I Can an Altered Thought Experiment Reconcile the Special Relativity Conundrum?

[Herman Trivilino]

Imagine the device known as a carpenter's level in free fall towards a horizontal surface. The device is horizontal as it falls, as verified by the fact the bubble is in the center. Both ends of the device hit the surface at the same time. All of this is in a frame of reference in which the device falls vertically downward. The vertical direction being of course perpendicular to that horizontal surface.

When all of this is observed from a passing train the two ends of the device do not hit the surface at the same time, the bubble is in the middle, and the direction of the fall is not perpendicular to the surface.

The trailing end of the device will strike the surface $\frac{Lv}{c^2}$ before the leading end, where $L$ is the proper length of the device, $v$ is the speed of the train relative to the surface, and $c$ is the speed of light.

As @Dale stated in Post #3, what's horizontal in one frame isn't necessarily horizontal in another.

 

[FactChecker]

@Mister T , What would the bar look like after the trailing end hits and the leading end is still falling? Is the trailing end flat on the ground for some length and then the bar makes an angle straight to the leading end still in the air? I guess then one observer would see the bar as straight all the time and the other would see it as bent as it hit the ground. That seems strange, but I don't see any other possibility.

 

[PeterDonis]

Here is a much simpler problem

Your problem differs from the OP in that in your case, the barbell's ends hitting the floor are simultaneous in the train frame instead of the ground frame. I think it's instructive to consider both cases, though.

 

[Orodruin]

If the car falls downward once the support cables are broken, then it did not start out at rest in an inertial frame. It started out at rest in a non-inertial frame that is accelerating upward.

Indeed, I wilfully and explicitly ignored the physics of how things would actually happen as described and instead considered a case where the entire cart is a horizontal line that starts accelerating down at the same time as the supports are removed (in the ground rest frame). This is of course a simplifying assumption and something I was pretty sure the OP has not considered but just assumed. The problem is that this

The assumptions I think are pretty basic. Cut the cords on a moving car and watch it fall.

is not as basic as the OP thinks it is. Obviously, if cutting the cord is the reason things start falling, then it will also take some time before the structure in the middle no longer supports the wagon and the OP is clearly assuming that this occurs instantaneously.

While I think it is fine to ask what happens to the idealised line, the OP runs into much deeper waters than he realizes when he asks about the marble because it is a case he tries to cover with "intuition". The marble has several problems, one of them being that the OP assumes that it is gravity that accelerates it towards the direction which the wagon is sloped. I am also not very fond of SR questions involving gravity for obvious reasons. Even classically, if the wagon falls in a sloped position at the same acceleration as the gravitational acceleration, the marble will not roll anywhere because it will be falling with exactly the same acceleration and there will be no normal force from the floor on the marble. I think it is fair to say that the OP has taken water over his head in thinking that this is a "pretty basic" question without many further qualifying assumptions.

Here is a much simpler problem I worked on in the past. I believe it contains most of the geometric consequences that are your concern.

This problem is exactly equivalent to my guillotine problem in post #32.

@Mister T , What would the bar look like after the trailing end hits and the leading end is still falling? Is the trailing end flat on the ground for some length and then the bar makes an angle straight to the leading end still in the air? I guess then one observer would see the bar as straight all the time and the other would see it as bent as it hit the ground. That seems strange, but I don't see any other possibility.

If the bar stops as it hits the floor in the train rest frame, then it will be bent at a single point in the ground frame.

 

[MikeLizzi]

You mean trailing end, right?
Your example is very good. It shows that acceleration is not essential to the issue. I am afraid that I can't see how there is no axial force and it seems as though the bar would have to "flop down" on the floor like a rubber hose. I'll have to think about that, but it may be beyond me.

EDIT: I guess that at the point of contact of the bar with the floor, there is acceleration. So that might account for an angle of the bar at that point.

The Trailing end hits the floor first. Yes, I need to correct that. Also, as you indicated, once one end hits the floor, acceleration is unavoidable and one must abandon the weightless, frictionless, rigid assumption.

 

[MikeLizzi]

@Mister T , What would the bar look like after the trailing end hits and the leading end is still falling? Is the trailing end flat on the ground for some length and then the bar makes an angle straight to the leading end still in the air? I guess then one observer would see the bar as straight all the time and the other would see it as bent as it hit the ground. That seems strange, but I don't see any other possibility.

If the bar undergoes any (Edit: permanent bending) bending with respect to the train track observer, that would constitute a paradox since there can be no bending with respect to the train car observer.
So, once one end hits the floor, one has to abandon the weightless frictionless, rigid assumption. I did a crude finite element analysis for this. It gets messy. The key is to recognize that each element in the tilted falling bar has a somewhat diamond shape (vertical sides). Each element experiences a shear force from the stopped end and passes it on. The shear force reduces the vertical component of the velocity for each element and each element changes shape to a contracted rectangle in sequence. The result is the bar pivots and shrinks till the other end hits the floor.

Edit: Now that I think about it, the rubber hose analogy from FactChecker has value.

 

[MikeLizzi]

This problem is exactly equivalent to my guillotine problem in post #32.If the bar stops as it hits the floor in the train rest frame, then it will be bent at a single point in the ground frame.

Sorry, I was occupied writing my reply and did not see your post #32 before I posted.
With respect to the bending, I tried to address that in my post above #56. The bending conclusion was the original paradox I had to deal with.

 

[MikeLizzi]

Thanks much.
Ok, so if there is a ball at the midpoint of the barbell (and is subject to the same initial force downward), what does the ball do as seen by the tracks observer? For the car at rest perspective, the ball stays put, right in the middle. It never touches the ends. I assume for the tracks view, the ball must also stay in the center, even if the bar goes from tilted to finally horizontal in the end.

So what if you flip your experiment, so that, to the car at rest perspective, the bar receives the downward force at the front before the force is applied at the back in such a way that there is no rotation, he would see the bar fall diagonally. To the ground observer, if he sees the force to the front and rear of the bar applied at the same time, can it be so that he could see the bar falling horizontally? What happens to the ball in the middle here? To the ground observer, it would not move. To the car observer, the bar being tilted, somehow he also concludes the ball doesn't move? If he sees a tilted bar, why wouldn't he see the ball move?

Thanks.

With respect to placing a ball at the center of the barbell. As has been mentioned by other posters, since the ball and bar experience the same accelerations, the relationship (relative position/relative velocity) between them cannot change even in a Newtonian world.

With respect to your follow up question involving flipping the experiment, your suggestion is that a downward force is to be applied to one end before a similar force is applied to the other end but no rotation (angular velocity) is to occur. That can't happen. (Edit: I spoke too soon. The angular velocity will be canceled after the second force is applied) Regardless, your focus seems to be on the ball now. Hold a bar vertical with a ball beside it. Then let go. Do they not fall together as if glued?

 

[Dale]

This is of course a simplifying assumption and something I was pretty sure the OP has not considered but just assumed

This is similar to my experience in the past. The questioner has a whole bunch of unstated simplifying assumptions in mind, and hasn't the background to consider which are compatible with relativity and which are not. The fact that some of the unstated assumptions are incompatible with relativity is a big problem because nobody can work the problem they have in mind.

I am also not very fond of SR questions involving gravity for obvious reasons.

Me too. I won't even attempt such problems as an educational exercise for SR. Those should be reserved for courses in GR.

 

[Dale]

I guess then one observer would see the bar as straight all the time and the other would see it as bent as it hit the ground.

Yes, that is correct. This is one place where the "no rigid objects" thing is glaring and the described motion is not Born rigid.

 

[hatflyer]

Imagine the device known as a carpenter's level in free fall towards a horizontal surface. The device is horizontal as it falls, as verified by the fact the bubble is in the center. Both ends of the device hit the surface at the same time. All of this is in a frame of reference in which the device falls vertically downward. The vertical direction being of course perpendicular to that horizontal surface.

When all of this is observed from a passing train the two ends of the device do not hit the surface at the same time, the bubble is in the middle, and the direction of the fall is not perpendicular to the surface.

The trailing end of the device will strike the surface $\frac{Lv}{c^2}$ before the leading end, where $L$ is the proper length of the device, $v$ is the speed of the train relative to the surface, and $c$ is the speed of light.

As @Dale stated in Post #3, what's horizontal in one frame isn't necessarily horizontal in another.

[/QUOTE]

With respect to placing a ball at the center of the barbell. As has been mentioned by other posters, since the ball and bar experience the same accelerations, the relationship (relative position/relative velocity) between them cannot change even in a Newtonian world.

With respect to your follow up question involving flipping the experiment, your suggestion is that a downward force is to be applied to one end before a similar force is applied to the other end but no rotation (angular velocity) is to occur. That can't happen. (Edit: I spoke too soon. The angular velocity will be canceled after the second force is applied) Regardless, your focus seems to be on the ball now. Hold a bar vertical with a ball beside it. Then let go. Do they not fall together as if glued?

This is similar to my experience in the past. The questioner has a whole bunch of unstated simplifying assumptions in mind, and hasn't the background to consider which are compatible with relativity and which are not. The fact that some of the unstated assumptions are incompatible with relativity is a big problem because nobody can work the problem they have in mind.

Me too. I won't even attempt such problems as an educational exercise for SR. Those should be reserved for courses in GR.

Ok, so forget accelerations. This is in a non-gravitational space, or just on the ground, flipping the experiment so that the bar is moving parallel to the ground, with it attached to 2 supports traveling in the bar direction. There then is a force applied parallel to the ground, perpendicular to the bar movement direction like a constant wind (tho probaby better a force faster than wind if there is a problem trying to compare wind speed with speed of force translation along the bar).

The bar is being held against the wind by a cable on the front and back. A marble sits in the middle. So initially the bar and marble are locked in, no relative movement in the wind direction. Only in the direction it is moving along the ground.

Now, in the frame of the bar, you cut the support of the front cable only. You see the front end start to move away from the wind direction. The rear cable has yet to be cut. So it would seem the marble would start to roll towards the front of the bar, being pushed by the wind, as the bar rotates.

Now, from the stationary observer on the ground, he sees the bar and cables traveling along all at the same orientation, perpendicular to the wind. No movement in the direction of the wind. He on the other hand sees the 2 cables cut simultaneously and so the bar stays in the same direction as it started, and the marble stays in the middle.

Where does this go wrong? [I guess there are still accelerations, going from still to the speed of the wind, but hopefully that phase of acceleration does not take away from the initial point where the marble is compelled to move]

BTW, if my assumptions are wrong, I'd like to know how so I can learn. This is very educational. I sensed my initial analysis was off, but wasn't sure how.

[note this version of this post was edited from the original post]

 

[FactChecker]

To keep it simple, forget about cutting cables and accelerations. In @MikeLizzi 's post #48, he supposes that the bar is already falling at a steady velocity and it just happens to be in an exact horizontal position at the starting time in the car's point of view. (I think Mike switched the point of view, but that is not critical.) Because there is no acceleration, a marble moving with the bar will stay centered in place, no matter who is looking at it. Acceleration brings in many complications of General Relativity.

 

[hatflyer]

To keep it simple, forget about cutting cables and accelerations. In @MikeLizzi 's post #48, he supposes that the bar is already falling at a steady velocity and it just happens to be in an exact horizontal position at the starting time in the car's point of view. (I think Mike switched the point of view, but that is not critical.) Because there is no acceleration, a marble moving with the bar will stay centered in place, no matter who is looking at it. Acceleration brings in many complications of General Relativity.

Did you see my post from a minute ago before yours?

 

[phinds]

Did you see my post from a minute ago before yours?

It wasn't "a minute ago", it was 21 minutes after your post #29 and clearly was addressing that post.

 

[Orodruin]

Did you see my post from a minute ago before yours?

Yes he did. I agree with him. Forget about cutting cables and focus on understanding uniformly moving objects first. As soon as you start cutting cables and applying forces, you will need a model for how forces are propagated through the cables and the objects and your assumptions will not be as clear as you might thing that they are. Understand how uniformly moving objects appear in different inertial frames first. Your assumptions seem to assume some sort of rigidity, but objects are not rigid in SR. See this Insight for example: https://www.physicsforums.com/insights/can-i-send-a-signal-faster-than-light-by-pushing-a-rigid-rod/

 

[hatflyer]

It wasn't "a minute ago", it was 21 minutes after your post #29 and clearly was addressing that post.

He mentioned accelerations, and I removed them from my post, ergo why i wondered if he saw my post.

Maybe I need to ask this a better way to resolve this specific experiment, and not just get non-specific replies to my experiment (I do get the bar experiment that was first posted, but I'm having trouble applying that to my version of the experiment):

- with any rigidity, any propagation force behavior, any wind speed, and any other parameters set to all possible values...is it possible in any of these cases that the observer on the bar sees the marble start to roll because the front bar end starts to move first, whereas the ground observer sees the 2 ends cut simultaneously and thus no movement of the marble?

It seems the theories would say no, but i don't see why not?

 

[phinds]

I admire your perseverance in this thread. It's gotten so convoluted it makes my head hurt :smile;

 

[hatflyer]

I admire your perseverance in this thread. It's gotten so convoluted it makes my head hurt :smile;

I'm having fun ;) I love learning, like horizontal in 1 frame doesn't have to mean horizontal in another. There's just this 1 concept I'm trying to understand that has eluded me, and so I have to try to create a thought experiment just so so as to isolate the issue, but thanks to getting feedback here, I realize I have had to alter the experiment as the initial 1 was not proper.

 

[FactChecker]

I think that when forces and accelerations come into play, strange General Relativity(?) effects become important. In post # 18, @PeterDonis explained that acceleration due to gravity will distort space-time so that the bar sags in the middle in exactly the right way to keep a marble from rolling. In several posts, people have said that the bar hitting the ground causes accelerations that make the tilted bar appear to bend sharply to a stationary observer even though it remains horizontal and straight to the traveling observer. These effects are all beyond my understanding, so I can not help further and will withdraw.

PS. I hope that I have not butchered the explanations of the posts that I mention here. If so, I apologize.

 

[Janus]

@Mister T , What would the bar look like after the trailing end hits and the leading end is still falling? Is the trailing end flat on the ground for some length and then the bar makes an angle straight to the leading end still in the air? I guess then one observer would see the bar as straight all the time and the other would see it as bent as it hit the ground. That seems strange, but I don't see any other possibility.

Try think of the bar as made up of vertical "sheets" of atoms (something like a tall stack of playing cards on its side). Sheet 1 is the trailing end. It hits first, then sheet 2, 3, etc. Now unlike the stack of cards, each sheet is bonded to the next sheet. So when sheet 1 hits, the result of the impact is propagated by these bonds down the bar. However, the propagation speed is limited to c relative to the ground observer. The end result is that as far as the ground frame is concerned, sheet 2 hits the ground before it can "feel" the force from sheet 1 hitting. Sheet 2 sends the result of its impact propagating through the bar, including back towards sheet 1. Because it is propagating in the opposite direction of the bars motion, its speed with respect to the bar will be greater than that of the impact propagating from sheet 1 to sheet 2. So even though sheet 1 hit first, the two forces propagating through the bar would meet at the midpoint between the two sheet. (lust like in the bar frame where the two sheets hit simultaneously and the forces propagate at equal speeds).
The point being that each consecutive sheet hits the ground before it can ever sense that any of the prior sheets have hit the ground, and the effect of these impacts propagating through the bar as seen from the ground frame will match up with those as seen from the bar's frame.

 

[jartsa]

Ok, so forget accelerations. This is in a non-gravitational space, or just on the ground, flipping the experiment so that the bar is moving parallel to the ground, with it attached to 2 supports traveling in the bar direction. There then is a force applied parallel to the ground, perpendicular to the bar movement direction like a constant wind (tho probaby better a force faster than wind if there is a problem trying to compare wind speed with speed of force translation along the bar).

The bar is being held against the wind by a cable on the front and back. A marble sits in the middle. So initially the bar and marble are locked in, no relative movement in the wind direction. Only in the direction it is moving along the ground.

Now, in the frame of the bar, you cut the support of the front cable only. You see the front end start to move away from the wind direction. The rear cable has yet to be cut. So it would seem the marble would start to roll towards the front of the bar, being pushed by the wind, as the bar rotates.

Now, from the stationary observer on the ground, he sees the bar and cables traveling along all at the same orientation, perpendicular to the wind. No movement in the direction of the wind. He on the other hand sees the 2 cables cut simultaneously and so the bar stays in the same direction as it started, and the marble stays in the middle.

Where does this go wrong? [I guess there are still accelerations, going from still to the speed of the wind, but hopefully that phase of acceleration does not take away from the initial point where the marble is compelled to move]

BTW, if my assumptions are wrong, I'd like to know how so I can learn. This is very educational. I sensed my initial analysis was off, but wasn't sure how.

[note this version of this post was edited from the original post]

That was too complicated for me, so I created my own thought experiment:

Let's say we are observing a group of spaceships, made of steel, forming a moving wall, reflecting radio-waves emitted by a long-wave radio, that is moving with the wall.

Then we observe every spaceship simultaneously using a rocket motor for one second. The rockets point to direction perpendicular to the motion. Intuition says we do not observe any change of direction of reflected radio waves.

But if we go to the wall frame, then intuition says we would observe a change of direction of reflected waves.

But in the wall frame an observer changes his ideas of all directions, when that observer's velocity changes.

So we, who's ideas of all directions does not change, can say that the direction of the waves did not change, just some observer's idea about that direction and all other directions changed.(I don't know what happens to an individual spaceship's orientation, that's why I used EM-waves that can't see an individual spaceship's orientation)

 

[Herman Trivilino]

...is it possible in any of these cases that the observer on the bar sees the marble start to roll because the front bar end starts to move first, whereas the ground observer sees the 2 ends cut simultaneously and thus no movement of the marble?

No. If the marble moves relative to the bar in one frame it does so in all frames.

After posting about the bubble of a carpenter's level I realized my argument is specious because the location of the bubble tells you nothing about the orientation when the device is in free fall.

Same argument applies to the rolling ball. Place a ball on a ramp and it rolls down the ramp. But if the ramp is in free fall the ball doesn't roll.

 

[hatflyer]

Solved?

the simpler experiment (this takes place flat on the ground or in space so no gravity involved) - a bar is held to an overhead track by its 2 ends via a cable on each end. A marble sits in the middle. A wind force is trying to push the bar down away from the track, but the 2 cables hold it there.

Scenario A - reference frame as seen sitting on the bar: the cable is detached from the front end of the bar. The rear is still attached. So the change in force on the front allows the wind to blow the front end away from the track. The front dips down, this propagates towards the middle, and the marble moves with that wind pushing on it.

That's pretty clear. You sit on a bar, you release the front only, the front will drop.

Scenario B - a reference frame where all this is in forward motion: this time, to the observer watching this, both ends of the bar are cut off at the same time. It would "seem" that if you cut both ends of a horizontal bar, it would be symmetrical in reaction and so the bar would fall horizontally away from the track, and so the marble won't move.

A or B must be wrong, since the marble moves or not in both. It must be B. I think because of the force propogation speed, by the time the end forces spread towards the middle, the marble, they will not meet at the same time. So the bar is not horizontal in this frame, and the marble also moves. The bar, or cable car in the initial experiment, does indeed dip when seen from the ground. It does not fall flat

Yes?

 

[Dale]

Now, in the frame of the bar, you cut the support of the front cable only. You see the front end start to move away from the wind direction. The rear cable has yet to be cut. So it would seem the marble would start to roll towards the front of the bar, being pushed by the wind, as the bar rotates.

I like the idea of the wind instead of gravity. That definitely is important.

Let me ask you, though, forget relativity for a moment. Do you know how to solve this problem in the frame of the bar? I mean, remember that there are no rigid objects allowed, and the tension may not be perpendicular, and the wind may not be perpendicular. How would you solve this problem?

That's pretty clear. You sit on a bar, you release the front only, the front will drop.

But when and where does it drop?

 

[hatflyer]

I like the idea of the wind instead of gravity. That definitely is important.

Let me ask you, though, forget relativity for a moment. Do you know how to solve this problem in the frame of the bar? I mean, remember that there are no rigid objects allowed, and the tension may not be perpendicular, and the wind may not be perpendicular. How would you solve this problem?

Yes, I know basic mechanics. This was an excercise

I like the idea of the wind instead of gravity. That definitely is important.

Let me ask you, though, forget relativity for a moment. Do you know how to solve this problem in the frame of the bar? I mean, remember that there are no rigid objects allowed, and the tension may not be perpendicular, and the wind may not be perpendicular. How would you solve this problem?

But when and where does it drop?

Yes, I remember some basics of mechanics. But because this was a thought experiment in relativity, I assumed in the bar reference frame, it was an ideal, symmetrical, smooth condition. The simple idea if you are sitting on a stationary swing, and 1 of the chains is snapped, the swing will start to fall from the end of the swing where that chain was. Nothing else is needed for that reference frame. Not how long the chain is and such. It starts at the point of release of the cable, the end of the bar,and works its way along the bar in some fashion. If you want to get into real world, non-ideal discussions, then yes, there are variations and waves and vibrations and materials. But that was not the point in the rest frame.

However, in the moving frame, mechanics and force propagation are important, such as how the force change travels along the bar at the speed of sound, and when you combine that speed with the speed of the bar, you have to use relativistic speed additions. Thus the bar, or car, doesn't fall horizontally. That was my thought experiment question, will it fall horizontally from the ground, but no one could say, and then other experiments were thrown in but didn't show how it would relate to my experiment.

So, that's the solution I'm presenting, and hope if my conclusion is wrong someone will correct me. Now that I think I understand the material, the question and answer seem relatively straight-forward, in terms of an einsteinian-like ideal thought experiment, not involving wave propagations and degree of stiffness of the material and local accelerations when the force hits, or is removed, from the bar. Just more general in nature.

Thanks.

 

[PeterDonis]

so forget accelerations

You can't if you're applying forces to objects. If there are any forces involved, then the objects in question are not moving inertially, and you can't analyze the situation as though they are.

I think that when forces and accelerations come into play, strange General Relativity(?) effects become important.

Only if spacetime is curved, i.e., if gravity is present. You can set up scenarios in flat spacetime, with no gravity, in which there are still forces and accelerations, but everything can be analyzed using SR. The alternate scenario hatflyer proposed is an example of such a scenario. However, such a scenario can't be analyzed using SR under the assumption that all objects are moving inertially and "forgetting" the forces and accelerations.

 

[FactChecker]

Suppose that by some mechanism, there is a force in the car causing the bar to accelerate horizontally (in the car reference frame) to the floor at less than the acceleration of gravity. Then the bar would still tilt from the point of view of the ground observer and we would be back to the original question -- would the observers agree that a marble stayed in place on the bar. The answer must be that they agree. It seems like this is true regardless of where the marble originally was on the bar. Then we still would ask why the ground observer does not see the marble roll backward toward the lower rear end of the bar. The acceleration must have effects.

 

[FactChecker]

Only if spacetime is curved, i.e., if gravity is present. You can set up scenarios in flat spacetime, with no gravity, in which there are still forces and accelerations, but everything can be analyzed using SR. The alternate scenario hatflyer proposed is an example of such a scenario. However, such a scenario can't be analyzed using SR under the assumption that all objects are moving inertially and "forgetting" the forces and accelerations.

I think this straightens out a misconception that I have had for a long time. I always assumed that non-gravitational acceleration was treated in GR similarly to gravity. If I understand you right, you are saying that non-gravitational acceleration are not treated in GR. Is there something in addition to SR and GR that addresses acceleration, or would it be considered part of SR?

 

[jartsa]

That was too complicated for me, so I created my own thought experiment:

Let's say we are observing a group of spaceships, made of steel, forming a moving wall, reflecting radio-waves emitted by a long-wave radio, that is moving with the wall.

Then we observe every spaceship simultaneously using a rocket motor for one second. The rockets point to direction perpendicular to the motion. Intuition says we do not observe any change of direction of reflected radio waves.

But if we go to the wall frame, then intuition says we would observe a change of direction of reflected waves.

But in the wall frame an observer changes his ideas of all directions, when that observer's velocity changes.

So we, who's ideas of all directions does not change, can say that the direction of the waves did not change, just some observer's idea about that direction and all other directions changed.(I don't know what happens to an individual spaceship's orientation, that's why I used EM-waves that can't see an individual spaceship's orientation)

The 'wall' corresponds to the cab floor, the radio wave corresponds to the marble.

Hey, let's make it two parallel 'walls' and a radio wave bouncing between the 'walls'. And let's ask does the wave stay between the 'walls' or does it roll/bounce out.

So my opinion is that it does not bounce out. But, if a the two walls are two large metal panels with rockets on two sides, then ... I guess that that wave-guide bends, and the wave bounces out.

 

[PeterDonis]

If I understand you right, you are saying that non-gravitational acceleration are not treated in GR.

No. I'm saying that GR is only required if spacetime is curved. But in a curved spacetime, GR can treat non-gravitational acceleration.

Actually, even this doesn't quite make the full point. The full point is that, in relativity, there is no such thing as "gravitational acceleration", because "acceleration" in relativity normally means proper acceleration, and objects moving under gravity have zero proper acceleration--they are in free fall.

Is there something in addition to SR and GR that addresses acceleration, or would it be considered part of SR?

Once again, as long as spacetime is flat, SR is sufficient. So proper acceleration in flat spacetime can be analyzed using SR. Proper acceleration in curved spacetime requires GR--for example, when analyzing an observer "hovering" at a constant altitude above a gravitating mass.

 

[Dale]

The simple idea if you are sitting on a stationary swing, and 1 of the chains is snapped, the swing will start to fall from the end of the swing where that chain was

The thing is that it isn't that simple. Particularly when the things you are interested in are happening faster than the speed of sound in the chain. Take a look at this:





With relativity, once you can completely describe a scenario in one frame then you can determine what happens in another frame, but you have to describe things completely in the first frame (and to a higher level of detail than usual)

 

[gnnmartin]

This conundrum is a variation of another. Imagine a thin ruler of rest length 30cm traveling at close to the speed of light across a thin board, heading over a hole that is 30 cm wide. Does the ruler fall through the hole? The ruler 'sees' the hole contracted to negligible width, so you might expect it would not fall through, but the hole sees the ruler contracted to negligible length, so is confident the ruler does fall through.

The answer is that the ruler does indeed fall through. The phrasing of the conundrum fails to address the rigidity of the ruler, and the ruler cannot remain perfectly rigid (or rather, the notion of perfect rigidity contains a self contradiction). The ruler will droop as it passes the hole, and so thread itself through the hole, even though the hole measures 'very short' in the ruler's rest frame. The effect of gravity (or more exactly of curved space/time) have been neglected in a thought experiment which takes other values to such extremes that the distorting gravitational effects can no longer be ignored.

Oh, I didn't realize that there were already pages of replies: I thought the first page was all that had been posted.

 

[PeterDonis]

The effect of gravity (or more exactly of curved space/time) have been neglected

This scenario can be set in an accelerating rocket in flat spacetime, and works the same way. So curved spacetime is not really necessary. But the acceleration--proper acceleration--is.