# Can you shake a charged object fast enough to create light?

Electromagnetic radiation (a photon) is generated by an oscillating charged particle. Therefore, is it possible to vibrate an object at say 585 THz and create a green light source?

Alternatively: what's the highest frequency we've achieved on a macroscopic scale?

• By macroscopic scale, you meant to move a charge, not with currents in a circuit, but mechanically ? Jan 28, 2021 at 21:41
• Glow stick? Warm it up a little for faster result! Jan 29, 2021 at 6:51

Ok, I will start. Quartz oscillators run up to 300 MHz according to Wikipedia. With the speed of sound in quartz being 5800 m/s, the wavelength in the material is then $$\lambda_q = v/f \approx 20 \mu$$m. It would be difficult to make a resonator that moves like the tines of a tuning fork much smaller and faster than that.

Another answer mentions the excitation of sound waves in piezoelectric materials at 70 GHz, so at a wavelength of about $$0.1 \mu$$m, maybe not quite on a macroscopic scale anymore.

In theory from what I know when you shake/accelerate and decelerate a charge succesively it'll radiate through Bremsstrahlung radiation, as in a synchroton accelerator. The frequency of the radiation emmited increases as the charge energy becomes higher, so if you shake with enough energy I don't see what could stop you from having a green light source. Hope this was helpful :)

Edit: I forgot the macroscopic object point on your question. But I don't think that is possible, once the Bremsstrahlung is inversely proportional to the mass of the charge in question you'd need a lot of energy being transfered to the object, entering the high-energy realm, which means relativity.

And there are no rigid bodies in the relativistic limit for one simple reason, light takes time to travel, so when one part of your object is boosted near a relativistic limit, it'll take time for the surrounding particles of your object to receive the information(electromagnetic information through photons, with velocity $$c$$) that the first particle moved.

But we are in relativistic velocities so in the interval of time needed to the surrounding particles to receive this information, the first particle is already in another position, and thus our object is being deformed, it's not anymore a rigid body.

I didn't carry the calculations exactly, but from orders of magnitude I think it's enough to see that for a rigid body it's needed way more energy to accelerate it enough to emit Brehmsstrahlung radiation, so that we fall in relativistic limits.

• Sure, electrons in an undulator or a wiggler produce x-rays. Good answer, but electrons do not count as the OP's macroscopic objects, I guess.
– user137289
Jan 28, 2021 at 22:16
• Oh sure, my mistake on that, thanks for clarifying the intention of the question. Jan 28, 2021 at 22:23

First, let's have a look at the amplitude $$A$$ of the movement. Assuming you want to create monochromatic light, the movement is of the form $$x(t) = A \sin (\omega t)$$. The velocity is then $$\dot{x} (t) = A \omega \sin (\omega t)$$. We also know that massive particles can't move faster than the speed of light, so $$A \omega < c$$. This means that the maximum amplitude of movement to create a wave of frequency $$\omega$$ is $$A < \frac{c}{\omega} = \frac{\lambda}{2 \pi}$$, where $$\lambda$$ is the wavelength of the emitted light.

This tells us that high-frequency electromagnetic waves are created by small charge displacements. Typically, optical light is emitted by molecules or atoms in which the cloud of electrons oscillates with respect to the nuclei/nucleus.

To actively shake a charged object very fast you always need some control over it which changes polarity at the frequency $$\omega$$ the object is supposed to move. Normal motors can go up to a few kHz, piezoelectric actuators typically achieve frequencies up to a few GHz. Everything which controllably oscillates at higher frequencies to the best of my knowledge only moves the electrons in the material, but leaves the nuclei stationary.
There are various difficult ways to generate waves of THz frequencies, and very established ways to create optical frequency waves, for example with lasers. I think this is not anymore answering the question in the way you asked it, but strictly speaking if you use a laser to drive the eletrons of an atom into motion, the light which is emitted from this motion is created by an oscillating charge.

In some sense, this is indeed the working principle of modern accelarator-based x-ray sources. There, an electron beam (the charge in the question) is accelarated to high velocities and then "shaken" by so-called wigglers or undulators. The latter are essentially alternating magnets. See this picture from wikipedia:

This is indeed also the principle used at free-electron lasers and x-ray free electron lasers, so it can be used to produce very high frequency radiation. The record (as of April 2020) currently seems to be a photon energy of 25 keV corresponding to $$\lambda = 0.05~\mathrm{nm}$$ wavelength or a frequency of

$$f = \frac{c}{\lambda} = 6.0 \cdot 10^{18} \mathrm{Hz} \,.$$

Note, however, that the wavelength is not equal to the shaking wavelength here. Instead, for small wiggler strength parameter (see wiki), the wavelength is given by

$$\lambda_\mathrm{radiation} = \frac{\lambda_\mathrm{shaking}}{2\gamma^2} \,,$$

where $$\gamma$$ is the Lorentz factor of the accelerated electrons. So essentially the radiation wavelength is proportional to the shaking wavelength, but you have an additional Lorentz boost factor due to relativistic effects.

So a fast charge is shaken here to produce light of very high radiation. Not sure if that qualifies as "shaking" as defined by the OP though.

• This is very interesting! This doesn't answer the question of this post, but I stumbled across undulators recently and this helps me understand how x-rays are harnessed from particle accelerators. Thanks! Jun 5, 2021 at 21:29