studiot

I was (politely) disagreeing with the statement "Time is rate of change". Change is not necessary to time. It can proceed perfectly well without change. Time is a variable, sufficient to distinguish between events or situations and to make predictions (in the sense of make deductions in accordance with physical laws) about them.

Repetition does not strengthen verification. That is the province of reasoned argument. In your previous post you claimed that they were qualititatively the same, but haven't addressed my comment on that. For instance is gravitational energy qualitatively the same since it arises from a distortion of space? Mordred has made a good point about which mass. I noted that the increased mass appears to observers in (increased) relative motion to the molecules concerned. Do the molecules concerned observe any increase in their own mass? Why should there be an increase in mass when there is no increase in relative motion? What is the mechanism for this?

Since we are discussing this, what do the rules say about the reflexive voice? Say for instance I posted Silly me (or worse)?

Isn't that a tautology, especially since you posted it in two threads. Mathematically can a variable be its own rate of change?

Just saying this doesn't make it so. And no I do not agree that the nuclear binding energy is qualitatively the same ie it does not spring from the same mechanism. In a chemical reaction, if the products are heated by the reaction then the molecules are moving faster. That is they experience an increased relative velocity. So, as with any moving mass, they will appear to gain mass to that which they are moving relative to. But this would also be true if they were just heated up some other way and did not react chemically. That is the same effect could be realised without changing the bonds. So how can you attribute the mass change to the bond energy? By contrast the nuclear particles are not in such vigorous relative motion and the forces in play are from a different source.

Thank you for the article Mordred. this seems self contradictory to me.

Thank you for the link, strange. It does rather disagree with itself in the discussion. Worse the first answer listed is actually wrong. My copy of Semat: Atomic and Nuclear Physics has 'Mass defect' as due to the binding energy of the nucleus, not any chemical bond the atom may enter into. This effect is measurable.

So you want to have your cake and eat it! Classically the component particles are the only contributors to the mass. Forces from any source act on the mass of the component particles or their aggregates, but do not change them. Modern physics does not work in terms of force at all, but considers mediating exchange particles, or other effects such as spacetime curvature instead. Since this side of physics is still undergoing rapid development you really need to ask that question in the modern physics section and understand that any answer will keep changing, depending upon which theory you are studying. I was aware of the difference due to nuclear binding energy, but not aware of any due to chemical bonds. Do you have any references?

Are you suggesting that matter that is chemically bonded has more mass than matter that is not chemically bonded? I note that this is the classical physics forum, so Deepak are you looking for a particle physics answer or a classical answer?

Would you agree that if you have two somethings interacting you then have three things viz the two things plus the interaction?

This is the nub of my comment, since this is only half the story. This is also what I mean whe I say that I don't see any mathematical solutions posted in this thread, since you are all only discussing half the story. Think carefully about Zeno's concise description, then compare with the comments in this thread. Why are most of the posts are much longer than Zeno? It is because most are distracted by 'reality', 'hypothetical', infinity and whether or not it is reached and so on. A hint there is not one 'infinity' inherent in the question but two different ones.

All distance measurement is by difference. If you have done any serious hermodynamics you will have met the thermodynamic absolute temperature scale which is defined independently of any thermometer, unlike distance, for which we have no absolute unit.

I've yet to see it in this thread. Nonsense, it's the other way round. Every symbol in maths has a name that can be spelled in English. Every line in maths can therefore be written as a proper english sentence. English is composed of proper english sentences.

I agree, the method of measurement is not a definition. I don't have a complete definition or description but my idea is that there are many phenomena in our observable world that are best modelled or explained by introducing a mathematical variable we call time. I hesitate to suggest this thread about the same subject because it suffered much misdirection but look at my post#62 on page4 http://www.scienceforums.net/topic/82939-explanation-of-time/page-4 The introduction of a new variable to ease the mathematics has other precedents, for example the introduction of entropy in thermodynamics to pair with temperature on an indicator diagram. Of course we do not have the same up close and personal relationship with entropy that we have with time but the maths follows a similar path.

The ancient Greeks did a lot of thinking, some of perhaps due to the peculiar quality of the wine made from the grapes that grew on Mt Olympus. They were particularly fond of paradoxes, Zeno remaining the most famous in modern times, but there were many chroniclers. Most of their 'paradoxes' can be resolved by adding our further knowledge to their less developed state knowledge. But I am not really a classics scholar so I don't know the full story of Zeno. Today we have our own 'paradoxes' to wrestle with such as quantum tunneling and quantum entanglement. Perhaps later generations will have the proper understanding to fully resolve these. For example Proclus has that " Not every triangle is also a trilateral figure", simply because they did not fully understand angles.

Why am I dodging the issue? No one, not even Zeno, pretends that Achilles does not catch and overtake the tortoise. That is not the issue. He just saddles up his trusty kangaroo and hops right past. Zeno's issue is/was "Where is the mistake in my homework, Miss? I can't see it" In order to explain the inadequacy of Zeno's reasoning we need to do something equivalent to that presented in physica's video, and then some, because the good doctor of maths in that video didn't complete his 'proof'. This can be done either mathematically or liguistically, following the same route. What I have not done, but left in the air for the moment, is state what I think is missing from existing explanations in this thread. What do you think that might be?

Like many I have been following this thread with interest and would like to make the following comments. 1) The OP did not contain a question, but since this is the speculations thread I assume that the statements made were a proposed analogy for explaining Zeno, and this is borne out in the Title statement, which is also not phrased as a question. 2) The thread deteriorated into a dispute about mathematics v linguistics. 3) Now since there is nothing that can be said in mathematics that cannot be said linguistically this is or was a pointless diversion. 4) Since there are those who will wish to argue against (3) they should note that this may involve going back to the basic axioms of maths, which are all stated linguistically and developing the necessary mathematics for resolving the problem. Using Maths is of course more concise. So a linguistic answer may be very very long winded but it can be done. 5) The most interesting point is that neither side has actually resolved Zeno. Not even the 12 minute youtube video did that. So far only part of the solution has been presented. 6) No, calculus is not required, but a study of convergence either mathematically or linguistically is. A good textbook for this is the classic by Ferrar at Oxford, suprisingly entitled " A Textbook of Convergence ". I look forward to someone presenting a complete solution.

Well let's hope I have succeeded then.

I have thought long on this topic.......it's still at the back of my mind. I am afraid you won't like my response........... My response is as follows............. I think that proportionality is the result of a choice rule......and.......choices can be many. It is not a question of whether I like or dislike your response - actually neither. I don't understand your response. I have no idea what you mean by a choice rule. The definition of proportionality was set at least four hundred years ago. If you are proposing an alternative, I have pointed out it's arithmetical flaw since we cannot divide by zero. A further arithmetical flaw is that is does not define what happens when the constant is zero. Do you think an alternative definition for a relationship between three quantities that is undefined for two of them in certain important cases is worthwhile?

Yes, it is true that whatever clock ticks measure it is not time and that a ruler directly compares one length with another. But it is also true that neither tells us what space or time are. In fact we cannot measure time itself, only time difference, and that is what the clock tick measures. There are many quantities in Physics that we can only measure by difference, eg voltage. Again in fact the ruler length is a distance difference not a true measure of space either. One of the few absolute quantities that we can measure is absolute temperature (at least in theory). One further note is that for quantities that we account in either absolute or difference terms such as voltage, time etc, both the absolute and difference measurements are made in the same units. go well

This is not a satisfactory definition of proportionality. What happens when x=0? We do not allow division by zero. I have already given you one that works in all cases. Use it! Quoted is your last statement on proportionality, followed by my reply and further explanation. You have not responded to this. Further your last statement was a contradiction of my long post explaining proportionality. I have suggested we discuss forces, masses and energy when we have finished proportionality. Proportionality is a very very important concept in Physics, that we use whenever we can, so it is vital to fully understand it and to be able to get it right.

None of this is necessarily true. It is all, as you said, hypothetical. Further it suggests you have not bothered to work through the material I carefully spent time writing out for you. You started this thread about proportionality. So let us keep on topic and discuss that.

Not at all so long as you have a genuine interest. You are nearly there, but remember that x is the independent variable and y the dependent variable. The idea is that changes in y depend upon changes in x ie they only happen because we change x. This is because we normally know x but not y. We obtain y by calculation from the equation or formula. So an expression of the type y/x or y-x contain an unknown. However you are skirting around the fact that we can sometimes change things (ie find a different x) so that we can recover proportionality. for example The length of a stretched spring is not proportional to the force required to stretch it. but Another variable, the extension, e, is proportional. If we double F we double e and so on e=kF. e, of course is the difference between the current length at force F and the original that is e = (L-L0) This is not a satisfactory definition of proportionality. What happens when x=0? We do not allow division by zero. I have already given you one that works in all cases. Use it! Force fields do not exert forces on each other. They exert forces on material objects placed in the field(s). So what you are asking is how do the effects of the fields combine when they both act on the same object. Do you understand this, this is essential before proceeding.?

In short , no the definition in green does not. But the statement in black is not correct either. A word of friendly advice here. I have noticed in your threads that you bring in far too many ideas far too quickly. The result is that you confuse yourself and possibly others as well. Further you have scattered your subject over several questions, where it is apparent that a difficulty in one also comes out in each thread. So let us stick to proportion in this thread. It will help in the others as well. When two quantities, say B and A are in proportion we say that B is proportional to A. This means that B depends upon A in a particularly specified manner. You should realise that there are many other ways for B to depend upon A where they are not in proportion. What is meant by in proportion is that if we double A we double B, if we triple A we triple B, if we halve A we halve B and so on. We use this as follows: If A is 10 and B is 14, then For A = 20 B = 28 and if A=10 and B = 5 For A = 20 then B = 10 Note I have not needed to employ a constant of any sort in this definition. The above is always true regardless of the constant I shall introduce below. But I can go on pairing values of A and B in the manner above without any constant. We can convert the above to a general equation connecting A and B by introducing a multiplicative constant. We call this the constant of proportionality. So B = pA, where p is the constant of proportionality. In the examples above the first p = 1.4 and the second p = 0.5. Note I have said a multiplicative constant. This is very important. If I do anything else then B is no longer proportional to A In particular if I add anything at all, even a constant, B is not proportional to A. So if I have a second additive constant such that B = pA + D then I loose proportionality. ajb has mentioned 'linear', but I recommend you avoid the term since linear and proportional are not always the same. So we move on to what happens if B is proportional to two quantities, A and C. So B is proportional A and B is proportional to C How can I write an equation to combine A and C so that my definition will hold? Well if I add C to A what happens? That is if I double A but do not alter C for the moment. so if B = p(A+C) I want B2 to be double B1, when I double A Let us work out B1 = p(A+C) and B2 = p(2A+C) B1 = pA+pC and B2 = 2pA+pC This shows that B2 is not double B1 so an equation adding C to A will not work in proportion. OK so what about multiplication? If B = pAC B1 = pAC and B2 = p2AC So B2 = 2B1 as required. So far, I have kept C constant but if the constant of proportionality for C is q then B = pqAC, maintains proportionality. We can then combine p and q into one constant of proportionality r = pq. So B = rAC Finally I have councilled avoiding the term 'linear'. This is because we can extend the concept of proportionality to more complicated (non linear) expressions so that we can say B is proportional to the reciprocal of A, or B is proportional to the square of A. Our equations now become B = p(1/A) and B = p(A2) To cope with this extension we add qualifying words to the original statement. We now call our original simple proportionality direct proportionality, Then we say that being proportional to the reciprocal is inverse proportionality and Being proportional to any other expression is proportional to any other expression so our example with the square of A says that B is proportional to the square of A. We often omit the 'direct' when we mean simple proportionality. Does this help?

This is a better link http://www.power-technology.com/projects/strangford-lough/