Special relativity implies very odd results

[discountbrain]

Do you want to interpret this as a fallacy in relativity? I posted part of this example before. Which is: what if you had 2 rocket ships a and b traveling from planet X to planet Y and they were both going 0.9999 times (or very close to) the speed of light, let d be the distance from X to Y, and the ships are 7/8d distance apart and a was only 10mi or so from Y and b was only 10mi or so from X. Then observers on both crafts would observe that the distance from X to Y would only be about 20mi or so (Ʃ of all the distances) because of the very well known length contraction formula. And what if rocket ship 'a' suddenly took a right angle turn? Then the distance from b to Y would suddenly seem to increase to many thousands of miles!

I didn't go as far with this the last time I said there appears to be a contradiction here and one of you very intelligent physicist wannabees told me this is physics, not math. But, Einstein's conclusions were all based on these very same sort of math calculations. It was because many of his results were verified by experimental observation that they became accepted. What say you to the above?

 

[DaveC426913]

The error is in your understanding of relativistic contraction.

what if rocket ship 'a' suddenly took a right angle turn?

This is ambiguously worded. In particular, the word 'suddenly'.

At .9999c, rocket a has a transverse (sideways) velocity relative to all other observers of zero. When it "turns" sideways, it still has transverse v of zero. It is simply pointing its nose to the side. Absolutely nothing else has changed. Rocket a could happily set itself spinning on its axis and it would have no effect on any aspect of the experiment.

Rocket a continues to have a transverse v of zero so until and unless it begins to accelerate transversely - which it does so at normal accelerative rate.

Do you acknowledge this?

 

[discountbrain]

I shouldn't have said only 10mi+10mi=20mi or so because this would be 1/8th the distance from X to Y which would make the planets awfully close.

 

[ghwellsjr]

Special Relativity is all about describing and analyzing everything from a single inertial Frame of Reference. If you do that, there will be no odd results, no fallacies, and no contradictions.

 

[DaveC426913]

I shouldn't have said only 10mi+10mi=20mi or so because this would be 1/8th the distance from X to Y which would make the planets awfully close.

It doesn't matter. Yes, at extremely high relativistic velocities, the planets could get awfully close. Not a problem.

What you're failing to recognize is that the rocket cannot 'suddenly' make a 90 degree turn. It must accelerate from zero in the new direction. As it does so it will eventually reach relativistic velocities in this new direction. As it does this, length contraction in the new direction will become apparent.

 

[discountbrain]

I'm thinking rocket 'a' is still going at the speed of near c, but at right angle to the path from X to Y. But, this doesn't matter. Its now that its velocity on the path from X to Y is now zero. Thinking of rocket ships should be analogous to 2 point charges moving in a wire. Since a current in a wire would have thousands of charges moving it would be hard to observe anything like this. If one ship was moving at near c velocity the distance from X to Y would be very slightly less for people on the ship. I think you see what I'm saying in my previous post.

 

[DaveC426913]

I'm thinking rocket 'a' is still going at the speed of near c, but at right angle to the path from X to Y.

No it isn't.

But, this doesn't matter. Its now that its velocity on the path from X to Y is now zero.

No it isn't.Ignoring circuitry analogy...

If one ship was moving at near c velocity the distance from X to Y would be very slightly less for people on the ship. I think you see what I'm saying in my previous post.

This is not a problem. Let it go.

Distance from X to Y can be much much less. At extremely high v, distance from X to Y could, in fact, be reduced arbitrarily small. Again, no problem here.The only problem here is in your mistaken concept that a rocket ship can suddenly turn from going "North" at .9999c to going "West" at .9999c. It simply can't. That is the crux of your misunderstanding. Embrace this. Let everything else go.

In order to go from .9999c "North" to .9999c "West" the spaceship must do two unrelated course changes:
1] It must begin to accelerate in a Westerly direction starting from 0 to .9999c
2] It must decelerate in its Northerly direction of travel from .9999c to 0.
Until it does at least one of these things, nothing in the experiment will change.

The one you're really stuck on is 1]. It must begin accelerating Westerly starting from zero. Only when it has been accelerating so long that it's reached relativistic velocity in a Westerly direction, will it begin to experience any contraction along that axis.

 

[discountbrain]

So, what if ship 'a' crashed into the surface of planet Y instead of making the right angle turn-oops, major screwup? You say with its relativistic mass and extremely high velocity it would transfer a huge amount of kinetic energy to Y. Maybe even enough to give Y some new velocity. And it might even travel over a mile deep before it completely stopped, but in 2 or 3 seconds observers on ship 'b' would see planet Y suddenly shoot off into the distance.

What if there were no rocket ship 'a' and in its place there were a piece of dirt of arbitrarily small size moving with the same velocity vector as 'a' had and it hit the surface of Y? Then Y would barely know it. And, in this case those on ship 'b' would originally think they could almost reach out and touch Y. So then, if a ship is moving at near c and other objects were moving in front of it in the same direction at the same speed the ship's destination would be far closer.

 

[discountbrain]

I think I might have answered my own question. What if no actually particle is considered at all, but just a point in space is considered to be moving this velocity and these points would always exist. So, If you could get up to near the speed of light distant planets etc would only be a stone's throw away.

 

[Dale]

What say you to the above?

Your scenario describes a non-inertial reference frame. Why shouldn't distances suddenly increase a thousand-fold in a non-inertial reference frame?

As ghwellsjr mentioned, if you avoid non-inertial reference frames then you would never get such a situation, and if you don't avoid non-inertial reference frames then you expect such situations. (btw, the standard formulas, such as length contraction, don't apply in non-inertial frames)

 

[Fredrik]

I think you should consider a simpler scenario instead. What if there's just one rocket and its pilot slams the breaks and comes to a quick stop (relative to X and Y)? Will the distance between that rocket and the destination planet increase?

Short answer: It won't increase in any inertial frame.

Longer answer: Suppose that we compare the following two distances:

a) the distance between the rocket that has just "stopped" and the destination planet, in an inertial coordinate system in which the rocket was stationary before it "stopped",

b) the distance between the rocket that has just "stopped" and the destination planet, in an inertial coordinate system in which the rocket was stationary after it "stopped".

Then yes, the distances will be very different, but there's no reason to think that this is a contradiction, since we're talking about coordinate assignments made by two different coordinate systems.

 

[Fredrik]

The only problem here is in your mistaken concept that a rocket ship can suddenly turn from going "North" at .9999c to going "West" at .9999c. It simply can't.

I don't have a problem with this. I just think it's an unnecessary complication, because now we'd have to do velocity addition in 2+1 dimensions.

It's of course impossible to do it with an actual rocket engine, but no matter how small a region of spacetime you would choose for me, I'd still say that it's possible in principle to make that velocity change inside of that region, because there's nothing in SR that says that it's impossible.

 

[DaveC426913]

I don't have a problem with this. I just think it's an unnecessary complication, because now we'd have to do velocity addition in 2+1 dimensions.

It's of course impossible to do it with an actual rocket engine, but no matter how small a region of spacetime you would choose for me, I'd still say that it's possible in principle to make that velocity change inside of that region, because there's nothing in SR that says that it's impossible.

The OP is having trouble seeing a sharp turn as an acceleration like any other. The OP thinks that going to .9999c North to .9999c West is merely turning a corner. The OP is envisioning a dramatic change in length contraction along the north axis to along the West axis because of this and thinks this is paradoxical.

 

[DaveC426913]

So, what if ship 'a' crashed into the surface of planet Y instead of making the right angle turn-oops, major screwup? You say with its relativistic mass and extremely high velocity it would transfer a huge amount of kinetic energy to Y. Maybe even enough to give Y some new velocity. And it might even travel over a mile deep before it completely stopped, but in 2 or 3 seconds observers on ship 'b' would see planet Y suddenly shoot off into the distance.

What if there were no rocket ship 'a' and in its place there were a piece of dirt of arbitrarily small size moving with the same velocity vector as 'a' had and it hit the surface of Y? Then Y would barely know it. And, in this case those on ship 'b' would originally think they could almost reach out and touch Y. So then, if a ship is moving at near c and other objects were moving in front of it in the same direction at the same speed the ship's destination would be far closer.

None of this has to do with your original question. This is causing you, and everyone else, confusion and consternation. Can we stay on track? Can you ask one specific question and we'll try to answer it, then move on?

 

[D H]

The OP is envisioning a dramatic change in length contraction along the north axis to along the West axis because of this and thinks this is paradoxical.

That is what an observer in this magical spaceship will see. As per the title of the thread, "Special relativity implies very odd results."

There is no true paradox here. As is the case with all of the paradoxes of relativity, it is just an apparent paradox. The paradoxes of special relativity result from our first-hand experience making us think that space is Euclidean and time is that universal (all observers agree on how clocks tick). The resolution is that our first-hand experience is limited; it does not give a true picture of how the universe as a whole works.

 

[DaveC426913]

That is what an observer in this magical spaceship will see. As per the title of the thread, "Special relativity implies very odd results."

Yes, they would - if they could "turn a corner" while moving at .9999c. The OP thinks that a turn like that is like doing it in a car. He is not seeing that going from .9999c North to .9999c West in a time frame he calls "suddenly" would constitute an acceleration of billions of gs.

If the OP were to realize that the rocket ship would have accelerate from 0 to .9999c but could do so no faster than its initial blast off from Earth, then he would see why there's no paradox.

 

[D H]

Yes, they would - if they could "turn a corner" while moving at .9999c. The OP thinks that a turn like that is like doing it in a car. He is not seeing that going from .9999c North to .9999c West in a time frame he calls "suddenly" would constitute an acceleration of billions of gs.

Ignore that. Pretend that the singularity has come, that we can download our minds onto a tiny, tiny chip that can withstand thousands of gs of acceleration or more. Pretend that we can build a very tiny but very sturdy spaceship that can hold this tiny, tiny version of ourselves. Pretend that this tiny spaceship can unleash the energy of multiple H-bombs over a very brief span of time. Pretend that it can more or less turn on a dime at relativistic speeds.

The problem with the original post isn't the physical impossibility of making such a turn. The problem is that this sharp turn adds unnecessary complexity to what is already something that is very hard to grasp. Some people who don't grasp relativity try to look at it from the perspective of some "Rube Goldberg paradox" (google "Rube Goldberg device" if you don't know that term). There are apparent paradoxes galore that can be expressed simply. The key to understanding relativity is to understand these simple paradoxes. There is no need to invent yet another Rube Goldberg paradox.

Suppose our tiny spaceship is en route to the Andromeda galaxy (M31), moving at 0.999999999992 c with respect to that galaxy. There's no need to make a right hand turn to illustrate this apparent paradox. All our tiny spaceship needs to do is to come to a stop with respect to M31. The apparent distance to M31 will grow from about 10 light years to 2.5 million light years. There's nothing wrong with that. That is what relativity says our little spaceship will see. Just grok the weirdness.To the OP: You won't find mathematical inconsistencies in special relativity. The Poincare transformation forms a mathematical group.

 

[DaveC426913]

Ignore that. Pretend that the singularity has come, that we can download our minds onto a tiny, tiny chip that can withstand thousands of gs of acceleration or more.

You and I see the source of the OP's confusion differently, and have different ways of highlighting it.

The problem with the original post isn't the physical impossibility of making such a turn. The problem is that this sharp turn adds unnecessary complexity to what is already something that is very hard to grasp.

You and I know that but I'm trying to answer the question he asked with as little change to it as possible. In my experience, when someone is struggling with a problem, it sometimes does more harm than good to show them a different experiment and have them miss the parallels between them.

Not that I am saying yours isn't a good explanation; I hope one of us gets through.

All our tiny spaceship needs to do is to come to a stop with respect to M31. The apparent distance to M31 will grow from about 10 light years to 2.5 million light years. There's nothing wrong with that. That is what relativity says our little spaceship will see. Just grok the weirdness.

It is my belief that the OP already understands the basics of length contraction; he states it right in his opening post.

What he is having difficulty with is that he thinks this length contraction will spectacularly switch axes by "merely" turning his ship.

 

[Fredrik]

Yes, they would - if they could "turn a corner" while moving at .9999c. The OP thinks that a turn like that is like doing it in a car. He is not seeing that going from .9999c North to .9999c West in a time frame he calls "suddenly" would constitute an acceleration of billions of gs.

If the OP were to realize that the rocket ship would have accelerate from 0 to .9999c but could do so no faster than its initial blast off from Earth, then he would see why there's no paradox.

Would he? When you emphasize how enormous the acceleration would be, it sounds like you're saying that the resolution of the imagined paradox is that "your rocket's engines are too weak", or "if you would try this, your rocket would be instantly vaporized". At least, that's what I think it must sound like to him.

The imagined paradox is not resolved by any practical issues, but is resolved by the observation that in order to claim things like "the rocket will experience a dramatic change in length contraction", we must first define what we mean by "the rocket's experiences" in a way that makes the claim true. We can do this for example by choosing to always call the coordinate assignments made by the momentarily comoving inertial coordinate system "the rocket's experiences".

The key to understanding most, if not all, of the imagined paradoxes in SR, is that experiences are defined by coordinate systems. Things only look paradoxal if you compare the coordinate assignments made by two different coordinate systems, and forget that you're looking at assignments made by two different coordinate systems.

 

[DaveC426913]

Would he? When you emphasize how enormous the acceleration would be, it sounds like you're saying that the resolution of the imagined paradox is that "your rocket's engines are too weak", or "if you would try this, your rocket would be instantly vaporized". At least, that's what I think it must sound like to him.

Well, I'm simply framing his (correct) understanding that the length contraction would change directions if the rocket's direction of travel changed, but that it would not happen "suddenly". The contraction would happen just like he knew it happened when the ship first blasted off from Earth and began accelerating from zero.

Anyway, not sure it matters. The OP has moved on several times now since that first fleeting thought.

 

[discountbrain]

Whoa, he is confused and is struggling with this concept! Are you kidding me? Do you know how simple this stuff is relative to many things? Did you read my following scenario of the ship crashing into the planet? Actually, I've concluded that there is no inconsistency here at all since I've decided that one only needs to consider 2 points moving in space at near velocity c with no mass at all and there would be a length contraction between them. One could be a rocket ship. This implies if you could travel at near c distant planets would be a mile or two away. Of course, you could go to that new Earth like planet in maybe two weeks. But, if you came back you would notice time had gone by more than as from the age of the most basic life. We don't have the technology to even imagine such a thing and it would be a weird experience anyway.

Anytime anyone questions the dogma they must be confused.
Oh, and anyone who doesn't understand tries to complicate the problem. Right? We don't want that do we?

 

[Fredrik]

Oh, and anyone who doesn't understand tries to complicate the problem. Right? We don't want that do we?

Not when the main point can be illustrated by a much simpler problem.

 

[discountbrain]

I think I need to explain my original thinking here which most of you probably can't fathom. When I spoke of a ship suddenly making a right angle turn I was thinking of what has often been reported as observations of UFOs. One pilot described them as looking like they hit a solid plane in space and bounced at another angle. Since you say conventional physics says there is a problem with inertia here you would probably say this behavior is impossible. You don't seem to grasp that their technology could be way in advance of ours and they know how to do this while you don't. I was also thinking of electrons traveling in a wire which had a sharp right angle bend in it. How is it that an electron with very little mass, but at the speed of c now has a huge mass and is able to decelerate to zero in one direction and almost instantly accelerate to c in another direction? Am I over complicating because I'm struggling? Or it could be protons which cause the current.

 

[Fredrik]

It's OK to discuss a super sharp turn at super high speeds, simply because there exist timelike curves in Minkowski spacetime that describe that sort of motion. There's no need to discuss technology. However, the sharp turn seems like an irrelevant complication. Why not just stop the ship?

 

[discountbrain]

In my 2nd example the ship crashed into the planet. That would stop it quicker than any other way I can think of.

 

[Dale]

I have no problem with the sudden turn or the sudden stop. My earlier point which you avoided responding to was simply that any frame where distances are changing is non-inertial. Odd things are expected to happen in non-inertial frames.

 

[Fredrik]

In my 2nd example the ship crashed into the planet. That would stop it quicker than any other way I can think of.

Yes, but you seem to be asking something else entirely in this scenario (quoted below). Also, it's not clear to me where you intended ship 'b' to be when this happened. Weren't they traveling side-by-side? What do you mean when you say that ship 'b' would see planet Y suddenly shoot off in the distance? Do you mean because the impact will forcefully push the planet away (conservation of momentum)? Or are you suggesting that there will be some kind of length contraction effect?

So, what if ship 'a' crashed into the surface of planet Y instead of making the right angle turn-oops, major screwup? You say with its relativistic mass and extremely high velocity it would transfer a huge amount of kinetic energy to Y. Maybe even enough to give Y some new velocity. And it might even travel over a mile deep before it completely stopped, but in 2 or 3 seconds observers on ship 'b' would see planet Y suddenly shoot off into the distance.

I think you need to choose the simplest possible scenario that illustrates the point that you want to make, and then ask specifically about that. It's hard for us to help you if you describe lots of different scenarios and ask lots of different questions all at once.

 

[discountbrain]

I meant for ship 'b' to be behind 'a' traveling the same path. My original thinking was if 'a' crashed it would suddenly stop and there would no longer be a distance contraction between them. But, one can consider an arbitrary point moving at c in space so the whole exercise is pointless.

Also I recall that it is said electrons or charges travel in a wire by each one making a quantum leap in turn to the next atom so having a right angle bend in the wire should present no problem here either.

 

[Fredrik]

I meant for ship 'b' to be behind 'a' traveling the same path. My original thinking was if 'a' crashed it would suddenly stop and there would no longer be a distance contraction between them.

This is wrong. 'a' is now at the planet, and in the coordinate system comoving with 'b', the distance to the planet is still contracted by the same factor as it was before.

 

[michelcolman]

The problem is that nothing can happen "instantaneously", everything needs a certain amount of time, no matter how short. You say that there are supposed to be UFOs that can turn instantly, but if someone were to tell you that they actually take 3 nanoseconds to turn, would you think that's an acceptable alternative? Because if you do, at least one part of your paradox is solved. Nothing stops immediately, even the ship that crashes into the planet will take a fraction of a second to come to a stop. Even if it's some sort of alien indestructable undeformable ship, the information "front end hit planet" will only travel to the back end at less than the speed of light before it can even "know" that it's supposed to come to a stop.

Anyway, back to the original question: if the ship stops (in some very small amount of time), the distance between a en b increases back to its normal value during the deceleration. In fact, the destination will suddenly be further away than it was before the ship stopped. Nothing wrong with that.

You have to understand what the word "distance" really means. It's basically nothing more than a difference in coordinates. You might measure a distance with a tape measure, but that tape measure itself might be contracted or expanded. It gets worse if you start measuring moving objects, since you can't even agree on what positions they were at at any particular time. Simultaneity is always causing problems, or rather, solving them whenever you think you found a contradiction. Google "relativity of simultaneity" to see how fundamental this part of relativity is.

So in order to define "distance", you have to agree on how you would measure this distance. Special relativity provides one way of measuring distances (using rays of light), while General Relativity can accommodate different ways of measuring. You just "tell" the theory "I would like to define the time and space coordinates in different places according to this formula" and General Relativity takes your definition into account. All that matters are the events that will happen, and they will be the same no matter which coordinate system you use.

For example, special relativity would say that, as you "look" further and further into the expanding universe, things are aging more slowly due to time contraction (the universe is younger) and they are closer together due to length contraction, so that the entire universe fits into a finite sphere with an infinite number of objects close together right next to the "border" which is just beginning to experience the big bang right now. I used "look" between quotation marks because I mean the infinitely fast way of looking you might use in a mathematical model without having to wait for light to get here (which would add more delay). Now, since this model is a bit awkward to use, most astronomers prefer a different way of defining the clocks everywhere in the universe so that the universe is the same age and looks about the same everywhere. General Relativity allows you to define time and space using pretty much any coordinate system you like, so why not? Now, the universe is infinite after all. The disadvantage of this model is that, at great distances, the speed of light is no longer the same relative to us. Light is pushed away from us with the speed of the expansion of the universe, and the light from certain distant places will never reach us because the universe is expanding faster than the speed of light. (In the first model, the light will never be emitted in the first place, because local time is moving too slowly, coming to an asymptotic standstill before the event even happens in our reference frame). Two totally different explanations with the same result: we will never see certain things happen in certain faraway places.

All of this is just to say that the notion of "distance" depends on definition. If you take a picture of the planets before and after stopping, they will not suddenly look like they have moved in time and further apart. If anything, they will appear to be closer (bigger) after stopping because of relativistic perspective effects. But you will infer that something changed with the local time and distances because you are now measuring the speed of rays of light differently, and any calculations you make from any observations after stopping will give different results for distances and times. That's because your mathematical reference for defining distances and times has changed from a moving reference system to a stationary one.

You can't extend your arm to touch the planet to find out how far it is. You can't use a tape measure while flying towards it. All you can do is, for example, send out a light signal and time how long it takes for the light to come back. And then you will come to the conclusion that a and b are further apart after you stopped. But lots of other things have changed as well! Clocks in different places are no longer running at the same speed, and they will even jump ahead or jump back during your decelleration. It's a miracle that relativity manages to still give consistent results when all these variables have changed so much.

It all only makes sense once you put it into a formula and figure out that, no matter which perspective you take, it all ends up not contradicting even if your gut says it should. Any actual event (like "this comet will hit the planet at the exact time that the clock on the tower right next to the impact will hit 12 o'clock) will take place no matter what coordinates you use, but any other subjective values (what time it will be on your own clock, how far away everything is) will be different. That does not matter, only the events do.

You only get paradoxes if you think about things like "the distance suddenly changed" while in fact, if you make any kind of experiment with those old and new distances, the results will never cause any actual contradictions. The problem is with you thinking that "distance" is some fundamental value while in fact it's just a variable that depends on what kind of reference system you happen to be using. Coordinates are only a means to the end of figuring out what would happen if you did some particular experiment. With different coordinates (like the ones you were using before and after stopping), the numbers will change but the results won't.

 

[harrylin]

I think I need to explain my original thinking here which most of you probably can't fathom. When I spoke of a ship suddenly making a right angle turn I was thinking of what has often been reported as observations of UFOs. One pilot described them as looking like they hit a solid plane in space and bounced at another angle. Since you say conventional physics says there is a problem with inertia here you would probably say this behavior is impossible. You don't seem to grasp that their technology could be way in advance of ours and they know how to do this while you don't. I was also thinking of electrons traveling in a wire which had a sharp right angle bend in it. How is it that an electron with very little mass, but at the speed of c now has a huge mass and is able to decelerate to zero in one direction and almost instantly accelerate to c in another direction? Am I over complicating because I'm struggling? Or it could be protons which cause the current.

Only if UFO's exist and are made of massive objects. Some people speculate that they are a kind of projections. Anyway, I guess that you'll agree, now that you've concluded that there is no inconsistency here at all, this is more a matter of "UFO's imply very odd results". :tongue2:

 

[michelcolman]

By the way, when I said that the results are the same no matter which coordinate system you use and it doesn't matter what the numbers are, you might get the impression that relativistic effects are somehow "not real" and that things like length contraction are only caused by the funny reference systems we like to use to measure things. However, this is not the case, the effects are very real indeed. Take, for example, the passing trains paradox.

Two trains, each 100 meters long (at rest) have to pass each other on an 80 meter long section of double track. Of course this should be impossible unless... both are traveling at 0.6c. Someone standing on the platform will see that the trains are now only 80 meters long and can pass each other just fine. He can measure this any way he likes (for example using a photo detector next to the rails, timing the passage of the front and back end of the train) and it will really be 80 meters. However, if you are sitting on one of the trains, that train is still 100 meters (it is not moving relative to you), but the platform is only 64 meters (contracted by 80%). Fortunately though, the other train is coming towards you at 0.88c so it's only 47 meters long. It has just enough time to pass between the two ends of the double section in the time it takes for your long train to get through.

This is a perfect example of how different points of view can describe a situation differently while coming to the same result: both observers will disagree on the length of the trains and the platform, and the timing of the passage of the front and back ends, but they will agree that the trains just missed each other on each end. And that's all that matters.

Now, if you would jump from the platform onto the train, would you suddenly see that train expand and the platform shrink? Yes, no matter how strange that may seem. Of course the word "see" is not the right word for it, "infer from your observations" would be more appropriate. If you time how long it takes for you to pass the two ends of the double section and multiply that with your speed, you will find it's really 64 meters. But of course you would be using a clock to measure that, and someone on the platform will say your clock suddenly started to run more slowly the moment you jumped onto the train.

I would encourage you to read more of this kind of paradoxes on wikipedia or other sources on the internet, they are what finally got me to understand relativity. It will take a while for it to really sink in, though.

Maybe start with http://en.wikipedia.org/wiki/Relativity_of_simultaneity

 

[discountbrain]

I think you are trying to explain things that are well understood by everyone. I don't need to look at your references. I answered my question myself with no help from you. Read what I said about considering points in space which need not be associated with physical objects. The one who said I was wrong in say there would no longer be a distance contraction if one ship crashed is right, but I agree for the above mentioned reason.

I had originally thought I came across a paradox.

Everyone knows nothing happens instantaneously (but maybe some things do) and this doesn't need to be explained even to non science people.