Space/Time Non-Commutativity and Causality

L. Susskind; N. Seiberg; N. Toumbas

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Space/Time Non-Commutativity and Causality

N. Seiberg, L. Susskind, N. Toumbas

High Energy Physics - Theory · Submitted 1 May 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Stringy effects conspire to cancel the acausal effects that are present for the non-commutative field theory.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.74 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Field theories based on non-commutative spacetimes exhibit very distinctive nonlocal effects which mix the ultraviolet with the infrared in bizarre ways. In particular if the time coordinate is involved in the non-commutativity the theory seems to be seriously acausal and inconsistent with conventional Hamiltonian evolution. To illustrate these effects we study the scattering of wave packets in a field theory with space/time non-commutativity. In this theory we find effects which seem to precede their causes and rigid rods which grow instead of Lorentz contract as they are boosted. These field theories are evidently inconsistent and violate causality and unitarity. On the other hand open string theory in a background electric field is expected to exhibit space/time non-commutativity. This raises the question of whether they also lead to acausal behavior. We show that this is not the case. Stringy effects conspire to cancel the acausal effects that are present for the non-commutative field theory.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Field theories based on non-commutative spacetimes exhibit very distinctive nonlocal effects which mix the ultraviolet with the infrared in bizarre ways.	background 1.00	0.06	0.03	asserted 1.00
s1	In particular if the time coordinate is involved in the non-commutativity the theory seems to be seriously acausal and inconsistent with conventional Hamiltonian evolution.	background 1.00	0.08	0.04	hedged possibility 0.95
s2	To illustrate these effects we study the scattering of wave packets in a field theory with space/time non-commutativity.	contribution 0.72	0.86	0.02	asserted 0.94
s3	In this theory we find effects which seem to precede their causes and rigid rods which grow instead of Lorentz contract as they are boosted.	result 1.00	0.92	0.04	asserted 0.68
s4	These field theories are evidently inconsistent and violate causality and unitarity.	interpretation 0.63	0.33	0.08	asserted 0.96
s5	On the other hand open string theory in a background electric field is expected to exhibit space/time non-commutativity.	background 0.94	0.05	0.03	hedged possibility 0.92
s6	This raises the question of whether they also lead to acausal behavior.	gap 0.88	0.06	0.03	unclear 0.49
s7	We show that this is not the case.	result 1.00	0.89	0.68	asserted 1.00
s8	Stringy effects conspire to cancel the acausal effects that are present for the non-commutative field theory.	result 0.87	0.81	0.66	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.95.

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Original abstract

Field theories based on non-commutative spacetimes exhibit very distinctive nonlocal effects which mix the ultraviolet with the infrared in bizarre ways. In particular if the time coordinate is involved in the non-commutativity the theory seems to be seriously acausal and inconsistent with conventional Hamiltonian evolution. To illustrate these effects we study the scattering of wave packets in a field theory with space/time non-commutativity. In this theory we find effects which seem to precede their causes and rigid rods which grow instead of Lorentz contract as they are boosted. These field theories are evidently inconsistent and violate causality and unitarity. On the other hand open string theory in a background electric field is expected to exhibit space/time non-commutativity. This raises the question of whether they also lead to acausal behavior. We show that this is not the case. Stringy effects conspire to cancel the acausal effects that are present for the non-commutative field theory.

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Cited by 13 Pith papers

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How the literature uses it

31 arXiv papers cite this in 44 sentences

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Papers citing it · 33 sentences without a confident label

Builds on it 1 paper

We now remark that, in the case of Neumann strings in the presence of a constant electric field, with intensity $E⃗$, as was considered in [ref] , the time delay is modified to become [equation] where $Ẽ_i ≡E_i/E_c$ and $E_c ≡1/2πα'$ is the Born-Infeld critical electric field, that characterizes open strings in an external constant electric field background [ref] .

Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model · A D-Brane Model for the Vacuum Refractive Index · 0.95

Cites it as support 3 papers

Remark, however, that even if certain constructions may appear to be unitary, causality is still violated – the use of causal Feynman propagators in the path integral approach, for example, does not render the theory causal, as can be seen from the macrocausality analysis of [ref] .

Noncommutative Time in Quantum Field Theory · Introduction · 0.98
Unlike in field theory, the presence of spacetime non-commutativity does not lead to causality violations [ref] .

Ascending the attractor flow in the D1-D5 system · Degeneration and decoupled six-dimensional string theories · 0.96
It is not surprising that this nonlocality leads to acausal effects, see, e.g., [ref] .

Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space · Acausality · 0.96

Cites it as background 7 papers

We remark that noncommutative field theories typically contain infinitely many time derivatives in their actions, which may lead to apparent violations of unitarity [ref] and causality [ref] .

Exponentially Long Evaporation of Noncommutative Black Hole · Introduction · 0.84
The non-commutativity has received a wide appreciation as an alternative approach to understanding many physical phenomenon such as the ultraviolet and infrared divergences [ref] , unitarity violation [ref] , causality [ref] , and new physics at very short distances of the Planck-length order [ref] .

Noncommutative of space-time and the relativistic Hydrogen atom · Introduction · 0.94
One famous example is provided by backgrounds with critical electric fields, where the string spectrum becomes non-relativistic and one is naturally led to the NRST/NCOS regime [ref] .

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