I would appreciate views on the following understanding of length and distance in SR, restricted here to inertial movement. This is the beginning of a follow up to the thread: https://www.physicsforums.com/showthread.php?t=724025 1. The spatial length of an object is the spatial separation (distance) between its ends measured at the same time. 2. One can measure length (distance) using a number of methods, such as a specified rod, or coordinates set up in advance based on a specified rod. 3. Neither spatial separation nor simultaneity is invariant in SR. (see Taylor and Wheeler, Spacetime Physics, page 56: "not the same: space separations, time separations") 4. Because simultaneity and spatial separation are not invariant in SR, spatial length is not invariant in SR. 5. Any measure of the length of an object (or distance between two objects) in one reference frame is equally valid as a measure of the length of the object (or distance between the two objects) in any other reference frame. Can you see why this . . . would yield a different length for the rod . . . because of the relative motion between O′ and O? O′ simply measures the rod to be a different (in fact shorter) length from its length as measured by O (the "rest" length since O is carrying the rod); however neither measurement is any more correct than the other i.e. they are both equally valid after being attributed to the respective observers. WannabeNewton at https://www.physicsforums.com/showpost.php?p=4625309&postcount=6 These seem to be fundamental to any further analysis. But I have read a number of pieces that seem to take a different view. For example, sometimes it seems that people think of proper length (spatial separation of ends of an object measured at the same time in the object's rest frame) as essentially real and invariant, and length contracted length as being coordinate dependent and not real. An example is: Time dilation and length contraction are artifacts of remote observers. That is, in your own frame of reference, you are always the same size and your clock always ticks at one second per second. Some other observer, from a different frame of reference, SEES you as being length contracted and with a slow moving clock. You, right now as you read this, are moving at almost the speed of light from the reference frame of an accelerated particle at CERN. Do you feel any different? phinds at https://www.physicsforums.com/showpost.php?p=4625297&postcount=5 But your length is also invariant in the other inertial reference frame -- it is just shorter there than in your frame. As WannabeNewton says, each length is equally valid. The muons in the classic experiment do not merely "see" the height of the mountain to be smaller than we do; the height of the mountain actually is smaller for the muons than it is for us. And neither measure of height is more valid or real than the other. Another example imagines a construct of an odometer to determine invariant length or distance that is not dependent upon any coordinates: The aim is not to involve frames per se, at all. Instead, generalize the idea of a 'road' going by. You reel out tape measure matching the speed of road as it passes. When done, you have a measure of how much road has gone by . . . The definition is coordinate and frame independent. The only thing specified is a congruence of world lines of 'reference objects'. This is much less than a coordinate system. Given this, only invariants are computed. https://www.physicsforums.com/showpost.php?p=4621820&postcount=3 But again, there is no invariant length or distance in SR. Thanks in advance.