Newton's Laws and The Bending of Light

[iamlucky13]

That's why yez gotta use limits
The Gravitational force on a massless particle is zero
a=F/m=0/0=???

I mean different thing. Suppose there's massless particle moving with 1m/s and 0 kinetic energy. Now you get your baseball bat and hit it. How much velocity would it gain?

Actually, isn't that essentially the same question? It's a darn good question, too.

If I remember right, in math classes we always took the ratio 0/0 = 1. I don't remember why, but at the same time it was clear that this was not necessarily true, although it was justifiable and very convenient.

[Qev]

That's why yez gotta use limits
The Gravitational force on a massless particle is zero
a=F/m=0/0=???

I mean different thing. Suppose there's massless particle moving with 1m/s and 0 kinetic energy. Now you get your baseball bat and hit it. How much velocity would it gain?

Actually, isn't that essentially the same question? It's a darn good question, too.

If I remember right, in math classes we always took the ratio 0/0 = 1. I don't remember why, but at the same time it was clear that this was not necessarily true, although it was justifiable and very convenient.

Naw, anything over 0 (including 0) is 'undefined', since you can pretty much assign it any value you like. The one that always bugged me is 0! = 1.

A massless particle, moving at 1m/s and hit with a baseball bat, under classical mechanics, would likely gain infinite energy, or do something else excessively weird. Fortunately, classical mechanics is just wrong enough for this not to happen in the real world. After all, no massless particle can travel slower than c.

[Qev]

I would observe a constant change in the location of the stars enough to know I wasn't moving in a linear path.

No it's not enough, there is a crazy chance that universal gravitational field makes stars to change location. You should use a pendulum instead

I think there might've been a misinterpretation of what was said. The photon (or other gravitationally acclerating body) would not be able to detect changes in its momentum when examining only itself, ie. it's not going to feel any forces acting on it.

If it's got eyes, it can certainly look around and see the universe wheeling around as it orbits... but that brings in all sorts of other things, since being able to see means you're getting hit with photons, etc, etc.

[Dr. Skeptic]

As an observer's speed increases to near c, objects seen peripherally or behind , would red shift, very near c the observer would view "tunnel vision", no light to the sides, at the speed of light the universe would appear as a single point of light in the direction of travel.

[dcmcp]

It would seem that "mass less" particle would be bound to gain infinite velocity and always travel along straight lines in that theory....

That's why yez gotta use limits
The Gravitational force on a massless particle is zero
a=F/m=0/0=???

I mean different thing. Suppose there's massless particle moving with 1m/s and 0 kinetic energy. Now you get your baseball bat and hit it. How much velocity would it gain?

Umm.
I see what you mean.

That means we have to postulate some unusual properties for massless particles. In the Newtonian world the only massless particles we know about are photons. So this has implications for reflection (and the speed of reflected light).

Maybe one of the unusual properties could be a universal speed limit for massless objects. That would get us around the infinite velocity conundrum. (Acceleration might still be a problem.) This is not as unreasonable as it might seem, because the speed of light has been measured and found to be the same in all directions (Michelson-Morley). The troubling thing is, speed with respect to what? (Can anyone spell R-E-L-A-T-I-V-I-T-Y)

So, my approach bumps into the problems Herr Einstein solved pretty quickly. To quote a New Zealand ad for a Japanese car: "Bugger!"

= = = = =

Maybe photons don't "bounce" off anything. Perhaps we postulate that they interact with the world around them only through gravity and electromagnetism. That would mean reflection/diffraction/optics in general should be able to be explained and predicted by Maxwell's equations. In fact this is an underlying tenet of classical optics - particularly diffraction theory. This has possibilities to rescue us from the singularity (0/0) but Maxwell's equations are typically unsolvable for real world boundary conditions, and my brain is starting to hurt.

[ckam]

The photon (or other gravitationally acclerating body) would not be able to detect changes in its momentum when examining only itself, ie. it's not going to feel any forces acting on it.

Oh, you shouldn't use "body" there How about being ripped apart by tidal forces? You don't need eyes to be ripped apart now, do you.

[Qev]

The photon (or other gravitationally acclerating body) would not be able to detect changes in its momentum when examining only itself, ie. it's not going to feel any forces acting on it.

Oh, you shouldn't use "body" there How about being ripped apart by tidal forces? You don't need eyes to be ripped apart now, do you.

Good point! I suppose photons couldn't really be considered 'bodies'... objects? I'm not sure what a better word would be.

Though gravitational gradients of that scale are what I'd call a special case, they still have to be considered. So do things like frame-dragging inside an ergosphere.

[ckam]

gravitational gradients of that scale are what I'd call a special case

why would that be special case? all of planets behind mars orbit have visible rings. earth (and perhaps all other three) has invisible dust rings. isn't that how these rings were formed?

[Qev]

gravitational gradients of that scale are what I'd call a special case

why would that be special case? all of planets behind mars orbit have visible rings. earth (and perhaps all other three) has invisible dust rings. isn't that how these rings were formed?

You're absolutely correct, of course. I guess I'm gonna hafta think about this more.

[ckam]

luckily, under relativity there's no such thing as a solid body, so you're no longer "hafta" think about it.