Electronic – How do compact AM radios establish a ground

That's a very very very very minimalist circuit and very 'laid back' construction. It will work with a suitably high impedance ear-piece and proper construction and enough transmitter power and close proximity and ... ie It MAY work but it's not surprising if it doesn't as there are too many potential pitfalls.

• The earpiece looks like it is low impedance - either 8 ohms or perhaps a few hundred ohms.

  Without a tuned circuit you need all the sensitivity and lack of loading that you can get. Use of a very very high impedance "crystal earpiece" will make a significant difference.

• Your general construction is excessively rough for what you are trying to do. You MAY make it work but one bad join may doom it and stability is unlikely.

• Your wiring lengths and stray capacitance and inductance are long for use at 145 Mhz.

• As MikeJ-UK noted in a comment - if your transmitter is FM (frequency modulated) then you will probably not hear anything as the diode acts to "recover" or "demodulate" the amplitude variations in the carrier wave of an AM (amplitude signal).

• Adding a tuned circuit at the frequency of interest - as seen in almost all crystal set designs you will see, is probably the single best improvement that you can make.

• Clip leads of the sort you are using usually use crimp construction. They can be high resistance or open circuit or have a thin skim of oxidation at the wire to clip contact so that you need a certain level of current flow before they will conduct.

  Soldering the core of the circuit with short lengths of wire is far preferable.

  Clip leads of the sort shown should ALWAYS be soldered at the wire to clip join. Failure to do this will give you many hours of harmless and unproductive fun. When I buy leads like this I put a loose knot in the wire and remove it once the lead has been soldered.

• The diode MAY be a 1N34a. That's a Germanium small signal diode. Rare and not cheap. More usual would be a 1N4148 or 1N916. Most small glass diodes are probably OK. Do NOT use a low Voltage power diode.(1N400x family etc)

• The "rabbits ears" antenna leg is OKish but a length of wire is just as good

• Power outlet ground MAY be safe as safe and MAY kill you when you put the earpiece in your ear.

Ground connection or referencing is used when it is used because long experience has shown it to be the best choice in practice. "Reinventing the grounding "wheel"" may have its place in some cases, but usually not. In many cases there are competing aspects, but the overall best result is gained by using ground. Power distribution systems are one such example.

Mains or grid voltage systems would be safer if the system was entirely NON ground referenced, and this is the principle that safety "isolation transformers" use BUT the moment that a fault fully or partially grounds one leg of the system anywhere on a circuit then the whole system becomes lethally dangerous to users.

Note that ONLY ONE tool should be used with an isolation transformer, and the transformer should be located near the tool. Using long cable runs after the transformer and two or more tools risks a fault to ground in one tool or wiring leaving the other unprotected.

The difficulty in keeping a system isolated is in practice (which is what counts) far harder than the issues caused by grounding. Some shipboard power systems do have both conductors floating relative to ship ground (= seawater potential when you are floating in salt water) BUT and fault to ground is dangerous, as above, ad great effort is made to track down and remove any ground faults. In a land based system that was not ground referenced, any fault to ground on the same phase would affect all users on the same phase. So a whole street of houses may be affected by a fault on one circuit in one house.

Once you have a ground referenced system the safety aspects of detection and management for individual circuits are easily handled. Earthed housings provide both protection and detection, fault currents flow to ground and can be either "encouraged" to allow easy fault termination (fuses) or detected at very low level (ELCB / GFI). Ground referencing is an overall positive in domestic power systems.

Few modern systems use ground as an actual conductor.
SWER (Single Wire Earth Return) power systems were much used at one time and are still used in some rural systems. I saw one here (NZ)some months ago but they are rare. They are in fact very useful and cost effective but are generally eliminated for reasons which often do not make technical sense. The cost of providing a good enough ground connection at each end is in most cases low compared to he cost of many km of adding an extra conductor.

19 kV SWER line:

Wikipedia SWER

SWER slidehow - good

SWER video - NZ

Superb SWER slideshow / tutorial

SWER - Australian experience with application to developing country use

SWER - Wikipedia

RF signals are often "launched" as imbalanced signals against a phantom image reflected in the ground. A typical quarter wave vertical radiator has an implicit image reflected in the ground plane. The tall towers of AM brodcast stations almost all use this system. There are economies in materials used compared with dipole or other antennas, radiation pattern is omnidirectional and radiation angles are suited to direct wave communications - most audiences are near the transmitter for AM broadcast stations.

• TV receiver antennas 9the traditional Yagi designs) and long distance broadcast stations used for intercontinental news etc often use beam or similar aerials instead. The HRH delta Loop non ground referenced antenna was developed specially for and from such applications.

In systems that need grounding, techniques have been developed to provide grounds which are adequately good to adequately minimise the effects of local conditions. Ground proper is of essentially zero resistance as it is of sensibly infinite size. Connecting the local ground to the actual ground is the challenge and methods and needs are well understood for each relevant application.