# Why can't energy change abruptly?

1. Sep 27, 2013

### anhnha

Hi,
Why can't energy change abruptly?
If energy E changes abruptly then power P = dE/dt = ∞. I would like to know why this is impossible?
I know that energy has to be conserved and they can only change from one form to the other. But why this process (transformation) can't change immediately?

2. Sep 27, 2013

### Staff: Mentor

Do you know any physical quantity changing abruptly in a real setup?

Can you imagine any setup where energy could change like that, without particles changing their position abruptly (which cannot happen)?

3. Sep 27, 2013

### anhnha

Now, I can't find out anything but I can't generalise it.
Yes, but in my mind :)

4. Sep 27, 2013

### Staff: Mentor

There is an uncertainty relationship between a change in energy of a quantum system and the time required for the transition. Perhaps that is of interest.

5. May 7, 2014

### anhnha

Now, I just read that the voltage across an ideal inductor and the current through an ideal capacitor can change abruptly.

6. May 7, 2014

### Staff: Mentor

Ideal components do not exist in real life.

7. May 8, 2014

### UltrafastPED

I work with very interesting lasers: average energy is quite low, about 1 watt, and the laser is pulsed: 1,000 pulses per second. Thus each pulse has about 1 millijoule of energy.

Not much, eh?

But this is an ultrafast laser, meaning that the individual pulses are very short - less than a picosecond in duration. In my case about 30 femtoseconds, or 3*10^-14 seconds.

Energy is delivered over an area; with adaptive optics this laser can be focused to a spot size of about one wavelength: 800 nanometers; round it up to 10^-4 centimeters (1 micron).

Putting this all together gives an energy flux of 10^-3 joules/pi*(10^-4 centimeters)^2 =
10^5 joules/cm^2/pi = 3*10^4 joules/cm^2.

Apply this energy flux over the very brief pulse duration and the power per unit of area is:
3*10^4 joules/cm^2/3*10^-14 seconds = 10^18 watts/cm^2. Actually we can do a bit better, and the actual output is slightly over 10^19 watts/cm^2.

This power flux is sufficient to generate electron-positron pairs when striking a metal target in vacuum - and has done so.

So you see that it is possible to increase power by quite a bit - but at each step the equipment becomes more specialized and expensive!

But like so many things, the scaling laws give less and less as you put in more and more - so unlimited power flux is beyond reach.