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What in the mathematics of the derivation of special relativity limits the model to inertial frames? How is an inertial frame defined in the context of the derivation?
I'm not aware that there IS any such thing as "the derivation of special relativity". Special Relativity is a theory (not an equation) based on two postulates, the first of which (The Principle of Relativity) is that it is talking about things in uniform motion relative to each other (and this generally means inertial frames of reference although as ibix states, it COULD be that two objects are both accelerating but not relative to each other)redtree said:What in the mathematics of the derivation of special relativity limits the model to inertial frames? How is an inertial frame defined in the context of the derivation?
What is derived are the Lorentz transformations, and those are defined relative to inertial frames - exactly as the "Galilean transformations" of classical mechanics. Very likely your question is therefore more basic, and belongs in the classical physics forum. Can you answer the question what in the mathematics of the derivation of classical relativity limits the model to inertial frames? How is an inertial frame defined in the context of that derivation?redtree said:What in the mathematics of the derivation of special relativity limits the model to inertial frames? How is an inertial frame defined in the context of the derivation?
Do you have a source for such a derivation?redtree said:Special relativity can be derived without reference to either inertial frames or the speed of light. In fact, special relativity is nothing more than an identity and can be derived as such.
An inertial reference frame is one in which objects at rest remain at rest and objects in motion continue to move in a straight line atspeeteady speed. Spacetime Physics by Taylor and Wheeler has some very readable and poignant discussions of inertial reference frames.redtree said:What in the mathematics of the derivation of special relativity limits the model to inertial frames? How is an inertial frame defined in the context of the derivation?
redtree said:Why does special relativity apply to acceleration relative to the inertial frame (proper acceleration) but not gravitational acceleration? What can't SR describe accelerations of the inertial frame?
vanhees71 said:This is often misunderstood. Even in some (minor) textbooks you can read that SR can't handle non-inertial frames, which is of course wrong. With the same right you can argue that you can't handle non-inertial frames in Newtonian physics, which is of course also wrong.
Mister T said:That's a good point. Newton's Laws (within their limits of validity) are valid only in inertial reference frames. Certainly one can use Newton's Second Law to describe motion in non-inertial frames, but that involves introducing forces that violate Newton's Third Law.
Mister T said:That's a good point. Newton's Laws (within their limits of validity) are valid only in inertial reference frames. Certainly one can use Newton's Second Law to describe motion in non-inertial frames, but that involves introducing forces that violate Newton's Third Law.
Isn't part of the confusion of Special Relativity's ability to handle non-inertial frames historical? What I mean is that didn't Einstein, after developing Special Relativity, immediately set to work on what became General Relativity and in the process introduce the formalism of non-inertial frames? Of do I have it wrong?
Presumably a typo, but that should be ## \frac{DV}{d\tau}##, where ##\tau## is proper time.stevendaryl said:[itex]m \frac{dV}{dt} = F[/itex]
DrGreg said:Presumably a typo, but that should be ## \frac{DV}{d\tau}##, where ##\tau## is proper time.
stevendaryl said:No, it's not a typo. I was talking about Newtonian physics, where [itex]t[/itex] is universal.
Special relativity is a theory developed by Albert Einstein in 1905 that explains the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, regardless of their relative velocity. This theory also introduces the concept of the speed of light being the maximum speed at which all matter and information can travel.
Inertial frames are frames of reference that are not accelerating and are in a state of constant velocity. According to special relativity, all inertial frames are equivalent and there is no preferred frame of reference. This means that the laws of physics should appear the same to observers in different inertial frames.
Special relativity challenges the classical understanding of space and time, which was based on the ideas of Isaac Newton. It introduces the concept of spacetime, where space and time are not separate entities but are interconnected and affected by the presence of mass and energy. It also challenges the idea of absolute time and instead proposes that time is relative and can be perceived differently by different observers.
Special relativity has many practical applications, including GPS technology, nuclear energy, and particle accelerators. The theory is used to account for the effects of time dilation on GPS satellites, which travel at high speeds relative to the Earth's surface. It also plays a crucial role in understanding nuclear reactions and the creation of energy in stars. In addition, particle accelerators use special relativity to accelerate particles to near the speed of light in order to study their behavior.
Special relativity only applies to inertial frames, while general relativity extends the theory to include non-inertial frames as well. General relativity also takes into account the effects of gravity on the curvature of spacetime. It is a more comprehensive theory that explains the relationship between gravity, mass, and energy. Special relativity can be seen as a special case of general relativity when gravity is not a factor.