APOD: Powers of Ten (2011 Feb 01)

[GoBears]

I have a used set of gravitational tenterhooks for sale on eBay if anyone is interested.

How many hours are on them? Is a warranty still available? Does the Buy Now price include free shipping?

"How many hours are on them?" you ask. How in the heck could I know that? Gravitational tenterhooks stretch spacetime, so the number of hours on them depends on the observer's frame of reference. But I will say this--they are relatively new. Get it? Relatively? A little Einsteinian humour.

PS Free shipping included.

[cljohnston108]

Ray and husband Charles, the film's creators, were known as quite visionary spirits and even invented their own popular chair.

I believe their more iconic chair is the Eames Lounge Chair and ottoman, which is seen in pretty much every classy abode in movies & TV.

[Javachip]

Note: Velocity doesn't start at zero once the motion has actually begun; (it is more like 0.23 m/s).

• t = 10 log(z)
  
  z = 10^t/10 = e^{(ln(10)/10) t}
  v = (ln(10)/10) z ~ 0.23 z
  a = (ln(10)/10) v ~ 0.23 v ~ (z/185) g's
  
  c ~ 3 x 10⁸ ~ 0.23 z_c
  z_c ~ 1.3 x 10⁹ meters
  t_c ~ 10 log(1.3 x 10⁹) = 91.14 seconds

Thank you neufer. Is z the distance traveled at time t? And, why do you say that initial velocity is 0.23 m/sec, rather than 0, at t=0? Is that necessary for the math to work out? I see that 0.23 appears in the equations for v and a.

[neufer]

Note: Velocity doesn't start at zero once the motion has actually begun; (it is more like 0.23 m/s).

• t = 10 log(z)
  
  z = 10^t/10 = e^{(ln(10)/10) t}
  v = (ln(10)/10) z ~ 0.23 z
  a = (ln(10)/10) v ~ 0.23 v ~ (z/185) g's
  
  c ~ 3 x 10⁸ ~ 0.23 z_c
  z_c ~ 1.3 x 10⁹ meters
  t_c ~ 10 log(1.3 x 10⁹) = 91.14 seconds

Thank you neufer. Is z the distance traveled at time t?

The parameter z is the height above the picnic assuming a field of view of ~53º (i.e., 1 m² is observed at a height of 1m).

Of course all this is calculated non relativistically.
A relativistic calculation would have to take into account
both time dilation and the relativistic distortion on the size of the field of view.

And, why do you say that initial velocity is 0.23 m/sec, rather than 0, at t=0?
Is that necessary for the math to work out?

Yes; every thing is increasing exponentially from the microscopic to the macroscopic;
the breaks at either end and at the picnic are artificial to the calculation.

I see that 0.23 appears in the equations for v and a

The factor 0.23 comes from ln(10)/10.
If this was "Powers of N" the factor would have been ln(N)/N.

[NoelC]

Has anyone calculated an upper-limit to the speed of imagination?

It would, for example, be silly to show the entire movie in a millisecond. People could not perceive it at all.

So does that say there is an upper-limit to the speed of imagination?

I can imagine two objects, one at one side of the known, observed universe, and one at the other, some tens or hundreds of billions of light-years apart. But it took me a few seconds to do so. Does that say that the speed of imagination something like a hundred billion light years per second?

Once we achieve faster than light speed travel, will we strive for faster than imagination speed travel?

-Noel

[WHRoeder]

Okay, so we don't know how to create a black hole yet.

Isn't that one of the possible outcomes of the LHC

[Javachip]

The parameter z is the height above the picnic assuming a field of view of ~53º (i.e., 1 m² is observed at a height of 1m).

In other words, z is the distance traveled at time t. I am with you so far.

...every thing is increasing exponentially from the microscopic to the macroscopic; the breaks at either end and at the picnic are artificial to the calculation.

What if the break at the beginning is not artificial? Suppose a rocket ship blasts off from the picnic blanket with a velocity of zero and acceleration of zero at time zero. Upon liftoff, every 10 seconds it travels 10 times the distance traveled in the previous 10 seconds. Ignoring relativity, how do the equations look for velocity and acceleration at time t? Does your assumed starting velocity of 0.23 m/sec become negligible?