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Let’s Discuss Relativity of Simultaneity

Mathematics *Physics
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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?

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Let’s Discuss the Lorentz Transforms – Part 1: Einstein’s 1905 Derivation

Mathematics *Physics

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.

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Let’s Discuss the Lorentz Transforms – Part the Last: The Real Derivation, or The Nail in the Casket

Mathematics *Physics

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.

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