How to explain Einstein's Special theory of Relativity.

[Dale]

If you limit the x' in the LT to x'=0, you will get x=vt and after you replace the x in the time equation by "vt", then you will get the time equation of SR.

If the x' in LT is not always 0, then the time equation of LT will be different from the one of SR. In this situation, which equation do you go by?

You seem to be under the very incorrect impression that SR is limited to the time dilation equation. This is false. The time dilation equation is a subset of the LT, which is in turn a subset of SR. In the situation you mention you go by the LT since the time dilation equation does not apply.

 

[JonDrew]

Lochlan.h,

If you are still confused a bit try this YouTube site. After you click the link and the webpage loads, click "Browse videos", then once that page loads, click "Playlist" and there will be a whole playlist of videos on one dimensional special relativity waiting for you. They're awesome, I watched them myself.

http://www.youtube.com/user/InvariantSpace

 

[John Huang]

You seem to be under the very incorrect impression that SR is limited to the time dilation equation. This is false. The time dilation equation is a subset of the LT, which is in turn a subset of SR. In the situation you mention you go by the LT since the time dilation equation does not apply.

Thanks for the comment. I know that Einstein also supported LT and he claimed that he proved LT by 2 postulates. Actually I also know that after Einstein introduced his SR in the section 3 of his 6/30/1905 paper, he extended SR from "constant relative velocity" to "constant relative speed" in the section 4 right away. Even with the new expansion, I think SR should continue its support to the situation of "constant relative velocity". So, could you explain why in the situation that {the observed event happened at a location other than O'} we should use LT, not SR?

I think the main purpose of SR is to introduce the time dilation equation. However, if you could show me what else SR has provided to people, I will appreciate and study it.

Regards,
John

 

[Nugatory]

I also know that after Einstein introduced his SR in the section 3 of his 6/30/1905 paper...
I think the main purpose of SR is to introduce the time dilation equation. However, if you could show me what else SR has provided to people, I will appreciate and study it.

You should start with the title of that paper... Einstein introduced Special Relativity to resolve the great unsolved problem of the second half of the 19th century, namely the incompatibilities between Galilean relativity and Newtonian mechanics on the one hand, and Maxwell's theory of electricity and magnetism on the other hand.

 

[tensor33]

If you limit the x' in the LT to x'=0, you will get x=vt and after you replace the x in the time equation by "vt", then you will get the time equation of SR.

If the x' in LT is not always 0, then the time equation of LT will be different from the one of SR. In this situation, which equation do you go by?

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]

You should start with the title of that paper... Einstein introduced Special Relativity to resolve the great unsolved problem of the second half of the 19th century, namely the incompatibilities between Galilean relativity and Newtonian mechanics on the one hand, and Maxwell's theory of electricity and magnetism on the other hand.

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]

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.

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]

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.

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]

Thanks for the comment. I know that Einstein also supported LT and he claimed that he proved LT by 2 postulates. Actually I also know that after Einstein introduced his SR in the section 3 of his 6/30/1905 paper, he extended SR from "constant relative velocity" to "constant relative speed" in the section 4 right away. Even with the new expansion, I think SR should continue its support to the situation of "constant relative velocity".

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 ?

 

[Dale]

Thanks for the comment. I know that Einstein also supported LT and he claimed that he proved LT by 2 postulates. Actually I also know that after Einstein introduced his SR in the section 3 of his 6/30/1905 paper

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.

he extended SR from "constant relative velocity" to "constant relative speed" in the section 4 right away.

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.

So, could you explain why in the situation that {the observed event happened at a location other than O'} we should use LT, not SR?

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

I think the main purpose of SR is to introduce the time dilation equation. However, if you could show me what else SR has provided to people, I will appreciate and study it.

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.

 

[Dale]

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

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 doesn't 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]

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 ?

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]

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.

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

 

[John Huang]

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.

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]

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

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]

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?

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?

 

[Dale]

Do you mean, only when x'=0 we can use SR, otherwise, we should apply LT?

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.

 

[Dale]

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

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

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

 

[John Huang]

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?

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.

 

[tensor33]

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?

I don't know where you got this idea. In SR Δt' = γΔt not Δt/γ. It is the same for LT. That is where your confusion lies.

 

[Vorde]

You are wrong with these equations. In both LT and SR (it seems stupid as I previously mentioned to distinguish between the two like that but I'll cave for argument's sake), $\Delta t'=\Delta t \gamma$. You may be confusing the time dilation equation with the length contraction equation, which is $\Delta L'= \frac{\Delta L}{\gamma}$

 

[Doc Al]

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?

The simple explanation is that you do not understand how and when to apply the time dilation formula. (And please stop saying "SR claims...".)

Events that happen at x = 0 can be treated similar to a clock at that point that is stationary in the unprimed frame. From the primed frame, that clock is moving and obeys the 'time dilation' formula (which is derived from the LT). You'll get Δt' = γΔt no matter how you slice it.

 

[Dale]

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?

The explanation is easy: You made a mistake.

SR claims the same as the LT claims, specifically that in any given inertial frame a moving clock will tick more slowly. Your assertion to the contrary is simply a mistake on your part.

 

[John Huang]

The simple explanation is that you do not understand how and when to apply the time dilation formula. (And please stop saying "SR claims...".)

Events that happen at x = 0 can be treated similar to a clock at that point that is stationary in the unprimed frame. From the primed frame, that clock is moving and obeys the 'time dilation' formula (which is derived from the LT). You'll get Δt' = γΔt no matter how you slice it.

I knew that you might claim the event at x=0 would reverse the moving and stationary status. I also mentioned "If you like the event to stay in the moving system, then you may let x'=1." in my response. When the event happens at x'=1, the time dilation equation of SR remains the same Δt' = Δt/γ but the time dilation equation of LT will include the variable x.

Now, we have a SPECIFIC event happens at x'=1, the SPECIFIC event period measured at two systems, Δt' and Δt, should be SPECIFIC as well. That means, logically speaking, we have three possible answers for this logical issue: 1) SR is correct, 2) LT is correct or 3) both of them are wrong. That is my logical issue. Could you please explain this logical issue? Thanks.

 

[Vorde]

I knew that you might claim the event at x=0 would reverse the moving and stationary status. I also mentioned "If you like the event to stay in the moving system, then you may let x'=1." in my response. When the event happens at x'=1, the time dilation equation of SR remains the same Δt' = Δt/γ but the time dilation equation of LT will include the variable x.

Now, we have a SPECIFIC event happens at x'=1, the SPECIFIC event period measured at two systems, Δt' and Δt, should be SPECIFIC as well. That means, logically speaking, we have three possible answers for this logical issue: 1) SR is correct, 2) LT is correct or 3) both of them are wrong. That is my logical issue. Could you please explain this logical issue? Thanks.

You are not listening to the rest of us. You have your equations wrong, and you are going to continue to be wrong until you acknowledge and fix that. I don't want to repeat what has been posted already by several people, so I would go back and read their posts. Furthermore, it seems you are confusing the time dilation equation with the lorentz boost in the time dimension, which are two separate (not competing) equations.

 

[John Huang]

You are not listening to the rest of us. You have your equations wrong, and you are going to continue to be wrong until you acknowledge and fix that. I don't want to repeat what has been posted already by several people, so I would go back and read their posts. Furthermore, it seems you are confusing the time dilation equation with the lorentz boost in the time dimension, which are two separate (not competing) equations.

Thanks for your comment. But I did listen, otherwise, how could I respond?

You said that ".. it seems you are confusing the time dilation equation with the lorentz boost in the time dimension,..". I think SR is independent to the Lorentz boost. A Lorentz boost in any direction can be turned and moved to match the boost in the x-direction mathematically. I think I am fine with the term of boost.

 

[Vorde]

No, you are misunderstanding the equations. A lorentz boost, given the input of a time coordinate of an event for one observer, and the x-value and velocity of a second observer, will tell you the time coordinate of the event for the second observer.

The time dilation equation, given an input of an interval of time and the velocity of a second observer, will give you the interval of time measured by the second observer.

They are two totally different equations, and one can be derived from the other, so it's preposterous to claim one is true and the other isn't.

 

[John Huang]

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

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

Your "No," after your quote of my response {If you think LT is part of SR, that's fine. Now, we have two "time dilation" equations.} in the # 42 confused me. Now I know your "No," is for my second statement in your quote. Thanks for the clarification.