Is Freefall Really Not Accelerated Motion? Debunking Common Misconceptions

  • #51
write4u said:
https://en.wikipedia.org/wiki/Terminal_velocity

I read that to mean that at "terminal velocity" acceleration becomes zero. But what happens in between stationary and terminal speed, is the object accelerating until it reaches terminal speed?

If you're talking about coordinate acceleration relative to the surface of the Earth (coordinate acceleration is always relative to something else) then the object is accelerating between stationary and terminal speed, with the acceleration greatest at the beginning and decreasing until it reaches zero as the object reaches terminal speed.

If you're talking proper acceleration, it starts out zero and increases until it stabilizes at -1g when the object reaches terminal velocity. Note the negative sign - the proper acceleration at terminal velocity is upwards, and that's what keeps the object's speed relative to the surface of the Earth (which is also experiencing proper acceleration of 1g upwards) constant at terminal velocity.
 
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  • #52
write4u said:
I read that to mean that at "terminal velocity" acceleration becomes zero.

Yes, if you mean coordinate acceleration relative to the Earth, when an object is falling through air. (And, as Nugatory notes, even though coordinate acceleration relative to the Earth is zero, proper acceleration is not.)

In any case, "terminal velocity" in this sense has nothing to do with what I though we were discussing, which is motion in a vacuum.

write4u said:
is "c" not a terminal speed, even in a vauum?

No, because there is no finite time at which an accelerated object in a vacuum reaches ##c##. In a vacuum, an object can have a given constant proper acceleration indefinitely and never reach ##c## relative to any inertial observer. Its velocity gets closer and closer to ##c## but never reaches it.
 
  • #53
inertiaforce said:
Yes there are two more videos in that similar thread where both Brian Greene and Brian Cox are saying the same thing, that the Earth is apparently accelerating upward. I will link the videos here for reference:

This video from 9:30 onward (Brian Greene): youtube, HneFM-BvZj4

This video, where Brian Cox says that a ball and a feather aren't falling to the earth: youtube, E43-CfukEgs

So that's a total of 3 videos including the one in the original post.

So what the hell is going on here lol?
inertialforce,

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.
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write4u said:
Just for clarity. Is a photon in a constant state of acceleration? Is anything that ceases to increase in speed still in a state of acceleration?
write4u,
Rootone has rather pegged this first question, I would say;
Quote: "In relativity it is axiomatic that photons cannot accelerate in the classical sense, 'c' is a constant for all photons."

Einstein asserted in his postulates for Special Relativity (SR), "that light is always propagated in empty space with a definite velocity c" (one might assume relative to any "measuring tool" using any method). Einstein has frankly asserted that light enjoys a privilaged motion (a constant privilaged motion) by postulating it, making it axiomatic. It has worked so well, almost no one has looked any further.

In the second question, regarding your question, "anything that ceases to increases in speed as still in a state of acceleration"... yes. I believe Einstein has also in effect, asserted this in his Equivalence principle in General Relativity. Matter, according to Einstein, has a distinct separate property of acceleration, even when it is standing still, or merely only moving in an inertial frame, which is essentially the same thing since we cannot presently differentiate them. Since matter is not since considered to be actually moving in this manner, it is considered to curve space (spacetime).

I think Poincaré very much enjoyed thinking about this quandry around 1897, a bit before Einstein published SR.

Wes
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  • #54
Thank you all for clarifying.
 
  • #55
Wes Tausend said:
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.
 
  • #56
DrGreg: Nigel Calder in "Einstein' Universe" gives an interesting perspective on falling apples and I presume other fruits.

" A falling apple loses rest energy and gains energy of motion." I'll paraphrase Calder on this.No force acts on the apple so it can't gain or lose energy. It's rest energy plus energy of motion remains the same as it falls.It loses rest energy as it descends by entering regions of slower time{higher gravity} and must pile on energy of motion to keep the same total energy. At 32 ft/sec per second it compensates for loss of rest energy. According to Calder in relativist language the" unchanged quantity is the scalar product of the tangent vector with the Killing vector". Good bar talk if you can afford to buy rounds.
Ynon
 
  • #57
Initial thoughts, before watching the video is ... :False. (well 14 seconds in) because what if 2 people , on opposite sides of the Earth drop an apple. the planet can't move in both directions at once, and yet both apples fall to the Earth at the same rate.

now i'll watch the video and see if it changes my mind. :)

Very interesting.. it does change my mind a bit, but mostly i started to get lost in the back half of that video.

there is much i need to learn to understand that video better.
 
  • #58
A1337STI said:
on opposite sides of the Earth drop an apple. the planet can't move in both directions at once,
Proper acceleration and movement are different things. The surface pieces on opposite sides have opposite proper acceleration, but in curved space-time that doesn't imply moving apart.
 
  • #59
I need to find some "curved spaced time" reading for dummies.. i feel like my understanding of how things work is severely lacking. :(
 
  • #60
A1337STI said:
I need to find some "curved spaced time" reading for dummies.. i feel like my understanding of how things work is severely lacking. :(

See the cone at the end of the below video (right side):



It always gets wider towards the Earths center, so in order to fit those patches together you need curvature as shown here:

http://www.adamtoons.de/physics/gravitation.swf
 
  • #61
A.T. said:
Wes Tausend said:
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
...
 
  • #62
Wes Tausend said:
"...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.

Wes Tausend said:
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.
 
  • #63
...

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.

A.T. said:
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?

A.T. said:
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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  • #64
Wes Tausend said:
...
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.
 
  • #65
Wes Tausend said:
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.

Wes Tausend said:
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.

Wes Tausend said:
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.
 
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  • #66
...

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
...
 
  • #67
Wes Tausend said:
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.
 
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