On 12/4/2024 8:43 PM, Alan Grayson wrote:
On Wednesday, December 4, 2024 at 2:41:25 PM UTC-7 Jesse Mazer wrote:
On Wed, Dec 4, 2024 at 4:06 PM Alan Grayson <[email protected]>
wrote:
In the case of a car whose rest length is greater than the
length of the garage, from pov of the garage, the car *will
fit inside* if its speed is sufficient fast due to length
contraction of the car. But from the pov of the moving car,
the length of garage will contract, as close to zero as one
desires as its velocity approaches c, so the car *will NOT
fit* *inside* the garage. Someone posted a link to an article
which claimed, without proof, that this apparent contradiction
can be resolved by the fact that simultaneity is frame
dependent. I don't see how disagreements of simultaneity
between frames solves this apparent paradox. AG
Can you think of any way to define the meaning of the phrase "fit
inside" other than by saying that the back end of the car is at a
position inside the garage past the entrance "at the same time" as
the front end of the car is at a position inside the garage but
hasn't hit the back wall? (or hasn't passed through the back
opening of the garage, if we imagine the garage as something like
a covered bridge that's open on both ends) This way of defining it
obviously depends on simultaneity, so different frames can
disagree about whether there is any moment where such an event on
the worldline of the back of the car is simultaneous with such an
event on the worldline of the front of the car.
Jesse
Let's suppose that in the frame of the car, the front and back of the
car are simultaneously inside the garage at some speed v. How does
this account for the fact that the length of the garage schrinks
arbitarily close to zero as v approaches c, which ostensibly leads to,
or tends to the opposite conclusion? AG
Think about what that mean operationally. You have a photon detector at
the middle of the car and mirrors at each end of the car positioned to
send photons from lights at each end of the garage. When the detector
receives a photon from each direction at the same time that means the
ends of your care are simultaneously at the ends of the garage IN THE
CARS REFERENCE FRAME. Now think about what it means in the garage
reference frame.
Brent
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