Review the speedy limousine in the garage paradox:
I)  In the garage frame:
Both doors are open.
The car enters.
As soon as the rear fender enters, both doors close.
Car fits, no crash.
Rear door immediately opens, car transits.

II)  In the limo's frame:
Car is too long to fit.
The rear door closes, then opens before the front,
permitting the car to transit, without crash.
The car is saved by relative simultaneity.

Note a subtle point:  no communication occurs within
the garage.  The door actions are pre-programmed; the
controller knows precisely the car's trajectory.

New scenario:
I) In the garage frame:
As soon as the limo's rear fender enters, the front door
closes, and sends a radio signal to the rear door, which
then closes.
Car fits (as above).
Rear door immediately opens.  Car transits.

Hence, in this case, there is a causal sequence in the
door actions... which must apply to EVERY OTHER frame.

 II)  In the limo's frame:
As described above, the rear door closes AFTER the
front. Both doors are therefore closed while the car
is inside the garage. But the limo is too long, doesn't fit,
and crashes!

The causal relation means that relative simultaneity no
longer applies. The vehicle is doomed in (II), yet survives in (I) -

As an exercise, the student might calculate what constraints
on the limo's length and speed permit safe transit.

--
Rich

Op 19-aug.-2021 om 04:49 schreef RichD:
> Review the speedy limousine in the garage paradox:
> I)  In the garage frame:
> Both doors are open.
> The car enters.
> As soon as the rear fender enters, both doors close.
> Car fits, no crash.
> Rear door immediately opens, car transits.
>
> II)  In the limo's frame:
> Car is too long to fit.
> The rear door closes, then opens before the front,
> permitting the car to transit, without crash.
> The car is saved by relative simultaneity.
>
> Note a subtle point:  no communication occurs within
> the garage.  The door actions are pre-programmed; the
> controller knows precisely the car's trajectory.
>
> New scenario:
> I) In the garage frame:
> As soon as the limo's rear fender enters, the front door
> closes, and sends a radio signal to the rear door, which
> then closes.

The rear door can't close, as the front of the limo has
already passed it.

> Car fits (as above).
> Rear door immediately opens.  Car transits.
>
> Hence, in this case, there is a causal sequence in the
> door actions... which must apply to EVERY OTHER frame.
>
>  II)  In the limo's frame:
> As described above, the rear door closes AFTER the
> front.

Again, the rear door can't close, as the front of the limo
has already passed it.

> Both doors are therefore closed while the car
> is inside the garage. But the limo is too long, doesn't fit,
> and crashes!

Impossible.

>
> The causal relation means that relative simultaneity no
> longer applies. The vehicle is doomed in (II), yet survives in (I) -
>
> As an exercise, the student might calculate what constraints
> on the limo's length and speed permit safe transit.
>
>
> --
> Rich
>

You should have drawn a little spacetime diagram and saved
yourself some time.

Dirk Vdm

Dirk Van de moortel wrote:

>> The causal relation means that relative simultaneity no longer applies.
>> The vehicle is doomed in (II), yet survives in (I) -
>> As an exercise, the student might calculate what constraints on the
>> limo's length and speed permit safe transit. -- Rich
>
> You should have drawn a little spacetime diagram and saved yourself some
> time.

since you insist, here we go

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On August 21, Dirk Van de moortel wrote:
>> Review the speedy limousine in the garage paradox:
>> I) In the garage frame:
>> Both doors are open.
>> The car enters.
>> As soon as the rear fender enters, both doors close.
>> Car fits, no crash.
>> Rear door immediately opens, car transits.
>>
>> II) In the limo's frame:
>> Car is too long to fit.
>> The rear door closes, then opens before the front,
>> permitting the car to transit, without crash.
>> The car is saved by relative simultaneity.
>>
>> Note a subtle point: no communication occurs within
>> the garage. The door actions are pre-programmed; the
>> controller knows precisely the car's trajectory.
>>
>> New scenario:
>> I) In the garage frame:
>> As soon as the limo's rear fender enters, the front door
>> closes, and sends a radio signal to the rear door, which
>> then closes.
>
> The rear door can't close, as the front of the limo has
> already passed it.
>
>> Car fits (as above).
>> Rear door immediately opens. Car transits.
>>
>> Hence, in this case, there is a causal sequence in the
>> door actions... which must apply to EVERY OTHER frame.
>>
>> II) In the limo's frame:
>> As described above, the rear door closes AFTER the
>> front.
>
> Again, the rear door can't close, as the front of the limo
> has already passed it.
>
>> Both doors are therefore closed while the car
>> is inside the garage. But the limo is too long, doesn't fit,
>> and crashes!
>
> Impossible.
>
>> The causal relation means that relative simultaneity no
>> longer applies. The vehicle is doomed in (II), yet survives in (I) -
>> As an exercise, the student might calculate what constraints
> on the limo's length and speed permit safe transit.
>
> You should have drawn a little spacetime diagram and saved
> yourself some time.

Nicely missing the point.
It wasn't for my benefit, but as a challenge to the mavens in this group,
to explain, like any paradox.

Rather than spacetime diagram, assume the limousine is longer than
the garage, as usual, then derive the minimum velocity such that it
shrinks to fit, per the Lorentz factor.

Then, with some further calculation, it becomes clear that the
car's front fender reaches the rear door before the radio signal.
Which is the sneaky point.
Hence it crashes, in either frame, as you surmised.

Some algebra required -

--
Rich

On Saturday, August 21, 2021 at 4:19:28 PM UTC-7, RichD wrote:
> On August 21, Dirk Van de moortel wrote:
> >> Review the speedy limousine in the garage paradox:
> >> I) In the garage frame:
> >> Both doors are open.
> >> The car enters.
> >> As soon as the rear fender enters, both doors close.
> >> Car fits, no crash.
> >> Rear door immediately opens, car transits.
> >>
> >> II) In the limo's frame:
> >> Car is too long to fit.
> >> The rear door closes, then opens before the front,
> >> permitting the car to transit, without crash.
> >> The car is saved by relative simultaneity.
> >>
> >> Note a subtle point: no communication occurs within
> >> the garage. The door actions are pre-programmed; the
> >> controller knows precisely the car's trajectory.
> >>
> >> New scenario:
> >> I) In the garage frame:
> >> As soon as the limo's rear fender enters, the front door
> >> closes, and sends a radio signal to the rear door, which
> >> then closes.
> >
> > The rear door can't close, as the front of the limo has
> > already passed it.
> >
> >> Car fits (as above).
> >> Rear door immediately opens. Car transits.
> >>
> >> Hence, in this case, there is a causal sequence in the
> >> door actions... which must apply to EVERY OTHER frame.
> >>
> >> II) In the limo's frame:
> >> As described above, the rear door closes AFTER the
> >> front.
> >
> > Again, the rear door can't close, as the front of the limo
> > has already passed it.
> >
> >> Both doors are therefore closed while the car
> >> is inside the garage. But the limo is too long, doesn't fit,
> >> and crashes!
> >
> > Impossible.
> >
> >> The causal relation means that relative simultaneity no
> >> longer applies. The vehicle is doomed in (II), yet survives in (I) -
> >> As an exercise, the student might calculate what constraints
> > on the limo's length and speed permit safe transit.
> >
> > You should have drawn a little spacetime diagram and saved
> > yourself some time.
> Nicely missing the point.
> It wasn't for my benefit, but as a challenge to the mavens in this group,
> to explain, like any paradox.
>
> Rather than spacetime diagram, assume the limousine is longer than
> the garage, as usual, then derive the minimum velocity such that it
> shrinks to fit, per the Lorentz factor.
>
> Then, with some further calculation, it becomes clear that the
> car's front fender reaches the rear door before the radio signal.
> Which is the sneaky point.
> Hence it crashes, in either frame, as you surmised.
>
> Some algebra required -
>
> --
> Rich

"Relativity of Simultaneity is non-local".

As the car and garage join frames,
space is contracted as about the car.

Excuse my, my idee has fixated that "space contraction"
is a better explanation than "length contraction and time dilation".

What if it solves the field equations is just a super-theory about GR....