Can an Altered Thought Experiment Reconcile the Special Relativity Conundrum?

[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)

 

[Mister T]

...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.