studiot

Since neither Heisenberg nor Bohr were responsible for the quantum wave funtion why do you ask this? The Schrodinger wave function, has units of metres -3/2, since The units of [math]{\Psi ^2}[/math] are those of volume the units of Psi are the square root of volume. Mass in not mentioned and so Psi is independent of volume. What more do you want?

very apt descriptive... two key words of strong note. Observable possibilities takes into account the probability nature of wave functions. Not sure who this is addressed to or why. The bulk of the post seems out of place here ? Perhaps it has something to do with this Yes I agree, though I would ask is everthing that is physical also measurable? You can measure properties of a shadow, but can you measure the shadow itself? Of course a shadow is also not a substance. Yes I think Time is physical. It is instructive to consider a situation where more than one time related process are overlaid or combined. For instance consider what can be measured or observed in this thought experiment. A fluid is passing down an obscured pipe in steady uniform laminar flow. There is an observation window on the side of the pipe to see what is going on. Within the pipe there is a nozzle that can release a second material which then enters the flow as streak lines. The observation window is sufficiently downstream that steady laminar flow is resumed, whether injection is on or off. For instance the production of that famous striped toothpaste. Every so often the injection is switched on or off so the streak lines appear and disappear in the observation window. Here we have two different time regimes superimposed producing changes in observed pattern in the window. It is instructive to consider this in realtion to time.

Exactly, a fine example.

The 2mg is the mass (not weight) of active ingredient in a pill, not the mass of the pill. When measuring pharmaceutical amounts the difference between mass and weight and bouyancy in air can become important. I agree with others, there is insufficient information and the whole question is clouded in extraneous detail, some of which is conradictory. I would further observe that a proper trial would never supply the placebo and actual pills differently as apppears here. Otherwise it would be possible to distinguish simply from these differences alone.

Personally I have no axe to grind, one way or the other about the use of flow in connection with time, although I can see the potential difficulties since some other flows are measured in terms of time. But we use flownets in complex and other forms of analysis. Some of these, eg electrostatic fields (note the word static), or shear flow in structural engineering have no connection to time at all. Yet others eg geological water flows under a dam are definitely time dependent. But this simply reinforces the connection to time as a coordinate axis and we should work in terms of this to get it right. Talking of coordinate axes, I meant to put into my last post to Argo the following One point in time over all space or one point in space over all time. This 'split' is characteristic of wave motion where you can do exactly that. Either sit at one point and watch the waves go by in time Or Observe the phase of the waves at every point in space at one particular instant.

I claim no originality for this approach, it was introduced to me by Roy Turner of the department of Theoretical Physics at Sussex University. I don't think he claims originality either, but allow it is very useful. My take is that it is a kind of separation of the Constitutive and Compatibility relations. Maybe the next installment will make things more clear, I was disappointed that folks appeared to only want to mock, so I held back on that today. The Principle enunciated place more severe limits than general kinematics, although it does imply non discontinuous paths, due to compatibility requirements. N1-N3 amopunt to the constitutive relations which come next.

You are doing a grand job checking the detail.

Have you considered there might be other possibilities than your either or ? The whole definition of a dimension in a coordinate system is that any given coordinate axis exists for each an every other coordinate axis value. For instance would you say the the negative y axis does not exist for the function y = x2, just because there are no y values for any x value? As regards time particles, if you have introduced them in this thread, I have not noticed it. The nearest thing we have to time particles would be Planck Time. I do not know if you have read the other material I posted, but here is a bit more that might help you here. Note that they cans till be measured in seconds and that we have no direct evidence that these form quantum units.

No I was not deriving the Principle from the first or second or third laws. It is not necessary to even introduce any of them at this stage. That was just a preamble to place things in context, since we have these laws and are trying to discuss them. Do you disagree that the first and seciond derivatives of a position - time graph are purely geometrical? IOW acceleration is a purely geometrical property, that can be considered quite independently of forces or masses or temperatures or other properties of a body. That is not to say what the causes of that acceleration are, simply its measurement.

You have presumably completed part (a). Did you use moments to do this? You will need to use moments to complete part (b) What are your thoughts on the values of Fa and Fb at the instant the plank starts to tip?

How does that work if the rotors are going in the same direction ?

Thank you for your comments, Mordred. That was not the chain of reasoning I was pursuing, and is in grave danger of becoming the circular argument everyone is talking about. Let us see if there is any more interest in the subject. Ah, I missed that post. Thank you. That is why we replace N1 to N3 with a Principle, (as stated). So we are working on pure kinematics to start with. We end up with N1 to N3, we don't start with them because that way does lead to circularity. Do you disagree with that principle?

I have started a thread about Newton and circularity in Philosophy ,as promised. I have no idea why Newton's 3rd law would define mass. It does? Thank you for the correction.

This thread was prompted by the surprise expressed in some quarters that Newton’s laws of Motion (N1 to N3) was not only not a circular argument but could be recast in an alternative manner with beneficial results. The originating thread can be found here:_ In Mathematics we have axioms and we deduce relationships resulting from these axioms in mathematical systems, which obey or follow these axioms. Note this does not disallow the possibility of mathematical systems that do not follow a givens set of axioms, as well as systems to which any particular set of axioms has no relevance. In Physics we have Principles, rather than axioms, and we deduce effects resulting from these Principles in physical systems which follow or obey them. Principles may be explicit for example Huygen’s Principle, The Principle of Relativity (to which I will return) Or they may be implicit as for example the maxim ”Like charges repel, unlike charges attract.” So to reinvent Newton we shall start from a stated Principle. But since we do not (yet) have a definition of mass or force, we cannot use them in our statement of principle, if we wish to avoid circularity. So instead we start from something more general. By way of introduction, let us look at what N1 tells us. N1 effectively introduces Frames, and indeed defines an inertial frame as one in which a body “continues in a straight line.” So what does that give us? Well a general frame is a coordinate system in which we can plot the path of a body in motion (or at rest). Such a frame provides variables of space and time as generating the coordinate axes. Taking one of each of these we can plot a path taking a space coordinate (s) as a function of time (t). Then we can derive the velocity (v) as the first derivative of our plot [math]\frac{{ds}}{{dt}} = v[/math] And acceleration (a) as the second derivative. [math]\frac{{{d^2}s}}{{d{t^2}}} = a[/math] Note that these are kinematic quantities, entirely independent of any mass we eventually attribute to the body or any forces we eventually consider as acting. Also we are discussing a purely mechanical system. Now to state the first Principle “If the system contains two otherwise isolated but interacting bodies then, at any point in time, the ratio of the magnitude of their accelerations is a constant. Further their respective accelerations are oppositely directed. So for accelerations a1 and a2 and acceleration vectors a1 and a2 we can write the following equations following this principle. (1) [math]\frac{{{a_1}}}{{{a_2}}} = {k_{12}}[/math] (2) [math]\frac{{{{\vec a}_1}}}{{{a_1}}} = - \frac{{{{\vec a}_2}}}{{{a_2}}}[/math] We have taken the meat from N1 and stated a Principle that nearly leads to N3, however Newton’s laws are a trinity and should be considered as such. So to complete the job we need to bring in mass and force via N2. Which is the next stage of the development. There is much to be gained by completing this journey, to whit a conservation law and a version of Newton that is compatible with the Principle of Relativity.

How good are our models? I'm no expert on population dynamics but I wonder if there isn't a chaotic possibility, given the number of factors in play. I know for instance that a simple population model, dependent upon one factor eg food supply is purely classical. But introduce a simple complicating factor such as the predator- prey equation and the dynamics become chaotic in nature, exhibiting the characteristic wild fluctuations characteristic of Chaos theory. That is the equations become unstable.

Argo As far as I can see you posted essentially the same subject a few months ago and entered into a 5 page battle, posting statements that confused everybody and eventually abandoned that thread of yours without conclusion. In order to try to help your understanding along I suggest you take a long read of this extract from the Stanford Encyclopedia of Philosophy about Newton's definitions of Time. Take particular note of the section I highlighted; it says much the same thing as I posted in my original reply to this trhead, wo which you have not responded. There is much wisdom to be had from this text.

Yes it is a good plan really. The Church provides the instrument and the venue for free. The renouned organist comes down from Bristol Cathedral and plays for free. The volunteers organise for free. So at £5 a ticket it is all profit. The only fly in the ointment was the weather which kept some away, reducing the overall take. Lot's of events like this are how the 'Friends of the Hospital' have just raised over £1million for a third MRI scanner in just over a year. This is a much better way than the sort of problems Daedalus is facing.

The problem is that there is no evidence that Spacetime needs to be quantised. The quantisation of energy comes quite naturally out of the equations. That is at least some of solutions to the equations of energy are periodic or quantised. The equations of Spactime, and in particular Einstein's equations are not, and do not have quantised solutions. Rather they require a continuous distribution.

And I thought it was something to do with corona

I'm off to an organ recital, raising money for another scanner at the District Hospital. Now that Eise's response on Newton is in I plan to start a new thread, developing the modern view of N1 - N3, as promised. I will post it as and when. It has implications connected with the points of dimension we are discussing here.

All functions are dependent. That is built into the definition of a function. But not all functions are variable since there exists such a thing as a constant function. It is independence we are talking about.

Further, those tensors are not independent variables. They are dependent upon the basis variables for the space, in some regular and definable manner, unlike my example.

Sometimes. But not always. As a for instance we can plot atomic weight against atomic number. This example has the advantage of not including any of the spacetime variables. We cannot overlay them.

Thank you for attempting that clarity, you have perhaps identified and picked out the major fallacy in the OP. +1 By definition one dimension does not overlay another ever. Dimensions are representations of independent variables. The rest of the OP is just an unsuccessful attempt to break this independence. Pixels references, for instance, are a red herring.

For which record? Newton well understood the difference between inertial mass and gravitational mass. Was the above definition a definition or an interpretation? Back to the question I asked you Note I said "in modern terms" So I was clearly not thinking of Newton't interpretation. Furthermore he did not write an equation. Equations were not invented until after his death. He wrote (as I put above) 'proportional to' as was the custom of his time to work in terms of proportionality. However I think detailed discussion, if desired, belongs in another thread, not one about timeflow. Apologies for the poor spelling earlier.