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Thread: Relativity and Light (problem understanding something)

  1. #1 Relativity and Light (problem understanding something) 
    Forum Junior DivideByZero's Avatar
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    To my understanding, nothing other than light can travel at or faster than the speed of light.

    I am having some trouble with relativity in the example below. I keep getting an object traveling the speed of light when we know that its impossible.

    ok here it goes:
    Object A is moving left to right 50% the speed of light relative to a fixed point C somewhere.
    Object B is moving right to left 50% the speed of light relative to a fixed point C somewhere.
    You can see this in the image below:


    The problem is that relative to object A, object B is traveling (0.5+0.5) 100% the speed of light. This is theoretically impossible but I have just shown an example of traveling the speed of light in this scenario. What did I do wrong?


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    You have looked at the problem from a third reference frame which will only see each blob moving at 0.5c. When taking the point of view from a blob reference frame you have to take into account time dilation and length contraction. They won't appear to be moving at c because of these.


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    The Doctor Quantime's Avatar
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    Can you mathematically prove this here using maths? Or can you reference this?
    "If you wish to make an apple pie from scratch, you must first invent the universe". - Carl Sagan
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    Quote Originally Posted by 425 Chaotic Requisition
    Can you mathematically prove this here using maths? Or can you reference this?
    There is no other reference as I just came up with this post.

    I can try mathematically because its safe to say that if A moves 10 miles an hour and B moves 15 miles an hour in the opposite direction, the relate speed between A and B would be |u|+|v|=|10|+|-15|= 25miles an hour

    note: post edited.
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    No I mean Cynapse. But I agree with him. There would have to be a third reference frame, all that is happening is that ship A assumes that it is moving at 1c, or that ship B is. However, if you can measure the energy you are using to travel at the speed you are, you should be able to deduce what velocity you are supposed to be travelling with that energy-thus determining who is travelling in which direction and how fast.
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    Grrrr ok il do the maths, will refresh my relativity anyhow!
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    Quote Originally Posted by 425 Chaotic Requisition
    No I mean Cynapse. But I agree with him. There would have to be a third reference frame, all that is happening is that ship A assumes that it is moving at 1c, or that ship B is. However, if you can measure the energy you are using to travel at the speed you are, you should be able to deduce what velocity you are supposed to be travelling with that energy-thus determining who is travelling in which direction and how fast.
    For object A, if the reference is point B, then object A's speed should be 1c.

    Imagen that object "B" is a space ship and so is object "A". For the person inside space ship "B", space ship "A" seems to be traveling right at him at the speed of light.
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    Yes I agree. But only as the unique observor can we determine that they are travelling towards each other at 0.5c. You'd need nultiple more reference points to determine the speeds, and even then you are at the mercy of light's constancy. But yes I fully agree, B sees A travelling towards themself at 1c, or do they? I guess they can because we as the third observor know they are not either at 1c, only at 0.5c. We have to tweak relativity to truly know who is travelling at what speed. :-D
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    Quote Originally Posted by 425 Chaotic Requisition
    Yes I agree. But only as the unique observor can we determine that they are travelling towards each other at 0.5c. You'd need nultiple more reference points to determine the speeds, and even then you are at the mercy of light's constancy. But yes I fully agree, B sees A travelling towards themself at 1c, or do they? I guess they can because we as the third observor know they are not either at 1c, only at 0.5c. We have to tweak relativity to truly know who is travelling at what speed. :-D
    sweet!

    Modifying relativity will be fun!
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    :-D.

    Or we can use my idea, that a localised area of the spacetime continuum moves at the same speed (or near the same speed). Therefore we can have a third observor (technically).

    It would be nice to modify Relativity, and fun. Thats exactly the word I was going to use . Joking, it sounds promising being fun .
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    Quote Originally Posted by 425 Chaotic Requisition
    :-D.

    Or we can use my idea, that a localised area of the spacetime continuum moves at the same speed (or near the same speed). Therefore we can have a third observor (technically).

    It would be nice to modify Relativity, and fun. Thats exactly the word I was going to use . Joking, it sounds promising being fun .
    I really don't understand how having a third observer would be accurate.
    Each observer will have his or her own different relative speed to each object A or B. Therefore the third person would not necessarily produce an accurate result of relative speed.

    Its like a person in a train running towards the direction the train is moving.
    The person outside the train will view the other person run at a speed of (man running speed)+(train speed).
    However, that relative speed is different for the person actually side the train.
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    The formula of relativistic addition of velocities is given as:

    V = v2-v1/(1-[v1v2/c^2])

    So doing the maths A would see B going at:
    [taking right as +ve]

    V = -0.5c-0.5c/(1 - [-0.5c*0.5c]/c^2)
    = -c/(1+0.25c^2/c^2)
    = -c/1.25
    = -0.8c or 0.8c coming towards it

    The summation of velocities is not simply v1 + v2 = vOBSERVERD

    Instead with relativistic speeds, the relativistic addition of velocities must be made...
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  14. #13  
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    Quote Originally Posted by Cynapse
    You have looked at the problem from a third reference frame which will only see each blob moving at 0.5c. When taking the point of view from a blob reference frame you have to take into account time dilation and length contraction. They won't appear to be moving at c because of these.
    To be strictly accurate, you also have to take the Relativity of Simultaneity into account.
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    Quote Originally Posted by Cynapse
    The formula of relativistic addition of velocities is given as:

    V = v2-v1/(1-[v1v2/c^2])

    So doing the maths A would see B going at:
    [taking right as +ve]

    V = -0.5c-0.5c/(1 - [-0.5c*0.5c]/c^2)
    = -c/(1+0.25c^2/c^2)
    = -c/1.25
    = -0.8c or 0.8c coming towards it

    The summation of velocities is not simply v1 + v2 = vOBSERVERD

    Instead with relativistic speeds, the relativistic addition of velocities must be made...
    When I was reading this I immediately thought about the phrase "with relativistic speed". The point is that when v1 and v2 are small compared to c then (1-v1v2/c^2) is basically 1 and you get the usual velocity addition/subtraction V = v2 - v1 that we get in non relativistic physics.

    But then it occured to me to think about when ony one of the two velocities is small compared to c. So I did a tailor's explansion around v2/c to get a formua that would be valid for this and the first order apporoximation gives you:

    V = v1 + v2(1-v1^2/c^2) or V = v1 - v2 (1-v1^2/c^2)

    the factor (1-v1^2/c^2) should be familiar as a part of the contraction factor called gamma = 1/sqrt(1-v1^2/c^2)

    so using g1 for the gamma calculated for v1, the approximation becomes

    V = v1 + v2/g1^2 or V = v1 - v2/g1^2

    So back to our planet going .99c, let see how well this approximation works with adding a velocity of .01c remembering that the gamma we calculated for .99c was 7

    V = .99c + .01c/(7)^2 = .990204c

    Now lets compare this with the result from the full formula

    V = (.99c +.01c)/(1+(.99c)(.01c)/c^2) = c/1.0099 = .990197c

    which is the same to 5 significant figures so this approximation works pretty good.

    OK now lets abuse this terribly and apply it to the case in the OP where we are adding .5c and .5c. Well for .5c the gamma squared is 4/3 and so instead of adding .5c we would add .375 c to .5c in order to get .875c so even in the worse case the approximate formula still doesn't give a result greater than the speed of light, athough it does overestimate the velocity by nearly 10%.

    So what is all the point of this? Well it is to see that allong with all the other relativistic effects that contract time and lengths we can add an effect on velocity addition which reduces the effect of added velocity by a factor of gamma squared (as a first order approximation).
    See my physics of spaceflight simulator at http://www.relspace.astahost.com

    I now have a blog too: http://astahost.blogspot.com/
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  16. #15  
    The Doctor Quantime's Avatar
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    And remember folks, this is only theory :wink:.
    "If you wish to make an apple pie from scratch, you must first invent the universe". - Carl Sagan
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    Forum Radioactive Isotope mitchellmckain's Avatar
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    Quote Originally Posted by 425 Chaotic Requisition
    And remember folks, this is only theory :wink:.
    and theory is only science.
    See my physics of spaceflight simulator at http://www.relspace.astahost.com

    I now have a blog too: http://astahost.blogspot.com/
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  18. #17  
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    And I am theorising :wink:.
    "If you wish to make an apple pie from scratch, you must first invent the universe". - Carl Sagan
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  19. #18  
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    without scienence
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