I have a few simple questions regarding the key equation in Verlinde's paper, which is(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \Delta S = 2 \pi k_B \frac{m c}{\hbar} \Delta x ~~~~~~(3.6) [/tex]

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 [tex] \Delta x [/tex] 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"?

Thanks in advance,

Patrick

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# Simple questions about Verlinde's gravity=entropic force

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