Is Poincaré's Space Dilemma the Key to Understanding Gravity?

[yoron]

Yes, I know :)

But if you let a moment of doubt into it you will see that I write "And that is what gravity does to you too as I read it"
What I do there is to connect it to the idea of Higgs particles. I've had, and still have, a lot of doubt in the view that 'gravity' is a result of a 'Higgs field'. Somewhere I read a rather good explanation to why it, to some, can be seen as equivalent though. I should probably have been clearer on that subject. Never the less, if we ignore a Higgs field, the equivalence principle presume that this 'spaceship' and 'Earth' both are equivalent as I understands it.
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And, just to not clutter this thread.. Wes, what you write about 'global' relative 'local' interpretations is one of my big dilemmas for the moment. I like the local interpretation myself, and are not sure what a global should be. Although Einstein defined one. Where I differ is in what makes a universe. I presume it to need a logic, to become 'whole', that meaning explainable without needing to refer to magic. But, logic is a mindset.

 

[PeterDonis]

What I do there is to connect it to the idea of Higgs particles. I've had, and still have, a lot of doubt in the view that 'gravity' is a result of a 'Higgs field'

First, this is completely unrelated to the equivalence principle, which is what you had previously said you were talking about.

Second, gravity is not a result of a Higgs field. Nonzero rest mass is, according to the Standard Model of particle physics. But nonzero rest mass is not the same as gravity; it's not even the same as being a source of gravity. The source of gravity is the stress-energy tensor, and objects with zero rest mass (like photons) still have a nonzero stress-energy tensor.

if we ignore a Higgs field, the equivalence principle presume that this 'spaceship' and 'Earth' both are equivalent as I understands it.

The EP says that proper acceleration due to being in a spaceship with its engine firing, and proper acceleration of the same magnitude due to standing on the surface of a gravitating mass, are equivalent, yes. And it says this regardless of whether a Higgs field is present or not. See above.

 

[yoron]

"Second, gravity is not a result of a Higgs field. Nonzero rest mass is, according to the Standard Model of particle physics. But nonzero rest mass is not the same as gravity; it's not even the same as being a source of gravity. The source of gravity is the stress-energy tensor, and objects with zero rest mass (like photons) still have a nonzero stress-energy tensor. "

Nicely put Peter, and that goes back to how one want to define a universe, to me. I don't remember where the link is, to how you connect a Higgs field to gravity, but it was that one I was thinking of when commenting. Maybe someone else have a link to it? Otherwise I'll try to find it again, been some time since I read about it.
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And no, I'm not speaking about inertia in this case, although that is the view I have myself when it comes to a Higgs field influence. Typical, isn't it :) then again, was another laptop I had it on. This is actually a minefield I'm traversing, thinking of it again. Einstein had this to say about it.

"Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the Earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordinates? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation."

And if now 'inertia' is 'gravity'?

Ouch. And I think that was it Peter, even if I don't find a specific article discussing it. It doesn't really explain how one 'type' of gravity can be so different from another, well, in my eyes then. Inertia do exist everywhere, as soon as you accelerate, but?
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Also, if I imagine a perfectly spherical restmass, non rotating, evenly distributed, in a presumed empty space. Then 'gravity' points inwards, doesn't it? If I now somehow shrink this restmass into a 'black hole' then the direction still will be the same, right? (This last question actually has a relevance to me wondering about 'locality', which is how I view what really (reality) is. The 'Global' interpretation is not what I will observe, other than theoretically. And this saddles meta physics too I'm afraid)

 

[PeterDonis]

I don't remember where the link is, to how you connect a Higgs field to gravity

That's because there isn't a link, as I said. There's only a link between the Higgs field and nonzero rest mass.

no, I'm not speaking about inertia in this case

But you seem to think that "inertia" and "gravity" are analogous, since you ask:

And if now 'inertia' is 'gravity'?

But inertia and gravity are not analogous, so this question doesn't make sense. What Einstein meant (bear in mind that you are reading an English translation of something he wrote in German, so you can't go by the exact words used) was that "inertial mass" and "gravitational mass" were the same thing--which is just the equivalence principle: proper acceleration due to being in a rocket in empty space with its engine firing, is the same (locally) as proper acceleration due to standing on the surface of a planet, at rest in a gravitational field. He did not mean that "inertia" and "gravity" were the same thing.

if I imagine a perfectly spherical restmass, non rotating, evenly distributed, in a presumed empty space. Then 'gravity' points inwards, doesn't it?

If by "gravity" you mean "the direction a freely falling object would fall if released from rest by a static observer", then yes.

If I now somehow shrink this restmass into a 'black hole' then the direction still will be the same, right?

Yes.

 

[harrylin]

[..]
If you are [..] standing on the surface of a planet, then yes, you feel acceleration, and you "notice inertia acting on you"--but the reason you feel those things is not gravity; it's [..] the planet's surface pushing on you. In short, something other than gravity is acting on you, preventing you from being in free fall. So feeling acceleration, noticing inertia acting on you, is not what gravity does to you; it's what something other than gravity does to you.

(emphasis mine)
Without gravity, the surface of the planet would not push against you. What you feel is the force of the planet's surface that is countering the action of gravitation. Apart of that, you meant of course "proper acceleration" [EDIT I notice that you clarified that in your next post]; relative to a free falling reference system you accelerate at g, but not relative to others such as the ECI frame.

 

[A.T.]

Without gravity, the surface of the planet would not push you back ...you feel is the force of the planet's surface that is countering the action of gravitation...

(emphasis mine)

How do you determine what is merely "pushing back" / "countering" as opposed to "action"?

 

[harrylin]

(emphasis mine)

How do you determine what is merely "pushing back" / "countering" as opposed to "action"?

Good question! How does one determine that if one feels a force between oneself and the floor, that it is not that one's body has an active force that is pushing downward on the floor, and the floor is merely passively pushing back with inertial reaction? I suppose that it is by the method of establishing cause and effect; indeed, that is a main scientific method. Try to stand on the floor of a free floating spaceship and you will feel no force.

PS. it's really too far off topic to elaborate further in this thread about Poincare's space imagination; but it could be an interesting discussion topic for the general physics sub-forum where by chance a similar discussion is going on now, e.g. #2 "[..[ mass causing [..]" and the link to the wiki with a paper on "active gravitational mass".

 

[A.T.]

Try to stand on the floor of a free floating spaceship and you will feel no force.

Switch the rockets on, and you feel the force. So the "cause" here is the thrust from the engines, while for the Earth's surfcace it's the pressure forces acting on it from below.

 

[harrylin]

Switch the rockets on, and you feel the force. So the "cause" here is the thrust from the engines, while for the Earth's surfcace it's the pressure forces acting on it from below.

In both cases "there are pressure forces acting on it from below".
The Earth's gravity has an equivalent effect as the rocket engines; that's the equivalence principle. If you disagree with the concept that gravitation is causative or active, please bring up your disagreement in the other thread to which I already linked. I will not elaborate more on that in this thread.

 

[A.T.]

The Earth's gravity has an equivalent effect as the rocket engines

The pressure forces pushing the Earth's surface from below are equivalent to the pressure forces in the rocket engine, pushing the rocket.

 

[stevendaryl]

(emphasis mine)
Without gravity, the surface of the planet would not push against you. What you feel is the force of the planet's surface that is countering the action of gravitation

But what you feel isn't any different in the case where the ground is pushing up on you to counteract gravity or the case where the ground is pushing up on you because it is being accelerated upward by rockets. So the point is that you aren't "feeling" gravity; you're feeling the ground pushing up on you.

We can make the situations even more similar by assuming that there is a platform that is held up by rockets firing. You are standing on that platform. Then in both cases, what you feel is the platform pressing up on your feet. In both cases, the reason the platform is pressing up on your feet is because there are rockets attached to the platform. So it is even more inappropriate to say that you are in any way feeling gravity, or feeling a force that is caused by gravity. Gravity isn't causing the rockets to fire.

What gravity does is to make it possible for the rockets to fire continuously without going anywhere.

 

[stevendaryl]

The Earth's gravity has an equivalent effect as the rocket engines; that's the equivalence principle.

No, that's not the equivalence principle. The equivalence principle doesn't equate gravity and the effect of rockets. It equates (1) using rockets (or other means) to stay stationary in a gravitational field, and (2) using rockets to accelerate in gravity-free space. It equates (1) falling in a gravitational field and (2) drifting at constant velocity in gravity-free space.

 

[PeterDonis]

Without gravity, the surface of the planet would not push against you.

The way we put this in GR is, without spacetime curvature, the surface of the planet would not push against you. It pushes against you because "free fall", i.e., zero proper acceleration, in your vicinity does not mean being at rest with respect to the planet. This is not due to any "force" of gravity; it is due to the curvature of spacetime in your vicinity. If you equate "gravity" with spacetime curvature, then yes, you could say it is "gravity" that explains why the surface of the planet has to push against you to keep you at rest relative to it. But on this interpretation, again, "gravity" is not a force and is not felt as a force.

What you feel is the force of the planet's surface that is countering the action of gravitation.

But "action of gravitation" here just means "the natural state of free fall"--the state every object is in if it is not being pushed on by something. In other words, according to GR, free fall does not have to be explained; it's the default state. What has to be explained is proper acceleration, and "gravity" does not cause proper acceleration; some non-gravitational interaction must be taking place.

 

[PeterDonis]

The Earth's gravity has an equivalent effect as the rocket engines; that's the equivalence principle.

No, it is not. The EP says that the Earth's surface, pushing up on you, has an equivalent effect to the rocket engines. It also says that free fall--the state you would be in if the rocket engines were not firing--has an equivalent effect to "gravity". (I see stevendaryl has made this same point.)

The reason this is so important is that people so often try to view the "acceleration due to gravity"--the coordinate acceleration that a freely falling body experiences relative to either the rocket with its engine firing, or the Earth--as equivalent to the proper acceleration imposed by the rocket engine. As many, many, many threads here on PF bear witness, that confusion is both common, and a cause of much further confusion. So we try very hard to prevent it from ever starting in the first place. Even if you understand the difference, other readers of this thread might not, unless we make it crystal clear: free fall and proper acceleration are not equivalent.

 

[harrylin]

[..] you're feeling the ground pushing up on you to counteract gravity [..]

Almost correct: the ground is passive, it's countering your downward push - as I explained in #42. If any further discussion, I will simply quote and reply in the linked thread as it's off-topic here and on-topic there.

 

[harrylin]

No, it is not. The EP says that the Earth's surface, pushing up on you, has an equivalent effect to the rocket engines. It also says that free fall--the state you would be in if the rocket engines were not firing--has an equivalent effect to "gravity". [..]

Yes it is. As I cited, the EP according to Einstein also says that a gravitational field exists for the man in the chest; that is, a gravitational field has an equivalent effect on the man in the chest as a rocket engine that is pulling the chest (he did not mention a rocket engine but stressed that is immaterial by what means the chest is accelerated). This is really standard knowledge, and again off topic... however the "action" aspect is on topic in the other thread which I now follow, waiting for your comments there.

The reason this is so important is that people so often try to view the "acceleration due to gravity"--the coordinate acceleration that a freely falling body experiences relative to either the rocket with its engine firing, or the Earth--as equivalent to the proper acceleration imposed by the rocket engine. As many, many, many threads here on PF bear witness, that confusion is both common, and a cause of much further confusion. So we try very hard to prevent it from ever starting in the first place. Even if you understand the difference, other readers of this thread might not, unless we make it crystal clear: free fall and proper acceleration are not equivalent.

I find it difficult to imagine people confounding a free fall experience with an accelerating rocket experience.

 

[A.T.]

the ground is passive

So am I.

it's countering your downward push

I can just as well say that I'm countering the ground's push on me. Newtons 3rd Law is symmetrical, so this is an arbitrary choice.

 

[A.T.]

a gravitational field has an equivalent effect on the man in the chest as a rocket engine that is pulling the chest

The equivalence is:

chest floor ~= Earth's surface
rocket thrust ~= pressure force supporting the Earth's surface

It's these interaction forces that result in proper acceleration which can be felt.

 

[stevendaryl]

you're feeling the ground pushing up on you to counteract gravity.

The way you quoted that makes it seem that you are quoting me, but that is not what I said. My sentence ended with the words "pushing up on you"

 

[stevendaryl]

I find it difficult to imagine people confounding a free fall experience with an accelerating rocket experience.

That's what it appeared that you were doing, when you equated gravity with rockets. As I said, the equivalence principle claims the equivalence of:

1. Standing on a platform hovering above the Earth using rockets.
2. Standing on a platform accelerating through empty space using rockets.

In both cases, what you "feel" is the platform pressing up against you, and the reason the platform is pressing up against you is because it has rockets attached.

 

[harrylin]

The way you quoted that makes it seem that you are quoting me, but that is not what I said. My sentence ended with the words "pushing up on you"

I cited the part on which we agree; the other part is the part that I comment on, as promised, in the appropriate thread. Enough hijacking!

 

[stevendaryl]

I cited the part on which we agree; the other part is the part that I comment on, as promised, in the appropriate thread. Enough hijacking!

Well, when you use quotes, you have to be careful that it's actually a quote.

 

[harrylin]

That's what it appeared that you were doing, when you equated gravity with rockets. As I said, the equivalence principle claims the equivalence of:

1. Standing on a platform hovering above the Earth using rockets.
2. Standing on a platform accelerating through empty space using rockets.

[..].

Strange! See again the post that you cite; you overlooked, once more, according to Einstein also:
1a. Standing in a chest that is in rest on the surface of the Earth
2a. Standing in a chest that is pulled with a rope.

 

[stevendaryl]

Strange! See again the post that you cite; you overlooked, once more, according to Einstein also:
1a. Standing in a chest that is in rest on the surface of the Earth
2a. Standing in a chest that is pulled with a rope.

You think a rope is different from a rocket, in this regard?

My point is that in neither case are you feeling the force of gravity.

 

[A.T.]

1a. Standing in a chest that is in rest on the surface of the Earth

It doesn't make a difference what supports the chest on Earth. The upwards contact force (for a standing chest) and the upwards rocket thrust (for a hovering chest) are both interaction forces that result in 1g upwards proper acceleration, that the man on the chest floor can feel.

2a. Standing in a chest that is pulled with a rope.

You can have the chest in 1a. also hang on a rope, from a tree.

 

[yoron]

I don't know Peter.
Can you define the difference between inertia and inertial mass? And gravity and gravitational mass so I can see how you think there?
=
Don't read me wrong please. This have been a puzzle to me for a long time, and even made me consider that a Higgs field 'might' describe it all, both gravity and inertia. So make it as clear as you like.

 

[harrylin]

Well, when you use quotes, you have to be careful that it's actually a quote.

Oops, I thought that it was a quote - but you are right, it is what you said but I copy-pasted by mistake from two different sentences, sorry!
We agreed on the "counteract gravity" part. You actually wrote
"the case where the ground is pushing up on you to counteract gravity [..] you're feeling the ground pushing up on you." Discussed in the other thread now.

 

[harrylin]

It doesn't make a difference what supports the chest on Earth. The upwards contact force (for a standing chest) and the upwards rocket thrust (for a hovering chest) are both interaction forces that result in 1g upwards proper acceleration, that the man on the chest floor can feel.

You can have the chest in 1a. also hang on a rope, from a tree.

I explained that they are both contact forces in post #44. And as promised, I continued in the other thread.

 

[PeterDonis]

the EP according to Einstein also says that a gravitational field exists for the man in the chest

First of all, as has been pointed out to you many, many times before, "Einstein said X" is not a valid argument, and Einstein's use of terminology, particularly in his works for non-scientists, is not a good reference.

Second, as has also been pointed out to you many, many times before, by "gravitational field", Einstein meant "nonzero connection coefficients in a particular coordinate chart". Connection coefficients are coordinate-dependent. Physics does not depend on coordinates (as Einstein also said). So this "gravitational field" is not a valid physical cause of anything.

that is, a gravitational field has an equivalent effect on the man in the chest as a rocket engine that is pulling the chest

Even on Einstein's terminology (which has the issues I just described), this is not correct. The "gravitational field" in the chest makes freely falling objects within the chest accelerate "downward" (in the coordinate sense) relative to the chest. What makes the man in the chest not accelerate downward (in the coordinate sense) relative to the chest is not the "gravitational field"; it's the force exerted by the bottom of the chest on his feet.

This is really standard knowledge

There is standard knowledge involved here, yes, but it's not what you've been saying.

I find it difficult to imagine people confounding a free fall experience with an accelerating rocket experience.

Obviously you haven't read enough PF threads on this topic. (Not to mention that, as stevendaryl pointed out, you appear to be making exactly this error.)

 

[PeterDonis]

Can you define the difference between inertia and inertial mass?

"Inertia" can have several meanings, but it is usually used, at least as I've seen it, to refer to the fact that objects travel on free-fall trajectories unless acted upon by some force (where gravity in this connection doesn't count as a force--a "force" here is something that is actually felt as a force, can be measured by an accelerometer, etc.). Note that these free-fall trajectories depend only on an object's initial position and velocity; all objects with the same initial position and velocity will follow the same free-fall trajectories, regardless of their size, composition, or any other property. (This is true in Newtonian mechanics as well as GR, but in Newtonian mechanics there is no explanation of why it's true; see further comments below.)

"Inertial mass" is the quantity $m$ that appears in Newton's Second Law, or its relativistic generalization; in other words, it tells you how much an object "resists" being acted upon by a (non-gravitational) force (something that is felt as a force). As this and the above should make clear, the only way to differentiate objects with different inertial mass is to actually subject them to a felt force, since otherwise they will all travel on the same trajectory and there's no way to tell objects apart.

Perhaps the difference can be illustrated quickly by this observation: you can only measure an object's inertial mass if it is not moving purely under its own inertia.

And gravity and gravitational mass so I can see how you think there?

"Gravity" can also have several meanings, some of which no longer apply in GR. For example, "gravity" in GR is not a force, unlike in Newtonian mechanics. Sometimes "gravity" is used to mean "acceleration due to gravity", which is itself a misnomer in GR: this "acceleration" is the coordinate acceleration that a freely falling object has, relative to an observer that is at rest relative to the gravitating body (like the Earth). However, by the equivalence principle, this "acceleration" can always be eliminated, locally, by adopting appropriate coordinates. In GR, the term "gravity" is most properly used to refer to tidal gravity, which is the same thing as spacetime curvature; spacetime curvature is the aspect of "gravity" that cannot be eliminated by adopting appropriate coordinates.

"Gravitational mass" is the quantity $m$ that appears in Newton's gravitational force equation; in Newtonian physics, it is assumed to be equal to inertial mass, but no explanation is given for why this is true. In GR, there is no concept of "gravitational mass" because gravity is not a force; objects that, in Newtonian physics, are "affected by gravity", in GR are just moving in free fall, under their own inertia; and, as noted above, all objects in free fall follow the same trajectories (given an initial position and velocity), so there is no property that differentiates objects that are "moving under gravity" from one another.

 

[yoron]

Will definitely need to reread this later Peter, but it was a very nice explanation of your thoughts. Seems there is a difference between uniform motion and a gravitational acceleration though. I don't think there is a coordinate system in where a uniformly moving object, measured by another uniformly moving object, will be found to 'accelerate', although in a gravitational acceleration this becomes different globally defined, or observer dependent if one like that better (which I do then:). Locally defined though there is no difference that I can find between a gravitational acceleration and a so called 'free fall' (geodesic).
=
Ignoring spin as always.

 

[PeterDonis]

I don't think there is a coordinate system in where a uniformly moving object, measured by another uniformly moving object, will be found to 'accelerate'

Not in flat spacetime, no, because you specified two "uniformly moving" (by which I assume you mean freely falling) objects, and in flat spacetime the relative velocity of two such objects is constant. In curved spacetime, however, that's not the case, and one can certainly construct coordinates in which one freely falling object is accelerating (in the coordinate sense) relative to another.

Locally defined though there is no difference that I can find between a gravitational acceleration and a so called 'free fall' (geodesic).

Assuming that by "gravitational acceleration" you mean "free fall in a curved spacetime", then yes, you are correct; the worldline of an object undergoing "gravitational acceleration" is a free fall geodesic.

 

[yoron]

Yes, I was thinking of a flat space time, as the universe at large. binary stars should become one nice example of a curved space time with gravitational acceleration, shouldn't it?

 

[PeterDonis]

Yes, I was thinking of a flat space time, as the universe at large.

The universe at large is not a flat spacetime. It's a flat space, at least according to our best current models, but that's not the same thing.

binary stars should become one nice example of a curved space time with gravitational acceleration, shouldn't it?

Yes.

 

[yoron]

You lose me there, How do you differ between a flat space and a flat space time? As long as there is curved space included you mean?
=

To me space is time, so even when flat time is existent?
( Minowski spacetime and manifolds?
Da* :)