Hacker News Reader

Comment by sundbry | Hacker News Reader

Not if there's a cell tower every 100 yards putting out 30dB more power than your phone. The inverse square law also doesn't apply when you have phased arrays doing beamforming if you're directly in the path.

View on HN

The inverse square law totally applies in the case of phased array beamforming, you just have a much higher gain to start with.

You get a lower exponent than the square with a beam. For a perfectly parallel beam the exponent is technically 0 (same intensity regardless of distance - like a laser pointer) For a focused beam intensity will actually increase with distance up to the focal point. Some energy can be absorbed by the medium (air/moisture/rain), but that is not covered by the inverse square law.

Not with a planar or linear array. I'm skeptical, but prepared to learn something: what sort of array can generate a square beam?

Even lasers spread. This guy agrees with me: https://www.quora.com/Is-the-light-from-lasers-reduced-by-th...

It depends. The inverse square law applies to spherical wavefronts. Due to diffraction, wave fronts always become spherical in the far field.

But in the near field, that's not the case.

Beamforming arrays have planar wavefronts close to the source, so the inverse square law does not apply. The wave fronts will become spherical again at a "large" distance from the emitter, where the meaning of "large" depends on wavelength and emitter size.

Focussed lasers also do not have spherical wave fronts in the near field. The distance at which the inverse square law starts to apply to lasers depends on beam width, coherence, and focus.

The cross section of the beam can be any shape, the important thing is the signal source is an area not a point. The value of the inverse square (of distance from source) is dominates power density when the signal source is effectively a point - this becomes the situation for a laser or anything at long enough distance, but at distances where it is effectively a beam, the strength of power density does not dissipate by that value. The geometry of the beam concentrates the power density at its focal point, which can be far behind the source or in front of it. For an ideal beam focused to infinity (parallel rays) its power would never dissipate with distance - as all of the power goes in the same direction. We don't need to form an ideal beam to say its doesn't follow the inverse square rule, any focusing of rays breaks the rule (at scales where it is reasonable to treat it as a beam and not just rays emanating from a point)

I hope that helps picture the situation. My original comment that a beam can have a different exponent was incorrect except in some approximate sense. The inverse square value will still apply, but from the beams real or imaginary focal point (if it is a point) But it the case of a transmitter beaming a signal at another, that focal length can be far beyond the reciever, so the 'rule' can be completely confounded.

the inverse square law always applies, hence the law part.

Laws of Physics are in general not always applicable. Ohm's Law, for instance, is only applicable in a narrow range of conditions.

"Laws" tend to be less rigorous and more narrowly applicable than "theories," though the colloquial meaning of the terms is switched.

Actually the difference between law and theory is nothing whatsoever.

There is a substantial difference in my opinion. Laws rarely put forward a mechanism or seek a complete understanding of a relationship, while theories often do.

Ohm's law was a law long before the electron was discovered. It's an emperical linear relationship that just seemed to work. Since no mechanism is suggested, it's not possible to determine whether ohmic behavior is expected or not. In contrast, The Drude Model's explantion of ohmic behavior could be considered a theory. It makes an attempt to understand the underlying physics, and from this it is possible to predict whether a material will follow Ohm's Law or not.

Have you noticed that nothing is called a law anymore? It's a difference in word choice not meaning.

I think modern scientists are a lot less likely to call any empirical relationship a law. Theory is still pretty widely used, and not for things that could be called laws.

You can say the "the theory of quantum chromodynamics," but not "the law of quantum chromodynamics". 'Law' implies a small number of simple equations, while theory allows for a much larger scope of complexity or rigor. The meaning is absolutely different. Modern science is pretty complex compared to what went on 200 years ago, so it's not surprising law has fallen out of favor.

Yes, except in this case there isn't an exception.

Incorrect analysis can give the correct answer.

There are excpetions to many inverse square laws, they just aren't relevant to the problem at hand.

Reply on news.ycombinator.com