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Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of light.

  1. Feb 17, 2009 #1
    I am a new fish to SR and I have some questions about light clock. Hope someone to clear my concepts.

    Q1.
    As we all know, the speed (scalar) of light is "c" and is independent to the motion of the light source, but what about the velocity (vector) of light (with magnitude "c" but what direction ? )?

    Q2.
    Suppose the direction of a light ray is prependicular to the velocity of the light source (like the one in light clock.), can the light ray get the horizontal speed from the light source?

    Q3.
    In the frame of a person who stand beside a light clock on a moving train which having speed "u" to right,
    why the path of a photon that he observed is vertically up and down ? Is it because the photon got the horizontal speed ("u" to right) .If yes, then it become a classical veloctiy addition ?; If no, the photon got no horizontal speed from the source, then how can the person on the train see a vertical up and down path instead of diagonal path?

    I hope you can understand what I am talking about.

    Thank you!!
     
  2. jcsd
  3. Feb 17, 2009 #2

    Doc Al

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    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    While the speed is observer independent, the direction of the light is not. Different observers will see the same beam of light traveling different in different directions. (This is called aberration.)

    Yes. In the sense that someone observing the light clock pass by will see the light moving on a diagonal. The horizontal component of the light's speed will equal that of the light clock.

    It's not classical velocity addition, but relativistic velocity addition. In the frame of the train, the light beam travels vertically. To find the velocity of the light with respect to the ground, one adds--relativistically--the horizontal speed of the train. The net result of that addition is that the speed stays the same (still c) but that the light moves on a diagonal.

    Look up: relativistic addition of velocity; aberration
     
  4. Feb 17, 2009 #3

    Fredrik

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    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    (Everything below is in units such that c=1).

    1. The direction of the velocity depends on the frame. This is obvious in the case of rotations, but less obvious in the case of a velocity boost. If the velocity is in the direction of the vector (1,1) in the xy-plane, the velocity in a frame that's moving with speed v in the positive x direction of the first frame is in the direction of [itex](1-\sqrt 2v,1)[/itex].

    2. Yes, but the velocities add up in a complicated way:

    [tex]\vec u\oplus\vec v=\frac{1}{1+\vec u\cdot\vec v}\bigg(\vec u+\vec v+\frac{\gamma_{\vec u}}{1+\gamma_{\vec u}}\vec u\times(\vec u\times\vec v)\bigg)[/tex]

    The definition of [itex]\gamma_{\vec u}[/itex] is

    [tex]\gamma_{\vec u}=\frac{1}{\sqrt{1-\vec u^2}}[/tex]

    The specific case you're asking about is [itex]\vec u=u\vec e_0,\ \vec v=\vec e_1[/itex].

    3. Why wouldn't it be up and down? The observer and the light clock have the same velocity (if I understand your description correctly), so from their point of view, it's the ground that's moving. So the only way the direction could be anything else is if a) the motion of other objects in the vicinity drags the light with it, or b) if this observer's point of view is less valid than the point of view of someone standing on the ground outside.

    Edit: After reading Doc AI's answer I think I probably misunderstood your description. If the clock is resting on the ground outside the train, then the answer is what he said.
     
    Last edited: Feb 17, 2009
  5. Feb 17, 2009 #4

    robphy

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    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    As written, NO.
    The light ray "does not get" the horizontal speed from the light source (since there is no force acting horizontally to change the direction of the light ray).

    Rather,
    the light ray "happens to have" the same horizontal speed as the light source.

    I think of it this way.
    The initial flash has light rays in all directions.
    The particular light ray that has the same horizontal component of its velocity as the moving light clock will be the one that will be reflected by the distant mirror of the light clock... and remain with this inertially moving light clock. The other light rays are lost (if not reflected by other light clocks moving inertially with different velocities).
     
  6. Feb 17, 2009 #5
    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    Thank you all of you, I think I wil adopt what Doc Al said at the stage.
    The idea from robphy is what I guess originally, but I don't think it is a appropriate explanation. What I want to know is why the light ray "happens to have" the same horizontal speed as the light source?
     
  7. Feb 17, 2009 #6

    Fredrik

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    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    Because if it the horizontal speed has any other value, the observer on the train will disagree with the observer on the ground about which spot the light hits. Imagine that the ray of light is a laser that hits an ant and kills it. The two observers would disagree about whether the ant is alive.
     
  8. Feb 17, 2009 #7

    robphy

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    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    As I described, it's the only one that gets reflected by that mirror.
    Watch my video: [URL [Broken]
    physics.syr.edu/courses/modules/LIGHTCONE/LightClock/VisualizingProperTime-y-pair-A-with-photons.avi[/url]
     
    Last edited by a moderator: May 4, 2017
  9. Feb 17, 2009 #8

    tiny-tim

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    A fishy welcome to PF!

    SR needs more fish! :wink:

    :smile: Welcome to PF! :smile:

    Preserve the bowliverse! :wink:
     
  10. Feb 17, 2009 #9

    atyy

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    Re: A fishy welcome to PF!

    Welcome indeed! :smile:

    But how can SR have fish? Wouldn't the water define a preferred frame of reference? :confused:
     
  11. Feb 17, 2009 #10

    tiny-tim

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    Re: A fishy welcome to PF!

    water? what's water? :confused:
     
  12. Feb 17, 2009 #11
    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    What I am asking is what "JustinTime " asked in his post : Light shone in a train bouncing off mirrors
     
  13. Feb 18, 2009 #12

    tiny-tim

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    Hi Canaan_C! :smile:
    ooh, that's a very long thread :cry:

    let's go back to …
    It depends what angle the light starts.

    If the light goes through two pinholes in plates attached to the train which are arranged vertically (as viewed by someone in the train), then the light will go vertically up in that frame, hit the mirror on the ceiling, and be reflected back along its path (as viewed by someone in the train), but will be seen as zigzagging by someone on the track.

    If the light goes through two pinholes in plates attached to the track which are arranged vertically (as viewed by someone on the track), then the light will go vertically up in that frame, hit the mirror on the ceiling, and be reflected back along its path (as viewed by someone on the track), but will be seen as zigzagging by someone in the train. :smile:
     
  14. Feb 18, 2009 #13

    Saw

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    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    That is not the answer I usually get for this question, which I presumed was the standard SR answer. I'll explain myself.

    In your configuration, tiny-tim, it seems light is allowed to spread in all directions, as it is its tendency. Thus it is quite understandable that, no matter the state of motion of the frame in question, if not one photon, another one (if not one ray, another one, if you want to put it in terms of the ray model), will find its way through the pinholes.

    But the question becomes more challenging if you consider another configuration where light does not have that liberty. Think for example of light projected from a laser gun, which follows a considerably restricted path in parallel to the arm of the laser gun.

    In this second scenario, Lorentzian relativity (based on the existence of the ether) would claim, if I’m not mistaken, the following: if the frame in question has residual acceleration (by this I mean the net effect of all its historical accelerations wrt the ether) zero or whatever but along the line joining the laser and the target, it would reach its destination, but if the frame’s velocity wrt the ether has a component perpendicular to that line, the light would not make it to the target, it would hit the top of the train somewhere else.

    Instead, the standard SR answer is that the laser light will “never” miss its target in the slightest. Why? Because light does not take the speed (scalar component) but does acquire the direction of the frame from which it is projected, the direction of the source, in other words. Why so? Because of the principle of relativity, which states that all experiments render the same results in all frames, no matter their diverse states of motion. Otherwise, you would be able to classify frames according to this criterion: those where the laser light hits the target and thus conform to the general laws of physics and those where it doesn’t. Why should we adhere to that principle, formulated in such a rigid manner? Because experiments have always corroborated it, even if we have no “physical” explanation for it.

    That is why in the other thread mentioned by Canaan_C I asked this question, which remained unanswered: We usually say that LR and SR are conceptually different, but predict the same practical results. However, this seems to be a difference, doesn´t it? I think we should simply accept there is such difference, whatever it means.
     
  15. Feb 18, 2009 #14
    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    Hello Saw.

    Perhaps this will help.

    Imagine a laser beam, as thin as you like, pointing at a spot immediately above it on the ceiling. If you considered the whole system, laser/ceiling stationary you woulr have no problem imagining the laser hitting the spot. Now the question is - How do you know whether the system is moving or not? The answer of course is that you cannot know. So as the frame the laser/ceiling is in is completely arbitrary, and will be moving relative to other frames, the laser will hit the spot in any case. Its path will of course look different to someone in the laser/ceiling frame than to someone not at rest in that frame.

    There is probably a better way of phrasing it but this was quick answer.

    Matheinste.
     
  16. Feb 18, 2009 #15
    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    Light always propagates spherically, it just don't always have the same frequency and/or amplitude on a particular part of this spherical "wave front" emitted. A laser is just a device designed, tuned, and optimized to produce these waves with a specific frequency along only one part of this spherical wave front (mirrors and other optical materials are good at this. So, next time you see a laser beam, remember you are only seeing one tiny thin fraction of the spherical "light wave" because the rest of it is outside (probably far, far outside) the visible.

    For pedagogical purposes let's consider the waves to propagate in some fluid-like medium. In this case you can think of a ball in water which suddenly expands and then contracts. A spherical region of the water around the ball will be alternatingly compressed/rarified, similar to how sound propagates, and as such will have a characteristic wavelength w and frequency f. The wavelength is just the distance between compressed (or rarified) regions and the frequency is just the length of a single compressed (or rarified) region. Empirically we know that the ball cannot know if it is moving in this fluid or not (and, by extension, if the fluid is even there). How come? Let's analyze the situation in some detail.

    When the ball moves in this fluid the waves are compressed/shortened in its direction of motion and lengthened behind it. This is the standard Doppler effect, which you should familiarize yourself with if you haven't already. The ball moves a little forward, emits a wave, then moves a little forward and emits another, making the waves "in front" of it closer together and the ones "behind" it further apart, shortened and widened exactly by the magnitude of the velocity. If the ball is moving at 0.5*c (where c is how fast the waves propagate with respect to the fluid) then the wavelength of the light in the direction of the ball's motion (forward wavelength wD') is:

    wD' = 1-(0.5/1) = 0.5*w

    and its wavelength in the direction away from its motion (wD'') is:

    wD'' = 1+(0.5/1) = 1.5*w.

    These relations come from understanding the standard Doppler effect.

    So it should be readily apparent from measurement that the wavelength of light emitted by a moving body is 50% smaller in one direction and 33% larger in the other, right? This is an asymmetric effect and should be indicative of an aether.

    Unfortunately, the ball itself expands/contracts more slowly when it moves through this fluid, because of the way it interacts with the fluid. The wavelength (forward and backward) increases (greater distance between similar regions). The wavelength emitted by the ball moving at 0.5*c in the forward direction (before applying the regular doppler effect) is:

    wG'=w/sqrt(1–(0.5/1)^ 2) = 1.1547

    In the reverse direction it's the same because the ball's slower expansion/contraction applies in all directions:

    wG''=w/sqrt(1-(0.5/1)^2) = 1.1547

    So, the forward and reverse wavelengths with respect to the fluid are just the products of the doppler broadening/contraction and the Lorentzian symmetric wavelength broadening:

    w' = wD'*wG' = 0.577
    w'' = wD''*wG'' = 1.732

    The forward and backward wavelengths are exact inverses, w'*w'' = 1.

    So, if the ball is moving away from us we will see exactly the same wavelength shift as in the case were we are moving away from it! Since the wavelength is shifted by an identical proportion in both directions, the ball's directional motion within the aether cannot be identified. We can only detect relative motion.

    If I'm holding the ball and I detect its wavelength is w and I push it away from me, I cannot tell whether it's moving away from me or I'm moving away from it. The wavelength shift is the same proportion either way. This symmetry, which makes it impossible to observe this fluid medium directly, led most physicists to discard the fluid aether.
     
    Last edited: Feb 19, 2009
  17. Feb 19, 2009 #16

    Saw

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    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    Matheinste, I can perfecty visualize, even for the LASER beam, a vertical path as measured in the coordinate system of the source frame and a diagonal path as measured in the coordinate system of the observer frame. I just wanted to point out that, if the beam is not part of a spherical wave (it is a laser beam), in the conceptual framework of SR there is no explanation for that effect, other than that if it were otherwise we would be able to detect the relative motion of the source frame wrt others.

    altonhare, the second part of your post is a brilliant description of why SR and LR are said to render the same practical results..., as a general rule. However, in the first part of your post, you seem to give me a reason why the issue posed in this thread should not be an exception, but I do not see the reason. According to LR, if there is an ether, that "tiny thin fraction of the spherical "light wave" that is visible should follow a path that is dependent on the state of motion (or no motion or whatever) of the ether but it should not follow the direction of motion of the source and should not hit the target it was pointing at in the source frame...
     
  18. Feb 19, 2009 #17
    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    Hello saw.

    According to SR the speed of light is constant and the same for all frames. This means that the point of emission, or source, remains central to the expanding sphere of light. In the case of a laser beam or ray, the ray is just a radius of this sphere. In LR the point of emission, or source would move away from the centre of the expanding light sphere if the source were moving relative to the ether.

    What i am trying to say is that in SR the source remains cetral to the expanding light sphere but in LR it can move away from it depending on whether or not the source is in motion relative to the ether.

    Does that help.

    Matheinste.
     
  19. Feb 19, 2009 #18
    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    Thank you kindly for the compliment, I was hoping it was clear!

    Perhaps I can help make things more clear, I hope.

    In the Lorentzian aether view, light's qualitative characteristics are *no different* than sound with the exception of the Lorentzian velocity-dependent symmetric wavelength broadening.

    In the Einsteinian view this wavelength broadening is called "time dilation" because an atomic clock, which measures this "time" by the number of photon emissions N, emits light of a longer wavelength (fewer photon emissions) when in relative motion. Therefore each photon emission indicates a longer "time" has elapsed for the clock in motion wrt the aether as compared with a clock that is stationary wrt the aether.

    An object that traverses a distance d through the aether emits N1 photons as another object traverses d/2. If there were no Lorentzian wavelength broadening we would expect the second object to emit exactly N1 photons as well, i.e. each photon indicates the precise same interval whether emitted from object 1 or 2. However, as Lorentz discovered, the second object will not emit N1 but rather N1/(1+(d2/(4*c2)). The slower object's unit of time (a photon) is shorter than the faster object's unit of time.

    So, just like sound, wrt the medium carrying the signal its velocity remains the same i.e. the basic formula c=f*w always applies. Only the wavelength changes and frequency is both the physical and mathematical opposite and inverse of wavelength so their product is always 1.

    So, since light behaves just like sound, it does not acquire the speed of its source. The velocity of sound in air is always constant wrt the air, and the speed of light in the aether is always constant wrt the aether. An observer moving wrt the aether would detect a Newtonian/Galilean velocity shift except that their clock always ticks slower to counter this and produce the same result for velocity of light.

    Observer 1 is carrying a light emitting object as a clock. It emits light signals that are the distance w apart when the observer is not moving relative to a ball that also emits light signals a distance w apart. (rest wavelength of light emitted by both objects is identical).

    Observer 1 and the ball are a distance D from each other before moving. The speed of light is, then, D/w by definition i.e. it is the number of photons emitted by the clock as a single photon makes the path between ball and observer.

    If they are not in relative motion then the observer counts identical numbers of photons from his/her own clock and from the ball. The observer has no idea what w or D is, nothing really. All the observer knows is that the propagation speed of a photon is its distance-traveled (D) divided by the number of photon emissions of his clock during that distance-traveled.

    The observer (or the ball) moves an infinitesimal bit back (distance d1) while the observer counts photons from his/her clock. Obs 1 determines his/her velocity to be d1/N1, where N1 is the number of photons released by the observer's clock as the observer traversed d. The observer also determines the wavelength of light emitted by his/her clock (w) to be d1/N1. The observer also counts Nb1 photons from the ball. The observer determines the velocity of light, according to his own clock/reference, to be C1 = (N1*D)/d1. The velocity of light relative to the ball is also C2 = Nb*D/d2. The observer doesn't know Nb because Nb is the number of photons emitted by the ball, not the number of photons the observer sees from the ball. The latter is Nb1.

    Are N1/d1 and Nb1/d1 related such that C1 and C2 always come out the same? First of all, the observer has to account for the standard doppler shift when calculating Nb. That's easy enough:

    Nb0/d1 = N1*D/d1 - d1/N1

    But also the observer must account for Lorentzian broadening:

    Nb/d1 = Nb0/sqrt(1-[(d1/N1)2/(N1*D/d1)2]

    = N1/d1 if you do it right.

    So the velocity of light is always measured the same.

    There is one experimental test that has yet to be done and probably never will be done for practical reasons. The aether is described as "pervading all space" but, to constitute an absolute or preferred frame it must have a boundary. Otherwise how can anything move with respect to it? From whence would motion be gauged within it? Indeed, if the aether were truly "infinite" i.e. without a boundary it's worthless rubbish. For an object alone in such 'an' infinite "entity" it would be impossible to determine its change in location, from where would it determine its location? It would need another object, something with a boundary, in order to determine this.

    So, if there's an absolute/preferred frame, it must have a boundary. If it doesn't have a boundary it is not only empirically and practically useless but scientifically and philosophically unsound. The final test for such a hypothesis is to hop in a ship and start flying in search of the aether's boundary itself. Good luck.

    Saw, ultimately if you want to understand how light works you have to first understand how waves work. Whether there's an aether or not light behaves like a wave with the exception of Lorentzian broadening. So familiarize yourself (or review) your wave physics.
     
  20. Feb 20, 2009 #19

    Saw

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    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    Hello, Matheinste, it does help. Since LR's model for light waving in the ether is, somehow, analogous to sound in the air, please consider this thought experiment: sound creates a circular (we only consider 2 dimensions) perturbation in the air = air molecules push their neighbors; we imagine that each molecule has a different color (this is not an analogy with light's frequency, but just a way to identify molecules in an imaginary manner); we further imagine that each molecule communicates its color to the neighbor that it pushes; the molecule that occupies the place that is right on top of the source creating the perturbation is red and the molecules touched by it become red and so on; after some time, the source frame, if it is moving rightwards, will find that the red column has followed in its coordinate system a path bent to the left; another column (a shorter one, by the way), let us say a green one, does follow a vertical (wrt the moving source) path and after some time it will become long enough to reach the target (the centre of the top mirror in the light-clock example); conclusion: if the source had only produced the red column, the perturbation would have not hit the target. Hence LR's conceptual model only conforms partially (under certain conditions, contingently) to the principle of relativity, while SR fully complies with it...

    Here we come to althonhare's explanation. Yes, I will revise my knowledge of wave physics, because I must confess that I still don't see why your comments answer or even address my concern! I would say I fear I have time dilation in my mind, if I didn’t also fear that you could interpret it ala relativity!

    I will study your text carefully. But before that, I beg you to review some comments that your text has elicited from my moving mind.

    I usually visualize the problem as photons or light pulses bouncing between two longitudinal mirrors and two transversal mirrors, like in a MM device. Let us imagine that the frame of the source and of the MM device was initially at rest wrt the ether and has been accelerated to the right. In this context, under my current understanding of LR:

    - the longitudinal light, during its go trip (i.e., in the direction in which the moving frame has been accelerated wrt the ether, i.e. rightwards), should in principle take more time to do that trip to the right edge (than one chasing a mirror at rest wrt the ether), because the target is racing away, while its return trip (to the left) should take less time, because the target is heading towards the light; the average speed of this longitudinal light is (1-v^2/c^2)c = 0.75 c if v = 0.5c, c being the speed of light wrt the ether and time being measured for this purpose by a clock at rest wrt the ether; by the way, if this longitudinal light had been projected to the left and returned, it would have arrived at the moving source at the same time as the one projected to the right (the average speed and the time for the go-and-return trip is the same in both cases);

    - instead the transversal light travels upwards and downwards at a faster pace, namely sqrt(1-v^2/c^2) = 0.866 c in our example, so in principle it should return to the origin earlier, but this does not happen because the longitudinal arm of the MM device has contracted by precisely sqrt(1-v^2/c^2), which enables the longitudinal light to arrive in time for the meeting with the transversal one.

    In your example, instead, the actor is a sort of pulsing ball (an atomic clock?). This is interesting because it incorporates a physical description of time dilation, at the same time as length contraction… In my example nothing would prevent the source from emitting a second pulse while the first one is travelling; in yours, the “ball”, having emitted a first pulse, will only emit the second one after getting the first back, that is to say, a little later than a clock at rest wrt the ether. Thus we have Lorentzian time dilation.

    But this is even more suggesting if we consider that there is “space” between the centre of the ball and its internal “target mirror”, if we put it in terms of an analogy with my own example. In other words, before releasing the light wave (or photons) to the outer world, the electron must traverse an *internal* path: it has to be excited in order to reach a higher-energy state and more physical height (“orbit” or “step” or whatever we call it) and only after covering this internal path does it rebound, relax, release the acquired energy in the form of a photon and return to its ground-state. This entails, coming back to the point of the thread and to my concern, that this photon that glimpses out will only be a “green” photon (see my image above), i.e., it will only appear in the RF of the source as a perpendicular beam, if it has followed, as judged from the RF and cartesian CS of the ether, a diagonal path, bent rightwards, if the acceleration of the source frame is to the right.

    This sounds nice, because it matches with the idea of stellar aberration (Doc Al’s hint at the beginning of the post)…, if you put the phenomenon of aberration upside down and watch it from the point of view of the emitter: if you wish to generate a “vertical” laser beam as viewed in the source frame, that is to say, one that goes through the “pinhole” (tiny-tim’s image also earlier in this thread) of the atom (or maybe of the apparatus) that points at the target, you have to make it travel, beforehand, within the internal structure of the atom (or the apparatus), through an inner “telescope” tilted in the direction of travel of the source wrt the ether.

    In view of this “explanation” (a clumsy speculation, actually, but I read somewhere one must cherish new ideas…), one could affirm, no matter if SR or LR is right, that light takes the direction of the source. So I would change my mind in this respect.

    Is this (a) a truism, (b) simply wrong, (c) an original idea that might be pursued…?
     
    Last edited: Feb 20, 2009
  21. Feb 20, 2009 #20
    Re: Questions abouut:Special Relativity, Time Dilation, Light Clock, Velocity of ligh

    Saw,

    Not sure if you understood my "pulsing ball". It doesn't have to wait for anything to "come back", it physically pulses more slowly because moving wrt the aether inhibits the pulsing. It can pulse again while the first pulse is traveling away... of course.

    The ball is meant to simulate an atom. The expansion of the ball is the expansion of the electron shell. In this fluid aether view the shell simply pushes against the fluid next to it, compressing it, then when it contracts this induces a region of low fluid density (vacuum) around it. Of course atoms don't actually work this way. When the ball moves its diameter is contracted in the direction of its motion because the fluid pushes against the shell, similar to what Lorentz posed. It's possible that the internal structure of this ball is such that deformation from its native state (stationary wrt the aether) makes pulsing more slow/difficult. This is not my theory of light or the atom, it's just a helpful illustration.

    If you understand a standard MM setup I'm not sure what the difficulty here is. You seem to understand things quite well.

    Q1:Light does not acquire the speed of its source because it behaves like sound. It does not acquire the direction of its source because it propagates spherically, in all directions. If part of the spherical wave front is at a different frequency (visible perhaps) we have a laser "beam". Let's also place several targets stationary wrt the aether for the beam to hit. If the pulsing ball is emitting these then, as it moves to the right, the visible region of the spherical wave front will still move straight ahead and hit the target. However each successive visible wave front will be emitted a little to the right, which will overall trace a diagonal path on the targets. The ball may calculate a horizontal velocity component of these wave fronts. This is no different than sound. A person emitting sound and moving to the right can (and will!) measure 2 perpendicular components of the velocity, which resolve to the magnitude c.

    Q2: See above

    Q3: If the train is moving to the right wrt the aether and the observer is standing in the train firing a laser straight up, then s/he will see a straight, rectilinear path. This is different than the example in Q1 because the targets in Q1 were *stationary* wrt the aether, i.e. the source and target were in relative motion. Now the target is moving with the source (both are on the train). Therefore the target is moving WITH the source, and the wave fronts always hit the same spot on the target.

    Make sense?
     
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