How to explain Einstein's Special theory of Relativity.

tensor33

The time equation of SR is LT. the lorentz transforms are a set of equations for transforming from one reference frame to another. They are a part of SR.

John Huang

Thanks. Do you think the "time dilation equation" is the solution created by Einstein?

No one else mentioned about it, right? At least I don't know who else mentioned about it. That is why I assign that solution (the time dilation equation) as the main purpose of SR.

John Huang

If you think LT is part of SR, that's fine. Now, we have two "time dilation" equations.

As I know, SR can be used for two systems with constant relative speed; however, in case of constant relative velocity SR should be correct as well. I mean, in cases of constant relative velocity, should I use LT or SR? Do you have website where I can find the answer of it? Thanks.

Vorde

There is a lot in SR. The Lorentz Transformations were a set of coordinate transformations that Lorentz first developed with regards to electromagnetism. It was Einstein who first used them to describe space itself, and the time dilation and length contraction equations come directly from the lorentz transformations.

You keep saying that LT and SR are seemingly two distinct things, which is completely wrong. The Lorentz Transformations are a part of SR. To ask whether to use Special Relativity or the Lorentz Transformations is like to ask whether to use Newtonian Mechanics or Newton's Second Law; the question doesn't make sense.

tensor33

I'm not quite sure I understand your question. When you say "Should I use LT or SR?", it makes no sense. It is my understanding that LT is a part of LR. There is no need to choose between the two.
Maybe if you gave me an example of what you consider to be an equation of SR and an equation of LT I would better understand your question.

Mentz114

The changing of the term 'velocity' and 'speed' makes no operational difference. Speed is defined as s = √(v_x²+v_y²+v_z²) where the v terms are the magnitudes of the x,y and z velocities. It is always possible to rotate the coordinates so only one component is non-zero in these coords.

What difference do you think it makes ?

DaleSpam

In that section he clearly derived the LT from his two postulates. Therefore, the LT is part of SR, and has been from the beginning of SR.

In section four he derives the time dilation equation from the LT with the additional restriction that the other clock is "at rest relative to the moving system, to be located at the origin". I.e. That is the only time that derived formula applies.

Can you explain in playing football why you should use your leg, not your foot?

Please re read the 1905 paper. Clearly he includes more than just the time dilation equation. So for you to make this statement is absurd. Furthermore, going beyond Einstein, SR now includes also Minkowski's spacetime, and even pseudo-Riemannian geometry on flat manifolds.

DaleSpam

No, you have the LT which simplifies to the time dilation equation under specific circumstances. When the circumstances match then you can use the simplified equation or the LT equally since they agree. When the circumstances don't match then you cannot use the simplified equation since it doesnt apply.

John Huang

That is the best answer I have received so far. Thanks. Do you mean, only when x'=0 we can use SR, otherwise, we should apply LT?

John Huang

With constant velocity, LT works for inertial systems only; with constant speed, SR can expand to circling or any kind of constant speed situation.

John Huang

According to # 42, my understanding is that SR is part of LT. What do you think?

John Huang

For example, if we focus on the events happen at the origin point of the stationary system, the point O, then we will have x=0. If LT is part of SR, then, both of the time equations in LT and SR should apply and under this situation, the time equations are inverse. Which one should apply?

Doc Al

Realize that in common usage SR means "Special Relativity". The LT is part of SR, of course.

You seem to be using "SR" to mean the time dilation formula, which is a special case of the LT (as has been explained). Your non-standard use of "SR" is creating some confusion.

Doc Al

If you want to convert measurements from one frame to another you can always use the LT. In certain cases the simplified 'time dilation' formula can be applied.

In this example, since the events in question all take place at x = 0, you can convert the time between them (Δt) to the moving frame (Δt') using the time dilation formula: Δt' = γΔt. But that's just an application of the LT.

What's your point?

DaleSpam

No, I mean what I said. The LT is part of SR. The time dilation formula (which is part of the LT) only applies when x'=0.

You continue to identify SR with only the time dilation formula. That is simply WRONG.

DaleSpam

No, you have this backwards. The LT is part of SR.

I think there is some language barrier. Perhaps this will help:
[itex] SR \supset LT \supset time \; dilation [/itex]
[itex] SR \neq time \; dilation[/itex]

John Huang

My point is a logical issue.

In above example, two systems have constant relative velocity so that the speed of time in the moving system t' and the speed of time in the stationary system t should be decided once we select the point O as the stationary point, and the O' as the moving point. Under this SPECIFIC arrangement, when we talk about a period of time for ONE SPECIFIC EVENT then we should have ONLY ONE event period Δt as recorded in the stationary system and ONLY ONE event period Δt' as recorded in the moving system.

Now, what SR claims is Δt' = Δt/γ and what LT claims is Δt' = γΔt for the ABOVE example. Logically speaking, this should not happen UNLESS γ=1, isn't it? How do you explain this logical issue?

If you like the event to stay in the moving system, then you may let x'=1.