[nilak (OP)]

I understand information as anything you need to know to define a portion of space identically to what it is in reality.
In my opinion, the information within a limited volume of space is infinite. That is because I also have an own concept about fundamental like aspects space and matter (I actually call it information). If that is the case entropy would need to be redefined as an order of deviation from similar properties of different points in space.

Can this be true in in Quantum Mecanics ?

Basically, when you plot a mathematical wave function on a 2d surface for example you need an infinite number of points, assuming the space is continuous . That means the particle has a probability to be found in any of those positions.

[evan_au]

In my opinion, the information within a limited volume of space is infinite. ...Can this be true in in Quantum Mechanics ?

Mathematically speaking, you could measure the position and velocity of every fundamental particle to infinite precision, which would produce an infinite amount of data.

However, quantum theory tells us that:
- The position and velocity of subatomic particles is a bit "fuzzy", so you can't actually measure it to infinite precision
- If you did try to measure to great precision, the measurement process itself would disturb the trajectory of the particles you are measuring
- Measurement requires energy, and measurement to infinite precision would require infinite energy; expending infinite energy in a finite volume of space would represent a severe disturbance to this volume of space!

So there is an effective maximum amount of information that could (in principle) be extracted from a given volume of space.

[jeffreyH]

From which follows that there should be a maximum amount of entropy in a given volume of space. Leading to the conclusions of Beckenstein and on to the holographic principle. This ties together entropy and information theory.

[nilak (OP)]

From which follows that there should be a maximum amount of entropy in a given volume of space. Leading to the conclusions of Beckenstein and on to the holographic principle. This ties together entropy and information theory.

Actually I have assumed entropy as total number of states but there are some other definitions.

[nilak (OP)]

In my opinion, the information within a limited volume of space is infinite. ...Can this be true in in Quantum Mechanics ?

Mathematically speaking, you could measure the position and velocity of every fundamental particle to infinite precision, which would produce an infinite amount of data.

However, quantum theory tells us that:
- The position and velocity of subatomic particles is a bit "fuzzy", so you can't actually measure it to infinite precision
- If you did try to measure to great precision, the measurement process itself would disturb the trajectory of the particles you are measuring
- Measurement requires energy, and measurement to infinite precision would require infinite energy; expending infinite energy in a finite volume of space would represent a severe disturbance to this volume of space!

So there is an effective maximum amount of information that could (in principle) be extracted from a given volume of space.

Alright, but probability distributions are continuous. A particle can be anywhere regardless of what we can measure.
The precision is actually given by the probability distribution.

[nilak (OP)]

I just realized that even if there a are an infinite possible configurations it doesn't mean the information required to describe one of them is infinite.

[jeffreyH]

If you could define an infinite compression algorithm, then in theory you could have infinite information in terms of computation. If this were true then it would suggest the possibility that a singularity does in fact compress matter into an infinitely small volume. Therefore entropy reversal occurs within the singularity.