The twin paradox from the quantum information perspective.pdf

Bob and Alice are twins at the same location in space time and at the same frame of reference.

Based on the holographic principle their entropy (information) is limited by the area of the surface of
Their surrounding sphere divided by units in the size of Planck area.

Alice moves to another frame of reference relative to Bob.

Based on special relativity , from Alice perspective only, Bob’s information sphere undergoes length
contraction in the axis of the relative velocity between them.

Based on the holographic principle, from Alice perspective only, the length contraction will decrease
the surface information that she can experience from Bob’s frame of reference.

When Alice returns to Bob’s frame of reference, her loss of information during the period that they
separated in their frames of reference, will cause a unique situation in which Bob her twin brother,
who was exposed to more information (entropy) in their original frame of reference, will be older than Alice.

That’s the twin paradox from the perspective of quantum information (entropy).

1. The twin paradox from the quantum information perspective
https://en.wikipedia.org/wiki/Twin_paradox
https://en.wikipedia.org/wiki/Special_relativity
https://en.wikipedia.org/wiki/Holographic_principle
http://www.scholarpedia.org/article/Bekenstein-Hawking_entropy
https://en.wikipedia.org/wiki/Length_contraction
This presentation will illustrate the twin paradox ( Alice stays younger than Bob) based on :
•The holographic principle ( derived from Bekenstein – Hawking black hole entropy equation).
•Special relativity length contraction.
Eran Sinbar
Ela 13, Shorashim, Misgav, Israel
[email protected]
31 August 2024

2. Summary
Bob and Alice are twins at the same location in space time and at the same frame of reference.
Based on the holographic principle their entropy (information) is limited by the area of the surface of
Their surrounding sphere divided by units in the size of Planck area.
Alice moves to another frame of reference relative to Bob.
Based on special relativity , from Alice perspective only, Bob’s information sphere undergoes length
contraction in the axis of the relative velocity between them.
Based on the holographic principle, from Alice perspective only, the length contraction will decrease
the surface information that she can experience from Bob’s frame of reference.
When Alice returns to Bob’s frame of reference, her loss of information during the period that they
separated in their frames of reference, will cause a unique situation in which Bob her twin brother,
who was exposed to more information (entropy) in their original frame of reference, will be older than Alice.
That’s the twin paradox from the perspective of quantum information (entropy).

3. Bob Alice
Alice and Bob are twins at the same frame of reference at the same location
The blue circle illustrates the
space time sphere around Bob
The blue circle illustrates the
space time sphere around Alice
Bob Alice
Alice and Bob share the same frame of reference and the same space time sphere

4. The space time sphere information (entropy), from Bob’s
frame of reference perspective (same as Alice)
Bob Alice
Alice and Bob are twins at the same frame of reference at the same location
The space time sphere information (entropy), from Alice
frame of reference perspective (same as Bob)
Each small rectangle represents an information bit in the size of Planck area on the
surrounding surface of the space-time sphere ( based on the Holographic Principle)

5. Alice moves to a new frame of reference with a horizontal constant velocity relative to Bob
Bob
Alice
Alice and Bob do not share the same frame of reference and the same space time sphere.
From Alice perspective her original space time sphere , which is now only Bob’s spacetime
sphere, undergoes length contraction in the direction of her relative velocity compared to Bob.
This is based on Einstein special relativity .
V
The blue circle illustrates Bob’s
space time sphere from Bob’s perspective
The blue ellipse illustrates Bob’s
space time sphere from Alice perspective

6. Alice moves to a new frame of reference with a horizontal constant velocity relative to Bob
Alice and Bob do not share the same frame of reference and the same space time sphere.
From Alice perspective Bob’s spacetime frame of reference sphere, undergoes length contraction in the
direction of her relative velocity compared to Bob and a decrease in the surface area and in the number of
information bits. Due to the decrease in the number of information bits, from Alice perspective, in Bob’s
frame of reference she will age slower.
V
Bob’s space time sphere information (entropy), from Bob’s
frame of reference perspective
Bob’s space time sphere information (entropy), from Alice
frame of reference perspective

7. Alice moves to a new frame of reference with a horizontal constant velocity relative to Bob
Bob
Alice
Alice and Bob do not share the same frame of reference and the same space time sphere.
From Alice perspective her original space time sphere , which is now only Bob’s spacetime
sphere, undergoes length contraction in the direction of her relative velocity compared to Bob.
This is based on Einstein special relativity .
The blue circle illustrates Bob’s
space time sphere from Bob’s perspective
The blue ellipse illustrates Bob’s
space time sphere from Alice perspective
-V

8. -V
Alice moves to a new frame of reference with a horizontal constant velocity relative to Bob
Bob’s space time sphere information (entropy), from Bob’s
frame of reference perspective
Bob’s space time sphere information (entropy), from Alice
frame of reference perspective
Alice and Bob do not share the same frame of reference and the same space time sphere.
From Alice perspective Bob’s spacetime frame of reference sphere, undergoes length contraction in the
direction of her relative velocity compared to Bob and a decrease in the surface area and in the number of
information bits. Due to the decrease in the number of information bits, from Alice perspective, in Bob’s
frame of reference she will age slower than Bob.

9. Bob Alice
Alice and Bob are back at the same frame of reference at the same location
The space time sphere information (entropy), from Bob’s
frame of reference perspective (same as Alice)
The space time sphere information (entropy), from Alice
frame of reference perspective (same as Bob)
Alice returns to Bob’s frame of reference, and they share now the same space time sphere.
Based on the holographic principle they share now the same amount of information( entropy) number of
Planck area sized bits. Since for a period of time, Alice lost information (lower entropy) from Bob’s frame of
reference, she aged slower compared to Bob, once she returned to Bob’s frame of reference.
Time flow in a frame of reference, is the amount of information (entropy) in that frame of reference.

10. Bob Alice
The blue circle illustrates the
space time sphere around Bob
The blue circle illustrates the
space time sphere around Alice
Alice and Bob are back at the same frame of reference at the same location
Alice and Bob share the same original frame of reference (the one in which Bob stayed
the entire period) and the same space time sphere.
Alice is younger than Bob since for a period of time she lost information from Bob’s frame of reference.