On 1/16/2025 6:09 PM, Alan Grayson wrote:
On Thursday, January 16, 2025 at 5:56:55 PM UTC-7 Brent Meeker wrote:
On 1/16/2025 10:07 AM, Alan Grayson wrote:
On Monday, January 13, 2025 at 11:54:56 PM UTC-7 Brent Meeker wrote:
On 1/13/2025 10:39 PM, Alan Grayson wrote:
On Monday, January 13, 2025 at 11:20:05 PM UTC-7 Brent
Meeker wrote:
On 1/13/2025 10:04 PM, Alan Grayson wrote:
On Monday, January 13, 2025 at 10:21:28 PM UTC-7 Brent
Meeker wrote:
On 1/13/2025 9:02 PM, Alan Grayson wrote:
Using the LT, we have the following
transformations of Length, Time, and Mass, that is,
x --->x', t ---> t', m ---> m', where the primed
quantities are the transformed values in the
primed frame, given their values in the unprimed
frame. The question is this; which of the
quantities in the primed frame are actually
measured in the primed frame, and which are
appearances in the primed frame as seen by
unprimed frame?
All of them. That's why it's *relativity* theory.
x and t are measurements in one frame and x' and t'
are measurements in another frame moving *relative*
to the unprimed frame. And note the use of
"measurements" not "as seen". The two are
different when you consider things moving at a
significant fraction of the speed of light.
*But length in primed frame is contracted from the pov
of unprimed frame, but in primed frame it isn't
measured as contracted, so it APPEARS contracted from
the pov of unprimed frame*
No, it will *appear* rotated (c.f. Terrell rotation).
It will *measure* contracted (using light and clocks, as
with radar).
Brent
*Terrell rotation over my head, *
It's probably within your capability to Google it.
*but length contraction allegedly measured in primed frame
contradicts the discussion of the paradox, where car and
garage lengths aren't contracted when viewing each other. *
That doesn't even parse.
*Here the garage is in the primed frame but isn't actually
contracted. *
No object is ever contracted in it's own frame, but you
haven't said which is the primed frame, thus introducing
ambiguity.
*So the LT seems to deal in appearances, not what's actually
measured in the primed or transformed frame. AG*
*I already told you that LT transforms what it measured NOT
what appears.
Brent
*
*I'm referring to the primed frame in the LT formula x --> x'.
The LT gives us the length contracted from the pov of the moving
frame, of the primed frame, but the primed frame never measures
its length contracted_._ If this is correct, isn't it reasonable
and accurate to say the LT give us appearances of what the moving
frame measures, but not what is actually measured in the
stationary or primed frame? *
*Roughly speaking, yes. So long as you mean "appearance" broadly
to include what you measure, not just what you would see.'
*
*For example, on a near light speed trip to Andromeda, the
distance is hugely contracted from the pov of the traveler, what
the traveler measures, but from the pov of the stationary
observer, the distance remainS 2.5 MLY. AG
*
*Right.
Brent*
*
*
*"Houston, we have a problem!" Now let's consider time dilation using
SR in the Twin Paradox. Imagine the traveling twin moving in a circle
and returning to Earth, and imagine the circle contains a polygon
consisting of straight paths, which will later be infinitely
partitioned, whose limit will be that circle. As measured by the
stationary twin, the traveling twin's clock is dilated along each
segment, so when the twins are juxtaposed, the traveling twin's
elapsed time is LESS than clock readings for the stationary twin. If
this is correct, it demostrates that what the stationary twin
measures, is actually what the traveling twin's clock reads. IOW, what
happens to time dilation in this case is OPPOSITE to what happens to
the frames for the trip to Andromeda! Do you understand what I am
alleging -- that length contraction acts in an opposite manner
compared to time dilation, when I would expect them to behave
similarly? AG*
No I don't understand what you're alleging, nor what "moving in a circle
and returning to Earth" refers to. But yes length contraction and time
dilation go together, that's what makes the speed of light the same in
all frames.
Brent
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