Difference between LQC and Causal Sets

In summary, Casual Set theory and Loop Quantum Gravity both propose that spacetime at the fundamental level is discrete, made up of "atoms" or "chunks". However, they have different conceptual approaches - CST uses partially ordered causal sets while LQG uses spin networks. Both theories also assume that spacetime is fundamental rather than emergent. Additionally, there is another theory called Causal Dynamical Triangulation that suggests spacetime is made of higher dimensional triangles.
  • #1
windy miller
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Ive read that Casual Set theory says that spacetime is made of spacetime atoms. But doesn't LQG says something similar? Or is just space atoms in LQG? A laypersons expansion fo the main difference would be very much appreciated?
Also does Cause Set theory assume spacetime is fundamental rather than emergent?
Many thanks
 
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  • #2
I will try to explain main differences between Causal Set Theory (CST) and LQG. First of all, both proposals "predict" that spacetime at the fundamental (quantum) level is discrete - in other words made up from "grain", "atoms". However, from conceptually point of view these theories are different. CST essentials are partially ordered causal sets (causal posets) i.e. sets of events with some chronological order. Those posets encode causality and since they are locally finite - discreteness (finite volumes of continuum contain finite amount of elements of the causal set).
On the other hand, LQG assumes that spacetime at the fundamental level is composed from spin networks - nodes and links with assigned quantum properties - spacetime will be discrete and built from "chunks".

CST just like LQG assumes that spacetime is fundamental (but discrete), so gravity/spacetime isn't an emergent phenomena.
 
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  • #3
thanks for this, much appreciated.
 
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windy miller said:
thanks for this, much appreciated.
There is also Causal dynamical triangulation where spacetime is made of simplexes(higher dimensional triangles).
 
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FAQ: Difference between LQC and Causal Sets

What is the main conceptual difference between Loop Quantum Cosmology (LQC) and Causal Sets?

Loop Quantum Cosmology (LQC) is a theory that applies the principles of Loop Quantum Gravity (LQG) to cosmological settings, focusing on the quantization of spacetime geometry. Causal Sets, on the other hand, propose that spacetime is fundamentally discrete and consists of a set of events with a partial order that represents causality. The main conceptual difference is that LQC deals with quantized spacetime geometry, while Causal Sets emphasize the discrete nature and causal relationships between spacetime events.

How do LQC and Causal Sets approach the problem of singularities in cosmology?

LQC addresses singularities, such as the Big Bang, by replacing them with a quantum bounce due to the discrete nature of spacetime at small scales, effectively resolving the singularity. Causal Sets do not directly address singularities in the same way; instead, they provide a framework where the structure of spacetime at the most fundamental level is discrete, which could potentially offer new insights into the nature of singularities.

What are the mathematical foundations of LQC and Causal Sets?

LQC is based on the mathematical framework of Loop Quantum Gravity, which uses techniques such as spin networks and holonomies to describe the quantum states of spacetime. Causal Sets are based on order theory and graph theory, where spacetime is modeled as a partially ordered set (poset) of discrete events, with the order representing causal relationships.

Do LQC and Causal Sets make different predictions for the early universe?

Yes, LQC predicts a quantum bounce, replacing the classical Big Bang singularity with a transition from a contracting to an expanding phase. This has implications for the early universe's dynamics and potentially observable effects in the Cosmic Microwave Background (CMB). Causal Sets, while not providing a detailed cosmological model like LQC, suggest a fundamentally discrete structure of spacetime, which might lead to different predictions for the early universe's behavior and the emergence of spacetime geometry.

Are there any experimental or observational tests that can distinguish between LQC and Causal Sets?

Currently, there are no definitive experimental or observational tests that can distinguish between LQC and Causal Sets. LQC might leave imprints on the Cosmic Microwave Background (CMB) or influence the primordial gravitational wave spectrum, which could be tested with future observations. Causal Sets may lead to observable effects due to the discrete nature of spacetime, such as deviations from Lorentz invariance at very small scales, but these effects are challenging to detect with current technology.

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