joigus

You mean shrinking space? Or also time? What about mass, electric --and other charges-- etc? Would they be shrinking in your picture? x-posted with @studiot

This is very deep. If I understood it correctly, it's like what Swansont said about phonons. There are other examples: Defects in a crystal, different 2-dimensional modes that live on the surface between insulators (topological insulators.) These things live in a context: Surface phenomena, modes in a lattice, etc. They are not 'real' in the sense that you can take, say, a phonon and separate it from its context, and study it in isolation from everything else. You can't take any of these instances, isolate them, and study them independently of the embedding context. There are contingencies --I think that's the right word-- that define their 'being there.' If you dissolve the contingency, you dissolve the 'thing.'

I would call it a lemma or proposition --small theorem-- that's easy to prove.

To me, the funny thing about it is that every so often the mathematical model does suggest to us that the previous model in terms of inalienable properties A, B, C, etc. does suggest that we'd better drop say, C, no matter how cherished a property of this 'reality' it is. In QM, this 'C' could be 'position' or 'momentum.' In SR, it could be position and/or velocity, and in GR it could be the concept itself of an inertial system, or coordinates by themselves. For lack of a better term, I would define this as a very ordered process of 'letting go' of anchors to what we think to be real. x-posted with @exchemist Agreed. But I think that's more an over-simplification that some people do when they don't understand time-tested principles like operationalism --the theory should have a counterpart in laboratory operations--, Ockam's razor --the theory should never create arbitrarily complicated constructs, and should be as logically simple as possible; it should produce falsifiable propositions --Popper--, etc. I recognise that as a risk, but I think an acquaintance with some principles of the philosophy of science generally operate as a good antidote. If one is well-versed in the history of science, I think one can minimise the risk.

This is probably the best starting point for this question --no pun intended. If x, y are in R, and x \( \neq\) y. Then, Either x>y or x<y. Assume x<y. A property of the real numbers is there always exists a z in R such that x<z<y if x and y are different. So there isn't such a thing as 'next number' in R. x-posted with @Genady

In the short term, yes. I've got friends who trusted me with their dog every now and then when they were away. I'm told I'm pretty good with pets when it's just for, say, a month, or some weeks. In the long term, no. I can't afford taking care of a pet on a daily basis. Having a pet is an enormous responsibility. It seems like it was yesterday when you mentioned it. CPT symmetry suggests they would. When you include magnetic monopoles in Maxwell's equations, you have both electric charges q, and magnetic charges g. For every particle with charge q there must be the corresponding anti-particle of charge -q. So for every particle with magnetic charge g there should be an anti-particle of magnetic charge -g, or else CPT symmetry would not hold. We think CPT symmetry holds. It would be a total re-think of quantum field theory if CPT symmetry failed. For more details, ask @Markus Hanke.

You're confusing a group with a representation of a group. Any Abelian group can be represented by addition of parameters. Example: \[ e^{x+y}=e^{x}e^{y} \] The Lorentz group is represented multiplicatively on wave functions, but additively on other objects. Again, take a look at, https://www.amazon.com/Theory-Application-Physical-Problems-Physics/dp/0486661814 and it will dawn on you. There's nothing else I can do for you here. I'm sorry my help wasn't enough.

Mr. @Abouzar Bahari, I'm reinstating all the negative points you're giving everybody, just out of spite on your part, apparently. You've already gotten your answers, non-scientifically. Thank you. That's all I wanted to read from you.

I understand you got a new cat. Is that right? I love pets, but I can't be trusted with them. Neither do I. I'm just wondering where we can get from just nothing. Maybe something's in store for us all.

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.