studiot

That was going to be my next question. +1 But the issue here is How do Bob and Alice know when to start their clocks ticking ? Obviously they must have lived 14 thousand million years in order to make the measurement, plus a little bit to build their clocks and synchronise them.

So why is that a problem ? Bob is at the bottom of a gravity well, compared to Alice, so expects his clock to run more slowly. But you haven't demonstrated that your figures are correct for the time of flight and height difference.

Thanks, Joigus. +1 I think you may well be right, although I try to avoid these more exotic non mainstream symbols. You have done better than the author who had the opportunity to this is what he meant, but chose not to for some reason. If nabla squared is meant then in my opinion that is what should be said. The square is often called the box operator but it suffers from the disadvantage that I have seen it confused (used for in lecturres) with the Hodge star operator and also is presented by some parsers as a general symbol when they come across something not in their vocablulary. Word is bad in this respect. Also remaining is the mathematical demonstration that the second order differential equation obeys the Lorenz transformation, using the speed of sound as an invariant. The simple fact is that to an inertial observer moving differently from the air, the speed of sound appears different.

Or set the problem out correctly, filling in the missing lines telling us where your figures come from and showing us how exactly the two photons can have followed exactly the same path (world line ?)

Guiding would be better than telling. You still haven't answered my questions. Since you are doing this in preparation for a real exam it is no good just looking up formulae on the net (especially as I suspect it is wrong but I can't see the rest of what you found). You need to understand what you are doing. And that is exactly what both Seth and I are trying to help you with. So let us go back to first principles and answer my simple questions. Do you have to derive your equations or have you been given them in lectures ? Using your knowledge of Physics is the internal ressure greater than or less than the external ? Why did I suggest you will have a circular blob ? You new picture is wrong because the vertical meniscus is not a complete semicircle. Why do you think this is the case ?

How's that ? We all have trouble with the TEX of one sort or another. I have a ridiculously expensive commercial generator called Mathtype. Alternatively you can use free sites Codecogs or Sciweavers to have a TEX editor and copy paste from it. Another possibility (though limited by the inability to produce almost any sort of fraction) is to combine this SF super and subscript and use windows charmap to pick out special characters such as greek letters. You can actually achieve quite a lot this way.

I was going to examine your 'mathematics'. I can't make head not tail of this equation unless you have nabla the wrong way up ? If you have written Δp then the equation is nonsense. You seem to have corrected this few posts further on but a recognisable wave equation is stated and is indeed the equation you seem to have copied from Wikipedia. Unfortunately you seem not to have read the text where Wikipedia clearly states that this is the equation of a standing wave. My example involves a travelling wave and Wiki refers you to a simpler first order differential equation, which it call a one way wave equation in its own style. Note Wiki clearly states these 'preferred frames' to be hypothetical for the purposes of exploring what if there were such a frame. It makes no guarantees that there is one and indeed states there is not such a frame in an inertial set of frames (as we all know).

Love it to bits.

Is that incompatible with what I said ? Glad to hear it. We need We need philosophers to ruminate, but it is better if they chew on what we know rather than guessing, of if and when they do guess then they cary out testing of their guesses.

Part 1 You are working in the right direction, but if r = h/2cosθ (which is correct) then how is 1/r = 1/(h/2) in your first line ?

What makes you think this sort of thing hasn't been done before ? Apart from a 200km transmission path across the atmousphere (It's much easier for satellites up throught he atmousphere) beig far from isotropic or homogenous, What is the effect of a 1m, 10m, 100m, 1000m error in the placement of your helicopters on your calculations? Before we had all the satellite stuff, (and swansont is far better placed than I to discuss them) folks did this sort of thing by an instrument called the Tellurometer. This was invented / developed for the surveys of South Africa, Australia and Canada. Mountain tops, rather than helicopters were used as they do not move about and their positions can be independently verified. My experience of lasers is that they do not have the range, across the atmousphere, most have a range of a few km at best and the Wild Distomat was really up to a km. They had corner reflectors rather than independent clocks aand there is now such a reflector on the Moon using up through the atmosphere techniques. You still haven't told me how you are goung to create your pulse for 1000gHz signals.

Appreciation for the plus marks, but answers to our questions are even more appreciated. We can't tell you the answers, just help you find them for yourself. So what about R ? And what about the other questions, What for instance did you get for Seth's suggestion?

Is this homework ? Then it belongs in the homework section. Hints 1) is the liquid pressure greater than or less than the outside pressure ? - Why ? Then do a force balance between the pressures and the surface tension along the curved interface. It is usual for the liquid to be considered as a circular blob so you can calculate the area Over to you to put the values into your formulae.

Only one hundred years, gosh that's nothing. Pythagoras lived a lot more than two thousand years ago yet his theorem has yet to go out of fashion. So much so that I probably used most every day of my working life.

Two methods spring to mind. In the analog world electrometers and potentiometers measure voltage directly. In the digital world the digital version of the potentiometer also measures voltage directly, hence my comment about digital multimeters.

Please gentlemen stop pointless arguing over semantics. Is this what Fred Flintstone has in mind when he invented the neolithic hammer ? They are both hammers.

Because in the matter wave interpretation neither p nor E are conserved for short intervals of time, as determined by the quantum uncertainty principle. This is what I was leading up to when I said

Don has died aged 92. Here is his story.

But that would be incorrect. Quantum uncertainty leads to the conclusion that certain quantites cannot be determined (or known by any means) either by calculation or by measurement. It is more than just a limit on meassurement, and of quite a different nature from clasical uncertainty as set out so ably in Robinson and Whittaker The Calculus of Observations.

When they were first introduced electron microscopes became the bees knees of instrumental analysis. But they were large, cumbersome and expensive. And the supporting instrumentation was even more so. (no modern computers in 1931) Today they are used in conjunction with both computers and other instruments such as Field ion microscopes, X ray flourescence spectrometers, Ion traps, and laser technology to gain significant quantitative information as well as the qualitative shapes from the past. They are of course also more compact and there are cheaper versions and many variations on their method of applications. Was your question prompted by the Nobel 2023 prize for electron imaging ? https://www.weforum.org/agenda/2023/10/mrna-vaccines-electrons-nobel-prizes-in-2023/

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.