studiot

Since you don't want to answer my questions, whilst I answer yours, this is not a discussion. I am out of here.

Yes, he generally wrote for his peers (those who are at least as clever as he was). A small very select band.

How do you get the LPG out then? You didn't answer either of my questions.

Not always. For example the power set of the empty set is the empty set. I am not actually sure that we can create a set of "what God knows" within set theory in any case. We may be in 'type theory country'.

Is a petrol soaked rag (any more) difficult to ignite? Remember that the L in LPG stands for liquid (under high pressure) but when you use it, you expand it (a great deal) to a gas. So a bottle of LPG takes up much less space than the gas in it under more normal pressure. If it was absorbed in a sponge, what would happen to the sponge (or any sponge) under pressure?

Yes there are some misguided popular explanations about. It is also true that the modern development of the subject proceeds along a different path from the one Einstein originally took. Further, textbooks and scientific papers are often quite brief in their explanations. Einstein is particularly terse as shown by his introduction of "double index convention" abbreviation for the summation process. So his statement you picked out Is the result of quite a chain of reasoning, but it is all he says about it. So here is a start to the process of unpicking the original 1905 paper and the chains of reasoning behind it. These do not presuppose modern knowledge (as modern treatments often do) but leads us from simpler ideas to the theory. So consider let us consider a journey from a point A to a point B in a given system of intertia - note there is only one system of inertia at this stage. The velocity of travel from A to B is defined as the ratio of the distance AB and and the time of travel of the light. Now working entirely within the one system of inertia we have no difficulty measuring the distance AB by laying out a standard measuring stick (for ease and without loss of generality, this comes to an exact whole number of these). But measuring the difference in time is much more difficult. Indeed both the concepts of time itself and therefore velocity (which depends on time) become bogged down in circular arguments and therfore meaningless unless the issue of simultaneity can be addressed as we shall see. If t1 is the time of emission at A as read on a clock at A and t2 is read on arrival on another clock at B then (t2-t1) is only the time which light has taken to travel from A to B if there is a known correspondence between the two clocks at A and B. We call setting this correspondence to zero synchronising the clocks. So, the all important question, how do we do this? Well one method is to employ a third clock which we place next to the clock at A (this is what is meant by Einstein's comment " It is possible for the observer at B to determine the times of events in the neighborhood of B" - (no special geometric arrangements of clocks are needed or mentioned) in his paper. We set the third clock to the same reading as A, whilst it is 'at' A and then transport it infinitesimally slowly to B. Once at B we set the clock at B to the same reading as this third clock. We can then move this clock to other places and repeat, thereby ensuring that we have as many clocks as we wish distributed where we wish to make measurements simultaneous with our clock at A, all in the one single inertial system. A variation (simplification) occurs if we only have points A and B since we can simply origianlly place the B clock at A, sychronise it, and then move it as described to B. Einstein assumed that this theoretical process of movement would work satisfactorilly, (that is would not change the synchronisation of the travelling clock) but he did not prove it. Proof was left to Eddington and you will find his prooof in his book "The Mathematical Theory of Relativity" on page 28. This proof relies on the calculus of small quantities, but of course the actual taking and interpretation of such measurements were his field. A more modern method would be to use a very fast 'time signal' sent out from A to B eg a light signal. If the signal was sent from A when time = t1 = zero, we would then set the clock at B to t2 = AB/v where v is the velocity of the time signal. But then we would have to know the velocity and propagation characteristics of that time signal. But to know the velocity of the time signal or the effect of transport on a calibrating clock we would need the know the other. That is to know the synchronous time we would need the velocity. But to know the velocity we would need the synchronous time. Both the above methods end in a circular argument, and indeed all methods of the regulation of multiple clocks end in such a difficulty. This is why (all too briefly), Einstein states that we must define the concept of simultaneity. If continuing this is of interest, next time we can look at the way out of this impasse, by means of using a single clock and a closed polygon path.

It won't.

Use your common sense. Are there any dinosaurs around now? Were there any cattle around when dinosaurs lived? So there are many many species that died out before others appeared. In fact the fossil record shows there have been 6 major expansions and developments of life (call it evolution if you wish) on Earth and the first five (we are the sixth) all ended with a 'mass extinction' in which most life and species perished. If you want to know more read this https://www.goodreads.com/book/show/616394.When_Life_Nearly_Died

Thanks No further questions? I must have done something right.

A new satellite, intended to be one of a network of monitoring satellites with 6m resolution capability. https://www.bbc.co.uk/news/science-environment-46312874 First images from Sydeny Harbour, The Pyramids and marine locations.

Ismail do you understand the concept of vectors and adding vectors together?

The speed of light is neither infinite, nor unbounded. But it is contingent upon the properties of spacetime. Someone recently asked speed a similar question "why is the speed that particular number ?" https://www.scienceforums.net/topic/116678-why-light-speed/ Here is my reply there which demonstrates exactly the contingency you refer to. I apologise in advance if this daft forum cannot display the quote correctly. I suggest you read through this thread and then come back with any further questions.

Here you go, hope this helps.

No I’m not aware of the ambiguity of the Law of Sines. It has been 20 years since I had a trig class. The rules and Laws are “imbedded” in my mind. By that I mean that I know trig, I just don’t remember how I learnt it. I’m usually good after reviewing a Law or identity. I thought the ambiguity was the tangent of angles above 180; a difference in the direction of the vector. I f you are given two sides and the angle which is not included in the triangle two solutions may be possible by the sine rule. I'm sorry, I can't do a sketch tonight but I can try to describe it. Draw a long horizontal line - you don't yet know its length so make it long. draw a second line to intersect the first one, towards the left hand end, at the given angle to the first and of the given length. The leaves the third side of the triangle to construct Do this by setting a compass to the second given length and set the centre point of the compasses to the free end of the sloping line. scribe an arc, cutting the horizontal line in one two or no places. The case of two cuts describe two different triangles which satisfy the initial data and arise because in (180-a) = sin a I will post a sketch when I can.

So did you pass yout graduation? I would have thought that anyone who wants to get enlightened about a subject would find out about it when told that there is a Fundamental Theorem of that subject. (I have been doing just exactly that after I read the thread on magnetostatics recently posted by beecee) The Fundamental Theorem of Calculus asserts (in one dimension) [math]\int_a^b {df} = f(b) - f(a)[/math] Clearly Pythagoras is not involved since there are no squares or square roots involved. Does this mean anything to you? (It should tell you that there is so much more to 'calculus' than differentiation) Wikipedia has a reasonable discussion of this theorem. https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus Since you appear to think calculus is only about derivatives here is a definition of the derivative [math]f'\left( x \right) = \mathop {\lim }\limits_{h \to 0} = \frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}[/math] Once again neither squares nor square roots are involved. You really need to know and properly understand more about basics before shooting for the moon trying for tensors and tensor calculus. Confusingly tensor calculus was called 'the absolute differential calculus' when it was first introduced. This was first applied to many and varied geometrical situations such as surfaces, shapes, curves and curvature as well as position. This is now all part of the subject now known as 'differential geometry'. Here is a typical multidemensional form of the Fundamental Theorem of Calculus, recast in multimensional form. [math]\int_{\partial \omega } \omega = \int_\Omega {d\omega } [/math] Where it relates the integral over some n dimensiona l differentiable manifold, [math]\Omega [/math] to the integral over the (n-1) dimensional boundary of that manifold, [math]{\partial \omega }[/math] via the (n-1) differential form, [math]\omega [/math] with differential [math]{d\omega }[/math] this can be directly related to the one dimensional version i gave earlier. and there is still no Pythagoras in sight. As an aside What is known as the triangle inequality or the CauchySchwarz inequality also appears as heisenberg's uncertainty principle and in many other fundamental places in Physics and applied Maths. Perhaps you are confusing this situation with Pythagoras??

Hey, last time I rented the White House that was the rent. But I hear Big T has doubled it since.

I recommend you stick to your excellent observations you also made about excess waster and not making things last long enough +1 for that. You also said you are non technical, so take it from one who has 1) Worked on the Ronan Point disaster 2) Predicted the Grenfell Tower disaster 3) Watch the live video of the Twin towers disaster. and is a very technical person. There was no conspiracy (apart from the terrorists) The other disasters I mentioned were the result of individual incompetence and greed, not coordinated malice. But surely this thread has now had its day and doesn't need resurrecting?

Please provide a reference for this claim. And there's me thinking 'calculus' is based on something called "The fundamental Theorem of Calculus" Reference Spivak : Calculus. Silly me.

I am an applied mathematician, not a cosmologist so I am looking at the mathematical and logical consistency of what someone in another mathematical discipline is telling me. So for instance, 5% (baryonic matter) compared to 25% (dark matter) is 1:20 not 1:100 as seems to be suggested in line 4 of your reply. You still have not said % of what.

Yes thank you, it is now simple and clear what you are doing But Wiki clearly did not do that In particular they did not add 1 + 3 = 4

Why, you didn't specify that, nor did the example I quoted from the Wiki article ? Be aware, as a new member, you have a total of 5 posts in the first 24 hours.

From your link Following the example 9 + 8 + 7 = 24 You need to provide further explanation.

How does 9 + 8 + 7 = 6, which appears in line 16 of your table?

I know the input editor of this forum is crap but please make sure that quotes from others and your own input are separated. Thus:- So this is the pie, and the % add up to 100, but what is is made of? The above description makes no sense.

OK, thank you for what you have told me. But you did not answer my question. I asked Look carefully at where the question mark is. I did not ask if you know what a sine function is, I gave it as an example. All too often students do exactly this in exams and answer the wrong question (which was not asked). The whole point of periodic functions is they they lead back to or feed into MigL's short post about Quantum Theory in general. Since you have answered sensibly I am going to have a quick punt here to push the discussion on. A periodic function has y = f(x) has the same value y for (indefinitely) many values of x. So the graph or plot of the function repeats itself periodically or at regular intervals of x. As a result, if we know one solution at one value of x, say y1 = f(x1), we can write a solution in terms of n times x1 where n is an auxiliary counting variable so yn = nf(xn) Hopefully you can see how this is true for the sine function y = sin(x). So what does this have to do with Quantum Mechanics and Gravity? - The subject of this thread Well if you have a solution to an equation for some property of a system which is a periodic function then it can be written in the form just shown. Generally in QM this property refers to energy (though it may be more complicated) and the solutions are periodic (though more complicated than sine functions). In turn this leads to quantum levels of energy and the resultant transitions between them having distinct values being the difference between them. It is an axiom or proposition of Quantum Theory that the values of x and y between these values are 'forbidden' to the system. There may also be other, non periodic, solutions with no forbidden values over a certain range. These are often called the continuum solutions that occur once a certain energy threshold has been exceeded. For example when an electron has sufficient energy to leave an atom. In Wave theory the properties involved are somewhat different and there are no forbidden values of x and y. It is also axiomatic that there are no other solutions to the equations. I think that is enough for now, but there is a lot of water to pass under the bridge yet.