On 1/17/2025 1:55 PM, Alan Grayson wrote:
On Friday, January 17, 2025 at 2:11:01 PM UTC-7 Brent Meeker wrote:
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 limitbse 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.
*It's a model of the path of the traveling twin in the TP. I wanted to
use SR, so I needed the path to be composed of segments where there is
only inertial motion. So I used a circle with an inscribed polygon,
and then, as in calculus, I imagined this partition as infinitely
fine, to approach the circle for the round-trip path. I then noted
that from the pov of the stationary twin, time is dilated on those
straight line inertial segments, so the traveling twin ages slower
then the stationary twin. Note that in this situation not only does
the stationary twin observe time dilation, but the traveling twin's
clocks actually slows down. Otherwise the traveling twin won't be
younger when the twins juxtaposed. But much more important, when
considering the Andromeda case, the traveling observer (traveling with
respect to the Earth) can be assumed to be at rest, and the frame of
the rod representing the distance from Earth to Andromeda, can be
assumed to be moving. So this situation mirrors the TP, since now the
moving frame containing the rod is analogous to the traveling twin, *
No it's not. The traveling twin is like a point particle that traces
out a path thru spacetime. Since the path is closed in space (a circle)
it's endpoints can be joined by an inertial (Earth bound) twin. None of
this is true of a rod from Earth to Andromeda. The rod doesn't go
anywhere, much less circle back.
*and the rest frame *
Which is what?
*whose observer is observing the moving rod, is analogous to the
stationary twin, *
If it's moving why isn't it analogous to the moving twin?
*the only difference is that now the Andromeda case is calculating
length contraction, *
Andromeda is just one end of a long rod. It doesn't have a "case". What
length is it calculating the contraction of?
*whereas the TP case is calculating time dilation. *
Of what clock?
*So what's the point of all this -- simply that the traveling twin's
clock physically slows, *
This is the twin that made a big circle.
*whereas length contraction is NOT measured in the frame of the moving
rod in the Andromeda case. *
Length contraction of what is not measured in the frame of the rod? It's
always the case that length contraction of X is not measured in the
frame of X. Remember it's called "relativity" theory.
*I think this is a problem, that the frame containing the rod, does
not manifest length contraction similar to the TP case*
What length was contracted in the TP?
*, where the traveling twin's clock actually slows down. AG*
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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