# B Can the law of conservation of energy of be broken?

1. Jun 5, 2017

### Lunct

A consequence of Heisenberg's Uncertainty principle is that particles energy level can fluctuate their amount of energy, e, for a short amount of time, t, as long as e x t < h/4pi (where he is = to planck's constant). So does that not violate the law of conservation of energy?

2. Jun 5, 2017

### Voltageisntreal

Doubt it, wouldn't that break Noether's theorem?

3. Jun 5, 2017

### Staff: Mentor

I don't think the answer you got in the previous thread can be improved on as a general answer:

https://www.physicsforums.com/threa...rg-uncertainty-principle.916740/#post-5777389

A good start at something more specific might be to give the exact source where you got this:

4. Jun 6, 2017

5. Jun 6, 2017

### Voltageisntreal

That's still rather vague. This has been answered a few times on the stack-exchange, i'll link you the links see if they help.

https://physics.stackexchange.com/q...ple-violate-the-law-of-conservation-of-energy
https://physics.stackexchange.com/q...conservation-limited-by-uncertainty-principle
For the above link, it appears to be a violation but it cannot actually be physically measured.
https://www.researchgate.net/post/D...nciple_violate_the_conservation_of_energy_law

6. Jun 6, 2017

### Staff: Mentor

I suspect the word "fluctuation" is the problem here. In quantum mechanics, it doesn't imply variation with time. In this situation it's more like a synonym for "uncertainty" or "indefiniteness".

In the end, the energy that we actually measure is always conserved. Same for other conserved quantities like momentum. What "really happens", "inside" the $\Delta E$ or $\Delta p$ or whatever, before we make a measurement, is unknowable. Quantum mechanics is silent about what is "really happening" with unmeasured or unmeasurable quantities. This is the province of interpretations of quantum mechanics, about which people argue endlessly, here and elsewhere.

7. Jun 6, 2017

### Staff: Mentor

This is a pop science book, which means that, even though it's written by scientists, it's not held to the same standards as a textbook or peer-reviewed paper. Which means it's not a good source to learn the actual science from; at best it can whet your appetite to go and learn the actual science.

8. Jun 6, 2017

### Lunct

So it is like Schrodinger's cat in that the energy levels do not actually change, it is just that we are unsure on it, so it is thought as a fluctuation in energy. Like Schrodinger's cat is probably not dead and alive, but it is just simply easier to think as it that way.

9. Jun 6, 2017

### Staff: Mentor

Exactly:
http://phys.columbia.edu/~nicolis/NewFiles/Noether_theorem.pdf

Its also a bit circular - energy not conserved - you dont have time symetry in your system and conversly.

This is in fact a big problem for GR since it deals with non flat space-times.. That means time may not have symmetry ie the same experiment you do does not necessarily give the same results at different times, so Noether breaks down. It leads to energy not being able to be defined in the usual way as the conserved quantity from time symmetry in GR:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Thanks
Bill

10. Jun 6, 2017

### Staff: Mentor

The easiest way to think about Schrodinger's Cat is that everything is classical after the detection of the atomic decay. That of course means the cat can never be in a state of dead an alive because those kind of superposition's cant occcur classically. The kind of superposition's that can occur in the ordinary world are very contrived eg the famous double slit but that is a whole new thread.

Thanks
Bill

11. Jun 6, 2017

### Staff: Mentor

Note carefully, though, that this is only an issue for global definitions of energy, i.e., "how much energy is there in total in some volume"? It is not an issue at all for local conservation of energy: in GR, this is guaranteed by the fact that the covariant divergence of the stress-energy tensor is zero (which is in turn a consequence of the Einstein Field Equation and the fact that the Einstein tensor obeys the Bianchi identities).

In other words, even in a curved spacetime, energy can't be created or destroyed locally. There is only an issue when you try to add up all the local pieces of energy to get a global quantity. There are multiple ways of doing this in GR, but all of them only work in special classes of spacetimes (the ADM and Bondi energy are only defined for asymptotically flat spacetimes, and the Komar energy is only defined for stationary spacetimes--the latter is the closest analogue to "the conserved quantity from time symmetry") or for special choices of coordinates (the various energy pseudo-tensors).

The Baez article you linked to expresses this distinction as the differential (local) vs. integral (global) form of energy conservation.

12. Jun 6, 2017

### Staff: Mentor

There's more going on here than that; the physics of a macroscopic system like a cat is very different from the physics of a single quantum particle subject to the uncertainty principle.

You should be aware that anything you've heard about Schrödinger's cat that didn't come from a college-level textbook or peer-reviewed journal article is almost certainly wrong. When Schrodinger suggested this thought experiment, he was pointing out a problem that arose in the then-current (1930 or thereabouts) understanding of quantum mechanics, not trying to argue that the cat would be in a superposition of dead and alive. It took a few more decades to resolve the problem, but unfortunately by then the idea of the neither/both dead and alive cat had leaked into the popular imagination and lives on as a stubborn urban legend.

Two books that you might want to try:
1) "Where did the weirdness go?" by David Lindley is a layman-friendly and math-free description of the most important post-1930 development.
2) "Sneaking a look at god's cards" by Giancarlo Girardi is a good non-rigorous explanation of quantum mechanics as applied to subatomic particles; understanding QM at this level is necessary to properly answer your question about energy conservation. A high school student can get through this book with some effort.

13. Jun 7, 2017

### hilbert2

Energy conservation is so important in physics that if there were some experiment where it would appear to be violated, physicists would rather imagine some 'invisible' form of energy that the missing energy is being converted to, than discard the conservation law. One example of this is the explanation of beta-decay with an electron neutrino (which was impossible to observe at the time when it was first postulated).

An isolated system has a Hamiltonian operator from which the possible total energy values are deduced, and the probabilities of each of these values remain constant for an indefinite time, as does the statistical expectation value of the total energy.