Without passport stamps, can my country's authorities still know what countries I've visited?

Of course, the real answer is don’t do it.

As usual for this type of questions, the answer is ambiguous. Will they know right away with the info available at the tip of their fingers? Probably not. Can they find out if they really want to? Nearly certainly. With all sorts of levels in between.

Whether you want to or not, you leave a LOT of traces:

• flights on the same PNR will almost certainly be available to them easily
• flights booked with a frequent flyer number will leave a trace
• flights booked using a local credit or debit card will leave a trace
• ditto for hotels, restaurants and any other expenditure
• your phone carrier will know
• if they examine your phone there are good chances there will be traces (like Google maps history and tracking)
• of course all your social media posts

Some of that information may be difficult for them to get. Some maybe extremely easy. Depends on local laws, arrangements in place with airlines, and other companies, whether they can get access to your phone (for completely different reasons of course)… and of course any information you may give them without even realising.

Of course if you manage to have a total blackout on what you did during that time that will look even more suspicious.

So don’t even try. Maybe you’ll get away with it. But if you don’t it can end quite badly.

TL;DR: The government may not know outright, but they may find out if they have any reason to look into you.

Officially there may not be a way for them to know when you land, if your passport isn't being scanned anywhere.

However, if you cause an infection outbreak and the epidemiological investigation concludes that you're the source and that you've lied/concealed information on the entry forms - you may be subject to some heavy penalties of which 5000ILS fine would only be the beginning, since technically you'd be committing a crime (things have happened before).

Since someone asked for statistics in the comments, here are some:

• According to the State Comptroller of Israel, in about 50% cases the source of the outbreak is identified (i.e.: they find the person who contracted the disease first).
• The Ministry of Health publishes weekly reports on the epidemiological investigations, which may be very detailed. Note that the actual investigation is conducted by the local authorities and the military (????? ?????), with some help from the police and the internal security (??"?). You don't want to mess with them.

Some countries share information (see the Five Eyes agreement) for example. It's not universal though. However, my mother was stopped in Singapore years ago (late 90s) and the officials were able to pull up her recent travel history on their system - NZ, Aus and South Africa.

I'd presume it's gotten better since, but for example, many visitors to Israel don't get a stamp so that they can travel to say, Dubai later on the same passport without issues.

In practice, our advise on Travel.SE is to just follow the law, no matter how silly or illogical the law is. The reason is that doing otherwise means you're trading a very small upside (skipping a bit of quarantine) for a massive downside (big fines, potential criminal record, social shaming, etc). No one can give you exact percentage odds of getting caught but at the end of the day its easier to just cancel your travel or do the quarantine instead.

That being said, lets think of how the government could find out.

1. They could use fancy Mossad databases to track down your movements, though the odds of this are basically nil unless you're a major person of interest.
2. They might do a successful contact tracing and figure out that you've started a chain of Omicron cases, but given the ongoing explosion of Omicron cases in Israel the odds of this are basically nil too.
3. They could ask the Interpol or some other international partner and track down your movements down to a minute, but again - this is insanely unlikely for 99.9% of the population.

So how will you most likely get caught? Same way a huge chunk of crimes has been caught since the dawn of time - by having someone report you to the police. An angry ex-girlfriend, a random Instagram subscriber, a disgruntled business partner, a nosy neighbor - anyone could notice you've been to country X but then never reported to quarantine. The police might not necessarily investigate the report but if they do, you'll be in a world of trouble.

Is there any possible way for Israeli authorities to know I've been to the second country.

Yes. They can ask you where you've been.

They have other ways, mentioned in other answers, but asking you where you have been is much more likely to happen than those other ways.

I don't know what the consequences for you are if:

• You lie and they find out.
• You lie, they find you've lied, and they find out you haven't respected quarantine requirements.
• You lie, they find you've lied, they find out you haven't respected quarantine requirements, and they find out you've brought the next new variant into the country.

Please don't lie.