studiot

There are many wild statements about the speed of light and the mathematics of relativity. You should beware of them. The mathematics of relativity does not prohibit superluminal speeds (faster than light). What is does is contain a singularity as a result of division by zero at the the speed of light for any massive object (a massive object, in Physics, is an object with (not necessarily large) rest mass). As you probably know division by zero is not defined in the normal system of mathematics that we use. There is no singularity in the equations at greater than light speeds. This is not an uncommon situation in the mathematics of physics. But what we don't know is if the same equations apply at these greater speeds. If they do there are consequences, not least being that we cannot communicate with anything travelling at these speeds, or even see them. Two examples of other situations where the equations have a barrier like this. Firstly consider the thermal expansion of chocolate, placed in an oven at 15 degrees centigrade and slowly heated. We have an equation that describes the expansion of said chocolate as it heats up, until the chocolate temperature reaches the melting point. At this point the equation fails as the chocolate melts. We can, however, continue to raise the chocolate temperature and the now liquid chocolate expands edit nearly as before, but with a different equation. Secondly there is a quantity known as the specific energy of a flowing liquid described by an equation along the flow surface. Under certain conditions this equation results in a singularity and the flow surface changes abruptly. We do not have a mathematical desciption of the fluid motion in this region. Beyond this region the equations reassert themselves and the flowe surface is again predictable, and the same equations apply again. The phenomenon is known as the hydraulic jump and is used to slow water down at the base of dams to prevent channel scouring.

"For example, i can have a set such as; A={a, b, 4, 3e, boy, &, apple, 0}" That much is true, but the rest is nonsense. The set you describe has negligable significance in Mathematics or Physics. Your mind appears closed to the offerings of others. The word vector has at least four different meanings in Maths, Physics, Computing Science, and Biological Science. I offered you the beginnings of an informal discussion and asked a polite question to find out if it could be tightened up and made more formal. You did not deign to answer. How does this lead to fruitful discussion?

Have you been on holiday? I hope it was somewhere nice. Whilst you were away your question was also developed in another thread. http://www.scienceforums.net/topic/65768-paddle-wheel-calculations-please/

Aircraft carriers are often tilted an/or facing the wrong way. I don't have the knowledge, but what we need is a pilot with carrier experience to tell us his/her thoughts.

Actually. O'Nero your thoughts are not far from the truth. There are in fact several key ideas or words that differ in mathematics and physics. Are you familiar with set theory and the construction of the real numbers from elementary sets? Informally mathematicians distinguish two versions of 'nothing'. Null and Zero. Consider sets of numbers. There is a set that has one member, a set that has two members, as set that has three members and so on. That is {a} ; (a,b}; {a,b,c} and so on. The letters a, b, c etc can stand for any number so b could be the number that solves the equation 2+2=b (ie 4) a could be the number that solves the equation x + a = x for all numbers, x. That is another name for zero. It must be a valid number since it solves an equation. So the set {0} is a set that contains just one number zero. But in additions to the sets above there is another set of numbers that has no members whasoever. This is called the empty set or the null set {} and is different from {0}. Does this help?

Yes, I agree that's the way it works, but that is not the point I have been trying to make. So I will try again. In an otherwise empty universe Take 1kg of mass. I can calculate the total energy in Joules I would receive if I were able to convert that to energy, using the expression E=mc2 Now compare that with charge In an otherwise empty universe Take 1 coulomb of charge. As far as i know there is no formula, similar to the mass one, to replace all that charge with a specific quantity of Joules. Worse, in the mass universe part only of the mass may be converted to energy, leaving a smaller amount of mass. But in the charge universe there is I know of no corresponding process that can partly destroy charge. Now in each universe if you introduce a second entity In the mass universe there will be gravitational potential energy between the two masses. In the charge universe there will be electric potential energy between the two charges. So they are more similar here.

So you are stating that the total energy of any charge depends upon the volume of the surrounding ball of space, which in turn depends upon its radius all the way out to infinity, regardless of the presence or absence of any other charge?

No, a definition of a closed system is that mass does not enter or leave, not that it remains constant. Consider the system to be the following reaction 2He4 + 5B10 [math] \to [/math] 6C13 + 1H1 + Q Where Q represents 4.03 Mev of energy. This can be compared with the measured mass differences as follows 2He4 4.00388 amu 5B1010.01611 amu Tot 14.01999 amu 1H1 1.00815 amu 6C1313.00751 amu Tot 14.01566 amu Difference = 0.00433 amu (loss of mass) ~Since 1 amu is equivalent to 931.2 Mev, this amounts to 4.032 Mev, which is usually Here we have mass converted to energy. I apologise for using old fashioned units but I studied this stuff a long time ago. (Source of figures Semat : Atomic and Nuclear Physics 4th ED)

OK, I understand, I seem to remember you mentioned this before. Then you will need to become slick and quick at writing out maths in words. This is why I offered a description in my post#5 and also what I meant by my question in post#7. These were meant for practice. So in words Since PQ is parallel to YZ Angle XPQ is equal to angle XYZ and angle XQP is equal to angle XZY Thus triangle XYZ is similar to triangle XPQ (Three angles the same) Thus the area XYZ : area XPQ is in the ratio of the square of the sides ie XPQ / XYZ = (2/5)2 Thus XYZ = (25*24)/4 = 150 cm2 Area XYZ = Area XQP + Area PQZY Thus Area PQZY = 150 - 24 = 126 cm2 If you can learn how to layout your working so the examiner can follow it you will get better marks. You will also find it easier to check your own work and follow it at a later date.

I'm sorry, which Professor Pippard are you (or Bohm) referring to? Your first paragraph notes that 'classical physics' does not explain or predict all observed effects/phenomena. So QM came into being since it explained/predicted observable effects/phenomena additional to those explained by classical physics. Since the calculation effort for QM is much greater than for classical physics, this was retained where it produced reliable results. There remained other effects, explainable by neither system, notably at that time relativity, and the simultaneity inherent in action at a distance theories. So in the 1920s we gained a dual system and maybe in the future we will gain a triple one............... Final point, QM does not rest upon probability, it is just one possible interpretation. But these days we have learned to live with mutiple theories and how to select the most appropriate for the phenomenon in hand.

If that was a comment on my posts, I didn't say pair production was not real. I actually said: Now field theories are only one possible explanation of the interaction - there are others. However that is not the point. Take a closed system with mass M. There are measurable internal (radio) chemical process that can change M to M', the difference appearing as energy given by E = (M-M')c2. This can happen spontaneously without any interaction with the surroundings. Radioactivity is such a process as are some chemical reactions. This mass M or the end mass M' can also participate in energetic processes via other mechanisms that do not involve the partial conversion of the mass into energy. So far as I am aware, a similar effect involving the partial convertion of an elementary charge into energy has never been observed, or proposed. Charge conservation is rigidly maintained in all processes. Charge can, however, participate in energetic processes via other mechanisms that do not involve the partial convertion of charge into energy. Finally I believe I said charge can interact energetically with other charges. Is not pair production or annihilation interaction with another charge and is not total charge preserved by these processes? Edit, Apologies to Sensei who has let me know that his post was not a comment on mine but on something else. Hopefully he disn't find me too rude.

I think you have that wrong. Please show calculations to quantify this energy.

Do you not use a computer?

Why so? And that also begs the question what is real? We had a long discussion about that here recently. Before it was built, was the Sydney Harbour Bridge real? And did the designers have any knowledge of it, at that pre construction time? Or how about Hogwarts., Narnia or The Shire? Hundreds of millions of people have knowledge of these fictitious places.

Perhaps you would like to explain your calculation, including defining your terms and stating what laws you are invoking.

Because that was proven over two thousand years ago by the ancient Greeks. It is considered an elementary proof in number theory. There is no 'perhaps' about it.

See post#4 here http://www.scienceforums.net/topic/84417-boolean-equation-truth-table/

I didn't know that, thank you Acme. +1

The set of all real numbers between 0 and 1 is bounded below by 0 and bounded above by 1; it is limited. Is this set finite or infinite? Is the x axis finite or infinite? Yet the x axis does not include any numbers on the y axis and neither include any numbers that are in the quadrants between the axes. You need a better definition of infinite.

You got it. Can you write it out formally as an solution now? Edit I would have thought you could have used Paint to draw something as simple as that triangle for upload, if you don't have a scanner/camera.

I've no idea what I am to make of your link to a korean boy band. There is a difference between being unlimited and encompassing everything.

And where, pray, do you obtain your 1volt potential difference, if not from other charges?

Worse, in fact it is not even an equation, despite the equals sign.

OK it was a bit tricky with your description. To help you in the future, here is a statement of you diagram. Draw triangle XYZ with base YZ and vertex X Position P on XY such that XP:PY = 2:3 Draw PQ through P parallel to YZ, to intersect XZ in Q Now what about my questions designed to help? Have you looked up the similar triangle areas theorem?

So far as I'm aware, there has never been a formula for charge, equivalent to E=mc2 for mass, relating charge to energy. An electric charge only has energy by virtue of its interaction with another electric charge or charges. A mass has intrinsic energy by virtue of its mass.