6 ms·

So... Special relativity is called "special" because it specifically assumes no acceleration and therefore, no force. That formula you have is an approximation

So... Special relativity is called "special" because it specifically assumes no acceleration and therefore, no force. That formula you have is an approximation for "small" forces. General relativity is what actually explains space with acceleration (using Riemann Geometry, another fascination and extremely complex topic in of itself relying on tensor calculus, which is another fascinating and extremely complex topic in of itself). Secondly, the Lorentz transformation is critical to special relativity, because that is what gave rise to the entire theory and also because the Lorentz transformation is exact (up to QM effects and 0 acceleration). Also, the Lorentz transform is sufficient to derive the result e = mc^2 among many other useful results on momentum and particle collisions (or at least the aftereffects thereof, since we can have no forces) which is why special relativity is even taught in isolation. As to the textbooks, all I can say is that you haven't come by the right textbooks yet. I would advise reading the Feynman's lectures on physics (all 3 volumes). Expensive but worth it and if you want, you could probably find free pdfs online. FLs does indeed go into the gory details of special relativity (v1 I think) and even shows how to derive most of the useful results including (I think) information on how to derive the Lorentz transformation from the Special Relativity's base assumption: the speed of light is constant in all time frames. ENM along with several applications is also discussed in FLs (v2 I think). FLs V3 covers QM is great detail (well... the parts that we humans can solve mostly). Another very good book on ENM would be Electricity and Magnetism by Purcell, Berkley Physics Course Vol. 2. Oh btw. the central assumption of General Relativity is that force and gravity are just 2 different manifestations of the same phenomenon. Thus, for very weak gravitational fields, you could actually use the formula you have. Just that it would not be very useful because a) you would have to interpret it as constantly changing time frames over small time intervals, and b) because I don't think the Earth's gravitational field (or the moon's) is weak enough to justify the approximations inherent in your equation. A note on finding good textbooks: Pick a good university. Any good university (I would advise Caltech but thats because thats where I study) and chances are very good that said universities will publish the course textbooks for their classes. Some will even publish the homework assignments and solution sets along with lecture notes. Eg. http://www.pma.caltech.edu/GSR/physicscourses.html http://www.pma.caltech.edu/GSR/physicscourses.html is the place where CIT has currently placed a convenient listing of all the physics courses offered with links to their web pages which contain among other things: the textbooks, syllabus, and in most cases, the homeworks for the class. Finding textbooks from there shouldn't be very difficult.

cool-RR 18y ago
There are many objections I have to raise to your post. But let's just look at the first thing you say. You say that SR can't handle acceleration. I disagree. Let's examine this issue. My first question about it is: Assume you have a "twin paradox" situation. One twin stays on earth for a year, while the other twin goes somewhere far away in space and returns, in relatvistic speed. The travelling twin accelerates smoothly in his journey. Given the twin's trajectory, the mission is to calculate in how many years he has grown old. Do you think that SR can't handle this case? Second question. Observe the Lienard-Wiechert potentials. They say the exact value of the EM field at any given point. What is the significance of the value of the field E, if not the chrage of the body times the force that acts on it? If it does mean that, then "force" in which context, if not SR? Newtonian? GR?
- newt0311 18y ago
  The twin paradox cannot be handled by SR. The difference in aging comes about due to time dialation caused by the differential acceleration that the twins experience (the twin in the spaceship is accelerated and the other is not). SR can be used to judge the middl period after the acceleration but it will not give any useful information because you can always switch viewpoints. If you have two bodies moving at some relative velocities, both can claim that the other is moving slowly in time. The mathematics of communication and speed of light work out so that this system is consistent. The difference in measured time comes from the acceleration that one of the bodies must undergo to enter the same time frame as the other. Secondly, electric fields have intrinsic effects as in EM radiation (colloquially known as light) and need not apply any force to have effects. The movement of emitters of electrical fields through space and acceleration thereof actually give rise to magnetic fields. Read Berkley Phys. Vol. 2 ch. 5 which shows how this happens in the framework of SR. It later hints how tensors can be used to generalize this result to GR. So... in response to your question, if force is applied, either it must be approximated in a Newtonian or SR context, or GR must be used in its full generality. Usually, the forces and particles involved are sufficiently small that approximations work (see success of Newtonian mechanics), but that is not the general case. Also, very common is the tendency to derive general results and then use them is special cases. Maxwell's equations are an excellent example. They refer only to EM fields and are exact (uptil QM of course).

cool-RR 18y ago

There are many objections I have to raise to your post. But let's just look at the first thing you say. You say that SR can't handle acceleration. I disagree. Let's examine this issue. My first question about it is: Assume you have a "twin paradox" situation. One twin stays on earth for a year, while the other twin goes somewhere far away in space and returns, in relatvistic speed. The travelling twin accelerates smoothly in his journey. Given the twin's trajectory, the mission is to calculate in how many years he has grown old. Do you think that SR can't handle this case? Second question. Observe the Lienard-Wiechert potentials. They say the exact value of the EM field at any given point. What is the significance of the value of the field E, if not the chrage of the body times the force that acts on it? If it does mean that, then "force" in which context, if not SR? Newtonian? GR?

newt0311 18y ago
The twin paradox cannot be handled by SR. The difference in aging comes about due to time dialation caused by the differential acceleration that the twins experience (the twin in the spaceship is accelerated and the other is not). SR can be used to judge the middl period after the acceleration but it will not give any useful information because you can always switch viewpoints. If you have two bodies moving at some relative velocities, both can claim that the other is moving slowly in time. The mathematics of communication and speed of light work out so that this system is consistent. The difference in measured time comes from the acceleration that one of the bodies must undergo to enter the same time frame as the other. Secondly, electric fields have intrinsic effects as in EM radiation (colloquially known as light) and need not apply any force to have effects. The movement of emitters of electrical fields through space and acceleration thereof actually give rise to magnetic fields. Read Berkley Phys. Vol. 2 ch. 5 which shows how this happens in the framework of SR. It later hints how tensors can be used to generalize this result to GR. So... in response to your question, if force is applied, either it must be approximated in a Newtonian or SR context, or GR must be used in its full generality. Usually, the forces and particles involved are sufficiently small that approximations work (see success of Newtonian mechanics), but that is not the general case. Also, very common is the tendency to derive general results and then use them is special cases. Maxwell's equations are an excellent example. They refer only to EM fields and are exact (uptil QM of course).