I When Does a Train Passenger Experience Complete Darkness in a Tunnel?

[ESponge2000]

I might have done the rear part wrong let me see. So It’s easier to work with basic standard units is what I’m doing. To recap:

Speed of light travels at distance 1 length unit per 1 time unit
So v =80% of c is just say it travels 0.8 units per 1 time unit

a tunnel in a tunnel’s rest frame is 10 length
Train in the train’s rest frame is also 10 length (but 6 length due to length contraction from special relativity)

Tunnel resting frame:
X = 0 is right at entering tunnel
X = 5 is middle of tunnel
We want where at X=5, which it would take the length contracted train 3/0.8 =3.75 time units for the mid section of train to enter the tunnel , and then 5/0.8=6.25 more time units for the mid section of shrunk train to reach middle of 10-length tunnel = t=10

And we want to know the X value for the rear of the train , which will be less than 5 , and at T=10… what is this X value

So… tunnel resting frame here
the rear of the train hits the mid of tunnel at 6/0.8 + 5/0.8 =13.75 time units, when (t’ = 0 when t = 0, t=13.75 when t’= 8.25 )

We are interested in the X position at 3.75 t time units prior … That would be where observer sees a t’ value on the rear end of train visible
To observer is 3x3.75 =11.25 units less than 8.25. 8.25-11.25 =-3 . And t’=-3 when t=-5, When t=-5, The front of train is at x = -5x0.8 =-4 . And the rear of train is at x = -10

So at T=10 the tunnel observer visually sees the rear of the train to be -10
Length units and 10 backwards from even having yet entered the tunnel, eventhough the the rear is actually already 2 length units into the tunnel but the light hasn’t yet reached the observer

Let me redo the X appearance at front of train. The observer sees the front of the train at t = 5/0.8 =6.25. At that time t’ = 3.75. The t’ value visible to tunnel observer from train clock from the front end of train is 3.75/3 + 3.75 =5 . When t’ =5, t = 8.33333 And when t=8.33333 the front of the train has traveled an X distance from the entrance of the tunnel of 6.666666667, And so :

The distorted appearance of the train as visually seen by the mid tunnel stationary observer at T=t=10
And is a visual appearance of a train with a length of 1.66667 from mid section to front instead of 3, has a visual appearance of being 15 length units instead of 3. This is despite the train being equidistant at t=10 from both ends , and all because the change in light pulses emitting from the oncoming vehicle is much much much more rapid than then light pulses emitting backwards from the part of the train that has already passed the observer and is moving away

So 0.8c approaching rear that is 15 units away from the observer will reach the observer in 3.75 time units. Validating that … The units of displacement = 4 times t.

Twin paradox … 0.8 velocity to 4 light years round-trip … earth observer sees traveling twin turnaround at t=9 , 1 year later the twin returns to earth at t=10, appearing to make the 4 ly trip in 1 year . Same multiple 4 times t and same velocity relationship

 

[Halc]

So It’s easier to work with basic standard units is what I’m doing.

They're called natural units and we're all fine with them.

I thought the question was if anybody on the train experienced total darkness. The spacetime diagram would really help with that problem. Figuring out what the mid-tunnel guy sees when the middle of the train is in his presence is not something that directly helps answer this question.
However, since he's at the midpoint and the doors close simultaneously in his frame, he's obviously going to experience some total darkness.

Given the length and speed figures you provided, the doors are shut for 5 time units (track frame), which is a lot. Those shadows are going to cross each other somewhere. Question is, will there be part of the train there when they do, and what part of the train exactly?

The engineer at the front obviously will not since he's already out of the tunnel before the doors close behind the caboose, so he's going to see the rear light the entire time he's in the tunnel.

 

[ESponge2000]

I worked this out a few months ago

They're called natural units and we're all fine with them.

I thought the question was if anybody on the train experienced total darkness. The spacetime diagram would really help with that problem. Figuring out what the mid-tunnel guy sees when the middle of the train is in his presence is not something that directly helps answer this question.
However, since he's at the midpoint and the doors close simultaneously in his frame, he's obviously going to experience some total darkness.

Given the length and speed figures you provided, the doors are shut for 5 time units (track frame), which is a lot. Those shadows are going to cross each other somewhere. Question is, will there be part of the train there when they do, and what part of the train exactly?

The engineer at the front obviously will not since he's already out of the tunnel before the doors close behind the caboose, so he's going to see the rear light the entire time he's in the tunnel.

I worked this out a few months ago and my find was that the part of the tunnel that experiences simultaneously no light emitted from either end of the tunnel occurs at t=15 only at the middle where the appearance of the closings are simultaneous , and no
part of the train gets to see it since the rear of train passes the middle of the tunnel at time 13.75. Which actually means all passengers on the train SEE an exit tunnel door shut first and the one at the tunnel entrance shut second. The more in front you are on the train the more the time gap between the first and second closing door.

However , my more recent find is that nowhere at any time is is truly pitched black inside the tunnel only because there’s more sources of light than the front and back end of tunnel, such as the light from any part of the train that is exposed to the light at T eventhough the ends of the tunnel at T correspond to a “t” where the tunnel doors are shut. The effect should be much like how you can’t see the sun when it’s deep below the horizon but you can see a visible lit moon in the sky that is lit by being exposed to the sun and you can see here similarly that you’re looking at parts of a train at times the doors were not shut in the same snapshot where you can see the doors are shut. Well not quite the same phenomenon but somewhat related. The earth creates a shadow blocking the sun and the moon is outside that shadow, But here it’s the doors casting a shadow together on any new light , but theoretically if the tunnel
Had no holes in it and perfectly opaque, you could see photons trapped in and just bouncing back and forth until the photons disperse and scatter more and more and more … and it would be an echo chamber (I can see that you saw the light that came from the light that came from the light that came from the light that must have come from the light from when the tunnel door had been open).

Edit:
And THIS took me till now to see. What now does a passenger riding in the back of the train see? Well that passenger is at rest with a train that’s 10 Units in length! If the train has been holding at 0.8c then the passenger will see the train at the exactly the size that it is! However, that passenger will notice a length-contracted Tunnel is moving backwards at 0.8c.
Now this took me some thinking and got it. Since the tunnel is moving “backwards”, If the passenger is in the back of a train moving forwards and seated in the forward direction, The passenger will SEE in the rear view mirror a tunnel that is appearing to get shorter in the rear direction and be “stretched” in the front direction due to the speed at which the tunnel is moving backwards … the closer photons reaching the passenger eyes a very very short time after it took the photons from farther away to reach the same passenger’s eyes, creating an illusion of a stretched tunnel, eventhough the passenger “calculates the tunnel” to be length contracted 6 units in length .
This means the passenger in the back of the train will actually “see” in one snapshot , Being passed what should be the middle of the tunnel , as tunnel that is supposed to be only 6 units , and in a train that’s is and appears to be 10
Units, But witness with eyes… the exit tunnel door shutting and with the entire front of the train not yet out of the tunnel ! How is this possible ? Because the rear traveling passenger will “see” an illusion that the tunnel in front of him is sssssstreeeeetchhhheddd” out such that it contains the entirety of the 10
Length train , while in the rear view will be a very very very short compressed tunnel. This is despite the fact that the passenger on the train will “calculate” that the exit tunnel door actually closed before he even entered the tunnel from the entrance side ; and that the entrance tunnel door closed later after he was already inside the tunnel. (One way to see this is that the speed of light does NOT speed up when you rapidly approach the light source so from a tunnel observer we tend to disagree with what the passenger is seeing to be the speed of c relative to their resting frame such that it conforms to their reference frame).

So tunnel observer sees a train go from stretched to shrunk as train moves in its direction of motion, but with a normal tunnel of length 10. A passenger on the train sees its actually the “tunnel” not the train that goes from stretched to shrunk as the tunnel is what’s moving and in the reverse direction, where train is what’s at rest at normal length 10 the whole time.

 

[ESponge2000]

The question now I have is if no matter how fast you approach the speed of light, will you in the moving vehicle ever actually see lengths contracting out the front windshield?

What you actually see if you near approach light speed, (ignoring color distortion and all of practicality) is not what I thought. You will See the opposite of length contraction in the very front actually. and rather a very very very fast suction of everything in the universe with high frequency of photons hitting eyes at once. With objects from side angles rotating to in front of you and even impacts from objects behind appearing distorted from being behind. Still you will just find that distances traveled are relatively shorter to reach due to special relativity length contraction and time dilation.

 

[pervect]

Right but if we can gather
1) there is a dark “point” in the center of the tunnel …. At a certain time , And for any moving frame when they are on a point the simultaneity on that point is invariant it’s dark it’s dark

I haven't been able to follow your entire scenario, because you haven't documented it (I'll join the chorus that points out that the space-time diagram would be the best documentation. And it would also be likely to help you work out the problem).

However, you have established that there is some dark point in whatever scenario you are visualizing. You h ave not established (and it seems rather unlikely) that this dark point occurs at the center of the train, considering the propagation speed of light, which I am guessing you have ignored? It's hard to be sure, because you haven't really explained things in the necessary detail.

Example. Suppose the tunnel is 100 feet long, and lets assume that the speed of light is 1 foot/nanosecond. (That's not exact, but it's close enough for my purposes).

If the doors close simultaneously at t=0 in the lab frame, the "dark spot" will occur in the center of the tunnel at t=50 nanoseconds due the the propagation speed of light, which takes 50ns to move 50 feet from each end. Note that I'm being specific here to follow my own advice - yes, I'm being somewhat lazy and not drawing a space-time diagram, but I'm taking an alternate approach of assigning coordinates to events and identifying what frame those coordinates apply.

Now, is the center of the train in the center of tunnel 50ns after the doors close? It seems rather unlikely, as I would guess that the center of the train was supposed to be in the center of the tunnel at t=0 in the lab frame when the doors both closed. But you haven't really specified enough information for me to really know for sure.

So in conclusion, you have stated that there is a dark spot somewhere in the tunnel. You now need to figure out exactly when and where on the train that dark spot occurs. In my example, we know the dark spot occurs in the center of the tunnel at t=50ns, but I don't know where the train is supposed to be 50ns after the doors close. If there is some point on the train at that location at that point in time, it will be dark there, though.

 

[Ibix]

The question now I have is if no matter how fast you approach the speed of light, will you in the moving vehicle ever actually see lengths contracting out the front windshield?

https://www.physicsforums.com/threa...f-the-lorentz-contraction.520875/post-5117075

 

[Halc]

Because the rear traveling passenger will “see” an illusion that the tunnel in front of him is sssssstreeeeetchhhheddd” out such that it contains the entirety of the 10 length train , while in the rear view will be a very very very short compressed tunnel.

Indeed. To illustrate, I did a spacetime diagram illustrating the view of the tunnel from a moment in time when the train is sticking out both ends.

The stationary train is the red bar at the top. I did not show its position in the past since it doesn't move, so the lines would go straight down. The front of the train is on the left, the rear at the right.

The black lines are the two tunnel doors, 6 units apart in this frame, moving at 0.8c.
Orange is the light lines of our two observers, one at each end of the train. It's half their light cone, and represents what they see when looking at the tunnel from outside.

The guy in front is looking back at the tunnel he already passed through, It appears of length ~3.8 or so, quite short. The guy at the rear is looking forward at the tunnel yet to be entered. That tunnel appears to be of length 30.

So indeed, it appears stretched out when approaching, but very short after it has gone by.

None of this answered the shadow question, which you seem to have waved away by pointing out that reflected light will never leave the observer in total darkness. But the point of the question wasn't that, the point was which observers on the train will see a period when both doors appear closed. To do that, a diagram similar to the above, but in the tunnel frame, would really help.


Edit: I drew the front light line wrong, off by 1 square. Hard to fix. The 3.8 should be more like ~3.4, but still pretty close.

 

[ESponge2000]

I haven't been able to follow your entire scenario, because you haven't documented it (I'll join the chorus that points out that the space-time diagram would be the best documentation. And it would also be likely to help you work out the problem).

However, you have established that there is some dark point in whatever scenario you are visualizing. You h ave not established (and it seems rather unlikely) that this dark point occurs at the center of the train, considering the propagation speed of light, which I am guessing you have ignored? It's hard to be sure, because you haven't really explained things in the necessary detail.

Example. Suppose the tunnel is 100 feet long, and lets assume that the speed of light is 1 foot/nanosecond. (That's not exact, but it's close enough for my purposes).

If the doors close simultaneously at t=0 in the lab frame, the "dark spot" will occur in the center of the tunnel at t=50 nanoseconds due the the propagation speed of light, which takes 50ns to move 50 feet from each end. Note that I'm being specific here to follow my own advice - yes, I'm being somewhat lazy and not drawing a space-time diagram, but I'm taking an alternate approach of assigning coordinates to events and identifying what frame those coordinates apply.

Now, is the center of the train in the center of tunnel 50ns after the doors close? It seems rather unlikely, as I would guess that the center of the train was supposed to be in the center of the tunnel at t=0 in the lab frame when the doors both closed. But you haven't really specified enough information for me to really know for sure.

So in conclusion, you have stated that there is a dark spot somewhere in the tunnel. You now need to figure out exactly when and where on the train that dark spot occurs. In my example, we know the dark spot occurs in the center of the tunnel at t=50ns, but I don't know where the train is supposed to be 50ns after the doors close. If there is some point on the train at that location at that point in time, it will be dark there, though.

I did point this out. The dark spot occurs at t=15 on the tunnel resting frame clock , using Einstein convention for relativity of simultaneity , and the dark spot means no light from either end of the tunnel, but not excluding light reflected off the concrete or the train Within.

I established the train will be passed the middle of tunnel at t=15 which means that no part of the train will visually see both doors close simultaneously, and all will see the same sequence of which door shuts first though amongst different intervals of time in between, with front of train finding the longest gap
And back of train the shortest gap

Of course this would mean either some pretty impressive eye glasses and/or some super super fast reaction times because either this train is absolutely gigantic or the time interval is too fast for the human brain to ever process but this is all thought hypothetical.

It’s also depressing that we can never actually see simultaneity but only infer it from ascertaining what we observe must be because this must be true… which spoils a whole lot of fun. For instance length contracted train inside a trapped tunnel kabam will never be something we can ever photograph ever although most likely if we ever made something like this most likely the train would instantly vaporize the tunnel
And continue its course . Or would the tunnel vaporize the train? That’s a different question and i think both would evaporate in fractions of seconds with not even a residue of lost life and the vapor content maintaining momentum
For an unfathomable distance past the tunnel… what it will sound like is also a fun thought because it will be a release of astronomical energy but over such a dispersed distance at such a supersonic speed

 

[Nugatory]

For instance length contracted train inside a trapped tunnel kabam will never be something we can ever photograph ever

We could line the tunnel with cameras, trigger them all simultaneously (in the tunnel frame), and then paste the images together together to produce a composite.

 

[ESponge2000]

We could line the tunnel with cameras, trigger them all simultaneously (in the tunnel frame), and then paste the images together together to produce a composite.

I had a similarly related idea where you only need one video camera but after you take your video you examine all the snapshots comprising the video and from those snapshots you select the earliest one for the center of the photo and as for objects captured farther and farther distance you select later and later pixels so that your photo captures all in a single “t” rather than all in a single “T”. For example if we go with the simple example of just a photo of a thumb and the sun …. You select your own location’s T=0 for the finger and your own T= 8 minutes for the sun , since at T=8 , you capture the sun’s T=0 for the sun.

“t” means under Einstein convention, assuming all clocks in a single resting frame but different locations, tick the same and can be synchronized . Using t

T means we take a photo at location and time and the photons you see are what you get

 

[ESponge2000]

Ibix thank you for the stretch diagram by the way that was great and I must have missed over when you sent that