On 1/12/2025 5:24 PM, Alan Grayson wrote:
On Sunday, January 12, 2025 at 6:00:33 PM UTC-7 Alan Grayson wrote:
On Sunday, January 12, 2025 at 5:52:42 PM UTC-7 Brent Meeker wrote:
On 1/12/2025 8:38 AM, Alan Grayson wrote:
On Saturday, January 11, 2025 at 8:48:21 PM UTC-7 Brent
Meeker wrote:
On 1/10/2025 11:29 AM, John Clark wrote:
On Fri, Jan 10, 2025 at 2:15 PM Alan Grayson
<agrays...@gmail.com> wrote:
/>>>If I believe in SR, then I can use
length contraction to establish the car
won't fit in garage in car's frame./
*>> That depends entirely on what you mean
by"the car won't fit inthe garage". In the above
I've told you exactly what I mean by the term.
What do you mean? *
/> What do I mean; what any sane person would mean;
that the car's length is fixed from the pov of the
car's frame when car is moving, but the garage's
length is shortened from an initial condition where
it starts out shorter. AG /
*That's all very nice but that's not what I asked. What
_exactly_ do you mean by "the car won't fit in the
garage" if it's not "the front of the car is fully
within the garage while _SIMULTANEOUSLY_ the back of the
car is also fully within the garage"?*
I think you meant "the car *will *fit in the garage."
But there's been so much unproductive back and forth on
this thread, which I thought I had put to bed, that I'm
going to try again and to make everything even more
graphic and explicit. Here's the spacetime diagram in the
reference frame of the garage (which we would ordinarily
refer to a stationary):
*
*Here we see that the car, whose proper length is 10',
traveling at 0.8c is Lorentz contracted to a little over
6'. We start with the entrance open and the exit closed
and we see that we can close the entrance door before we
have to open the exit door because there is a brief
period in which the car is fully within the 8' garage,
the red trapezoid. If the distances are in feet then the
times are in nano-seconds. So the exit door can stay
closed for about 2.5 nano-seconds after the entrance door
closes, as measured in the garage reference frame. For
those 2.5 nano-seconds the car is fully inside the garage.
Now consider that same events in the car's frame of
reference. Keep in mind the technical meaning of "event"
is a point in spacetime, not a "happening" as in casual
parlance. So points in the above diagram, like "FRONT
ENTERS" are events and the Lorentz transformation
preserves events but it in general changes their
spacetime relation. Here is the Lorentz transformation,
point-by-point, of the above diagram. The two diagrams
are physically identical; differing only in being viewed
from different states of motion:
Specifically in this case the time order of "REAR ENTERS"
and "FRONT EXITS" is reversed. This is typical of
space-like separated events: their order is different in
different reference frames. So from the car's point of
view there is a period of about 7 nano-seconds during
which both doors are open and so the car sails thru
without hitting a door.*
*Brent
When you write the time order of events is reversed,
presumably in the car frame, does this mean the rear of the
car enters the garage before the front enters (which is
physically impossible)? If not, what do you mean? AG
That's the sort of question that gets you a troll reputation.
The events are clearly labelled and the axes have time and
position variables. If you can't read the diagram you won't
understand a written explanation any better.
Brent
As I was scrolling down to your reply, I was expecting a BS answer
and that's what I got. F the troll BS. When I worked at JPL no one
questioned my ability of reading plain English. But you know
better. AG
In the car frame, the Front Exits and Rear Enters, in this order, so
the car doesn't fit. In the garage frame, the Front Enters and Rear
Enters, in this order, so the car fits, but the latter isn't the
opposite of the former, AFAICT. AG
That's right. You can read the diagram!
Brent
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