I When and how can I apply Born rigidity condition?

[PeterDonis]

This is the difference in force required to produce the Born rigid condition.

Ah, I see. I was misinterpreting what you were trying to do. Yes, any difference in force less than that will produce a positive expansion scalar (though not necessarily of the same magnitude as the Bell congruence expansion scalar) and will therefore break a sufficiently fragile string.

 

[member 728827]

As long as force is measured in the rocket momentary rest frame, and the mass is momentary rest mass of the rocket (important, since a rocket expelling thrust has changing rest mass), then the ratio is proper acceleration (even in SR), and the scenario is no different than the Bell case.

EXAM PROBLEM.-

A vehicle's engine exerts at every moment an exact force, that always keeps the same proportion to the current mass of the vehicle, and so we can say that the Force/mass ratio is a constant. Call it F/M ratio.

We do this in order to compensate the mass loss due to the engine burning fuel, and keep the same acceleration initially.

The vehicle burns fuel, and losses 10 gr of mass every second when running. No propulsion force is considered from the exhaust gases.

The constant F/M ratio is adjusted to 0.25, so the engine will exert 0.25 N of force per 1 Kg of mass of the vehicle, which means that the vehicle will accelerate initially at 0.25 m/s².

The vehicle starts moving, and after a short transient time, it reaches the initial acceleration of 0.25 m/s². We start the timer watch at that moment, and also we measure the distances from that position. Also, the mass of the vehicle is 1000 Kg and the initial speed is 3 m/s. We don't consider any aerodynamic air resistance.

QUESTIONS.-

1. Which distance has the vehicle traveled @1 minute? (1 point).

2. Which is the total mass of the vehicle @1 minute? (0.5 points).

3. Which is the acceleration of the vehicle @1 minute? (0.5 points).

4. After 1 minute, the vehicle enters a steep road, with a constant slope of 5%. Which is the acceleration of the vehicle 10 seconds after? (8 points).

 

[member 728827]

Dale,

Thanks, I'll read carefully you very interesting and instructive answer, that has led to some very interesting and instructive comments by others, but I'll disagree fundamentally in one detail, not really related to you exposition, which has nothing to do with the "fragility of the string", and holds its validity undisturbed by that minor detail.

Fragile means that any tension breaks the string. A fragile string does not have any tensile break resistance.

What you describe then is not a string, is a mathematical line than extends from point to point with a defined length, and some properties defined by an Euclidian geometry or whatever, but has no physical material properties - such as tensile strength. That line can't neither break because lines don't break and then you have two lines, or a lot of bits of lines.

"fragile thread" that "finally breaks" due to "intolerable stress" ... is Bell's wording, not mine, in the statement of the original paradox. He's not talking about a zero tensile resistance thread, he's talking about a string than has some relatively weak resistance, but obviously not zero, because then it's not a string... such thing doesn't exists, a line do exists as a mathematical object, a zero tensile string doesn't exists, not even conceptually, because breaks spontaneously, just in the action to try to tie it to the hook in the spaceship.

I agree that if it's a community consensus that when in a paper you write "we consider a fragile string", every Physics literate will read "ah, it's a zero tensile break resistance string, nothing to worry about, will not molest us with any force", then I should have to include that fact in the summary. At the very first paragraphs of my huge post, no need to deep further, you already get immediately that I consider a string with some mechanical characteristics, it's not hidden anywhere.

But, what a problem! Consider modified the summary of the post, and read also "considering a weak string with a small tensile break resistance", and that's it.

PD.
Putting the numbers into you equation, and for a 10 Km string, and for a 10⁹ Kg spaceship pulling, I get that the force threshold is 0.01 N.

I was considering as "fragile" a cable with a tensile strength limit of 840 N, and at the proper scale of the huge spaceship - with 10⁹ Kg mass - that's fragile enough for me, but as Groucho Marx said: if that's not enough fragile for you, I have others, because from 840 N to 0.01 I have some margin to play.

And, by the way, not everybody gets what the F/M constant ration means, or what effect it has in the Bell's paradox. Really. I'll try using sock puppets to explain me better :)

Thanks

 

[member 728827]

That doesn't have to be the case. Suppose the two spaceships started out with a proper acceleration of $10^{10}$ g instead of $1$ g.

Then I would use a $10^{11}$ Km diameter cable, made of Vibranium, bought in the Borg Amatzon galactic page. And, by the way, I guess such an acceleration would break, not the string, but something in the very current standard model of physics... just a guess.

 

[jbriggs444]

What you describe then is not a string

You seem to want to rail against idealizations. You will presumably rail against "test particles" as well. Such particles have a mass that is strictly positive but negligible. Strictly positive so that the particle may follow a space-like trajectory. Negligible so that it will not significantly affect the geometry of the space within which its motion is analyzed.

Bell's string has neglible tensile strength. It is a string so that it has a defined length and gives us a mental picture. It has sufficient tensile strength to hold itself together (in a Born rigid fashion, one assumes) but insufficient tensile strength to significantly alter the trajectories of the ships to which it is attached.

I see no need to attack the idealization instead of attacking the problem.

 

[member 728827]

Right, but them I don't understand why the people don't get it, when I say: "Alternative scenario, different to Bell's one, in which..." And, believe me, some people don't get it at all.

So, if you consider your "test particle" - no problem for me at all - and I then make a post that reads "considering a different scenario, in which the particle has the smallest mass even measured... what would be the outcome? I think that...", then is criticism to you? That would make your tolerance pretty fragile, in the sense of the Bell string as you consider.

 

[Dale]

What you describe then is not a string, is a mathematical line than extends from point to point with a defined length, and some properties defined by an Euclidian geometry or whatever, but has no physical material properties - such as tensile strength. That line can't neither break because lines don't break and then you have two lines, or a lot of bits of lines.

You can complain about the terminology if you like, but what I described is what every scientist understands by the term.

You yourself have repeatedly been misunderstood when describing this scenario. This is why. When you say “Bell’s scenario except for this F/m change” people include Bell’s fragile thread they understand to mean a thread which breaks with the slightest tension. And with that inclusion they conclude that it is the Bell’s scenario.

If you wish them to understand that your scenario is different from Bell’s then you have to describe to them that you do not want them to make the assumption that the slightest tension is intolerable. You need to explain that a certain finite tension is tolerable.

You can complain to me about terminology, but that is rather unproductive and you will continue to be misunderstood.

I don't understand why the people don't get it, when I say: "Alternative scenario, different to Bell's one, in which..."

Do you really not understand now? Or are you just complaining?

 

[member 728827]

I'm not a scientist, nor a physicist, and reading what Bell's paradox wrote in his book, for me "fragile" means being a physical tangible thread, but that in the relative scale of the scenario, can be considered "fragile".

I can consider an spider thread to be fragile, if I'm talking about Naval ships that displace 300,000 Tons, and everybody will agree. If I say the same thing talking at the scale of an ant, people will say me that I'm not right, that the spider thread has a huge tensile strength for an ant.

Any way, I "conceptually" changed (I can't do it physically) the statement and summary of the post, so, where's the problem? I've already said so... another thing is that you change my mind about the "fragility" property and its context... you won't change it, and will be futile and unproductive discussion.

That's closed for me.
Thanks

 

[Dale]

I'm not a scientist, nor a physicist, and reading what Bell's paradox wrote in his book, for me "fragile" means being a physical tangible thread, but that in the relative scale of the scenario, can be considered "fragile".

Yes, that is why I explained the issue to you. You were communicating to physicists and being misunderstood.

Any way, I "conceptually" changed (I can't do it physically) the statement and summary of the post, so, where's the problem? I've already said so... another thing is that you change my mind about the "fragility" property and its context... you won't change it, and will be futile and unproductive discussion.

That is fine. I am just explaining the communication issue you were facing. How you choose to think about it is your own business. At least now, you know how to communicate your idea to this audience.

 

[PeterDonis]

EXAM PROBLEM

This belongs in the homework forum, not this one.

 

[PeterDonis]

At this point the thread topic has been sufficiently explored. Thread closed.