Is Freefall Really Not Accelerated Motion? Debunking Common Misconceptions

[Orodruin]

Would an accelerometer measures a non-zero acceleration aboard the ISS?

No.

 

[yoron]

Accelerations are definitely weird, looked through the eye of GR. whether one view should be seen as more correct than another I will leave unsaid here, and I think Einstein would have agreed on that even though the observers view always take a precedence .The real enigma is how you define a universe, as I see it then. You want it to be 'whole', as some consistent volume containing 'forces'? Describable from where, if so? Or you may want a universe consisting of information? Forming a logic, describing limits? I prefer the second option myself.

 

[write4u]

IMO, a massive object in free-fall does accelerate until terminal speed is achieved.
As I understand it, only massless particles are able to quantum jump instantaneously to "c"?

 

[Warp]

What is essentially happening is that when both the Earth and the apple are traversing on the time axis of curved spacetime (the curvature being caused by mass, in this case the largest mass around being the Earth), both being in an inertial (ie. non-accelerating) frame of reference, they will move along their respective shortest paths in this curved spacetime (ie. the so-called geodesics). There are no forces being applied to the apple in this system, and this is why there is no acceleration, only inertial motion. It looks to us like the apple is accelerating because we have this very limited view of the four-dimensional space: We only see a three-dimensional slice of it. This makes it appear like there is accelerated motion where there really isn't. (This isn't very much different from railtracks in a photo looking like they converge, although in reality they don't. It's just that in the limited 2D representation of the 3D world it looks like they converge.) If we somehow had the ability to see (or even visualize) the actual curved spacetime, we would then see that "yeah, the apple is not accelerating; it's just moving inertially along the shortest path. That shortest path happens to intersect with the surface of the Earth (which in fact is accelerating) at one point in the future."

(This is also a very rough explanation of why time passes at different speeds at different heights in a gravity well: Traversing through more curved spacetime makes perceived time pass at a different rate than traversing through less curved spacetime. The more detailed explanation of this is, however, too complicated for me to understand or explain, so I won't even try.)

 

[inertiaforce]

Similar issues discussed here:
https://www.physicsforums.com/threads/einstein-says-objects-do-not-fall-to-the-earth.781200/

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):

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

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

So what the hell is going on here lol?

 

[write4u]

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?

 

[victorneto]

No, this is the wrong interpretation. You are not accelerating in free fall. (We are here talking about what is called proper acceleration, which is what an accelerometer measures.) Movement is relative.

Imagine the free fall of a body toward the earth, like falling off a ladder, or an astronaut in a spaceship orbiting the Earth. Both are in free fall situation. A fixed observer on the Earth's surface, notice the astronaut or body in free fall with an acceleration g. Already for a comoving observer, or on the falling bodies, there is no acceleration. "They do not feel their own weight."

For these reasons the state of motion will be seen in different ways by different observing systems.

 

[Orodruin]

Imagine the free fall of a body toward the earth, like falling off a ladder, or an astronaut in a spaceship orbiting the Earth. Both are in free fall situation. A fixed observer on the Earth's surface, notice the astronaut or body in free fall with an acceleration g. Already for a comoving observer, or on the falling bodies, there is no acceleration. "They do not feel their own weight."

You need to differentiate between coordinate acceleration and proper acceleration. It was clearly stated in my post that I was talking about proper acceleration (which is the frame independent quantity). Regardless of the observer, a free falling object has zero proper acceleration.

 

[yoron]

Photons does not have a acceleration. What they have is a uniform motion, if described as propagating. They also have been measured to leave a recoil in wherever they propagate from. You can ignore a propagation and still find explanations for how a recoil can exist (conservation laws) and then think of it as excitations in a field. Although that doesn't explain it perfectly either, in a wider context involving observer dependencies. Because if you do that, accepting Lorentz contractions and time dilations, this 'field' becomes a very plastic experience, definitely observer dependent. To get around that one you either have to introduce more, or less, dimensions, where hopefully one of them will present a non observer dependent description. Or you can use a classical definition of propagation, with all what that means.

 

[A.T.]

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.

Yes, that's also what any accelerometer will tell you. You probably have one in your phone. The surface has a proper acceleration upwards, just like the green apple still hanging on the tree (in Einsteins model):

 

[stevendaryl]

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?

No, a photon isn't accelerating. However, it's kind of interesting to relate it to accelerated motion.

If you have a rocket that is undergoing constant proper acceleration in a straight line of magnitude $g$ (that's the acceleration that would be "felt" by people on board the rocket), then its position as a function of time (as measured in an inertial frame) is given by:

$x = \sqrt{c^2 t^2 + \frac{c^4}{g^2}}$

(if you choose the origin for $x$ appropriately--that's my third parenthetical remark in a single sentence; is that some kind of record?)

Anyway, the path of a photon is $x=ct$, which is the limit as $g \rightarrow \infty$. So it's not accelerating, but its motion is sort of the limit of infinite acceleration.

 

[write4u]

No, a photon isn't accelerating. However, it's kind of interesting to relate it to accelerated motion.

If you have a rocket that is undergoing constant proper acceleration in a straight line of magnitude $g$ (that's the acceleration that would be "felt" by people on board the rocket), then its position as a function of time (as measured in an inertial frame) is given by:

$x = \sqrt{c^2 t^2 + \frac{c^4}{g^2}}$

(if you choose the origin for $x$ appropriately--that's my third parenthetical remark in a single sentence; is that some kind of record?)

Anyway, the path of a photon is $x=ct$, which is the limit as $g \rightarrow \infty$. So it's not accelerating, but its motion is sort of the limit of infinite acceleration.

Thank you. I based my question on the fact that there is a limit to speed (c) and even if we applied acceleration to a massive object it would not be able to even reach (c) and it would be accelerating without gaining speed.
Thus the question if a photon is also constantly accelerating but unable to break (c).

As I said, this was for clarification only. I understand the common definition of acceleration, but wondered if things could sometimes be trying to accelerate without an increase of speed (velocity).

 

[PeterDonis]

IMO, a massive object in free-fall does accelerate until terminal speed is achieved.

Accelerate (in the sense of coordinate acceleration--an object in free fall has zero proper acceleration) relative to what? "Terminal speed" relative to what? Since we're talking about objects in a vacuum, what does "terminal speed" mean?

 

[rootone]

Thus the question if a photon is also constantly accelerating but unable to break (c).

In relativity it is axiomatic that photons cannot accelerate in the classical sense, 'c' is a constant for all photons.

 

[write4u]

Accelerate (in the sense of coordinate acceleration--an object in free fall has zero proper acceleration) relative to what? "Terminal speed" relative to what? Since we're talking about objects in a vacuum, what does "terminal speed" mean?

Terminal velocity is the highest velocity attainable by an object as it falls through air. It occurs once the sum of the drag force (Fd) and buoyancy equals the downward force of gravity (FG) acting on the object. Since the net force on the object is zero, the object has zero acceleration.[1]

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?

p.s. question: is "c" not a terminal speed, even in a vauum?

 

[Nugatory]

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.

 

[PeterDonis]

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.

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.

 

[Wes Tausend]

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.
------------------------------------------------------------------------------------------------------------------

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
...

 

[write4u]

Thank you all for clarifying.

 

[A.T.]

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.

 

[ynon]

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

 

[A1337STI]

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.

 

[A.T.]

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.

 

[A1337STI]

I need to find some "curved spaced time" reading for dummies.. i feel like my understanding of how things work is severely lacking. :(

 

[A.T.]

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

 

[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
...

 

[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]

...

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
...

 

[stevendaryl]

...
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]

...

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
...

 

[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.