Relativity paradox

[Markus Hanke]

Interesting - good post.

Thank you, but I must qualify that post by saying that this is my own solution to the puzzle. That is not to say that there are not other, better ones. The point is simply that the physical outcome as seen from the two frames cannot differ.

Motordaddy is one of our local relativity deniers. He pops up every now and then with arguments that are shown to be wrong but he never learns. Talking to him is like trying to reason with an artichoke.

Yes, I can see that. Since he hasn't learned at thing in 2700+ posts, I think it is safe to say that responding to him is a complete waste of time.

 

[Markus Hanke]

There is nothing to "determine" about the reference frame's state of motion: by definition, it is at rest relative to itself. Motor Daddy may be trying to squeeze into the discussion his belief in absolute motion, not realizing it isn't relevant here. Instead it just makes it look like he has trouble understanding basic physics.

I agree.

 

[Motor Daddy]

Motion, as you say yourself, is not instantaneous, it is a change in position over time. In this case we are comparing two frames of reference.
You don't detect motion at 12:00, that is intrinsically impossible. All you do is take note of the spatial positions of objects in the other frame at that time, and then you let time elapse. At, for example, 12:01 you note the spatial positions of the other frame again, and compare them to the ones noted before. If there is any difference in readings, then there is motion relative to you. If not, then the other frame is at rest relative to you.

Of course all you are doing here is trying to deliberately create confusion, in order to detract from the fact that you don't know the answer to the puzzle in the OP. Or would you like to present such an answer here for us ?

And why did you not answer my question about giving an example for a physical scenario where time has stopped elapsing ?



Why would you need a watch if it always shows 12:00 anyway ?

Too much avoidance of my questions to have any credibility with me. When you answer my direct questions then we can talk. Until then I am wasting my time with you. Carry on.

 

[eram]

Motordaddy is one of our local relativity deniers.

Motor Daddy denies just about every single thing.

 

[eram]

Not my kind of movie
But then again, she didn't end up suspended from the ceiling, as in the OP...

At the end, they all do, with meat hooks. He also finds out the police are covering it up.

 

[Markus Hanke]

Too much avoidance of my questions to have any credibility with me

Why would it matter if we have credibility with your or not ??

 

[Motor Daddy]

Why would it matter if we have credibility with your or not ??

For instance, one rainy night I am driving down a dark road and I see somebody, standing on the side of the road, soaking wet, cold, and miles from home. I stop, put down my driver's window and notice it's you. I quickly remember that you couldn't care less about me, so I adjust my actions accordingly by putting up the window and driving off, leaving you to your misery.

 

[Markus Hanke]

For instance, one rainy night I am driving down a dark road and I see somebody, standing on the side of the road, soaking wet, cold, and miles from home. I stop, put down my driver's window and notice it's you. I quickly remember that you couldn't care less about me, so I adjust my actions accordingly by putting up the window and driving off, leaving you to your misery.

That's just fine, because what you will find is that the two frames of reference are perfectly symmetric - swap the guy on the roadside with yourself in the car, and the physical outcome of the scenario would be the exact same.

Relativity works !!!!

 

[Motor Daddy]

That's just fine, because what you will find is that the two frames of reference are perfectly symmetric - swap the guy on the roadside with yourself in the car, and the physical outcome of the scenario would be the exact same.

Relativity works !!!!

See, you are so far up Einstein's butt that you can't see the light! You do not own my car and you are not the one driving, I am! You are the one on the side of the road that's cold and wet!

 

[eram]

That's just fine, because what you will find is that the two frames of reference are perfectly symmetric - swap the guy on the roadside with yourself in the car, and the physical outcome of the scenario would be the exact same.

Relativity works !!!!

Ah, a most practical application of relativity.

In the freezing rain, or in a cramped car with Motor Daddy? That's a tough decision.

See, you are so far up Einstein's butt that you can't see the light! You do not own my car and you are not the one driving, I am! You are the one on the side of the road that's cold and wet!

Talking to him is like trying to reason with an artichoke.

An artichoke is probably easier to reason with.

 

[RJBeery]

There is a human body suspended horizontally by two wires in a train car moving on the tracks. The body is positioned symmetrically wrt to the center of the car. The wires are simultaneously cut (in the frame of the car). Obviously, the body falls parallel to the car floor hitting the floor simultaneously with all its points (in the car frame).
But in the track frame the two wires are not cut simultaneously and the body does not fall parallel to the car floor : one end of the body will hit the floor before the other end. This will result into one end (say, the head) absorbing the full impact. The same experiment has differing results in the two frames. Hence there is a paradox in special relativity.

Markus Hanke's explanation is interesting but I believe the correct answer is much simpler. The body's end points hitting the ground are spatially-separated events; there is only a single frame in theory which would claim that they happen simultaneously. The OP makes the presumption that all frames should agree on the concept of simultaneity...the impossibility of which is one of the very first elementary lessons to be deduced from SR.

 

[Neddy Bate]

4. Thus, despite the wires not being cut at the same time in the embankment frame, the body nevertheless falls down straight in both frames.

I'm not sure what you mean by "Falls down straight", so I will just have to give you the benefit of the doubt on that one. However, one thing is for sure, according to the embankment frame, the head of the body does not hit the floor at the same time as the feet. That is the whole significance of relativity of simultaneity. There is no paradox though, because the embankment frame can easily transform the time coordinates of the impacts of the head and feet and determine they are simultaneous in the train frame. Thus, the head does not absorb the full impact of the fall. That is the beauty of the Lorentz transformations.

 

[Tach]

the embankment frame can easily transform the time coordinates of the impacts of the head and feet and determine they are simultaneous in the train frame.

Yes, so what? This is given from the beginning.

Thus, the head does not absorb the full impact of the fall.

This doesn't follow. In the embankment frame one end would hit first, so you cannot "transform away" that effect, the same way one cannot "transform away" gravitational fields in GR.

That is the beauty of the Lorentz transformations.

The Lorentz transforms are very beautiful indeed but you haven't proven anything of any value in this case.

 

[Tach]

The OP makes the presumption that all frames should agree on the concept of simultaneity...

No, it doesn't. There is no implication in the OP about agreeing on simultaneity, there is a different implication, though. Could you figure what that is?

 

[Neddy Bate]

In the embankment frame one end would hit first, so you cannot "transform away" that effect,

How would the embankment frame explain the head not absorbing the entire impact? I propose that they would transform the time coordinates to the train frame, and determine that the impact of the feet happened at the same time, thus absorbing some of the impact. If you have a better explanation, why not post it?

 

[Tach]

How would the embankment frame explain the head not absorbing the entire impact?

By the fact that , in the embankment frame, if one considers the effect of RoS alone, one end of the body hits before the other end. It is pretty clear in the OP, read it.

I propose that they would transform the time coordinates to the train frame, and determine that the impact of the feet happened at the same time, thus absorbing some of the impact.

Nope, you need to take each frame at face value, you keep trying to transform away the effect in the embankment frame. I already explained that you are not allowed to do that.

If you have a better explanation, why not post it?

Re-read Markus' explanation at post 2. I agree with him.

 

[RJBeery]

Re-read Markus' explanation at post 2. I agree with him.

I was hasty in my post. I thought the objection in the OP was that the body did not fall "straight down" in both frames. It appears that the objection is that the impact on each end of the body would apparently differ in one frame; let's replace the body with a steel I-beam and on the floor let's put a series of accelerometers; do the accelerometers' readings equal in all frames after the entire I-beam has impacted the floor? Of course, they must. I did not appreciate Markus' explanation because he appeared to be saying that Thomas precession would guarantee that the body would hit the ground in parallel fashion; this part cannot be true. At relativistic speeds the body [I-beam] does not remain straight when there is torque involved. However, perhaps Thomas precession could introduce a negative torque in such a way as to perfectly balance the impact of each end of the body [I-beam] on each accelerometer on the floor...even if those readings did not occur simultaneously in all frames.

 

[Neddy Bate]

Nope, you need to take each frame at face value, you keep trying to transform away the effect in the embankment frame. I already explained that you are not allowed to do that.

If you are telling the embankment frame that they are not allowed to use the Lorentz transforms to determine that the head and feet impact at the same time in their own frame, then I disagree.

Re-read Markus' explanation at post 2. I agree with him.

My explanation is consistent with his. I don't know what he means by "Falls straight down", because the body will be tilted on an angle as it falls, and the direction of the fall will not be vertical, according to the embankment frame. But his explanation for why the head will not absorb the whole impact is consistent with my explanation.

 

[Tach]

I was hasty in my post. I thought the objection in the OP was that the body did not fall "straight down" in both frames. It appears that the objection is that the impact on each end of the body would apparently differ in one frame;

A rare admission of error from you, must mark the calendar.

let's replace the body with a steel I-beam and on the floor let's put a series of accelerometers; do the accelerometers' readings equal in all frames after the entire I-beam has impacted the floor? Of course, they must.

So?

However, perhaps Thomas precession could introduce a negative torque in such a way as to perfectly balance the impact of each end of the body [I-beam] on each accelerometer on the floor...even if those readings did not occur simultaneously in all frames.

How is this different from what Markus is saying?

 

[Tach]

If you are telling the embankment frame that they are not allowed to use the Lorentz transforms to determine that the head and feet impact at the same time in their own frame, then I disagree.

That's not what I am telling you, what I am telling you is that you are trying to use a sleigh of hand to re-transform the problem in the train frame. You are an observer in the embankment frame, you must judge the experiment based on what you observe in the embankment frame, consider the fact that you can't see what happens in the train frame.

My explanation is consistent with his. I don't know what he means by "Falls straight down", because the body will be tilted on an angle as it falls, and the direction of the fall will not be vertical, according to the embankment frame. But his explanation for why the head will not absorb the whole impact is consistent with my explanation.

No, it isn't. "Straight down" for Markus means parallel with the ground, un-rotated. The Thomas precession cancels out the effects of RoS. You are considering RoS only (and trying to re-transform the problem back into the frame of the car through an inverse Lorentz transform, where the ends strike the floor simultaneously). Nowhere in your posts does the Thomas precession show up.