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How to explain Einstein's Special theory of Relativity.

  1. Oct 28, 2012 #1
    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.
     
  2. jcsd
  3. Oct 28, 2012 #2
    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 thier 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.
     
    Last edited: Oct 28, 2012
  4. Oct 28, 2012 #3

    jtbell

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    You can help us by asking specific questions.
     
  5. Oct 28, 2012 #4
    I asked two questions, being; can someone help me understand the theory, and how would I explain this theory to another person.

    Better?
     
  6. Oct 28, 2012 #5

    Doc Al

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    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
     
  7. Oct 28, 2012 #6
    I dont mind getting a long answer, I'd prefer it.
     
  8. Oct 28, 2012 #7

    DrGreg

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    You might like to read ZapperZ's blog entry https://www.physicsforums.com/blog.php?b=3588 [Broken] for some advice on how to better phrase your question.
     
    Last edited by a moderator: May 6, 2017
  9. Oct 29, 2012 #8
    why?
     
    Last edited by a moderator: May 6, 2017
  10. Oct 29, 2012 #9

    russ_watters

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    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.
     
  11. Oct 29, 2012 #10

    Nugatory

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    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.
     
  12. Oct 29, 2012 #11
    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
     
    Last edited: Oct 29, 2012
  13. Oct 29, 2012 #12
    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!
     
  14. Oct 30, 2012 #13
    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).
     
  15. Oct 30, 2012 #14
    I dunno about the other people, but I am happy! :smile:
    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. :confused:

    * the illustrations start here: http://galileoandeinstein.physics.virginia.edu/lectures/srelwhat.html
     
  16. Oct 30, 2012 #15
    No I just don't understand how other people cannot understand what I meant when I wrote it, but thank you.
     
  17. Oct 30, 2012 #16
    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. :smile:

    PS for example: https://www.physicsforums.com/showthread.php?t=478252
     
    Last edited: Oct 30, 2012
  18. Oct 30, 2012 #17
    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 travelling at around thousand km/h measures it, it will still be 2.5m. In fact any one 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 untill 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.:smile:
     
  19. Oct 30, 2012 #18

    PeterDonis

    Staff: Mentor

    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.
     
  20. Oct 30, 2012 #19
    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:
    BlockUniverse_DaviesSketch.jpg
    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 any one 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.
    4D_Beam_Extrusion.jpg
    (...continued in part 2)
     
  21. Oct 30, 2012 #20
    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.

    4D_Beam_Extrusion_RelativisticSpeed.jpg


    4D_Beam_UniversePicture.jpg


    (end Part 2)
     
    Last edited: Oct 30, 2012
  22. Oct 30, 2012 #21
    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.
    Worldline_Speed.jpg
     
  23. Oct 30, 2012 #22
    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).
    Loedel-Diagrams_2.jpg

    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.
     
  24. Oct 31, 2012 #23
    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.
    Einstein_Train3.jpg
     
  25. Oct 31, 2012 #24
    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! :smile:
     
    Last edited: Oct 31, 2012
  26. Dec 9, 2012 #25
    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?
     
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