studiot

Actually I agree with the spirit of KJW's paragraph, allbeit the letter is verey loosly worded and certainly the restriction to sinusoidal waves is inappropriate. With this correction the distinction he makes is relevant to 'matter waves' - the subject of this thread. It is really also part of the larger relevant question 'what is a wave ?' and the confusion that has accrued over the last century. It is also true that the physical dimensions (units) for the quantum wave function are weird in that they vary according to the number of spatial dimensions you are working in. Not necessarily. Applying 'Quantum Uncertainty' to matter waves leads to some interesting results. I am preparing a 'road map' for you so that you can see the development of De Broglies original idea over the last century, where it has gon in and out of mainstream fashion and is currently coming back into fashion at the (not so early) beginning of the 21st century, being revived by such bodies as NASA and CERN.

Well don't tells Sunak or Biden, and whatever you do don't tell Trump. 😀

I do understand what you hoping to do so, as a mathematician, you should be able to understand my difficulty with finding such an analogy. Einstinian relativity depends upon finding an invariant such that it will be measured the same by all (inertial) observers. Other relationships are then mathematically adjusted to conform with this requirement. He then developed special relativity conformities on basis of the idea the speed of light in vacuo. is such an invariant. (Note this was not one of his original two axioms, which were simpler. He actually had to deduce this invariance from his original axioms) Right at the outset he states that he is taking into account the then up to date experiments to find an observable variation If you wish to use the speed of sound in an analogous way you need to go through the same process and declare and experimentally support your invariant. Unfortunately experiment is not with you on this, and I do not know of any such quantity that is observer invariant in the propagation of sound. So I ask you one more time. What is your invariant, please supply the necessary mathematical and experimental support ? So why is the paper entitled On the electrodynamics of moving bodies ? And why is page 1 of the paper all about Maxwell, electrodynamics and what the paper is going to do with them (which he subsequently does) ? And why is his concluding technical statement "These three relationships are a complete expression for the laws according to which, by the theory here advanced, the electron must move." ?

So many forget this fact that in our mathematical idealisations functions like sinx , solutions to the linear wave equation, and many more have no beginning and no end. They extend to infinity in all directions. +1 But functions and waves in the real world have a beginning and an end. So we must employ artificial mathematical devices to suppress beyond initial and end conditions. Sometime we have to go further and match curvatures at initial and end points as well.

You are just playing silly games. Goodnight.

The STM can indeed be used to measure electron densitiy, but I left university 10 years befor they were invented so my pics are from an earlier technique in the days before we had massive computer backup. Fourier analysis took months the old fashioned way so more direct methods were used such as the Weissenberg technique. See above. You are correct that the phase problem is insoluble without either massive computer support or some jiggery pokery. A Photographic plate can also perform a material fourier transform in the exposure and developing processes. Note also that many of the so called diffraction methods are (were?) actually reflection methods including the X ray rotation method. The point about the mineralogist that is replicated when you rotate the Xrays or the crystal is that as you do so only certain planes are active at any given angle of rotation so measurement of this activity against angle give useful structural information. Another piece of jiggery pokery is to artificially introduce heavy nuclei into the structure at known positions to act as markers. Finally neutron scattering can also provide useful structural information although the techniques are many times more difficult. Googling Oxford Universities pages on the techniques will yield many better (and colour) images than mine. Just as a matter of interest I think this whol argument about direct measurement is a red herring. Any measurement can be called non direct, it just depends upon how far you take it. For example If I connect my modern digital multimeter into a circuit and 'directly' measure the current, I am not really measuring the current at all. I am measuring voltage. If I connect my old fashioned analog meter into that circuit and measure voltage, I am not really measuring voltage at all. I am measuring current. But then I could take this argument one stage further. I am not measuring current or voltage at all, I am measuring an illuminated pattern of lines/dots on a screen on one hand and a needle deflection on the other and I could go on and on down this rabbit hole. But nobody does in reality.

Your specification is insufficiently detailed. You say you have 3 colinear frames. You say velocity, but do not specify what it is relative to, since all velocity is relative to something. You say you don't have a diagram. Why not ?

So familiar that you didn't ask where the picture I posted came from. In fact it was a scan of a photgraphic plate record of an actual measurement made in the early 1960s. Today we would probably uise different techniques for making the record. I further suppose that you would say that all the mineralogist and metallurgists in the world, beavering away examining their specimens on their polarising microscopes are not doing direct measurements. I had prepared a discussion of the equivalent X ray technique for molecules, called the rotating crystal method. Including scans of photgraphic plate records of such experiments.

Indeed you did an thereby contradicted yourself since if there was to be a change in velocity the frames would not be inertial.

Then you haven't shown anything. You are the one making the claim so you are the one who needs to substantiate that claim.

What I pity your mind is made up before you have seen the evidence. So I will not bother with all that explanatory work I did again but just refer you directly to this department of industry paper

What have you got against magic dragons, wizards and the like ? My nephew's speech was greatly improved bynquotes from Harry Potter. 😀

I'm sorry I don't see my answer to your question any more. It was definitely there this morning. I will try to recreate it for you, since you are obviously unaware of 50 years of experimental Chemistry. though it will not be as comprehensive since i put o lot of apparantly wasted effort into it.

You have a diagram of this arrangement ?

I asked partly because my nephiew got AI help to 'improve' a wedding speech. This help was actually rather good.

thanks was that quote from chatGPT ? +1 Aren't all answers 'made up' ? 😀

How would that work, bearing in mind that the length contractionformula is only correct in the direction of motion and the measuring rod cannot be oriented in two different directions at once ?

It is important to have a clear idea of where you want to go. This discussion started off as a discussion about the validity of Relativity. DeBroglie- Bohm theory is about Quantum theory, not Relativity. Your hypothesis should be posted in the usual way in speculations, not in this thread. Then it can be properly examined and discussed. Since it has beecome important here is the full page 1 of the 1924 paper A pdf of the full paper can be found at https://www.pwein.at/physics/Lectures/Famous-Papers/Phil-Mag-47-446-1924.pdf Please note just how humbly he writes. the key points are 1) He is using Einstein's notion of 'quanta' and Einstein's terminology (he also later refers to Einstein's use of 'fields') 2) He sets out to explore the possibilities of reconciling the quantum notion with the wave theory. He ends up finding that a great many experimental observations can be explained by his approach, but owns that not all of them can. Pilot waves and Matter waves come in the 1927 paper and the Nobel prize for this work in 1929

Unlike your formula that I quoted, I don't see momentum mentioned at all. But most importantly is the statement "The light quanta would have velocities of slightly different values" What you are referring to is a modern summary after 30 years of development of the De Broglie - Bohm theory. There have been other offshoots , the Yukawa potential and the meson field theory. The factor of 2 that you note is explained in the section following the introductory piece I posted where he discussed radiation pressure an note the relativistic calculation agrees with the electromagnetic value, although momentum is still not explicitly mentioned.

What would be the answer ?

Really ? Have your read his paper ? Then how do you explain this ? Taken directly from his paper. Indeed we do. Here is a directly measured electron density map of hexamethylbenzene (after Spice 1964) I think it shows the structure rather well.

It would help if you took note of the steps I am offering. I think (and I may be wrong about this) that you have been following the wrong exposition of De Broglie's work (1924 and 1927 papers). Far too many (some well respected) texts offer this explanation of what he supposedly said. Consider a beam of EM radiation with energy E = hf, where f is the frequency. The wavelength. λ, is thus λ = w/f where w is the velocity of the wave. For EM radiation w = c so λ = c/f = hc/E This is all fine and dandy but But he did not say this. By analogy take the pair of equations k = 1/λ = E/hc and f = E/h because this false derivation does not lead to appropriate results, in particular matter waves as pilot waves, with a correctly defined group and phase velocity. They lead to a phase velocity, w = v/k = c and a group velocity g = df/dk = (dE/h) / (dE/hc) = c This is correct for a quantum which always equals c but not correct for a particle which moves with a velocity, different from c.

Please tell us more when you reply as more detail makes it easier to help. Differentiation is a process. A differential is the result of that process. (That is differential as a noun) But differential as an adjective refers to the difference between two values eg the differential pressure between inside and outside = (inside pressure - outside pressure) But there is considerably more required to understand things. Why is this posted in homework help ? Is this really homework or are you asking about mathematical theory, in which case you will attract more attention and answers if you placed it in the mathematics section.

Watch these animations. There are lots of youtube animations, this one is good because you can play with it, setting the vp and vg parameters to all possibilities to see the effect on the 'particle' carried. https://www.surendranath.org/GPA/Waves/GroupPhase/GroupPhase.html

Sadly you missed both of my points. By your own admission, anything you do from an armchair will be coloured by your experience. The blind man was an analogy and no analogy is perfect. Again I repeat the blind man must omit feature of the landscape.