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Assume a bullet travels 99.9% the speed of light fired at a slow moving target.

If an ant was strapped to that bullet, allowing enough distance, from the ants point of view time is moving much slower than that of the target.

From the ants perspective it would see the target moving very fast out of the way.

However to an observer watching the bullet it flew through the air and hit the target before it had time to move.

How can the bullet hit the target from the point of view of the ant?

Dan
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    Does this answer your question? How can time dilation be symmetric? – Marius Ladegård Meyer Nov 07 '23 at 21:06
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    A bullet either does or does not hit its target. "Perspective" has nothing to do with it. – WillO Nov 07 '23 at 21:58
  • Could you please try to rephrase your question in order to be more intelligible or follow the link proposed by Marius and see if that helps. – José Andrade Nov 07 '23 at 22:08
  • I’m looking for help understanding which is why I asked. Since the bullet is going so fast from its perspective the target is moving very fast relative to it and thus has plenty of time to get out of the way. To an observer the bullet is moving faster than the target can move and will see it hit the target. My confusion is how can the bullet hit the target but had you been on the bullet you’d have see the target get out of the way? – Dan Nov 07 '23 at 22:38
  • From the ants perspective it would see the target moving very fast out of the way. How did you arrive at this conclusion? The ant sees the target moving slowly, not quickly. – Allure Nov 08 '23 at 03:44
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    My thinking was as the ant is experiencing time slower everything it sees not at its speed would be moving fast around it as those things experience time faster. But now I realise this is the flaw in my understanding. Still trying to grasp how those things can be moving faster through time but the ant sees them moving slower through time, it’s like they (the moving and non moving) experience reality differently – Dan Nov 08 '23 at 07:23
  • The word "see" has been devalued to nonsense by poor SR teaching. Beware of taking it literally! – m4r35n357 Nov 08 '23 at 09:52

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A bullet is fired from a gun, then it hits a target.

Alice says that the bullet traveled ten miles in one minute. Bob says it traveled twenty miles in two minutes. They can still agree on the speed of the bullet.

They are certainly not going to disagree about whether the target gets hit.

WillO
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  • I am sorry, but it's obvious OP is confused about special relativity and its consequences when it comes to time-dilation and space contraction for different observers. Your answer does not seem to clear any of those doubts. I do agree that the question is ill posed, but I would still say it is asking about special relativity. – José Andrade Nov 07 '23 at 22:10
  • But the bullets experience of time and an observer watching the bullet and its target are moving faster through time than the bullet so how will the bullet converge to hit the target at the same time? (From the point of view of the bullet) – Dan Nov 07 '23 at 22:43
  • @Dan: Bob is on the ground next to the gun; Alice is riding the bullet. Bob says the bullet is fired at 1:00 and hits the target at 1:02. Alice says the bullet is fired at 1:00 and hits the target at 1:01. They agree that it hits the target. – WillO Nov 07 '23 at 23:18
  • @WillO so the mistake I am making is thinking Alice would see the target moving faster she’d see it moving slower? Or would she see it moving exactly the same as an observer just that she reaches it in less time than the observers clock? – Dan Nov 07 '23 at 23:32
  • @Dan: Bob sees the bullet moving at (say) ten miles per minute. Alice sees the target moving at the same ten miles per minute. Bob says the bullet moves twenty miles in two minutes. Alice says the target moves (at, yes, exactly the same speed), covering ten miles in one minute. – WillO Nov 07 '23 at 23:45
  • @Dan the mistake you are making is thinking that the word "see" used in most SR explanations means what it means to you and me in real life. The one thing that you can take from this answer is that there is only one end result and everyone agrees on it. I say again, learn about spacetime diagrams or you will never learn! – m4r35n357 Nov 08 '23 at 09:50
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The first point to remember when thinking about special relativity is that if an event happens in one frame it also happens in every other. You cannot have, for example, a situation in which a bullet hits a target in one frame of reference but misses it in the other.

So, let's assume the target is moving east to west and the bullet is moving south to north, and they meet at some point P. Your question is how does this appear to work in the two different frames?

The answer lies in 'the relativity of simultaneity'. Broadly what that means is that in the ground frame of an observer who is performing the experiment, when it is some time t for the observer, it is that time everywhere in the observer's frame- however, it is not that time everywhere in any other frame moving relative to the observer. In the moving frame, time in the observer's frame is out of synch, and the extent to which it is out of synch increases with speed and distance. So if the observer fires the gun at t, they consider the target's position at the start of the experiment to be its position at time t. However, in the frame of the speeding bullet, the position of the target at the start of the experiment is not the same as for the observer. If the target in one frame seems to have more time to move out of the way, then that is compensated for, by the relativity of simultaneity, because the target in that frame starts off further from the point of collision, so the extra time they have is used up in reaching the more distant collision point.

I suspect you will struggle to understand that, because I have never known anyone who has assimilated the implications of the relativity of simultaneity without having to spend a lot of time cogitating on it and re-programming their mind to rid it of the effect of years of having thought of time in a Newtonian way. Nonetheless, it is the answer, and if you want to understand relativity them my recommendation is to start with the relativity of simultaneity, as that is the key to understanding all the other strange phenomena such as time dilation, length contraction and so on.

Marco Ocram
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  • So when the person doing the experiment fires our 99% light speed gun the bullet would see the the target move slower through time but the bullet is still traversing space normally even though time is slowing for it? So the target will not have moved and the bullet hits it but from its perspective it took less time to get there than the observer timed it getting there? I’m confused regarding the point on distance but will lookup the topic you advised thanks! – Dan Nov 08 '23 at 07:34
  • No, not really. If you are approaching a stationary target at .9c, for example, then you can consider yourself to be stationary and the target to be moving towards you at 0.9c, so speed is always symmetrical in that sense. – Marco Ocram Nov 08 '23 at 08:30
  • Suppose in the frame of the person who fired the gun, both the target and the bullet are a second way from the point of collision, so each arrives there at the same time and they collide. In the frame of the bullet, the target might be two seconds away from the point of collision when the gun is fired and further away from it. – Marco Ocram Nov 08 '23 at 08:34
  • Downvoted for pimping "relativity of simultaneity" (yet again) to gain easy karma. @Dan, if you want to understand this, learn about spacetime diagrams instead, and avoid this "ROS" stuff like the plague! Pass it on! https://en.wikipedia.org/wiki/Spacetime_diagram Marco, you say yourself that this is hard to understand, so why do you persist? It is the most confusing, deconstructive and non-visceral view of SR that it is possible to conceive. – m4r35n357 Nov 08 '23 at 09:45
  • @m4r35n357 : The reason spacetime diagrams are so effective is that they make the relativity of simultaneity evident (because two spacelike lines can meet in only one point). Marco is right that relativity of simultaneity is key here; you are right (and I bet Marco would agree) that the best way to grasp it is with a diagram. This is a good answer. – WillO Nov 08 '23 at 10:46
  • @m4r35n357 and WillO, many thanks. In my answers I tend to stress the ROS because a failure to understand it is the most common denominator to the conceptual questions about SR on this site, and also in the many 'refutations of SR' papers on the internet. There's also published research that says most university students having completed an introductory course on SR still don't get ROS. Failing to understand ROS was also a block to my personal failure to come to terms with SR many years ago, even though I had seen lots of spacetime diagrams... – Marco Ocram Nov 08 '23 at 11:19
  • ...so it's a personal mission of mine to pimp it. I get that some people might not see it as so important and might be sick of reading it in my answers, so I'm fine with that. All the best! – Marco Ocram Nov 08 '23 at 11:21
  • @MarcoOcram "Too hard for university students" is a weird justification for using it on non-students IMO. Still, we have both made our positions clear I suppose! – m4r35n357 Nov 08 '23 at 11:51
  • @m4r35n357 with the greatest respect, you are spouting your personal opinions. You like spacetime diagrams- fine, I get that, but my view is that by themselves they are a very poor teaching aid. Feel free to write your own answers, but you will make me think you are an opinionated asshole if you carry on attacking mine. – Marco Ocram Nov 08 '23 at 11:54
  • @WillO it is not clear from your response whether you are talking about true spacetime diagrams (where simultaneity in the chosen frame is a horizontal line), or those Lorentz Transform "scissor" diagrams, where simultaneity is a sloped line. It is the latter that I have a problem with, as they invariably fail to teach anything worth learning. – m4r35n357 Nov 08 '23 at 11:55
  • @MarcoOcram not an "opinionated asshole", but just an ex-victim of those very methods. I am not a physics student, but I remember well the reasons I could not understand SR and gave up trying for about thirty years. I recognize the disorientation of those confused by ROS, and sympathize with them. – m4r35n357 Nov 08 '23 at 11:59
  • @m4r35n357 sure, I get that. But your path to understanding was different from mine, which doesn't make mine invalid. I studied SR at university and didn't get it. It was some years later, having spent literally hours trying to figure it out in my head, that it clicked. If someone had properly explained the ROS to me initially, I would have got it straight off. So my style of explanation should help other people like me, and yours should help other people like you. There's room for both. – Marco Ocram Nov 08 '23 at 12:03
  • Just one problem, the Andromeda Paradox: "That no inherent meaning can be assigned to the simultaneity of distant events is the single most important lesson to be learned from relativity." https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument I'm with Penrose on this. – m4r35n357 Nov 08 '23 at 12:28
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    What's that got to do with it? Why is that a problem in this context? The Andromeda 'paradox' is obvious on a spacetime diagram too. My narrative description of the ROS is just putting into words the meaning of what you see in a spacetime diagram. (As an aside, I think Penrose is v clever but an atrocious teacher.) – Marco Ocram Nov 08 '23 at 12:43
  • I am not claiming that spacetime diagrams "hide" the "AP". I am claiming that simultaneity itself is an antipattern in SR. I did not learn any of this from Penrose, but he captures the "absurdism" behind ROS quite nicely IMO. – m4r35n357 Nov 08 '23 at 13:09
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    Simultaneity is just a word for events on a line parallel with an x-axis in a spacetime diagram. Why is that an 'antipattern'? Why is it absurd? If you are the bullet at the origin of the spacetime diagram at the instant after the gun is fired, in your frame the target lies on your horizontal x axis, while in the frame of the observer the target at the start of the experiment is somewhere along their sloping axis. The point is that the position of the target at the 'start' of the event is not a unique event. That's what the diagram says and what ROS says. – Marco Ocram Nov 08 '23 at 13:27
  • Again: "That no inherent meaning can be assigned to the simultaneity of distant events is the single most important lesson to be learned from relativity." Attempting to define "the position of the target at the 'start' of the event" when it is observer-dependent is pointless and misleading. I don't know how many ways there are to express why unique events and scalars are preferable to velocity-dependent quantities, but I guess I am gradually finding out! Velocity-dependent mass anyone? – m4r35n357 Nov 08 '23 at 13:58
  • @m4r35n357 this has reached the point where the mods will move us to chat, I suspect. In summary, I couldn't agree with you less. As I said earlier, you have your preferred perspective and I have mine. Neither conflicts with the theory- they are just different angles on how to explain it. I can't understand why you are so enamoured of yours and intolerant of mine, but that's up to you. – Marco Ocram Nov 08 '23 at 14:27
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Let me draw a picture: a linear accelerator (la), accelerates a projectile to velocity V/C =0.999~1, in negligible time (e.g. a nuclear decay), at a target fixed with respect to the la. The observer with the projectile hits the target in time. T =D/(gamma*V) in projectile's rest frame, where D is the distance from emission from the la to the target, and. 1/gamma = sqrt(1-(V/C)^2) is the length contraction factor. The time of flight with respect to the lab (la) is T = D/V. The point of confusion in this scenario is why the ant ages less than the folks back home ... much less at that speed. That's The Twin Paradox. Since V is symmetric between the ant and approaching target and the Target and the approaching ant, why don't the homies age the same as astroant? Astroant was accelerated into a different frame which contracted the Distance.

LiveProton
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  • Not downvoting at this stage, but I recommend you either take a deep breath and present this properly, or delete your answer. – m4r35n357 Nov 08 '23 at 09:54