How to explain Einstein's Special theory of Relativity.

[Lochlan.H]

Can someone help me with understanding and explaining the Special theory of relativity.

I know the basics (time dilation, the speed of light, ect), just what's left is Lorentz transformation and I'll understand the theory.

And also help with explaining the theory to a friend.

And help is appreciated.

 

[JustinRyan]

I am no expert and I am sure some here may be able to explain clearer...

The Lorentz transform is used to relate co-ordinates of one frame of reference K to another frame of reference that is moving with uniform motion relative to K. It was conceived by Einstein to explain the proven fact that velocity of light is constant to all frames regardless of their motion or the motion of the source of light.

Previously the principle of relativity could not account for this. The lorentz transform basically does away with the concept of absoloute time and absoloute space. Space and time will change in just the right way to allow any observer in any reference frame to measure the speed of light to be c.

 

[jtbell]

And help is appreciated.

You can help us by asking specific questions.

 

[Lochlan.H]

You can help us by asking specific questions.

I asked two questions, being; can someone help me understand the theory, and how would I explain this theory to another person.

Better?

 

[Doc Al]

I asked two questions, being; can someone help me understand the theory, and how would I explain this theory to another person.

Better?

Not really. Those are pretty broad questions! Usually answered in book form. Try to ask more narrowly focused questions.

You did ask about the Lorentz Transformation, which is specific enough to get a handle on. Here's a place to start: Lorentz Transformation

 

[Lochlan.H]

I don't mind getting a long answer, I'd prefer it.

 

[DrGreg]

You might like to read ZapperZ's blog entry https://www.physicsforums.com/blog.php?b=3588 for some advice on how to better phrase your question.

 

[Lochlan.H]

You might like to read ZapperZ's blog entry https://www.physicsforums.com/blog.php?b=3588 for some advice on how to better phrase your question.

why?

 

[russ_watters]

Because it is rude to ask people to write you a book when you could just go find one yourself! It also shows a lack of effort which will make it hard for you to learn.

 

[Nugatory]

I know the basics (time dilation, the speed of light, ect), just what's left is Lorentz transformation and I'll understand the theory.

The Lorentz transformation is used to derive time dilation, length contraction, and the like; so if "what's left" is the Lorentz transformations, then in fact you haven't even started yet.

But because you're asking where to get started... You might try this thread https://www.physicsforums.com/showthread.php?t=628574&highlight=self-study and my post #6 in it.

 

[bobc2]

Can someone help me with understanding and explaining the Special theory of relativity.

I know the basics (time dilation, the speed of light, ect), just what's left is Lorentz transformation and I'll understand the theory.

And also help with explaining the theory to a friend.

And help is appreciated.

Lochlan, I've been disappointed in some of the responses to your inquiry. It's quite reasonable for someone who has a passion for probing the mysteries of relativity to seek help on a forum like this, even for someone who may not have too much of a background in math or physics.

It is not easy for us forum members with experience in the subject to provide an explanation of the basic ideas in a way that is easy to grasp. Trying to describe the Lorentz transformations is one way. Another would be to try to tell the story with pictures. We never know to begin with which approach is the more fruitful for a given individual.

I will try to describe special relativity using pictures, but it will take a while. After putting something together I'll get back to you here if I think the approach has a chance of working for you. But of course, Nugatory has pointed you to some good posts.

[Edit] Looks like you won't need my help. Check out the links just provided in this more recent thread:

https://www.physicsforums.com/showthread.php?t=647425

 

[harrylin]

Can someone help me with understanding and explaining the Special theory of relativity.

I know the basics (time dilation, the speed of light, ect), just what's left is Lorentz transformation and I'll understand the theory.

And also help with explaining the theory to a friend.

And help is appreciated.

Hi Lochian,

You may be surprised by some of the answers; let me try to explain why you didn't get a simple three-sentence answer.

For explanations of how to calculate, you received links to explanations, including one with nice illustrations and animations.
Apart of that, regretfully, different people understand the theory differently. Of course, everyone who knows SR, agrees on what it predicts; and making correct predictions is what it was meant to do. But even not everyone who knows how to calculate it, also has the feeling to really understand it. Even Feynman had problems to understand a prediction about an accelerating rocket that he correctly calculated!

 

[Lochlan.H]

What makes you people so unhappy?
I'm just asking for someone to explain to me the aspects of the theory (i.e Maxwell's, time dilation, length contraction).

 

[harrylin]

What makes you people so unhappy?
I'm just asking for someone to explain to me the aspects of the theory (i.e Maxwell's, time dilation, length contraction).

I don't know about the other people, but I am happy!
And you received the explanations that you asked for (they are in the links, with nice illustrations* and animations by Fowler), but you do not sound happy.

* the illustrations start here: http://galileoandeinstein.physics.virginia.edu/lectures/srelwhat.html

 

[Lochlan.H]

I don't know about the other people, but I am happy!
And you received the explanations that you asked for (they are in the links, with nice illustrations* and animations by Fowler), but you do not sound happy.

* the illustrations start here: http://galileoandeinstein.physics.virginia.edu/lectures/srelwhat.html

No I just don't understand how other people cannot understand what I meant when I wrote it, but thank you.

 

[harrylin]

No I just don't understand how other people cannot understand what I meant when I wrote it, but thank you.

You're welcome!
Perhaps what you really want is some more explanations about deriving the Lorentz transformations; if so, just ask; we can give you links to past discussions with detailed explanations.

PS for example: https://www.physicsforums.com/showthread.php?t=478252

 

[ibungo]

hi lochlan
i don't know much about the math involved in deriving lorentz transformation from SR or deriving length contraction and time dilation but if it help the following paragraphs are my basic understanding of the topic under discussion
Before SR the entire laws of Physics were Govern by Gallelian Transformation, which is nothing but our basic intuitive knowledge that space and time are absolute. Or in a more simplified manner it is like this, you measured the length of your study table to be say 2.5m and someone say an astronaut traveling at around thousand km/h measures it, it will still be 2.5m. In fact anyone in the Universe measures it, it will be 2.5m. This is so evident in our day to day lives that physicist before SR had taken it to be for granted.Even Newtons laws are base on this.
But when Maxwell started his electrodynamic experiment, he found an anomaly in the Gallelian transformation itself. Physicist of his time had this view that it was Maxwell's electromagnetic theory at fault rather than Gallelian transformation , in which they have a firm believe. They tried to disprove Maxwell's theory only to find Gallelian transformation as the Culprit. Since the entire Laws of physics until their time were build upon Gallelian transformation, the physicist were plunge into a dark abyss with this BIG QUESTION; ARE ALL LAWS OF PHYSICS INVALID.
The answer to this question was given by a young fellow name "Einstein" who proposed that there was nothing wrong with the laws of physics(1st postulate), the only thing that was wrong was our perception of absolute space and time (Gallelian transformation) and it must be changed to Lorentz transformation( as a side note lorentz had already introduced a transformation according to which there won't be any anomaly in the electrodynamic experiment but couldn't prove) which Einstein proved using his second postulate.
So this time, according to SR the length of your table that you measured and that measured by some astronaut moving thousands of km/h w.r.t the table will be different i.e THE MEASUREMENT OF SPACE, TIME ARE RELATIVE. The only thing that is constant is the speed of light which is the basis for such relative measurement of space and time.

 

[PeterDonis]

I'm just asking for someone to explain to me the aspects of the theory (i.e Maxwell's, time dilation, length contraction).

Explaning that in general is well beyond the scope of a forum post; as others have said, it requires a book, or something of similar length. That's why you have not been getting much of a response.

For the basics of SR, I recommend Taylor & Wheeler's Spacetime Physics. The first few chapters are available online:

http://www.eftaylor.com/download.html

This should give you a start. It should also help you to formulate more specific questions that are more suitable for answering in a forum like this.

Another thing you could try is to come up with a specific, simple scenario that illustrates the things you are interested in knowing about. It's a lot easier for us here to respond to specific scenarios than general questions like those you've asked; the latter are too open-ended.

[Edit:] One other good resource online is the Usenet Physics FAQ:

http://math.ucr.edu/home/baez/physics/

Some of the pages there on relativity questions may also help you to formulate more specific scenarios that you can ask about.

 

[bobc2]

Can someone help me with understanding and explaining the Special theory of relativity.

I know the basics (time dilation, the speed of light, ect), just what's left is Lorentz transformation and I'll understand the theory.

And also help with explaining the theory to a friend.

And help is appreciated.

Well, maybe I'll give the picture approach a try here. I'm afraid it will get lengthy and annoy some folks with the amount of space taken up by sketches. Maybe we can break it up into a sequence of posts.

Here's part 1. For this approach it is critical that you initially try to wrap your head around the concept of a 4-dimensional universe. In some sense all observers move at the speed of light straight into the 4th dimension. So, I start with this picture of a piece of the 4-dimensional world showing a rendition by Paul Davies:

To further think through the 4 dimension concept, consider sketch A below. We start with a 3-dimensional beam, then see if we can focus on just one surface of the beam at a time. You can build a picture of a 3-D beam by starting with anyone of the surfaces and then extrude it into the direction perpendicular to the starting surface. In sketch B we similarly build a 4-dimensional beam by starting with a 3-D beam and then extruding it into the 4th dimension. The only trouble is that we can't show all 4 dimensions in a sketch, so we just show X1 and X2 and indicate an extrusion along the 4th dimension, X4.

(...continued in part 2)

 

[bobc2]

Part 2. I will try taking a giant step here. We can insert more background and detail if needed. We have constructed a 4-dimensional beam. Now we describe a situation with two observers (two physicists studying special relativity effects) one guy at rest in the black inertial frame of reference below and another guy moving at relativistic speed along black's X1 axis. Blue is actually at rest in the blue inertial frame. The blue guy carries along the 3-dimensional beam as he moves along the black X1. But, actually, since all objects are 4-dimensional (including the bodies of the observers), there is actually no motion at all in the 4-dimensional world--only the consciousnesses move at the speed of light along the 4th dimension world lines.

Here is the whole point of insisting you wrap your head around the concept of a 4-dimensional universe: When the black guy gets the impression that the 3-D beam is moving along his X1 axis at relativistic speed, it's just because the beam is really a 4-dimensional object and that object is slanted relative to black's vertical X4 axis.

Now, the big clincher for understanding special relativity is catching on to a very strange and mysterious thing that nature does for an observer whose X4 axis is slanted, i.e., the blue X4 axis in our example: Nature somehow rotates the blue X1 axis such that a 45-degree line always bisects the angle between the blue X4 and X1 axis--no matter what the angle of blue X4 is. And of course that same 45-degree line bisects the black X4 - X1 angle as well. And guess what--that 45-degree line is the world line of a photon. The 4-dimensional photon particle is always oriented as a straight line bisecting X4 - X1 angles for all inertial frames of reference. More on that later.

(end Part 2)

 

[bobc2]

Part 3. Just to emphsize the strange effect associated with relativistic motion of an observer, we show sketches (1) thru (4), where observers moves at ever increasing relativistic speeds with respect to the black rest frame. Notice that the instantaneous 3-D cross-section of the 4-D universe experienced by the blue guy corresponds to the X1 axis (X2 and X3 not shown for simplicity), and that X1 axis is always rotated such that the 45-degree worldline of the photon always bisects the angle between X4 and X1. This is why the speed of light always has a value of c for any observer, no matter what his speed.

Again, I want to emphsize the importance of understanding the example of the upper inset box showing that the black guy and the blue guy literally live in two different 3-dimensional worlds, each one just a different cross-section of a 4-dimensional universe.

 

[bobc2]

Part 4. Finally, the payoff. If you have understood what we've done so far, then if you remember the Pythagorean theorem from high school algebra you are now in a position to derive the time dilation equation (Lorentz transformation--although not in it's most general form). This time we have the black guy in his rest frame observing the blue guy moving at relativistic speed along black's X1 axis (same as before). But now we add a red guy moving at the same speed along black's negative X1 axis (blue and red move in opposite directions).

Notice in the bottom sketch that we have both blue and red carrying a beam along with them. You can compare the lengths of the beams as viewed by each. You can see right away why we have the length contraction phenomena of special relativity. If you look along blue's X1 axis at his time 2 you will see that the blue beam (in his 3-D cross-section view) is longer than the red beam (look along blue line labeled "Simultaneous Blue"). So, blue says, "Hey, the red guy's beam has contracted--it's shorter than mine." But, the red guy's instantaneous 3-D cross-section of the 4-D universe extends along a different direction in the 4-D universe (red line labeled "Simultaneous Red"). So, red says, "Hey, the blue guy's beam has contracted--it's shorter than mine."

We could derive the Lorentz transformation for that, but I'll just let the picture tell the story.

 

[bobc2]

Part 5. We'll conclude the series with an example of the well known lightning flashes at the train station. A train is moving through the station at relativistic speed with one observer standing on the platform (in the black rest frame below) and another observer seated in the middle of the train. The observer on the platform sees simultaneous flashes of lightning, one at the front and one at the rear. What does the passenger on the train see? The green lines drawn at 45-degree angles are the world lines of the photons. We idealize the flashes of lightning as single individual photons of light.

 

[rjbeery]

Hi Lochlan.H! While Bobc2 is doing a very thorough job giving you information, I thought I'd give you my personal "executive summary" of SR. Note that this a very informal description which I use as the basis for my intuition on the subject. There's a big difference between memorizing formulas and developing a "feel" for something like this. Anyway...

Special Relativity simply says that light is measured to propagate at the same velocity from all inertial frames of reference. Once we accept this premise, everything else (twin paradoxes, length contraction, time dilation, etc) is basically a consequence of it. Length is measured by rulers, which are constructs whose molecules are ultimately held in place by EM (and other) forces propagating at the speed of light. Similarly, clocks are devices whose internal clocking actions ultimately depend upon the local speed of light. The same is true of the electro-chemical processes in our body and brain cells which determines how we age as well as the "rate" at which we experience reality. All of reality is ultimately determined by the speed of light.

Now, if a distant observer declared that our local speed of light just slowed down...how could we tell? The answer is that we could not. Our clocks, our rulers and our body's cells would all conspire to hide this fact from us. It would be impossible to measure anything but c for the speed of light due to the very fact that we are ultimately measuring the speed of light against itself! It would be like asking how long the shadow of a ruler is as measured with the shadow of another ruler. You're always going to get the same answer, regardless of the "actual" length of the shadow.

That explains c as measured locally, but it doesn't really explain Lorentz transforms. I think of LTs like this: all bodies travel at a constant c, but what changes are the vector components making up travel through time and space. If you're stationary in space, you are maximizing your "velocity through time". Alternatively, if an object is moving very quickly through space, its "velocity through time" vector component is small (with the extreme example being a photon, whose "velocity through time" vector component is zero). Thought of in this manner, LTs are simply a tool to calculate a nonlocal body's velocity time- and space-travel vector components from a particular point of view.

The last thing I'd say here is that you must never get caught up in what the "real" answers are (as in, what is the "true" length of an object). The point of Relativity is that there is NO SUCH ANSWER. There is only length "as measured from this perspective"; time passage "as measured from this perspective", etc. Anyway everyone learns in different manners, I hope my description helps solidify things in the minds of you and your friend. Good luck!

 

[John Huang]

Can someone help me with understanding and explaining the Special theory of relativity.

I know the basics (time dilation, the speed of light, ect), just what's left is Lorentz transformation and I'll understand the theory.

And also help with explaining the theory to a friend.

And help is appreciated.

Lorentz transformation (LT) is for all kinds of event. Special theory of relativity (SR) is for events happen at the origin point of the moving system (the point O') only. I think SR is exactly the time equation of LT with the restriction of x'=0. And that is all SR can be, part of LT. Why?

If we use SR beyond the restriction of x'=0, that means if we let observers to observe some event happens at different location than O', then we will have to decide which time equation to use, SR or LT. Do you think so?

 

[JesseM]

Can someone help me with understanding and explaining the Special theory of relativity.

I know the basics (time dilation, the speed of light, ect), just what's left is Lorentz transformation and I'll understand the theory.

And also help with explaining the theory to a friend.

And help is appreciated.

If you want to understand relativity conceptual, it's also really important that you understand about the relativity of simultaneity--99% of the time when people find something paradoxical about relativity, it has to do with a failure to understand how simultaneity differs in different frames.

I posted some good intros to SR on this thread: https://www.physicsforums.com/showthread.php?t=441257

 

[bobc2]

If you want to understand relativity conceptual, it's also really important that you understand about the relativity of simultaneity--99% of the time when people find something paradoxical about relativity, it has to do with a failure to understand how simultaneity differs in different frames.

I posted some good intros to SR on this thread: https://www.physicsforums.com/showthread.php?t=441257

Great advice. Some folks here seem to minimize the significance of relativity of simultaneity. A shame your references have collected so much dust over the last couple of years. So, here are JesseM's references again:

http://www.oberlin.edu/physics/dstye...ein/SRBook.pdf -- "Relativity for the Questioning Mind", nice Q&A style book

http://en.wikibooks.org/wiki/Special_Relativity -- another good intro with a lot of helpful stuff about spacetime diagrams

http://www.einstein-online.info/elementary and http://www.einstein-online.info/spotlights -- conceptual introductions to both special and general relativity

http://www.upscale.utoronto.ca/PVB/Relativity.html -- Physics virtual bookshelf section on relativity, lots of good articles

http://www.pitt.edu/~jdnorton/teachi...410/index.html -- series of illustrated lectures, "Einstein for Everyone".

For books, Relativity from A to B by Robert Geroch is a good conceptual intro, some good undergrad textbooks are Special Relativity by A.P. French and Spacetime Physics by Taylor and Wheeler, and An Illustrated Guide to Relativity by Tatsu Takeuchi (haven't read this one yet as it just came out, but was admiring the illustrated approach in the sample pages on google books). For a popular introduction to the ideas of general relativity, Black Holes and Time Warps is very good.

 

[Dale]

Special theory of relativity (SR) is for events happen at the origin point of the moving system (the point O') only. I think SR is exactly the time equation of LT with the restriction of x'=0.

This is not correct at all. Where did you get such a strange idea?

If we use SR beyond the restriction of x'=0, that means if we let observers to observe some event happens at different location than O', then we will have to decide which time equation to use, SR or LT. Do you think so?

No, in fact the LT is part of SR, so anything that the LT says is part of what SR says. You never have to decide between SR and the LT. That is nonsense, and very strange nonsense.

 

[John Huang]

No, in fact the LT is part of SR, so anything that the LT says is part of what SR says. You never have to decide between SR and the LT. That is nonsense, and very strange nonsense.

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?

 

[Nugatory]

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?

It is not at all clear what you mean by the "time equation of SR". If you mean the time dilation formula... That's derived from the Lorentz transformations, which are an integral part of SR.

 

[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