# Special Relativity nonsense

#### Zeno

Registered Senior Member
We have two airplanes passing each other at high speed. The planes are the same length. We will call the airplanes A and B. The planes are passing each other at a speed close to the speed of light.
Here is the view from airplane A at rest...
Code:
``````T--------------------------------------N                      airplane A
<-------      N-----------------T                      airplane B``````
Here is the view from airplane B at rest...
Code:
``````                             T-------------------N ----->               airplane A
N-------------------------------------T                      airplane B``````

Both of these views are from the moment that the nose of airplane A reaches the tail of airplane B.
This must be the same moment in time between both frames of reference because there is only one moment
in time when the nose of airplane A is lined up with the tail of airplane B. If it isn't the same moment in time then the nose of airplane A passes the tail of airplane B more than once, which of course is nonsense. At this moment, the observer at T on airplane A looking down sees space and the observer at N on airplane B looking up sees airplane A, according to airplane A. At this moment, the observer at T on airplane A looking down sees airplane B and the observer at N looking up sees space, according to airplane B. We obviously have a contradiction. We have a paradox. Both situations can't simultaneously be true.

Maybe these vids will help you get the correct SR picture; in particular what non-simultaneity is and implies:

The mistake is here:
At this moment, the observer at T on airplane A looking down...
Watch Q-reeus' movies, and you'll see that the relativity of simultaneity means that this "at this moment"-statement is the culprit.

The mistake is here:

Watch Q-reeus' movies, and you'll see that the relativity of simultaneity means that this "at this moment"-statement is the culprit.
Too generous - I'd like to think I could create vid's of that quality, but anyway they are imo good as a non-mathematical way to visually comprehend SR's apparent paradoxical nature.

Too generous - I'd like to think I could create vid's of that quality,
I did not mean to imply author- or ownership; merely to refer to the video's you posted.

but anyway they are imo good as a non-mathematical way to visually comprehend SR's apparent paradoxical nature.
Yes, wrapping ones head around SR for the first time can be quite a challenge, but hopefully, these video's can assist Zeno is doing just that.

This must be the same moment in time between both frames of reference because there is only one moment
if each plane has 1000 passengers on and 20 crew, how many moments are going on at once ?

I did not mean to imply author- or ownership; merely to refer to the video's you posted.
Yes I knew that but decided to play on the syntax provided.
Yes, wrapping ones head around SR for the first time can be quite a challenge, but hopefully, these video's can assist Zeno is doing just that.
Yes, but.... in thinking about them again, it should be pointed out there a few blemishes:

In the first linked to 'Tunnel' vid, the later part featuring the train crossing a bridge with a gap in it, there is an inconsistency in the visuals. From ~ 8:55 mark, Sarah sees the entire train tilt over and plummet - as a whole rigid unit. Later, from ~ 10:00 mark, Adam's train from his frame collapses progressively as a kind of shear flow.
That violates the principle that both observers must agree on the structural dynamics involved. It falsely creates the opportunity for a skeptic to say 'a ha - it doesn't work'. Rather, it's simply a visual oversimplification that should have been done better. Another aspect less obvious, is that the sudden plunge from Adam's moving train frame should have been linked to the fact that Earth's gravity has greatly increased there compared to Sarah's 'stationary' frame. Hence a much more rapid downward acceleration seen in that frame that is consistent with falling through the gap.

In the 2nd linked vid, while 'stationary' Sarah's perspective is always consistent, from 'moving' Adam's perspective, non-simultaneity is consistently portrayed, but Lorentz contraction of those gaudy crumbling structures & clocks is not. Not as serious as issues in first vid, but still not entirely visually consistent.

All in all, I will now say those two vids are good to a point, but leave opportunities for a hardened 'sharp' SR skeptic to be convinced the wrong way!

Yes I knew that but decided to play on the syntax provided.
Well, technically, both interpretations are correct.

Yes, but.... in thinking about them again, it should be pointed out there a few blemishes:

In the first linked to 'Tunnel' vid, the later part featuring the train crossing a bridge with a gap in it, there is an inconsistency in the visuals. From ~ 8:55 mark, Sarah sees the entire train tilt over and plummet - as a whole rigid unit. Later, from ~ 10:00 mark, Adam's train from his frame collapses progressively as a kind of shear flow.
I noticed that as well; I assume it's just a graphical oversight.

That violates the principle that both observers must agree on the structural dynamics involved. It falsely creates the opportunity for a skeptic to say 'a ha - it doesn't work'. Rather, it's simply a visual oversimplification that should have been done better. Another aspect less obvious, is that the sudden plunge from Adam's moving train frame should have been linked to the fact that Earth's gravity has greatly increased there compared to Sarah's 'stationary' frame. Hence a much more rapid downward acceleration seen in that frame that is consistent with falling through the gap.
Actually, I think gravity is overall increased. If a train is moving at a significant fraction of the speed of light, it wouldn't fall into such a gap in the first place. But I think that's another simplification the creator made.

In the 2nd linked vid, while 'stationary' Sarah's perspective is always consistent, from 'moving' Adam's perspective, non-simultaneity is consistently portrayed, but Lorentz contraction of those gaudy crumbling structures & clocks is not. Not as serious as issues in first vid, but still not entirely visually consistent.

All in all, I will now say those two vids are good to a point, but leave opportunities for a hardened 'sharp' SR skeptic to be convinced the wrong way!
Yes, it's difficult because you have to find a balance between (over)simplification and correctness. But the video's do illustrate the main points nicely.

Actually, I think gravity is overall increased....
As I stated. And in Adam's frame by factor γ² not γ, where as usual γ = 1/√(1-v²/c²), v the train speed in Sarah's frame.
If a train is moving at a significant fraction of the speed of light, it wouldn't fall into such a gap in the first place. But I think that's another simplification the creator made.
Indeed. Probably a better example would have been entering a tight fitting tunnel slightly lower on the right side. With a crash if slightly off dead-center entry.

As I stated.
I don't think you did? You only mentioned a gravity difference between Sarah and Adam, not between the scenario's Earth and real Earth, as far as I can tell?

And in Adam's frame by factor γ² not γ, where as usual γ = 1/√(1-v²/c²), v the train speed in Sarah's frame.

Indeed. Probably a better example would have been entering a tight fitting tunnel slightly lower on the right side. With a crash if slightly off dead-center entry.
Perhaps, but that scenario doesn't have the (oversimplified) elegance of a long/short train fitting in a gap the way the original has.

I don't think you did? You only mentioned a gravity difference between Sarah and Adam, not between the scenario's Earth and real Earth, as far as I can tell?
???? Relevant passage in #7 again:
"Another aspect less obvious, is that the sudden plunge from Adam's moving train frame should have been linked to the fact that Earth's gravity has greatly increased there compared to Sarah's 'stationary' frame. Hence a much more rapid downward acceleration seen in that frame that is consistent with falling through the gap."

Seemed clear-cut enough to me. In Adam's frame, Earth is whizzing by beneath at velocity -v. It's gravitating mass is raised by factor γ, and additionally there is Lorentz contraction of vertical acting gravity 'field lines' spacing by the same γ factor. Net gravitational boost in Adam's frame is thus the product γ*γ. Note how that compares to the case for an electrically charged Earth, where because of charge invariance, perpendicular (i.e. radial) E field rises only by factor γ in Adam's frame.

By now I rue not having picked some other vid(s).

???? Relevant passage in #7 again:
"Another aspect less obvious, is that the sudden plunge from Adam's moving train frame should have been linked to the fact that Earth's gravity has greatly increased there compared to Sarah's 'stationary' frame. Hence a much more rapid downward acceleration seen in that frame that is consistent with falling through the gap."
I've done that multiple times now. You said: "compared to Sarah's 'stationary' frame.", and your entire statement is in that context.

Seemed clear-cut enough to me. In Adam's frame, Earth is whizzing by beneath at velocity -v. It's gravitating mass is raised by factor γ, and additionally there is Lorentz contraction of vertical acting gravity 'field lines' spacing by the same γ factor. Net gravitational boost in Adam's frame is thus the product γ*γ.
And I've not argued against that. I'm talking about this: take Sarah's perspective. A train whizzes by at a significant speed. In order to be pulled into the gap (far enough downwards that it doesn't hit the track on the other side), it thus needs a very significant downward acceleration. That means the gravity of the planet must be huge; certainly much, much larger than Earth's.

Note how that compares to the case for an electrically charged Earth, where because of charge invariance, perpendicular (i.e. radial) E field rises only by factor γ in Adam's frame.
(Irrelevant, so no comment.)

By now I rue not having picked some other vid(s).
The videos are fine. It appears we are both nitpicking, and talking past each other.

Thank you for the responses. However, I still believe that there is a paradox. Let's say there is an observer in the nose of airplane A who is looking down and sees an observer in the tail of airplane B at the moment the nose of airplane A is passing the tail of airplane B. Likewise, let's say there is an observer in the tail of airplane B who is looking up and sees an observer in the nose of airplane A at the moment the nose of airplane A is passing the tail of airplane B. If you think about it for a little bit you will realize that these two moments in both frames of reference must be the same moment. If the observer in airplane A looks and sees the observer in airplane B looking back at him, it is impossible for the observer in airplane B to be anywhere else or doing anything else at that moment. Therefore, when the nose of airplane A is lined up with the tail of airplane B it must be the same moment in both frames of reference. I can therefore rightly say 'at this moment' because it is only one moment. You can see that 'at this moment' the tail of airplane A has simultaneously both passed and not passed the nose of airplane B. This is an impossibility.

Thank you for the responses. However, I still believe that there is a paradox. Let's say there is an observer in the nose of airplane A who is looking down and sees an observer in the tail of airplane B at the moment the nose of airplane A is passing the tail of airplane B. Likewise, let's say there is an observer in the tail of airplane B who is looking up and sees an observer in the nose of airplane A at the moment the nose of airplane A is passing the tail of airplane B. If you think about it for a little bit you will realize that these two moments in both frames of reference must be the same moment. If the observer in airplane A looks and sees the observer in airplane B looking back at him, it is impossible for the observer in airplane B to be anywhere else or doing anything else at that moment. Therefore, when the nose of airplane A is lined up with the tail of airplane B it must be the same moment in both frames of reference. I can therefore rightly say 'at this moment' because it is only one moment. You can see that 'at this moment' the tail of airplane A has simultaneously both passed and not passed the nose of airplane B. This is an impossibility.
In those last few sentences, you introduce new observers. Look at your original sketch: they are at the tail of airplane A, and in the nose of airplane B. This is where the problem of syncing clocks between observers and the non-simultaneity of events come into play. Effectively, you're describing the same scenario as in the first video Q-reeus posted; just with two airplanes, instead of the ground+tunnel and a train. The exact same reasoning as in that video applies here.

The video would be the same as the situation that I've described if it covered what happens when the front of the train reaches the end of the tunnel. The video doesn't cover that. At the moment the front of the train reaches the end of the tunnel the back end of the train has both passed and not passed the entrance of the tunnel simultaneously. The video doesn't cover that.

The video would be the same as the situation that I've described if it covered what happens when the front of the train reaches the end of the tunnel. The video doesn't cover that. At the moment the front of the train reaches the end of the tunnel the back end of the train has both passed and not passed the entrance of the tunnel simultaneously. The video doesn't cover that.
From 3:47 onwards it shows clocks above the tunnel that indicate what is happening: what the two people on the train (front and back) will say happened simultaneous an observer from the ground will claim wasn't simultaneous. In other words, when you ask the question what happened at the back of the train when the front of the train reaches the end of the tunnel, whose variant of simultaneity are you using? Both cases are cover by the video, and both are right; but both will claim the others didn't check at the same time.

The situations with the back of the train between both frames of reference are simultaneous because they occur at the moment the front of the train reaches the end of the tunnel. The moment the front of the train reaches the end of the tunnel must be the same moment between both frames of reference. If we imagine airplane A as the train and airplane B as the tunnel we have an analogous situation. According to the observer on the ground the front of the train reaching the end of the tunnel is simultaneous with the back end being inside the tunnel. According to the observer on the train the front of the train reaching the end of the tunnel is not simultaneous with the back end being inside the tunnel. Both situations are considered correct and we have a paradox.

The situations with the back of the train between both frames of reference are simultaneous because they occur at the moment the front of the train reaches the end of the tunnel.
Except that, as Q-reeus and I have been trying to point out to you, it's not. Simultaneity doesn't work like that in SR. I suggest getting a good book about the subject, because my explanatory powers (clearly) aren't up to the task of explaining this extremely basic SR-fact to you.

The moment the front of the train reaches the end of the tunnel must be the same moment between both frames of reference.
True.

If we imagine airplane A as the train and airplane B as the tunnel we have an analogous situation. According to the observer on the ground the front of the train reaching the end of the tunnel is simultaneous with the back end being inside the tunnel. According to the observer on the train the front of the train reaching the end of the tunnel is not simultaneous with the back end being inside the tunnel. Both situations are considered correct and we have a paradox.
No, there is only an apparent paradox if you don't understand how simultaneity works in SR. Again, read an introductory textbook on the subject, and you'll see why this paradox isn't a real contradiction.

So, where is the back end of the train when the front end reaches the end of the tunnel?

So, where is the back end of the train when the front end reaches the end of the tunnel?
According to whose perspective? Again, there isn't a global agreement in the order of things happening at the front of the train and the back, due to the relativity of simultaneity.