Blue-Shifted Photons & Infinite Computation
Audio Brief
Show transcript
This episode covers how the physics of blue-shifted photons challenges the viability of Malament-Hogarth spacetimes and infinite supercomputation.
There are three key takeaways from this discussion. First, signals sent from an infinite future compress into highly energetic, blue-shifted waves. Second, this physical limitation serves as a diagnostic tool to evaluate theoretical cosmological models. Third, even mathematically sound spacetimes often remain physically impossible when considering real-world constraints.
In Malament-Hogarth spacetimes, a finite observer could theoretically receive the results of an infinite computation. However, the incoming signals bunch up, creating an infinite energy concentration that destroys the transmission. Physicists use these extreme physical boundaries to rule out unrealistic mathematical models.
Ultimately, the blue-shift problem demonstrates that mathematical consistency in general relativity does not guarantee physical reality.
Episode Overview
- Explores the concept of "blue-shifted photons" within the context of Malament-Hogarth spacetimes.
- Explains how these theoretical spacetimes allow a finite observer to witness the infinite future of another entity, such as a computer.
- Discusses the physical limitations and arguments against the feasibility of such spacetimes due to the extreme blue-shifting of signals.
- Highlights the academic effort to model a physically reasonable Malament-Hogarth spacetime and the inherent difficulties in doing so.
Key Concepts
- Malament-Hogarth Spacetime: A theoretical spacetime structure where a spacetime event's past light cone contains the entire worldline of an observer who experiences infinite proper time. This theoretically allows for "supercomputation," where an infinite computation can be completed and its results received by a finite observer.
- The Blue-Shift Problem: As signals are sent from an observer experiencing an infinite future back to a finite point in spacetime, the signals "bunch up." This causes their wavelengths to shorten drastically (blue-shift), leading to potentially infinite energy concentration and rendering the signals highly unreliable or physically impossible.
- Unphysical Properties of Spacetimes: Physicists look to exclude certain spacetime models based on physical constraints, such as the blue-shift of photons, violation of standard energy conditions, or the requirement of infinite fuel and extreme acceleration for observers.
Quotes
- At 0:07 - "The blue shift happens because... what a Malament-Hogarth spacetime is, is you identify a point, an event in the spacetime, and you look at its past light cone, and in the past light cone you have an observer with an infinite future." - explaining the fundamental setup of a Malament-Hogarth spacetime that enables supercomputation.
- At 0:51 - "When the computer is sending signals back to that point, they can start to bunch up... so the wavelength will go towards the blue side of things." - clarifying how the physical clustering of incoming signals causes the problematic blue-shift effect.
- At 2:13 - "The irony is that this model is pretty unphysical, even by my standards." - highlighting that even when carefully constructing a model to avoid typical unphysical pitfalls, the resulting spacetime remains highly unrealistic.
Takeaways
- Use the blue-shift phenomenon as a diagnostic tool to evaluate the physical viability of highly theoretical spacetime models in general relativity.
- Consider multiple intersecting constraints (energy conditions, acceleration limits, signal reliability) rather than a single metric when attempting to rule out or validate exotic cosmological models.
- Recognize the limits of mathematical toy models in physics, understanding that constructing a mathematically consistent model free of known "unphysical" traits can still result in a scenario that is practically impossible.
