[William87]

There's a well-known paradox in special relativity involving two rockets connected by a string, accelerating constantly with equal proper acceleration.* In an inertial frame relative to the rockets, they maintain a constant distance apart. The question is whether the string breaks. The most accepted answer is yes, due to length contraction.

I'm curious if the answer would be the same from a flat Earth perspective. If it differs, why? If it is the same, is length contraction also the reason? A couple of things to consider are that since this is special relativity, gravity isn't a factor, and whether the string breaks isn't relative. If it breaks or not in the inertial frame, the result must be the same in the accelerating frame.

*edited to clarify

[mahogany]

There's a well-known paradox in special relativity involving two rockets connected by a string, both accelerating equally and constantly. In an inertial frame relative to the rockets, they maintain a constant distance apart. The question is whether the string breaks. The most accepted answer is yes, due to length contraction.

I'm curious if the answer would be the same from a flat Earth perspective. If it differs, why? If it is the same, is length contraction also the reason? A couple of things to consider are that since this is special relativity, gravity isn't a factor, and whether the string breaks isn't relative. If it breaks or not in the inertial frame, the result must be the same in the accelerating frame.

Flat Earthers on this site believe that space travel is an elaborate hoax and a scam put on by private companies like SpaceX and government agencies like NASA, and so one of the initial replies you'll likely get is that because space travel is fake, your rocket paradox can't be tested.   

[markjo]

There's a well-known paradox in special relativity involving two rockets connected by a string, both accelerating equally and constantly. In an inertial frame relative to the rockets, they maintain a constant distance apart. The question is whether the string breaks. The most accepted answer is yes, due to length contraction.

It could probably be argued that the string would not break because the distance between the rockets would contract along with the length.

[Tom Bishop]

The string won't break because SR is false nonsense used to explain the results of experiments which contradict the Round Earth Theory.

[AATW]

The string won't break because SR is false nonsense used to explain the results of experiments which contradict the Round Earth Theory.

Why is it explained in your Wiki page about UA then
https://wiki.tfes.org/Universal_Acceleration#A_brief_explanation_of_special_relativity
I thought this was part of your explanation for why UA doesn't accelerate things past the speed of light.

[Tom Bishop]

The string won't break because SR is false nonsense used to explain the results of experiments which contradict the Round Earth Theory.

Why is it explained in your Wiki page about UA then
https://wiki.tfes.org/Universal_Acceleration#A_brief_explanation_of_special_relativity
I thought this was part of your explanation for why UA doesn't accelerate things past the speed of light.

The idea of a speed of light limit is part of SR. However, this is a misconception of SR that things would suddenly stop accelerating. That section begins with "According to the Special theory of Relativity, the Earth can accelerate forever..." and does not discuss whether SR is actually valid. It is correcting the misconception of what SR claims.

[William87]

The idea of a speed of light limit is part of SR. However, this is a misconception of SR that things would suddenly stop accelerating. That section begins with "According to the Special theory of Relativity, the Earth can accelerate forever..." and does not discuss whether SR is actually valid. It is correcting the misconception of what SR claims.

The “neo-classic” model in the wiki includes both of the SR postulates.  Every other consequence of SR follows logically from from those two postulate. You can call it something else, but the “neo-classic” model will still have all the same effects as SR, including length contraction. It follows from the speed of light being c in all inertial frames.

The idea of a speed of light limit is part of SR

That’s not exactly true.  SR says that it’s impossible to reach the speed of light, relative to an inertial frame.  There’s nothing preventing exceeding c in an observer’s proper frame. (frame the observer is attached to).  When measured that way, its called rapidity.

And SR doesn’t say that everything suddenly stops accelerating. Mostly because you can’t ever reach c.  But if you could, SR says that time will stop.  Velocity thru time plus velocity through space always equals c.  That’s why the faster you go, the more time slows down, to keep the balance at c. if you’re moving through space at c, you would stop moving through time but theoretically continue to accelerate through space.  Light would never be able to catch up to you, though.

It could probably be argued that the string would not break because the distance between the rockets would contract along with the length.

In the inertial frame, the distance between the two rockets always stays the same because of their equal accelerations and velocity.  That’s part of the set up, in the inertial frame, the distance between the rockets never changes relative to an inertial frame. I probably could’ve been more precise in my wording, so I edited the original post.  Maybe that will give you a hint.

Flat Earthers on this site believe that space travel is an elaborate hoax and a scam put on by private companies like SpaceX and government agencies like NASA, and so one of the initial replies you'll likely get is that because space travel is fake, your rocket paradox can't be tested

.  

The paradox doesn’t really have anything to do with rockets or space travel specifically.  Its just an analogy to illustrate an idea.  Could be any two accelerating objects.  According to FE/UA even the earth and the moon, if they were connected by a string.

[markjo]

The idea of a speed of light limit is part of SR. However, this is a misconception of SR that things would suddenly stop accelerating.

SR does not say that "things suddenly stop accelerating" as they approach the speed of light.  SR says that as things accelerate toward the speed of light, it approaches asymptotically.  It can get ever closer, but can never quite equal c.  It's right there in the velocity addition formula that is so well documented in your wiki article.
https://wiki.tfes.org/Universal_Acceleration#Why_doesn.27t_the_Earth.27s_velocity_reach_the_speed_of_light.3F

[Tom Bishop]

And SR doesn’t say that everything suddenly stops accelerating.

That's right. The vast numbers of the people who come to this website and make that argument are wrong.

The idea of a speed of light limit is part of SR. However, this is a misconception of SR that things would suddenly stop accelerating.

SR does not say that "things suddenly stop accelerating" as they approach the speed of light.

Correct. That's what our visitors say.

[AATW]

The string won't break because SR is false nonsense used to explain the results of experiments which contradict the Round Earth Theory.

You are this meme



Special relativity is used or accounted for in many real-world applications such as nuclear energy and GPS.

[alpha07]

From a flat Earth perspective, some might argue against the validity of SR altogether. However, if we stick to the principles of SR, the string would indeed break due to length contraction. This paradox serves as an interesting thought experiment to understand the effects of relativistic physics.

[William87]

You are this meme

To be fair, I've come to realize that when someone's identity is so tied up with what they believe, pushback isn't surprising. When beliefs are challenged, a person can feel personally attacked, as if you are challenging not just what they belive, but who they are. 

Whether it's religion, politics, flat earth, anti-vax, any number of things, I think we all have personal, deeply ingrained beliefs that have their roots in what we consider our core identity.  When you don't have a sense of self independent of what you believe, changing what you believe can be very scary. 

I'd like to believe I have the intellectual honesty, and frankly, maturity to know that accepting something that contradicts my "world view" doesn't invalidate me as a person.  But the truth is most of us have some hill we would die on to justify what we have chosen to invest in.

Most people just aren't that invested in what shape the Earth is, which is what makes the pushback seem so bizarre. 

[William87]

From a flat Earth perspective, some might argue against the validity of SR altogether. However, if we stick to the principles of SR, the string would indeed break due to length contraction. This paradox serves as an interesting thought experiment to understand the effects of relativistic physics.

Thank you, it is all about understanding the effects of relativistic physics.  John Bell even included in his book in a chapter called "How to teach Special Relativity".

The lack of understanding of some of the most basic concepts by people who believe they have a level of understanding good enough to develop a new theory that contradicts thousands of years of established science is kind of mind blowing. 

Stating that SR is a bunch of bunk made up to discredit flat earth while acknowledging that the two postulates of SR are valid is a perfedt example.  If you don't understand that every effect of SR flows from those two postulates, you don't understand anything about SR. 

The whole of UA is built on a misunderstanding of the equivalence principle.  It only applies locally, in the immediate vicinity of the observer and for short periods of time.  That makes all the difference. 

Assuming SR, then why does the string break in the frame attached to the accelerating rockets?  There is no length conractionm in that frame.

[markjo]

The idea of a speed of light limit is part of SR. However, this is a misconception of SR that things would suddenly stop accelerating.

SR does not say that "things suddenly stop accelerating" as they approach the speed of light.

Correct. That's what our visitors say.

That's also what your wiki says.

[mahogany]

From a flat Earth perspective, some might argue against the validity of SR altogether. However, if we stick to the principles of SR, the string would indeed break due to length contraction. This paradox serves as an interesting thought experiment to understand the effects of relativistic physics.

Thank you, it is all about understanding the effects of relativistic physics.  John Bell even included in his book in a chapter called "How to teach Special Relativity".

The lack of understanding of some of the most basic concepts by people who believe they have a level of understanding good enough to develop a new theory that contradicts thousands of years of established science is kind of mind blowing. 

Stating that SR is a bunch of bunk made up to discredit flat earth while acknowledging that the two postulates of SR are valid is a perfedt example.  If you don't understand that every effect of SR flows from those two postulates, you don't understand anything about SR. 

The whole of UA is built on a misunderstanding of the equivalence principle.  It only applies locally, in the immediate vicinity of the observer and for short periods of time.  That makes all the difference. 

Assuming SR, then why does the string break in the frame attached to the accelerating rockets?  There is no length conractionm in that frame.

The lack of understanding isn't mind blowing if you consider the Dunning-Kruger effect; Tom being a prime example where he believes his level of competency and understanding is high but it's actually very low -- and he lacks the self-awareness to know this. 

[flannel jesus]

There's a well-known paradox in special relativity involving two rockets connected by a string, accelerating constantly with equal proper acceleration.* In an inertial frame relative to the rockets, they maintain a constant distance apart.

If the rockets are accelerating, then what could it possibly mean to say "an inertial frame relative to the rockets"? An inertial frame cannot be an accelerating frame.

[William87]

If the rockets are accelerating, then what could it possibly mean to say "an inertial frame relative to the rockets"? An inertial frame cannot be an accelerating frame.

No it can't, but you can have an frame that is moving inertially with the same speed as the accelerating frame at any given moment. It's called a Momentarily Comoving Inertial Frame.  That is what is meant by a frame that is inertial relative to an accelerating frame.

If what you meant was that, technically, there is no such thing as an inertial frame relative to a frame with proper acceleration, you are correct. That would be because the "inertial" frame would have coordinate acceleration relative to the frame with proper acceleration.  Nevertheless, the MCIF is what is used when the coordinate acceleration of the "inertial" frame isn't relevant. 

You may be on the right track, though because the resolving the paradox is all about understanding the difference between proper and coordinate acceleration and recognizing that they aren't always equal. It's the answer to why the string breaks in the rockets' frame, even though there is no length contraction in those frames.