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, and the rest frame whose observer is observing the moving rod, is analogous to the stationary twin, the only difference is that now the Andromeda case is calculating length contraction, whereas the TP case is calculating time dilation. So what's the point of all this -- simply that the traveling twin's clock physically slows, whereas length contraction is NOT measured in the frame of the moving rod in the Andromeda case. I think this is a problem, that the frame containing the rod, does not manifest length contraction similar to the TP case, 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 72bf93a9e508n%40googlegroups.com <https://groups.google.com/d/msgid/everything-list/ea38929b-8824-4aca-bf16-72bf93a9e508n%40googlegroups.com?utm_medium=email&utm_source=footer> . -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/2fb2d3bf-5642-4ddf-a230-ee2f6a1bdca2n%40googlegroups.com.
