On Wed, Jan 22, 2025 at 2:58 PM Alan Grayson <[email protected]> wrote:
>
>
> On Wednesday, January 22, 2025 at 10:32:58 AM UTC-7 Dirk Van Niekerk wrote:
>
> Sorry rear door closed and then opened...typo. D
>
> On Wednesday, January 22, 2025 at 9:30:29 AM UTC-8 Dirk Van Niekerk wrote:
>
> Forgive me if this was already done but I would like to clarify the
> experiment. Let's assume a covered bridge with two sliding doors. The
> bridge is 10 m in length. There is also a car 12 m in length. The front
> sliding door is closed and the car drives onto the bridge until the front
> almost touches the door and stops. The driver of the car and the bridge
> operator both agree that the back of the car sticks out 2 m at the rear.
> They propose an experiment. The driver will drive through the bridge at
> near the speed of light. When the front of the car is almost at the front
> door the bridge operator will quickly close and then open the front door.
> And when the back the car is just inside the bridge he will do the same
> with the rear door. They complete the experiment and compare notes.
>
> The bridge guy says that when he was about to close the front door he
> noticed that the rear of the car has already passed the rear door, so he
> opened and closed both doors at the same time. The driver disagrees. He
> sped up to the front door and saw it close and then open. He noticed in his
> rear view mirror that that back door was still open and the car still
> outside the bridge. As he sped through the front door (now open again) he
> notice the rear of the car moving past the rear gate, which then opened and
> closed behind him. To resolve the APPARENT paradox they have to account for
> length contraction and time dilation. The doors opened and closed
> simultaneously in the garage operator's frame but not the driver's
>
> Dirk
>
>
> *All you've proven, if anything, is that the car fits from the pov of the
> garage frame, but doesn't fit from the pov of the car frame, AT THE SAME
> TIME. *
>
Dirk said "The doors opened and closed simultaneously in the garage
operator's frame but not the driver's", so how do you figure the two frames
are talking about what happens "at the same time"? One frame says the front
door closed "at the same time" as the back door, the other frame says the
front door closing did *not* happen "at the same time" as the back door
closing.
> *So what? I don't see how this resolves the paradox? Presumably they
> disagree about fitting at small or large different times.*
>
>
They disagree about whether there is *any* moment where both the front and
back of the car are within the garage "at the same time". If we say
the garage frame uses time coordinate t and the car frame uses time
coordinate t', there is absolutely no value of the car frame's t'
coordinate where the position coordinates of front and back of the car are
both within the garage--the car frame does not say the car fits even for a
"small" time, it simply never fits at all in that frame. And that's exactly
what's illustrated in Dirk's diagrams, where in image #2 from the
perspective of the car frame you can see the back of the car is still
outside the garage (having yet to reach the entry) when the front reaches
the exit of the garage ('event A'), and in image #3 you can see the front
of the car already well past the exit of the garage by the time the back of
the car reaches the entry of the garage ('event B').
Jesse
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