The idiot savant Cecil Moore wrote:

Therefore, those bright rings are just an illusion and
don't contain more than the average energy in the two
superposed waves.

You couldn't be more wrong in your interpretation.

Perhaps you will understand it this way: the bright rings have an
intensity which is equal in energy to the sum of the energy in the two
superposed waves. Energy doesn't have to come from anywhere else to
balance the equation.

The error you're making is the assumption that since the intensities
don't add up, something has to come from somewhere else. But that's a
wrong assumption to make. One shouldn't expect intensity to add like
that. Obviously it doesn't add like that. The fields are what add and
subtract, not intensity (or power). Power is the time derivative of
energy - that's the reason a squared term comes in. But power and
intensity don't propagate, therefore they don't superpose, and
shouldn't be added algebraically. Fields, voltage, current, energy -
it makes sense to sum those things algebraically.

When you double something and then square the sum, you get a factor of
four. But you're still only doubling the 'thing' of interest.
Depositing two paychecks and squaring the sum doesn't make your bank
balance go up by a factor of four. But it is certainly true that you
would have to borrow money from someone to make that happens. The
point is that it's not a realistic expectation.

I assume you know that the meter face on your Bird wattmeter is
calibrated exponentially. So, when your Bird power meter reading goes
up by a factor of four, what do you think the voltage across its meter
movement has actually increased by? The thing is, the Bird company
understands that when power reading quadruples, the circuit voltage
has only doubled. You'll note they don't claim that since the reading
quadrupled instead of doubling, the "extra" power had to come from
somewhere else.

If you can't understand this, that's fine. But it's not an excuse to
get so bloody belligerent with people about it.

ac6xg