studiot

1) Wave functions are, by definition, solutions of the wave equation. There is no other choice. Perhaps joigus means where is choice of wave eqaution (which there is). 2) No hidden variables are needed and the wave function again cannot be 'hidden' by definition. 3) Solutions can be complex, but we only want the real part. 3) The way to introduce probabilistic maths into this is to introduce a 'statistical weighting function', This has to be a function of a real variable, and again cannot be hidden.

The probabilistic nature od QM is not truly random in that the outcomes are not truly independent, the condition for a random variable. At all times the wave function 'probability' must obey the normalisation condition. This means that any change (motion) must affect the entire function, not just its value at a coordinate point. This leads you back to my mist analogy.

My smoke tree is particularly fine this year.

careful here. 'measurable has a different specific meaning from observable in mathematics, esp in respect of Hilbert spaces. I quite agree. But again some care is needed as you also need a physical mechanism to pass from one state to another. That mechanism must have defining or describing (mathematical0 statements. What they cannot be is a statement of the form that the system passes from state A to state B etc by some random jump process that take zero time and/or passes directly from one point in space to another without passing through the intervening points. Unfortunately, this is exactly what you see if your model involves taking successive 'snapshots' of the position of a 'point particle' , say an electron in an orbital. The way I see it (physically) is the electron cloud or density picture that is built up is not a patchwork of jumps but more like a mist in front of you,, which thins and thickens in patches, as you watch. That is in accordance with the fact that the wave function occupies the entire region under consideration, rather as the mist occupies the entire region around you.

I agree that is a very real danger and leads to a very real fear. One of the reasons I asked you what field of Science was involved is because one way towards overcoming this lies in the correspondence pages of respected journals, for instance the journals of professional institutions. Obviously a suitable journal would have to be selected. Your friend could then write a 'letter to the editor' giving brief outline details, perhaps suggesting what new understanding the idea could lead to. This would then establish his or her right to be the first to come up with it. Over to you. Here is a true story of the discovery of the microscope by a non scientist, which lead to the very deep scientific idea by a self confessed dreamer. When a cloth mechant called van Leeuwenhoek needed to examine the quality of his cloth he taught himself to grind strong lenses. This also led to him discovering the microscope and microbes. A writer, called Jonathan Swift, heard about this and penned this thought which actually is incredibly deep, scientifically. Little fleas have smaller fleas Upon their backs to bitem. And these small fleas have lesser fleas and so on ad infinitum

A point function is one that has one and only one value at any point in the coordinate system. quantiles ae not points. A point is specified by the coordinate system, the value is specified by the function. Pretty basic really. But in QM you cannot identify a specific point and assign a specifc value to it. By specific I mean exact. You can do one or the other.

Actually you are correct there is a difference between probability and probability density that is often forgotten and folks just use the word probability. As i undeerstand matters that is because of the way QM is formulated so we have probability is a point function which is a map from the sample space to an interval between zero and 1 of the reals. Locality is not involved. On the other had there is no such thing as a point function in QM. probability density is the (classical) probability of the Event E lying between say x and (x + dx) for one axis, suitably adjusted for the normalisation condition.

Thank you, but you don't need need a Markov , or any other, chain to state the probability of a single event. However you do need to state unequivocally what you mean by the probability of event E is, for the three cases P(E) = 0 P() = 1 0 < P(E) < 1 since depending upon the type of classic probability you are using these cases, at least, will be different.

Possibly the best council in the whole bible. Yet not something cannot be appreciated by the non religeous or that even needs religeon. Interestingly the sermon on the mount was almost word for word the same as the teaching by Loa Tsu in the tai ching many years beofre.

swansont has already asked for examples and so I am asking for them as well. At the moment you are just piling generality upon generalitywithout the detailed support these claims require. I would have thought it would have been wise to start with a statement of which of the the three classic types of probability, as taught for UK state school exams, you are referring to and also giving a specific example from QM that runs contrary to it or them.

I wonder what sort of AI might have been involved this this 1000 time overcharging BBC NewsWoman charged £4,586 for two-hour car park stay in SloughIt took three weeks for the mum to receive a refund for the accidental overcharge. I note that the human organisation failed to correct the error promptly until pushed by the BBC.

New stuff to me. +1 One thing about the Bible is that you always learn something new everytime your ead it in the way I suggested

Well if it is one idea, it rather depends which science it appertains to. Some science such as Astrophysics have little or no meaning without maths. In some other sciences such as geology you can establish a whole lot without mathematics. One man's meat is literally another's poison.

If neither of you are scientific persons how do you know this idea is scientific ? Since you have just joined, you (or your 'friend') may not realise that members may only have one account by the rules.

You are doing exactly what I recommend. Trying to pick the bones of the matter out of several mixed up reports, +1

I am sure that chinese medicine has worthwhile things to teach western medicine, but I am equally surel that his works the other way round as well, ie western medicine has things to teach chinese medicine. From your posts to date you are proposing a 'one size fits all' solution whereas whereas one fact that western medicine has learned is outstanding. There are a range of responses to any treatment (including no treatment) covering the range from absolute success to abyssmal failure. What is wrong with lactulose ?

That’s why I put “map cleanly,” I’m acknowledging their existence in America, but it was never whole heartedly supported by the American public in the same fashion it was in Nazi germany Actually you said none of which map cleanly so I got your meaning thank you that modern America and prewar Nazi Germany are not the same. But then again I said "history books" . Modern America is not History but the rise if Nazi Germany is so you completely missed my point and addressed something else. The important points I mentioned concern that rise, which is how they are connected to history. One of which is the training and military development they Germany received, before WW II , supporting the rise of another fascist dictator in Spain.

Perhaps you have different histoy books in the US ? You certainly missed important elements in your summary.

Yes why not ? But you have you use your intelligence, whether you consider it natural or god given, to asses what you find. For example I Kings VII 23 is in perfect harmony with Science, whereas Revelation 13 : 18 is just theatrical drama to create awe in the reader.

Thank you for answering, my questions are designed to be helpful. And although you have not quite hit the bullseye you are near the centre of the target. Good thinking +1 The simple reason is that no one, not just doctors etc had seen or known of or thought of a single cell until more than a thousand years after the bible was writtten, when microscopes were invented. So no writer could have written about them before that. Now this is important because it shows there is no conflict there between Science and the Bible. And my advice is to look for agreement and compatibility, not division and opposition. The Bible does not always agrees with itself but then again nor does Science always agree with itself either.

Remember what I said about reading the Bible in the light of what we now know today ? OK so here is your chance to do some critical thinking of your own. There are many references to plants and animals in the Bible and indeed in other ancient teachings. Today we know that plants and animals are made of many many many cells. We also know that there are simpler creatures that are made of only one cell. Why do you think the Bible has no references whatsoever to single cell creatures ? Please not I am not saying it is wrong. It is not wrong it just says nothing whatsoever about them.

Yes, but why only Mathematics ? +1 Surely this can be applied to most if not all sciences ? Also I suggest adding the words "and Philosophy of..........." as History by itself can become a boring list of facts it is the philosophy of a subject that history helps bring out.

Yes my bad. I cross posted with my edit when I realised.

I know what hot standby means, AGCR stations are the fastest fossil fuel stations for this. But battery based supply a la Shetland is even faster. The staines gravel is already pretty level. I do remember a proposal to move London airport to a more suitable site, with a proper transport link, on derelict land. Heathrow would have then been sold off and the state could have made a massive profit from the real estate value of the site, in the midst of London.