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Ok.....Now I need some 'pigeon english ' explanations here...1: How come the speed of light is constant ?...is there no fluctuation at all ?2:...regarding the above question abut the constant speed of light(and this is where I probably will get a headache).....but...surely light has to accelerate up to C yes ?.....no ?.....How can something travel at a speed without having originally been traveling below that speed ?THANK YOU so much for my impending headaches !!!
Waves (all sorts) don't build up speed but they do build up amplitude as they start. If they changed speed, their wavelength would have to change and I don't think that has ever been observed (except, of course, when moving from one medium to another). I think that would violate boundary conditions.
This defines the speed of light in vacuum to be exactly 299,792,458 m/s. This provides a very short answer to the question "Is c constant": Yes, c is constant by definition!However, this is not the end of the matter. The SI is based on very practical considerations. Definitions are adopted according to the most accurately known measurement techniques of the day, and are constantly revised. At the moment you can measure macroscopic distances most accurately by sending out laser light pulses and timing how long they take to travel using a very accurate atomic clock. (The best atomic clocks are accurate to about one part in 1013.) It therefore makes sense to define the metre unit in such a way as to minimise errors in such a measurement.The SI definition makes certain assumptions about the laws of physics. For example, they assume that the particle of light, the photon, is massless. If the photon had a small rest mass, the SI definition of the metre would become meaningless because the speed of light would change as a function of its wavelength. They could not just define it to be constant. They would have to fix the definition of the metre by stating which colour of light was being used. Experiments have shown that the mass of the photon must be very small if it is not zero (see the FAQ: What is the mass of the photon?). Any such possible photon rest mass is certainly too small to have any practical significance for the definition of the metre in the foreseeable future, but it cannot be shown to be exactly zero--even though currently accepted theories indicate that it is. If it wasn't zero, the speed of light would not be constant; but from a theoretical point of view we would then take c to be the upper limit of the speed of light in vacuum so that we can continue to ask whether c is constant.Previously the metre and second have been defined in various different ways according to the measurement techniques of the time. They could change again in the future. If we look back to 1939, the second was defined as 1/84,600 of a mean solar day, and the metre as the distance between two scratches on a bar of platinum-iridium alloy held in France. We now know that there are variations in the length of a mean solar day as measured by atomic clocks. Standard time is adjusted by adding or subtracting a leap second from time to time. There is also an overall slowing down of the Earth's rotation by about 1/100,000 of a second per year due to tidal forces between the Earth, Sun and Moon. There may have been even larger variations in the length or the metre standard caused by metal shrinkage. The net result is that the value of the speed of light as measured in m/s was slowly changing at that time. Obviously it would be more natural to attribute those changes to variations in the units of measurement than to changes in the speed of light itself, but by the same token it is nonsense to say that the speed of light is now constant just because the SI definitions of units define its numerical value to be constant.
Ok, but electrons (e.g.) are waves too...
QuoteOk, but electrons (e.g.) are waves too...OK you've thrown down the gauntlet. I had to think for a millisecond about this one.Here goes.The energy equation E = hf explains this one away.As you give the electron more KE, its frequency increases. The frequency of a photon, however, stays the same so its speed would, reasonably, stay the same. The frequency of the electron wave would stay constant if its speed were constant.How's that?
An old text book I had described the radiation from an antenna as starting of with the magnetic and electrostatic fields in phase and needing a quarter wavelength to settle down into proper electromagnetic radiation
I thought that there was a 90° phase difference between the peak intensity of the magnetic field and that of the electrical field in an electromagnetic wave.
Ah no!The E and B fields are in quadrature phase AND direction.As with all waves, the energy flow is shared between a potential energy (E ) and kinetic energy (B). The two energies add up to a constant. (sin squared plus cos squared). If it were not this way, the energy would arrive in 'dollops' and not smoothly.Pressure and velocity in a sound wave are obviously in quadrature - peak pressure when gas is stationary. It just has to be the same idea with em waves.If you look in every A level textbook (and even some degree texts), the diagram is wrong. In the more advanced books they get it right.There is no surprise there because the proper diagram is very hard to draw, compared with the wrong one.
You could see it quite easily on a cheapo oscilloscope, I should think. Don't know why I didn't do it. myself, when I had the chance - I used to have access to a Range Rover, kitted out as a mobile lab and did frequent field strength and other measurements at all frequencies - including 198kHz.I guess it was all so 'obvious' at the time that I didn't need to prove it for myself.Lightarrow - I will have to look at your stuff in detail. Did you look at the link on my previous post?
My first reaction is that, when you integrate your E, do you not get an 'i' multiplier for your B?
www.play-hookey.com/optics/transverse_electromagnetic_wave.htmlI've just spent ages trying to find a reference. Here it is.It says it better than I have.
I am now convinced that remote from the antenna B & H are in phase but is there not a difference close to the antenna before the electro magnetic wave becomes established.I believe the text book I referred to was by 'Sterling' but I can find no reference to it but I recall drawings of a vertical antenna with the current running up and down and a horizontal circular magnetic field spreading out from it
It is sometimes claimed that light is slowed on its passage through a block of media by being absorbed and re-emitted by the atoms, only traveling at full speed through the vacuum between atoms. This explanation is incorrect and runs into problems if you try to use it to explain the details of refraction beyond the simple slowing of the signal.
whereas absorbtion tends to occur at relatively well defined frequencies.
http://www.shef.ac.uk/physics/teaching/phy205/lecture_18.htm9th row from below:<<This equation can only be satisfied if a=0 (i.e. E and B are in phase)>>
I sometimes feel like one of the panelist on the Stephen Fry quiz program "Q".I offer the commonly held answer to a question only to have it demolished by greater experts.
Lightarrow:Quotehttp://www.shef.ac.uk/physics/teaching/phy205/lecture_18.htm9th row from below:<<This equation can only be satisfied if a=0 (i.e. E and B are in phase)>>I hate to disagree (he lied) with established thinking but the expressions used in all the texts contains the complex form of the wave. Can we be sure that the relevant part has been chosen in producing the final answer? My maths is not good enough to be certain but there seems to be a loophole here. Not all solutions have reality in maths.
But, more to the point, can you answer my objection on the grounds that free em waves appear to be fundamentally different from all other waves in how they transport the energy?Even an electric wave travels along an LC delay line with a phase difference between volts and current - or E and B fields on a transmission line. What happens when it gets to the end of a transmission line and encounters a dipole radiator? Can there be a sudden hiccup in the phase of one of the fields?I am confused.
I think I can prove that E and B are in quadrature using Maxwell's Theory of Electromagnetism: A changing electric field generates a magnetic field of a strength that is proportional to the change in the E field.(Ampere's Law). A changing magnetic field generates an electric field of a strength that is proportional to the change in the B field. (Faraday's Law)..
Lightarrow's sums must be right. (He IS pretty reliable in this direction)SO there is a problem with my interpretation of the energy flow in a wave.No one has argued with my idea that all other waves consist of PE and KE variations which are in phase quadrature. So put me straight: is not the E field a potential form of energy and is not the B field a dynamic / kinetic form of energy?
The fact that they are transverse and spacially in quadrature makes the em different from other waves, I admit but em waves follow the general principle of phase quadrature when guided by a wire / wires / waveguide so what is the difference, once they get launched into space (or a medium; it all can't change just because you have the occasional molecule of air in the way)?Help me with the physical interpretation of this - there must be one which can reconcile my misgivings - unless the in-phase idea is wrong (god I would so like it to be wrong! Just think of all the experts being gutted! Even Lightarrow!!!)
I think that I have the solution to the problem of phase. Light arrow has not quite completed the analysis. He has shown that the electric fields and magnetic fields stay in the same phase with respect ot each other but he has not proved exactly what that phase is (There is always a constant in the integration ) to do that you have to go back to the original equations to determine the constant. If you do that you will find that is where the phase difference lies.
lightarrow, I am aware of the mathematical formulation of the two laws that I referred to. They mean exactly what I said, except that I didn't mention that the fields that these changes in E or B create are in a direction perpindicular to the direction of the wave's propagation (if the left was nabla•E or nabla•B then the fields generated by the changing fluxes would be in the same direction as c). I took it as a given that the fields were perpindicular to the direction of propagation as light is a transverse wave. I know that your calculations are correct (they appear many different places and I have taken the time to check the math, assuming that rot(rotV))=grad(divV)-nabla2V is true, they work out), my problem is that this solution seems to be just as infallible as yours, yet only one can be right.Does anybody see what's wrong here?
Lightarrow...What is your reaction to the 'conservation of energy flow' idea? To me, that sounds like a clincher. It applies to all other sorts of wave, so why not em waves?