studiot

My apologies, it was nothing personal nor a trick. I realise now that I must have got mixed up trying to set up this thread and introduce the appropriate background posts from the 'space' thread. You did in fact reply here not there. So the mix up was totally my fault. The point is that we are supposed to stay on 'topic here'. So discussion of spacetime invariants and coordinates are off topic in a thread about space. Now consider the following network of 5 points and the geometric figure they describe. The geometric figure is quite independent of any coordinate system. This is a basic property of Euclidian geometry, which is primarily about shape. Wherever you place this shape and in whatever orientation it remains the same. This is not true of the geometry of Descartes since as you move it about or turn it round the coordinates of each of the 5 points will, in general, change, although the distance between each point remains invariant. This difference is also common to a network of points in the spacetime of special relativity. The interval between each point does not vary so the whole of spacetime could be described, without a coordinate sytem at all. Just a simple list of intervals. The network is fixed.

Slight misunderstanding there. It is the spacetime intervals tha are invariant ie measured or reckoned the same by all (inertial) observers. Both space intervals (ie lengths) and time intervals (ie durations) vary with observer. Remember, Mordred started this thread to discuss space as separate from time. He refers to space as 'volume' , wghich is a pretty fair description. You are correct that Minkowski invented spacetime, (but then unfortunately died.)

Actually they are just starting this type of trial in the UK. direct infection of selected volunteers. This was announced a few days ago on the BBC. Sorry I don't have more details at the moment. Since about the first 2 months the UK government has been announcing (daily and cumulative) totals of all those who 1) Had a positive covid test within 28 days before death 2) Has covid specifically stated on the death certificate. The government announces confirmed cases only in the totals. London University has carried out mass testing within the general population (my family has participated in this) over a 3 month period to assess these figures. This was done by distributing home self test kits and collecting the results. Those who were revealed to be asymptomatic on thesewere sent for further tests /advised to self isolate. Further data is being gathered on so callled excess deaths. This is the increased number of deaths experienced over the long term average for the time of year. This is larger than just the covid deaths since other increases have also occurred and attempts have been made to allow for this.

@Prof Reza Sanaye I cannot imagine why, when the moderator told you to start another thread and I helped by doing so you are continuing to wish to discuss spactime in a thread where the original poster quite clearly and specifically said he was discussing space as distinct from spacetime.

Which government would this be ? We in the UK understand that different countries are measuring these figures differently. Even the UK government changed its method of reporting part way through. Further I'm sure there will be revisions after the event as mistakes will also have been made.

Nasty little snide remark there. I did not say that equations of motion do not contain information about trajectory. Swansont and I were discussing affably the possibility of such an equation containing information about energy. Not every conceivable equation of motion contains trajectory information or for that matter information about every conceivable variable. So the equation distance = speed times time contains no trajectory information and has other 'missing' variables as does the equation acceleration = time rate of change of speed.

So you wouldn't describe the equation for the motion of a falling weight Kinetic energy gained = loss of potential energy as an equation of motion? Fair enough.

It means that it's gibberish. Be done with it.

I have started a new thread here for your convenience, containing my answer to your comments

I am starting this as a split from Mordred's what is space topic as the subject has been broached. Henri Bergson's disagreement with Einstein is nearly one hundred years into the past. HB was observably wrong in at least the twins paradox. However he was right in this His metaphysics made matters worse rather than better in that he introduced two kinds of time ! I had to check with my copy to make sure you were not referring to another philosopher, Professor Berkson, whose book "Fields of Force" offers a rather different view. I don't think that either Bergson or yourself understand what I meant by " without an underlying coordinate system", particularly as Bergson used 'duration' differently. It is possible to mathematically replicate Special Relativiety (SR) without any coordinate system whatsoever by means of a network of linked invariants. This difference is the difference between Euclidian geometry and that of DeCartes. I look forward to your discussion.

A good observation. +1 As to experiments, I agree that the AG were more theorists than experimentalists, but no (zero) experiments ?

[math]\frac{{{d^2}\psi }}{{d{x^2}}} + \frac{{8{\pi ^2}m}}{{{h^2}}}\left( {E - U} \right)\psi = 0[/math] ?? And yes, I know this is only the one dimensional version, but it's easier to write.

Yes toroids, along with tesseracts, pyramids and crystals. Funny how often geometric words figure in the mystique.

Accepted. Anyone can overlook things and most new members here seem to overlook the rules, hopefully you are more careful with important documents before you sign them. But I also offered you my guesswork as to what this might be about. Guesswork since I haven't been able to read the article. Penrose is a world authority on mathematical physics and has tried to introduce a physcological aspect to quantum entanglement. You will find reference to this in his massive book the 'Road to Reality'.

+1

There was a BBC Horizon programme about this story in 1998 http://news.bbc.co.uk/1/hi/sci/tech/241228.stm

Edited 23 minutes ago by Abhirao456 1) I didn't say the words in red so making it seem as though I did is bad form and against our rules. 2) Not posting enough description of the link so that I have to go offsite to find out what the thread is about is also against our rules. The mods were kind enough to allow you to continue. Please don't abuse that privilege. Having said that, I wonder if you have heard of Professor Penrose's speculation about some unresolved isses in quantum mechanics. These are not mainstream but might have something to do with the alleged research you have asked about.

You have been told it's BS and I, for one, object to finding this intrusive BS on my screen when I click on your link.

Along with Faraday and our own Markus Hanke, Harrison presents yes a lesson to all that self education works and class distinction is bad. +1

It's also worth remembering that the Schroedinger equation is about the motion of the electron in the field of the nucleus. And the field of the nucleus is spherically symmetrical. This can be derived from the solution to the equation being varaibles separable ie the product of independent functions of R theta and phi. You can have the math if you like.

We are back to the old question What direction does the zero vector point in ? Or. as I said earlier, What are the principle axes of the stress tensor when the imposed load is zero ? until we effectively impose a coordinate system by measuring any which one of the angular momentum components as well as the total angular momentum We cannot do this without an external agent.

I think we are saying basically the same thing, with a different emphasis. Perhaps a more formal version of what you are saying might help. https://pubs.acs.org/doi/pdf/10.1021/ed042p397 There is also an interesting discussion about this point on StackExchange. https://physics.stackexchange.com/questions/610064/are-all-atoms-spherically-symmetric-if-so-why-are-atoms-with-half-filled-fille

Doesn't the spherical symmetry arise like this: When you choose the actual direction of the X axis you automatically set the diections of the Y and Z axes. Then you can solve (Markus, other atoms have been solved numerically and so called 'hydrogen like' atoms can be solved analytically) you obtain the various wavefunction plots. But your choice of the initial direction of X is arbitrary and has spherical symmetry, because whatever direction you choose you will get the same set of solutions along your particular X,Y and Z axes. It is the whole set of solutions that has 'spherical symmetry'. So in a normal sized aggregate of atoms you will 'see' an average sphere. Note this is not the same situation as the Principal Axes in the stress and inertia tensors where the X, Y and Z directions are set by an external influence such as a load, there are no such principal axes in the solution to the quantum wave equation.

Perhaps you mean this ?

Welcome, scruffymonkey. We are all scruffymonkeys during lockdown as there are no barbers available 🙂 This type of question is common with folks who "love science, but are not scholars". Science for non scholars can be great fun , so ask lots of questions to better your understanding. You need to bear one thing in mind however. In order to be able to work with concepts and quantities, Science has some pretty tight definitions of many common words and ideas. Swansont's answer is a good example of that and it reappears in this book by Dr Meetham "Basic Physics", as does an explanation of Force, Strength, Pressure, vacuums, frequency and many other terms that cause confusion. It is a small old book, but easy to read and easy to find references to explain basic ideas simply but correctly. Such a book is an invaluable companion to finding out more. Here is the preface first page.