Why can't energy change abruptly?

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Discussion Overview

The discussion revolves around the question of why energy cannot change abruptly, exploring the implications of such changes on power and the conservation of energy. Participants examine theoretical and practical aspects, including quantum mechanics and real-world scenarios involving electrical components and ultrafast lasers.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the impossibility of abrupt energy changes, linking it to the concept that such changes would imply infinite power.
  • Another participant asks for examples of physical quantities that can change abruptly, suggesting that such changes would require particles to move instantaneously, which is not feasible.
  • A later reply introduces the uncertainty relationship in quantum mechanics, suggesting a connection between energy changes and the time required for transitions.
  • One participant mentions that while ideal components like inductors and capacitors can exhibit abrupt changes in voltage and current, they note that ideal components do not exist in reality.
  • A participant shares their experience with ultrafast lasers, detailing how energy is delivered in short pulses and calculating the resulting power flux, which can reach extremely high values, raising questions about the limits of power scaling.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of abrupt energy changes, with some suggesting theoretical possibilities while others emphasize practical limitations. The discussion remains unresolved regarding the implications of these viewpoints.

Contextual Notes

Participants reference concepts from quantum mechanics and electrical engineering, but the discussion does not resolve the assumptions or limitations inherent in these fields. The implications of energy conservation and the nature of ideal versus real components are also noted but not fully explored.

anhnha
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Hi,
I want to ask your help about energy.
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?
 
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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)?
 
Do you know any physical quantity changing abruptly in a real setup?
Now, I can't find out anything but I can't generalise it.
Can you imagine any setup where energy could change like that, without particles changing their position abruptly (which cannot happen)?
Yes, but in my mind :)
 
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.
 
Do you know any physical quantity changing abruptly in a real setup?
Now, I just read that the voltage across an ideal inductor and the current through an ideal capacitor can change abruptly.
 
anhnha said:
Now, I just read that the voltage across an ideal inductor and the current through an ideal capacitor can change abruptly.

Ideal components do not exist in real life.
 
anhnha said:
Hi,
I want to ask your help about energy.
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?

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.
 

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