Relativity paradox

[Tach]

Ah, I was considering an inelastic collision that ended with the rod flat on the floor of the train.
pp
So, the rod bounces elasticly.

Maybe yes, maybe no. I presented two different possibilities. Both cases, the observers disagree.

After the collision in the train reference frame, the rod is straight and moving inertially with the reverse of its previous velocity.

Err, "inertially"? You sure about this? against the gravitational field?

It seems obvious that this straight inertial rod will be straight in all reference frames.

Well, "it seems obvious" is not a scientific argument. What is needed is an analysis in the platform frame.

Why would you suspect the rod to be bent in the platform reference frame after the collision?

I already answered this three times, you even agreed with the analysis at post 86.

 

[Tach]

Let's remove gravity from the problem.

Let's not. Without it the rod doesn't fall.

Consider the rod, train, and platform all moving inertially in flat space, such that all elements of the rod collide with the floor of the train simultaneously in the train rest frame.
In the platform frame, the collisions between the rod elements and the floor of the train are not simultaneous.

But RoS is NOT the only effect in this dumbed down exercise.

 

[Pete]

Let's not. Without it the rod doesn't fall.

Start the scenario like this:
In the train rest frame, the rod is moving toward the floor at constant velocity.

But RoS is NOT the only effect in this dumbed down exercise.

So address one effect at a time to avoid confusion.

 

[Tach]

Start the scenario like this:
In the train rest frame, the rod is moving toward the floor at constant velocity.


So address one effect at a time to avoid confusion.

The way to avoid confusion is to consider all effects, as in a realistic problem, not some dumbed down version.

 

[Pete]

The problem is that the rod is bent in the platform frame as it collides with the train floor, but is never bent in the train frame.
You assert that SR is the wrong formalism for addressing this problem, because of the gravitational field, and we need to use GR instead.

Right?

 

[Tach]

The problem is that the rod is bent in the platform frame as it collides with the train floor, but is never bent in the train frame.
You assert that SR is the wrong formalism for addressing this problem, because of the gravitational field, and we need to use GR instead.

Right?

You got it.

 

[Pete]

So if we alter the scenario such that the problem remained in the absence of a gravitational field, we can address it using SR.
Right?

So, consider this:
Consider a train and platform moving inertially past each other in flat spacetime.
In the train rest frame, a rod is parallel to the floor, and moving toward the floor at constant velocity, such that all elements of the rod strike the floor simultaneously. The rod is straight and parallel to the floor at all times.

Transforming to he platform reference frame, one end of the rod strikes the floor and either stays there or moves upward as the rest of the rod is still moving down, so the rod must bend.

Now we can address the bent/not bent problem with SR, right?

 

[Tach]

So if we alter the scenario such that the problem remained in the absence of a gravitational field, we can address it using SR.
Right?

Would you please stop trying to dumb down the problem?

So, consider this:
Consider a train and platform moving inertially past each other in flat spacetime.
In the train rest frame, a rod is parallel to the floor, and moving toward the floor at constant velocity, such that all elements of the rod strike the floor simultaneously. The rod is straight and parallel to the floor at all times.

Transforming to he platform reference frame, one end of the rod strikes the floor first, so the rod must bend.

...resulting into a "paradox". There are no paradoxes in SR, so, your above attempt at dumbing down the problem is just an ill-posed problem.

 

[renislaj]

Would you please stop trying to dumb down the problem?

Pete is making it easier to proceed with the problem.

 

[Tach]

Pete is making it easier to proceed with the problem.

You just copied this exercise and you added your own crackpot twist at the end, so, please shut up.

 

[Pete]

Would you please stop trying to dumb down the problem?

I'm clarifying the problem.

...resulting into a "paradox". There are no paradoxes in SR, so, the above is an ill-posed problem.

It is true that there are no paradoxes in SR.
And what you said before is also true in this gravity-free scenario:

Take two points separated by the distance $$\Delta x$$, there is going to be a NON_NULL interval $$\frac{v \Delta x}{\gamma c^2}$$ during which one endpoint will be subjected to the reaction force of the ground while the other point isn't subjected to any such force.

So now the problem becomes "Why is this not a paradox?"

The rod is bent during the collision in the platform rest frame.
The rod is never bent in the train rest frame.

But, this is not a paradox. It can't be used to have a switch turned on according to one frame, and not according to the other, for example. After the collision, the rod is straight in both frames, for another.

Do you agree?

 

[Markus Hanke]

A uniform gravitational field also implies the absence of curvature.

That is completely incorrect. Take for example the Lagrange point between two massive bodies, like the earth and the moon. The field there is uniform, i.e. there are no tidal forces. However, the gravitational field, and thus curvature, is not zero. If you send ( for example ) a radar beam through that point you will find that the beam is delayed, a phenomeon known as Shapiro delay.

Do not confuse curvature with net forces. They are not the same thing. You can have regions without net gravitational forces, but non-vanishing curvature. I recommend "Gravitation" by Thorne/Misner/Wheeler for an in-depth treatment of this matter.

 

[Pete]

That is completely incorrect. Take for example the Lagrange point between two massive bodies, like the earth and the moon. The field there is uniform

Over how large a volume?

 

[eram]

Over how large a volume?

depends on how uniform you want the field to be.

 

[RJBeery]

Would you please stop trying to dumb down the problem?



...resulting into a "paradox". There are no paradoxes in SR, so, your above attempt at dumbing down the problem is just an ill-posed problem.

Tach, simplifying a complex problem is the best way to get an answer. If we can restate it without gravity why wouldn't we? I don't understand why there seems to be a problem with accepting that the rod curves in one frame yet remains straight in another. That doesn't present a paradox as far as I'm concerned.

Consider this: a relativistic rod moving over a gap (in this scenario we will impose gravity as a downward force). Will the rod fall into the gap?

From the ground's frame of reference we have

However, from the rod's frame of reference, the rod is much longer and the gap itself is shortened. There is only one way for the rod to fall into the gap now

Now we can either accept that curvature is greater in the second picture, or we can choose to ignore it completely and consider the entire problem solved by greater rotation of a perfectly rigid rod, but we are forced to accept that one of these are necessary in order for both frames to agree that the rod falls through the gap.

 

[Pete]

depends on how uniform you want the field to be.

Or how flat you want the spacetime to be

 

[Tach]

But, this is not a paradox. It can't be used to have a switch turned on according to one frame, and not according to the other, for example. After the collision, the rod is straight in both frames, for another.

Do you agree?

The two observers disagree on the outcome of the same experiment. This means that the problem is ill posed.

 

[Tach]

Tach, simplifying a complex problem is the best way to get an answer.

This is a reductionist view coming from a person utterly incapable of solving problems.

If we can restate it without gravity why wouldn't we?

Simply, because you are unable to solve the problem as stated , you are trying to transform it into a dumbed down version that you STILL can't solve.

I don't understand why there seems to be a problem with accepting that the rod curves in one frame yet remains straight in another. That doesn't present a paradox as far as I'm concerned.

Of course you can't: the same experiment has contradicting outcomes depending on the observer.

Consider this: a relativistic rod moving over a gap (in this scenario we will impose gravity as a downward force). Will the rod fall into the gap?

Please spare me the pop-sci, you copied this from Taylor-Wheeler, problem 54 without mentioning the source, of course.
The funny thing is that in this scenario, the outcome is the same in both frames.

 

[RJBeery]

This is a reductionist view coming from a person utterly incapable of solving problems.
Simply, because you are unable to solve the problem as stated , you are trying to transform it into a dumbed down version that you STILL can't solve.
Of course you can't: the same experiment has contradicting outcomes depending on the observer.
Please spare me the pop-sci, you copied this from Taylor-Wheeler, problem 53.

Uhh, no I didn't. But regardless, the problem applies here. Relativistic torque necessitates varying degrees of rod curvature. In the train's frame the torque is zero; hence, zero curvature. I said this 100 posts ago and if you choose to stick your fingers in your ears about it, so be it.

 

[Tach]

Uhh, no I didn't.

You are lying. Shamelessly. Bottom of page 99 ,problem 54. You copied the solution from back of the book. Just go away.