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Dude, you are SERIOUSLY barking up the wrong tree. I am constantly astounded by the patience of the mentors here but I predict that this thread has run its course.DanMP said:
Dude, you are SERIOUSLY barking up the wrong tree. I am constantly astounded by the patience of the mentors here but I predict that this thread has run its course.DanMP said:No, I'm pretty sure that this is "the best tree", if we want to solve the mystery of dark matter and to finally/really understand relativity.
I think that my questions are legitimate and deserve to be answered.phinds said:Dude, you are SERIOUSLY barking up the wrong tree. I am constantly astounded by the patience of the mentors here but I predict that this thread has run its course.
This analogy is wrong. The relevant one is why is it a longer distance over the hill than through a straight tunnel. What answer would you consider acceptable to that question?DanMP said:The geometry is good in explaining how to understand and apply the theory, but it is as good in "explaining" what is really happening as contour lines in a topographical map: we can say that we get more tired walking between A and B because we cross contour lines (climbing a hill), but we need to explain why/how contour lines are responsible for this.
Wow. That came from nowhere. Are you really telling all these scientists how to do their job?DanMP said:No, I'm pretty sure that this is "the best tree", if we want to solve the mystery of dark matter and to finally/really understand relativity.
My analogy is not wrong, because it is about causality. The one with the tunnel is, again, just geometry.Ibix said:This analogy is wrong. The relevant one is why is it a longer distance over the hill than through a straight tunnel. What answer would you consider acceptable to that question?
You are confusing doing work against gravity (countours) with traveling a further distance (route).DanMP said:My analogy is not wrong, because it is about causality. The one with the tunnel is, again, just geometry.
But they have BEEN answered. You just don't seem to LIKE the answers.DanMP said:I think that my questions are legitimate and deserve to be answered.
So "it's just geometry" is, to you, an acceptable answer for "why are the distances different", but not for "why are the times different". Do I understand you correctly?DanMP said:My analogy is not wrong, because it is about causality. The one with the tunnel is, again, just geometry.
You're fixated on the idea of objects interacting with space(/time) probably because most of our experiences happen on Earth, where we are physically attached to an object with a certain geometry, so it makes for a convenient example. Please understand: this analogy is leading you astray because you are not, in fact, interacting with space (you are not interacting with geometry) you are interacting with an object.DanMP said:How exactly they do that? According to Dale, clocks are counting oscillations. I can't see the direct connection between that and the spacetime, or "the time part of space-time".
The geometry is good in explaining how to understand and apply the theory, but it is as good in "explaining" what is really happening as contour lines in a topographical map: we can say that we get more tired walking between A and B because we cross contour lines (climbing a hill), but we need to explain why/how contour lines are responsible for this. The same is valid, in my opinion, for world lines / paths through spacetime: we need to show the direct connection, if there is any, between them and the clocks.
No, I'm pretty sure that this is "the best tree", if we want to solve the mystery of dark matter and to finally/really understand relativity.
No. I obtained interesting results doing that, so I offered a hint. Nothing more. Take it or leave it (to me) :-)m4r35n357 said:Are you really telling all these scientists how to do their job?
Yes. Distances in space are easy to deal with, but with time is different:Ibix said:So "it's just geometry" is, to you, an acceptable answer for "why are the distances different", but not for "why are the times different". Do I understand you correctly?
Why (if I understand correctly) a clock measures less time in a bent (longer) path in spacetime? This (at least) requires an explanation, but also:Dale said:the geometry makes it so that a bent path in space always requires more wheel rotations and a bent path in spacetime requires fewer hyperfine transitions.
DanMP said:clocks are counting oscillations. I can't see the direct connection between that and the spacetime, or "the time part of space-time".
It really isn't.DanMP said:Yes. Distances in space are easy to deal with, but with time is different:
Because Minkowski geometry does not work like Euclidean geometry. Rather than having the Pythagorean theorem ##c^2 = a^2 + b^2##, you have the corresponding relation ##(c\tau)^2 = (ct)^2 - x^2##. This geometry is required in order for the speed of light to be invariant.Why (if I understand correctly) a clock measures less time in a bent (longer) path in spacetime? This (at least) require an explanation, but also:
DanMP said:Why (if I understand correctly) a clock measures less time in a bent (longer) path in spacetime? This (at least) requires an explanation
Ok, so one question was answered. Thank you!Orodruin said:... Minkowski geometry does not work like Euclidiean geometry. Rather than having the Pythagorean theorem ##c^2 = a^2 + b^2##, you have the corresponding relation ##(c\tau)^2 = (ct)^2 - x^2##. This geometry is required in order for the speed of light to be invariant.
To measure distance you see how many times a thing of known constant length fits between point A and point B. To measure duration you see how many times a thing of known constant time fits between event A and event B. We call the first thing a ruler and the second a clock.DanMP said:This (at least) requires an explanation, but also:
We can measure the distance along a path in space with meter sticks: place the meter sticks end to end and then count the number of meter sticks needed. Equivalently we can use just one meter stick, repeatedly picking it up and putting it down again with the near end where the far end had been, and count the number of times we placed the stick before we reached the end of the path.DanMP said:How exactly they do that? According to Dale, clocks are counting oscillations. I can't see the direct connection between that and the spacetime, or "the time part of space-time".
Your post only contained one question.DanMP said:Ok, so one question was answered. Thank you!
What about the other one?
Yes, this is a nice explanation. I like it. Thank you!Ibix said:To measure distance you see how many times a thing of known constant length fits between point A and point B. To measure duration you see how many times a thing of known constant time fits between event A and event B. We call the first thing a ruler and the second a clock.
Another very nice explanation. Thank you!Nugatory said:We can measure the distance along a path in space with meter sticks: place the meter sticks end to end and then count the number of meter sticks needed. Equivalently we can use just one meter stick, repeatedly picking it up and putting it down again with the near end where the far end had been, and count the number of times we placed the stick before we reached the end of the path.
Counting oscillations is the analgous procedure for measuring the interval along a timelike path through spacetime.
Let me ask you a closely related question here. If we draw a triangle on a piece of paper and then measure the length of one side with a ruler and compare it to the length of the other two sides measured with similar rulers, then we always find that the two sides together are longer than the one side. How would you explain that?DanMP said:The geometry is good in explaining how to understand and apply the theory, but it is as good in "explaining" what is really happening as contour lines in a topographical map: we can say that we get more tired walking between A and B because we cross contour lines (climbing a hill), but we need to explain why/how contour lines are responsible for this. The same is valid, in my opinion, for world lines / paths through spacetime: we need to show the direct connection, if there is any, between them and the clocks.
Dale said:Let me ask you a closely related question here. If we draw a triangle on a piece of paper and then measure the length of one side with a ruler and compare it to the length of the other two sides measured with similar rulers, then we always find that the two sides together are longer than the one side. How would you explain that?
The reason I ask is because I think that the geometry is a complete answer, but you do not. So if I can understand what sort of answer you would find satisfying for the triangle question then I can probably make a similar answer for time that would be satisfying for you.
Excellent!DanMP said:I finally accepted geometry / spacetime as a good/valid answer.
Agreed. It is well known that it is not the only explanation possible. These explanations are called “interpretations” and all use the same math and make the same experimental predictions. They just differ in how the variables are interpreted and what parts are considered “real”.DanMP said:I still don't think that this is the only explanation possible (I actually found one myself, in agreement with the current one, but different in the understanding of reality)
Then it would be a new theory and not a new interpretation. Almost certainly it would be experimentally falsified already. However, we cannot discuss it here until after it is published in the scientific literature.DanMP said:And there are ways to experimentally test the new model.
Dale said:However, we cannot discuss it here until after it is published in the scientific literature.
Because distance in Minkowski space has a different formula. It's not a2 + b2, it's a2 - b2DanMP said:Yes. Distances in space are easy to deal with, but with time is different:
Why (if I understand correctly) a clock measures less time in a bent (longer) path in spacetime? This (at least) requires an explanation, but also:
Hey Dale, regarding the actual math, correct me if I'm wrong, but there is only one possibility that is consistent with isotropy, the principle of relativity, and a finite universal speed limit, right?Dale said:Excellent!
Agreed. It is well known that it is not the only explanation possible. These explanations are called “interpretations” and all use the same math and make the same experimental predictions. They just differ in how the variables are interpreted and what parts are considered “real”.
However, do be aware that it is the answer which directly generalizes to GR. For that reason it is by far preferred by the community. I personally encourage you to know and use all interpretations as mental/organizational aids without getting bogged down in debating the philosophical superiority of one or the other.
Then it would be a new theory and not a new interpretation. Almost certainly it would be experimentally falsified already. However, we cannot discuss it here until after it is published in the scientific literature.
I already insisted too much with this, so I think it is better to stop, at least for a while. I may come back, in a new thread, with questions about the experiments. Until then, thank you all for your patience and for your useful answers.Grinkle said:As far as I know, though, its allowed to ask if some idea has historically been proposed / published / discarded etc. That said, it doesn't seem this thread is headed that way.
Yes, that is correct.Sorcerer said:regarding the actual math, correct me if I'm wrong, but there is only one possibility that is consistent with isotropy, the principle of relativity, and a finite universal speed limit, right?
Indeed, for me this is the most beautiful derivation, but it's very mathematical, and that's why you usually don't find it in textbooks about SRT:Sorcerer said:Hey Dale, regarding the actual math, correct me if I'm wrong, but there is only one possibility that is consistent with isotropy, the principle of relativity, and a finite universal speed limit, right?
I've seen several general derivations of coordinate transformations between inertial reference frames, and even managed to do a fairly general one myself, and I don't see how there is any other possibility. Granted, you could use the same math and interpret an invisible, impossible to detect absolute reference frame for example, but wouldn't the math always work out the same?
As a "non-professional" I like to start by addressing the differences between Galilean and Special Relativity by direct comparison. So, starting from the Galilean transform ("assume Newton's laws hold good"), we ask why is there a zero element in it, and what would be the consequences of allowing it to be non-zero? Well straight away you see that it would destroy the notion of universal time. so that is already dealt with in advance ;) Then we ask what other properties does the Galilean Transform have, and the only one I think you need is that the determinant is one (which eliminates annoying scaling issues going forward and back).vanhees71 said:Indeed, for me this is the most beautiful derivation, but it's very mathematical, and that's why you usually don't find it in textbooks about SRT
Really? I have seen it in several textbooks (at least in one of Rindler's books that I remember off the top of my head) and it is the way I usually like to introduce it - although I gloss over some points rather quickly - in class. However, I would agree that this is not the approach taken in most "modern physics" treatments, which would be in the first two years of university and a more superficial treatment.vanhees71 said:Indeed, for me this is the most beautiful derivation, but it's very mathematical, and that's why you usually don't find it in textbooks about SRT:
Assuming only the special principle of relativity, the existence of inertial frames, and the "Euclidicity" of the space wrt. to any inertial observer, leads to two possible spacetimes, i.e., Galilei-Newton or Einstein-Minkowski spacetime.
Interesting. I should read Rindler's book in more detail. I was aware about this derivation only through the artikel by Frank et al from 1911, which was cited in some Am. Jour. Phys. article (I forgot which one). Thanks for the hint anyway.Orodruin said:Really? I have seen it in several textbooks (at least in one of Rindler's books that I remember off the top of my head) and it is the way I usually like to introduce it - although I gloss over some points rather quickly - in class. However, I would agree that this is not the approach taken in most "modern physics" treatments, which would be in the first two years of university and a more superficial treatment.
Certainly, that practice should be frowned upon. A common way of a more "light" introduction is to first derive time dilation and length contraction and then use them to derive the Lorentz transformations using different constructions. We do it that way in an introductory online course that I developed for the department a few years back.vanhees71 said:Well, if you just tell your students how the Lorentz transformation looks without any physical nor mathematical argument, I'm pretty sure they'll miss the whole point why to introduce relativity to begin with.
If I remember correctly, he starts with a (rather hand-waving) argument to conclude that the transformation must be linear and the relative velocity to be ##v## to further reduce it somewhat. Then he first assumes ##t' = t## to get the Galilei transformation and later that ##c## is invariant to get the Lorentz transformation. (This is what he does in "Introduction to Special Relativity", I do not know what he does in "Relativity: Special, General, and Cosmological".)vanhees71 said:Interesting. I should read Rindler's book in more detail.
I would strongly disagree about TD and LC. We are witness pretty much daily here to casualties of that approach. You end up with people who don't know what (me or you) is dilated, think that clocks really change their speed, and try to do SR and GR problems with Newtonian equations and ##\gamma##.Orodruin said:Certainly, that practice should be frowned upon. A common way of a more "light" introduction is to first derive time dilation and length contraction and then use them to derive the Lorentz transformations using different constructions. We do it that way in an introductory online course that I developed for the department a few years back.
m4r35n357 said:... which enables the "tricky" stuff like TD, LC to be postponed (perhaps indefinitely, as they are rarely used to calculate anything but muons!)