studiot

OK so you say you are happy with paragraph in the other thread. The vital thing to know and remember is that The tangents do not exist in the same universe as we do. They have their own complete coordinate system and touch our universe at one point only, Further the tangent system at each point has its own universe and coordinate system, different from the universe and tangent system touching at any other point of our universe. This is what is meant by a local coordinate system. All the points in our universe make up the global coordinate system that we use in relativity. I have said this before but the relationship between the local coordinate system at any one point containing a tangent (or other) system and the global one is mathematically called a chart. Each point therefore has its own chart. The relationship between two charts is called a connection. This is usually established by the 'parallel transport rule' Without such a rule we could not relate or connect measurements made at one point with those made at another. The 1 :1 mapping of the tangent plane (or other surface) onto the base universe is called a patch. In general you need more than one patch to 'cover' the entire universe.

I think (a large) part of the problem with 'real' is that people seem to want it have only one meaning, rather than a range of meanings. The English language is much better equipped than scientific people often realise.

Have you looked at posts 24 through 27 here? http://www.scienceforums.net/topic/89395-what-is-space-made-of/page-2

What did you make of my reference? One way to look at what you are asking is like this. Consider the parabola y = x2. What do you need to be able to draw it (for it to exist) ? Well you need the +x axis and the -x axis and the +y axis. But you do not need the -y axis. In fact you do not need the entire half plane below the x axis. So you are asking the equivalent of Does that half plane exist for my purposes? Would you agree?

Also good thoughts +1

So where is your working? y1 = 2sin2pi(10t-0.4x) =2sin(20pit - 0.8pix) =2sin(20pit)cos(0.8pix) - 2 cos (20pit)sin(0.8pix) Y2 = 4sin(80pit)cos(1.6pix) - 4cos(80pit)sin(1.6pix) What is the relationship between sin (a) and sin(2pia) ? etc for other multiples of pi and the cos functions? What happens if you form the sum y1 + y2 and collect terms, allowing for the above?

Instead of separating the two notions of space and time, combine them together and then there is can be?motion. But +1 anyway for a good comment.

What happened to k in your working? It is in there because ther are multiple solutions to the equation v = x/t

Not exactly but I think you are referring to what is known as intrinsic geometry. Perhaps if you would like to explain in greater detail? This extract from Elementary Geometry : Roe : Oxford University Press might help. Read paragraph 12.1 in particular.

Yes, String Junky offers wisdom, getting the right; getting the right books is important. Further the right books for one person may be wrong books for someone else. Perhaps that is why there are so many books. If you would like to expand on your question and tell us about the level and area of your interest we can usually produce suitable recommendations to look at.

You need to separate the t and x in the original equations as they are both independent variables. Have you heard of the trigonometric transformation to do this - otherwise known as the sum and difference formulae? https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=sum+and+difference+formulas+in+trigonometry&gbv=2&oq=sum+and+difference+formula+i&gs_l=heirloom-hp.1.3.0i22i30l10.3438.10797.0.13297.28.14.0.14.14.0.187.1622.5j9.14.0....0...1ac.1.34.heirloom-hp..0.28.2310.ngHuv_uG_7k

Where did I say radioactivity was deterministic or non deterministic? The problem with binary logic is just that. It is binary. It does not allow shades of grey or the statement it is partially deterministic. For instance if you start with an even number of atoms the process is deterministic (if we set aside statistical variations) for an unknown number of steps. If the initial number of atoms is 10 then 10/2 = 5 which is deterministic, but 5/2 is not. Yet 128. 64 . 32 . 16 . 8 .4 . 2 is deterministic all the way down to 1. I am sorry I did answer that part of your previous post, but I was trying to separate questions using the quote function and deleting the unwanted bits in each case. Somewhere along the line it got lost. So here it is again. Yes we can statistically say that if we repeat the experiment of many trials we will obtain a range of actual outcomes with a mean of exactly half. So random variation also affects the process. But I come back to the fundamental requirement of determinism. That to be deterministic a process must be capable of determinism. That it it must be possible to deduce the outcome from the initial conditions exactly, each time the process is run. The same deduction on the same process must produce the same result each time it is run. Saying the process that outputs half of 5 sometimes produces 3 and sometimes 2 is not good enough.

This is quite illogical and unphilosophical. One proven counterexample is sufficient to disprove any proposition. Of course it does not mean that you (or anyone else) can determine it. It means that the process is capable of being determined. If I can prove that it is not capable of being determined then it follows that the process is not determinate. And I have proven just this with dividing an odd number in half. That's a ridiculous statement. Of course maths (our maths in particular) cannot do everything we ask of it. Prove it please.

Dimension Theory Hurewicz and Wallman Princeton University Press / Oxford University Press

I specifically ruled out Bells or other quantum theory in my discussion so why are you linking it to anything I said? I already made it as clear as I possibly can that is this not a quantum or statistical statement. Perhaps I should have said it is an arithmetic issue. If a process is deterministic then it is possible to determine the outcome of that process. This is philosophy, pure and simple. So I gave you a counterexample where you can demonstrate arithmetically the fact that the outcome can be deterministic or it may be impossible for the outcome to be deterministic, according to whether the process starts with an even or odd number of indivisible units. I chose radioactivity, since it is a commonly known process known as a first order process. First order processes are very common in Nature. Would you prefer an example from Pharmacokinetics? I actually don't know why you are arguing about this since it supports your proposition. Yes indeed there is also a statistical effect at work here. But there is no statistical example that will yield exactly half an odd number of indivisible units. I can only explain this if you understand how pressure is generated in the first place. Pressure is a mechanical property that is the result of momentum exchange between the (indivisible) molecules of a fluid and its container. This is definitely a property with a statistical basis that is not amenable to mechanics applied in regions smaller than the molecules. If you like I am putting forward a third way that proposes nature to be more complicated than the original question allows. If you are to ask the simple question "Are all process deterministic or non deterministic at some level" You must accept the responsibility of showing that the qualities 'deterministic' and 'non deterministic' form disjoint sets that are comprehensive in covering all qualities.

Thank you yes I'm aware of cavitation effects and was planning to introduce it into the discussion if it proved to be about submarines. I was also pleasantly surprised to find that my envelope calc produced a frequency employed in modern sonar. http://hypertextbook.com/facts/2001/EmranYusufov.shtml Two points about cavitation. Firstly it is a local effect - Could you envisage a sphere surrounding itself with a void by cavitation? Secondly as the pressure in the cavitation bubble is lowered, water boils into the low pressure within the bubble, so the bubble is not a true void.

You would need to consider gravitational waves for that. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=gravitational+waqves&gbv=2&oq=gravitational+waqves&gs_l=heirloom-hp.3...1056.6657.0.6858.20.11.0.9.6.0.189.1060.9j2.11.0....0...1ac.1.34.heirloom-hp..4.16.1007.TGnqpm8s9GY

Wish I could help but this is beyond me so I take my skull cap off to you. Meanwhile my answer may help keep this thread in sight until those who do understand this stuff are around. and yes, there some of those folks here.

Just looking at science education tables and 'PISA' results. We come along way down the list. http://www.bbc.co.uk/news/education-38157811

We have progress at last. But don't forget that in the entire universe we only need one single non deterministic subject or event to disprove determinism. So please don't change the example I gave, but discuss it. Of course it is based on the simple fact that you cannot divide an odd whole number exactly in half using only whole numbers. There need be nothing random about it at all. There are more complicated examples in physics of non deterministic events. These are based on taking any physical law that uses an average, whether the driving agent is random or not. For instance if I measure the pressure at a small enough area of container wall to be less than the strike zone of a gas molecule What pressure will I record? This is a perfectly feasible experiment these days, well within our technology today.

Yes of course the temperature and pressure will affect the water molecule speed. Don't forget this is back of the envelope stuff. I simply googled average water speed at 20o C and came up with 590m/s Also dividing 6 by pi does not exactly equal 2. But I thought it provides a feel for the question. Also note that the waves have to be transverse to push the water away. Longitudinal (surface) waves will not do. @connor Was this for some sort of spaceship/submarine story?

OK let us look at some figures. At room temperatures the average speed of water molecules is about 600 metres/second. Say the surface of your sphere pulses in and out at some frequency, f. As the surface moves out it pushes the water back and as it moves in the water molecules will move in to occupy the void at an average speed of 600m/s. So if the surface is moving faster than this it will leave a void behind as the water molecules cannot catch it up. For an object vibrating in simple harmonic motion the maximum speed is given by [math]Maxspeed = 2\pi fA[/math] Where A is the amplitude and f the frequency as already noted. The maximum speed occurs as the surfaces passes through the undisplaced position so for a total displacement of 1mm (0.5mm outwards and 0.5mm inwards) A = 0.5 x 10-5 metres. Substituting values [math]600 \le 2\pi f(0.5*{10^{ - 3}})[/math] [math]600 \le 10\pi f*{10^{ - 4}}[/math] [math]\frac{{6*{{10}^5}}}{\pi } \le f[/math] [math]f \ge 200,000[/math] So a frequency above 200 kilohertz will just begin to create such a void, but two things 600 is the average speed of the water molecules. Some will be moving quite a bit faster. The frequency calculated is for the maximum speed of the vibrating surface. The surface speed will actually slow down to zero over the 0.5mm so the water molecules will soon catch it up. Both of these effects serve to raise the necessary frequency, probably into the Mhz range, the exact value will depend upon just how much water you are prepared to let into your empty space and just how thick you want it to be.

Since when did opinion take precedence over observation, especially if the opinion runs contrary to observation?

I asked you two polite questions in my post#31, correctly identified by the question marks at their ends. . You have subsequently refused/failed to offer any answer on either of them Why do you expect others to answer any of your questions under such circumstances?

Just to add a small extra to Mordred's excellent piece. +1 The whole point of (radioactive) decay is that is happens regardless of the state of motion or lack of motion of the particles involved. In other words the decay does not depend upon the motion. Note there are many processes like that in Physics. i.e. those were there are many things going on. So separation as to what affects what can be quite difficult.