Non-traceable radio emitters

I remember an episode of the live action TMNT series in which Mike had a pirate radio station. To make detection harder, the transmitter was in his truck.

I believe everyone here has been thinking about stationary radio sources so far. By keeping your transmitter moving, and going dark as needed, you may avoid detection for a while longer. They will only be able to track you while you are transmitting, and by the time they arrive where they thought you were, you may be long gone.

There are several techniques.

first physically hide the transmitter and antenna. While this is hard for large antennas, it becomes more feasible at higher frequencies. I read a story about a HAM radio fox hunt where the fox (transmitter / antenna) was hidden in a coed's swim suit as she was sunbathing in a park. The hunters knew the transmitter was in the park, but no one dared to ask the young lady if they could inspect her suit.

Use low power. Low power signals are hard to detect. This does limit how far the signal can reach and to an extend how much information it can carry.

Spread spectrum / frequency hopping. To partially overcome the information issue, broadcast using several frequencies at the same time. You can lower the signal strength down to the noise level or even a bit below. This works best with digital data and error correction.

Directional antennas. By putting the majority of the RF in a narrow lobe, you will make it harder for others who are not in lobe to detect the signal.

Scattering, sometimes you can effectively "bounce" a signal of off another object like a bridge or building. doing this does require higher power as the reflected signal loses much of its energy.

Final hijacking. This would be illegal, but inject your signal into another broadcast system so it is coming from their equipment. it is easier to hide your tap on their hardware than it is to hide your broadcast.

Another possibility to look into is meteor burst communication. This is a well-established technology. You beam a VHF signal up into the sky, it bounces off a meteor trail, and your recipient picks up the reflected signal. Since transmission is upwards, picking up the transmitter's location would require being above the transmitter at the time (making certain assumptions about directionality).

There is a short article in NSA Cryptologic Quarterly and a Navy Postgraduate School thesis from 1989. An article I have been unable to locate online is: Elliott, Ronald D. "Meteor Burst Communications in Tactical Intelligence Support," SIGNAL, November 1986, pp. 80-88.

Amateurs, it seems, tend to experiment with lower frequencies, which may have implications for directionality: see, for example, this page. The RSGB also has a page.

It would be interesting to know if anyone on this forum has had any experience with this. It may be well known.

at least in the world where I come from

Assuming this is the world of arrogant computer security experts (sorry I'm a bit allergic to this):

Well, unlike computers, physics wasn't designed by humans.

So, any signal that contains significant information needs to contain significant power (that's a direct result of Shannon capacity), and if it has significant power, it's also localizable.

Of course, localization resolution is proportional to wavelength. But, so are antennas. So, while you can not be very sure from where an extremely low frequency (ELF, typically used for communication to submerged submarines) transmission came from, but once you look at an aerial picture, you will notice the 500 km long antenna in the Russian forest...

Rodrigo recommended "Burst transmission", but that's really no solution. If I can detect it as anything but noise with a high probability with multiple receivers, then I can also localize it. This is done, and has been done, since the 1970s for bursty military transmissions in HF bands (because they reach very far on earth). For higher frequency signals, you really don't need state actor equipment: a two- or better four-channel MIMO receiver allows you to put an unambiguous direction on where a signal came from. Use two of these, and you know where a transmission came from. In fact, a transmission being a very short burst implies a high bandwidth, and that is good for location accuracy. (You need good SNR for low estimator variance, on the other hand, so there are limits. It's just not as easy as "use a bursty transmission scheme".)

So, your only choice is to make a signal that someone can't detect as being anything but noise, not even if he correlates multiple observations. Sadly, such signals have practically no information content.

The only thing you can do is hope that you find a part of the spectrum where the propagation properties are so random, and so different in different directions, that the probability of simultaneous detection at multiple points approaches zero. Good luck with that; in essence, that channel would have what is called a "secrecy rate" in physical layer security research (i.e. an observation of one channel doesn't give you all the bits of information in the entropy of a different channel), and we're talking about secrecy rates of < 100 bits per minute for indoor channels. That is an upper bound for how much information you could send there, without giving away information about the channel, and thus your location.

TL;DR: Nope.