In this post there are a lot of references to the previous one – it is essential that you read it before getting down to this.
In my previous posts (see the list below below) I tried to express my doubts whether there is a real physical substrate to the Lorentz transforms. The assumptions about the constancy of the speed of light, the homogeneity of space-time, and the principle of relativity do not and cannot lead to the deduction of the Lorentz transforms – Einstein himself, for one, gets quite different transforms, and from those he goes over directly to the Lorentz transforms obviously missing a logical link (see Einstein p. 7, and also Part 1 of this discussion). As for the light-like interval being equal to zero, we saw that it can be attached to such assumptions only in error and cannot in itself be a foundation of a theory. I have to conclude that all that fine, intricately latticed construction of scientifictitious, physics-like arguments with the air of being profound is nothing but a smokescreen creating the appearance of a physical foundation while there is none.
What is then the real foundation of the Lorentz transforms? Let’s start from the rear end, the Minkowski mathematics. Historically, this appeared later than special relativity as a non-contradictory model of the Lorentz mathematical world; previously mentioned Varićak was among those who took part in its creation. Notwithstanding its coming later in history, it can be used as the starting point for derivation of the Lorentz transforms.
Let’s Discuss the Lorentz Transforms – Part the Last: The Real Derivation, or The Nail in the Casket
Я администрирую серверы на базе Astra Linux и хочу рассказать о своем видении настройки ALD домена: серверной части, клиентской, использовании файла hosts (по сравнению с DNS сервером). Также дам описание настройки резервного сервера.
ALD мне интересен в первую очередь потому, что уже имеет интеграцию с Astra Linux. Статья будет вам полезна, если вы собираетесь узнать больше о Astra Linux не только из официальной wiki. Кроме того, эту операционную систему (вместе с рядом других решений компании «Астра») смогут поставить на виртуальную машину клиенты публичного облака #CloudMTS.
Настройка домена ALD в Astra Linux
I thought my previous post rather funny, and was surprised seeing it initially receive so few views. I thought the entertainment flopped, but fortunately I was wrong. I therefore feel it my duty before my readers to address the subject of the Landau & Lifschitz proof of the invariance of the interval.
You can find the summary of it in Wikipedia. Making their starting point the light-like interval always being equal to zero, Landau & Lifschitz seem to make a great fuss about it. The Wikipedia article even says: ‘This is the immediate mathematical consequence of the invariance of the speed of light.’ No, it is not.
I beg everyone’s pardon, but the light-like interval always being equal to zero is nothing else but the following statement: ‘The length of a ray of light will always be equal to the length of this ray of light’. Sounds like a cool story, bros and sis, but I cannot see what further inferences can be drawn from it. The ‘proof’ of this truism cannot fail under any circumstances whatever – whether you keep the speed of light invariant, or keep or change the metric of space or time or both – or make both metric and speed of light change – the light-like interval will remain equal to zero. I am okay with anyone wanting to prove it if they feel like it, but you cannot make it an ‘immediate mathematical consequence of the invariance of the speed of light’. Neither is it possible to make the constancy of the speed of light a consequence of the invariance of the light-like interval for the reason already mentioned: this is a truism. It does not prove anything, nor can it be a consequence of anything. When Landau & Lifschitz insist that this is a consequence of the constancy of the speed of light, that is either an error or a downright subterfuge, a means employed to create a spectre of logical connection between two unconnected notions, and charge this ghostly connection with pretended significance. And, since the following proof of invariance of an arbitrary interval hangs on the invariance of the light-like interval, we can altogether dismiss it: the necessity of introduction of such a measure as interval cannot be derived from the statement that a length of something will be equal to itself in whatever frame of reference it is measured.
Let’s Discuss the Lorentz Transforms – Intermission: Rapidity, and What it Means
The previous discussion done, we have surmounted the difficult waters and are now sailing into something much more pleasure-like and hopefully even entertaining.
As I promised, we will be discussing the invariance of the interval, that is to say, the following relation:
Let’s Discuss the Lorentz Transforms – Part 2: The Equation of the Sphere, or Is It?
This question comes up for a lot of us as we trying to advance our career and reach new heights. At the moment when I was challenged by it, I came across a wonderful book by Edmond Lau «Effective Engineer».
As always going through the book, I write new thoughts down. And today I want to share the compilation of things that I have found useful from the book. This is by no means an ad for the book, but I think it has some really interesting approaches for us to explore together.
How to be an effective engineer?
Even as I am posting this, I can see that my previous post received a hundred and twenty plus views, but no comments yet. I am saying again that my pursuit is not to give an answer, but to ask a question. I only wonder if there is in fact no answer to the questions I am asking – but anyway, I will continue asking them. If you know how to deal with the problems I am setting – or happen to understand they are not problems at all, I will be most grateful for a constructive input in the comments section. I am sorry to say I was unable to make this post sound as light and unpretentious as the previous one. This one deals with harder questions, is a little wordy, and requires at least elementary knowledge of calculus to be read properly.
In my previous post we discussed the ‘Galilean’ velocity composition used for introduction or substantiation of relative simultaneity. It is not the only point where Einstein resorts to sums c + v or c – v: he does that actually to deduce the Lorentz transforms, notwithstanding the fact that a corollary of the Lorentz transforms is a different velocity composition which makes the above sums null and void. It looks like the conclusions of this deduction negate its premises – but this is not the only strange thing about Einstein’s deduction of the Lorentz transforms undertaken by him in his famous 1905 article.
In Paragraph 3 of that paper Einstein is considering the linear function τ (the time of the reference frame in motion) of the four variables x′ = x – vt, y, z, and t (the three spatial coordinates and time of the frame of reference at rest) and eventually derives a relation between the coefficients of this linear function.
Let’s Discuss the Lorentz Transforms – Part 1: Einstein’s 1905 Derivation
Testers and developers are the driving force of any IT enterprise. Their work directly influences the quality of the final product. Pavel Petrov, our Lead tester-engineer of the risk detection monitoring service for corporate clients, shares his insights on building a productive relationship between two different IT camps.
[Translation] What causes testers and developers to feud and how to avoid it
There is one only too obvious problem with relativity of simultaneity in the way it is normally introduced, and I have never found an answer to it – what’s more, I never read or heard anyone formulate it. I will be grateful for an enlightening discussion.
The framework of the thought experiment introducing relativity of simultaneity is this. Two rays of light travel in opposite directions and reach their destination simultaneously in one frame of reference and at different moments in the other.
For example, in the Wikipedia article on the subject you can read:
‘A flash of light is given off at the center of the traincar just as the two observers pass each other. For the observer on board the train, the front and back of the traincar are at fixed distances from the light source and as such, according to this observer, the light will reach the front and back of the traincar at the same time.
‘For the observer standing on the platform, on the other hand, the rear of the traincar is moving (catching up) toward the point at which the flash was given off, and the front of the traincar is moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times’.
I am always not a little surprised at the modesty displayed by the authors of such illustrations. If we grant the statement ‘the light headed for the back of the train will have less distance to cover than the light headed for the front’ to be true – how then do we evaluate the magnitude of the effect? Or, in other words, how much longer is one distance in comparison to the other?
Let’s Discuss Relativity of Simultaneity
e-Learning is an extension of/ alternative to a traditional classroom setup. e-learning, commonly known as ‘online learning’ or ‘virtual learning’ is ideally a one-way or two-way digital communication established on a device with video and voice call integration using internet access. The last two years made us realize how technology can facilitate and improve communication. Digital technology had its impact in almost every industry including the sensitive education sector.
How in-app chats help e-learning platforms to be more interactive?
I wonder why IT developer interviews are so strange most of the time. It feels as if the people are looking for computer science teachers, not engineers. All those theoretical questions that have no relation to the working reality. It is strange to be looking for eloquent teachers, who can perfectly explain any term or pattern, and then ask them to do the actual work. Maybe it is the imprint from the years spent in university when the teachers looked like all-knowing gods and seemed to solve any issue in your life. May be, may not. Anyway, these teachers stay in unis and don’t do the work.
You know, what would be my universal answer to all interview questions? “I have no idea how and why it works, but I can use it, and I can use it for good”. This is the reality. Actually, no one knows exactly these hows and whys. What is a computer? What is electricity? What is an electron? No one knows for sure. But it works and we use it.
Imagine a famous author, like Stephen King, asked a question about the difference between deus ex machina and Mary Sue. Would his answer change the quality of his books? He may or he may not know all those scientific literature terms, but he can use the language and use it for good.
Every time I turn on my computer it is a wonder. I have no idea what is going on, but it awakes, it becomes alive, and I can communicate with it in its own sublime and subtle language.
Have you ever realised that all these electronic devices are monsters, Frankenstein’s monsters? Some pieces of dead matter were put together, and then, with some electricity involved, it suddenly awoke. “It’s alive!”. Had Frankenstein any idea why it turned alive? Of course not, or why he was so surprised? Every developer experiences this feeling almost every day. “It’s working!”