Is Freefall Really Not Accelerated Motion? Debunking Common Misconceptions

[Wes Tausend]

In a nutshell, Equivalence principle. The earth, consisting of matter as cause, acts just as though it's surface is moving upward, or at least outward in an accelerated manner. The floor rises to meet "falling" objects.

The movement of a piece of surface is frame dependent, but the surface definitely doesn't move outward as a whole because the radius is constant. The frame invariant proper acceleration of the surface doesn't imply movement.

A.T.,

"...The radius is constant"...

I find I must conveniently accept this convention too, but I'm not so sure it is that easy to confirm. For instance we may assume that there is no movement, no spatial change in space between and/or within the atoms forming the radius of earth, but how do we positively know that is true? Poincaré explored this very principle in his publication, The Relativity of Space, and it likely deserves it's own new thread. Afterall, students and members alike here, should expect extraordinary claims to require extraordinary proof.

Initially we could just firmly assert a steady radius as you have just done. But I suspect in the end we will have to rely solely on SR for our final proof.

As Einstein remarked in his thought experiment, the drawn chest, "would reach unheard of speeds". Yes, but we must insist, not faster than lightspeed. SR may our only salvation needed, or even available, to logically assert, "The frame invariant proper acceleration of the surface doesn't imply movement."

Per Poincaré, the possibility emerges that we may not in any other way, be able to otherwise derive an acceleration frozen in non-movement, which may be best simply explained by Poincaré himself, and we can discuss this in more depth in a new thread I have started, called Poincaré's Space Dilema. That title is based upon his astute thinking in his 1898 publication, The Relativity of Space.

A.T., I suggest you, and others, review and reply (if you wish) to my post in the new thread (Poincaré's Space Dilema link above) to avoid derailing the OP's thread.

Wes
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[A.T.]

"...The radius is constant"...

I find I must conveniently accept this convention too

The proper physical radius doesn't change according to GR, which we should stick to in this forum.

SR may our only salvation needed, or even available, to logically assert, "The frame invariant proper acceleration of the surface doesn't imply movement."

No, it's space-time curvature that allows proper acceleration in opposite directions, without changing the proper distance. The speed limit c is irrelevant here, because the opposite surface pieces don't move at all relative to each other.

 

[Wes Tausend]

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I expected a healthy argument and I will reply one more time in this thread out of courtesy to inertiaforce, the OP. I will also repeat this post on my new thread to maintain continuity.

The proper physical radius doesn't change according to GR, which we should stick to in this forum.

I agree. I am merely pointing out the extent of Equivalence by simple observation. Equivalence, along with SR are definitely always part of GR. My references to acceleration and motion are Einstein's thought experiment (see post #33) which resulted in Equivalence and therefore GR. Do you have an equally good reference why we cannot refer to such equivalent motion in GR?

No, it's space-time curvature that allows proper acceleration in opposite directions, without changing the proper distance. The speed limit c is irrelevant here, because the opposite surface pieces don't move at all relative to each other.

I disagree. I see the curvature as the direct result of the bending of light, therefore incorporating SR, also discussed in post #33.

I will say that if we do not allow some argument and a variety of perspectives of observation here, we might as well refer all PF member questions to Wikipedia. Please reply only in the new thread.

Wes
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[stevendaryl]

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I disagree. I see the curvature as the direct result of the bending of light, therefore incorporating SR, also discussed in post #33.

I think you have things backwards. Bending of light doesn't cause curvature, it's the other way around.

 

[A.T.]

I agree. I am merely pointing out the extent of Equivalence by simple observation.

The equivalence principle applies only locally, and cannot be used to deduce that the radius of the Earth changes, because space time curvature is not negligible over this large area.

Do you have an equally good reference why we cannot refer to such equivalent motion in GR?

See the interior Schwarzschild solution, where the proper radius doesn't change over time.

II disagree. I see the curvature as the direct result of the bending of light, therefore incorporating SR, ...

This is backwards, vague and doesn't disprove what I said:
- Space-time curvature allows proper acceleration in opposite directions, without changing the proper distance.
- Opposite pieces of the Earth's surface are at rest relative to each other.

 

[Wes Tausend]

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I only feel confident in replying in my own thread (see #5, my most recent post).

We are discussing something controversial. I have this distinct fear of stepping on the wrong toes and inadvertently closing someone elses valuable thread.

Please help me avoid accidentally harming someone else in my enthusiasm for Equivalence by replying in my thread, which I am willing to sacrifice, to satisfy my own curiousity.

Wes
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[PeterDonis]

We are discussing something controversial.

No, you aren't. The statements that A.T. and stevendaryl have made in response to you are not controversial at all. That's true of both this thread and the other one you linked to.