studiot

Tensor mathematics contains a deal of notation designed to achieve compactness in writing. There is also Einstein's own summation notation, dropping the sigma symbol and leaving the reader to understand (guess?) when a sum is meant and when it is not. Unfortunately it takes years to become familiar and comfortable with the notations and, when it comes down to it, they don't reduce the calculative effort one iota. As every engineer knows, the fancy compact notations in the textbooks do not mean that when you want to actually calculate a result you can shortcut. You still have to perform the full calculations kin each direction (dimension).

This very recent book contains an interesting history and discussion of the various versions of General Relativity, including the introduction, retirement and resurgence of the cosmological constant. http://www.amazon.co.uk/Perfect-Theory-Century-Geniuses-Relativity/dp/1408703106/ref=sr_1_5?s=books&ie=UTF8&qid=1407610640&sr=1-5&keywords=general+relativity

What makes you think they are not independent?

So long as you put more effort into understanding what we already have and know than into wishful thinking and guesswork you will continue to make progress. Perhaps one day all that knowledge will enable you to make what we call 'inspired guesswork' and actually discover something new.

It is a really counterproductive idea to keep introducing extra words that have a particular, well defined, meaning in Science. No, pressure, vapour pressure which is a particular form of pressure are connected with humidity by definitions they are not 'like' or the same. Note that the term humidity itself comes in more than one form. Please also look at my edit to my last post, where I commented on your making up another bogus science term.

Not always, Liquids exert a vapour pressure, into volume above their surface. This may or may not be not enclosed (contained). Evaporation will continue if the pressure in this space is less than the saturated vapour pressure of the liquid. Energy and pressure are different quantities. There is no such entity as 'energy pressure'

Only certain types of energy are associated with motion of molecules, and in this case also pressure, which is not a form of energy. Some other forms of energy are also associated with motion of other entities.

Since no one seems to have taken this statement up I offer that it is really a variation of Paul Ehrenfest's Paradox, which has been explained, in terms of relativity. http://en.wikipedia.org/wiki/Ehrenfest_paradox

Your equation says what x equals. So what does y equal? That is what I mean by rearrange your equation, find what y equals.

Yeah, maybe, but if I was a rock face I would still endure. Incidentally we are lead to the necessity of time in our analysis of our sensory input data about our surroundings.

Why do you want to do this? I ask because there is a recognised allied technique called audio signature analysis. This works in one of two ways. Structures and machines naturally produce vibratory signals that can be picked up with a microphone and analysed for fault conditions. It is said that a good mechanic can tell what is wrong with your car by listening. Additionally response to imposed signals can be tested in the same way.

Can't see why you can't experience duration without motion. I am doing it right now by just sitting in my chair.

Is this your own theory? 'functional' has a particular well defined meaning in maths and mathematical physics. Neither time (your other post) nor energy meet this definition.

Let us start with a body at rest at the mean position and then apply a disturbing force. For instance let a pendulum hang freely at rest, and be drawn aside a small distance and held at this side position. When at rest the (total) energy of the pendulum is zero. That is its KE and its PE are both zero (not equal and opposite). As it is drawn aside the disturbing force raises the pendulum against gravity imparting potential energy and kinetic energy to the pendulum. The kinetic energy is undefined, but when the pendulum is again at rest at the side position it has zero KE and a defined PE. Up to this point the pendulum is not executing SHM. If the pendulum is now released it will fall back to its original level under gravity. As the pendulum swings its PE is converted to the KE of motion until it reaches its lowest point at which time it again has zero PE, but now has substantial KE. So it swings on through the lowest point and start to climb back up. As it climbs it looses KE and gains PE, until in a frictionless system it has gained the same height on the other side of rest as it was originally released from. At this point it again comes to rest. All the KE has now been converted to PE, which is again positive. The pendulum is now executing SHM and the cycle continues indefinitely. At all times in this cycle the PE (and the KE) are non negative ie zero or positive. The pendulum starts off SHM with a specific PE and zero KE. Initially, the change in PE is negative, the change in KE is positive. Once this negative change in PE has reduced the PE to zero the change becomes positive and the PE increases again. If we can agree these factual observations we can proceed to discuss how this is implemented as a force-displacement-work calculation.

Agreed you would have far better pay and job security if you bacame a plumber and kept the theoretical physics as a hobby. If you must stick with physics then one growth area for the future is the manipulation of microscopic entities. This has applications in biology, chemistry, materials science, micromachinery as well as physics and the potential for you to create a company and reap the benefit if you discover anything. go well with your career.

A further distinction in law is worth mentioning, and again I appeal to imatfaal for amplification. Several posters have mentioned being sued for damages. There is a big difference between UK and US law about this, I do not know about Dutch or other EU laws. The difference is that in the US so called 'punitive damages' can be awarded and are often substantial. Further they are awarded by juries and their amount are often a political act. In the UK you have to be able to prove you have suffered material harm and are only liable to receive compensation for that harm and nothing more. That is why compensation in the UK is some much less than in the US for corresponding actions.

A simple distinction. The study of how fast, how far and for how long bodies travel, without worrying about the forces involved, is often called kinematics. The study of motion including forces, energies etc is called dynamics. Your problem above links the two together. Kinematics includes equations such as distance = speed x time and the more complicated one above that you mention. Have you studied kinematics yet?

A qualitative explanation? First to remember that the applied field and the field due to the material add (vectorially) to form the total field. This diagram may help. For diamagnetic materials there is no material field so the magnetic moments a zero without an applied field as shown in the first diagram. If we apply an external field the induced moments oppose the applied field reducing its intensity as shown in the second diagram. For paramagnetic materials there is a material field that averages zero without an applied field because every molecule has a random orientation. When we apply a field to a paramagnetic material all the random molecular moments align with the field, reinforcing it and increasing its intensity. Paramagnetic materials also exhibit diamagnetism, but paramagnetism and diamagnetism spring from a different mechanisms and the numbers just work out that paramagnetism is quite a bit stronger so with paramagnetic materials the diamagnetic effect is masked.

Thank you , John, for your reply. I fully appreciate that mathematically the direction of rotation is a matter of convention and perhaps choice. But the question I asked was about teaching the subject to youngsters. You may have been lucky with your professors or older or both but this question was prompted because I looked at the teaching material supplied to some 9/10 years olds about rotational symmetry., ie in primary school. They are being taught that the 'natural' direction of rotation is clockwise, having not long been taught about clocks. They will also be taught about bearings in Geography, which are also measured clockwise. I have seen much confusion arise in secondary schools when the maths teacher attempts to teach anticlockwise angles. So my question still stands for discussion.

Actually my graphs are merely a plot of the correct formulae, which are also stated on my diagram. A body executing simple harmonic motion is subject to two forces. A disturbing force and a restoring force. The equations that lead to SHM and the energies involved are as a result of the restoring force only. It is a common mistake to try to calculate with the disturbing force. The restoring force always acts towards a fixed point. That is the restoring force changes direction halfway through the cycle. We normally place the origin of coordinates at this point. In your analysis the restoring force is kx for half the cycle and -kx for the other half. You do not need to worry about the angle between the restoring force and the displacement since they are along the same line (the x axis). Because the restoring force direction reverses you need to separate the work integral into two integrals, each with its correct sign. See if you can work through this now and come up with the correct formulae. This is a bit like asking the question What is the integral of sinxdx from x=0 to x=2pi? The answer is zero, but the area between the curve and the x axis is obviously not zero. Again you have to split the integral to obtain the area. So far this is all mathematical, but thinking about the Physics may also help. What exactly is x? ie what does it represent? Well not only is SHM motion under the action of a restoring force always directed towards a fixed point, but further the value of that restoring force is proportional to the distance from thatpoint ie the displacement. x is the displacement from the mean point. Now if you wish to consider work and energy we can say that When the body is moving towards the fixed point the restoring force and displacement are in the same direction. So the restoring force is doing work on the body, accelerating it, ie increasing its KE. When the body is moving away from the fixed point the body is doing work against the restoring force, storing the work energy in the source of the restoring force as PE. This energy comes from diminishing the KE of the body.

1) I am no expert in life sciences, even I have heard of Darwin's Finches. I will leave you to do some research about this. 2) I understand Mendel was a contemporary of Darwin and published his (query more mathematical) rules not long after Origin. Again I will leave you to look up the comparison.

I don't understand the comment. The moving demonstrations clearly rotate clockwise.

Since light is just a form of EM wave, in wave terms, one of the simplest to measure might be to use radio waves rather than light and use lecher lines. Wiki offers them to measure wavelength but they can also be used to measure amplitude. http://en.wikipedia.org/wiki/Lecher_lines Of course a light intensity meter provides a measure of amplitude.

Because shining two light sources on the target produces a single combined light beam not two separate ones side by side. And of course a single light source produces only one light beam.

When we discuss angles in mathematics we consider anticlockwise angles as the positive direction of rotation. In particular this is carried through to phasor theory in electrical engineering and many other fields. But when mathematicians and physicists discuss rotational symmetry the clockwise rotational direction is chosen as positive. eg http://www.mathsisfun.com/geometry/symmetry-rotational.html Is this anomaly not potentially confusing for young minds?