[Bob Walance]

I don’t see it at all. How does a comparison of a contact vs a non contact room teach the equivalence principle? For equivalence I would think you would want the same situation in gravity and under acceleration.

It's going to be hard for me to describe.

When I read the book 'Relativity - the Special and the General Theory' by Einstein, it was a jaw-dropping moment when I realized that the real acceleration on a body that is not following a geodesic is EXACTLY the same as a rocket with its motor on (in the local limit). It was also a similar AHA! moment when I realized that the following-a-geodesic case and the rocket-with-its-motor-off case are same, too.

Thinking about the two different cases has made it easier for me to understand the basics of GR. It might not help everyone, but it absolutely did with me. That's all.

 

[Dale]

When I read the book 'Relativity - the Special and the General Theory' by Einstein, it was a jaw-dropping moment when I realized that the real acceleration on a body that is not following a geodesic is EXACTLY the same as a rocket with its motor on (in the local limit). It was also a similar AHA! moment when I realized that the following-a-geodesic case and the rocket-with-its-motor-off case are same, too.

Thinking about the two different cases has made it easier for me to understand the basics of GR.

So it seems to me that what you want described is actually four cases, not two. You want a contact case with gravity and a contact case with acceleration and then you want a non contact case in free fall in gravity and a non contact case in free fall away from gravity.

 

[Bob Walance]

So it seems to me that what you want described is actually four cases, not two. You want a contact case with gravity and a contact case with acceleration and then you want a non contact case in free fall in gravity and a non contact case in free fall away from gravity.

I'm paraphrasing, but I'm sure that I've read that Einstein stated that a "gravitational field" disappears when the contact disappears. If we can assume that a gravitational field and curved spacetime are two independent things then two of your four cases are the same. Being inertial in a region of spacetime that's flat or curved is the same. Similarly, being non-inertial (i.e., a non-zero net external force) is the same whether the object is in a flat or curved region of spacetime.

 

[Dale]

I'm sure that I've read that Einstein stated that a "gravitational field" disappears when the contact disappears

That is not correct.

Being inertial in a region of spacetime that's flat or curved is the same. Similarly, being non-inertial (i.e., a non-zero net external force) is the same whether the object is in a flat or curved region of spacetime.

That doesn’t teach the equivalence principle then. If a person understands that those are the same then they already understand the equivalence principle. So just doing a contact and a non contact scenario does not teach the equivalence principle, it simply assumes it has already been learned.

I think this is why those scenarios are not often covered as you suggest.

 

[Bob Walance]

Dale,

I am genuinely curious:

Do you see a difference between the external forces on a rock that's out in deep spacetime and that same rock a while later as it's approaching the event horizon of a black hole?

Bob

 

[Bob Walance]

That doesn’t teach the equivalence principle then. If a person understands that those are the same then they already understand the equivalence principle. So just doing a contact and a non contact scenario does not teach the equivalence principle, it simply assumes it has already been learned.

According to this snippet from the the Wikipedia article on Equivalence, Einstein made the free-fall/inertial-motion connection after he published the Equivalence Principle. To me, the non-inertial and inertial cases go hand-in-hand and should be clearly portrayed. I understand that you and others don't feel this way, but as I stated before it absolutely has helped me. Perhaps in my next life when I study Quantum Cosmology (did I invent this phrase?) I will see things differently.

we ... assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.
— Einstein, 1907

That is, being on the surface of the Earth is equivalent to being inside a spaceship (far from any sources of gravity) that is being accelerated by its engines. The direction or vector of acceleration equivalence on the surface of the Earth is "up" or directly opposite the center of the planet while the vector of acceleration in a spaceship is directly opposite from the mass ejected by its thrusters. From this principle, Einstein deduced that free-fall is inertial motion.

(end of Wiki snippet)

 

[PeterDonis]

the Wikipedia article on Equivalence

I assume you mean this article?

https://en.wikipedia.org/wiki/Equivalence_principle

It's always a good idea to give a link.

 

[PeterDonis]

Einstein made the free-fall/inertial-motion connection after he published the Equivalence Principle

I'm not sure the article is correctly presenting Einstein's thought process. In many other references, you will find Einstein's description of what he called "the happiest thought of my life", which he described (translated into English) as "if a person falls freely, they will not feel their own weight". This in turn led him to the equivalence principle. So on this reading, the free-fall/inertial-motion connection came first, then the equivalence principle came after that.

To me, the non-inertial and inertial cases go hand-in-hand

Misner, Thorne, and Wheeler discuss this, as you note.

What other relativity textbooks have you read?

 

[A.T.]

So it seems to me that what you want described is actually four cases, not two.

That would make sense, to clarify which pairs of cases are "equivalent", like done below:

From:
https://physics.stackexchange.com/q...the-equivalence-principle-and-inertial-frames

 

[PeroK]

While I've read and watched numerous interpretations of the Equivalence Principle, explaining when an object experiences external forces - and when not - has never been presented in a succinct and easy-to-understand way. If you know of any sources that do this I would really like to know, too.

Your wish is @A.T. 's command!

 

[Dale]

Do you see a difference between the external forces on a rock that's out in deep spacetime and that same rock a while later as it's approaching the event horizon of a black hole?

No, I do not. Provided the rock is small enough and the black hole is large enough for the equivalence principle to apply.

 

[Dale]

To me, the non-inertial and inertial cases go hand-in-hand and should be clearly portrayed. I understand that you and others don't feel this way, but as I stated before it absolutely has helped me.

I don’t think that taking just two scenarios, one inertial and one non inertial teaches the equivalence principle. Note that the Wikipedia page you cite uses two non-inertial cases to teach the equivalence principle.

I am glad that it somehow helped you, but your question was why those specific examples are not used. The reason that they are not used is that they don’t teach the equivalence principle.