# Simple questions about Verlinde's gravity=entropic force

1. Jun 16, 2010

### nrqed

I have a few simple questions regarding the key equation in Verlinde's paper, which is

$$\Delta S = 2 \pi k_B \frac{m c}{\hbar} \Delta x ~~~~~~(3.6)$$

First, Verlinde mentions that this is for a particle close to the screen. Does that mean that we have to keep changing screen as the particle moves in order to derive F=ma?
And what does $$\Delta x$$ represent here? Is it to be taken positive when the particle moves towards the screen or away from the screen?

Let me now focus on the derivation of F=ma.

In either case, there is something strange in that the equation does not refer to the acceleration at all.
Even if we know that the particle moves in a given direction, it does not tell us in what direction the
acceleration is! So following Verlinde's derivation, we can get a force pointing in the same direction as
the acceleration or opposite to the acceleration! The problem with his derivation is that he does not pay attention to directions and to signs, so this point is completely obfuscated.

There is a second problem. Let's say that the entropy increases when the particle moves towards the screen. Then, if we consider a screen ahead of the paricle, the entropy on that screen is increasing wih time, which means that the entropic force pulls the particle towards that screen (irrespective of the direction of the acceleration, which is the problem I mentioned in the previous paragraph). On the other hand,
if we consider a screen behind the particle, the entropy on *that* screen is decreasing in time, which
implies that the entropic force is pulling the particle in that direction!

It seems to me that we cannot place the screen wherever we want. I can think of an argument that would determine a preferred location of the screen in the constant acceleration case, but I don't see this issue discussed by Verlinde and I am wondering if I am missing something. Verlinde does talk about a side of the screen on which space has "emerged" and a side on which space has not emerged yet, but it's not clear to me how this is determined. For example, in his derivation of Newton's law of gravity, he talks about the side on which space has not emerged being inside the spherical screen. I am not sure what the rationale behind this is.

To summarize, my questions are

a) What does equation 3.6 mean? The entropy increases or decreases as we move towards the screen?

b) Does the direction of the acceleration play any role?

c) Where do we place the screen on which we compute the change of entropy?

d) Is there a clear rule to determine the side on which space has "emerged"?

Patrick

2. Jun 17, 2010

### Demystifier

3. Jun 17, 2010

### czes

This problem bothers me since 3 years.
Verlinde shows that entropy of the information tends toward the Event Horizon.
A. Inside an object the entropy means an expanssion of the space because of the supply of the information (our observable Universe).
B. Outside of an object means a collaps of the space (a Black Hole).

There is the Compton wave length in equation (3,6). I assume it is the most fundamental and non-local quantum information (discussion needed). If we integrate it over dx from 0 to R we have S=2 pi R k / (h/mc) for one particle. If there are N=M/m particles (Mass of object/mass of particle) for a Black Hole with a relation M=c^2 R /2G we calculate the contents of the information:
(M/m) [2pi R / (h/mc)] = pi R^2 / (hG/c^3 ) = A /4 Lp^2

Sabine Hossenfelder wrote about a gap when it comes to General Relavity.
I wrote a relation Gravitational/Electromagnetic interaction:
Fg/Fe=(1/alfa)(Lp/Lc1)(Lp/Lc2)
where:
Lp = Planck length, Lc1, Lc2 = Compton wave length of particle 1 and 2.
Why this relation is just a simple geometrical relation ?

I assume (discussion needed) each interaction between charged particle cause a deflection of the space of the Planckian length contraction and it is also non-local.
If we sume it over the Radius of the object the maximum density when the non-local information of one particle covers the Radius of the object:
[(Lp / (h/2mc)]= (R/Lp)
How many particles N=M/m we need ?
(M/m) [(Lp / (h/2mc)]= (R/Lp)
From this simple calculation we receive known solution for static Schwarzschild Black Hole:
2MG / c^2 = R

I think the Holographic Principle is the most fundamental in the physics and it shows our Universe is a hologram made of interfered quantum information..
http://www.cramerti.home.pl/ [Broken]

May be, you think, it is not true, so lets discuss it.

Last edited by a moderator: May 4, 2017
4. Jun 18, 2010

### nrqed

Thanks Demystifier, it's a very interesting paper indeed!
Unfortunately, she does not address the F=ma part of Verlinde's paper, so that still leaves most of my questions unanswered. It's still a very interesting reference and I thank you for bringing it up to my attention.

Cheers