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    Einstein's thought experiments

    Two of Einstein's thought experiments bug me. Here's one.

    A train moves at near light speed across the land from left to right. An observer is on the train, and an observer stands on the ground.

    As the train observer comes into direct alignment with the ground observer, simultaneous lightning flashes occur so that, to the observer on the ground, the flashes appear simultaneous, but to the observer on the train, the flash to the right will appear before the flash from the left, since the observer is moving in that direction.

    If the two observers are in direct alignment, their "place" on the ground at the instant of the flashes is exactly the same distance, then the effects should be the same as if both were actually sitting still.

    The reason I say this is the Michealson-Morley effect, in which Einstein explained that the speed of light will remain the same no matter what speed or direction we are traveling. There is the Lorentz transformation that makes light always appear to be traveling at the same speed.

    Wouldn't the Lorentz transformation affect the train observer so that the light flash would also appear simultaneous?

    Kazza?

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    Re: Einstein's thought experiments

    Quote Originally Posted by doojie View Post
    Wouldn't the Lorentz transformation affect the train observer so that the light flash would also appear simultaneous?

    Kazza?
    I suppose there are two ways of answering this, intuitively or mathematically, so I'll go with the first since it's hard to write mathematical equations here.

    Imagine you are the person standing on the ground, watching the train go past, and at the exact instant the person in the train passes you lightning flashes and strikes the front of the carriage and the back of the carriage.

    For you, on the ground, the light from both lightning strikes travels at the same speed and the light from both ends hits you simultaneously.

    But what about the person on the train?

    Obviously, since he is moving towards one lightning strike, and away from another, the light from one of those strikes will hit him first (the one from the front of the train).


    So now imagine you're on the train. Light from the front of the train hits you, and then a few instants later, light from the back of the train hits you. You want to know whether the strikes happened simultaneously, or whether one happened first.

    You reason that since light always travels at the same speed, if light from the front of the train hit you first, then it must have occured first. Your reasoning is perfectly fine, and in fact, in that frame of reference the lightning did strike the front of the train first.


    If two events occur simultaneously in some frame of reference, and they are separated by some distance in that frame of reference, then there will always exist other frames of reference in which they did not occur simultaneously. None of these frames are special, and it is as equally true to say that it occured simultaneously as it is to say that one occured first.

    I hope this makes some sense, it's difficult to explain without a pen and paper to draw diagrams.

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    Re: Einstein's thought experiments

    Quote Originally Posted by kazza View Post
    I suppose there are two ways of answering this, intuitively or mathematically, so I'll go with the first since it's hard to write mathematical equations here.

    Imagine you are the person standing on the ground, watching the train go past, and at the exact instant the person in the train passes you lightning flashes and strikes the front of the carriage and the back of the carriage.

    For you, on the ground, the light from both lightning strikes travels at the same speed and the light from both ends hits you simultaneously.

    But what about the person on the train?

    Obviously, since he is moving towards one lightning strike, and away from another, the light from one of those strikes will hit him first (the one from the front of the train).


    So now imagine you're on the train. Light from the front of the train hits you, and then a few instants later, light from the back of the train hits you. You want to know whether the strikes happened simultaneously, or whether one happened first.

    You reason that since light always travels at the same speed, if light from the front of the train hit you first, then it must have occurred first. Your reasoning is perfectly fine, and in fact, in that frame of reference the lightning did strike the front of the train first.


    If two events occur simultaneously in some frame of reference, and they are separated by some distance in that frame of reference, then there will always exist other frames of reference in which they did not occur simultaneously. None of these frames are special, and it is as equally true to say that it occurred simultaneously as it is to say that one occurred first.

    I hope this makes some sense, it's difficult to explain without a pen and paper to draw diagrams.
    I see what you're saying. Each referential frame is correct from that frame, with no special frame or absolute frame. This was not made clear in the explanation I read.

    I was intuitively trying to select an "absolute frame", the speed of light itself, and basing my judgement from that viewpoint.

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    Re: Einstein's thought experiments

    Quote Originally Posted by doojie View Post
    I see what you're saying. Each referential frame is correct from that frame, with no special frame or absolute frame. This was not made clear in the explanation I read.

    I was intuitively trying to select an "absolute frame", the speed of light itself, and basing my judgement from that viewpoint.
    Yes, that's exactly what I tried to do the first hundred times I read through the thought experiment. I think it's what everyone tries to do. It's very difficult not to think of one person as having the "right" answer and the other person as having the "wrong" answer. Both people are equally correct in what they claim.

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    Re: Einstein's thought experiments

    so if they are both correct relative to their point of view, the outside observer is POTENTIALLY the absolute/superior observer as to objectivity !? :freak3: :spin2: :
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    Re: Einstein's thought experiments

    Quote Originally Posted by lexx View Post
    so if they are both correct relative to their point of view, the outside observer is POTENTIALLY the absolute/superior observer as to objectivity !? :freak3: :spin2: :
    Nope, that's precisely the point. Neither of them is absolute or superior. They are both equally objective.

    In fact, one of the two principles of special relativity is that there is no such thing as an absolute reference frame (ie. absolute velocity).

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    Re: Einstein's thought experiments

    Quote Originally Posted by kazza View Post
    Nope, that's precisely the point. Neither of them is absolute or superior. They are both equally objective.

    In fact, one of the two principles of special relativity is that there is no such thing as an absolute reference frame (ie. absolute velocity).
    Lexx's thought was similar to mine. If each of the two had an objectively correct understanding from their position, and if a third person could see this, would not the third person, recognizing no absolute frame of reference, have the right frame of reference, which is no absolute frame of reference?:spin2:

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    Re: Einstein's thought experiments

    Quote Originally Posted by doojie View Post
    Lexx's thought was similar to mine. If each of the two had an objectively correct understanding from their position, and if a third person could see this, would not the third person, recognizing no absolute frame of reference, have the right frame of reference, which is no absolute frame of reference?:spin2:
    Sorry, I should have defined what I meant by frame of reference. I don't mean in it the colloquial sense - in physics it has a special meaning.

    In physics, and particularly in special relativity, an "inertial frame of reference" is a set of coordinates that is moving at a constant velocity (ie. not accelerating).

    So there is a frame of reference that is moving with the train (the person standing in the train would be in this frame of reference), there is a frame of reference that is stationary with respect to the ground (ie. the person watching the train), and there are an infinite number of other frames of reference (ie. one moving straight up at 34m/s, and one moving in the opposite direction to the train at 4km/h....).

    So you can see that with this definition it's not possible for someone to have no frame of reference, but in the colloquial use of the term, then yes, someone who recognised there was no absolute frame and hence had no frame of reference would be correct.

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    Re: Einstein's thought experiments

    okay... but theres still a hitch. If it is pitch black other than these light flashes... Let eliminate one and just have the back light flash - the one that we are in dispute as to when it hits the person on the train. Lets say that one light flash is an impulse.

    The effect on any observer will be a flash of light at the back of the train, and an image of a person when the light bouces off that person on the train.

    So... if the frame of reference is different based on the speed of light relative to the event, we should be able to have many objects moving around this event who all see the light in the same position, but the person on the train in another position?

    It occurs to me that you could make changes in reality and the laws of physics dependant on what speed you pass this event.
    Last edited by Lord_jag; 05-13-2009 at 06:58 AM.
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    Re: Einstein's thought experiments

    Ok, new thought experiment, with the same basic idea, but working backwards, and with help from diagrams on wikipedia.

    Again we have a person on a train and a person on the ground, but instead of two bolts of lightning, the person on the train emits two beams of light that travel to the ends of the train.

    Lets consider it from the perspective of the person on the train...



    So it takes 2 seconds for the light to reach the ends of the train, and reaches both ends at exactly the same time. In the frame of reference of the person on the train, the light reaching the back of the train and the light reaching the front of the train happened simultaneously.


    Now let's consider the person on the ground.


    (Note that the red circle represents where the flash was emitted, not where the person on the train is standing.)

    Now, for the person on the ground, after 2 seconds the light has reached the back of the train, but it has not yet reached the front.

    Since light travels at the same speed for everyone, no matter what, the person on the ground is absolutely correct to say that it hit the back of the car first, and then hit the front.


    I didn't quite understand what you were getting at before Lord Jag. Is it possible to rephrase it in terms of this experiment where we have diagrams? It's hard to communicated diagrams without a pen and paper or a blackboard...

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    Re: Einstein's thought experiments

    Hm... okay... I don't know if I can make such pretty diagrams as that.

    But... I can work with what you have. Okay so say you are using the second example you show, with the perspecive of the person on the ground. Lets say the train was moving at 100 m/s below light speed. Say the train is 10m long from the source to the front. Forget the backwards facing light for now.

    1) A stationary person would see the light hit the front in 10/100 or 0.1 seconds, right? The car is moving just below light speed, so the light moving AT light speed would catch up at 100 m/s... He would see the front of the train light when the train is a mere 30,000,000 meters away (3x10^8/0.1s)

    2) a person moving in the same direction as the train (100m/s) would see the front of the train light up twice as fast because the train would seem slower and light is the same speed. in his case, the light would be 200m/s faster than the train, so it would get there in 10/200 or 0.05 seconds. He owuld see the front of the train light up when it was 15,000,000 meters away.

    3) A person moving in the opposite direction of the train (100m/s) would see the train moving at the speed of light. The front of the train should never light up for him.

    so.... at what point does the front of the train radiate light in reality?

    Further... if the light was used to set off a sensor that did something... say fire a bullet off the side, could you determine where the bullet is fired based on your own relative speed? That means all three people would experience 3 different realities where a bullet is fired at 3 different locations?
    Last edited by Lord_jag; 05-13-2009 at 04:15 PM.
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    Re: Einstein's thought experiments

    Quote Originally Posted by Lord_jag View Post
    Hm... okay... I don't know if I can make such pretty diagrams as that.

    But... I can work with what you have. Okay so say you are using the second example you show, with the perspecive of the person on the ground. Lets say the train was moving at 100 m/s below light speed. Say the train is 10m long from the source to the front. Forget the backwards facing light for now.

    1) A stationary person would see the light hit the front in 10/100 or 0.1 seconds, right? The car is moving just below light speed, so the light moving AT light speed would catch up at 100 m/s... He would see the front of the train light when the train is a mere 30,000,000 meters away (3x10^8/0.1s)

    2) a person moving in the same direction as the train (100m/s) would see the front of the train light up twice as fast because the train would seem slower and light is the same speed. in his case, the light would be 200m/s faster than the train, so it would get there in 10/200 or 0.05 seconds. He owuld see the front of the train light up when it was 15,000,000 meters away.
    You are absolutely correct here. What you've hit on is the phenomena of time dilation. Let's say the person in the train is wearing a watch, and the person outside is wearing a watch as well. Both set their watches to 0.00 when the flash of light goes off.

    Like you mentioned in (2), for the person on the train the light will hit the front when his watch reads 0.05 seconds. For the person on the ground, the light will will reach the train when his watch reads 0.10 seconds. Both people are 100% correct, so what's going on?

    Time is passing slower for the person on the train. If the person on the ground could see both watches at the instant the light hits the front of the train, then he would see his own watch say 0.10 and the train watch say 0.05 and he would correctly deduce that the watch on the train is running slower than his own.

    (Confusingly, the person on the train would actually see the watch of the person on the ground running slower as well, but this resolution to this sort of paradox requires general relativity.)

    The closer the train gets to the speed of light, the slower time runs.

    3) A person moving in the opposite direction of the train (100m/s) would see the train moving at the speed of light. The front of the train should never light up for him.
    This isn't quite correct. If he was moving in the opposite direction to the train at 100m/s, he wouldn't see the train moving at light speed. It would take me a bit of maths to show why this is the case.

    Basically, when you change from one reference frame to another but keep the speed of light constant, you end up using Lorentz transformations instead of Galilean.

    At 100m/s, he would end up seeing the train moving at maybe 90m/s below the speed of light, or something like that. If he were moving at almost the speed of light himself, then he might see the train moving at 0.000001m/s below the speed of light, but never at the speed of light or faster.


    so.... at what point does the front of the train radiate light in reality?
    This is one of the hardest concepts to loose when dealing with special relativity. Both people are correct, there is no absolute answer. In one reference frame the front and back light up simultaneously, in another the front first, in another the back first. For one person it's 0.10 seconds after the flash, for another it's 0.05.

    Further... if the light was used to set off a sensor that did something... say fire a bullet off the side, could you determine where the bullet is fired based on your own relative speed? That means all three people would experience 3 different realities where a bullet is fired at 3 different locations?
    Lol. I guarantee you'll find a question like that on almost every undergraduate exam on special relativity.

    A couple of different things can happen when you deal with speeds that are close to light - time slows down, simultaneous things are not always simultaneous, and distances contract. To work out where the bullet would be fired would need to take into account all three of these things.

    However, once you work it out, all three people will agree on the same events occuring. Let's say you fire the bullet into a tree. The person on the ground and the person on the train will not agree on when the bullet was fired, and they will not agree on where the tree was, or how thick it was, or how long it took the bullet to reach the tree, but they will both agree that a bullet was fired from the train into a tree.


    Also, there's a bit of a caveat to the thought experiment with the train - I mentioned that there exist frames in which the light hit the front of the carriage first, and others where it hit the back of the carriage first. This is only possible because the two are not causally connected. That is to say, no information could have passed between the two in the time it takes for one to happen and then the other.

    Change reference frames can change times, distances, and simultaneity, but it can not change the causal order of things. If A could have caused B, then in all frames of reference A came before B.

    (The way this actually comes about is because information travels at the speed of light (well, that's the max anyway) and for A to cause B information must have travelled between them)

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    Re: Einstein's thought experiments

    Wow... my head is spinning now... Thanks. :)

    I forgot about time dilation. I do remember studying this many years ago and doing some of these calculations.

    This is the fun part of physics. When things all start to go a little hairy. :)
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    Re: Einstein's thought experiments

    Quote Originally Posted by kazza View Post
    Ok, new thought experiment, with the same basic idea, but working backwards, and with help from diagrams on wikipedia.

    Again we have a person on a train and a person on the ground, but instead of two bolts of lightning, the person on the train emits two beams of light that travel to the ends of the train.

    Lets consider it from the perspective of the person on the train...



    So it takes 2 seconds for the light to reach the ends of the train, and reaches both ends at exactly the same time. In the frame of reference of the person on the train, the light reaching the back of the train and the light reaching the front of the train happened simultaneously.


    Now let's consider the person on the ground.


    (Note that the red circle represents where the flash was emitted, not where the person on the train is standing.)

    Now, for the person on the ground, after 2 seconds the light has reached the back of the train, but it has not yet reached the front.

    Since light travels at the same speed for everyone, no matter what, the person on the ground is absolutely correct to say that it hit the back of the car first, and then hit the front.


    I didn't quite understand what you were getting at before Lord Jag. Is it possible to rephrase it in terms of this experiment where we have diagrams? It's hard to communicated diagrams without a pen and paper or a blackboard...
    That's a good diagram. But, assuming that the speed of light is the same for everybody, regardless, and the man on the car above is exactly in alignment with the man on the ground when he turns on the light.

    Since the speed of light is the same no matter how fast you are traveling or what direction, then the flashlight beam will still be 186,000mps(give or take) for both of them.

    As I understand it, there is no addition of velocities for the speed of light. If the observer were standing on the ground in exact parallel to the moving observer when the light is turned on, why would not the Lorentz transformation not occur so that both observers see the same thing?

    I visualize a man ion a train car with an old pull chain light bulb. As he pulls in direct alignment with me on the ground, he hits the light switch. I see the same instant lighting that he sees.

    As for the two lightning flashes, it seems to me that the train, at whatever speed, provides an inertial frame of reference that coincides with my own as the observer sees the two flashes of lightning. Since there is no addition of velocities with the speed of light, both see simultaneous flashes. To light, an inertial frame is an inertial frame.

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    Re: Einstein's thought experiments

    Quote Originally Posted by doojie View Post
    That's a good diagram. But, assuming that the speed of light is the same for everybody, regardless, and the man on the car above is exactly in alignment with the man on the ground when he turns on the light.

    Since the speed of light is the same no matter how fast you are traveling or what direction, then the flashlight beam will still be 186,000mps(give or take) for both of them.

    As I understand it, there is no addition of velocities for the speed of light. If the observer were standing on the ground in exact parallel to the moving observer when the light is turned on, why would not the Lorentz transformation not occur so that both observers see the same thing?

    I visualize a man ion a train car with an old pull chain light bulb. As he pulls in direct alignment with me on the ground, he hits the light switch. I see the same instant lighting that he sees.

    As for the two lightning flashes, it seems to me that the train, at whatever speed, provides an inertial frame of reference that coincides with my own as the observer sees the two flashes of lightning. Since there is no addition of velocities with the speed of light, both see simultaneous flashes. To light, an inertial frame is an inertial frame.
    Ok, perhaps try imagining two lightbulbs. One with the person on the train, and one with the person on the ground. Both turn on their lightbulb at exactly the same time, when they are in alignment with one another.

    As far as the person on the train is concerned, he is not moving, the ground is moving under him, so he correctly reasons that the light from his light globe will hit the front of the train and the back of the train at the same time.

    As for the person on the ground, he says that he isn't moving either, that it's the train that is moving, and so he correctly says that while the light is travelling, the train will have moved to the right, and so the light will hit the back of the train before it hits the front.


    You can add together velocities in special relativity, but you instead of

    w = u + v

    you need to use

    w = ( u + v )
    ------------
    (1 + uv/c^2)

    Any two values for u and v that are less than c, will never add to give a value greater than c.

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    Re: Einstein's thought experiments

    As far as the person on the train is concerned, he is not moving, the ground is moving under him, so he correctly reasons that the light from his light globe will hit the front of the train and the back of the train at the same time.
    He correctly reasons.

    [/quote]As for the person on the ground, he says that he isn't moving either, that it's the train that is moving, and so he correctly says that while the light is travelling, the train will have moved to the right, and so the light will hit the back of the train before it hits the front.[/quote]

    But there would be no logical reason for him to say that, since he can also reason that the light will travel in relation to the traveler , meaning that they have both come to the same conclusion. :liefde:


    The diagram above is confusing to me because of the t=1 and t=2 representation. If the flashlight is turned on and both are in alignment, both will see the flashlight turned on at the same instant. The speed of light being ab absolute frame of reference, both observers will view the light itself as an absolute frame of "everywhereness". That is, the speed of light, being absolute, will seem instantaneous.

    Assume the traveler is on a flatbed car with no walls, and he comes into alignment with a stationary observer.

    At the exact point of alignment, the traveler hits the flashlight switch so that the beams are going sideways to the observer with no wall to restrain them. To both frames of reference, light speed will be absolute, so that both will see light projecting equally in both directions. Granted, the range of the light will move with the traveler, due to the limitations of the flashlight, but for one instant dictated by the speed of light(time/space), both will see that light within an absolute frame. To say otherwise is to say that light travels at a speed less than it travels. less than absolute within any time frame.

    I'm not trying to be nasty or argumentative, just trying to reconcile this in my mind.

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