Einstein's GR passes extreme test

Jul 15, 2008 44 Replies

attractive force between objects. In fact if it were, it would not be able to have any effect on (massless) photons -- but it most certainly does (look up "gravitational lensing"). The ability of gravity to affect photons (electromagnetic radiation) was predicted by Einstein. When it was finally observed, Einstein instantly became a lot smarter than he was previously. It was huge.

No they don't. They have energy and momentum but no mass. This is a common misconception see for example:

formatting link

I hate appeals to authority though so for a quick derivation. If you take the formuala for relativistic mass given a rest mass mo and a velocity v = c(1-e) then as e -> 0

m = gamma.mo

where gamma = 1/sqrt(1-v^2/c^2) = 1/sqrt(1-(1-e)^2) = 1/sqrt(2e-e^2)

so lim e->0 of m = 0 / sqrt(2e-e^2) = 0/sqrt(0) = sqrt(0) = 0

Convention today is to consider the rest mass as the clear definitive characteristic of fundamental particls to avoid hair splitting semantic arguments about the relativistic mass of massless particles.

Mathematicians please excuse the sloppy use fo limits here.

We still don't know for certain that photons are truly massless although there is a very low experimental upper bound on it. Nuetrinos are looking increasingly like they are not quite massless and have different masses to boot.

Of course *provided* that they start out with a non-zero rest mass in the first place.

Regards, Martin Brown

** Posted from
formatting link
**

attractive force between objects. In fact if it were, it would not be able to have any effect on (massless) photons -- but it most certainly does (look up "gravitational lensing"). The ability of gravity to affect photons (electromagnetic radiation) was predicted by Einstein. When it was finally observed, Einstein instantly became a lot smarter than he was previously. It was huge.

That ain't what my physics teacher told me. Now I have to find a copy of "University Physics" by Sears, Zemansky and Young - I used to have that one but loaned it out. IIRC, that book also says photons have mass - just no rest mass.

Meanwhile, what gains mass when one charges a capacitor with a vacuum dielectric? The capacitor does gain mass. The stored energy is located in the vacuum.

- Don Klipstein ( snipped-for-privacy@misty.com)

Otherwise, a laser would have no effect.

As it is, the photons perform work.

attractive force between objects. In fact if it were, it would not be able to have any effect on (massless) photons -- but it most certainly does (look up "gravitational lensing"). The ability of gravity to affect photons (electromagnetic radiation) was predicted by Einstein. When it was finally observed, Einstein instantly became a lot smarter than he was previously. It was huge.

It is more of a shift in convention than anything real, but it was somewhere between the early 70's when Motz & Duveen who still used the photon relativistic mass to modern day texts like Carrol & Ostlie (1996) that studiously avoid it. The invariant based on rest mass has become dominant and m=p/c deprocated.

E^2 - p^2c^2 = mo^2c^4

Photon rest mass has become more heavily emphasised in modern texts. In part because otherwise students tend to stuff the relativistic mass for a photon into Newtonian equations and get the wrong answers.

We don't strictly know that photons are massless either. Only that their mass if non-zero is exceedingly small.

The physical structure that keeps the plates with opposite charges on apart ;-)

I wonder if anyone has actually been able to measure the change in mass of a classical capacitor under these circumstances experimentally. The apparatus for measuring the Casimir effect is exquisitely sensitive.

Regards, Martin Brown

** Posted from
formatting link
**

That probably explains it - I had high school physics (with Sears, Zemansky and Young) in 1979-1980, and college physics (with Sears, Zemansky and Young) in 1980-1981.

That reminds me of when life forms were all considered to be in just three kingdoms - prokaryotes, plants and animals. Prokaryotes had cell walls and no nuclei. Animals had nuclei and no cell walls. Plants had both, and nothing had neither. Then they came up with protists, maybe because too many people did not like thinking of a slime mold as an animal. THe animal kingdom was reduced to have organized multicellular creatures whose cells had nuclei and no cell walls.

Suppose that part was infinitely rigid and no work is done compressing it as the capacitor is charged. The capacitor would still gain mass.

I would think that if a mass change in anything storing electrical energy is detected, it would first be detected in a battery (or a cell as they call them if they have only one cell).

- Don Klipstein ( snipped-for-privacy@misty.com)

Join the Discussion

Have something to add? Share your thoughts — no account required.

Didn't find your answer?

Ask the community — no account required