studiot

Then perhaps you need a limit. Do you know any calculus? Straightforward density at a point for instance is [math]\mathop {\lim }\limits_{\delta v \to 0} \frac{{dm}}{{dv}}[/math] Where m is mass and v is volume.

Let's try to approach this a different way . What is there about light speed that needs explaining ? The quantum wave function has nothing to do with light speed.

Did you mean this piece ? (From the 1964 edition) In future it would be very helpful to refer to the page(s) from the book. This is a discussion of Newtonian-Galilean mechanics, not Einstinian relativity. Actually he says the effective speed is 4 miles an hour for crossing the river. I think I understand you worry though. Bondi could have perhaps worded his text a little more clearly but technically he is correct. Here is my explanation, I hope it helps. In all such problems it is essential to qualify or specify the word 'speed' as there are several different speeds involved. I am not sure that using 'effective' is a good choice but since we are presented with it I will use it. The boat is stated to travel through still water at 5 mph. I have seen the terms 'actual speed' or 'real speed applied', but the best (clearest) term is 'the speed through the water is 5mph'. But remember that the water is not still. I would also like to make it very clear that you are mistaken in saying that the boat travels further than the width of the river. The boat travels exactly the width of the river, no more and no less. It does not travel in some curved path, whcih would be longer. This is because our frame of reference is the ground, not the water. So perhaps Bondi might have said that the speed, relative to the ground when directly crossing the river is 4mph, rather than calling it the effective speed. So we have a situation that the boat has a speed relative to the ground and the water has a speed relative to the ground. The first of these we don't know, but must calculate. The second we are told as being 3mph. These two speeds can be composed to eliminate the ground to obtain the speed of the boat relative to the water, and we are told this. This composition is done using an ordinary vector triangle or parallelogram which can be done. I will stop there and post since you have just come on line.

Why should it not tend to zero ? Zero is a valid state of charge. Further your integral is taken from zero to Q.

Thank you all for your replies. Peterkin's point is sadly demonstrably falsified by the recent events, at least in the UK. I think that we need a radical socio-political economic change to address the problem. This is the second once public collective service that has cost people dear in their failure to plan and provision for predictable emergencies that are known to have happened in the past. Last time was serious flooding and there were not enough pumps (and pump expertise) in the whole country to deal with the situation. This time it was failed electricity distribution systems and there were (and still are) not enough standby generating capacity.

You should not have any trouble with this brief description. https://astronomy.swin.edu.au/cosmos/v/Virial+Theorem The virial theorem was originally introduced in the mid 1800s in thermodynamics and describes the distribution of the total energy of a system of interacting particles between their energy of motion (KE) and their energy of configuration (PE) but is applicable to any such system with these characteristics. Hence itcould be applicable to galaxies, universes etc.

+1 for a genuine and very reasonable attempt to address the topic.

I don't think you were here when I described the teaching method of the best teacher I have ever had. (A level Maths) It may also be worth mentioning the Oxbridge (where I never went) Tutor system and how they differ from teachers and also the fact that 'tutors' in other UK universities are a pale imitation of this.

A week ago we had a moderately severe storm in the UK which lefts tens of thousans of properties without electricity. A week on and there are still thousands stranded. Watching the TV pictures of the emergency vehicles, I wondered what would happen if they were all electric ? More precisely how would they be recharged if there was no mains power available ? There are obviously not enough generators available to replace supplies to even the most needy as nursing and care homes went without electricity for nearly a week. What might happen or be needed if we had another really severe storm of the magnitude of the late 1980s and early 1990s ?

I would say that sensei has raised a serious concern about the safety of electric batteries that should be addressed by proper engineering considerations by the designers. Battery technology is progressing so fast I can't keep up with it. So I am forced to look at indirect measures. In several towns in the UK trials of electric scooters are taking place and results of the trials are now available. Amongst these results has been the observation of a high incidence of impact accidents including severe damage. However no fires have been reported as a result of any of these impacts. I repeat that proper engineers would have looked into the fire safety of impacts. If anyone knows for sure I would be interested to hear their views. Meanwhile the whole business of safety and reliability is surely off topic in a thread about chips ? I am starting a spin off thread to discuss something that occurred to me recently as a result of the storms in the UK in relation to these issues.

What does that mean ? Why nuclear ? Why assume ? Higgs operates on isolated particles. Both epsilon and mu are tensors in the general case, not scalar constants. Be warned that you only have 5 posts total in your first 24 hours here so don't waste them. I look forward to learning more in the discussion after that.

I don't know enough about the Higgs field to comment, I'm sorry. Perhaps some others better aquainted with particle physics will comment on this. But the Gauss' law you refer to has much much wider applications than electromagnetism. It is a piece of pure mathematics expressing the fundamental theorem of calculus. In Physics in various guises it appears in conservation laws as it applies to a conservative field.

I don't seen anything I said that disagrees with your post, anymore than anything you have said disagrees with mine. In fact I think you have also made some excellent and valid points.

Excuse me for butting into your vendetta against CNN. This is my thread and I will thank you for keeping on topic.

Especially if you don't know enough to critically appraise what you are quoting. Not necessarily. It depends upon the 'size' of that universe. What, pray is a flat curvature ?

Thank you for this interesting article, which complements the information I gave. +1 I see that it can be obtained as a single page pdf from the link you quoted.

In your pursuit of gravitational potential are you interested in the application of 'the virial theorem' to cosmology ? Markus' advice to move on is good when you consider relativity. You have to look inside Einstein's tensor equation, which is not really one equation at all but sixteen coupled equations, minimum, to find the relevent part. That is why I prefer matrix methods, which display them explicitly. If you want them the derivation is about 10 pages and also involves derivatives (or jacobians) of the Einstein equation and its solutions. This will give you something akin to the Newtonian gravitational potential (one of the gijk components) and the cross products will bring in time as Markus says. But this 'g' is a variable not a constant.

Why don't you just pile them in a nice heap and let them rot down ? Mine go into the compost in layers at this time of the year, replacing the grass cuttings from earlier months. The layering method is useful to separate too much kitchen peelings etc.

I had hesitated about introducing group theory, but now you have gone and done it. +1 I doubt there is much group theory in Engineering, but the following development of your linear transformations may be accessible to Caruthers. Note that linear transformations (in the sense of Linear Analysis or Linear Algebra) are the simplest but not the only possible transformations. Linear transformations work so some texts say we need a transformation so we will start with the simplest a linear transformation and leave it at that. However @Caruthers you may be familiar with (linear) rotations in mech eng theory so I will link to them as follows. If we change the coordinates from x, y, z, τ to x', y' z', θ τ' by rotating an angle the coordinate axes in the plane (x, τ) through an angle θ from τ towards x, where τ = ict - it is common and convenient to introduce the new variable tau as ict here (Again I am moving the axes this time, not the position vector so moving the axes from tau towards x is equivalent to moving the vector from x towards tau) then the transformation becomes x' = xcosθ - τsinθ τ' = τcosθ + xsinθ y' = y z' = z Using the familiar circular trig functions but in 4D. Comparing these with the Lorenz version in xyzt and x'y'z't' (ie ordinary time) [math]x' = \frac{{x - vt}}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}[/math] [math]t' = \frac{{x - \frac{{vx}}{{{c^2}}}}}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}[/math] [math]y' = y[/math] [math]z' = z[/math] we see that [math]\cos \theta = \sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} [/math] and [math]\sin \theta = \frac{{ - iv}}{{c\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}[/math] so theta is an imaginary angle since cosθ is greater than 1 and sinθ recovers the imaginary symbol i. If you are familiar with hyperbolic trig functions you will immediately recognise that this can also be done with hyperbolic sine and cosine (sinh and cosh) and real angles. These are all the different approaches you will find in the texts. Good luck with your bedtime reading with your candle in your boat cabin.

To return to the topic of the thread, Let me see, 2 headlights, 2 sidelights, 2 fog lights, 2 reversing light, 2 brake lights, 2 lights, 4 interior lights, 4 indicator lights. Each of these, being LED will have an average of 10 chips making a total of 200 chips. Door locks, alarms and ignition keys (do you count the mobile phone if it's a Tesla ?) perhaps another 200. Air conditioning sensors and controls. perhaps 50 It soon adds up. But yes, I agree, we may well be making cars overly complex. However a big part of the problem lies in the poor programming of the control systems which mean that many minor faults, some of which may add to safety, compromise the actual functioning of the vehicle for no good reason. The problem is exacerbated but the lack of human override capability.

Thank you for this useful information. I fully understand about sailing vessels. My brother goes through this routine twice a year, once to lift the boat in and once to lift it out. The club at Gillingham hires a big crane twice a year to effect this for members. So calendars and timetables have to scramble to meet the appointed dates. So it's no problem to spread your excellent conversation out. As regards rotation, I have been rotating axes for simplicity. The actual spacetime rotation is of what amounts to rotating the position vector of the moving object (a bit) towards the time axis and away from the space axes. This increases the projection of the position vector onto the time axis and decreases it on the space axes - In other words time dilation and length contraction. But to have physical meaning the time axis must be modified by a factor with the units of velocity. I am saying units not dimensions to avoid confusion with the dual use of the word 'dimension' as in MLT etc, and the quantities measured by the coordinate axes. Hopefully you are not in the storm zone with your boat.

You beat me to it with a better post to boot! +1 I was just about to say melt the wax and filter. The carbon particles won't be affected by the heat.

The attachement from the international libraries association is self explanatory. Although not specifically for scientific matters I thought it was particularly well presented and a good candidate as a sticky on this site.

I think sensei is right, I think it is a liquid impellor, rather than an airscrew. The picture at the bottom left suggests that it might be a prop shaft and prop for an outboard engine

Since 'fields' have been mentioned in connection with this subject It is perhaps worth noting that this is the Physics definition / usage of a field. It is not the Mathematics definition, which is somewhat different. If that property is a scalar then the field is a scalar field. If that property is a vector then the field is a vector field. If that property is a tensor then the field is a tensor field. The 'fundamental theorem of calculus' is the relation between the integral of that property over region and the integral over the boundary. A closed boundary will have one fewer dimensions than the region.