On Wednesday, January 29, 2025 at 9:23:31 AM UTC-7 Jesse Mazer wrote:
On Wed, Jan 29, 2025 at 3:30 AM Alan Grayson <[email protected]> wrote: On Wednesday, January 29, 2025 at 12:24:33 AM UTC-7 Jesse Mazer wrote: On Wed, Jan 29, 2025 at 1:24 AM Alan Grayson <[email protected]> wrote: On Tuesday, January 28, 2025 at 9:01:14 PM UTC-7 Jesse Mazer wrote: On Tue, Jan 28, 2025 at 8:54 PM Alan Grayson <[email protected]> wrote: On Tuesday, January 28, 2025 at 2:56:32 PM UTC-7 Brent Meeker wrote: On 1/28/2025 6:49 AM, Alan Grayson wrote: I figured you'd jump on my word "separation". You have no idea what I mean? Of course, events with different coordinates are separated in a physical sense. Otherwise they'd have the SAME coordinates! But separated wrt spacetime events means no causal connections; whereas timelike events DO have causal connections. Of course, you know this, so please stop splitting hairs to make an argument. As for relative velocity, if you don't know what I mean, then you don't know what the v means in the gamma function. Again, stop splitting hairs. Oh, about GPS, I will look up this issue, but I was informed of it from a Ph'D in physics from Brent's Ph'D alma mater, University of Texas at Austin. It's surely NOT a distraction if it establishes that results in SR are physically real, not just appearances. AG There's an unfortunate but common confusion. The un-intuitive aspects of special relativity are physically real, but not it the sense that they happen to the moving object. If SR predicts length contraction, is the object is really shorter? (1) It's really shorter in the reference frame where it's moving. (2) It's not shorter in it's own frame. And (3) it's a different degree of shorter in other reference frames where it is moving with different velocities. Just looking at (2) people assume that it means (1) and (3) are just appearances. What's true is that *the contraction, relative to things in some reference frame, with respect to which it's moving, is real. *Brent *It's a baffling result. The LT doesn't tell us what will be MEASURED in a moving target frame being observed from a rest frame wrt length contraction and time dilation, so the result is just an APPEARANCE from the pov of the rest frame; and yet, from the pov of GPS clocks, these effects are real and measureable. This was the conclusion I argued, which is why I referenced the GPS clocks. * Brent's comment wasn't saying there was any disagreement between what coordinates the LT predicts for a given frame and what is really true (or really measured) in that frame, just like I wasn't saying that (see my last response above). You're really deluding yourself by rushing to read every explanation people give you as confirmation of your pre-existing fixed opinions. Jesse IMO you're deluding yourself in one important respect; your insistence that the results of the LT from the pov of some rest frame predicting length contraction in a frame moving wrt to it, can be measured in that moving frame; This statement is hard to follow because you ignore the distinction I made between frames and objects-- *I can't help you if you refuse to use your imagination. A rod or any object moving wrt a fixed source frame using the LT, or an object in moving frame at rest in that frame when the LT is applied from a fixed source frame, will be predicted as contracted. Period. AG* Your idiosyncratic way of talking is very hard to follow, I don't really understand the phrase "an object in moving frame at rest in that frame when the LT is applied from a fixed source frame". Can you please just use my terminology of v_rs representing the velocity of the rod in the source frame's coordinates, and v_rt representing the velocity of the rod in the target frame's coordinates? What I'm asking about is a scenario where v_rs is nonzero in the source frame's coordinates, then we use the LT to predict the coordinates of the worldlines of the front and back of the rod as defined in the target frame, and get the result that in the target frame the rod has v_rt = 0 so it's at rest in the target frame (i.e. both front and back have position coordinates which don't change with time in the target frame). If we then calculate the predicted length of the rod as defined in the target frame (where 'length' just means subtracting the position coordinate of the back of the rod from the position coordinate of the front), are you saying it will be predicted to be CONTRACTED compared to the length as defined by the original coordinates of the source frame? if we have some object whose length we want to talk about, and we know the coordinates of the worldlines of the front and back of the object in the first (source) frame and then use the LT to predict its coordinates (giving us its length) in the second (target) frame, you can't make any general statement about whether the LT will be "predicting length contraction" of the object until you know the velocity of the object itself in each frame. If the object has a higher velocity v_rt in the target frame than its velocity v_rs in the source frame, the LT will predict the object will be contracted in the target frame; on the other hand, if the object has a lower velocity v_rt in the target frame (including the case I analyzed where v_rt = 0) than its velocity v_rs in the source frame, the LT will predict the object is EXPANDED in the target frame, not contracted, compared to its length in the source frame. In the past you disagreed with this, do you still disagree or have you changed your mind? Please give a clear answer on this, telling me whether you now AGREE or DISAGREE that when the rod has v_rt in the target frame lower than its v_rs in the source frame, the LT predicts the rod's length in the target frame is expanded, not contracted. And if you disagree, please address the questions I asked in my last reply to you (the one before my reply to your comment on Brent's post). *The target frame is moving wrt the source frame. Objects in the target frame are at rest within that frame,* More verbal confusion here, *If you claim you don't understand my statement, you're either lying or I can't help you to understand what I consideer to be a simpe statement. A*G when I said "its length in the source frame" I just meant the coordinate length assigned by the source frame, whereas your last comment "Objects in the target frame are at rest within that frame" seems to say you are using "within that frame" to specifically mean a velocity of zero using the frame's coordinates. If you don't like my wording, just tell me what wording YOU would prefer for talking about the coordinates assigned to an arbitrary object by a given frame, regardless of whether it has a velocity of zero relative to that frame or not. For example if the source frame uses unprimed coordinates x and t, and the position as a function of time for the back of the rod as defined in the source frame is x = 0.8c*t while the position as a function of time for the front of the rod is x = 7.2 + 0.8c*t, then at any given value of t in the source frame the coordinate distance between the x-coordinate of the front and the x-coordinate of the back will be 7.2, so that is what I meant by "its length in the source frame" even though the rod is not "at rest within that frame" according to your terminology. (I would also say in this case the rod's velocity in the source frame is 0.8c) Is it OK with you if I continue to say things like "its length in the source frame" or "its velocity in the source frame" to refer to coordinate judgments like this, and if not what wording would you prefer? * and contracted according to relativity. One can also consider a moving rod as the frame AND the object under consideration. This is how to model and analyze a shortened trip to Andromeda. If you have a better way to model it, I am all ears. AG* You didn't answer my straightforward question: "Please give a clear answer on this, telling me whether you now AGREE or DISAGREE that when the rod has v_rt in the target frame lower than its v_rs in the source frame, the LT predicts the rod's length in the target frame is expanded, not contracted". Keep in mind that a lower v_rt in the target frame could include the case we were discussing where the rod is at rest as measured in the coordinates of the target frame (v_rt = 0)--do you AGREE or DISAGREE that in this case the LT predicts the rod's length in the target frame is expanded, not contracted? In your followup reply you said "The source frame is always fixed if the LT is applied, so offhand I can't say I agree or disagree in this case. If the rod is moving, it is contracted from the pov of the source frame. If you want the source frame to be moving, then the only way to apply the LT is to consider relative motion, with one frame at rest. Offhand I can't say I agree or disagree, except to say that from the pov of whatever frame is fixed, to new target is contracted. AG" Here your confusing terminology, where you sometime use "moving" and "at rest" in a standard way (relative to a specified frame) and sometimes in a non-standard way (where you arbitrarily designate one frame as "at rest" and the other as "moving" thoughout the whole problem), again makes it hard for me to follow what point you are trying to make here. What does it even mean to say "if you want the source frame to be moving"? I thought in Alan-speak the designation of one frame as "moving" and the other as "at rest" in your terminology was supposed to be an arbitrary linguistic label, one which therefore should have no effect on the answer to any physical question like whether the rod is contracted in the coordinates of either frame? Again, the standard terminology is just to use explicitly relative phrases like "the rod is moving relative to the Earth" or "the rod is moving in the Earth's frame", both of which just mean that the position coordinates assigned to the rod by the Earth frame are different at different values of the time coordinate (as in the example above where the back of the rod has coordinates x=0.8c*t, so for example at t=10 it would have x=8, then at t=20 it would have x=16 etc). Likewise saying "the rod is at rest in the rod frame" just means the position coordinates of the front and back of the rod are unchanging in the rod frame, they don't change at different values of the time coordinate. Modern physicists don't use non-relative phrasing like "frame A is moving", and it's not just a terminological matter because in cases like the above where you talk this way I genuinely can't parse how your statement would translate into a statement about the coordinates assigned by different frames, which is all that the LT is ultimately dealing with. Likewise "length" in each frame is ultimately just a coordinate matter, defined purely in terms of the coordinate distance between the ends of the object at any single value of coordinate time. If you think SR involves any concept of "velocity", "rest", "length" in a given frame that is *not* just a shorthand for talking about coordinates assigned to objects by that frame (with all coordinates based on local measurements by a system of rulers and clocks at rest in that frame), then you are confused. If you agree it's all ultimately about coordinates, you need to find a way of talking that doesn't lead to so much confusion about how your statements could be translated into coordinate terms, like my request to speak in terms of v_rs and v_rt. So we're both correct from different points of view, but you were mistaken to ignore my comments about GPS. Also, to be candid, I don't appreciate your comment that I am rushing to accept an opinion that confirms my pre-existing fixed opinions. You like to focus on coordinates, but the fact is you were mistaken in claiming the LT makes a measurable prediction of what a source frame predicts. It does in the GPS case, but not in the case of what a target frame predicts internally. AG You never addressed my response to you about the GPS in my post at https://groups.google.com/g/everything-list/c/ykkIYDAL3mTg/m/ximYgKzKDAAJ <https://groups.google.com/g/everything-list/c/ykkIYDL3mTg/m/ximYgKzKDAAJ> -- any coordinate system covering a non-infinitesimal region of curved spacetime is non-inertial, and the LT isn't relevant to non-inertial coordinate systems. *An object in free fall is in inertial motion, called a geodesic in GR. The LT is probably applicable for infinitesmal motion notwithstanding that this is occurring in curved spacetime. But I'm NOT an expert on how or why SR is used in GPS to make clock corrections. What I do know is that it IS used, that consequently the LT is likely applied in some way, and I gave this example just to show that whereas the LT does NOT give predictions concerning what is predicted for objects moving wrt a fixed frame, one cannot categorically claim that it never does.* If we're talking about a scenario where a GPS type system was used in flat spacetime, the LT would certainly "give predictions concerning what is predicted for objects moving wrt a fixed frame", as I said in the last sentence below you'd just have to include the way the clocks are artificially slowed down (relative to standard clocks) in the source frame before doing things like calculating elapsed time on a clock for some interval of coordinate time in the source frame, or applying the LT to predict the clocks' behavior in the target frame. Jesse But looking into this a little more, it seems based on p. 2-3 of http://math.bme.hu/~matolcsi/gpsmegjelentejp.pdf that at some point in the GPS calculations they do use an approximation that treats the spacetime around the Earth as flat so an inertial coordinate system can be used, and then they add higher-order corrections to account for the fact that the spacetime is actually curved and this is relevant to gravitational time dilation. But even if there were no gravity and we were just trying to define a GPS-like system to adjust clocks with various states of motion so they were all synchronized in a single inertial frame (as in the 'Suppose for a moment there were no gravitational fields' comment in the second to last paragraph in 'the realization of coordinate time' section of the GPS paper at https://pmc.ncbi.nlm.nih.gov/articles/PMC5253894/#Sec4 ), say the frame where the center of the Earth is at rest, I still don't understand why you think this would indicate any conflict between what the LT predicts and what is measured--the whole point of a GPS system is that the ticking rate of the clocks is being artificially adjusted so it no longer matches the "proper time" of an un-adjusted clock following the same trajectory, but instead matches the coordinate time in some preferred coordinate system you've programmed the clocks to keep pace with. If you have a system of adjustments like this for clocks in flat spacetime where inertial frames can be used, then if you know the adjusted ticking rate of a clock in some source frame (along with the coordinates of its worldline in this frame), you can use the LT to correctly predict the adjusted ticking rate of that same clock in a different target frame. Jesse -- 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/c9881ede-422c-433d-8f4a-b7fe4e295519n%40googlegroups.com <https://groups.google.com/d/msgid/everything-list/c9881ede-422c-433d-8f4a-b7fe4e295519n%40googlegroups.com?utm_medium=email&utm_source=footer> . -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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