See subject. I presume light would bend around me in some small amount. I weigh 170 in earth gravitation. All muscle.
Light always goes in a straight line. It’s space that’s bent.
Yes, I’m down with that. It depends where you’re looking from though, right? Suppose I’m Mercury, in the famous first demonstration. But with less mass, at sea level.
And I’d prefer, if you guys could provide the Straight Dope. None of these “negligible effects” cop outs. 
In the small-angle and spherical-mass regime, light is bent by an angle (4GM)/(R**c[sup]2[/sup]), where G is the gravitational constant, M is your mass, c is the speed of light, and R is the distance away from your center of mass that the light passes. Assuming R=30 cm, I find an angle of 8x10[sup]-25[/sup] radians.
Yeah, but is the small-angle approximation really justified here? The OP did say that he didn’t want to hear anything about “negligible”. 
Plus, although I didn’t specify it, I was thinking of R=handshake distance away, but that part I can do the math. Let’s call it 1.5 meters (does that sound right?).
Extra credit, for SR question: I’m standing hand-shake distance away from my friend. As I reach out to shake his hand (I’ve been Googling for 15 minutes to find a speed) at, call it 1ft/0.25 sec, how much shorter is my arm from his point of view than my own, due to Lorenz contraction?
These questions are kind of stupid, but fun; they are, however, a serious part of my interest in objectivism and its brother, scientific realism.
But my GR question is first…
What remains of the GR question? Just the length of your arm? 1.5 m is on the large side, but I wouldn’t quibble over it.
When you say “from you own point of view”, do you mean from the point of view of an imaginary observer on your hand, or from the point of view of your eyes in your head, or something else? Unless you have some very weird handshaking technique, your head and your companion’s head are viewing your arm from the same reference frame (at rest with respect to the ground, say), so you’d see the same effects.
Also, Lorentz contraction takes place along the direction of motion. So, again barring a strange handshaking technique, you’d observe a thinning of the arm rather than a shortening.
All this aside, an arm traveling away or toward you along its length at your stated 4 ft/sec speed would “appear” shorter by 1 part in 10[sup]17[/sup]. (I put “appear” in quotes to emphasize the experimental side of this question – that a change this small is not something you can just see.) The math here is given at the top of the Lorentz contraction Wikipedia page.
(Also, note: Lorentz)
First off, thank you for the light-bending answer.
- That figure is observable by Us vs-a-vs R; is there a way to pronounce “my effect on space-time curvature is x?” independent of anything? My guess: the answer is no, that’s the whole point. I strongly suspect that I have my head totally screwed on backwards…
Re Lorentz: I’ve gone back to the woodshed, conceptually. I’m narrowing this thing down to the “moving rod in a barn” idea for me to consider.
I was thinking of my friend watching me extend my hand to him preparatory for a hand clasp. Does that change your conclusions here:?
I think you might have had a quotesplosion in your post, but I think I can parse it.
You might say, “The spacetime at a point separated from my center-of-mass by a distance R is curved by approximately x, where x=2GM/(Rc[sup]2[/sup]).” Of course, you would then need to define what “curved” really meant, but the idea is that general relativistic effects will be of size x, give or take a factor of 2 here and there. Note that the size of these effects are necessarily dependent on how far away you are from the spacetime point you’re interested in.
Normally, one would encapsulate a fuller description of what a mass like your own does to spacetime by specifying an appropriate metric, but my impression is that you are after something more qualitative, like the statement above.
I see. I was picturing the actual shaking maneuver, which goes up and down. In the arm-extending phase, yes, your friend would see your arm shortened by the amount I gave before. So would you, since your eyes aren’t moving with your arm. (I’m ignoring the nuance that your hand will be moving faster than your elbow, which will be moving faster than your upper arm.)
You are correct that it really would be, but that’s not what my scare quotes were scaring off. I was just noting that this change is so tiny that one needs to be just as careful about what it means to measure something this small as one is about whether GR effects are important. Or, to be less precise but more specific: you can’t just see the change with a camera or nuthin’, so “appear” is a bit of a loaded word. But this aside is more of a distraction than a help, so feel free to forget I used those quotes in the first place.
You’re correct of course, and I apologize for putting my queries sometimes above, sometimes below. Just learning nested writing here…
Well, I went to the cite. I hope you’re happy. Salt in the wound, salt in the wound.
Why oh why didn’t I become a physicist, like I wanted to ever since I read about the Twin Paradox in Junior High School? And then I went to Stuyvesant, where they churn out Nobelists and other smart people regularly?
Instead I became a musician. And so I made the bed I lie in.
But I can’t help but be envious of you guys who play handball with this stuff.