studiot

The best starting point would be a good junior high school book in physical geography,that deals with Weather patterns and Climate. This will not assume any prior knowledge or maths. It would give an excellent background into how the natural planetary systems work(ed) before Man's activity interfered significantly. Yes catching up on some background in maths, physics geology etc is a very good idea. Fortunately the science is not mind blowingly difficult and can be acquired alongside progress in climate study. This out of print book (but you can get is second hand for next to nothing) will provide all the scientific background you need and more. https://www.amazon.co.uk/Atmosphere-Ocean-Our-Fluid-Environments/dp/0851412955 Good luck in your journey.

Thank you for your exceptionally rude response to a member who took your 'enquiry' at face value as genuine and offered serious discussion about your stated subject.

Duality has many guises and forms over a very wide range of situations. It is instructive to study some simple types of duality to gain understanding of the phenomenon. This picture, for instance, offers a simple type of duality applicable to the property of shape.

"What might be the state of motion within a black hole?" Once again I council fully grasping a simple model before trying to tackle the most difficult ones that even our best scientists have yet to grasp. In posting in this thread I am trying to continue the foundation I posted in your other thread on this subject. Here is a simple example. Take Newton's second law. [math]F = ma = m\frac{{dv}}{{dt}} = m\frac{{{d^2}x}}{{d{t^2}}} = m\frac{d}{{dt}}\left( {\frac{{dx}}{{dt}}} \right)[/math] Where F is the force applied, to mass m, x is a one dimensional coordinate in frame X1 and v is the velocity. This is an equation of motion, the one I was asking about in your other thread. This can be solved to give a simple equation without the calculus derivatives, especially if F is set equal to 0. Much can be learned by studying this for both your threads.

Many have wrestled with this question over the centuries But in asking it you are pulling in some of the territory of Philosophy. So you have said The relationship... That begs the first question if there is a relationship is it unique or are there more than one? You seem to expect there to be multiple relationships since you have said; Then again others have noted that Declaring at least space to be a property. That clearly begs the question Property of what? Can a property posses a property? Which merely pushes the question further back up the line. Again exploring the geometrical and trying to link it to other physical notions we have I would suggest that one important link between space and time, whatever their nature, is motion. But saying 'motion' is just a wooly word by itself and also begs the question Motion of what? Which introduces both the need for (mathematical) formalism and some 'object' or 'objects' to which we can attribute 'properties'. Given the mathematical formalism of a frame of reference we can introduce properties such as position and orientation along with temporal property of elapsed time. Combining these leads to motion, both translational and rotational. These objects may also have other properties (such as temperature) that are unrelated to space or time.

Please answer this question directly. Otherwise I can see no point continuing the conversation.

To move this thread forwards here is a simple variation to your example yet substantial enough to demonstrate the detail and the difference between invariant and relative variables. Let the two bodies having masses m1 and m2 and located at x1 and x2 move only along the x axis, subject only to any force they exert on each other. Establish the equation of motion of each body.

Finite differences are not infinitesimals. Further have you considered the second analytic derivative in your example, which is a constant ?

No It is not even properly true of the atmosphere! Atmospheric pressure is the pressure of the atmosphere. Which is true but useless since the pressure depends upon location and temperature and even whether or not a wind is blowing. So it is necessary to specify more detail. How about more detail?

This is a purely analytical example, so why are you wanting to use a definition from an article entitled Do you understand the distinction between the finite difference calculus and the analytical calculus?

Good point, it could also be much higher that atmospheric if the tank is part of an old fashioned 'gasometer'. So more information please Liz.

It would help if you answered this question. For instance are you attempting a numerical solution of a differential equation, looking for end point matching curvatures in a finite difference mesh, or trying to calculate over a finite element mesh? I wonder if you are mixing up the finite or discrete calculus with the analytical calculus? The definition in post 1 is missing the Limit that is used to avoid the division by zero in analytical calculus. But It is an extremely poor way to undertake finite differences. That may be due to the reluctance of some Americans to acknowledge and use the capital Greek delta for the differences.

Perhaps a little more detail is needed here ? What is the fluid represented by the blue lines? I am guessing the following: Your text is about the rate of flow or speed of flow of something like water out of a hole in the bottom of the tank (called orifice discharge), using Bernoulli's theorem and the continuity equation. I expect that somewhere your text indicates that atmospheric pressure is sensibly the same at the top and bottom of the tank, because 'h' will be very small compared to the height of the air column causing p0 , the pressure at A1. So the discharge will depend only on the head (h) and density of the fluid in the tank.

OK let's go at this Gently (did you like the tv series?) Also +1 for working hard at it.. Note I started this a while back, but never quite finished it. Not quite. Einstein's first Postulate is the Principle of Relativity which states, not that the result is the same but The Laws of mechanics have the same form in all inertial frames. This is called 'form invariance'. Note Einstein did not claim this postulate he knew it had been around since the time of Galileo and Newton. It's what he did with it that was brilliant. I think it is a very good idea of yours to study some examples. Now your links make it very complicated by looking at the most general cases in 3 or 4 dimensions. I suggest starting with just one dimension in your frames - Your example can be put in this form. But do you realise that you have specified 3 frames ? The frame of each moving observer and " the site of the experiment". Also I am not sure if you think the energy is a constant mass times velocity. So perhaps you can clarify a few points to employ your example. 1) Restrict the frames to 1 dimension (the x axis and time) plus time. 2) Confirm what 'a' is ? 3) To actually do some Physics, assign mass m1 and m2 to each observer. Then we can explore this statement from To find out that some physical quantities are 'invariant' that is the same in all frames and some vary with frame, when you calculate them according to the same equation in different frames.

Perhaps you could explain why there is so much shielding around nuclear reactors or how hydrogen, helium and methane gases can pass through several feet thickness of solid concrete?

If one variable decreases as the other increases then they have an inverse relationship. Is this not true of L and f thus? [math]{\rm{L(plus}}\,{\rm{a}}\,{\rm{constant)}}\quad {\rm{ = }}\quad \frac{{{\rm{(a}}\,{\rm{constant)}}}}{{\rm{f}}}[/math] So do you know any relationship (for sound waves ?) involving any of the quantities in the original given equation ? You are looking for an equation of the form [math]{\rm{something = }}\frac{{{\rm{something}}\,{\rm{else}}}}{{\rm{f}}}[/math]

If you must have atoms, rather than electrons, the gadget you want is called a field ion microscope.

I am assuming you want to achieve a straight line of the form y = mx + b, where m and b are constants. Strange though it may seem, this is not actually a 'linear' equation, so it is better not to use that description. 'Linear' has a special meaning in maths. y = mx is linear y= mx + b is what is known as affine. Back to your questions. starting with number 5 Your two variables are length L and frequency. f. the velocity, v and end correction, e are stated to be constants. But there is an inverse relationship between variables L and f. So you need to somehow introduce a new variable by inverting one of these. Can you think of a relationship (another equation) for either L or f that will do this?

Well explain what your rules are and what your objectives are. Interaction of matter waves is an everyday common or garden event in this universe. The point is twofold (1) To have a wave you need a wave equation to be satisfied. There are varying degrees of sophistication of wave equations. (2) To pick out the appropriate solution to said wave equation you also need to apply boundary conditions. In both (1) and (2) we normally use appropriate versions to the situation.

You specified unrelated 'matter waves' If you are using particles (matter waves) generated by the same source, how do you guarantee that they are unrelated? If they are already in separate orbitals, this is guaranteed.

I didn't say they did, but how do you think an electron microscope works?

Why wouldn't I? Or is your question "do I consider an electron to be exclusively a matter wave?"

If the two objects are orbital electrons belonging to different atoms, the two may combine to form new molecular orbitals, one a bonding orbital and the other an antibonding orbital. These new orbitals have new wavefunctions, different to but formed from the original wavefunctions.

You are getting there. The tolerance standards refer to laboratory glassware in general and include glassware (flasks, pipettes etc) that have only one measuring line and no scale. As such they are designed to deliver the rated quantity /- rated tolerance. Since you compared this with engineering practice, consider this. A tape measure with one inch missing from the end will 'measure' a 10 foot wall as 10 feet and 1 inch, from the end. But by measuring from the 1foot marking to the 11 foot marking, the correct length of 10 feet will be obtained. This is because the tape has an error everywhere of 1 inch so using a mesurement by difference this cancels. Length of wall = (11' 0") - (1' 0") = 10 feet. The burette allows this measurement by difference so the resolution and accuracy are not necessarily limited by the overall tolerance. But inEngineering you also have 'limits and fits' tolerance. Suppose you are turning a bar down to 'just fit' through a particular hole. What tolerance would you enforce to turning the bar down? This is equivalent to using a measuring flask where you cannot measure volume by difference. Your tolerance refers to the whole diameter and again you cannot use difference. Remember also that there are other considerations that affect accuracy with a burette and if you try to get too accurate you need to start to consider air bubbles, temperature, liquid density and the scale accuracy of the burette and techniques to ensure that all the liquid you think is transferred actually reaches the receiving vessel. At this point you might move to weight measurement rather than volume.

You need to distinguish between tolerance (which affects accuracy) and reading resolution (which affects precision). Tolerance is a specification of full scale ie a nominal delivery of 50ml will be within the range 49.95mL to 50.05 mL. This is a characteristic of the instrument (in this case a burette or buret in US) This gives a relative tolerance of 0.13% The actual scale can be read more finely than this. This effect is common in many instruments where a scale is read rather than a digital readout obtained. For example mechanical verniers, analogue voltmeters. For both of these latter tolerance is usually given as the relative (of full scale) %. Such a voltmeter would always be specified as 1% (very good) 5% (good) 10%(El cheapo variety). Remember for readings that are made by difference (as in a burette) the tolerance is a systematic error that affects both reading equally and with the same sign so cancels out on subtraction. That leaves reading resolution. This is measured as the smallest scale graduated interval (usually 0.1mL for a 50 mL burette), or some fraction of it. (ASTM E287-02) has half of this at 0.05mL. Vogel suggests this for "all ordinary work", but reading to 0.01 or 0.02 mL with the aid of a lens, "for precision work". Precision work could also entail establishing a calibration curve for use over the whole length of the burette or alternatively repeating the measurement over several different parts of the sscale and averaging.