Storing the Location of Every Particle in the Universe: Theoretical Limits and Realities

Imagine the enormity of the task: storing the location of every particle in the universe since the beginning of time. How many bytes would be required to achieve this? Would such a vast storage capacity crush the universe under its own weight? Let's dive into the theoretical underpinnings and practical considerations of this fascinating problem.

Theoretical Storage Requirements (Section Title)

When discussing the storage requirements for the location of every particle in the universe, we are quickly faced with the enormity of the task. Given that space may be continuous, and particles are in a constant state of motion, it seems like the necessary storage would be practically infinite. However, let's consider a more concrete scenario and calculate the approximate requirements.

The observable universe is about (10^{26}) meters in diameter. If we measure space with the Planck length, about (10^{-35}) meters, each measurement can have about (10^{64}) possible values. Since we are measuring in three dimensions, we need (10^{64} times 10^2 10^{66}) possible values, which translates to approximately 215 bits of information per position.

The observable universe contains around (10^{80}) particles. At each instant, we need to store the position of each particle. Therefore, we need (10^{80} times 10^{66} 10^{146}) bits of information at each instant. Given that the universe is about (10^{17}) years old, and each second is approximately (10^{-44}) Planck times, we have (10^{17} times 10^{44} 10^{61}) such instants. Thus, the total storage required is about (10^{146} times 10^{61} 10^{207}) bits, or (10^{205}) bytes. This is significantly more than a googol (i.e., (10^{100})), but it is a finite number.

Here, it's important to recognize that the actual storage requirements are likely not random and can be compressed. For example, the differences in particle positions might be clustered around discrete values, leading to substantial compression. Therefore, while the theoretical requirement is more than a googol, the actual practical storage requirements may be closer to a lot less.

Storage Capacity Compared to the Universe (Section Title)

Now, let's consider whether a storage capacity of (10^{100}) bytes would take up less matter than the universe. First, the mass of the observable universe is on the order of (10^{50}) kg. Even if we use the entire universe for storage, the mass available is still limited. In an electronic device, the maximum number of bytes that can be stored in 1 kg is approximately (10^{21}) bytes. With (10^{50}) kg, we can store (10^{50} times 10^{21} 10^{71}) bytes, which is not even close to a googol.

However, if we consider advanced technologies like computronium (the hypothetical material with the fastest possible processing speed and storage capacity), we can achieve much higher storage densities. Some estimates suggest that using the boundary of an evaporating black hole of the size of the observable universe (a factor of (10^{37})) could provide a storage capacity of (10^{108}) bytes, which is indeed more than a googol. Alternatively, the Bekenstein bound, which defines the maximum information content of a region of space, can also yield a similar result: a mass of (10^{50}) kg could fit into a black hole of about (10^{23}) meters in radius, leading to a storage capacity of (10^{115}) bits or (10^{114}) bytes, again just barely above a googol.

So, the question of whether (10^{100}) bytes would take up less matter than the universe becomes a matter of the technology and the utilization of space. With current and foreseeable technologies, it would still be significantly more than the mass of the observable universe. However, if we could harness the potential of computronium or advanced black hole technology, it might be possible to match or even exceed this STORAGE requirement without necessarily overwhelming the universe's mass.

Conclusion (Section Title)

The theoretical calculation shows that storing the location of every particle in the universe since the start of time would require an immense amount of storage, potentially more than a googol bytes. However, due to the nature of continuous space and the compressibility of certain data, the theoretical storage requirements may not be as daunting as they initially appear. The practical considerations of storage technology, such as computronium or black hole storage, suggest that a storage capacity of (10^{100}) bytes might be more than the mass of the observable universe but could be achievable with advanced technology. The holographic information hypothesis further supports the idea that the information content of the universe is tightly constrained and can be stored in a surprisingly compact form.