studiot

But a structure cube or whatever is not a point. Can you describe what you mean using only one space axis (x) and one t acts (ct) ? Do you understand why the other axis has to be ct ?

I think both these graphs are perfectly compatible, but they show different things. Swansont's graphs are specifically the relationship between infection and vaccination. That is one effect only, with other effects not included Mistermack's graphs are a composite of different effects. Yes the trend in the 7 day average new cases within 24 hours and deaths tracked each other pretty closely. And they still do. But they also show a dramatic of deaths suppression following significant mass vaccination of the population. Nothing wrong with either of them

In what way ? I am not sure of what use the hypervolume is to anyone anyway ?

Yes, but what is the letter of the law ? The UK advisory body has just advised that fully vaccinated for folks in the age range 12 - 15 should be increased from one shot to two. But it is not yet law. I think age grouping of data is another effect not properly spelled out in these summary charts.

I haven't checked the arithmetic but some practical comments may be in order. 1 How would you heat the water ? 2) How would you extract the energy from your supertank ? Assuming 50oC, as soon as you had extracted half the energy the tank water would be down to 25oC. If you simply ran water from than tank through a domestic radiator system the system would cease to heat the house at about this point. Radiators at 25oC are of little use. 3) Very large houses for very rich people in the past had 'ice houses' capable of preserving winter ice during the summer heat against a temperature differential of perhaps 30oC. With modern insulation we could perhaps contemplate the larger differential, but it would still ad considerable bulk to any installation. Not a prospect available to most.

I am using the AGA, as I think druS did, to represent cast iron ranges which often had/have a domestic hot water capacity as well, not to represent any particular brand. I should perhaps take this opportunity to note that building owners in the UK, have a statutory duty to inform Building Control if they change the form of heating (water and I think space) in their property. I had to do this when I changed from oil to gas and again from gas to an electrically driven heat pump.

I am not sure how much you will find about vectors in Bondi's book, but the Einstein train experiments chapter is worth thinking about. Here is another train experiment which shows some interesting things. A man holding two bricks is travelling in a glass train. (Glass so he can see and be seen) He holds them side by side, one just inside the carriage and one just outside by the window. As he passes another man standing on a station platform he drops them both together. It is illuminating to consider what each man sees about the paths of the two bricks.

I have that beef about the UK Inland Revenue and tax forms.

Thank you it is useful to be able to compare data standards. One thing immediately stands out from that. When do you become 'unvaccinated' after the one or two shots ? The UK is managing boosters for about six months and two weeks. But many mean fully vaccinated = after the booster.

It should be noted that data from all countries/regions contains considerable hidden unknowns. Also the methods used for recording the data are different in different countries, making comparison a bit tricky. The UK defines death from covid as "Death within 28 days of a positive covid test" It defines infection rates as "recorded by a positive covid test", not as presenting with covid symptoms But only a minor % of the population undergoes routine testing. Most only test if the have symptoms. Also what is meant by 'fully vaccinated' has never been clear.

Actually I was a bit overdramatic there because you can still install an electric AGA, its just the gas ones at the moment. Interestingly folks come from all over the world (even Oz) to visit the splendid country kitchen showrooms near me. You can see not only AGA, but many other European and American manufacturers rages there. Some of these are absolutely enormous. We sometimes take our visitors there as it provides a good half day out.

Shape is a very difficult concept to tie down. I don't know of any way to define it without involving boundaries. So far as we know, the Universe has no boundaries.

I wasn't asking for myself, but thanks for your links. I was gently referring to the invariance of 4 dimensional distance in spacetime. Distance or length in 4 dimensions is the invariant '4 squares quantity' No one measures it lengthened or shortened. 3 dimensional distance is measured as shortened by many observers (but not all) And , of course time is then measured as lengthened. But I'm sure you know all this. My point is that many others mix up which distance they are foreshortening.

If you weren't persistently so rudely aggressive towards others, I might be inclined to resume conversation with you.

I did have a chuckle about the large negative spike in the green (death) graph. Reincarnation and Resuscitation Rules OK ?

You may wish to expand on this statement as i think it is easily capapble of misinterpretation.

Good to hear back from you. There is certainly a measure of truth in what you are saying. The equations of Einstein are not wrong, but they are not totally right either. Indeed he changed them a few times himself, in acknowledgement of this. Further he made some incorrect predictions. You are correct in wondering about the interpretation of the Mathematics, dimensions etc. Spacetime is only a (mathematical) model. It is not the real thing. Its equations are not wrong, but being a model its equations also require certain results that do not appear in reality. There is a (much) less mathematical discussion in progress about this right now, including ssome excellent links to Einstein's incorrect predictions about length contraction.

And also the method of observation, as pointed out by Penrose and Terrell. Observation can be direct, as in Penrode and Terrell, or indirect ie deduced from other observations and or calculations. Furthermore different observers have different interactions with a given object so it should not be suprising that they deduce different observations. I would say that is the philosophy of Relativity for you. I would completely agree with the rest of your post however.

What is frightening is just how fast this variant is getting around the world. Yesterday 61 persons on two flights from SA into Amsterdam tested positive on arrival.

No I didn't say they were a risk. I said the government chose to ban baxi bermuda style back boilers as 'inefficient'. And yes they are planning to ban the AGA and gas boilers in new build properties. I also said that the inflammable cladding that they did not ban, led to major tragedy. Or alternatively control issues. And yes the salesmen of this world claim that storage cures all known ills. But the reality is rather different. We can discuss this at length for the benfit of others if you like. As a member of 'the trade', surely you realise that all gas burners are less than 100% efficient in that you receive less than 100% of the combustion heat. However heat pumps deliver heat out using work in and can deliver well over 100% ( up to 400% depending upon conditions) heat out equivalent using the work in as the base.

Why no ? If you don't put in you won't get out. The more I 'want' is exactly what you wrote following this, say you did not understand and offering what you didn't understand. (2) says that spacetime is not reality Hopefully that is simple enough. If it is not reality then I offered a comment on what it is. Spacetime is a working model of reality. This is just as Engineers have working models of say beams structures. These models may be actual physical models or they may be mathematical models (often on a computer these days). But just as the Engineers models of beams have characteristics that do not act in the same way as all real beams (For instance plane sections remain plane on bending and the span to depth ratio is much greater then 50 to 1 or that stress is proportioanal to distance from the neutral axis) So Spacetime constrains the orientation of linked events because it involves the use of coordinate systems, just as drawing a triangle by coordinates on graph paper fixes the orientation of the triangle in a way that drawing the same triangle by scribing the lengths of the three sides does not. So (3) says that Spacetime does something that reality does not. Does this help ?

Since you have made some attempt to answer my comment this time I will offer some more help. It's clear that you have copy/pasted the expressions in question from a book or other source which should have provided proper background for the questions and the answers already provided. I don't know what resources you have access to but you are reaching a long way into theoretical physics/applied maths here. This subject really belongs in one of those two sub forums, not Analysis and Calculus. Anyway these three attachments should provide a good solid background for both your questions as they compares classical and quantum momenta and operators.

I think if you want folks to participate you will need to put more in yourself. I don't see much acknowledgement in the form of chat about my input here.

Thank you for observing the purpose of this thread which was to relate exchange exeriences involving heat pumps, for the benefit of all. A very interesting contribution, probably more in line with the commercial calculations I posted in the previous post. +1 I'm gald you have a good experience of instantaneous gas water heaters. Mine was nothing but trouble from installation in 1989 to replacement in 2016 and never met its advertised specifications. A few minor corrections to your post are in order however. Firstly I did not call the systms twaddle. I said that a lot of twaddle is being talked about them - I might have added "In order to sell them like a car salesman promised the Sun the Moon and The Stars". Secondly my experience of maintenance is that heat pump maintenance is far cheaper than hi tech domestic gas boilers. Since heat pumps are actually also somewhat hi tech there are old fashioned systems lo tech gas systems, such as I enjoyed in my previous house, that were indeed cheaper to maintain. Sadly our glorious government had chosen to declare these illegal, in preference to highly flammable building cladding, leading to significant loss of life and untold misery in the UK. A couple of points perhaps not made explicitly before. My heat pump system suffers from the same difficulty experience by the previous instantaneous gas boiler. It cannot provide both domestic hot water and central heating at the same time. Also in the UK domestic situation there is no use for the 'cooling output' as you put it. I can well see a use in Brisbane, where there is a much warmer climate.

[math]{s^2} = {x^2} + {y^2} + {z^2} + {\left[ {ict} \right]^2} = {\left( {{x_1}} \right)^2} + {\left( {{x_2}} \right)^2} + {\left( {{x_3}} \right)^2} + {\left( {{x_4}} \right)^2} = {x_\mu }{x_\mu }[/math] My apologies something went seriously qwrong with the LATex aftr inputting. Correcting the quote is the only way I can see to put it right.