How to explain Einstein's Special theory of Relativity.

DaleSpam

This is essentially correct. The standard term for "story" is "worldline".

For pedagogical reasons my recommendation is always to follow your last suggestion which I highlighted in bold. It automatically simplifies to the time dilation equation whenever it is appropriate and it avoids accidentally using it when it is not appropriate.

DaleSpam

SR still includes the LT. A specialized simplification of a general equation does not in any way invalidate the general equation.

John Huang

Thanks for your correction. Now, I will rewrite my sentence.

How do observers everywhere in the stationary system S measure the "time period" Δt of ONE SPECIFIC SECTION of continuous events from event 1 at point A to event 2 at point B? They use the synchronized stationary clocks in S. For the observers everywhere in the moving system S', they will use the synchronized moving clocks to measure the "time period" Δt' from event 1 to event 2. Now, we have a better defined case.

There are two ways to do the measure jobs.

The easy way is to measure event time t1 and t1' for event 1 at point A and measure event time t2 and t2' for event 2 at point B. We will have Δt' = t2'-t1' and Δt = t2-t1.

The difficult way is to measure event time by assigned observers, one in S and one in S'. The simplest assginment is let them stay at origin points O and O'. Let us look at this simplest situation. Since the distances of each pair of four points A, B, O and O' could be different, we must adjust the influence of the distance. When A=B=O', it will be the situation arranged by Einstein. We will have Δt' = t2'-t1' and Δt = t2-t1.

For this SPECIFIC SET of t1,t2, t1' and t2', SR states based on the relative speed "v", the relation of the speed of time in S' and S should be Δt' = Δt/γ, but regarding the "time period", we should go by Δt' = γ(Δt-(vΔx/c^2)). Am I correct?

Yes, "In words, the time dilation formula says that 'moving clocks run slow'." and for relative speed v, the time dilation formula Δt' = Δt/γ stands.

In Δt' = Δt/γ, Δt' is for the time period in the moving system S' of a given SECTION OF EVENTS and Δt is for the stationary system S of the same SECTION OF EVENTS.

John Huang

Thanks.

harrylin

That's much better defined.
OK so you now moved on to two ways of measuring the same interval: the simplest, "local" way of measuring and the indirect or "non-local" way. SR predicts the same for both set-ups; that is necessary for consistency.
Ok, you take here the special case that Δx'=0, just as you did before - correct? And for the LT we choose O=O' at t1=0. Here's a generic sketch of it:

t1................t2
O--------------------- S
A.................B

A,B
O'---------------- S'
t1'
t2'

That is not correct; Δt' = γ(Δt-(vΔx/c^2)) is valid for both; and there is no difference of prediction between using local clocks or distant observers. I copy-paste my earlier reply:

1. For x1'=x2' (Δx'=0, clock at rest in S', moving in S): Δt' = Δt/γ
2. For x1=x2 (Δx=0, clock at rest in S, moving in S'): Δt' = γΔt

Once more: you selected the time period of situation 1, with x1'=x2' and thus Δx≠0.
You should find from the LT that the time period Δt' = Δt/γ for that situation, based on the relative speed v.
If that is not clear to you, please ask.

Doc Al

OK, that's better. But so far you've not placed any restrictions on those events.


OK. I assume by 'easy way' you mean for there to be observers in both frames at the location of the events so that they do not have to account for light travel time. Good.

OK, these single observers must take light travel time into account when interpreting their direct observations. So what? The two methods of measuring the time intervals between those events will give the same answer. (What is your point in mentioning these "two ways"?)
OK, now you have restricted the pair of events to be events that take place at the same location in S'. (At least that's what I think you mean.)

No. You are incorrect in thinking that those methods (using the time dilation formula or using the LT) yield different results.

In this particular case, you can relate the time intervals using the time dilation formula since the events take place at a single location in S'. So Δt' = Δt/γ is perfectly correct.

Or you can use the LT: Δt = γ(Δt' + (vΔx'/c^2)). Since Δx' = 0, we are back to the same result, Δt' = Δt/γ.

Sure, for the simple case in question, the time dilation formula applies just fine. Of course, you get the same result by applying the full Lorentz transformation.

Δt' and Δt represent the time interval between those two events as seen in different frames.

I'm still not getting what your point is. And you still seem to speak as though you think "SR" just means time dilation. There is more going on than that. What about length contraction? What about the relativity of simultaneity? Sure, in certain special cases (like the one discussed here) you can directly apply the time dilation formula. But in general you must include all three relativistic effects. And the LT does that for you automatically.

John Huang

Thanks. Your point is clear.

harrylin

Sorry I did not mean if my point is not clear (although that is also useful to get feedback on), but if it is clear to you how to calculate it.

John Huang

Thanks. I will explain my point in a more spesific way. But before that, let me report what I understand about the history of SR:

1. Most physicists BELIEVED that MMX is not compatible with the Newtonian Space & Time and the Galilean Transformation (GT).

2. Mr. Lorentz SUGGESTED that we might let the moving rulers shrink 1/L(v) along the moving direction so that the distance measured in S' will expand L(v) times and the x'=x-vt ---(1) in GT will change to x'=L(v)(x-xt) ---(2). He then applied the principle of relativity to get the x=L(v)(x'+vt') ---(3) and combined (2) and (3) to derive t' = L(v)(t-(vx/c^2)) ---(4) then estabished the LT. Physicists use γ for L(v) but I like to use L(v) for γ.

3. Mr. Einstein CLAIMED that he proved LT. Then he extended the idea of ruler construction to time. He liked to let a moving clock speed up or slow down. If he let a moving clock speed up then combined with the shrinking rule the speed of an object would be measured the same in S and S', then it would be no fun at all so that he selected to let a moving clock slow down at the same rate 1/L(v), Δt' = Δt/L(v) ---(5). To make the situation even more interest, he did not use the symbol Δ to show the purpose of (5) is for the relation of speed only. Any way, he created SR in year 1905.

4. Mr. Einstein went further, ASSUMED that a clock will also slow down in a stronger gravitational field that dt=1-G(r) ---(6), G is the gravitational potential. Then he created General Relativity (GR) based on SR and (6).

5. Most physicists EXPALINED some observations and experiments to support GR and GR support SR so that SR is established in the 20th century.

I think it is the time to dig into all of the fun and interesting part of SR and eventually remove them. I think we can have fun to apply our knowledge or to make the learning of knowledge easier, but, in knowledge itself, we don't need fun and interest. All we need is to match fact with logic and math.

John Huang

I will explain my understanding regarding the math of SR later.

ghwellsjr

Einstein merely pointed out that if you consider the propagation of light to be c in any inertial state you choose and not just in one illusive inertial state referred to as the ether, then the same LT that was previously discovered to describe how clocks moving with respect to that illusive ether run slower and rulers contract along the direction of motion through that illusive ether, would also work the other way around. In other words, you can assume that any Inertial Reference Frame is just like the illusive inertial ether state and so you don't have to bother looking for that illusive inertial ether state anymore because you will never find it.
I think you're asking to get banned. This forum is dedicated to learning relativity, not fixing it because it's not broken. If you think it is, then it's your own misunderstanding that's broken and needs to be fixed.

DaleSpam

Agreed. Please see:
http://www.edu-observatory.org/physi...periments.html

John Huang

You may name the best experiment you like and I will study it in more detail.

Here is my first logical issue: Two stories of Mr. Time.

Let Mr. Time in the stationary system S of LT. Mr. Time moves from a point A at time t1 to a point B at time t2. I name the case when A=B=O' as story1 and when A=B=O as story2, O and O' are origin points respectively. After observers in S' records the event time t1' and t2' we will have two results.

In the story1, LT supports SR and in the story2 LT supports anti-SR.

We are ready for my first logical issue. If LT can support SR and anti-SR in separate situations then, lopgically speaking, should we say that anti-SR and SR are equally possible solutions for the actual time formula of the nature?

DaleSpam

Any alternative theory must explain ALL of those experiments (as SR does), not just one.

Nonsense. SR uses the LT to determine the answer in both cases. Any contradiction is entirely a figment of your imagination.

No, you are simply confused, despite having been corrected on this point numerous times. Your logical arguments are not arguments against SR, they are arguments against some strawman distorted theory of your own imagining.

In honor of its inventor I name this theory you are discussing "John Huang Theory" (JHT). JHT obviously has problems, as acknowledged by its inventor.

John Huang

That is my purpose here to fix my misunderstanding.

John Huang

Please just show me one experiment and explain it briefly why it is a good one. I will spend time on it. Thanks.

Sorry, I should make the event1 and event 2 easy to recognize, I will let Mr. Time do something at event 1 and event 2 as following:

Here is my first logical issue: Two stories of Mr. Time.

Let Mr. Time in the stationary system S of LT. Mr. Time points his forefinger upward and moves from a point A at time t1 to a point B at time t2 and curls his forefinger. I name the case when A=B=O' as story1 and when A=B=O as story2, O and O' are origin points respectively. After observers in S' records the event time t1' and t2' we will have two results.

In the story1, LT supports SR and in the story2 LT supports anti-SR.

DaleSpam

They are all good, you should spend time on each. At a minimum you need to understand Michelson-Morely, Ives-Stillwell, and Kennedy-Thorndike.

LT always supports SR.

In the story1, LT supports JHT and in the story2 LT supports anti-JHT. JHT has some serious problems.