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Comment by DavidHull | Hacker News Reader

As an interested amateur, I recommend the book "Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime" by Sean Carroll as a good overview of quantum fundamentals. The book discusses several interpretations of the reality of matter at the quantum level. Dr. Carroll himself believes that everything is waves/fields at the lowest level, and a many-worlds interpretation of why matter appears to be particles when we observe it, but also discusses de Broglie–Bohm pilot wave theory and spontaneous collapse theory.

https://en.wikipedia.org/wiki/Many-worlds_interpretation https://en.wikipedia.org/wiki/Interpretations_of_quantum_mec...

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seems to be my day for stupid questions...

Do quantum effects make solar sails work ? My High School physics said F=MA and photons have zero mass.. so where does the force come from ?

Thanks!

Technically the formula for force is F = dp/dt, or the derivative of momentum with respect to time.

For particles with mass the momentum of such a particle is p = mv, and so you can use that to yield F = ma. However for a massless particle like a photon, its momentum is p = E / c. If you use that momentum to describe a beam of photons being absorbed by a material, then you get F = n * E / c, where E is the average energy of the photons, n is the rate of photons per second, and c is the speed of light.

Oh Thanks! Should have known I was missing something basic :-)

edit: btw - thats a REALLY nice explanation :-)

Thanks

Things that move at the speed of light carry momentum, even though they have zero mass. For something moving at the speed of light, the momentum is the energy divided by c. (You can't have something with mass moving at the speed of light.)

Thanks - seems like it was the momentum thing I was missing. I got a far as nothing with mass can move at c and was out of my depth :-P

Thanks

Photons have momentum, while not having mass. Interestingly, Newton has formulated his second law in terms of momentum: F=dp/dt.

I guess we learned the f=ma format because we had it before calculus? TIL F=dp/dt form...

Thanks!

Since the photon has nonzero energy E and is moving at c, it has mass by virtue of E=mc^2. And since E=hv, the E part is determined by the photon's frequency v, so the equivalent amount of mass is as well. It shows up as radiation pressure when the photon hits an object, just as if something tangible had collided with it.

On a sunny day, I'd guess that sunlight exerts about the same force on an acre on the Earth's surface as a postage stamp lying on the ground.

E=mc^2 doesn't mean that a photon has mass. Photons do produce gravitational effects due to their energy, but not in the same way as a particle with mass m. See, for example, https://physics.stackexchange.com/a/6222

A photon has no rest mass but it most certainly has mass-energy equivalence.

Thanks for the explanation :-)

Zero rest mass

Sorry - again, only HS physics - does that imply they have mass when moving ? (hmm - can you even have a photon at rest?)

thanks!

Sorry, we're leaving HS physics with this one...

Objects in motion have kinetic energy, and Einstein says mass and energy are equivalent. This means in a very real sense objects in motion have additional "relativistic mass". When you annihilate that photon it's energy is transferred to whatever absorbed it.

Confused? You're not alone! Physicists are trying to move away from the terms "rest mass" and "relativistic mass" for reasons including one you've already identified: what does it even mean for a photon to be "at rest"?

https://en.wikipedia.org/wiki/Mass_in_special_relativity

Oh thanks! That article was interesting :-) Not gonna say I understood it...but it was interesting :-D

Waves on water have zero rest mass, but they hit hard.

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