studiot

Nah, the correct quote is "time is money, bub."

Strange I regard your post#104 as being one of your most restrained, quite undeserving of a negative vote so +1

1 and 2 are almost like finding two terms in a differential equation solution, one of which tens to infinity or dies away and the other represents the 'steady state' solution. However I must protest the slur upon physicists in your first sentence. There are an infinite number of points on the interval between 0 and 1. One of the most common processes in Physics is normalisation - or the rescaling of some quantity to lie between 0 and 1.

Unfortunately the link somehow doesn't work for me. Edit Stet Got it now. Thank you for all these links, I am aware of the bones of what they contain but they do offer some fresh views on the material. But they still suffer from a basic issue, from what I can see. I have deliberately restricted the system to one spacial axis and one forbidden rotation scaled time axis to try to preserve simplicity. So far as I can see this requires that all alternative frames of reference must be parallel to these axes. This is the basis of my second comment in post# 6 All the examples show an x' axis rotated with respect to the x axis. This is only possible in a system with 2 or 3 (or more) spatial axes.

One thing all the examples have in common is that the cones are referred to the same frame axes in any one diagram. What I am interested in is what those cones would look like if redrawn to a different set of frame axes. One thing I have realised whilst considering this is that there is only one direction relative velocity can take with only an x and a ct axis.

To reinforce my earlier comment (post#20 ) to steveupson P0, P1 and P2 are orthogonal (perpendicular if you like) but not independent.

Nothing you have said here in any way affects or even addresses my points in post 98. Nor have you answered my question.

There is no paradox. You need to read up on the difference in meaning between the words independent and perpendicular. No multiplication does not imply direction, nor is it contained in the definition of multiplication.

No-one is complaining about philosophy, just asking you to use the philosophy section of ScienceForums for philosophy. Is that unreasonable? If you want to convert this thread to philosophy, ask the moderators (nicely) to move it for you. You might be surprised how helpful they can be. As to your statement above I think you are falling into the trap of using words in too narrow a manner. Most definitely there are circumstance you do not need to measure to create certainty. For instance, in retirement, I have moved from a large house with an orchard to a small property with a single apple tree in the back garden. I do not need a measurement to tell me that I do not need a larger basket than I needed in the old house to accommodate this year's crop. That is reality. Mathematically too , there is more to 'certainty' than you allow. Do you know the three possible meanings of the mathematical statement The probability of event A is 1?

Because time is not directly one dimension of the 4 dimensional spacetime manifold. The fourth dimension is time multiplied by a physical constant, with suitable dimensions to make the product another length. We call this constant c and it can be deduced from several different routes in Physics.

Yes agreed, both those approaches are valid although the system is complex so I expect you will need numerical methods to solve either the simulation or the analytic solution. You should start by drawing a proper process diagram, including all the variables and fill in the known relationships. This will help order your thoughts and enable suitable approximations to be made to develop and simplify the overall analysis. Then you can separate your analysis into the part which tends to a steady state and the transients which introduce instability and compare their relative effects. But much more information is needed to describe such a complicated system.

Thanks Mordred, I will study them tomorrow, it's bedtime here right now.

Yes this was the motivation for the question. Here is some more background. With reference to the diagram, consider the instantaneous coordinate frame of A with one spatial and one transformed time axis ct (I have kept it simple). The part light cone represented by the triangle EAC contains all the points that particle A could concievably attain and a sample worldline is plotted as a dashed line. This worldline must lie with EAC. Now consider observers situated at B, C and D, all moving relative to A. Each will have its own lightcone represented by a triangle in its own frame. But each will see time as dilated and length as contracted along the ct and x axes of A. So each will see the figure A sees as triangle AEC and the worldline as distorted compared to the view from A. Hence the question, as it will take me some time to plot it all out.

Touche +1

A bit odd?? But what about the other bit ie the rest of you? So you are really like most functions, the sum of an odd and an even function.

What is trivial does indeed depend upon the context. Remember it only takes one except to disprove the most elegant theory in maths. The zero function is y = 0 for all x. This is not quite the same as for instance y = ax3 which is odd for all a except a = 0, when it is neither odd nor even. It is a subtle point and I wanted to move on from towards noting that in general functions are neither odd nor even, but may be decomposed into the sum of an odd function and an even function. Odd and even have significance in science, in that they are examples of a wider phenomenon known as parity. Even functions have parity +1 and odd functions have parity -1 Parity is related to symmetry, so an even function is symmetric with respect to the y axis, x = 0 and an odd function is antisymmetric with respect to the x axis, y = 0

This is really Mordred's area. I have started another thread with a question that might help here so please watch for his response. http://www.scienceforums.net/topic/100764-a-light-cone-question-for-mordred/

Do you have an images of what a light cone of a particle B might look like, when measured in the frame of another particle, A such that A and B are in substantial relative motion?

Every point on the world line of a particle generates a new light cone. So considering several observers can generate a complicated tangle of light cones. It is important not to unintentionally include an assumption of some sort of absolute spacetime in consideration of these. A good question to consider here would be: How do the light cones from particles outside the light cone of some given particle overlap with the light cone of the given particle?

+1 for spotting the circular argument, Tim.

I haven't worked it fully through, but does not the substitution z = x2 dz = 2xdx [math]I = \frac{1}{2}\int {{e^{ - z}}} dz[/math] Not suffice?

Nicely put, Janus. +1

Yes indeed I missed the order reversal so your two posts are consistent. Sadly they are consistently wrong.

You are nearly there. Note I said completely isolated empty space. In a 'chunk' of empty space near a massive ( = body with mass, not necessarily a large mass) body g will not be zero. So I guess the question Frank Wilczek posed refers to this case where the empty space is not isolated. What he is saying concerns the influence of the container/boundary of the empty space, along with whatever lies beyond it. zbi I have answered your question precisely. You have not acknowledged the answer. So how can I proceed to explain an additional gratis remark I made for your benefit? But yes I can not only explain at least one property of empty space I can confirm my prediction by direct measurement.

I presume you are referring to a definition of weight, W as W = mg. The problem is that g is zero in an isolated completely empty space.