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accdd
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Does relativity imply that everything that goes at a constant velocity must not emit radiation of any kind?
I assume that you mean "constant velocity in an inertial frame". But such objects can emit radiation. For example, suppose you have a hot black-body traveling at constant velocity. Such an object will emit black-body radiation just as easily as one "at rest".accdd said:Does relativity imply that everything that goes at a constant velocity must not emit radiation of any kind?
The mere emission of radiation does not necessarily lead to something slowing down. If the emission is symmetric in the object's rest frame then it will not cause a decrease in speed in any other frame. The momentum will decrease, as will the mass, leading to constant speed.accdd said:If something emits radiation, does it slow down? If it slows down then it would not stay in its own Lorentzian frame.
There is no such thing as "constant velocity" in relativity. There is only velocity relative to something else. And in GR, where spacetime can be curved, even that concept is only valid locally; there is no invariant "relative velocity" between objects that are distant from each other.accdd said:everything that goes at a constant velocity
In the context of SR (flat spacetime), an object that emits radiation (unless the emission is isotropic) will of course have to recoil, for conservation of momentum. So yes, that object will have nonzero proper acceleration and will not be at rest in any inertial frame.accdd said:If something emits radiation, does it slow down? If it slows down then it would not stay in its own Lorentzian frame.
As long as the radiation emission is isotropic, yes, such an object can be at rest in an inertial frame. If the radiation emission is not isotropic, then the object will have nonzero proper acceleration and will not be at rest in any inertial frame.Dale said:Such an object will emit black-body radiation just as easily as one "at rest".
Yes, I was assuming that but not stating it explicitly. It is good to state it because it is not always true that it is isotropic. For example, the famous Pioneer anomaly is due to anisotropic thermal radiation.PeterDonis said:As long as the radiation emission is isotropic, yes, such an object can be at rest in an inertial frame. If the radiation emission is not isotropic, then the object will have nonzero proper acceleration and will not be at rest in any inertial frame.
An isolated electron cannot emit radiation. This is not so much forbidden by relativity (as we have seen) as it is forbidden by conservation laws. Of course, relativity is not independent of the conservation laws, so it isn’t a question that can be answered in a strict yes-no senseaccdd said:But if I observe an electron at a constant velocity relative to me I expect it to emit no radiation, otherwise it wouldn't stay in its Lorentzian frame. Is this valid for all particles? Is this something that relativity implies?
The theory of relativity is essentially a theory of spacetime. It does not in itself tell you what the laws of physics must be. It doesn't tell you that the electron is an elementary particle, for example. The laws of electromagnetism must be compatible with relativity, but they they are not determined by it.accdd said:Thank you all.
Objects composed of many particles can radiate without slowing down with respect to the observer.
But if I observe an electron at a constant velocity relative to me I expect it to emit no radiation, otherwise it wouldn't stay in its Lorentzian frame. Is this valid for all particles? Is this something that relativity implies?
Well ... if you place some reasonably restrictive constraints ... relativity essentially spits out electromagnetism as the simplest relativistic force field.PeroK said:The laws of electromagnetism must be compatible with relatitivy, but they they are not determined by it.
Is there a branch of physics that studies what is possible to do or not to do starting from relativity? for example to obtain electromagnetism as you say.Orodruin said:Well ... if you place some reasonably restrictive constraints ... relativity essentially spits out electromagnetism as the simplest relativistic force field.
Do you mean the simplest relativistic vector force field? Based strictly on special relativity, I would argue that simpler yet is the relativistic massless scalar force field (although evidently no such field exists in nature).Orodruin said:... relativity essentially spits out electromagnetism as the simplest relativistic force field.
You are thinking a step too far ahead here in terms of mediators of gauge theories. I am talking exclusively of a force field here. If you want a particle to experience a force linear in the field and at most dependent upon scalar properties of the particle itself and its state of motion (i.e., 4-velocity) and at the same time not to change the mass of the particle, then the lowest tensor rank field you can use is an antisymmetric rank 2 field. This essentially gives you the Lorentz force law. The dynamical behavior of the field is a bit less straightforward but can be argued to at least some extent.renormalize said:Do you mean the simplest relativistic vector force field? Based strictly on special relativity, I would argue that simpler yet is the relativistic massless scalar force field (although evidently no such field exists in nature).
Thanks for detailing your criteria for singling out the electromagnetic force field in special relativity. But I'm still not sure that E&M is unique in this respect. According to Jackson, "Classical Electrodynamics (2nd edition)" section 12.2, it's possible to exponentially couple a scalar field ##\phi## to a point particle to get the covariant equation of motion ##m\frac{dU^{\alpha}}{d\tau}=g\left(\partial^{\alpha}\phi-U^{\alpha}U_{\beta}\partial^{\beta}\phi\right)##. This describes a particle of 1) mass ##m## experiencing a force that is 2) linear in the scalar field and 3) depends only on the particle's position and velocity. Doesn't this meet all your requirements?Orodruin said:If you want a particle to experience a force linear in the field and at most dependent upon scalar properties of the particle itself and its state of motion (i.e., 4-velocity) and at the same time not to change the mass of the particle, then the lowest tensor rank field you can use is an antisymmetric rank 2 field.
Consider the object in its rest frame. In which direction does the radiation point?accdd said:Does relativity imply that everything that goes at a constant velocity must not emit radiation of any kind?
This construction contains a coupling to the derivative of the field so it is not the force field itself. It is also not at most linear in the 4-velocity.renormalize said:Thanks for detailing your criteria for singling out the electromagnetic force field in special relativity. But I'm still not sure that E&M is unique in this respect. According to Jackson, "Classical Electrodynamics (2nd edition)" section 12.2, it's possible to exponentially couple a scalar field ##\phi## to a point particle to get the covariant equation of motion ##m\frac{dU^{\alpha}}{d\tau}=g\left(\partial^{\alpha}\phi-U^{\alpha}U_{\beta}\partial^{\beta}\phi\right)##. This describes a particle of 1) mass ##m## experiencing a force that is 2) linear in the scalar field and 3) depends only on the particle's position and velocity. Doesn't this meet all your requirements?
I grant you that I should have referred to ##\phi## as the potential for the scalar force-field ##\partial_{\mu}\phi##, analogous in E&M to the four-vector potential ##A_{\mu}## giving rise to the antisymmetric-tensor force-field ##\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}##. (Each potential must of course exist in order to give dynamics to their respective force fields using the principle of least action.)Orodruin said:This construction contains a coupling to the derivative of the field so it is not the force field itself. It is also not at most linear in the 4-velocity.
This is a good point and perhaps choosing EM was not the best example. More generally, the laws of physics are not implied by the structure of spacetime - otherwise, the existence and form of dark matter would be a case of logical deduction.Orodruin said:Well ... if you place some reasonably restrictive constraints ... relativity essentially spits out electromagnetism as the simplest relativistic force field.
Of course that's true. On the other hand a lot about the form the physical laws must take given a spacetime model is determined by the symmetries of this spacetime model. The symmetry group of Minkowski space is the Poincare group (generated by translations, rotations and boosts). This determines to a large extent the mathematical structure of physical models describing nature. Since it's an affine pseudo-Euclidean space the natural description is in terms of tensors (including of course scalars and vectors).PeroK said:The theory of relativity is essentially a theory of spacetime. It does not in itself tell you what the laws of physics must be. It doesn't tell you that the electron is an elementary particle, for example. The laws of electromagnetism must be compatible with relativity, but they they are not determined by it.
Constant velocity motion in relativity refers to the movement of an object at a constant speed in a straight line, as observed from a reference frame that is moving at a different velocity. This concept is a fundamental principle in Einstein's theory of special relativity.
In classical mechanics, the laws of physics are the same for all observers regardless of their relative motion. However, in relativity, the laws of physics appear differently to observers moving at different velocities. This is known as the principle of relativity.
One of the key effects of constant velocity motion in relativity is time dilation, which causes time to appear to pass slower for objects moving at high speeds. This can also lead to length contraction, where objects appear shorter in the direction of motion. Additionally, there may be changes in the perceived mass and energy of an object due to its motion.
According to Einstein's theory of special relativity, the speed of light is constant and the same for all observers, regardless of their relative motion. This means that no matter how fast an observer is moving, they will always measure the speed of light to be the same value.
Constant velocity motion in relativity has many practical applications, such as in the design of GPS systems and particle accelerators. It also helps explain phenomena such as the twin paradox, where one twin ages slower than the other due to their different velocities. Furthermore, relativity plays a crucial role in understanding the behavior of objects moving at high speeds, such as in space travel.