Sheldon Gao

Finally somebody started the real work; to accept or not, Verlinde's proposal. You can read this paper here in the arXiv.

I may sound like I already swallowed the whole argument by Verlinde. Remember that these are my notes, not a Scientific proposal. When I have one, you'll see it in the Los Alamos  electronic repository.

Gao is telling us that the contradictions come from what one assumes, and what one derives. Verlinde was not careful. This author works in the Unit for History and Philosophy of Science & Centre for Time, SOPHI, University of Sydney. I assume he has good training in logic.

"Even if Verlinde’s mathematical derivation is wholly right, we still need to determine whether gravity results in the change in entropy or the change in entropy results in gravity."

I know most physicists I know tend to avoid fundamental issues. What was first the chicken or the egg kind of things. We are not trained to do that. Very few times in History we are confronted with Philosophy of Science.

This is one of those times.

"In the following, we will further show that neither Verlinde’s causal chain nor the causal chain for entropic force is right for explaining the above interacting process between a holographic screen and a particle. First, we provide a proof by contradiction to show that Verlinde’s causal chain is wrong. Assume the causal chain is Δx → ΔS → F , as Verlinde implicitly argued. Then when Δx = 0 , we have ΔS = 0 and F = 0 . This means that there will be no interaction between two masses being at rest relative to each other. But this result obviously contradicts experience, as there is a gravitational interaction between them. In fact, we can reach the same conclusion from another contradiction. The formula FΔx = TΔS can only have two possible causal chains: one is FΔx → TΔS , and the other is TΔS → FΔx . But Verlinde’s causal chain Δx → ΔS → F contradicts both, which also indicates that it is impossible and wrong."