The Spaceships Paradox - Can You Solve It?

A delicate thread hangs between two spaceships. They start accelerating simultaneously and equally towards the speed of light. What happens to the thread?

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😎: Kyle
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[kylehill]

Thanks for watching, my nerdling swarm. I'm guessing there will be a lot of math-y questions on this -- take it to the comments!

[cyrosgold]

Kyle: If the string would snap then the same effect would cause the ships themselves to be torn apart as any 2 reference points within either ship would suffer similar stress and even atomic and sub atomic bonds would be stressed causing all mater involved to disperse as each atom would experience the same distortion to it's neighbors.

[Kickflips]

I love how he says "don't worry if you didn't get the right answer" as if I had any answer 😅

[robmack]

The way he worded it is that two ships at the same moment identically accelerate. He talks about different reference frames affecting the string, but he never talks about the reference frame of the string itself. Also, I think his analysis of the reference frame of the ships is wrong two. Thinking relativistically, absolute velocity relative to some universal reference frame doesn't matter at all. The only thing that matters is the relative velocities of the things you're comparing. Since the two ships and the string at all times have identical velocities while they accelerate, they all exist in the same reference frame. Even though it's an accelerating reference frame, they're all accelerating identically, so the acceleration cancels out in the comparison. So from the perspective of the ships or the string, no matter what speed they reach, they are not moving relative to one another. Therefore the string does not break.
If what you're really trying to ask is, "they accelerate such that to an outside observer they appear to always be equidistant, " then yes, the string would snap because an external reference frame gives erroneous information of an accelerating reference frame at relativistic speeds

[isaiahwallace]

I'm glad most of us can agree that he at best misrepresented how the paradox should be presented and at worst didn't understand it himself

[valenciaparchment]

Paradox solved... Or is it?
Me: *Vsauce flashbacks*

[odisclemons]

Kyle: Without getting too complicated-
Me: We're well past that Kyle...

[temorinkaari]

I love how comments made more sense of this than the video, and basically proved this paradox doesnt make any sense

[fritt_wastaken]

There are 2 mistakes in this video.
1st is in the premise of the paradox. Parafox implies that ships move identically from YOUR perspective. If they were accelerating at the same rate in their own frame, then no snapping would occur. So you needed to state which of the frames you're using explicitly.
2nd mistake is at 3:45. From your perspective my watches are also slowed down. Lorntz transformations are perfectly symmetrical for non-accelerating frames.

[EpicMathTime]

The paradox tricks us by giving the ships a property that cannot hold in all of the involved reference frames simultaneously.

There are two obvious choices of reference frames. The "ground-observer" that the ships are traveling relative to, or one of the ships themselves.

In the original question, the ships are accelerating together, and remain the same distance apart, from the perspective of the ground-observer.

Let's change it up.

Let's say that the ships will coordinate their acceleration and velocity with one another precisely. So, from the perspective of _one of the ships_ their distance remains perfectly constant. In this scenario, the string *does not break.* The ship/ship/string unit moves in perfect, beautiful unison.

However... ground-observer witnesses something different. As the ships speed away from him, he will observe relativistic effects on the ships, including length contraction. As a result, ground-observer witnesses the ships getting closer and closer to one another. They do not remain at a constant distance, and so the original premise, to the ground-observer, was violated!

Now, back to the original scenario. The ships are to remain at a constant distance apart relative to the ground-observer as they accelerate away. But... the ships are still accelerating from the ground-observer. The ground-observer will observe relativistic effects on the ship/ship/string. He will observe length contraction. However, we premised that the ships will remain at a constant distance as observed by ground-observer. So, how can the ships remain at a constant distance from each other to ground-observer, while ground-observer also witnesses relativistic length contraction of the ship/ship/string system?

There is only one way for this to happen. The ships have to be moving/accelerating such that, from _their own_ reference frame, they move apart from one another at a rate that precisely counteracts the length contraction observed by ground-observer. They move apart from one another from a ship's perspective, and the string breaks. Ground-observer sees the string break while the ships remain at a constant distance, but while he saw the string stretched to the same length the whole time, it was continuously being pulled more and more taught, as the ships moved away from one another in their own frame.

The subtle nuance here is that length contraction is just an observation from some frame of reference, and does not actually physically effect the string at all. Rather, length contraction effects only the _perception_ of the ground observer. The premise requires the ship/ship/string system to _actually_ grow in proper length in order to counteract the relativistic effects seen by the ground observer - the string breaks, because the ship/ship/string system _necessarily_ had to get longer (in proper length). The situation counteracts a relativistic length contraction (a perception) with an increase of the ship/ship/string system's proper length (an absolute phenomenon).

Moral of the story: the ships can either stay at a constant distance from their own perspective, or they can stay at a constant distance relative to the ground-observer's perspective, but they _cannot_ do both!

[cornelious]

So wouldn't the spaceships themselves eventually snap under the strain with the front distancing itself from the back?

[blodhthringa]

I was going to say, the string shouldn't snap at all, perspective doesn't effect the physical existence of the string.

[pihi]

3:48 - there is an error. From perspective of the moving object, you also look slowed down. The situation is symmetrical. Although this seems contradictory, it is not. it couldn't be any other way, in fact.

[Ajslade]

Is this your "string theory?" Lol

[thaias]

“...Space is not a perfect void, like my heart, ...”

[averagegamer]

Kyle: "Alot of processing power from somewhere"

Me: *sees Jupiter computer*

[lilithstardust]

"how can a road intersect with itself" you have nonstandard spacetime warnings everywhere for a reason kyle!

[shaggyspade]

"Space is not a perfect void, like my heart" - Anonymous Super Villain 2020

[unvergebeneid]

This explanation was just confusing and all over the place.

[ItsAsparageese]

"Basic like a North Face jacket and Ugg boots (you know who you are)"

"ANOTHER sushi place?"

*Suspicion that you went to CU Boulder intensifies* 😂