studiot

I am not sure why you are introducing tensors, when you still have questions about vectors. So I suggest we defer the introduction of tensors till we have dealt with your questions about vectors. It would be helpful to tell us in what connection you wish to use vectors and tensors and if you understand matrices ? OK so your arrow is what is also called a 'directed line segment' I have shown this in Fig 1 as the arrow Op, where 9a,b) are the coordinates of p and V is the length of Op Op is a line segment of the extended line shown dashed. This line makes and angle theta with the x axis. As you say this vector is one of a family of vectors that all start at the origin and are totally determined by their length v = Op and the anticlockwise angle theta they make with the x axis. In other words they are 'bound' to one point (the origin) and indeed are called bound vectors. Yes indeed if these vectors begin somewhere else they are called unbound vectors, as vector W in Fig 2 Now I am going to leave x y coordinates behind for a moment since it is obvious that an unbound vector will, in general, point to some other coordinate than (a, b) - let us choose one and call this point q again as in Fig2. Now to specify a vector in a plane we need two numbers and if we do not want to be stuck with starting at zero we need to use different properties of the vector than its end coordinates. So I am going to introduce the vector V with length v = Op and making an angle ϴ with the x axis as V = (v, ϴ) Similarly we can consider the unbound vector W with length w = O'q and making an angle Φ with the x axis. So W = (w, Φ) So if v = w and simultaneously ϴ = Φ Then we have an unbound vector we can place anywhere on the plane parallel to our bound vector. Does this help with your first question ?

Of course its not irrelevant. A body cannot move itself without external interation. (newton's first law) So there must be The walking involves some real force (probably friction). The exzample is not a good one for gravity. A bodies motion through the curved space is free fall.

A thought experiment question. In a universe with no light at all, but everything else, would these phenomena still occur ?

One definition of force is rate of change of momentum, which is what happens when you bump into someone.

I'm not debating with you an explanation from some armchair of a measurement that has actually been made. Length contraction is a measured observable fact. This was first done in 1941. http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html

Sorry I don't understand your comment.

Not necessarily. Pratchett does nothing for me, but some fantasies can be fun. You generally have to suspend (dis)belief for some aspect of the story in SF, whether it's people magic or technology magic.

Unlike the first number I misquoted, where I made a silly copying mistake 156,423,343 is not prime. 156,423,343 = the product of two primes 22,343 x 7001. I should have constructed this example in the first place as it is beginning to show just how far you might have to go to find any factors. This of course is also beginning to demonstrate the interest in large or very large primes for cryptography. To recap Apologies for the earlier mistake 9,991,991 is not prime and = 2833×3527 9,999,991 is prime .

Gosh yes you are absolutely correct, I miscopied it I should have written 9.999,991 (which is the largest prime number less than 10 million) Thanks +1

I must admit that it is a long time since I last looked at Einstein's train and lightning though experiments and I was thinking about the length contraction one. I no longer have the original text of these experiments, but I have found a reliable explanation online here. https://www.vicphysics.org/documents/teachers/unit3/EinsteinsTrainGedanken.pdf Note the authors' comment that there are a lot of versions about, some quite misinformed. No there is no third, fourth or what ever observer involved and there are only two frames, the frame of the train and the frame of the platform. The referenced article explains quite well what you may be thinking of as a third observer as the point of view that the train is standing still and the platform is moving past it. However, as far as I can see all this is entirely off topic and you have made no response at all to my comments on the actual topic of this thread viz spooky action at a distance. I suggest the relativity issue be further discussed in its own thread as it is entirely off topic to action-at-a-distance, spooky or otherwise.

This seems to be the only actual question here. The point about the Einstein lightening strike is that it marks both the train and the platform with a visible, permanent mark that can be seen and measured at a later time. The act of the strike in such a small space is considered instantaneous and appears in both frames of reference. Do you understand what the two frames of reference are ?

I missed the author of Jurassic Park off my list, Michael Crichton. He has many feasible near future scenarios, a gripping style with plenty of suspense ans suprises. This has led to several successful films.

So did you manage to factor 156,423,343 ? Doing this or not is a good test of a method.

Yup there certainly are and further the emphasis has changed over the years. So, as already said, it depends upon your own personal taste and also your own personal circumstances. I don't know where you are or what your resources are but let me congratulate you on wanting to read books. +1 So many these days only want stuff on a screen, or are you looking to use kindle or kobo or other online sources ? In which case you will obviously be limited by what is available. Going back to books, I don't know if you are proposing to get them from a local library, or but them (many are available cheaply second hand. Scinece fiction books come in two types. Collections of short stories, either by one author or by many authors collected by one editor. These have the great advantage that if you don't like one author or story type you can quickly go on tto the next. So I would recommend starting with some of these, before movi ng onto full size novels and even long works that span several or even many volumes. You can also look forward to all sorts of story types, from fast action with Matthew Reilly, macabre stories from Ray Bradbury, miscellaneous collections from thinking authors like A C Clarke, Human sagas from Anne McCaffrey, and of course the spins offs from TV and film like Star Wars and Star Trek and Dr Who. There were series especially for youger readers one about children born in space stations around Earth - the Kemlo series, another about a flying saucer that visited Earth and took the mad professor and his children on wondrous and adventurous journeys around the galaxy - the same author was responsible for the Biggles series.

Changing batteries in a friend's remote I noticed this as in the picture. I have never seen a battery with the positive terminal at the black end and the negative at the red end before. Comments ?

Principle of least energy

What I had in mind was you to demonstrate your multiplication test in full. All numbers greater than 5, that end end 5, are non prime since all are diisible by 5. In fact that is another way of shortening my test. But why 5,23 and 7 (in that order ?) ? Your guess is correct 9,991,991 is prime but your last line should be something like therefore 9,991,991 is prime. this is actually a better number for a prime test. 156,423,343

Which echoes my point. I can't think of anything that is opposite in every way. Fundamental particles still obey the same laws of gravity., ie they don't have anti or negative mass.

Yes it follows it but the field alone cannot adopt different energy distributions. The PofLE really comes into play when the field interacts with something else, resulting in a minimum energy configuration of that something else, for example Place a load of magents in a mag field and they will line up with it. MigL didn't say the energy was stressed. That is a meaningless idea. He was referring to what is known as the energy-momentum tensor in GR.

Not in Newtonian mechanics. But in General Relativity yes massless fields which store energy can also gravitate by virtue of that energy.

So how would that work with say this number 9,991,991

And antigens and .......... Yes the list is quite long.

I understand all this, and there may even be a part in the overall scheme of things to come for this but I don't see the manufacture of what amounts to artificial coal as being a big player. Firstly there are better alternatives than forestry for fixing carbon. We recently had a thread noting that sea grass is up to 30 times more effective than the amazonian forests. Recently there has been much interest in spagnum moss as it is apparantly something like five times as effective for boggy areas, where forest will not grow. Talking about areas where forests will not grow, Why do you think vast areas of the Andes and Rockies and Himalaya etc poke out above the forest ? How much forest can you groe in the tundra or on Shetland, where there are no trees because the prevailing winds are too strong for them ? What about the Sahara, gobi, atacama, Kalahari, Australia etc ? So where exactly would you grow these trees ? Spruce will not grow in the Amazon and tropical mahogany will not grow in Alaska. The sea grass and moss have another advantage. They are immediate. You do not have to wait 50 to 100 years for carbon sequestration payback. Talking of immediate, the main thing we could all do is change our ways to create less waste. To make things last, not have extravagant ways.

Yes many things come in pairs. I have no proof that everything comes that way however. Partly because for any X you can divide the universe into that which is X and that which is not X. But elephants are not anti-dolphins, they are something else entirely. The 'anti' bit is a special relationship.

That date thjing is interesting, thank you. +1