On Thursday, January 9, 2025 at 8:58:09 AM UTC-7 Quentin Anciaux wrote:
Le jeu. 9 janv. 2025, 16:51, Alan Grayson <[email protected]> a
écrit :
On Thursday, January 9, 2025 at 5:33:47 AM UTC-7 Quentin Anciaux wrote:
AG, your question is just another attempt to misrepresent the role of
simultaneity and derail the discussion. Let’s cut through the nonsense and
address this directly.
The car fitting in two different garages of different lengths depends on
relative lengths and simultaneity. Simultaneity doesn’t somehow override
length contraction—it works in tandem with it to determine whether the car
fits in a specific frame. Here’s how it works:
1. Garage1 where the car fits:
In the frame of Garage1, simultaneity determines that, at a specific
moment, the back of the car passes the entrance while the front is within
the exit. This conclusion is consistent with the car’s length being shorter
than or equal to the length of Garage1 in this frame due to length
contraction.
2. Garage2 where the car doesn’t fit:
In the frame of Garage2, the same principles apply. If the car is longer
than Garage2’s length (as measured in the frame of Garage2), simultaneity
will show that there is no single moment when the back of the car is inside
while the front is also inside. The relative lengths determine whether
fitting is possible, but simultaneity is what determines when and how you
compare the endpoints.
So, to answer your question: the car doesn’t fail to fit in Garage2 because
of simultaneity alone. The disagreement about simultaneity simply explains
why the two frames (the car frame and the garage frame) reach different
conclusions. Simultaneity is critical because it defines how you compare
events in spacetime. Without it, "fitting" would be an undefined concept.
Once again, your attempt to isolate simultaneity as some kind of side issue
misses the mark entirely. Relative lengths are part of the setup, but
simultaneity is what resolves the paradox. Ignoring this just shows that
you still don’t understand—or don’t want to understand—how special
relativity works. Your question doesn’t prove simultaneity is irrelevant;
it just shows your commitment to trolling.
*Forget my last question. I meant to ask about a situation where the car
fits in both frames due to choice of initial parameters, and I was
wondering if simultaneity continues to disagree and what will be the
situation in the second frame where it previously fit. AG *
AG, your attempt to shift the discussion yet again is nothing more than a
distraction. But let’s humor this new scenario and break it down clearly.
If the car fits in both frames, then the initial conditions are such that:
1. The contracted length of the car in the garage frame is less than or
equal to the length of the garage.
2. The contracted length of the garage in the car frame is less than or
equal to the length of the car.
*If you're discussing initial conditions, there is no motion of car and
thus no contraction. AG *
In this case, simultaneity still plays a role, because it dictates how
events are aligned in each frame. Let’s break it into the two frames:
1. In the garage frame:
The back of the car passes the entrance while the front is at or within the
exit simultaneously (according to the garage’s synchronized clocks). This
means the car fits, and simultaneity determines this alignment.
2. In the car frame:
The garage appears contracted, but simultaneity in the car frame still
ensures that at some moment (according to the car’s synchronized clocks),
the back of the garage aligns with the back of the car,
*So the car is leaving the garage here? AG*
and the front of the garage aligns with the front of the car. The car fits
here too.
*So the car is entering here? How is this a fitting scenario? AG*
Does simultaneity still disagree?
Yes, simultaneity still disagrees between the two frames because that’s a
fundamental aspect of special relativity. Even if the car fits in both
frames, the ordering of events will differ:
In the garage frame, the events of "back passing the entrance" and "front
at the exit" are simultaneous.
In the car frame, these events may not be simultaneous, but the alignment
of the endpoints still ensures the car fits due to the chosen parameters.
What happens in the second frame?
The car will still fit, but the perception of when it fits differs due to
the relativity of simultaneity. This doesn’t create a contradiction; it’s
just a reflection of how spacetime operates. Both frames agree on the
physical reality (the car fits), but they describe it differently.
Your question doesn’t undermine simultaneity—it reinforces its importance.
Even when the car fits in both frames, simultaneity determines how the
events align in each frame. Pretending simultaneity is irrelevant here, as
you’ve tried to do throughout this discussion, would render the entire
concept of "fitting" meaningless.
*As I have stated, one can have a viable concept of fitting using only
length considerations. I am not ruling out other definitions of fitting
which might have certain advantages. AG*
So yes, simultaneity continues to disagree. It always does. That’s
relativity. If you were expecting this to disprove anything, you’re barking
up the wrong tree—again.
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