studiot

This is progress. +1 😀 The plus 1 is because this is the first time you have laid things out in proper fashion. You see that immediately, even whilst I was writing this, folks have been able to see what you are doing and offer sensible and useful comment. However listing your symbols and stating what they stand for is really good practice and what I mean by progress. So many waste so much time and effort just writing algebra down. (did you know that although our word, algebra was, was named after early arabic 'al-jabr', which meant completion ?) I am sorry but yes your algebra is flawed. So let us look at your algebra. (I will only work the first equation) You claim this expression for your RR Force. [math]F = 1 - \sqrt {\frac{1}{{1 + \frac{{m{v^2}}}{{{c^2}}}}}} [/math] To show that this does not lead to the expression for the force per unit mass as you then stae, proceed as follows. [math]F - 1 = \sqrt {\frac{1}{{1 + \frac{{m{v^2}}}{{{c^2}}}}}} [/math] [math]{\left( {1 - F} \right)^2} = \frac{1}{{1 + \frac{{m{v^2}}}{{{c^2}}}}}[/math] [math]\frac{1}{{{{\left( {1 - F} \right)}^2}}} = 1 + \frac{{m{v^2}}}{{{c^2}}}[/math] [math]\frac{1}{{{{\left( {1 - F} \right)}^2}}} - 1 = \frac{{m{v^2}}}{{{c^2}}}[/math] [math]\frac{{1 - {{(1 - F)}^2}}}{{{{(1 - F)}^2}}} = \frac{{m{v^2}}}{{{c^2}}}[/math] [math]\frac{{1 - {F^2} + 2F - 1}}{{{F^2} - 2F + 1}} = \frac{{m{v^2}}}{{{c^2}}}[/math] [math]\frac{{{c^2}F\left( {F + 2} \right)}}{{m{v^2}{{(F - 1)}^2}}} = 1[/math] We have now reached the stage where we can isolate F/m, your force per unit mass. [math]\frac{F}{m} = \frac{{{v^2}{{(F - 1)}^2}}}{{{c^2}\left( {F + 2} \right)}}[/math] And we some that not only is the expression much more complicated than yours, but it still contains F. This is because the original expression is what is known as implicit. That is it is not possible to separate the variables F and m to obtain an explicit expression between them. An explicit equation would contain only an expression in F on one side and an expression in m on the other, which is what you are trying to do.

So you had a good idea that turned out to be wrong. So move on. The good news is that nobody was killed by your idea. Unfortunately that does happen with 'good ideas' from time to time, especially if someone clings to them in the face of mounting evidence to the contrary.

And I am still waiting for you to complete your side of the bargain. 😀

What is your variable that is measured in seconds ? Seconds alone is not a variable.

Where do F and F' magically come from in mechanics ? This has nothing to do with Group theory or Noether This simply require properly substituting for every force acting in two frames and comparing the results You need two particles to consider this properly. Consider two particles acting through a force F (x1, x2) where x1 and x2 are the x coordinates of particles 1 and 2 respectively and m1 and m2 are their masses. We have due to the force of interaction by Newton's third Law. [math]F\left( {{x_1},{x_2}} \right) = {m_1}\frac{{{d^2}{x_1}}}{{d{t^2}}}[/math] and [math] - F\left( {{x_1},{x_2}} \right) = {m_2}\frac{{{d^2}{x_2}}}{{d{t^2}}}[/math] now imagine a second frame (denoted by dashes or primes) translated so that its origin is at x0 in the original frame We have [math]{x_1} = {x_1}' + {x_0}[/math] and [math]{x_2} = {x_2}' + {x_0}[/math] Substituting the new parameters into out master equation we have [math]F\left( {x{'_1} + {x_0},x{'_2} + {x_0}} \right) = {m_1}\frac{{{d^2}x{'_1}}}{{d{t^2}}}[/math] and [math]F\left( {x{'_1} + {x_0},x{'_2} + {x_0}} \right) = {m_2}\frac{{{d^2}x{'_2}}}{{d{t^2}}}[/math] Now please explain why you think there is form invariance between the x and x' frames, when the form of the equations in the x' frame is so clearly different from that of the x frame ? Further the equation depends upon the origin of the x' frame, which the original does not.

So please confirm that s stand for the variable 'time' By which do you mean coordinate time, proper time, elapsed time, INR, viscoscity, or what ? They are all different but are all measured in seconds.

This makes it very clear that you have not understood what I said, since you have just stated very nearly the exact opposite. So let's take it one step at a time. The physics is there regardless of the presence or absence of a coordinate system. In what way does this contradict your statement ? So we appear to be agreed on this. However your statement differs from mine in that it seems to imply t5hat a coordinate system is necessary for all calculations in Physics. Whereas my statement allows for the possibility that the is no coordinate system in use for some calculations. Note this does not say that you cannot use coordinates, if you want, only that you do not need to. Off the top of my head, examples are Iin optics are the magnifying power of an optical instrument In mechanics, the velocity ratio, the mechanical advantage, and the efficiency. and of course the wave example I originally cited, which you don't seem interested in. It is very easy to show that Newton's Second Law [math]F = m\frac{{{d^2}x}}{{d{t^2}}}[/math] does not satisfy the Principle of Relativity. I look forward to your proof that it does.

@Bjarne-7 And, for the 6th time, the answer to my question is ....?

I see no connection whatsoever with my statement that coordinate systems are sometimes unecessary in Physics. That is a bold claim, because my university textbok (and many others) say otherwise. So can you prove it. I can definitely prove otherwise.

I asked you what you mean by s. S is the 19th letter of the english alphabet. Although there are one letter words in the english dictionary, s is not one of them. s stands for a word, which we can discuss. So for the 5th time of asking, what do you mean by s ? Or do I need to ask a moderator to enforce the rules here?

I see you totally ignored my second comment in the post you replied to. Why was that ? The equations of Physics are required by the Physics Principle of Relativity to be form invariant. Do you understand form invariance ? Do you realise that Newton's 'Laws' are not form invariant as commonly formulated ? This was the big issue, that was well understood before SR, and that special relativity addressed.

We almost never see light of a single frequency. Such light is called monochromatic light. Almost all our light sources generate a range of frequencies. Most depend upon the temperature of the body, the whiter the light it generates. When white light falls on anything some of that light is absorbed and some is reflected, but not all frequencies are either absorbed or reflected equally. In fact some frequencies are removed all together. So the incoming light is almost always a misture of a large numbr of frequencies. We do not have receptors in our eyes for all these frequencies, in fact, we have three different receptors, each sensive to a small range of frequencies. Some animals have only two receptor types and some only one. The strength of the signal (to the brain) from each of these types of sensor depends upon the strength of the light in the mixture that fall within its particular range. The brain then interprets this combination of signals as what we call a 'colour'. This combination can be replicated artificially using light sources filtered to produce light corresponding to our receptor ranges. The three are called the base coulours and the entire range of colours that can be distinguished or seen by out eyes. The base colours are red, green and blue. The entire range of colours is called the colour gamut or colour space These links might help https://en.wikipedia.org/wiki/Gamut https://en.wikipedia.org/wiki/Color_space

Frequency does not coorrelate directly with perceived colour because we have 3 separate and different colour receptors in our eyes and what we perceive is a mixture of the signals from each of these different receptors. Slow down and wait for others to amplify my answers. It may help alot.

Aha Colour (spelled) the English way refers to the our perception of light waves received by the human or animal eyes. This has no connection to the property 'color charge' in particle physics which is a quantum property. Please note that is has no connection to the property electric charge either. https://en.wikipedia.org/wiki/Color_charge

This was not your original claim, you claimed the wave equation to be invariant. A a person with a "background in maths" you should be aware that holding good in only one frame contravenes this big time. Invariants appear in both maths and physics in many places and both employ the same meaning for this term, unlike some other common terms like field and vector. The are physical phenomena associated with both light and sound which depend upon relative velocity, but do not need to be associated with any coordinatem syste at all and can be detected wothout any coordinates. The physics is there regardless of a the presence or absence of a coordinate system.

That is not a definition. Nor does it direct me to where you have used it and defined it in this thread. What is s please ?

A good response. +1

I was going to write a sympathetic and supportive response to your very recent post(s) in another thread. But sorry I feel significantly too insulted to post that response now by this blatantly false attack on others. Several claims in your post 'stick in the craw' but the emboldened one is so laughably false it is the last straw.

I'm sorry, where does s come into it. ? In other words where have you defined s before in this thread please ?

The heat capacity of dry air only varies in the second or third decimal place over the range -20C to + 20C so with dry air the eficiency is sensiby the same if your operating range is -20 to zero or zero to +20 since cooling either air 10 degrees will yield the same amount of heat. Obviously you need to chhose the refrigerant carefully to operate over the expected temperature range. The difficulty arises because most air is moist. Usually the range 0C to +6 is the worst because that is when the air mositure comes out of the air with avengance and condenses or freezes on the heat exchanger seriously impeding the heat transfer (reducing the heat transfer coefficient) significantly. Just the conditions we have in Southern England. Once you operate below zero most of the mositure has left the air and it is very dry. So near ideal conditions pertain. You then have to contend with wind blown snow.

Maxwell was the kiddie. Sadly he died comparatively young. He would probably have had relativity if he had lived another 10 years to then average age. There are always suprises around the corner. That is one of the strengths of Science. It is malleable enough to absorb change and be better as a result. The best reasoning in Science seems to often alternate between mathematical reasoning and physics reasoning, each one prompteing advances in the other. The best derivations I have seen of the famous Schrodinger quantum equation work like this, as do mnay others. It is now well past the witching hour here in England so I will take my leave for now.

When lots of clever people have worked hard to tie down specific meaning for many technical terms it makes sense to use those meanings and not try to start out with new ones. Unfortunately too often in my opinion even scientists fall down in this respect so when they start talking about some new subject, other people think they know what is meant and arguments ensue when they find out that they do not.

Space has no fabric. It is not made of anything. Space is a general term, best understood in context.

Quantum theory doesn't in general involve forces and reference to a 'fabric' is popsci. I am suprised that you jumped to such conclusions when I suggested to find out about some basics. I'm sorry but there is a lot of learning and work required between those basics and something as advanced as quantum theory. And as yet, you don't seem to have the basics. Energy does not exist by itself. There is no such thing as pure energy. Energy is, in fact, a property of things which do exist. One of its properties is that it may be transferred from one thing to another. Quantum physics arose from the description given by Einstein to the discovery that energy can only be transferred in certain definite quantities. This was only a description and referred to only one sort of transfer originally. It did not answer the questions of how or why this is so. Einstein called these definite quantities quanta. As joigus points out, it has later transpired that the restriction also applies to some other properties of things such as angular momentum. Quantum Physics is the study of such phenomena and its implications. Does this help ?

I suggest yoy look more closely into the nature of vibrations, oscillations, waves and other forms of motion. We have many names beacause they are all different in the way they work. Vibrations require what is called a 'restoring force', in addition to the original 'disturbing force'. If no such force is present then free motion occurs which may be random and if impeded ( eg by collisions) may generate a variety of phenomena, one of which we call pressure, another we call heat, another we call pair production and so on.