The Lorentz transform is the precursor to STR, and a departure from Galilean coordinate systems and Newton/Maxwell.
That is why it is important to understand it thoroughly before continuing to Einstein's postulates, and Quantum Mechanics (especially Quantum Field Theory and second quantization).
If you'd like to discuss it, let me know, and I'll start a thread where we can discuss the issue. In my experience, it takes substantial effort to get things right, and I found myself having to go back to fundamentals many times. Keep in mind that when I discuss "The Creation of the Universe", I am really discussing an initial condition X = CT' (in the semi humorous analysis, CT' is where god ignores the son's efforts, and claims that CT' = CT. If you read the pdf, I'll explain.... In any case, CT' (for that case) is the creation of a "ruler" or "rest mass" from nothing to an initial condition (at that point, VT' = 0, and CT'=CT. This corresponds to an initial measurement of an arm without a moving medium (or its "rest" mass in the mass/energy domain.
The point is that STR is gauge invariant, so space-time is irrelevant if the physical system is covariant (to understand the difference between covariance and contravariance, you have to deconstruct v/c into its space-time components, and provide an affine connection between (x,t) and (CT,VT') vector spaces, which means that is interpreted as a density. Einstein, by analogy with classical continuum mechanics includes this in the metric tensor, where he interprets contra-variant changes as force due to gravity (vs electromagnetism). This is only possible for him if the mass of light is zero.. so there is a lot to discuss about that.
Anyway, if you're interested in a serious discussion I can open a thread, and if we get spammed by a number of people I have experience with, we can move somewhere else to continue the discussion.... You have a solid technical background, but it is possible that you haven't yet thought about some of the fundamentals in depth; by clarifying them for you, I can further clarify them for me.
Let me know what you think... send me a private message if interested
Note: This is a free-wheeling forum which means good news and bad news. The other forum (BAUT) is manned by administrators who don't really understand fundamental principles, so they kick people off for life if they go against what they think is conventional wisdom. Therefore it is hugely stifling (I got kicked off in the first two weeks, because I had a question about the Time Dilation Equation - which resulted in my "Creation" document and a deeper insight into the Lorentz Transform - particularly the relation between the "Boost" and "Rotation" paradigms)...
Have you had any experience with Signal Processing and Analysis? (Eg Fourier Transforms?)
I know that a mathematical model is the next step in testing my ideas, but I hesitate to take that step. One part of me wants to dig in and learn the math from the beginning which I am not sure is Lorentz. Do you think he dummied down Maxwell? Oversimplified? Did we leave something in the original equations that may be important?
The rest of me thinks my time could be better spent on more practical pursuits. I appreciate your offer to walk through this with me. Let me think about it, because once I commit, I will be consumed with it and my day job will get in the way.
Maxwell interpreted c as "speed", but consider:
(and its consequences) as an alternative interpretation.
The constants were established experimentally from force laws, and the Lorentz transform is an attempt to describe the null results of the MM experiment (and later expansions on it). The "time dilation" equation is a vector subform which describes the relation for independent space time as an orthogonal vector space (x,t) related to mass-energy (M0) by the density relation in terms of v/c.
So it forms the foundation of physics after Maxwell/Newton, both for GTR (the complete transform) and quantum mechanics from E=hv (the photoelectric effect).
These are simple equations, but have profound interpretations as one delves more and more deeply into the experimental results and the mathematics necessary to describe them (eg electron spin, Casimir effect, Mossbauer effect, etc.)
So it is particularly important to "build from scratch" and understand where the basic building blocks come from. Because the most fundamental issues (and most difficult to understand) are questions of ontology ("being", "existence"; e.g., the Bohr/Einstein debates early in the last century)
Wikipedia is a great help, since it permits instantaneous reference to the textbook equations, and it gets better and better at explaining fundamental issues.
(look up quantum triviality, for example, for fun ...
(That said, a lot depends on your experience with mathematics; vectors, scalars, outer and inner products and their implementations in matrices, etc., etc. I've been on the journey to make sense of all this for the past couple of years, and a lot of it is pretty tricky indeed; but absolutely fascinating to me ....
Well Hello fredkratt its really beautiful question. In my opionon physic take place in every part of life such as how to exist the universe as well as the whole life before and after.
Physic is one of the basic and importand part of universe as well as human life. Thales of miletus He is the one who introduced physic in (650-480 BCE). He is the great philoopher. Physic is the Greek word meaning nature.Physics (from the Ancient Greek φύσις physis meaning "nature") is the fundamental branch of science that developed out of the study of nature and philosophy known, until around the end of the 19th century, as "natural philosophy". Today, physics is ultimately defined as the study of matter, energy and the relationships between them. Physics is, in some senses, the oldest and most basic pure science; its discoveries find applications throughout the natural sciences, since matter and energy are the basic constituents of the natural world. The other sciences are generally more limited in their scope and may be considered branches that have split off from physics to become sciences in their own right. Physics today may be divided loosely into classical physics and modern physics. Without physics you don't even know anything in the begning and what comes in future.
so your question is where does the gravity comes from??
Ans: The average person probably doesn’t think about it on a daily basis, but yet gravity affects our every move. Because of gravity, we fall down (not up), objects crash to the floor, and we don’t go flying off into space when we jump in the air. The old adage, “everything that goes up must come down” makes perfect sense to everyone because from the day we are born, we are seemingly bound to Earth’s surface due to this all-pervasive invisible force.
But physicists think about gravity all the time. To them, gravity is one of the mysteries to be solved in order to get a complete understanding of how the Universe works.So, what is gravity and where does it come from?
To be honest, we are not entirely sure. gravity.gif
We know from Isaac Newton and his law of gravitation that any two objects in the Universe exert a force of attraction on each other. This relationship is based on the mass of the two objects and the distance between them. The greater the mass of the two objects and the shorter the distance between them, the stronger the pull of the gravitational forces they exert on each other.We also know that gravity can work in a complex system with several objects. For example, in our own Solar System, not only does the Sun exert gravity on all the planets, keeping them in their orbits, but each planet exerts a force of gravity on the Sun, as well as all the other planets, too, all to varying degrees based on the mass and distance between the bodies. And it goes beyond just our Solar System, as actually, every object that has mass in the Universe attracts every other object that has mass — again, all to varying degrees based on mass and distance.
And about the universe i tell you that whole universe is consists of these things such as
Time and Space is consists of length, width, depth, time. Well Einstein was the One who was introduced the gravity as well as time and space. gravity can bend time. A four-dimensional fabric called space-time.When anything that has mass sits on that piece of fabric, it causes a dimple or a bending of space-time.
Time and Space also held on our entire life. In the beginning there were nothing but the thing or the energy had present its time and space and gravity. These three thing are matter on everything, In past, in presence and also in future.
When there is nothing there is space. Space make time and time make energy and energy make gravity. When time make energy energy make a light and that light become a big it blast and then the whole universe Exist. All are Exist with time and space.
Shall I begin with the Lorentz transform? We can then try to interpret it....
Or perhaps the Galilean coordinate system and Newton's laws of Motion?
Compare Newton's Law of Gravitation you quoted to Coulomb's law?
Just so we can do something besides quote Wiki, you might want to check out my .pdf
"The Creation of the Universe", where I derive the relativistic mass/energy equations and sho0w the significance of referring them to a coordinate system, where I tried to concentrate on the physics/philosophy in kind of a back-handed way. Also, the less "philosophical" derivation of the relativistic equations.
Then, what I'd like to discuss is how the so-called "Time Dilation" equation differs from the Lorentz transform, and more importantly, why? In my derivation of the Lorentz transform I used Peter Bergmann's derivation, with a slightly different take, just as my take is now slightly different...
I am personally fascinated by this - those guys were really bright.... And I find that I actually agree with Einstein, but it requires a lot of interpretation and foundational work (I had to go back to pre-calculus myself, which is why I got involved in the Math discussions, which has to be the dumbest thread in the whole history of man, but was kind of entertaining for awhile).
For gravity, one has to introduce the Minkowski metric, which (believe it or not) is based on STR..., so you have to understand STR first....
So... do you grok the equation:
BTW: Prof. Johnson resolved D'Alembert's paradox.
As for gravity, my theory is that it exists only because there is motion in the universe.
Quotes by Einstein:
The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction.
It is marvelous that man is capable of reaching such a degree of certainty and purity in pure thinking as the Greeks show for the first time to be possible in geometry.
Pure mathematics is, in its way, the poetry of logical ideas.
If the facts don’t fit the theory, change the facts.
One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly disco.
Mathematics are well and good but nature keeps dragging us around by the nose.
But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
But the creative principle resides in mathematics. In a certain sense, therefore, I hold true that pure thought can grasp reality, as the ancients dreamed.
How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom.
Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.