joigus

Thank you, @Genady. I must confess I didn't see your argument back then. If anything, the fact that we both concur on the same argument makes our case only more poweful.

A little bit more for you to ponder about, Mr. @Abouzar Bahari. You might want to take a look at, https://www.amazon.com/Theory-Application-Physical-Problems-Physics/dp/0486661814 The fact that the transformations are symmetric --in the sense you mean them not to be-- is not an exclusive property of Lorentz transformations. AAMOF, Galilean transformations must comply with the same property you are in denial of. So, for slow velocities v, your argument is in trouble too: \[ x'=x-vt \] \[ ct'=ct \] \[ y'=y \] \[ z'=z \] So, even Galilean transformations are inconsistent with what you say. There is a powerful theorem that guarantees that the only relativity principles that can be consistent with a F=ma (second-order evolution equations) formulation of dynamics are the Galilean principle of relativity or the Einstein principle of relativity. I rest my case. Or do I?

Agreed. Interesting, at the very least. P(N)=И P2(N)=N => P2=I Is there an anti-nothing? I mean, an anti-nothing worth distinguishing from the usual nothing? Always do. Irrespective of how much respect they deserve. They're there for a reason. Plus... people can be touchy. Arguments are not.

You do not understand what parity is. Parity is an involution, by definition. That is P2 = I. That's because, if you change the sign of the coordinates, and then you change it again, you must get back to where you started. Lorentz transformations, OTOH, are not. There is no reason why Λ2 should be the identity. Every symmetry transformation should be a representation of a group, for consistency. So Λ(v)Λ-1(v)=I. As it happens, Λ(v)Λ(-v)=I, so Λ-1(v)=Λ(-v). End of story as to the mathematics. If you are willing to present an experiment that contradicts this mathematics, that would be great. https://en.wikipedia.org/wiki/Involution_(mathematics) Are we done here? Another thing, Mr. Bahari. You can keep giving neg-reps every single time I take pains to explain to you why your idea cannot be right, if you are so inclined. I would like to see a reason why you're doing so, other than you thinking I'm 'illiterate.'

It's the standard dummy number, maybe it stands for 'Nature,' maybe it stands for 'nothing'... I stand for nothing. I like it.

What makes you think that's the relevant question, and not: "The table consists of the lower atoms of the apple? Distinctions are in our mind. Our most sophisticated distinctions are in our theories. Nature doesn't know about them. A hydrogen atom in the apple's molecular structure certainly doesn't "know" whether it's apple or table. Ultimately, there is no meaningful way to say "this hydrogen atom is an apple atom." Distinctions are in our mind, Nature doesn't know about them. Isn't this philosophy?

reported as well. Are you reporting yourself? No wonder you can't handle a sign inversion.

LOL. Cats are known to collapse wave functions. That's their job in this world.

I agree with main arguments developed by @Genady, @studiot, and @Lorentz Jr. I particularly liked Studiot's summary. I would call his argument about closed and open sets --as well as those that are neither open nor closed-- a "topological approach." A crash course in topology would include concepts such as, Topology: Existence of an inclusion relation in a set, \( \subseteq \) --contains--, \( \subsetneq \) --does not contain. => neighbourhoods of a point. Limit point --o accumulation point--: A point in a set that has neighbouring points also in the set that are arbitrarily close to it. Interior of a set: All its point are limits points of the set --if I remember correctly--. Boundary of a set: The set of all the limit points of its exterior Closure of a set: The union of the set and ist boundary ... etc. With these rigorous topological definitions, when applied to the real numbers, we can prove they constitute a topological space, and, eg, the set \( \left[0,2\right]=\left\{ x\,\textrm{in}\,\mathbb{R}\,\textrm{such that}\,0\leq x\leq2\right\} \) contains its boundary --and it is, therefore, closed; while the set, eg, \( \left(0,2\right)=\left\{ x\,\textrm{in}\,\mathbb{R}\,\textrm{such that}\,0<x<2\right\} \) does not contain its boundary --and it is therefore, open. https://en.wikipedia.org/wiki/Topological_space

c can have any value you want just by choosing the length and time units accordingly, as @Eise told you. Stop blaming your misunderstanding on others. I also told you.

-1. You would be well advised to stop insulting people and clean up your own house. Neither one of us is "dominant in the world of science." As to you, you are nowhere near the world of science. Reported.

It's a good start for General Philosophy though.

Owls are amazing in this particular department. http://www.instantshift.com/2014/12/12/hidden-camouflage-owls/

My most heartfelt respect. On my part: FSM is no vice-anything. It reigns supreme over all things, real and unreal. It swallows nonsense and spits out nonsense too, only funnier. What do you wish to discuss?

I don't know what you mean by "it's a physical parameter, and not a mathematical one." A physical parameter, in the usual sense of the term, most definitely it is not. A physical parameter is any quantity that we can vary either freely, or subject to some specified conditions. Eg, the magnetisation of a medium of given magnetic susceptibility, etc. In the context of relativistic physics, c is a universal constant, not a parameter. Theoretically, it is derived from principles of electromagnetismf. Experimentally, it is measured. If you mean otherwise, you should say so. Because I've been studying these things in excruciating detail for many years, I can tell you you're using the poor-man's version of boosts. The grown-up version of it is, \[ \boldsymbol{x}_{\Vert}'=\frac{\boldsymbol{x}_{\Vert}-\boldsymbol{v}t}{\sqrt{1-v^{2}/c^{2}}} \] \[ ct'=\frac{ct-\boldsymbol{v}\cdot\boldsymbol{x}/c}{\sqrt{1-\left\Vert \boldsymbol{v}\right\Vert ^{2}/c^{2}}} \] \[ \boldsymbol{x}_{\bot}'=\boldsymbol{x}_{\bot} \] Where you have to decompose position 3-vector \( \boldsymbol{x} \) as, \[ \boldsymbol{x}=\boldsymbol{x}_{\Vert}+\boldsymbol{x}_{\bot} \] \[ \boldsymbol{x}_{\Vert}=\frac{\boldsymbol{x}\cdot\boldsymbol{v}}{\boldsymbol{v}\cdot\boldsymbol{v}}\boldsymbol{v} \] \[ \boldsymbol{x}_{\bot}=\boldsymbol{x}-\boldsymbol{x}_{\Vert} \] So the expression in the numerator is actually not a positive 3-scalar, but a 3-vector projection in some inertial frame. You don't understand anything, and what's worse, you don't ask. So Markus's noble attempt to help you, my attempt to close down possible loopholes, and other members' attempts to walk you through the logic of Lorentz transformations, is --most unfortunately-- to no avail. Pitty. Good day.

β=v in any system of units such as light-years per year, light-seconds per second, etc. That is, any system of units in which c=1 . I thought you understood that, @Abouzar Bahari.

LOL. Yeah, on second thought that's not that clear, what I said. Sometimes I say things just to see how people react. I suppose you need to probe the other one somehow. Especially online, where a lot of usual clues are missing.

Yes, exactly, @Genady and @sethoflagos. Consciousness, we don't know what that is. In particular, we don't know whether it's an emergent phenomenon or there is perhaps basic physics we still don't know about involved in it. So it might be a bit adventurous to try and guess whether it makes a case for reductionism or not. On the other hand, things like Zipf's law: https://en.wikipedia.org/wiki/Zipf's_law IMO make a good showcase --if not a robust case-- for non-reductionist elements having to do with patterns we see across different phenomena. The explanation, it seems, is purely statistical. If that's the case, one could argue that it doesn't matter too much what constituent elements the ensemble is made of, and regularities appear because of the clustering of data for which the underlying law can be very different in nature. Very similar to the linear power law between internal energy and temperature in ideal gases, with specific gases having different specific heats depending on whether the molecule is monoatomic, diatomic, etc. => A statistical reasoning that gives you a pattern irrespective of the reductionistic model, but a concrete microscopic model that completes the parametrics of the problem --typically the constants. The question is not an easy one in general. There are cases --like the power law between metabolic rate and mass of a multicellular organism-- where the power law can be guessed at from some kind of reductionist first principles. See, eg, https://www.science.org/doi/10.1126/science.276.5309.122 Of which there is criticism too.

It's OK. There's a way to hold your own proudly in these anti-reductionist times. Just say you're a reductionist, only not just a naive reductionist.

Reductionism has been very heavily criticised in science in the last decades. One good reason for this is that there are emergent aspects of natural laws that seem impossible to fathom by simply looking at the basic law and its constituent 'parts.' For example, in recent decades there's been a lot of discussion about universality of certain power laws, which would occur no matter what constituent elements make up the 'stuff.' If such were the case, reductionism would take a big blow. I would say the increasing relevance of this concept 'emergence' has a lot to do with why increasingly scientists are crossing out their names from the list of devotee reductionists.

Oh, boy. I'm speechless, speechless I tell you. Nice touch. So do I. I'm going nowhere in no time.

Fingers crossed.

In a nutshell, it is the contention that you can understand a system by analysing its parts and the relationships between them. Assuming that it makes sense to consider it as made up of distinct parts, that is. https://en.wikipedia.org/wiki/Reductionism

I'd say that given that both \( \omega_{\textrm{Earth}}R_{\textrm{Earth}}\ll c \) --slow-rotating Earth-- and \( \frac{GM_{\textrm{Earth}}}{R_{\textrm{Earth}}}\ll c^{2} \) --not very intense gravitational field--, you're quite safe using Lorentz transformations that factor out into a boost --jump to a constant-velocity frame-- and a slow rotation. For finer effects you would want to consider GR --Lens-Thirring effect, and such. Does that answer you question?

Now that I think about it, it's also dangerous when you're in a Euclidean context too.