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=Special Theory Of Relativity=

  1. Aug 14, 2006 #1
    Ok. Let's say a fan is spinning at the speed of light. ( Imagine folks;)
    If i shine a light ray towards it, light would be able to pass through it almost instantaneously. Let's disregard one law of special theory of relativity stating that objects travelling at the speed of light would have 0 volume. What happens if the fan goes beyond the speed of light? To what i percieve, i have come to believe that light will still pass through it as there are " loopholes " ; as it is not a solid particle. I was imagininating that under what circumstances will the light not be able to pass through the fan blades?


    2nd.
    You are in a spaceship travelling at the speed of light; you are at the back of the spaceship; of course everything will appear as darkness infront. IF you run to the head of the spaceship whilst travelling at the speed of light, theoratically, you would have gone faster than the speed of light. Is this possible?

    :biggrin:
     
  2. jcsd
  3. Aug 14, 2006 #2

    selfAdjoint

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    Both of your examples suppose there is some absolute condition called "travelling near the speed of light". There is not. Two inertial frames can have a relative speed between them, but then people in each frame (such as a spaceship, or the place it took off from) will see ordinary physics in their own frame just as if they were "at rest at the center of the universe" (another state that doesn't exist). It's always the other guy who is travelling fast. Rethink your examples bearing this in mind.
     
  4. Aug 14, 2006 #3
    how about the fan question?
     
  5. Aug 14, 2006 #4
    Sorry but i do not quite understand your 1st question.
    However, regarding your second question, if the spaceship is travelling at the speed of light, then by right, u should not be able to reach the head of the spaceship. So, i think there is something flawed in the second sentence of the second example.
     
  6. Aug 14, 2006 #5

    JesseM

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    It isn't really possible for anything to go beyond the speed of light in relativity without causing problems such as backwards time travel. But even if we imagine an FTL fan, this problem doesn't have much to do with relativity, the answer would be the same as for a slower-than-light pulse and a slower-than-light fan--it would depend on the distance between the blades, the speed the blades rotate, the length of the pulse, and the speed of the pulse. It's just a problem of geometry, really.
    No, because it would be impossible for a massive object like a spaceship to travel at the speed of light. But say it was travelling at 0.9c relative to the earth, and you ran towards the front at 0.3c relative to the ship--would the earth see you moving at 1.2c? The answer is no, because velocities in different frames don't add the same way in relativity that they do in classical mechanics. The earth is using a different set of rulers and clocks to measure your speed than the ship is, so even though the ship measures you travelling at 0.3c relative to itself, the earth does not measure you travelling at 0.3c faster than the ship. Instead you have to use the formula for addition of velocities in relativity given here, which tells you that the earth would actually see your velocity as (0.9c + 0.3c)/(1 + 0.9*0.3) = 1.2c/1.27 = 0.945c, so you're only moving 0.045c faster than the ship in the earth's frame even though in the ship's frame you're moving at 0.3c relative to the ship.
     
  7. Aug 15, 2006 #6

    Chronos

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    Mass possessing bodies are, by current physics, prevented from travelling at the speed of light. The standard SR equations apply to objects approaching the speed of light. Note that near light speed velocities are not additive. As you approach the speed of light, your observable universe will contract into an increasingly bright and blue shifted point in your direction of travel:

    http://math.ucr.edu/home/baez/physics/Relativity/SR/Spaceship/spaceship.html
     
  8. Aug 21, 2006 #7
    But...I do not understand...although im just a high school student, but im really really interested into this area of physics and would like to learn more and specialize in this field when im older.
     
  9. Aug 21, 2006 #8

    Ich

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    Hint: If you want to learn, ask questions like "what does relativity say to..." and not "if we ignore relativity, what does relativity say to...".
     
  10. Aug 21, 2006 #9

    JesseM

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    Could you be specific about which parts of the various replies you had trouble understanding? I'm sure people would be willing to elaborate on particular things that were unclear, but just saying "I do not understand" isn't helpful.
     
  11. Aug 21, 2006 #10
    I recommend Richard Feynman's book, Six Not-So-Easy Pieces, or if you're truly inspired, the Feynman Lectures on Physics Volume I. The Lectures are very widely recognized as the book against which other physics books are measured, and Six Not-So-Easy Pieces is a subset of those lectures covering relativity (Special and even a little bit of General). The book introduces you to the theory of relativity and some of the reasoning that went into the formulation of the theory, and yet the book is only 150 pages, although shorter if you're travelling at the speed of light.
     
  12. Aug 22, 2006 #11
    Another good book on SR that develops the basics of the theory in a logically complete way but using only high school algebra is It's About Time by N. David Mermin. This is the most elementary SR book I'm aware of that doesn't just give impressionistic descriptions.

    Spacetime Physics by Taylor and Wheeler requires more math and physics, but should be accessible to anyone ready for freshman physics. I'm not sure I like the new edition; see if you can find a copy of the red paperback, which had all the solutions in the back, in a library. Working all the problems should give you a very solid understanding of SR.
     
  13. Aug 22, 2006 #12
    If your asking why aren't the two speeds added to make 1.2c that's because of the time dilation effect, the spaceships time is dilated according to how fast it is going, so that from Earths frame of reference it appears your only going .945c where as from the space ships frame of reference you are travelling at .3c. When the spaceship returned to Earth the Spaceships chronometers would show that a much shorter time period had past for it than the clocks on Earth, if you think of speed = distance / time taken this would show that for each frame of reference and allowing for the differences in time passing there would be no discrepancy. As a spaceship edged closer to light speed time would be so slowed that it would almost appear to stop to an outside observer.

    This Dilation effect is confirmed by experimental evidence that shows that Planes travelling around the Earth eventually show different times on their clocks, the effect is minimal at such slow speeds but it is there and it is consistent with the theory. It's also why satellites have to adjust there chronomoeters ocassionally to adjust for relative speed of them and the Earth. That's how I understand it, it's a bit confusing when you first read about it, but when you think in relative terms about time, it begins to make sense. Good luck in future learning:smile:
     
    Last edited: Aug 22, 2006
  14. Aug 22, 2006 #13

    JesseM

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    It's not only the time dilation effect though--to get the correct velocity addition formula you also have to take into account length contraction of the rulers that different observers use to measure the distance travelled in a given amount of time (velocity = distance/time, of course), as well as the "relativity of simultaneity" which means that different observers disagree on what it means for two clocks at different locations to be "synchronized". I gave a simple numerical example of how these three things come together to insure that all observers measure a light beam to travel at the same speed (which is a special case of the velocity addition formula) in this thread.
     
  15. Aug 22, 2006 #14
    Thanks for the info, I have a vague memory of the Michelson-Morley experiment and how it was used to question aether theory and how this lead to the idea of both time dilation proposed by Einstien and the next step which was length contraction, but it's so long since I looked into this I didn't want to cloud the issue with something I was a bit vague on, anyway, that thread is excellent although unfortunately the first two links on the thread don't work any more. I seem to remember time dilation has yet to be proven experimentally, is that still the case?

    That said and to help out a little beyond my basic understanding from memory, I found an interesting set of lectures that start with the Michelson-Morley experiment and go on to explain the reasoning behind time dilation and length contraction in special relativity. At the bottom of each page is a link to the next lecture.

    http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html
     
    Last edited: Aug 22, 2006
  16. Aug 22, 2006 #15
    Has been proven long ago. Look up Ives Stlwell or muon. And it is Einstein, not Einstien.


     
  17. Aug 22, 2006 #16

    DaveC426913

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    Fine, if he can be Einstien then I want to be called [tex]\overline{I}gor[/tex].

    :biggrin:
     
  18. Aug 22, 2006 #17
    I before E accept after C, drat, hey spellings something I never learnt at school, something I never learnt, if I could spell, I'd be an author or something.

    Can I still be SD?:smile:

    Yes I know it doesn't have the umlauts. Fargging hell, maybe I should change my name to thisweeksspeelingtarget. :tongue2:

    I don't know you try and make up for past mistakes and them some spelling Nazi comes down on your arse, and then you feel like everything you do is worthless because you can't talk English. Maybe I should learn French a bit better, at least then if I spelt something wrong I wouldn't get : ah nm :biggrin:

    Anyway, while I learn how to spell, enjoy the link.:smile:

    Could you elaborate about the muon clj4, a link maybe?
     
    Last edited: Aug 22, 2006
  19. Aug 22, 2006 #18

    selfAdjoint

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    I always thought Schrodinger's dog referred to Snoopy, in the Peanuts comic strip. I suppose he's really Charlie Brown's dog, but I have this memory of him draped in gaga fashion (imitating Lucy) over Schrodinger's piano.
     
  20. Aug 22, 2006 #19
    If you have taken calculus or precalculus you can probably understand the concept of a limit. Einstein discovered that mass is not a constant, and is variable based upon an objects speed relative to the speed of light.

    [ latex ]\[
    \[
    m = \frac{{m_0 }}
    {{\sqrt {1 - v^2 /c^2 } }}
    \]

    [ /latex ]

    So what you want to do is take the limit of m as v approaches c (because v/c where v=c produces a divide by zero error. You will find that m (the actual mass of the object) approaches infinity. What that means is that the closer an object becomes to the speed of light, the greater its mass. Thus, as v-> c, m-> infinity. And since the more massive an object becomes, the greater a force is required to accelerate it (remember, F=ma), the amount of force required to reach the speed of light also approaches infinity).

    Thus, you discover purely through mathematics that it is impossible for an object with mass to reach the speed of light using ordinary propulsion, so it is something of an inappropriate question (like asking what one divided by zero is). As for what could hypothetically happen if an object reached the speed of light, that is far, far beyond me.
     
  21. Aug 22, 2006 #20

    JesseM

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    The Peanuts character was "Schroeder", according to wikipedia he was named after a boy who was Charles Schulz's caddy at his golf course...it'd be pretty funny if he was named "Schrodinger" though!
     
  22. Aug 22, 2006 #21
    While I do not disagree with what you say it is not conform the special relativity theory. :smile:

    In SR the mass of an object X only increases from an observer perspective who is at rest relative to this object X.
    The object itself will not experience any mass increase, neither will it experience any change of clock speed or length.
     
  23. Aug 22, 2006 #22

    JesseM

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    In theory relativity need not forbid objects which always travel at faster than the speed of light though, these theoretical objects are called "tachyons". They probably don't exist because they would cause problems with causality (a tachyon signal could arrive before it was sent in some frames), though. Here's a more practical way to translate unscientific's scenario though. Imagine you have a large grid of pixels where each pixel can be made transparent or opaque to light electronically. Then you could create an image of fan blades made out of a collection of opaque pixels, and by rapidly switching pixels between transparent and opaque, the image of the blades could rotate around as fast as you want, even faster than light. No actual object would be travelling faster than light in this scenario, it would be an illusionary form of FTL like the FTL laser spot on the surface of the moon or the superluminal scissors, but in terms of whether light could pass through or not it would be as if you had actual fan blades moving at FTL speeds. Again, the answer to whether a light pulse would get through or be blocked would just depend on things like the width of the pixellated blades, how fast they appeared to be moving, and the length of the light pulse.
     
  24. Aug 22, 2006 #23

    JesseM

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    Yes, but the question is whether an object can be accelerated to light speed in a given inertial frame, so what's important is the object's mass/energy in that frame, not in the object's own rest frame. In the object's own rest frame it obviously cannot exceed light speed because by definition its speed is zero in its own rest frame!
     
  25. Aug 22, 2006 #24
    Note that the alledged "causality violations" are only an issue in SR, for instance in LET, which gives exactly the same results as SR, there are no causality issues.
     
  26. Aug 22, 2006 #25
    I realize that, but vociferous was arguing that "m (the actual mass of the object) approaches infinity", this is not the case in SR, in SR the actual mass stays the same, only the relativistic mass increases. Similarly with actual lengths and actual clocks speeds, they stay the same in SR.
     
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