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Can someone explain Einstein's relativity theory?

  1. Jan 11, 2005 #1
    I've read a piece on his theory and I'm having a little difficulty understanding it. I've used the famous E = MC^2 in calculations before but I want to have more understanding of the theory behind it.

    Any info would be great.
     
  2. jcsd
  3. Jan 11, 2005 #2

    dextercioby

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    I'm afraid it cannot be explained in one post from a frum...I would advise you to read the famous book:"A brief History of time" by Stephen Hawking.
    You'll understand many things.

    Daniel.
     
  4. Jan 11, 2005 #3

    Check out the text "string theory part 1" on page three in my journal. There is a short paragraphe on General Relativity. Ofcourse it is very introductory, but it sets the tone. Firther on i suggest you check the info on the web entry for further reliable references. The answer to your question cannot be given in a few posts. First question should be : "why the name RELATIVITY theory". What does relativity mean. The answer is in my text...

    regards
    marlon

    here is the link https://www.physicsforums.com/journal.php?s=&action=view&journalid=13790&perpage=10&page=3
     
  5. Jan 11, 2005 #4
    hmnnnn well einstein said something like " you sit next to a girl for an hour and it seems like a mintue, you sit on a hot stove for a minute, and it seems like an hour, that's relativity"
     
  6. Jan 11, 2005 #5
    Einstein based his special theory of relativity on two postulates:

    The First Postulate

    The laws of physics are the same in all inertial systems1. There are no preferred inertial systems, or reference frames2. When inertial reference-frames move with constant speed with respect to one another the laws of physics will be the same in both reference-frames.

    The Second Postulate

    The phenomenon of light is correctly described by Maxwell's equations. In other words, all observers will measure3 the speed of light in a vacuum to be a constant value c in all inertial systems.

    Conclusions to the Special Theory of Relativity

    Once given the above two postulates as premises, the theory of special theory of relativity pretty much falls out from normal intuitive reasoning. I won't go into the actual conclusions, other than to say that once you've accepted these postulates the rest of Relativity is fairly easy4 to deduce and accept.

    Footnotes:

    1. Inertial systems are reference frames that move uniformly and without rotation.

    2. A reference frame is just another name for an inertial system.

    3. Note that this postulate does not actually say that the speed of light is c in all reference frames, but rather it only requires that the speed of light is measured as c in all reference frames. This is a technicality that most physicists never seem to want to talk about. This is because for physicists, "to measure is to be". In other words, as far as physicists are concerned what you see is what you get, or only observables matter. They typically aren't interested in discussing the ontological implications of fundamental measurements.

    4. While the conclusions are fairly easy to deduce, the postulates are not without contradiction with respect to these conclusions. For example, Postulate One states that the laws of physics are the same in all inertial frames. Yet, one of the conclusions of special relativity is that time passes at different rates in different inertial frames thus contradicting the first postulate that states that the laws of physics are the same in all inertial frames. The twin brother's paradox proves this inconsistency between the theory and its postulates. The twin that ages less may have undergone an acceleration, however, his or her clock continues to run more slowly relative to the non-accelerated sibling even after the acceleration has ceased. Therefore, the twin who has undergone a change in an inertial frame has also undergone a change in his or her fundamental laws of physics (i.e. time passes at a different rate for that twin than for the first twin) So the theory does seem to be in direct contradiction with its very own postulates.

    Personal Comment

    It is not my intention to discredit Special Relativity in any way by stating the above facts. Special Relativity has indeed panned out quite nicely as a mathematical framework making unprecedented confirmed predictions. The mere fact that the theory itself seems to be in direct contradiction with one of the postulates from which is was deduced does not in any way prove, or even suggest, that the theory is incorrect (i.e. the postulates themselves are not really a part of the theory, they were merely stated as a basis for deducing the theory. Therefore the theory is not actually in contradiction with itself.) It does, however, cause one to ponder how a postulate can lead intuitively to a conclusion which denies the very postulate that gave birth to it. :confused:
     
  7. Jan 11, 2005 #6

    dextercioby

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    Where did u get the "fotnotes"???Check this one out:
    I THINK THAT WIPES OUT 10 YEARS OF MR EINSTEIN'S WORK...And did a hella of a favor to QFT...
    :rolleyes:

    Daniel.
     
  8. Jan 11, 2005 #7

    Doc Al

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    This is nonsense.
     
  9. Jan 11, 2005 #8

    Galileo

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    No, time passes at a different rate in an inertial frame that is moving with a constant velocity with respect to your inertial frame.
    The first postulate simply says that if you view the situation from the other reference frame, the physical description is exactly identical.
     
  10. Jan 11, 2005 #9

    JesseM

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    No. If you are travelling at velocity v in my frame, I will see your clock slowed by a factor [tex]1/(1 - v^2/c^2)[/tex]; in your frame, you will see me travelling at velocity v, and you will also see my clock slowed by a factor of [tex]1/(1 - v^2/c^2)[/tex]. So in each frame, a clock travelling at v is slowed by the same factor, thus the laws concerning time dilation work the same way in both frames.
    No, in the travelling twin's frame it doesn't run more slowly once the acceleration has ceased. After the acceleration has ceased, and the twin is returning to earth at constant velocity, the travelling twin's clock is running slow in the earth-twin's frame, and the earth-twin's clock is running slow in the travelling twin's frame. In both frames, though, you can predict that the travelling twin's clock will be behind the earth-twin's clock when they meet; in the travelling twin's frame, this is because at the moment the acceleration stopped, his clock was way behind the earth-twin's clock at the same moment, so that even though his clock is "catching up" to the earth twin's clock (since the earth-twin's clock is ticking more slowly in his frame), it still will be behind the earth-twin's clock at the moment their paths cross. In the earth-twin's frame the analysis would be different--at the moment the acceleration stopped, he would also say that the travelling twin's clock is behind his own, but by a smaller factor; but since the travelling twin's clock ticks more slowly in his frame, the difference between their clocks would increase rather than decrease. But things will work out so that each frame will have exactly the same prediction about how much the travelling twin's clock will be behind the earth-twin's clock at the moment they meet.
     
    Last edited: Jan 11, 2005
  11. Jan 11, 2005 #10
    In my opinion, one of the best popular explanations of the theory of relativity was written by Brian Greene in his "The fabric of the cosmos" book.
     
  12. Jan 11, 2005 #11

    JesseM

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    Actually, this footnote, along with the rest of his post up to footnote 4, is correct. The statement that the laws of physics work the same way in all reference frames is only true if you assume that we're only talking about the reference frames of observers who are moving inertially (ie moving at constant velocity relative to other inertial observers, not accelerating).
     
  13. Jan 11, 2005 #12

    dextercioby

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    Nope,notice the degree of generality.He said "reference frame=inertial frame" ,but he didn't say the key words:"in SR". :wink:

    Again,i'm convinced thatwas balloney.Either he invented the footnotes or took'em from a crack-pot source...


    Daniel.
     
  14. Jan 11, 2005 #13

    JesseM

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    Even in SR, you can have accelerated reference frames, you just can't assume the laws of physics work the same way in these frames. But in context, I think that footnote wasn't talking about SR in general, it was just qualifying a statement he made in the first postulate, namely "There are no preferred inertial systems, or reference frames". So in that context, the footnote need not have meant "whenever a physicist uses the words 'reference frame' they always just mean an inertial system"--it could have just meant "when I use the word 'reference frame' in my statement of the first postulate, I'm just using it to mean an inertial system".
     
  15. Jan 11, 2005 #14
    That's precisely what I meant to convey in that footnote. Sorry if it was taken to imply some kind of blanket definition for the term. That wasn't my intent. I probably should have added something like "when speaking in terms of SR, the term reference frame is generally taken to mean Inertial system.

    Sorry for the confusion. Ironically I put in the footnote to avoid confusion and it seems to have backfired.

    I probably should have also clarified that my original post refers only to SR. I assumed that since GR requires additional postulates, such as the equivalency of acceleration and a gravitational field, it wouldn't be necessary to mention the distinction.
     
  16. Jan 11, 2005 #15

    ohwilleke

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    Special relativity is much, much easier conceptually than general relativity. In special relativity you are basically talking about a small number of equations (the Lorentz transformations), in ordinary every day algebra like the rest of physics, that insure consistency in cases where there are high velocity motion while maintaining the speed of light in a vacuum as a constant.

    General relativity is much deeper. To be crude to the point of being inaccurate but heuristically useful, general relativity explains gravity by explaining how mass-energy and its pressure and motion (customarily broken out into ten numerical quantities) affect the curvature of space. General relativity does so using "tensors" (which are basically matrixes from linear algebra), most notably the "Ricci Tensor" and the "Stress Energy" tensor (which contains the ten numbers describing the mass alluded to above).

    Tensor math is good, because it through the form of the equations make it obvious that there can be no preferred reference frame, but to actually calculate them without major assumptions concerning how you choose your reference frame and symmetry is extremely difficult.

    Among the major qualitative predictions of general relativity are that:

    (1) E=mc^2
    (2) Light is deflected by gravity.
    (3) Gravity is a quadradic function of velocity. A first order term depends on mass (with various other assumptions in place), a second order term depends on velocity, and a third order term depends on the square of velocity. This creates effects such as "frame dragging" and an altered expected precession of Mercury.
    (4) Gravity is capable of being so great that light cannot escape, creating a black hole.
    (5) The equations of GR can be generalized to the universe as a whole with certain simplifying assumptions. This generalization leads to our notions of how much matter, dark matter, and dark energy is necessary to have a universe consistent with data on the Hubble constant, other data and the equations of general relativity. The fact that there appears to be "dark energy" in the universe can be explained through a disputed term in the equations of general relativity called the cosmological constant, which has little or no impact on events at the galactic scale and below.

    A nice primer is here: http://math.ucr.edu/home/baez/einstein/einstein.html

    The real short version of GR (from the Baez primer):

    We promised to state Einstein's equation in plain English, but have not done so yet. Here it is:

    Given a small ball of freely falling test particles initially at rest with respect to each other, the rate at which it begins to shrink is proportional to its volume times: the energy density at the center of the ball, plus the pressure in the direction at that point, plus the pressure in the direction, plus the pressure in the direction.

    The reader who already knows general relativity may be somewhat skeptical of this claim. After all, Einstein's equation in its usual tensorial form is really a bunch of equations: the left and right sides of equation (1) are matrices. It is hard to believe that the single equation (2) captures all that information. It does, though, as long as we include one bit of fine print: in order to get the full content of the Einstein equation from equation (2), we must consider small balls with all possible initial velocities -- i.e., balls that begin at rest in all possible local inertial reference frames.

    Before we begin, it is worth noting an even simpler formulation of Einstein's equation that applies when the pressure is the same in every direction:

    Given a small ball of freely falling test particles initially at rest with respect to each other, the rate at which it begins to shrink is proportional to its volume times: the energy density at the center of the ball plus three times the pressure at that point.


    Equation (8) here: http://math.ucr.edu/home/baez/einstein/node10.html is the Einstein Equation.
     
    Last edited: Jan 11, 2005
  17. Jan 11, 2005 #16
    I don't see how that can be correct?

    Say we have three twins, A, B, and C.

    Twin A stays on earth. Twin B and C both take off in rockets (separate rockets).

    To keep things as simple as possible imagine that both rockets take off in the same general direction and accelerate to something close to the speed of light side-by-side. They both cease to accelerate at precisely the same time, still being side-by-side. Then they travel along for some extended period of time until twin B decides to decelerate and then re-accelerated to return back to earth.

    When twin B gets back to earth he or she will be younger than twin A by say, x amount of time.

    In the meantime, twin C is still just drifting along at close to the speed of light at a constant velocity. Finally, after some arbitrary time twin C decides to decelerate and then re-accelerate back toward earth. (Note that in this experiment both rocket pilots experience precisely the same amount of acceleration)

    Now when twin C returns to earth he or she will be younger than twin A by y amount of time.

    If acceleration was the only deciding factor for time dilation then x=y. In other words, twin B and C are precisely the same age. I don’t believe that this is what SR predicts. I believe that it predicts that B will even be younger than C. In other words, x will not be equal to y.

    Therefore, time dilation must have been occurring during the non-accelerated part of the trip. This must necessarily be the case since twin B and C both experienced precisely the same amount of acceleration.

    Is this right or wrong? I'm open to criticism? :approve:
     
  18. Jan 11, 2005 #17

    JesseM

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    I didn't say that time dilation only occurs during acceleration--in fact I said that in the travelling twin's frame, the clock of the earth twin is running slow (this would be true in both the outbound frame and the inbound frame).

    The thing to keep in mind is that different reference frames define simultaneity differently. If I am moving away from the earth at constant velocity, and my clock was synchronized with clocks on earth when I left, then in my reference frame the earth clocks are all running slow, so my clock will keep getting further and further ahead of what the earth clock reads "at the same moment" in my reference frame. But then if I accelerate so I am now travelling towards the earth, I will have a new reference frame, and this reference frame defines simultaneity differently than my old one, so that now the earth clock is far ahead of what my clock reads "at the same moment". The earth-clocks will still be ticking slower than my clock in this reference frame, so my clock will be catching up to the earth clock, but the earth clock was far enough ahead when I first entered this frame that when I arrive at earth my clock will still be behind.

    If you find this hard to understand, we could try plugging some numbers into your scenario above to show exactly how this works, and why the time difference between the clocks of A and B will be smaller than the time difference between the clocks of A and C when they reunite.
     
    Last edited: Jan 11, 2005
  19. Jan 11, 2005 #18

    Janus

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    The problem you are having is that you aren't taking the Relativity of Simultaneity into account. Clocks that are simultaneous as measured in one frame will not be simultaneous in another frame that is moving with respect to the first, if the clocks are separated along the axis of relative motion. So, for instance, if there were clocks at Earth, the point where B turns around and the point that C turns around that are sychronized in the Earth frame, according to B and C, the clocks at the turn around points will read later
    than the Earth clock while B & C are moving away from the Earth. Since the distance of separation affects how much the Clocks are out of sync, the clock at C's turn around will read later than the one at B's turnaround.

    When B turns around he changes frames of reference. (now heading towards Earth). In this new reference frame it is the Earth clock that reads the later time. Thus, according to B, the Earth clock now reads later than his own (Before he made the change of frame the Eart clock read Earlier than his own). When he returns to Earth he will find that the Earth clock will still read more than his own. (even though the Earth clock ran slower than his own during th return trip). IOW, his Earth twin will be older than him.

    When C turns around, he is much further from Earth, thus from his new frame, the Earth clock reads much later. Again, when he returns to Earth, he will find that much more time has passed on Earth for him than it did for B, who made the shorter trip.
     
  20. Jan 11, 2005 #19
    Neut,


    "While the conclusions are fairly easy to deduce, the postulates are not without contradiction with respect to these conclusions."

    Nonsense. The theory IS the postulates, and there are no contradictions among them and the conclusions to which they lead.

    Consider another possibility: You don't know what you're talking about!
     
  21. Jan 11, 2005 #20
    I'm sorry for misunderstanding you. I thought you said,…

    No, in the travelling twin's frame it doesn't run more slowly once the acceleration has ceased.

    That sounded to me like you were saying that time dilation ceases to occur once the acceleration has ceased

    I never said that I find it hard to understand. Nor did I ever say that I don’t believe that it happens. I've taken modern physics and I've gone through all the calculations and the Minkowski diagrams. All I'm saying is that time does indeed flow differently in different inertial frames. I believe that Relativity actually bears this out.

    I never even mentioned simultaneity. Neither was that concept important to the experiment that I spoke of. Never once did I talk about what might be happening "simultaneously" between the twins during the experiment.

    Actually you're right. Technically the postulate merely states that the laws of physics are the same in all inertial frames. And I suppose that is true.

    What isn't the same is the actual physics.

    In other words, imagine that two observers are in frame A. They both age by the same amount. One of the observers goes off into frame B. When they return to frame A they did not age as much as the observer that remained in frame A. Therefore the only possible conclusion is that time flows more slowly in frame B.

    If time flows more slowly in frame B then the physics of frame be is different from that from A. However, the laws of physics may remain the same within that frame. So I suppose it isn't a contradiction of the postulate after all.

    I kind of fell into the trap of thinking that the laws of physics and the actual physics were basically the same thing. They're not.

    So you're right. Technically, Special Relativity doesn't contradict it's postulates after all. :approve:
     
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