Hello, I've really been enjoying reading these forums the last couple of weeks, and finally decided to register to ask a question. This is an earnest question about what the modern interpretation is, and how I and another student of relativity can learn more about the modern understanding. I ran into another poster from this forum elsewhere and while we both understand the basic concepts of relativity, there are some stark disagreements on things like coordinate systems and modern interpretations of relativity. Since there appear to be many physicists here, I was wondering if you could help us. I want us both to understand relativity better and if either of us, I or him, are misunderstanding I'd like to correct that so we don't accidentally spread incorrect information. ----------- Here is my understanding: My understanding is that the modern interpretations of relativity consider only coordinate system independent geometric objects or quantities as "real"/"physical". Therefore I would say that in the twin's paradox, most of the confusion comes from the time dilation equation comparing a proper time of a clock (a coordinate system independent quantity) to the coordinate time of a coordinate system (which is explicitly coordinate system dependent). So I would say the modern interpretation is that "time dilation" is just a coordinate system dependent effect and not physical. Wheeler's relativity books appear to me to be stating this. When asked "but doesn't one twin 'really' age less", my answer would be, yes their proper times (length of world lines) are indeed different (coordinate system independent). The magnitude of their four-velocity through spacetime however was always c, so the clocks always ran at the same rate ... but they didn't travel the same distance through spacetime. In Euclidean geometry, if two people leave a point at a constant speed and meet up later at another point at the same time, then they must have travelled the same distance. This is not so in the Minkowski geometry of spacetime. Just because the coordinate time at the end of the two paths was the same does not mean the spacetime path length was the same despite the magnitude of their 'speed' through spacetime was the same. Similarly, considering the length contraction of an inertial rod, different coordinate systems will give a different coordinate length. But the proper length is always the same. So this too would be a coordinate system dependent effect and not physical. (As I found discussed on this forum previously, a 'rigidly' accelerating rod (and thus appearing to contract/expand according to an inertial coordinate system) must have the proper acceleration different on the front and end of the rod (as can be seen explicitly in Rindler coordinates)... so in this sense (not the one usually discussed and/or meant by 'length contraction') the contraction is real/physical.) Basically, because we are free to choose any coordinate system, only coordinate system independent quantities should be considered 'real'/'physical' in modern interpretations of relativity. So that is my understanding of the modern interpretations of relativity and its relation to coordinate systems. ----------- Here is his understanding: Before I get to the opposing view, let me state a couple blatant things: - I don't really understand his view, so I will use quotes to help avoid misrepresenting them. Since I do not understand, this may still not be the best (I've asked him to join in on the conversation). - I realize that there can be multiple valid interpretations as long as they are self consistent. I do NOT want to get into a discussion of philosophy or ontology. This is an earnest question about what the modern interpretation is, and how I and another student of relativity can learn more about the modern understanding. His comments regarding coordinate systems (the context is I often give an example coordinate system to show something he considers 'physical' is indeed coordinate system dependent) So there seems to be a misunderstanding of what a coordinate system even is, and what its role in physics is. I have failed at explaining this to him, so maybe I'm misunderstanding his point. If someone else could offer advice here it would be helpful. He argues that coordinate dependent things are still "real"/"physical". So he can claim both: "that the other's clock is running slower" and "the clock is not physically changed" at the same time. This seems like falling for the twin's paradox, so when asked for clarification, the response is: "It is simply nonsense to say 'both clocks are running slower than the other'. " So he appears to both reject and accept coordinate dependent quantities as 'real'/'physical' depending on the scenario. When asked why, if one accepts coordinate depedent quantities as 'real', you can't say both clocks are running slow, his answer is: "Actually you would have to be in two places at the same time to do this." and states his solution to the twin's paradox is that "Proper relativistic comments can only be made from the viewpoint of an inertially moving observer considered to be stationary." When asked what coordinate system he uses to refer to whether someone is "stationary", he feels no coordinate system is referred to implicitly or otherwise with this statement. ----------- The quotes above are focussing on the disagreements. And therefore probably cast a negative light. This person is not a crackpot though. They understand the basics and can do some calculations with Lorentz transformations. I just feel that they missed the essence of relativity, and worse have self-conflicting ways of resolving the famous 'paradoxes'. I fully understand that I may be incorrect as well. Either way, please please help guide us to better understanding. If you could refer to specific textbooks (both of us own MTW, and there are probably other textbooks we own in common as well), that would be very very helpful. I thought MTW would be good as I have heard some students jokingly refer to it as the relativity 'bible', so I figured we could consider that a good representation of the modern understanding of relativity (no?). Quoting pertinent sections or "assigning us problems" from the book to help us learn would also be great ... thanks!