Why there are humans who look like they do not have empathy? Can we measure empathy?

Ampathy is a product of brain chemistry. We even know where to find it in the brain. Chiefly the limbic system and supramarginal gyrus of the cerebral cortex. And we can measure and quantify the electro-chemical impulses of this part of the brain in fMRI by using external audio/visual stimuli designed to trigger responses from a subject in isolation. We've been doing this very successfully for about 30 years now.

Measuring the response time and intensity of cognitive activity in this manner is part of how anti-social personality types (sociopaths) are diagnosed.

Even no amount of abuse can erase empathy. It's genetic. You cannot erase innate genetic cognitive functions. If you could, there would likely be no way of getting them back. What we are often  describing is behavior disorder resulting from trauma, stupidity, ignorance, double standard.

There are cases where abuse of a child can result in them developing anti-social personality disorder and as a result a loss of empathy. But these are rare (1% of abuse victims). While this may have adverse affects on the child's emotional centers (the same places their empathy emerges from), it doesn't make empathy impossible for them. There are also cases where children can develop anti-social personality disorder due to genetics, and it is quite possible his mother was a psychopath. But psychopaths are not devoid of the ability to experience empathy. They are devoid of the ability to make connections with other human beings. Therefore, they never get the chance to empathize. This is why the activity of them limbic system remains lower than the baseline subjects. People confuse this with having no empathy at all.

None of this points to an inability on the part of researches and cognitive scientists to measure the empathy potential of an individual using the right tools. It's scientifically proven that we are born with the capacity for empathy. There is no point in even arguing this. A fact is a fact.

In the past, people would view anti-social personality types as monsters who were incapable on empathy and caring for others. It did a lot of damage to those individuals because if people thought this was not a skill they could learn, they didn't even try to rehabilitate them in the case of trauma or abuse. I see that mentality hasn't completely gone away yet.

One should consider that empathy is a human emotional response triggered by your experience of an event. You can't really have an emotional response to a million affected individuals you have no connection with no matter how you rationalize it. Perhaps Stalin best conclude it, "One death is a tragedy, a million is a mere statistic."

But we can only measure output but not the internal mechanics itself?

The output IS the empathy. To say that we cannot also measure the "internal mechanisms" is like saying we can measure the amount of each color used in a painting, but we can't measure the image. Is the image something that actually has a property that can be measured in the first place? What is the measurement of a bird painting compared to a dog painting or a person painting? How do we categorize the shapes so as to quantify one over the other.

Determining the origin of a thing has nothing to do with the actual nature of the thing itself. Knowing how empathy came will tell us little about how much empathy has arisen at any given moment. Just why it has arisen.

Will we ever be able to quantify the taste of a cup of coffee compared to other cups of coffee, for instance? Well, we can. We can measure precisely the chemical makeup of the coffee beans, the process used to make it, the temperature of the water, and even the minerals dissolved in that water from specific sources. This measurement doesn't tell us what the coffee may taste like because the cognitive agreement between human knowledge and human sense is not that precise.

You'd have to become an expert in coffee tasting in order to perfect this skill, and even then, it could be hit or miss. But what we can do is predict what the coffee SHOULD taste like within a given range based on the measurement of its ingredients and the process used to make it. The reason being that these are physical properties, and all physical properties, like all natural entities, are entirely predictable according to composition and pattern. We call this predictability physical or natural law.

Empathy also shares these conditions with all physical properties. While we may not entirely understand YET exactly how the brain produced empathy, we do know where it produces it and what the effect looks like. We can measure this brain activity with increasing accuracy and this measurement is categorical. We know that certain levels of brain activity indicate certain levels of empathy; and we can use that to determine the output of said activity. We can measure our degree of empathy. Empathy is not some magical ether in the air that is devoid of physicality.

Measuring how you feel about your empathy, however, is not measuring the empathy itself. It's measuring the subjective nature of thought. Which is an entirely different thing and may be impossible given that there is no linear scale I can think of where one subjective thought can be place in a different category than another. Even if we could read other people's minds, we can't even do this in our own minds, let alone someone else's.

Possibly a computer could do it at some point. Measure the nature of subjective thought. But that still leaves us with the task of figuring out a non-arbitrary, systematic scale for where some subjective thoughts fall as opposed to others. This, in any case, is my realist assessment of the question.