Is Freefall Really Not Accelerated Motion? Debunking Common Misconceptions

[WannabeNewton]

The video in the OP is perfectly accurate; in particular, the video title and introduction are also as such.

I don't see what the issue is with it. This is pointless pedantry and an argument over semantics, which for some reason seems to be the norm as of late in the GR forum.

 

[stevendaryl]

Acceleration relative to an inertial frame is commonly defined by means of a to the inertial frame attached coordinate system as d²s/dt². At least, that's what textbooks teach and how most ordinary people understand it. However, that is irrelevant as at that point no mention at all is made of inertial frames

If we're talking about the same video, he makes a big point about inertial frames. At 1:35 into the video.

I think you're completely wrong about this. Certainly there can be criticism of the video, its accuracy, whether it's misleading, etc. But the points that the presenter tries to get across (and fails in your case) are absolutely essential in understanding GR and how gravity is treated differently by Newton and by Einstein. As I said, the thought experiment about the accelerating train is the same sort of thought experiment that led Einstein to GR in the first place.

 

[Wes Tausend]

...

According to this video, freefall isn't accelerated motion and is actually stationary. In other words, you aren't moving in freefall:

In other words, you aren't moving in freefall: ... is not necessarily always correct, but it could be in some instances. It would be more proper to say, "You (or an object) cannot ever feel any motion whatsoever in free-fall:"

Otherwise the video is a pretty good rendition of gravity as Einstein saw it. The easiest way to understand this is to simply consider Einstein's thought experiment that he himself used to form a slightly different perspective (conjecture) of gravity from that of Newton's now failed "attraction" theory. Now, in all fairness, Newton was pretty close, and Einstein certainly couldn't have completed his gravity theory (GR) without Newton's help.

The trick to understanding (as employed by Einstein himself) is to use a pictoral imagination of geometry to see why the above video rings so close to true. Math is important to our overall quantative understanding, and imperative to our conclusive geometric proofs, but there are those times, in my opinion, when the tedious intricate symbolic language of math tends to clutter up clear understanding of the stark geometric quality of natures basic principles.

To simplify his understanding, what Einstein did is imagine a chest (elevator) being drawn up in an earth-like accelerated manner (32 ft/sec/sec) in gravity-free space by a cable (A modern version might use a rocket ship under power with the scientists standing on the back wall, directly in front of the engine). Within the chest, he imagined two scientists that conduct simple experiments to see if they are in a gravitational field or not.

For example, one of the "thought" experiments might be to let a couple of balls fall off a table which is standing on what seems to be the floor. Let us do that. To make things interesting, we will have one ball heavier than the other. Next, both balls appear to roll off the table and fall to the floor, arriving simultaneously, just what the two scientists would expect in normal gravity, since that key point is exactly what is observed on earth.

In the previous above case, the balls, being accelerated by the chest and table top, initially stick to it as though they are attracted like Newton's erroneous "attraction-take" on gravity. In reality the balls are held there by the same inertial force one feels when a hotrod (or Space Shuttle) accelerates, pasting one to the seatback. We have always regarded this inertia as a form of artificial gravity and now Einstein has regarded the two to be "equivalent"... hence his Equivalence principle.

To continue, when these balls escape (roll past) the table edge, pure inertia causes them to merely continue to coast through space at the same last speed that previous contact with the accelerating table top gave them (threw them), while the floor speeds up even more (continues accelerating) to soon strike (meet) the balls. In this "chest" case, it is not so much that the different weight balls fall at the same velocity, as it is that the one-piece floor must logically rise evenly. Note that the floor will seem to strike the heavier ball with more force, the only difference between the simultaneous impacts. In effect, the side-by-side balls could be standing still, floating like you suggested, or moving along equally in any other form of inertial motion... when the rising floor simply strikes them both at the same time.

For Einstein, to furnish a theory of general relativity (GR) to include gravity, and yet accompany the special case of light (Special Relativity, SR), more thought becomes a nagging mandate. Inevitably, the curvature of space becomes evident in the same above "chest" scenario when Einstein considers what such a chest acceleration might do to the speed of light, which is regarded as merely constant. First, I imagine smiling in an understatement, Einstein remarks that the drawn chest, "would reach unheard of speeds", and leaves it at that. But he also realizes that if Equivalence is to be true, the acceleration of the chest will slightly outrun the ability of light to travel evenly across the room in a straight line. Consider the next paragraph.

In other words, a hole drilled in one side of an inertially moving chest might allow a perfectly perpendicular light beam to shoot across the chest and strike the other wall at exactly the same height as the hole in the first wall. But it cannot hit the same spot if the chest accelerates meanwhile. The acceleration of either the chest, or "equivalent" gravity on earth, means that the perfectly straight light beam will appear to bend in a minute curve and hit the adjacent wall slightly lower than it would in a non-accelerating chest (therefore an inertial chest; a chest either moving consistantly in an inertial frame or standing still). If we are to continue to regard light as traveling in a straight line, and we do, the conclusion is that both the acceleration of the chest and gravity itself, will bend space; our dear space which is always the path of light. Voila... light will be bent and it is! And that is the essence of Einstein's General Relativity.

It gets more complicated for many of us when we apply advanced math, especially beyond our training level, but the basic principle is not so complicated and should never be forgotten. We must all dust it off on occasion. Even Einstein, the king of visualisation and thought experiment, once remarked in mock confusion:
“Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.”
(source: In A. Sommerfelt “To Albert Einstein’s Seventieth Birthday” in Paul A. Schilpp (ed.) Albert Einstein, Philosopher-Scientist, Evanston, 1949.)

Wes
...

 

[A.T.]

Apparently the video doesn't pretend to present proper acceleration there.

From 1:35 on he explains how to determine if a frame undergoes proper acceleration.

 

[eltodesukane]

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.

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

 

[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