studiot

Are they ? That is the first I have heard of it. How can we then sometimes determine the ratio of two of them ?

I don't think you caught my drift. With the balls, determining the colour of one ball could tell you absolutely nothing about the colour of the other. Further you can't determine probabilities without further information.

Not sure how this plays out with you previous statement or my 'coloured balls in a bag' example. What if someone blind selected two gloves from a pile of gloves ? How would they be classically entangled unless you had the 'extra information' ( my version of your words I think) that they were a pair ?

Apology accepted. The point is that we often have youngsters from say 10 to 16 posting questions here about something they have just come across. Often they are very enthusiastic about their query, but need a pointer to the bigger picture. I try not to dampen their enthusiasm by presenting highbrow maths arguments, rather I try to offer a more suitable rationale. Since I wasn't sure if you are actually such a youngster I gave the benefit of the doubt as they say, with what I hoped was a gentler and more respectful approach. So I am sorry if this was taken the wrong way. Back to infinity. I have an older trigonometry textbook with a section entitled 'Passing through infinity'. The point is very simply that there are many different 'inifnities'. There is even a whole theory of the arithmetic of infinities, but this is quite different from the arithmetic of ordinary numbers. When you come to add all the light form all sources in an infinite universe you get and infinite quantity. But you also have an infinite universe so when this light is spread over another infinity you can get a finite light density. Mathematically the ratio of one infinity to another is often indeterminate as it could take on any finite value. Further information /theory is needed for those cases that can be determined. So the question becomes Is there sufficient theory to determine this value for the light density we can see and measure and how accurate do we think that theory is ?

The entire body of quantum identities can be entangled but we can only choose to discover one and entanglement is lost. A single observation destroys entanglement. How would you entangle the momentum of two photons, of identical frequency ?

So why haven't you ? I didn't compare you to anything. I told you a true story about encouragement, when it was apparent to me to did not and still do not understand the Science (Maths) of the term infinity. The true story was about how a better man the me helped me with something I did not at the time understand. Furthermore I offered you a polite and reasonable discussion to extend you knowledge of infinity to cover your original question, hopefully in a way that would not be to mathematical. Sadly all I have received in return is insult and either no response or peremptory ones. If I told someone the Pele once told me how best to kick a football, why would that rub them up the wrong way ?

Why do folks always miss my point of view ? I just don't care. But there doesn't seem to be a category for that.

Gosh seeing my last post quoted like that makes me wish my spelling was entangled. Need ? Nature has endowed it whether we need it or no, (to paraphrase the lady).

You keep referring me to other websites for basic information needed to understand your proposal. This is contrary to the rules here. References to other websites etc is OK for those who understand the proposal and wish to delve further. Thank you for telling me where the crystal cells are placed. That could have been said 50 posts ago when I was asking what was happening before the slits (since behind is after). RE polarisation. It could be that is because that is one of the few proprties of phtons that can be entangled.

I think swandont's point was about additional information. Let us conside a classical system of entanglement say two balls hidden in a bag. Measurement of the colour of one ball tells you nothing about the colour of the other ball unless you hve further information. But if you know that one is red and the other is blue then measurement of one colour tells you both.

Firstly thank you for a better description, though it is still not complete enough for dullards like me. Have you no diagram ? I am for instance not sure of the meaning of behind ?

You may have offered me an explanation I hadn't thought of, although I don't see why you have introduced a definition given by Philosophers since they have no patent on it. Possibly, even probably but I do not agree that the difference is superficial. Denying the existence of a God is much stronger than simply not possessing a God to believe in. It is noteworthy that the trusty OED uses the word 'denying' - an active state. I suppose that Philosphers might argue that the positive state (theism) is belief in a God and that atheism is simply the negative of this, which could be taken to include those who not only do not believe but also those who actively expound against.

Its more than juast word preference. It determines the lift of some pumps. I agree totally. +1 for the information additional to the lungs. What a pity the OP hasn't been back as he has reeceived some excellent answers.

It's not as simple as Wikipedia makes out. What happens is heavily fequency dependent. Here is a short extract from Kraus. Sorry for the poor quality but it is a thick book and difficult to scan.

I would like to hear bangstrom's complete description of an experiment where light of one polarisation is persuaded to pass through one slit and light of the other polarisation passes through the other slit.

Well puzzle no longer you already know the answer. The van can indeed be considered as the fly's own little world, as with all the contents of the van. The fly starts off on some interior surface of the van and is accelerated, like everything else, to 60mph. So when it jumps off to fly back or forwards, it is alredy going at 60 mph and it only has to generate its normal flying speed to reach the other end. Since the air inside the van is also going at 60 mph it offers no more than normal resistance to the fly. Does this help ?

Really? You said And yet you continue to describe your pet example to others as though it is of vital importance. You asked and you received my explanation to which you have made a defeaningly silent response. Yet you say cavalierly that you have dealt with my issue. You have also not responsed to my earlier offers of other simple explanations like invariants and Bob's speed etc and my proposal to discuss a different (and better) example since Bob's was irrelevant to you and impossible for me. In short you are just trolling.

I really logged into this thread to say +1 to Phi for his last post but on doing so I note yet another misunderstanding by the OP In Science there are several (probably many) ways that something can be finite yet unbounded (that means no magical wall or precipice) or alternatively infinite yet bounded. Both seem illogical at a quick glance, yet physical examples of both situations exist in our experience of Nature. Absolute zero of temperature is about -273.4 degrees centigrade, yet we can never reach it. Because the closer one gets the harder it become to get even closer. The so called Gabriel's Horn is an example in Maths. But hey perhaps the OP has found the wall or precipice because his excuse for not talking to me was the insult

It is indeed pretty shocking. It shocked a lot of people all over the word when it was first proposed, including some very important thinkers. I don't think this is the case. There is only one train. But there are many points of view and I am offering a slightly different route into them than usual. Especially as I see you have actually been at SF for a long time so must have seen quite a few arguments about the subject. It is a pity you don't address my questions about the example you specified since that example is impossible to conduct in practice. This is why I would like to introduce and discuss a real world example, the first exerimental verification that the formulae actually correspond to observation. Discussing why is made difficult since you seem to be ignoring my comments about both your example and mine.

Either you want to understand or you want to argue. Which is it ? Just remember that if you want to argue you are arguing with one of the two most experimentally tested theories in history.

Does this mean you wish to follow / engage with my chaing of reasoning ? It is logically possible because the circumstances of different observers are well, ..... different. It is necessary to find quantities that are not different for different observers and equate them. This will enable you deduce the contribution made by the differing circumstances. Markus' muon example is one good example of this because 'number' is invariant. We can also look carefully at your depiction of Bob. Do you realise what 'speed' he is going to achieve a 100 : 1 length contraction ? It works out at 0.99995c to 5 decimal places. This is why I asked you how you think Bob can 'see' this contraction. Are you going to consider and answer this ?

Category mistake! I must remember this one. +1

This seems to me to be the key to unlocking understanding of SR for you. Some of us find thought experiments such as the one you describe add to the confusion, rather than dispel it. Please bear in mind that it is not physically possible for Bob to directly observe the measurements you describe. He can, however calculate the effects in his own terms. Modern derivations of SR are much simpler than the original, which is comparatively quite hard to follow. Modern derivations start with the idea that different observers will make different measurements on the same phenomenon. They then go with the notion of finding something that 'observers' can agree about and establishing the maths that yields the same values. In other words, the Maths follows the Physics. The something that can be agreed upon is called an invariant. An invariant is the same for all observers. Do you want to develop this route to understanding SR ? Note GR and SR are actually different; understaning GR requires further considerations.

I think Zap deserved that. +1 Now please be scientific and answer the question properly.

Depends what you mean by a vacuum. If you mean a complete void - empty space with nothing in it, not even air the no there isn't. But if you adopt a polular (also scientific) notion as being any region where the gas pressure is below atmouspheric then yes. This is often called a partial vacuum and can be measured as so many milliletres or inches of mercury below atmouspheric pressure. As a sports scientist I hope you realise that the old phrase Nature abhors a vacuum is nonsense. Most of the Universe is empty space. Your lungs do not suck air into them when you breathe in. The outside air pressure pushes air in when you expand your lungs by lowering the diaphragm. This lowers the air pressure within your lungs to below atmouspheric. There is no such thing as suction.