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

[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?
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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).
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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* :)

 

[PeterDonis]

How do you differ between a flat space and a flat space time?

Because "spacetime" is the entire history of the universe, including all times, and "space" is just the universe at one instant of time. At one instant of time, the universe (according to our best current model) is flat; but when you include the time dimension, the universe is expanding, i.e., changing in time, and that means spacetime is curved.

 

[yoron]

Pleased to meet you Peter :)