Quote:
Originally Posted by bojan
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I read this paper which seemed suspiciously familiar until it dawned on me it was discussed over a year ago in the science forum.
The concept of gravity as an entropic force has compatibility issues with basic quantum mechanics and would contradict what is observed in the
double slit experiment.
Here are some of the comments made.
Quote:
sjastro wrote
Hmmm.
One argument against entropic gravity is the humble double slit experiment.
If you shot neutrons at the slits the quantum wavefunction of the neutron before the measurement is made is a linear combination of the Quantum states Ia> + Ib>.
Here Ia> could mean the neutron passes through the left hand slit and Ib> the neutron passes through the right hand slit.
If you rotate the slits 90 degrees so one slit is on top of the other, the slits exist in two different gravitational potentials.
Now according to entropic gravity if the holographic screen is at some distance below the bottom slit, the number of possible microstates which is a measurement of entropy increases as one gets further away from the screen.
Hence the top slit has many more microstates than the bottom slit even if the slits are separated by only the Compton wavelength of the neutron.
The problem is these microstates need to be considered in the quantum wavefunction. The quantum wavefunction is no longer simply Ia> + Ib>.
The difference in the number of microstates between the top and bottom slits would destroy the observed interference pattern as observed in the slit experiment as the probabilities of where the neutron hits the detector behind the slits have been changed.
Steven
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Quote:
sjastro wrote
Experiments show the orientation of the slits doesn't effect the observed interference pattern.
Before the observation is made the neutron is in a superimposed quantum state Ia>+Ib>.
Mathematically each state Ia> and Ib> has the same dimension or contains the same number of terms for superimposition to occur.
In the case of entropic gravity the neutron passing through the higher slit has many more terms describing it's quantum state when compared to when it passes through the lower slit.
Mathematically it is not possible to form a superimposed quantum state.
The lack of a superimposed state means that quantum interference cannot occur and one would not expect to see an interference pattern if the model of entropic gravity is correct.
One can use protons, electrons, even buckyballs instead of neutrons.
Steven
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Quote:
sjastro wrote
Alex,
Quantum states are described using Dirac's Bra-Ket notation.
The Quantum states are mathematically handled as single column or row matrices.
A superimposed quantum state such as a neutron before it hits the detector in the double slit experiment is in the form Ia>+ Ib>.
This involves matrix addition.
For matrix addition to occur the wavefunctions Ia> and Ib> must contain the same number of matrix elements.
However as has been pointed out if entropic gravity is correct the upper slit has many more microstates than the lower slit in which case Ia> and Ib> now longer contain the same number of elements.
Matrix addition is impossible and a superimposed quantum state cannot be formed.
The familiar interference pattern observed on the detector screen caused by the collapse of the superimposed quantum state should not be observed simply because there is no superimposed state to start with.
This a mathematical argument against entropic gravity.
The issue is on the validity of whether the thermodynamic microstates themselves can form the basis of the wavefunctions.
Another argument purely from a physics perspective is the different gravitational "environments" of the lower and upper slits results in quantum decoherence which would destroy the observed interference pattern.
Steven
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