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

altonhare

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.

Saw

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…?

altonhare

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?

altonhare

A handy one-liner for the difference between the Lorentzian view and Einsteinian view:

Lorentz would say that c is a constant of measurement, Einstein would say that c is a constant of nature.

Saw

I didn´t express myself well enough. Of course, your pulsing ball can pulse again while the photon it has generated is travelling to a distant galaxy, without having yet returned or without ever returning. But in this sentence we mean by pulse the “photon”, that is to say, what has appeared in the border-line between the electron shell and the outer world. However, when I referred to something that cannot depart again until it has not returned, I referred to what happens within the ball itself, within the electron shell. If we reserve the word “pulse” for the photon, then let us call what happens inside the atom the “internal oscillation” (the electron moving outwards and inwards but always within the shell). It seems obvious that this internal oscillation can only happen as I described: an electron cannot climb up for a second time as long as it has not climbed down.

Anyhow, it was just that, pure speculation, which seems unnecessary.

As to the rest, OK, I will come back to review my physics of waves…

altonhare

Ah okay, this makes sense. Of course an oscillatory mechanism, by definition, only repeats after a full oscillation.

You could think of the ball as a shell with springs attached to the inside, attached to a core. The outer shell can expand/contract as the springs push it out then pull it in. So the shell oscillates up and down, "pulsing".

Saw

Thanks, at least we clarified that little aspect of the speculation. But the question is still whether the speculation is necessary at all or not and whether it is well orientated or not.

I make a new try at explaining myself and understanding your answer. (If I refer to the aether, it is just because we discuss here what the solution of the problem would be under LR, so as to better comprehend its differences wrt SR. No need that someone tells us that the aether does not exist.)

* Source and target in a frame A at rest wrt the aether: the laser hits the target. The local observer A paints a vertical trajectory in his CS, another observer B moving to the right wrt A paints a diagonal trajectory in her CS, bent to the left. No problem with the pictures, no problem with why this has happened.

* Source and target in frame B moving rightwards wrt the ether: IF the laser hits the target, local observer B paints a vertical trajectory in her CS, while now external observer A paints in his CS a diagonal trajectory, bent to the right. I have no problem with the pictures, ONCE that we have assumed that the facts are those, that is to say, that the laser has hit the target. But I (as apparently others) do have a problem with understanding why the laser should hit the target. A picture is a representation of reality. Whenever you make a picture, you assume that something has happened. If that story has happened, it is obvious that it will be represented (by each party) in that manner, but the question is precisely whether that story should have happened.

You say:

So we concentrate on this “particular part of the wave”, which has a “specific frequency”.

When the laser releases this part of the wave, it is pointing at the target (source and target are co-moving). In this deal “instant”, the source is also pointing at a specific point of the aether that overlaps with the target.

The part of the wave in question is released. Well, from now on, the part of the wave we are talking about has nothing to do with the source and the target. It belongs to the aether. So it seems it should keep moving towards the point of the aether frame it was originally pointing at. During the trip time of the light, the source and the target have moved a little to the right, but that does not affect the part of the wave in question, which has nothing to do with the source and the target any more. Thus the light should hit the moving frame, its ceiling, somewhere behind the target.

If a new part of the wave is released, the same reasoning should apply. And so on.

Then you explain how the Lorentzian effects should mask motion to moving observers and lead them to measure c as the speed of light. I said I agree with that and produced my own understanding in order to show that I follow your explanation. But I do not see why all that should justify that the laser hits the target of the moving frame… Maybe I am missing something in your explanation that is relevant for this purpose.

Laser is created through atoms being excited by photons of a certain frequency and phase, within a resonance cavity. The excited atoms release new photons that sort of mimic the characteristics of the exciting photons. If the exciting photons have a certain direction (the direction towards the target), might a modern Lorentzian view be that the new photons also take that direction…?

altonhare

So we have a pulsing ball releasing spherical waves, which we'll treat mathematically in circular cross section for ease.

Target A is located on a straight line path from the center of the circle through a location on the circle defined as, say, 1.5*pi rads. Target B is situated on a straight line path through 0 rads. Target C is situated at 0.5*pi rads.

If the high frequency part of the spherical wave-front is released at 1.5*pi rads, it will hit target A no matter how the pulsing ball is moving. If it's at 0 rads on the circle it will hit target B, no matter how the pulsing ball is moving. Identically for C. The pulsing ball can be moving on any trajectory you can imagine, the location of the laser region on this spherical wave-front at the instant of emission determines where it will be, not the motion of the ball.

Canaan_C

why u guys keep talking about "ether" which doesn't exist? (at least in Einstein's relativity)

Saw

I've seen in this forum the two interpretations of SR: (a) the aether definitely does not exist and it is absurd to think it exists or (b) the aether may exist or not, but in any case it's a useless concept, since it cannot be detected and, even if it could be detected, its existence would not add anything to our knowledge.

Anyhow, the reason why we talk about the aether is that we are discussing the differences between the approaches of Lorentz's relativity (LR) and SR to this problem. If I'm not mistaken, SR gives the question an easy answer: light hits the target, because otherwise we could detect motion by watching if the light hits the target or not, otherwise the principle of relativity would be breached. To me, this is perfectly legitimate: this is a rule that, according to experiments, works and why should we care more? LR takes another approach: it looks for the physical cause of the principle of relativity. In the search of this cause, I do not find a reasonable answer within the framework of LR. And I think althonhare is giving reasons to accept that, also under the conceptual framework of LR, the answer would be the same as for SR. The whole discussion, for me, is interesting, because it permits to fix or blurr the differences between these two approaches to relativity. Thus if you "believe" in one or the other you'll know better what you believe in.

altonhare

LR does give the same results as SR. This issue of directionality is intuitive. If you run to the right and throw a ball then the "emission" point will be to the left of the "target" according to someone at rest. According to you it will appear to go "straight" and the target appears to move to the left. The ball's velocity wrt the air (or whatever absolute reference) is constant, neglecting air resistance and friction which increase when you move faster through the air.

Make sense?

atyy

I don't know about the historical Lorentzian theory. But the modern "Lorentzian" viewpoint of special relativity can be found in:
Bell, How to teach special relativity
http://books.google.com/books?id=FGn...cover#PPA67,M1

As for usefully mixing the two viewpoints, perhaps see:
Purcell Simplified: Magnetism, Radiation, and Relativity
http://physics.weber.edu/schroeder/mrr/MRR.html

Saw

Thanks, atyy, for the links.

By the way, I think I have at last the answer.

The solution was contained in many of the comments received and I almost caught it some posts ago, but had let it go.

This text of http://wiki.answers.com/Q/How_does_a_laser_work has been very helpful:

The application to the question of the thread is as follows:

- We have a source and a target at rest in frame A and either a laser pulse or a continuous laser beam (it doesn’t really matter) that departs from the source and actually hits the target. Then it bounces back and actually hits its origin and so on. A describes in his CS the trajectory of, for simplicity, the “pulse” as, for example, a line parallel to the Y axis.

- Frame B passes by moving wrt to A along A’s positive X axis (to the right). B paints in her CS the trajectory of A’s pulse as a zig-zag advancing to the left. But she tries the same experiment with her own laser and it hits her own target. So she paints the trajectory of her own pulse as parallel to her Y axis, while A observes that B’s pulse follows in his CS a zig-zag advancing to the right.

- If we accept that all this happens, the above pictorial description is undeniable. But why does this happen?

- Obviously, the pulse hits the target because it follows the appropriate direction, the “successful” one. In other words, it is projected with the adequate angle for that purpose. The local observer will describe this trajectory as vertical, an external one as diagonal with a certain angle and third one as diagonal but with higher slope…, but in any case they are all talking about a specific trajectory, the one that enables light to hit the target. But how does the light know which the appropriate direction is?

- The answer is in the instrument that creates the laser light. Photons are created by other photons that excite the atoms of a medium, inside a tube. The newly created photons mimic the characteristics of the stimulating ones. They thus take their frequency and phase, although that does not seem relevant for the purpose under consideration. What is relevant is that they take their direction.

- And why is the direction of the stimulating photons the right one, the one that will enable the photon, in the outer world, to reach the target? Because the tube is just a reproduction, at a smaller scale, of the direction that photons must follow outside in order to be successful. Photons are bouncing to and fro between two mirrors separated by a certain distance, one of those mirrors being a half-silvered one through which they will eventually go outside. If they are already doing so, it is because they will also follow that path outside the tube, that particular path which the local observer describes as vertical and the external observers as diagonal, the successful path.

- Somehow this is a manifestation of the phenomenon of stellar aberration. In order to catch the light from a star in her telescope, in spite of the motion of the earth, the astronomer tilts the apparatus in the direction of motion of our planet. Here we talk about emitting light, instead of receiving it, but the philosophy is the same. Here all “telescopes” are parallel, none of them is tilted, but what becomes tilted is the photon. The tube (through its mirrors) "teaches" the photons, it "coaches" them until a good number of them become of age and can do, in the outer world, the particular job that they are expected to do, in that specific environment, i.e., in the frame in question.

Under this interpretation, yes, LR would be “saved” and would render the same practical results as SR, which simply means that it would be compliant with the principle of relativity, also in this particular respect.

Saw

In case anyone is interested, I have found a similar interpretation in http://www.av8n.com/physics/light-cl...tm#sec-discuss

neptun

How do we know that really the speed of electromagnetic wave is the fastest speed in universe, and not something else? Ok, we know that wave doesn't travel instantly, but has its speed, and requires time to travel through space, but why is it then immediatly the fastest speed?