# Could superman fit his hand around a Basketball?

1. Jun 10, 2014

### Evanish

I know that you probably get tired of weird questions like this so I apologize in advance. I was thinking about length contraction in special relativity. I was thinking if superman was moving towards a basket ball at close to the speed of light when he passed it from his frame of reference it would look a bit like a disk. I was wondering If he could reach out and briefly place his hand around it. If he could this would seem odd to me because from the basket ball's frame of reference it would be superman that was undergoing length contraction. I know from my readings that problems like this are usually solved by understanding that event that are simultaneous in one frame of reference are not necessarily simultaneous in another. Looking at this particular scenario I find it difficult to imagine how things would look from the basketball's frame of reference. Would it seems like parts of his hand touched the ball before the other's? Would superman seem distorted in ways other then just length? It's really hard to picture.

2. Jun 10, 2014

### Evanish

I've thought about it some more, and now I realize that of course superman would seem distorted in ways other then length because his hand would have to accelerate towards the ball really fast. It's still hard for me to picture.

Last edited: Jun 10, 2014
3. Jun 10, 2014

### pervect

Staff Emeritus
I'm not understanding how one could put one hand's around a 2-d disk the same diameter as a basketball.

4. Jun 10, 2014

### Evanish

The same way one could put their hand around a frisbee. I'm sorry if my language is imprecise, what does one call a motion similar to catching a frisbee?

5. Jun 10, 2014

### jobermark

Quirky info related to this:

Archibald Wheeler has some cool computations about what various things would look like when moving at very high speeds because of the way light travels, in addition to the relativistic effects. There is also a film based on this of what someone would see flying down an immensely large highway at relativistic speeds.

In the 1980's my college had the original, but I found this: http://wn.com/relativistic_speed

6. Jun 10, 2014

### Evanish

Thanks for the link. I have to admit that now I feel like I understand relativity much less then I thought I did. There is a lot more going on then I thought. Maybe I should try looking up the various terms they used in the video.

Last edited: Jun 10, 2014
7. Jun 11, 2014

### pervect

Staff Emeritus
Ah, I get it now. Well, rather than "Superman's hand", I'd suggest the simpler, well-known, and well-documented problem of the barn and the pole vaulter.

http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html.

I find it difficult to envision superman's hand as well, and as a result one of my concerns is if the motions of his hand are physically possible. Let me illustrate with a specific model for the hand which we can evaluate. Model his hand as a hinged joint (the palm is a plate connected to another plate, which we can consider to be his fingers, by a hinge). The fingers, initially at right angles to the palm, start to close to catch it as soon as the ball reaches the fingertips.

ball=b
hand=x

\...distance d....\
xxxxxxxxxxxxxxx
b.....................x
b.....................x
b.....................x
b.....................x
b.....................x

then the leftmost (on the diagram) tip of the hand has to move along an arc of length pi/2 *d in the time it takes the ball b to travel a distance d. This means it has to move about 1.5 times as fast, and if b is above .7c, that just won't be possible.

In any event, one of the points of the paradox is that there is no such thing as an idealized rigid body, using Superman as an inspiration doesn't help one connect with the reality that even the stiffest objects aren't (and can't be) perfectly rigid.

8. Jun 11, 2014

### dauto

I strongly recommend you start by reading a good book on introduction to relativity from cover to cover. The other approach which is to read and learn about things as they come up leaves too many gaps.

9. Jun 12, 2014

### jobermark

Tying back to pervect, the way this is often discussed is in terms of who has to accelerate to determine the outcome. Forces change frames of reference in unexpected ways.

The question is whether Superman can have his palm on one side of the ball, say the side from which it is moving away from him, simultaneously with his having his fingertips close on the other side of the ball. But simultaneity of events happening at relativistic speeds is not something one can discuss in any absolute sense.

From his point of view, he can do so, from the ball's he cannot, but it does not matter because actually ascertaining whether or not his hand is destroyed would require one of the two of them decelerating. If this deceleration happened in a way that allowed his hand to stay intact, he will have done it.

Last edited: Jun 12, 2014
10. Jun 12, 2014

### ZapperZ

Staff Emeritus
Isn't this just a variation to the Pole-In-Barn problem that has been looked at ad nauseum?

Zz

11. Jun 12, 2014

### Staff: Mentor

Beat me to it... Yes it is.

12. Jun 12, 2014

### PAllen

Yes, definitely, but with a wrinkle: what does the 'hand' look like at different points of its motion in the ball frame. I've started to calculate this a few times, but keep getting side tracked. My abstraction is slightly different from Pervect's above:

1) I imagine a U shaped configuration, e.g. defined by the points (x,y)=(0,1),(0,0),(2,0),(2,1) connected in that order. I assume the ball is going by in this superman frame at e.g. .9999c parallel to the x axis, with its lower limit at y=1 (grazing superman's fingertips). I assume the ball is, say radius 5 in its rest frame.

2) The hand shoots up and down at near c. I assume instant change from 0 to near c up, then instantly to near c down. The constraint of the hand not moving ≥ c, while not being able to start before the trailing edge of the compressed ball is passed one side of the hand, and escaping down before being hit, put severe constraints on the shape of the hand.

3) Then, Lorentz transform to the ball frame, and describe the appearance.

13. Jun 12, 2014

### pervect

Staff Emeritus
I've snipped this part because I have some reservations on the "goodness" of describing things in this way.
I'm in agreement with this section.

I don't t think I agree with this part. With a specific realization of superman, and of the ball, I'm sure everyone would agree on what was destroyed and not destroyed at the end of the experiment.

I would agree that there are many, many issues in creating a physically possible implementation of "superman", furthermore that the comic book origins of superman tempts the reader to imagine comic-book like things rather than things that we could actually apply physical law to. This is one of several reasons why I prefer and would recommend the "pole valuter" treatment.

I also think that the term "caught the ball" sounds simple enough, but on further examination it's not clear what criterion one uses to determine whether or not the ball was "caught". For instance, if one requires that the catching process requires all the parts of the ball to be at rest at the end of the process, it's pretty clear that at the end of this process, superman's hand won't still fit around the ball, unless he's allowed to stretch his hand like one of the "stretching" heroes.

Rigid bodies are an idealization, an idealization that's moslty incompatible with relativity. The relativistic treatment of non-rigid, elastic bodies, the theory of "relativistic elasticity" is also still in its infancy, see for instance http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/SimpleElasticity.html and the refreences therin. I seem to recall that the state of the art is that there are still many basic issues such as existence and uniqueness of solutions .