studiot

Difficult or easy the link you provided stated an explicit mathematical derivation of the exact value measured from Lorenz . I was hoping for the same from your hypothesis. Also please explain why your ether has to be a fluid, and what property of this fluid restricts the vibrations of lightwaves to the transverse mode?

All this begets the basic question why is change in any guise needed? Surely it is a valid (experimental) result to report 'no change for 75 years' ? Matter and other observables endure or not as the case may be.

Well done you found that in record time. However you did not read it quite thoroughly enough. It clearly states the connection to the Lorenz-Fizgerald length contraction was deduced by Max Von Laue, not Einstein. Special Relativity was not involved or invoked. Of course SR has the same formula by a different route, so will yield the same end result. So far we have at least three routes to the result; I look forward to you posting your calculations, commensurate with your mathematical ether description, to arrive at this result.

Like Michelson, Fizeau performed many experiments. Which one are you referring to? Can you precis the experiment for us please, stating how the important conclusion is arrived at? And which theorist(s) claimed this as false?

First a small correction to Strange's post. Maxwell was a firm believer in an ether. In fact his ether theory was the first to offer mathematical analysis. The following table of who knew what, when is quite useful.

I am going to assume this question is more than just political soundbytes. I say that because there are many different ethers, each one addressing particular observable characteristics in the universe and the laboratory. However each one (to date) also has an Achilles heel in some experiment or other. Equally Michelson, later aided by Morley, conducted many experiments. You surely did not think that a good scientist would be satisfied by only one experiment do you? Heaviside, Lodge and most famously Trouton and Noble conducted alternative experiments. I believe swansont mentioned Bradley's observations. These were confirmed by more accurate repetition by Airy and by Hoek. Incidentally their method also confirmed Fizeau's experimental confirmation of Fresnel's idea about ether drag. This is important because these experiments proved that the measurable drag effect (yes there is one) on the velocity of light is far too small to be accounted for by a co-moving ether wind. This was important because it bears directly on another issue with ether properties - that of homogeny and isotropy. This experiment is important as a direct verification of the velocity addition theorem derived naturally with special relativity. It also shows that it is not possible to explain the null result of the MM experiment by saying the ether is completely convected with the apparatus. A convection coefficient of unity would be required for this explanation whereas the medium being air, the coefficient is nearly zero. Now that I have answered something for you, please confirm that you understand the difference between velocity and acceleration?

I am a little unsure from this reply where you want to go from her or even if you want to carry on the discussion? Can you not find out what the units of E and D and the k you mention in your version of Coulomb's law?

+1 John for showing more patience than I have to spare.

Since you were rude enough not to bother to read my last post, I am not well inclined to answer your question. However your analysis in incorrect, there are more than 2 options. I suggest your understanding and/or description of the scenario you present is incomplete as the reason. Provide a proper and complete description of the situation vis-a-vis object D and you will have your answer.

Thanks I will try that for a bit and see what happens. I had it set to ask rather than block all.

When I load Chrome I am getting popup messages which say "you have 12 (other number) of messages waiting" hanu.facebook.com I don't do f/b so I have no idea where this came from or if it is legit. Can anyone help? Particularly to get rid of it.

I would say yes, by considering this thought experiment. Say you have a very very powerful magnet whose field extends a substantial distance (ie throughout a substantial volume). Now say you get you super blow torch out and heat this magnet up past the Curie point so the field disappears. How will you distinguish the state of the system with and without the field, if time was not still there?

Here is some maths to help the discussion along. It is impossible, in Special Relativity, to compose two velocities to make a velocity greater then c in the same frame. Suppose A, B and C are three uniformly moving observers. B measures the velocity of A relative to himself as v and the velocity of C relative to himself as w. What does he make the velocity of A relative to C as both these approach c? Einstein's formula for composing velocities is (derived by a double application of the Lorenz transformation) [math]\frac{{v + w}}{{1 + \frac{{vw}}{{{c^2}}}}}[/math] where v and w are measured along the same line. So as the velocity of both A and C approaches light speed we have [math]\mathop {\lim }\limits_{v,w \to c} V = \frac{{v + w}}{{1 + \frac{{vw}}{{{c^2}}}}} = \frac{{c + c}}{{1 + \frac{{{c^2}}}{{{c^2}}}}} = c[/math]

But that 4 dimensional 'space' is a mathematical construct and does not correspond to the 3D space or volume mentioned by the OP. So yes you are right if you construct a phase space to include a time axis then time is necessary by tautology.

It's a good question that deserves a good straight answer. +1 Time is not a property of space. Yes it can be considered a 'property' of fields, but that suggests there is no time where there are no fields which presents a philosophical difficulty. The notion that Time is a necessary property of fields was first appreciated by Faraday and extended by Maxwell in their treatment of the interaction between material bodies and their rejection of 'action at a distance', inherent in Newton's and Coulomb's theories.

Your original question is too general to supply a specific answer and there is no universal answer available. So here are some possible lines of attack. Most functions defined by integrals have alternative definitions which may be more easily invertible. Every integral has a counterpart differential equation so using that may be fruitful in some cases. But there are pitfalls to inversion for instance the sine function maps the entire number line to the interval (-1, 1). So there will be no inverse at all for numbers outside this range. Bessel functions cannot be expressed in terms of simpler functions so must be inverted from tables or some other numeric procedure.

Hilbert Sequence Space (symbol l2) is an infinite dimensional vector space with a defined inner product. Rn and Cn are not infinite dimensional since n is defined as a number and therefore cannot be infinite. https://en.wikipedia.org/wiki/Hilbert_space Edit note you will need to scroll down to the section about Hilbert sequence space, the first part of the Wiki article is about finite dimensional Hilbert spaces.

OK thank you for that information. The teaching of electricity and magnetism nearly always runs along the following path these days. A force on a suitable body is noted and an electric/magnetic effect deduced to account for it. This effect is defined in terms of the force produced and the position in space and is a vector quantity. The work done as the body moves around is calculated and related to the position to define a potential field. Sometimes a second vector quantity is defined as a vector derived from the first one. Either E and B can be defined first, with D and H as the derived vectors or the other way round (which is the older method). But often the significance of the second vector is not presented, hence your question. So consider this statement in the light of the following. You need two vectors to have a dot (scalar) product and energy is a scalar. Starting with a mechanical example we have Stored Mechanical Energy per unit volume = 1/2 stress x strain Stored Electrical Energy per unit volume = 1/2 E x D Stored Magnetic Energy per unit volume = 1/2 B x H edit (note these are all dot products not cross products) Are you beginning to see a pattern ? There are differences in the nature of stress, E and B but scalar multiplied by another suitable vector they yield the energy stored in the system. There are actually many more examples that could be listed and they all spring from a common root in continuum mechanics. How are we doing?

How many Royal Colleges do you have in the US of A? A school leaver is someone who didn't die waiting for the bell.

Enjoy Life to mean life for GPs GPs will no longer be allowed to leave the profession, according to plans drawn up by the Department of Health. An imminent change of law will make it illegal to stop being a GP. The move is expected to eliminate the current shortage of 5000 GPs within a few years. The news follows a call from the Royal College of General Practitioners for urgent action to halt the exodus from general practice. Under the proposals expected to be announced by the government next week, the GP contract will become binding on both parties. A government spokesman said: “GPs have long enjoyed the protection of a contract for life, but they were free to end it at any time by quitting the profession, moving abroad or choosing to retire. These options will no longer be available. Life must mean life.” From now on, GPs will be expected to practice until they die, with an option to work on after death open to those who wish to take national clinical posts, leadership roles in professional bodies or jobs with the Care Quality Commission. Acknowledging that GPs would be unable to retire under the new rules, the government said that the benefits of stopping work in later life were “widely exaggerated”. “All the evidence suggests that people who retire are more like to die before those who are still in work. On that basis forcing GPs to work until they drop may actually improve their life expectancy,” the spokesman said. Ending GP retirements would have other benefits, including simplified funding and contractual arrangements for general practice, and a modest saving in pension contributions. GPs will be expected to surrender their passports to remove the temptation to move overseas to work. They would also no longer be able to take holidays abroad, an objection dismissed by the Department of Health as “largely academic”. The government accepts that not all GPs will welcome the changes, but said it had run out of options for ending the recruitment crisis. Incentive schemes giving GPs the opportunity to work longer hours, collaborate in more meaningful ways or meet helpful people with clipboards have had limited success. Initiatives to recruit overseas doctors have also suffered setbacks. One ended in chaos earlier this week after an undercover team of NHS England recruitment officers tried to snatch an American doctor from a United Airlines flight, provoking a storm of criticism on social media. The government says it is still considering other ways to “ease the supply” of new recruits, including a compulsory national service style scheme under which all school-leavers would work as a GP for two years. “Not only would this be character building for the young people concerned, those who discovered an aptitude for clinical practice might choose to go on to get proper qualifications and stay in the profession,” said the spokesman.

Does this question have anything to do with the original?

+1 for good help with this homework/coursework question. @the etc Please note the rules for the special homework section. http://www.scienceforums.net/topic/75772-read-this-before-posting-in-homework-help/

The first was by Heaviside, the originator of the operational calculus and Laplace transform. However he was not a pure mathematician and could not prove his new methods in pure maths so he was ridiculed by pure mathematicians. His answer was basically it works when other methods don't and I need answers. The quote was to the Royal Society at a dinner where he was a guest speaker. The second quote was from Lord Samuel essays in Physics. Pearls of wisdom can also be found in the most unlikely of places. There is no reason why Poet's should not create some. Coleridge wrote this to his brother Some scientific wisdom can even be found in the Bible The Book of Ecclesiastes offers this and the Book of Kings offers a respectable (for the time) value for pi.

That refers to by far the most rational, although by no means perfect, post I have seen from madmac so I have given +1. Such a welcome development deserves encouragement.

Both those quotations had deeper implications, did you recognise either?