What is Mass?

[StevenO]

That this statement is true can be proven in a simple way. E.g., calculate the gravitational deflection of light from the sun.

1. We all know that photons travel straight lines since the speed of light is a universal constant, so even the idea of
curved space is a little absurd since a curve always describes an acceleration...

Absurd? Apparently you are not familiar with having one's cake and eating it too. It turns out that if you talk in riddles and use math that only those with a college degree in a hard science can typically understand, you can have uniform nonuniform motion . If space is curved, then all trajectories are curved, and light just travels in the "least curved" trajectory.

Indeed. Most physicist do not notice since they skip the high school stuff to go straight for the tensor math. But how can you define something to be "curved" and "the shortest distance" in the same sentence if you also postulate that photons travel "uncurved" paths? A curved path is a path describing an acceleration. Point. So photons can only travel straight paths. Enfin. It is all a matter of relativity. One can assign curving to space or matter.

2. Putting the transit time of a photon grazing the sun to the earth at 500s, we get that the surface of the earth during this time expands an unexpected distance of:

s= at2/2 = (9.8m/s2)(500s)2/2 = 1,225,000m


3. The angle of deflection can then be calculated from:

tan(θ) = s/1 AU = 1,225,000m/1.5x1011m

θ = 1.68 arcseconds

4. Voila. The famous result from General Relativity that made Einstein a celebrity. Only this way you get the result in three lines of algebra instead of 40 pages of Tensor math...

Talking about the "angle of deflection" at all is fallacious. The photon takes the path it takes, period. The only path it deflects from is the one in the relativist's imagination. They calculate how far the photon traveled one way, then another way, take the difference and say the photon was deflected. What idiocy. Or they calculate how far they think the photon "should have traveled" according to some other measurements and compare this to what they measure, subtract the two, and again announce that the photon was deflected. Deflected from what? The distance a photon must travel to get from A to B may depend on neighboring bodies like the sun, and it may even depend on measurable parameters related to those neighboring bodies. That's not suprising...

Off course you are right. We have never observed the actual path of a photon, only it's arrival. But the postulate is that the travel speed of photons is constant.

[altonhare]

But how can you define something to be "curved" and "the shortest distance" in the same sentence if you also postulate that photons travel "uncurved" paths?

Everything takes "the shortest distance" between A and B. What else would it do, teleport to C, then travel to B? In physics there there are only trajectories. Perhaps the distance between here and there changes faster with respect to the distance between overthere and here, that doesn't make either trajectory curved.

A curved path is a path describing an acceleration.

Every object is accelerating with respect to some other object(s) in the U. It has to be. If there is a single object in the U that is "accelerating" then every other object is accelerating wrt it. If a curved trajectory describes acceleration then all trajectories in the U are "curved".

But if everything in the U were blue, there would be no concept of blue, or of color. So if every trajectory is curved, there really is no such "thing" as a curved path, or a straight path. Just paths.

[StevenO]

But how can you define something to be "curved" and "the shortest distance" in the same sentence if you also postulate that photons travel "uncurved" paths?

Everything takes "the shortest distance" between A and B. What else would it do, teleport to C, then travel to B? In physics there there are only trajectories. Perhaps the distance between here and there changes faster with respect to the distance between overthere and here, that doesn't make either trajectory curved.

Does the moon travel the shortest distance around the earth?

A curved path is a path describing an acceleration.

Every object is accelerating with respect to some other object(s) in the U. It has to be. If there is a single object in the U that is "accelerating" then every other object is accelerating wrt it. If a curved trajectory describes acceleration then all trajectories in the U are "curved".

But if everything in the U were blue, there would be no concept of blue, or of color. So if every trajectory is curved, there really is no such "thing" as a curved path, or a straight path. Just paths.

Indeed, everything in the universe is accelerating, since that is what we are measuring and calling "gravitation", "inertia" or "mass".

However, we have defined photons as our yardsticks and we have defined these yardsticks to be linear rulers and invariable clocks, so by assumption we take the photon paths to be straight and their frequencies to be unchanging. Seems to be a very workable hypothesis as photons are the main mediating particles. Even if it would not be true we could'nt prove it.

[altonhare]

But how can you define something to be "curved" and "the shortest distance" in the same sentence if you also postulate that photons travel "uncurved" paths?

Everything takes "the shortest distance" between A and B. What else would it do, teleport to C, then travel to B? In physics there there are only trajectories. Perhaps the distance between here and there changes faster with respect to the distance between overthere and here, that doesn't make either trajectory curved.

Does the moon travel the shortest distance around the earth?

Hold up, we were talking about traveling from location A to location B. Now you're talking about an entire itinerary, a multitude of locations.

A curved path is a path describing an acceleration.

Every object is accelerating with respect to some other object(s) in the U. It has to be. If there is a single object in the U that is "accelerating" then every other object is accelerating wrt it. If a curved trajectory describes acceleration then all trajectories in the U are "curved".

But if everything in the U were blue, there would be no concept of blue, or of color. So if every trajectory is curved, there really is no such "thing" as a curved path, or a straight path. Just paths.

Indeed, everything in the universe is accelerating, since that is what we are measuring and calling "gravitation", "inertia" or "mass".

However, we have defined photons as our yardsticks and we have defined these yardsticks to be linear rulers and invariable clocks, so by assumption we take the photon paths to be straight and their frequencies to be unchanging. Seems to be a very workable hypothesis as photons are the main mediating particles. Even if it would not be true we could'nt prove it.

Seems a hopeless business, postulating a particle that does not accelerate with respect to anything else, but insisting that everything else accelerates wrt it.

[StevenO]

Does the moon travel the shortest distance around the earth?

Hold up, we were talking about traveling from location A to location B. Now you're talking about an entire itinerary, a multitude of locations.

Too bad your physics approach is so limited in application. You were actually talking about photons then?

A curved path is a path describing an acceleration.

Every object is accelerating with respect to some other object(s) in the U. It has to be. If there is a single object in the U that is "accelerating" then every other object is accelerating wrt it. If a curved trajectory describes acceleration then all trajectories in the U are "curved".

But if everything in the U were blue, there would be no concept of blue, or of color. So if every trajectory is curved, there really is no such "thing" as a curved path, or a straight path. Just paths.

Indeed, everything in the universe is accelerating, since that is what we are measuring and calling "gravitation", "inertia" or "mass".

However, we have defined photons as our yardsticks and we have defined these yardsticks to be linear rulers and invariable clocks, so by assumption we take the photon paths to be straight and their frequencies to be unchanging. Seems to be a very workable hypothesis as photons are the main mediating particles. Even if it would not be true we could'nt prove it.

Seems a hopeless business, postulating a particle that does not accelerate with respect to anything else, but insisting that everything else accelerates wrt it.

I clearly stated that photons accelerate outward too. Be happy that there is gravitational acceleration. Helps you to stick to your chair and operate the keyboard.