Can we reach deep meditative states without teachers?

In my opinion, you can't do this unless you are a Paseka Buddha. Perhaps you have given the reasons in your own post.

Even Gautam Buddha was searching for a teacher. What to speak of us! We need teachers for ordinary material education and spiritual teachings are on the highest level of intelligence.

A teacher can also be in the form of a book. However, one who has extensive experience of serving a spiritual teacher is qualified to make advancement by reading a book. So you definitely need a teacher.

What the Buddha said in AN2.126 is:

“There are two conditions for the arising of right view. What two? The words of another and proper attention. These are the two conditions for the arising of right view.”

For more information, consult AN5.26, which describes "five opportunities for freedom" with details about the various circumstances of practice with and without teachers. The first opportunity is to have a good teacher. But good teachers are not always available, so the question you ask is quite relevant and the answer is found in the other four opportunities.

With internet one is not really without a teacher and one should look for people who have something you want and who are teaching how to develop those very qualities.

Of course a person could isolate themselves and experiment extensively with varying results according to the variety of developments which one could devlop. There is no cap on developments which are freely and practically available tl the reader; other than becoming a Buddha, a spiderman and such effective restrictions. In as far as deep meditative states there are no restrictions on the lay community as a whole.

One would attain in accord to the directed effort. Most teachers still teach based on their learned expression and both meaning and expression will vary among teachers according to their development. Therefore if one finds a teacher for something particular it is great to learn those particulars but if one knows what the particulars and only effort is to be put in then assuming no further motivation is required one is doing this on one's own.

Yes, you can reach higher states and if you reach enlightenment without a teacher that means you're a paccekabuddha. The appearance of a pacceka-buddha isn't that uncommon and many can arise at once.

It seems that paccekabuddhas usually encounter sammasambuddhas in some past existence and have developed certain kamma.

The majority of people regardless of what they try won't be able to reach certain states without a teacher because of their kamma. The majority of people I encounter do sinful deeds unknowingly and think of themselves as good people.

The practice of metta (loving-kindness) seems to be only slightly below the achievement of the jhanas so if having difficulty with training then practice metta, virtue, and generating good kamma.

“Bhikkhus, whatever grounds there are for making merit productive of a future birth, all these do not equal a sixteenth part of the mind-release of loving-kindness. The mind-release of loving-kindness surpasses them and shines forth, bright and brilliant." (Iti 27)

I'm not sure if the arahants disappeared but I feel that they did around the same time predicted (500 years after the parinibbana).

Without arahants, paccekabuddhas, or a sammasambuddha existing in the world the dhamma is lost.

The time-period we exist in now is more fascinating than ever because higher mathematics and the scientific method exists now (since around the 17th-18th century, it did not exist for most of history).

So if a fully enlightened being arises now and people question him it will likely shock everyone.

I personally believe meditation is about practice and learning through Insight as a result of what you experience. A guide is useful but I always wonder who taught the first person who ever meditated how to meditate. That's a bit like Adam being depicted with a belly button on paintings.

My first experience of a persistent inner light was aged 10 and no one taught me to experience that. I was intrigued and aged 71 that light still appears regularly. I don't say that it's anything special, it just is there.

I then learned somehow that focusing on something brings relaxation and was shown how to focus on the breath at the nostril tip, colder as it passes in and warmer as it passes out across the membrane at the tip of the nostril. I relaxed and persisted and someone said to look for joy and it was there, hiding all the time and so glad to meet me it swelled into something more easily perceived, and so on...

What I'm saying is go explore, use a map by all means but remember that a map is not the territory.

The question is if you don't know how to build a car can a regular Joe build a car. Yes but it will be much harder if that person has no idea what they're doing prior. The better truth is "No" you should get instruction from a monk or true Buddha if you're lucky enough to find them. "Lucky" here's the thing if you're getting blissful release from meditation that fine and dandy. But that's not what you're text is suggesting your looking for. Your chasing a high. It's ok to peruse directions like this but you trade your growth and potential. The stick comes from the supernatural power one gets or that runners high one discovers. Generally speaking satori comes after kensho and men don't grasp kensho as fast as women. What I'm saying is you can't have Chan realisation without one. They don't take on human beings that haven't already began to seek sentients. If you can put all that down then you might be able to do it. You might recognise a roshi because they are out there.

It's possible to reach enlightenment digging a hole in your back yard. It's possible to do it in a near death experience. It's possible to do it understanding what you're mother had told you your whole life. One of My students found profound enlightenment and reached full satori on the John. Recently I had one pass through and only had right effort. I have another student I've been working with for two years standing at the door of the 50000 gateless gates and turn around because they didn't realize it-this was yesterday. The buddhalands are infinite. The mind as we build it is limited. The roshi isn't a hall pass. You have to put in the work.

There is no teacher is necessary. Just believe the path showed by Buddha and act on it. He is our worthy teacher. He has crossed the flood of existence and equally shows us the way to cross it. Remember only one thing have patience, deep faith and surrender everything. So that there is blowing out of everything you posses before and in that blowing out one has insight. With that insight one can see the law of karma, past life kammathana, the seed of becoming and the one who burn that seed. With that insight there is knowledge, "Released"!

You need another's voice (parato ghosa) or spiritual friend to teach you dhamma. Other than for a Buddha and Private Buddha one cannot realise the Dhamma without someone else showing the path. So you need someone to show you how to get too deep meditation. Also, show you where you might have made mistakes.

Once you learn the path it is one's efforts and practice which takes you to the final goal. You should be an island to your self without relying on another.

So to learn the technique you need the guidance of a teacher. To walk the path you need to do it your self. No external party can help here. Generally, you lean a little bit of theory and put it to practice then learn more and put that into practice. Hence it is good to have a teacher who can show you the way.

The medium thought what is taught can be direct interaction with a teacher. Reading books. Or even directly from the Tripitaka. The ultimate teacher in the line of teachers is the Buddha who made the Dhamma know.

Anything that can be learned how to be done most likely could be learned more quickly with a teacher. This applies to deep meditative states. That being said, It does not apply to enlightenment.

Nothing is required to reach enlightenment. Nirvana exists with us in every moment of our lives. Because of this, all you need to do to "reach" enlightenment is to see it clearly. Reaching deep meditative states are not required to awaken. Spontaneous enlightenment is possible and has most likely happened many times before. Awakening is not something that is done. It is more like the opposite. It is a stopping of doing. And once you stop that doing, all that is left is Nirvana.

A teacher can be helpful only in pointing you in the direction of where to look, how to look, and how to stop looking. From personal experience though, I have seen no evidence that anything can expedite the process of awakening. Awakening is only a gradual process in very select circumstances. Most awakenings are happen in a single moment and are instantly life changing. My awakening happened over two meditation sessions. The first was a sort of half baked awakening, but then 2 days later the real thing happened and blew everything open. I would say I am probably the exception as opposed to the rule though.

TLDR; Teachers are not required to help you reach meditative states, but they can be very helpful. Teachers are not required to help you reach enlightenment, but they can point you in the right direction.

A teacher is generally required but difficult to find. The Pali suttas say:

Tathāgatappaveditassa dhammavinayassa desetā puggalo dullabho lokasmiṃ

Rare in the word is a person who teaches the teaching and training proclaimed by a Realized One.

AN 6.96

For an individual with a keen intellect, this 'teacher' could simply be the Pali suttas. However, even in this case, the discernment of what the Path is must be acutely discerned. Generally, even an intelligent person needs a 'rare teacher' to verbally guide through the true meaning of the Pali suttas.