DanMP

I'm sorry to disappoint you but what I posted was a theory (not experiment) about waves of light through a medium, not single photons passing through slits, so I don't think it can support your "theory". Indeed. The reason I posted it was the fact/idea that many physicists are not really interested in "how is energy conserved" ... But they should be. You can't create photons/energy without consuming/absorbing an equal amount ... According to wikipedia so, if "The charges thus radiate their own electromagnetic wave that is at the same frequency" and "The light wave traveling in the medium is the macroscopic superposition (sum) of all such contributions in the material: the original wave plus the waves radiated by all the moving charges", the resulted wave (the sum) appears to "contain" more photons than the original/incident wave but, as I wrote above, you can't create photons/energy without consuming/absorbing an equal amount, so something is wrong ... What is wrong? [This is a bit off-topic (sorry!), so maybe we should move it (and continue) in another location.]

This is a good point, in my opinion, but the microscopic explanation of how light is slowed in transparent materials suggests that new photons do occur (when we have a wave of light, not one photon at a time): and nobody seem to be bothered abut "how is energy conserved?" ... (Many physicists were more bothered by the fact that I asked the question: see 1, 2, 3).

Ok what you did wrong was not the actual swapping, but the fact that you didn't notice that the notations were different. In your LT calculation (not derivation, sorry) S' was moving to the right, while in the geometrical calculation, S was moving to the right, as you can understand from the picture and its caption: As I wrote above, in order to compare the results, you have to keep the same scenario/notations, because (unfortunately) the notations are not the same everywhere, as you may see also in other 2 examples/derivations: https://www.amnh.org/learn/pd/physical_science/week3/time_dilation.html https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/5%3A__Relativity/5.3%3A_Time_Dilation

The formula is the same. The problem is that you swapped the frames. Time dilation is usually calculated for a clock (it doesn't matter if it is a light clock as in your link or any other clock) and from a reference frame. In your LT derivation the clock was static in the origin of S' (the condition was x'=0), while in the geometric calculation the clock was static in S frame (the initial x' was different than the final x', while x was 0 all the time). So, in order to compare the results, you have to keep the same scenario/notations and to swap t' with t in one of the calculations.

The above shows (correctly) that for "SC1: x' = 0, x = vt", when the primed clock (consider it a light clock) is in the origin of the S' frame (x'=0), moving with the speed v away from the origin of the S frame (x=vt), Lorentz transformations yield: t'= t/γ (where t' and t are in fact Δt' and Δt, time intervals from the moment t1'=t1=0 when x1'=x1=0). On the other hand taken from: (more precisely https://en.wikipedia.org/wiki/Time_dilation#Velocity_time_dilation) is valid for x=0, not for x'=0 as in "SC1" (where x' and x are in fact Δx' and Δx), so t and t' are swapped ... This is the origin of the "error". In fact Lorentz transformations are correct, as we all know.

Ok, thank you! I apologize for insisting with this question.

I'm sorry but it was you who insisted to talk about that particular derivation : I referred to your source, so I'm not really off-topic. Sorry anyway, I just wanted to understand it better. When I wrote "you", I meant:

The origin of the confusion(?) is not really Jan Slowak, as you can see in the pdf offered here. This is odd, because it is the second time I posted this question in this thread. First time was yesterday. So, again, why v'=v (in value, because in fact v'=-v)?

It is also unbelievable that you don't have an answer to my question. I'm still waiting ...

Yes, but when in S' we write x' and t' ... Why not also v'? The speeds are not seen/measured identical from different frames, so why this time v'=v? [This question is addressed to all the participants in this thread, not just to Jan Slowak.]

After I wrote the above (something you may have considered redundant/obvious) I wondered why v is the same, I mean when x' = 0, x = vt but when x = 0, x' should be -v't'. Why v' = v ?

In the above quote (with y = mx + b) you are right, those two problems have nothing in common, but in the first quote (with x' = Ax + Bt) the "problems" are not independent, they are about exactly the same thing seen from different perspectives (different frames). When x' = 0, x must be vt, because at t=0, x' = x = 0 and the "x' frame" moved with the speed v. In the "Special Case 2", where x = 0, x' must be -vt', for the same reason. This is not random as in your example (SC1: x = 0, y = 5 and SC2: y = 0, x = 0). [I'm not absolutely sure that all I wrote is correct, but I think it may help.]

So I need to buy the above article in order to see how you(?) explain the Sagnac effect through optical fibers, where the speed of light is c/n?

If it really is "global/generalized", you must also take into consideration (and deal with) the cases where n, the refractive index, is greater than 1 (e.g. when light is traveling through optical fibers, with the speed c/n). Did you? Maybe it is (as I wrote in this here forum), but it is very well explained using special relativity, as you can see here.

Few indications towards my approach are mentioned in my Fizeau/Sagnac explanation. Maybe we should move & continue the discussion there, although I think it can wait. By the way, the F/S explanation is valid, no matter who (the electron in the atom or the atom/molecule as a whole) does the "absorption"+emission. Maybe I'll get back to this subject and answer your questions in a dedicated thread (my theory about the nature of light), but only when I'll finish with the main subject here. Regarding the above discussed proprieties/behavior of DM particles, take them as defined like that. If the theoretical tests I mentioned above will confirm my predictions, then I'll get back to the subject. Until then it would be a waste of time. As I said to Strange, let's wait for my new input (theoretical tests). Maybe they'll prove me wrong ...

Why not? My Fizeau/Sagnac explanation is correct (see the math), consistent with the observations and useful in understanding how photons travel through matter. In the beginning it was included in this theory, but I decided to split them. You like it or not, dark matter will change many things/theories. The above is only the tip of the iceberg ... I have much more. And this is the way to do it, step by step, but interconnected, consistent with each other and with observations. I wrote in that conversation enough. Just read it. In short: the idea that the atom as a whole is absorbing the photon and then it transfers the energy to one electron in the cloud (in order to raise it to a higher orbital) implies that the energy can be shared to more than one electron, and this wasn't, in my opinion, really demonstrated. On the other hand, if you read my Fizeau/Sagnac explanation, you may see why I think that individual electrons in the electronic cloud are receiving the photons and then absorb them (together with the rest of the atom) in a trial and error process. When I say "together with the rest of the atom", I mean that momentum (and some energy?) may be transferred from the receiving electron to the rest of the atom by virtual photons, as you can read in Wikipedia: Absorption + re-emission is something different than electromagnetic interaction. It doesn't necessarily imply electromagnetic forces. In Compton scattering there are such forces, that's why a charge or a magnetic moment is needed. Remember "2. Scattering cross section" and the magnetic moment/field? In my opinion, the photon, with its electromagnetic field, can reject a charged particle (Compton scattering) OR it can attract it or just neither of two (the absorption). With a neutral DM particle it would be always absorption, promptly followed by re-emission, due to conservation laws. That's why DM is "dark" (invisible, perfectly transparent).

Yes, technically the atom absorbs/emits the light, but, as you may see in this conversation, I think that the electron in the atom receives the photon and then absorbs its energy and momentum together with the rest of the atom. More about my reasons for this approach you may find in my other "speculation". I didn't know about "Neutron-photon scattering in the early universe" and I began to read the article you offered. Please read "2. Scattering cross section" and see that it is about magnetic moment/field ... Why should a DM particle have an magnetic moment? This wouldn't imply interactions with normal matter? I don't have time to read more, at least not now. Thank you anyway for the link. I found in wikipedia that: That's why, in my opinion, we can have Compton-like scattering off neutrons, like we have off electrons, but we can not have Compton-like scattering off DM particles.

You didn't accept my answers (e.g. math is the same, at least for Lorentz transformation, when the invariance of c is explained instead of postulated) so, I agree, it would be pointless. Let's wait for my new input (theoretical tests). Maybe they'll prove me wrong ...

The "existing definition"? Really? Important is to be consistent with observations, and I think my model is. Because DM particles are neutral, unlike electrons in atoms, where we have both absorption/re-emission and Compton scattering.

You should know (you read the material I posted here, while they didn't, because they don't accept "speculations", nor links to them) that my theory is not really similar to Lorentz Ether Theory. I didn't invent dark matter ... And my gas-like DM model is not physically impossible, as you may see in the link above. I don't think that my theory is a waste of time. A waste of time, and money, may be the mainstream approach to understand/detect dark matter ... My theory can be fairly easy tested, and not only practical but also theoretical, as you could see in the first prediction. I have ideas for more such tests, as you may see soon.

Beecee, thank you for your interest in my theory. You found it "superfluous at best and totally contrived at worst", but this may change with time. Einstein relativity was hard to grasp/accept to many people, and still is, after more than a century ... Experimental confirmation imposed it, and this may also be the case for my theory ... I asked "expert opinion of others" from another forum, regarding the change in math if the invariance of c is explained instead of postulated, and they backed my opinion, so my theory may be as valid as Einstein's, because the math is the same. I'll be back with more input, after I'll study the material offered here. From what I read so far, gas-like DM seems a good idea ...

I appreciate that you replied, but your input is not quite what I expected, especially the last part, with you own "theory" ... I think I covered this problem where I wrote: Thank you Strange for your input. What do you think about my "Classical explanation for the Fizeau experiment & for Sagnac effect in materials" above? I thought that you would like it, because:

There is DM there, between gas particles, but not able to refract ("gravitational lensing"). There are no DM layers of increasing densities, like around a galaxy, or a star. Yes. We know that already. That is one of the many reasons why your idea can't work. If weak interactions are possible, DM particles can collide, almost like gas molecules in air, resisting to compression. Remember that closer to the massive object the speeds are higher, due to the conversion of the potential energy in kinetic energy. The atom is not an elementary particle ... Again, not magic, just physics. Ok, thank you very much. Also thanks for the information you provided, for your time and for your interest.

You did, as you can see in Wikipedia: Two in one strike 1. DM traveled with the stars of the galaxies, being near (possibly coincident with) the visible galaxies. In my model DM atmospheres travel with massive objects (stars, planets) ... 2. DM particles are weakly interacting.

It does happen. One particle alone cannot absorb a photon. See here why. If in the "equation": x = y + a + 1 , a is postulated as being 2 or derived/explained as being 2 (from 1+1), the equation is, in both instances: x = y + 3 (I hope you agree). How it could be different? Of course, the GR math is much more complicated, and it involves geometry, but still, if this is the only change (and it is, mathematically speaking) the math and the results are the same. There is no Lorentz violation. Ignore gravitational potential/time dilation, by considering the satellite as flying at the same level with the clock at the pole. The clock on the satelite would fall behind the clock on the ground, as we know from H-K exp., so we can tell which clock was moving. If this is so, please show the mathematical proof. I did. You do. Why should I? I entered the forum today, mainly to say that a simulation (regarding the DM density around a galaxy) is not an absolute proof. It is just an indication. There are probably dozens of competing simulations, with different input parameters, all more or less consistent with what we observe (as there are more, competing, Big-Bang theories). There is always possible to make yet another simulation with good results. Another indication, for me, is how the distribution of DM should be, in order to be consistent with observations ... and it seems to fit my model. By the way, it is possible that the simulations are meant for galaxies just because we only have enough observational proofs for galaxies (inferred from star rotations) ... and not because a similar distribution is not possible around any other massive object ... Because the haloes formed over millions of years at the same time as the normal matter condensed to form galaxies. There is no mechanism to slow dark matter enough to form small scale structures. (Collisionless and dissipationaless, remember.) So younger galaxies are not having the same or similar DM distribution as the older ones? For me it's enough to have increasing DM densities from outside towards the gravity center. I don't know if collisions are important or not to my model. On the other hand, DM particles are having mass, so if they have no volume (point-like), they would have infinite density ... This is nonsense. So they probably have volume and collide.