studiot

Thank you for the reference to that long and rather rambling thread. I did note that there was a general failure to distinguish between inertial frames of reference and general frames of reference, with continual discussion at cross purposes as a result. Even I did just that in your quote. I also noted that at the outset swansont's comment, which I agree with. I do not think arguments about frames of reference add to this thread which is about the foundations of SR. The OP here posted populist listings of these, but in a science forum it is worth delving deeper and distinguishing between fundamental principles and consequenses.

CERN is not american and US copyright laws (whatever they are) do not apply in Europe. In particular in UK law copyright exists on any copyrightable material from the moment of its creation and does not have to be asserted or registered with anyone (with or without a fee). I'm sure imatfaal will have more detail to say about this.

Friction is not yet fully understood and quite possibly not due to a single mechanism. It is possible to develop quite accurate mathematical theories for some surface contacts, but every theory seems to have some exceptions as well as successes. What is your interest here?

Every observer is considered at rest in his own frame of reference. So that is what the light 'sees'. Edit xyzt, I would be grateful if you already have a thread with the requested maths, for you to add a link to your post.

Good morning Robin and thank you for your kind thoughts. I see that you are still online so I am posting this quickly, but will take the time to post a more measured response later today. Briefly to address your scenariao. I extracted your point about relativity of length because it was a good one. Essentially we can say that the source of the flash and the stationary observer (S) are in the same frame. So S measures a distance d to the source and the flash takes a time t to reach him, such that d/t =c. The strategy is to show that although the moving observer (M) sees a different distance to the source and a different time of flight of the flash, M still measures their ratio as c. Note also that S and M will see the light at different frequencies due to the doppler effect.

Thank you for drawing this to my attention. I see immediately where it went wrong right at the outset. I spend far too much time and effort getting the LaTex to present at all and end up without the expression coming out as I orignally had it on paper. Edit is not available to me and I am not going o write it all out again. I don't think I will bother in future.

Simultaneity is defined by time difference being zero. In particular the time difference between two events in space-time with coordinates (x1,t1) and (x2,t2) in some coordinate system is found by subtracting the time coordinates only [math]\Delta t = {t_2} - {t_1}[/math] If [math]\Delta t = 0[/math] That is t1 = t2 The two events are said to be simultaneous. Robin, the important thing to notice here is that this time difference is independent of the space coordinate, x. Since our coordinate system is completely general this statement applies to any coordinate system. So far we have only one coordinate system and all this has all been from the point of view of an observer in that system. So let us introduce a second coordinate system with coordinates (X,T), moving with velocity V relative to the first coordinate system. In this second system the same two points now have coordinates (X1, T1) and (X2, T2) and our second observer is moving with the second system at velocity V relative to the first. In this second system the coordinates of the same two points are given by the Lorenz transformation of the coordinates in the first system. In particular the time values in the second system are [math]T_1 = \frac{{\frac{{\left( {{t_1} - V{x_1}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] [math]{T_2} = \frac{{\frac{{\left( {{t_2} - V{x_2}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] Note that in general the time values in the second coordinate system depend upon both the space and time values in the first system. If we now do the same time subtraction in the second system [math]\Delta T = {T_2} - {T_1}[/math] we find that [math]\Delta T = \frac{{\frac{{\left( {{t_2} - V{x_2}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }} - \frac{{\frac{{\left( {{t_1} - V{x_1}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] [math]\Delta T = \frac{{\frac{{\left( {{t_2} - V{x_2} - {t_1} + V{x_1}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] [math]\Delta T = \frac{{\frac{{\left( {V{x_1} - V{x_2}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }} - \frac{{\frac{{\left( {{t_2} - {t_1}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] I am sorry for the arithmetic but it is only what is taught in junior high school maths. Anyway since we have stated that the events are simultaneous in the first system t1 = t2 So the right hand part of that huge expression becoms zero leaving [math]\Delta T = \frac{{\frac{{V\left( {{x_1} - {x_2}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] But we are asking the question Under what conditions is this simultaneous in the second system? ie when is [math]\Delta T = 0[/math] ? and the equation tells us that for this to happen x1 = x2 That is they are in the same place in the first coordinate system. So two simultaneous events that are measured as in the same place in the first coordinate system will be seen as simultaneous in any coordinate system, since our second one was completely general. However this equation tells us yet more. It suggests that there may be events seen as simultaneous in the second system that are not seen as simultaneous in the first. The condition for this is for the relative velocity times the space difference to equal the non zero time difference in the first. [math]\frac{{\left( {V{x_1} - V{x_2}} \right)}}{{{c^2}}} = \frac{{\left( {{t_2} - {t_1}} \right)}}{{{c^2}}}[/math] [math]V\left( {{x_1} - {x_2}} \right) = \left( {{t_2} - {t_1}} \right)[/math] To examine this let us perform the same process on the space difference in the second system, using the Lorenz space transformation in this instance to find the difference in position of the two points in the second system is [math]\Delta X = {X_2} - {X_1}[/math] [math]\Delta X = \frac{{\left( {{x_2} - {x_1}} \right) - V\left( {{t_2} - {t_1}} \right)}}{{\sqrt {1 - \frac{{{V^2}}}{{{c^2}}}} }}[/math] But since they are simultaneous in all systems, (t2 - t1) = 0 Thus [math]\Delta X = LorenzTransformation({x_2} - {x_1}) = LT(\Delta x)[/math] Since x1 was a general point this implies that for every point in the first coordinate system there is a second point, x2, where events seen as simultaneous in one system will also be seen as simultaneous in the other.

Well this shows how wrong today's thread saying we were a stuffy load of has-beens is. Congratulations mate. +1 Suggestions? When I first went to University there was a lad there called Martin, who had something in stone jars he was drinking. What's that? Martin we asked. After some arm twisting we got a sip. It was the nicest drink I have ever tasted. It turned out that his family had a tradition of making marrow rum. The father would make the rum and lay it down for the son to drink and lay down more for his son in turn.... This had apparently been going on for generations. So get started mate.

Did they? So what is the correct direction of current if I replace your battery with the AC mains? I would see the same (heating) effect in the external resistor. And are there not actually more AC circuits than DC ones in this world? And that still did not answer the question what is the direction from + to - within the circle you have drawn? The whole point is that most theory is independent of the direction of carrier flow. If this become necessary it is simply covered by assigning the same sign as that of the charge to the flow. Surely you cannot be suggesting that electrons simply move around your path through the resistor from - to plus and stay there at the + sign, building up an excess of negative charge, which would repel further electrons arriving?

What a pity you did not address the short piece I wrote since I was hoping you actually wanted a discussion. The above quote that you have now repeated several times has nothing whatsoever to do with relativity of any sort. It is a simple piece of classical mathematics to prove that the velocity of any wave is independent of the motion of the emanating source. This applies to sound waves, electromagnetic waves, waves on a violin string or whatever. So yes it is true but it is not a fundamental assumption of relativity. I did actually supply the one and only 'assumption' you need for Einstein's relativity.

The substitution swansont mentions involves change of variable. What does your Hamiltonian look like initially?

It would help if you stated the problem as written.

You have had a pretty good discussion from a number of people and there are plenty of really interesting subjects yet to be studied. So I would gently suggest it is time to move on to another one.

Yes that is true, but the atmosphere is travelling relative to the muon's frame of reference.

As a complete non sequiteur, but cheekily on topic, there used to be constituencies in Olde England called "Rotten Boroughs". http://en.wikipedia.org/wiki/Rotten_and_pocket_boroughs

No not exactly. From the muon's point of view there is no time dilation (or mass increase). The muon doesn't experience anything. But from the point of view of an observer on Earth both occur.

There are two separate issues. Firstly not all current flow is by electrons, or even negatively charged carriers. Sometimes carriers of both polarity are involved. So whichever is chosen will be 'wrong' for the other. Moreover carriers can be massive ions or small particles like electrons and 'holes'. In fact most theories do not require electrons, just 'carriers' which often need not be described further. Secondly all the equations in elctrodynamics and electrostatics are set up using the direction of conventional current. Many are vector equations which contain inherent directional information. All of these would be incorrect if we changed direction of current in conductors. So a direction was chosen a couple of centuries ago and we apply a plus or minus sign to any equation if the polarity of the charge affects it. That strategy resolves all known problems. Nevertheless there was a move in the 1990s to promote the reversal of the standard direction to make the direction of negative carriers positve (?!!??). That has caused much confusion as you note and is falling out of fashion. I would avoid it as far as possible.

Is it? A scientist on a rocket measures the mass of a test ball with him in the rocket. The rocket then accelerates to nearly the speed of light. The scientist performs the same experiment on the same ball in the rocket. Does he measure any change of mass? Compare with the muon experiment I referred to earlier http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html

Yes of course electron flow is in the opposite direction to conventional current. I do not want to get into an electron flow v conventional argument. What I am saying is like imatfaal's model elsewhere. We choose a direction and set up our models (mathematical equations) to suit. The electron flow model is actually unhelpful (IMHO) to most leaning circuit theory and leads to the difficulties I outlined. Remember circuit theory is a mathematical model designed to facilitate the calculation of componeent values for design and analysis purposes. It is not intended to offer a model of the physics of electricity. Treated as a design and analysis tool is works well.

Take a battery and a simple connected circuit. Which way does conventional current flow? Well it won't flow at all unless there is a complete closed path all the way round from terminal A of the battery through all the connected wires and components to terminal B of the battery and back through the battery to terminal A. All the connected stuff is called the external circuit, from A round to B. The part back through the battery is called the circuit within the battery. It takes both parts to make a complete circuit or loop or closed path. Usually the external circuit is much larger than the battery so we often refer just to this part as 'the circuit'. However consider a technicain testing a large lorry battery with an automotive battery discharge tester. The battery is very large compared to the size of the discharge tester, so which is 'the circuit' now?

I'm glad imatfaal brought up the subject of models. Not only are models valuable for on their own merit, they also form a basis for other theory used for other purposes, perhaps by engineers or applied scientists. Inappropriately 'accurate' or elaborate models can even get in the way. For instance golf balls move fast, but no one would apply the principle of relativity to their flight through the air. However relativity mechanics is the only way to explain the flight of muons through the same atmosphere.

Do they? In an incomplete external circuit they don't 'flow' at all, despite the electric field that exists between the terminals. In a complete external circuit the do indeed 'flow' from what we call the negative terminal to the positive terminal. But Within the battery they must flow the other way to complete the circuit.

Relativity discussion often arouses (excess) passion, and that seems the case here. Although your posts are long enough to be sermons, you appear to be seeking a rational discussion. First and foremost is the question what is relativity. Well relativity causes us to re-examine both space and time (and therefore all quantities derived from these such as velocity) so we cannot use them in our definition as that leads to circular arguments. That means that none of your three assumptions above are available. The guiding principle is a sort of conservation principle (but not a conservation law as in the conservation of energy) which can be phrased that we want (assume) that the laws of physics are such that they work out the same in all reference systems. Contrary to popular story much of this work was done (well) before Einstein. In fact so far previous to Einstein that Newton and Galileo before him held to this principle, but only knew of the laws of mechanics. We have named the earliest and simplest form of (mechanical) relativity after Galileo. Einstein extended this to other areas of physical laws such as electromagnetism. this did not invalidate Galilean relativity, merely restricted its domain of applicability. Today we use the following basic definition "It is impossible to distinguish between inertial frames by using any physical law)" The modern approach is to test exisitng and proposed physical laws against this principle. When this is done, and I'm sorry but this is where the maths comes in, we end up with the more famous formulae.

Philip Duke, you have recieved a number of negative votes for failing to discuss in a proper and scientific manner. (not from me I might add) I am going to say +1 here because, even if incorrect, your response corresponds to the spirit of this forum.

You have posted two questions in modern and theoretical physics that on the face of them could (should) be in classical physics. Unless you are looking at relativistic effects. So would you like to elaborate both on the context and detail of your question(s) so that others like myself can understand it?