On Wednesday, September 3, 2025 at 8:05:59 AM UTC-6 Alan Grayson wrote:
On Wednesday, September 3, 2025 at 6:05:55 AM UTC-6 John Clark wrote: On Tue, Sep 2, 2025 at 6:05 PM Alan Grayson <[email protected]> wrote: On Tuesday, September 2, 2025 at 2:16:15 PM UTC-6 Brent Meeker wrote: >>Thanks for the exposition. Brent *>But you, being the expert you are, already "knew" the answer. It had to do with the wf of a photon. But oddly, you haven't a clue what differential equation would have to be solved to obtain that wf. WTF. AG* *As seen below, the electromagnetic wave function is described by 4 differential equations discovered by James Maxwell about 10 years before Einstein was born :* *Gauss's Law for Electricity: ∇ ⋅ E = ρ / ε₀ Gauss's Law for Magnetism: ∇ ⋅ B = 0 Faraday's Law of Induction: ∇ × E = -∂B/∂t Ampère's Law ∇ × B = μ₀J + μ₀ε₀∂E/∂t * *To this day those equations are the bread and butter of electrical engineers, they don't include any of the quantum properties of light but they don't need to in order to explain the Doppler red shift. If you want to find the quantum wave function, and not just the electromagnetic wave function, and also include relativistic effects, then things become a little more complicated. * *In the two-slit experiment, if you quantize the electromagnetic field, the field amplitude takes on the role of a photon’s probability amplitude. That amplitude behaves like a wave, so it interferes, and the squared magnitude (|E|^2) gives the probability distribution for where a photon is likely to be detected on the screen.* *How can the amplitude give a probability if its value is generally not less than unity? AG * *Another problem with this is that the amplitude is defined for multiple photons, not for a single photon, whose wf I am seeking to acquire and understand. AG * *If you send photons one at a time, each detection looks random, but over many trials the hits build up exactly into the interference pattern predicted by |E|^2.* *When you use a bright source, such as a laser, you no longer just have a single photon but a huge number of them, so |E|^2 doesn’t just describe a probability distribution, it gives the average number of photons arriving at each point. And as the number of photons increases classical optics approximates quantum mechanics more and more closely. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* *tvi* -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/df84cedd-0740-4737-b077-7dc1b703a172n%40googlegroups.com.
