studiot

Usually the best way to test for conformity with the axioms is to concentrate on the operation. That entails knowing precisely what the elements are. You seem unclear as to what the elements of your proposed group are "I understand that Minkowski space is a group..." What elements are you proposing? Vectors? So what is the operation? (vector) multiplication ? Does the dot product produce another vector? Is there an inverse vector for this operation for every vector? Does the cross product produce another vector? Is there an inverse vector for this operation for every vector?

My comment was not a criticism or challenge, it was more to add information to the topic. That definition is consistent with a Physics view of randomness, which focuses on the route by which you get to the result, as opposed to the result itself. Mathematics (the Kolmogorov definition, which Wiki also discusses) focuses on the result and doesn't care how it is arrived at so answers my question Is 5 a random number? in the affirmative. We had a long thread a while back, that was before the current listing starts so I can't find, asking about the difference between random and chance. You will find precious few references to 'chance' in maths texts, but lots in Physics ones, because chance is about the route. There is a current thread here where 5 is defined as random. http://www.scienceforums.net/topic/97886-help-a-non-native-speaker-of-english-understand-this/

Take another look at group axioms. http://mathworld.wolfram.com/Group.html It is not necessary for a group to be commutative, only associative see axiom 2 in the link. The defined operation between the group members is called the group operation. This is part of the definition of the particular group in question, not an axiom. So we say multiplication over the real numbers forms a group. Such a statement specifies the elements and the operation. This operation must be between two elements of the group only and produce another member of the group. It is not necessary for the operation to be commutative; if it is the group is called abelian, but there are non commutative groups. Because it is between two elements it is called a binary operation (often it is called multiplication, but this depends upon what the elements are) Yes it has also been found most useful to require that the operation has an inverse and that there is an identity element. Note the the inverse and identity are both required, one will not do. Note that this is different from the definition of a vectors which requires two sets of elements, the set of vectors and the set of scalars.

A small point but what do you mean by random? Mathematicians and physicists operate on different interpretations of this word. So for instance is say the number 5 random?

It would be a real shame for several posters who have each contributed something worthwhile here to fall out with each other. For some English is not their first language and their posts are sometimes not quite what they meant as a result. We should all try to compensate for this. Here are two examples, at least one of which, may have lead to misunderstanding Obviously the word is pride not proud. but here a word is perhaps missing?? Did the poster really mean US citizens, usually poorly educated ones? bearing in mind that every country has well educated and poorly educated citizens.

There are many silicones, it is a class of compounds. It can be made as thick as grease or as an oil or thin enough to spray. As a sealant it can contain inert filler (there was a question here a few days aback about someone who wanted to do a thermogravimetric analysis) and be made sticky. The lubricants are usually non sticky. http://www.dowcorning.com/content/discover/discoverchem/si-lubricants.aspx

Nice and complete +1

Never heard of a WD40 version but sounds expensive, especially as they will not tell you the price. Knitmaster provided a can with my wife's knitting machine decades ago that we still use everywhere for a dry, non greasy lubricant. Curtain tracks, the window mechanisms, doors locks, things on the car....... It's like magic. We recently bought some unamed brand quite cheaply on _bay. Seems good.

Quantum theory presents its own mathematical difficulties to a block universe in the uncertainty principle, which is due to the non cummutativity of the operators. Incidentally this non commutativity is also present in some classical mechanics.

Just remember that acceleration is the second time derivative of distance and both quantities depend upon how you measure them. Oh! crossed with Mordred.

Silicone spray is good and easy, but will need renewing every couple of weeks or so on a bike chain.

I think we are both now agreed that the block universe has its merits, but also its shortcomings. Another one to consider is granularity. Relativity is a theory of continuum mechanics and continuous functions thereon. Quantum mechanics is the mechanics of a granular universe. It is not certain whether space and/or time are granular at some level.

Now you are thinking straight and asking sensible questions. +1

There is also no cause and no effect in such a four dimensional block, and therefore no determinism and no chance. Another way to put this is to observe that the relations between the points in such a block are not part of the block itself, but can be extracted from it or are external to it.

Yes I did end post#29 with that statement, but not quite with the meaning you inferred. I did not say that an external agent could not change one point or event (or even more than one). Indeed that whole argument was based on the proposition of an an external agent doing exactly that. What I was saying was that both chance and determinism refer to the relationship between at least two events or points. Therefore in a deterministic or chance or mixed universe there is a causal relationship between every point and at least one other point in that universe. So if one point only were changed then the relationship would become false. The block universe does not admit of relationships between points or events. Michel123456, I like your comments +1

Here is the back of my envelope for the unaided human eye. The receiving angle or angular field of view is 114o or 2 radians. Light travels at about 3 x 108 metres per second or 3 x 30 x108 metres in 30 seconds approx 1010 m So the arc of your max field of view is 1010 m. This is equal to [math]r\theta [/math] or the radius times the angle. The radius is of course the distance away of the travelling object. 2r = 1010 m r = 5 x 109 m or 5 million kilometers. Now if you will supply details of the illumination of the object, or if the object emits light in concentrated beams eg then the minimum size of object to supply the minimum eye sensitivity over this distance can be estimated.

Not at all. In fact I did say that the block universe model has some merits. I have just been trying to find an alternative way to explain why I assert that the block universe contradicts both determinism and chance. Here is another. Determinism F IFF E IFF D IFF C IFF B IFF A Is an example of a deterministic chain of causation leading from A to F. Chance F OR E OR D OR C OR B IFF A Is an example of a chance chain of events leading from A to F. where A through F are events or points in the block universe. If A leads to F in either route, deleting A will not delete B, C , D, E or F from the block universe, by definition. But the only way B, C, D, E or F can occur is if A occurs. This is a contradiction. Yet another way to put is would be to note that the block universe regards the axis variables as independent and equivalent. They are neither, because there is an additional constraint which reduces the number of degrees of freedom from 4.

Of course I will try to make my points more understandable, but it is a good job I waited as it seems you are getting there by your own efforts, which is always better. I wouldn't describe the block universe as rubbish, it has some merits as a model. But it is definitely not exact. In fact it is arguable that the only perfect model of anything is the thing itself. Back to the issue at hand, Consider just for the moment the possibility of a super being - Maxwellian Daemon or even a God, external to the block universe. Or perhaps a non intelligent agent but still external to the block universe. Such an agent could intervene in the future history of any sort of particle and prevent whatever the laws of physics had projected for it unless it was a block universe where that projection co existed with the past and present. Notice I have not said any such agent exists, just that a block universe would preclude any action by that agent.

It is easy to find counter examples if a proposal is either to narrowly constrained or to general. The trick is to find a happy medium between those two extremes. Your definition of the term model is far too restrictive, yet your comment that the modeled will always be one step ahead of the model is demonstrably false, because it is too general by the use of the word always. A model may be a pattern (in the sense used by pattern makers) or a copy. So it may lead or lag It is, however, instructive to consider the following. It is possible to make a real physical model for that of the abstract characteristics of something else, or something totally abstract. For example analog computers are real physical models of mechanical systems or abstract mathematical constructs.

None of that runs counter to what I said, except the no not really. I quite specifically said that both determinism and chance embody change. But there is no change in the block universe, or even the possibility of change. That is the meaning of the word immutable. A multiblockuniverse possesses the same characteristics. All the blocks must already be lined up.

Why so? Go to the Hydraulics Reasearch Station at Wallingford and look at all the modelling they do for design purposes. Both physical models and theoretical ones are used.

No problem, but you had been arguing so cogently that I thought I'd mention it. Intuition is a double edged sword that can lead one astray. Determinism basically means predictable by a chain of reasoning Now this was fine and dandy and led to many spectacular scientific successes, not least the kinetic theory. So it seemed a reasonable proposition in say 1890 that given enough data about every particle it would in principle be possible to predict the future course of each and every particle and therefore the universe. It was not quantum theory or relativity (special relativity is deterministic) that put the cat amongst the pigeons). It was radioactivity. It is not possible to determine the future course of any radioactive particle, only averages of aggregates of them. I said that the block universe refutes both chance and determinism. Both of these are about the process of arriving at a future course ie a process of change. In order for there to be a future course it is necessary for there to be change. But since everything is already set in the block universe and is immutable, but definition, there is no change. Does this help progress here ?

A model can still be a physical entity. Just because something is a model does not prevent it being an entity.

Well the book talks a lot more around the subject, but it is no picnic. Good reading. If you can't find the book I may be able help with a scan of the relevant pages, there's about a dozen.

Dodson and Poston Tensor Geometry Chapter VII part 3 Bundles and Fields The equations of special relativity are algebraic equations. As such they have algebraic solutions ie the solutions are one or more numbers. The equations of general relativity are differential equations. As such they have functions or equations as solutions. Some of these are equations of motion so it is not surprising that some of these solution equations of motion are a form of wave equation (which is an equation of motion)