# Stiffness of space

1. Mar 22, 2014

### Sonderval

Looking at the Einstein equation, stresses can cause a deformation of space time.
gives a value for the elastic modulus ("stiffness") of spacetime.
I think that the value of 10^24GPa must be related to Einstein's constant 8 pi G/c^4 - I suspect that one uses the equations for a small perturbation of flat spacetime (as Misner Thorne Wheeler, eq. 18.8b) to calculate this, but I don't see how it is done exactly.

2. Mar 22, 2014

Staff Emeritus
It would be helpful to have a source with more detail than twitter.

3. Mar 23, 2014

### Sonderval

Yes it would, but that's all I have found...

4. Mar 23, 2014

### Bill_K

I think this is just an example of the party game, Planck Scale Fun.

Take any physical quantity (pressure, say). Out of the Planck Mass, Length and Time, construct a unit with those dimensions. Then marvel about how large/small that unit is.

5. Mar 23, 2014

### Sonderval

But isn't there a physical meaning to it?
After all, the rhs of the linearised Einstein equation contains a stress (in the T_ij-part of the tensor), the lhs a change in the metric (which is similar to an elastic strain, it is a chenge of length relative to a length).
So I think it should be posisble to re-write things in a way similar to Hooke's law - at least that is what I thought when I read "stiffness of space". Or is this too simplistic?

6. Mar 23, 2014

### Bill_K

OK, more seriously.. This guy Anil Ananthaswamy is not a scientist, he's a popular science writer. Even if he had a valid point to make, Twitter is not the place of choice to publish it, I think!

Secondly, isn't it just a naming coincidence - the "stress" Tij in Einstein's Equation is the stress in a material body, not some stress being applied to spacetime. And the "strain" hμν generally results from T00 rather than Tij. Also it is a nonlocal effect - stress here produces strain over there.

There always have been attempts to imagine spacetime as some kind of elastic medium. I know when our class first learned about the dragging of inertial frames near a rotating body, we used to joke about calculating the "Viscosity of Free Space".

7. Mar 23, 2014

### Sonderval

@Bill_K
So even in this interpretation it is matter being stressed that causes a "strain" (change in the metric), but it is not spacetime that is "stressed" in any way.

"There always have been attempts to imagine spacetime as some kind of elastic medium."
I found this, for example