Constant Velocity Motion in Relativity: Radiation Effects?

[accdd]

Does relativity imply that everything that goes at a constant velocity must not emit radiation of any kind?

 

[DaveC426913]

No. What makes you think so?

 

[accdd]

If something emits radiation, does it slow down? If it slows down then it would not stay in its own Lorentzian frame.

 

[vanhees71]

We need a more specific description of the system you are considering. If you have a single point charge in otherwise empty space, of course nothing radiates, and it moves with constant velocity wrt. an inertial reference frame, which you can choose as the rest frame of the particle, where it is immediately clear that nothing radiates.

 

[DaveC426913]

Slow down with respect to what?

To a muon particle, you are currently moving at a substantial fraction of c. You are emitting radiation too. Will you speed up to the muon's FoR?

 

[Dale]

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".

If something emits radiation, does it slow down? If it slows down then it would not stay in its own Lorentzian frame.

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.

 

[PeterDonis]

everything that goes at a constant velocity

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.

 

[PeterDonis]

If something emits radiation, does it slow down? If it slows down then it would not stay in its own Lorentzian frame.

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.

In the context of GR (curved spacetime), there are no global inertial frames. But an object that emits non-isotropic radiation will still have nonzero proper acceleration, because conservation of momentum still has to hold locally.

 

[PeterDonis]

Such an object will emit black-body radiation just as easily as one "at rest".

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]

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.

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.

 

[vanhees71]

A famous example for that is the solution of the puzzle concerning the Pioneer anomaly.

https://en.wikipedia.org/wiki/Pioneer_anomaly#Explanation:_thermal_recoil_force

 

[accdd]

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? Is it necessary to have at least acceleration to have radiation? For each type of particle?

 

[Dale]

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?

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 sense

 

[PeroK]

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?

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.

 

[Orodruin]

The laws of electromagnetism must be compatible with relatitivy, but they they are not determined by it.

Well ... if you place some reasonably restrictive constraints ... relativity essentially spits out electromagnetism as the simplest relativistic force field.

 

[accdd]

Well ... if you place some reasonably restrictive constraints ... relativity essentially spits out electromagnetism as the simplest relativistic force field.

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.

 

[renormalize]

... 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]

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).

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]

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.

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?

 

[Vanadium 50]

Does relativity imply that everything that goes at a constant velocity must not emit radiation of any kind?

Consider the object in its rest frame. In which direction does the radiation point?

 

[Orodruin]

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?

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]

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.

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.)

But in my defense, your original "reasonably restrictive constraints" said nothing about needing the force to be "at most linear linear in the 4-velocity". In my view, because the equation of motion of a free particle in a general coordinate system takes the form $m\frac{dU^{\alpha}}{d\tau}=-m\varGamma^{\alpha}{}_{\mu\nu}U^{\mu}U^{\nu}$ even in flat-space, it seems quite reasonable in special relativity to consider hypothetical force-fields quadratic in the particle velocity.

So I concede that one can create a sieve of constraints for a relativistic force field so fine that only the electromagnetic field can pass through it, but I question if all those constraints are truly reasonable and necessary in special relativity.

 

[PeroK]

Well ... if you place some reasonably restrictive constraints ... relativity essentially spits out electromagnetism as the simplest relativistic force field.

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.

 

[vanhees71]

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.

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).

Taking in addition the observation that the physical laws can be described by the action principle you can use Noether's theorem to derive the conservation laws due to the part of the symmetry group that is smoothly connected with the group identity, the proper orthochronous Poincare group $\text{ISO}(1,3)^{\uparrow}$, and these are energy, momentum, and angular momentum (due to the homogeneity of time and space and the isotropy of spac) as well as the center-of-energy theorem (due to invariance under Lorentz boosts).

Taking also into account that matter must be described by a quantum theory, the group gets extended to its covering group (i.e., instead of $\text{SO}(1,3)^{\uparrow}$ you have to use $\mathrm{SL}(2,\mathbb{C})$) and possibly also central extensions, but in the case of the Poincare group there are none non-trivial central extensions. The upshot is that this adds to the tensors also spinors of various kinds (Weyl, Majorana, Dirac).

So a lot of the fundamental laws of nature can be deduced from the symmetries underlying the spacetime description. On the other hand you have of course a lot of freedom to build models, and at the end the observation of nature must decide, which describe our universe and which are mathematical possibilities "not realized in nature".