How to tell the current from the amp

Just trying to be more scientific and objective here.

Good luck with that. With solid state, if an amp doubles its power at 4 ohms and can handle low impedances, no worries. On the tube amp side, tube amps usually have current reserves to run the vacuum tubes but not always. 

The idea is that a high current amp will perform consistently well even as your speaker impedance changes.  If your speaker impedance is stable, or high enough this becomes pretty irrelevant. Sometimes you might even like the combination of a low current amp and low impedance speaker if the dips happen where you like or need them to.

The general first thing to look for is that the current doubles as impedance halves:

8 Ohms:  100 Watts

4 Ohms: 200 Watts

2 Ohms:  400 Watts

Another thing to look for is being rated to drive 2 Ohm loads. 

But unless you have unusually difficult to drive speakers this isn't usually a problem for most good solid state amplifiers. Electrostatic speakers are a notable "always a problem" speakers. :)

Most amplifiers are voltage devices that provide voltage gain and voltage based feedback.

The idea that they shove current out in a massive burst is not going to happen unless the speaker’s impedance is headed towards zero.

You may want to provide the impedance curve for your speakers?

I get the case where you have double the wattage with half the impedance, but such case only show the device is qualified as high current, but now by how high as a quantifiable measurement. It’s only a relative measurement. So there is no one measurement available to indicate the “current” capability? I don’t have electrical technical back, and I feel this concept is being mystified…

As eric said, the rating into different impedances tells you more about the amp’s capability, and you should couple that to your room size and speaker requirements for selecting a power rating.

Keep in mind amplifiers do not put out power, the speaker (or the load) consumes the power. The amplifier has to be capable of feeding the speaker as a constant voltage source and that capability is measured in watts, which is the voltage multiplied by the current carrying capability of the power supply transformer and filtering caps . The confusion about power and current can be cleared up with an example:

Suppose there are two amplifiers, each rated at 100 watts into 8 ohms. To get that rating, the amps must gain up the input signal to 28 volts and the power supply keeps at least a constant 28 volts with an 8-ohm load. Attach an 8-ohm resistor load to each amp, and crank up the volume until the signal maxes out at 28 volts. Both amps show a clean sine wave and that means each amp is at 100 watts. At 100 watts over 8-ohms, that is 3.5 amps of current.

Now replace the load with 4-ohm resistors. The first amp shows a clean sine wave to 28 volts. The other amp shows the sinewave clipping at 20 volts. It reached max output. The first amp is now putting out 200 watts and into 4-ohms that is 7-amps. The second amp is putting out 100 watts (power rating didn’t change!) and into 4-ohms the current is 5-amps. The second amp is putting out less current at 4-ohms.

Replace the load with a 2-ohm resistor. If the first amp still shows a clean sine wave at 28 volts, it is putting out 400 watts and 14 amps. If the second amp clips at 14 volts, it is still putting out 100 watts but only 7-amps of current.

Obviously, the first amp is more powerful and will feed difficult speaker loads better than the first, even though the second amp is "putting out" the same power. However, the second amp may work only as good as the first amp when the speaker load is fairly constant or maybe when playing at low volumes.

Tube amps are a different animal altogether. The power rating depends only on the output transformer and power tube because the load is reflected from the speaker to the tube. A changing speaker impedance on the xfmr secondary is reflected back to the xfmr primary, which presents a changing impedance to the tube. The power is pretty much constant no matter what the speaker impedance does, but in order to get the rated power the output xfmr tap (4,8 or 16 ohm) impedance has to closely match the speaker impedance.