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?

33 minutes ago, VilJ said:

This problem doesn't seem complicated, but I still can't get it done. I can't figure out how to write the equation with all the required parameters in the first part. I have used the Laplace equation for this one (This is probably correct). Also the third part, How can I calculate the force with knowledge of the dimensions of the plates?

Is this homework ?

Then it belongs in the homework section.

Hints

1. 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.
2. It is usual for the liquid to be considered as a circular blob so you can calculate the area
3. Over to you to put the values into your formulae.

3 hours ago, KJW said:

That was more than a hundred years ago. Relativity has moved on since Einstein. The concept of spacetime didn't even exist at the time of Einstein's paper on Special Relativity... that was Minkowski's innovation. And it was an important innovation because without it there would be no General Relativity. Relativity, both Special and especially General, is about spacetime, regardless of historical development.

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.

29 minutes ago, martillo said:

In which way could a voltage be measured directly?

Is there any known case where the voltage has been measured directly?

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 ?

42 minutes ago, martillo said:

Seems I would need to enter deeper into QM to be able to understand the thing...

I just want to ask you now the same as to @joigus:

55 minutes ago, martillo said:

What I don't get is that you have E, you have p so, why can't you have E/p. What does the quotient E/p means to you? Why to not just associate v_p = E/p? I don't get it.

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

1 hour ago, studiot said:

Applying 'Quantum Uncertainty' to matter waves leads to some interesting results.

Quote

https://www.bbc.co.uk/news/science-environment-67445718

 

Don Walsh: The man who made the deepest ever dive

 

Don has died aged 92.

Here is his story.

17 minutes ago, martillo said:

As I already said to @joigus "quantum uncertainty" just puts a limit in the precision on the determination of some quantity. It does not means some quantity would be not determinable. Different things.

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.

On 11/17/2023 at 11:04 PM, grayson said:

I have recently come across a dilemma. I can't figure out how electron microscopes detect the shape of electrons. Now, obviously you could just send them through a wire or something, but that would make them lose their shape. I am trying to make an electron microscope for a project (As the ones you can get are too cheap). I have figured out everything except detecting the shape of the electrons. Can somebody help me?

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/

14 hours ago, KJW said:

I see two meanings to "wave" in QM. Firstly, there is "wave" as in "wavefunction", a general term referring to any waveform. But there is also "wave" as in "wave-particle duality" which I see as referring specifically to a sinusoidal waveform. In other words, a particle with definite momentum, and therefore definite wavelength. But also definite energy, and therefore definite frequency. Phase velocity might not be meaningful for all wavefunctions, but that does not make it meaningless for all wavefunctions.

13 hours ago, joigus said:

No. You got this totally wrong. Quantum waves are not sinusoidal. For starters, they are not real functions. They typically go like complex exponentials.

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.

12 hours ago, martillo said:

Could I say then that the phase is not measurable but it is determinable? I mean we cannot experimentally measure it but we could determine it.

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.

10 minutes ago, Endy0816 said:

It's honestly pretty good for such tasks.

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

😀

6 hours ago, Killtech said:

i am mathematician

But definitions are just that - convention we choose. and we can construct something which size is governed by acoustics instead of electromagnetism and therefore conform to the relativity principle of acoustics and contracts accordingly. Admittedly such constructs do not appear very intuitive (except maybe for a bat which perceives the world around it via acoustics) but mathematically they are a perfect analogy.

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 ?

7 hours ago, KJW said:

Relativity is not about electromagnetism, it is about spacetime.

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."  ?

1 hour ago, joigus said:

a beam of light cannot be infinite in extent and duration, but must always have a beginning and an end, which introduces a range of spectral components to the signal.

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.

30 minutes ago, KJW said:

I don't think so.

 

And?

 

Yes, I did. The velocities of the two frames are relative to the third frame. Perhaps I should have simply said the velocity relative to the third frame of the second frame is equal and opposite that of the first frame.

 

Why would I?

 

You are just playing silly games.

Goodnight.

15 minutes ago, martillo said:

Wouldn't the image be a graphic of scanning electron tunneling microscopy on the molecules?

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.

42 minutes ago, KJW said:

Hmmm, perhaps I spoke too soon. The direct image from x-ray crystallography is an arrangement of spots of various intensities. A Fourier transformation of these intensities yields a Patterson function (a convolution of the electron density with its inverse) due to the "phase problem". So how does one obtain a photographic plate image of the electron density? Specifically, what is performing the Fourier transformation? In particular, how is the "phase problem" being solved?

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 ?

40 minutes ago, KJW said:

As I said, I'm familiar with chemistry.

 

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.

26 minutes ago, KJW said:

I did substantiate my claim. I said:

Quote

The simplest would be for the rod to be oriented parallel to the change in velocity in both frames of reference, and for the third frame of reference to be collinear to the other two frames of reference.

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

24 minutes ago, KJW said:

No, I don't have a diagram. I actually don't see the difficulty.

Then you haven't shown anything.

You are the one making the claim so you are the one who needs to substantiate that claim.

14 minutes ago, KJW said:

I'm familiar with chemistry. That's why I chose an example from chemistry. It seems to me that you don't understand the point I'm making.

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

Quote

https://pubs.acs.org/doi/10.1021/ed079p1141

This paper gives a simple pictorial introduction to the interpretation of electron densities to obtain information about bonding. The electron density of a molecule can be readily calculated using ab initio or density functional theory methods and it can also be obtained experimentally by X-ray crystallography. Unlike an orbital model of a molecule, the electron density is a physical observable.

46 minutes ago, iNow said:

We can argue, for example, about the best stratagems and series of moves to win the game of chess before us, but when our opponent chooses to drill holes through the board, set it on fire, and introduce magical dragons and wizards as game pieces, then we must fundamentally rethink our best path forward and acknowledge that it no longer much matters whether we decide to move to Queens Rook 7 or Kings Bishop 4.

What have you got against magic dragons, wizards and the like ?

My nephew's speech was greatly improved bynquotes from Harry Potter.

😀

5 hours ago, KJW said:

How is the above a direct measurement of electron density? I've already indicated above that x-ray crystallography is not a direct measurement of molecular structure. Producing a detailed image of the electron density of a molecule is not the same as being a direct measurement.

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.

39 minutes ago, KJW said:

I don't think it would be too difficult to arrange the frames of reference and the rod orientations to give the same length contraction, thereby establishing that the rod is the same length in both frames of reference. The simplest would be for the rod to be oriented parallel to the change in velocity in both frames of reference, and for the third frame of reference to be collinear to the other two frames of reference.

 

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.

11 hours ago, Endy0816 said:

For current UK Prime Minister:

 

Is a few years behind the times too. Could probably provide a better answer, if it were up to date on current events.

thanks was that quote from chatGPT ?  +1

11 minutes ago, Bufofrog said:

Some made up random answer.

Aren't all answers 'made up' ?

😀