studiot

The two electrons in a ground state hydrogen molecule are entangled (by spin). The two electrons in two separate hydrogen atoms are not. The process of bonding is also a process of entanglement. But entanglement is really off topic for a discussion of linewidths related to quanta. However this brings me back neatly to the question bangstrom keeps avoiding. If an electron in a ground state hydrogen molecule absorbs em radiation, thereby being promoted to an excited state. Which happens first ? The absorbtion or the promotion ? Or is bangstom promoting the idea that a system can exist in two different states simultaneously ?

Yes, is is the famous square root of minus 1 [math]i = \sqrt { - 1} [/math] The purpose of i is twofold. To rotate the axis in an imaginary direction. To turn a + into a minus, so not i does not appear on both sides of the equation since [math]{(ict)^2} = {i^2}{c^2}{t^2} = - 1{c^2}{t^2} = - {c^2}{t^2}[/math] Yes I am going to take time out of explaining graphs and frameworks and also because sometimes a peek ahead is motivational and I propose to use the just the x and t axes for this peek. I was going to say that If you are an electrical engineer, that I hope you know enough mechanics to work from Newton's laws to the Principle of Relativity. However you have answered that so I will introduce the diagrams. Nowhere is this more true than in Relativity. It is worth knowing that there are lots of different ways to arrive at SR and GR, but they all start with two basic Principles for SR and a third is added for GR. Different authors express these Principles in different ways, most suitable to their route. The strategy I am following is to look for relationships where one measurement is identical to another. Such situations lead to invariants. One such is called the form invariant, which is employed in the Principle of Relativity The idea is that a physical law must not depend upon the coordinate system. That is it should have the same form in all relevant coordinate systems. As an example take two particles A and B, interacting though some force F(xA, xB) and consider their equations of motion in one dimension (the x axis) Newtons tells us that if mA and mB are their respective masses and xA, xB their x coordinates then [math]{m_A}\frac{{{d^2}x}}{{d{t^2}}} = F\left( {{x_A},{x_B}} \right)[/math] and [math]{m_B}\frac{{{d^2}x}}{{d{t^2}}} = - F\left( {{x_A},{x_B}} \right)[/math] Now suppose we describe these same two particles in acoordinate system whose origin is at x0 in the original system and call this new system the x' system. Then xA = x'A + x0 and xB = xB + x0 Substitute these two equations into the first two we get [math]{m_A}\frac{{{d^2}x'}}{{d{t^2}}} = F\left( {x{'_A} + {x_0},x{'_B} + {x_0}} \right)[/math] and [math]{m_B}\frac{{{d^2}x'}}{{d{t^2}}} = - F\left( {x{'_A} + {x_0},x{'_B} + {x_0}} \right)[/math] since x0 is a constant [math]\frac{{d{x_0}}}{{dt}} = 0[/math] So the forces of interaction do not have the same form (are not form invariant) as in the original coordiante system. If they did they would be [math]{m_A}\frac{{{d^2}x'}}{{d{t^2}}} = F\left( {x{'_A},x{'_B}} \right)[/math] and [math]{m_B}\frac{{{d^2}x'}}{{d{t^2}}} = - F\left( {x{'_A},x{'_B}} \right)[/math] And the new equations depend upon the origin x0 of the new system. So Newton's equatiosn, as they stand do not conform to the Principle of Relativity. However all is not lost. the remedy is to work with coordinate differences, not directly with the coordinates so we write F(xA,xB) = f(xA - xB) yielding equations of motion in the new system in the required form [math]{m_A}\frac{{{d^2}x'}}{{d{t^2}}} = f\left( {x{'_A},x{'_B}} \right)[/math] [math]{m_B}\frac{{{d^2}x'}}{{d{t^2}}} = - f\left( {x{'_A},x{'_B}} \right)[/math] This is the motivation for using the pythagorian square root of the sum of the squares of the coordinate distances I mentioned in an earlier post.

Yeay excellent progress! A retired Engineer is good, some calculus is better, but not not essential now we have agreed that speed is given by dx/dt. If you would like to indicate what sort of Engineer, (electrical, mechanical etc) I will try to pick my examples from that. The important point is that the axes (x,y,z,t or x,y,z,ct) form a euclidian framework to work with. Einstein originally worked with the first set but his friend and maths advisor, Minkowski, realised that the second set offered theoretical and calculational simplicity, but sadly died not long afterwards. Minkowski took the standard euclidian distance between two points A (x1 , y1, z1) and B (x2, y2, z2, ) which is given by [math]\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}} [/math] and extended it to include time. So he faced the same question you are asking which is the time intervals are not lengths. Einstein had already implicitly covered this in his rendering of his Special Relativity equations, including the multiplication by c, but Mikkowski's is more elegant. Minkowski offered that if we not only convert the fourth axis of the framework to a length but get it to point somewhere other than along an already used space axis, we can extend the above formula for the 'distance' between two points, making the time axis a length but a bit different from the others. He did this by multiplying by ic so the expression becomes [math]\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2} + {{\left( {ic{t_2} - ic{t_1}} \right)}^2}} [/math] or [math]\sqrt {\Delta {x^2} + \Delta {y^2} + \Delta {z^2} + \Delta {{\left( {ict} \right)}^2}} = \sqrt {\Delta {x^2} + \Delta {y^2} + \Delta {z^2} - \Delta {{\left( {ct} \right)}^2}} [/math] This was a masterstroke. I will explain further and draw some diagrams once you have confirmed you are OK with this maths.

I would just like to point out that there is only one 'wavefront' - a better term than wave edge. This demarcates the boundary between the zone of space occupied by the wave and the zone where the wave has not yet reached.

+1 However here is a rendering of what us Brits do expect of far flung cousins.

Thank you for your reply. A pity you only bothered to comment on a small part of my last post so I don't know what you made of the rest of it. As regards the reply, "too short to observe by any means" is not quite the same as my proposal for the Earth as a point particle. It is necessary so show that the process is too short to observe, just as we have to show (and do) that the actual size of the Earth makes an insignificant difference to our calculations. Now entanglement is a process, which begins with two or more particles that are not entangled. At this time they cannot act as though they were entangled. At some time later they can definitely act as entangled particles. You need to show that the time difference between these two situations, states whatever you care to call it, is insignificant to whatever calculations you are making. Then you can say the magic words "May be regarded as Instantaneous. for my purposes." Just as with the Earth, it does not mean that the Earth actually has zero size or that the time interval is actually instantaneous. This definition is common in Engineering, for example with "Instantaneous water heaters".

It is really worth considering what is inherent in the best model we have and the phenomenon itself. Are there any truly instantaneous natural processes ? Or is it just that our best model offers this ? Or is is like the concept of a point particle where we can say the size of the particle is insgnificant compared to the size of the system under consideration. So does instantaneous really mean: of insignificant duration compared with the timescale of the process under consideration ? Here is a classical example to think about for comparison. In open channel hydraulic flow there is a phenomenon where the level of the water surface changes (rises) abruptly. This is called a hydraulic jump. The jump occurs where there is a sudden levelling off of the bed slope so the water coming down the slope is moving faster than the water in the level part. The very best hydraulic models (equations) that we have predict this is an instaneous rise, over zero distance, but in reality the 'vertical' part of the water surface always slopes slightly forward. So there is a process which forms of a step in the water surface with a definite start and end point in time and space over very short intervals. The step is due to the fact that the incoming faster water has more kinetic energy than the outgoing slower water. So the surface must rise to transfer the energy to pressure energy.

However you chose to classify it, the fact that we need a 'natural linewidth' , is an indication that the process is not instantaneous. And whether or not is is instantaneous is the subject of my comment. Since it is not instantaneous, it makes sense to discuss the duration of the transition, just as it makes s ense to take other effewcts and mechanisms into account.

Once again you are right to question that which you do not understand, Eise has caught my drift. However I am more concerned with this problem that needs to be resolved first of all. This is very important because you have a basic misunderstanding here. Here is a sketch of a distance-time graph linked to a speed-time graph. They have common sections A_B and B_C In the section A_B the body is proceeding at constant speed (note I say speed not velocity since we are only plotting the magnitude, not the direction), So the distance is increasing linearly form A to B. At B the body stops still so time continues but the distance remains constant from B to C. The lower curve shows the speed from A to B as some (positive) value. Whilst the speed from B to C is also constant at zero. If you measure the slope of the distance - time line you will find it gives you the numerical value of the constant speed. As you can see we are trying to help you. In turn it would help us to have an idea where you are coming from. That is what is your approximate level of knowledge, for instance do you know any calculus ?

Just to add an illustration for Markus (and return the favour) Here is a sketch illustration of the tangent function and its singularity at 90o. The ctangent function is said to 'pass through infinity' at and angle of 90o, where it incurs a change of sign. This illustrates Markus statement that Since there is nowhere on the manifold (which is the plane of the paper) where the tan of 90 exists. It also illustrates his point that there are different types of singularity just as I previously said there are differnt types of infinity.

I said absolutely nothing about electrons or orbits or quantum leaps through soace or time or wormholes or any such stuff. But I did ask a fundamental question about the sequence of events. Re phrasing for absorbtion, Are you telling me you that the electron can 'jump' before absorbtion takes place ? Surely the fundamental question is Which must happen first, absorption, or the electron transition ? or as swansont puts it The 'lifetime' is a convenient model to work (mathematically) with this concept, as is the resultant 'natural linewidth'. You should also note in the hyperphysics link they point out that the broadening due to lifetime is orders of magnitude less than other broadening mechanisms

I rather think it did in the examples at the end. question 7.3.1 specifically calculates line width. Saying both emission and absorbtion are processes with a beginning and an end and that they have a 'lifetime' are essentially the same thing. Take emission. Claiming this be instantaneous cannot be true by itself. At what point in the 'lifetime' does this instant occur ? The beginning ? , The end ? What happens during the rest of the time duration of the 'lifetime' ? Here is the conversation I was remembering from Physicshelpforums.com, where there was a similar question asked.

If you plot light-seconds against seconds it is the slope of the plot at any point would be the speed, not the plot itself. This would just be a standard distance v time graph. Having different quantities on different axes can make sense but then the plot must be interpreted in a different way. Usually the important quantity is the product of the two quantities on the axes and so the erea under such a graph give the total of the product quantity. For example Work done = Force x Distance so the work carried out by a force moving its point of application a distance is give by the areas under such a graph. You did the right thing in asking the question though, +1, because you need to get it straightened out before tackling Relativity. Edit here is a further example to illustrate the difference. Think about a surveyor measuring the land for a map. He sets up a grid and measures the horizontal distances along his grid to all the points on his grid. Hopefully you can see that both axes on that grid must be in metres. He then has two choices. 1) He can erect vertical distance axis and measure elevations of the points above his base grid, perhaps plotting contours, perhaps picking out building steps , roofs etc. Again this axis must be in metres. 2) He can take a magnetic field meter or a gravimeter, or a lightmeter and record the readings at points on his base grid. He can then use the readings to plot contour graphs of magnetic field strength or gravitational strength or sunshine falling. The Minkowski world has to be like case (1) because it is a measuring framework for the world in which we operate. Case (2) is a different sort of measurement - it is a 2D version of a force - extension graph for a spring and offers different information. Having length on some axes and time on another would make the reference framework like case (2) not like case (1)

Here are some calculations. https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.03%3A_The_Heisenberg_Uncertainty_Principle

Thanks, but no thanks.

Is it a distance ? or is it a composite which has the same mechanical dimensions as distance so is measured in the same units as distance ? If you had mixed axes what would be the units of measurement along an arbitrary line using those axes ? [math]\sqrt {{{\left( {{\rm{distance}}} \right)}^2} - {{\left( {{\rm{time}}} \right)}^2}} [/math] What sort of a unit is this ?

Being rude about fellow members whom you can have no possible knowledge of doesn't help your case either. Answer my question please, without trying to put words into my mouth. For your information it had nothing to do with class B or any other amplifiers. It was actually a national certificate electrical power engineering question. Again FYI, just as I already said, harmonics play a very important role in the national power grid because they can play havoc with the grid system if not managed properly.

I doubt it. My company used to destroy hard drives for customers and we used to put three hilti nails straight through the whole works, case and all. No recovery after that and no need to open up the case.

We have a teams meeting/lecture for the next couple of hours, but I will elaborate as soon as I can. Meanwhile there is a good sample calculation the hyperphysics website on a simple uncertainty calculation experiment. I tried tofind it to include in the last post but couldn't. I will try harder there as well.

You seem to have stumbled upon what is called projective geometry. Well done for that. +1 This is one step up from ordinary euclidian geometry and was much studied by the Victorians and part of the school curriculum until about 1930. https://www.google.co.uk/search?q=projective+geometry&source=hp&ei=RmOJYZezKKWJjLsPwNmIkAI&iflsig=ALs-wAMAAAAAYYlxVq4nlx8ovc4Tp-ElMP9Zy91-FdD8&oq=projective+geometry&gs_lcp=Cgdnd3Mtd2l6EAMyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEMgUIABCABDIFCAAQgAQyBQgAEIAEOg4ILhCABBCxAxCDARCTAjoLCAAQgAQQsQMQgwE6CAgAEIAEELEDOg4ILhCABBCxAxDHARDRAzoOCC4QgAQQsQMQxwEQowI6CwguEIAEELEDEIMBOhEILhCxAxCDARDHARCvARCTAjoFCC4QgAQ6CAguEIAEELEDOgsILhCABBDHARDRAzoLCC4QgAQQxwEQrwFQAFjIJ2DcKmgAcAB4AIABvgOIAfAVkgEKNS4xMS4xLjAuMpgBAKABAQ&sclient=gws-wiz&ved=0ahUKEwiX7tP4qYn0AhWlBGMBHcAsAiIQ4dUDCAg&uact=5 You should also look for 'The line at infinity' and 'the point at infinity' in geometry. There are further steps up the geometric ladder.

Spectroscopists have been successfully observing and predicting spectral line broadening for more than seventy years using swansont's (Heisenberg's) uncertainty principle. Formulae and explanations for predicting line broadening are available in any half ways decent spectroscopy textbook eg p19ff of Spectroscopy by D H Whiffen. It is worth notibng that uncertainty broadening is not the only broadening mechanism and Whiffen discusses all the differnt ons and methods of combining their effects, when present, to predict a total broadening. I have indicated the relevant paragraph.

Yes this is true. An 'event' refers to a point with unique or particular coodinates in a given frame of reference. This view has merit, not only in this situation but in many others besides. There are established mathematical techniques for handling the situation. Either We can show that the system of interest is 'small enough' to ignore its sizing in the coordiante system. Sadly this is too often taken for granted or not done explicitly. An example would be taking the Earth as a point particle in the solar system for the purpose of calculating obits etc. or We can use the mathematical limiting process to consider a 'control volume' in the coordinate system and tak the (mathematical) limit of the maths as we shrink the control volume to a zero sized point. An example of this would be ordinary density which is a point function that is defined as such a limit.

Expanding planets Expanding Earth ? How is this all mainstream ?

Absorbtion (and emission) is not instantaneous. Both processes take time. That is why spectral lines are slightly 'blurred' or 'spread'. Maybe not intuitive, but why suprising ? If you were to make a 100 trials of the roll of dice, would you expect any difference between rolling 1 die 100 times and rolling 100 dice 1 time ? What difference would you expect if you took outcomes of the 100 trials in different orders ?

Spot on as usual. +1