# What happens with causality at the Planck scale? Can effects precede causes?

• devhda
In summary: MathematicsIn summary, Rafael Sorkin's recent paper suggests that time may not be fundamental after all.

#### devhda

What happens with causality at the Planck scale? Can effects "precede" causes?

I would like to know what happens with causality at the Planck scale, explained in "educated layman" terms, if that's possible... :)

Might effects "precede" causes in time?

Do we have to redefine causality at the Planck scale?

The obvious answer is 'yes'. If time is an emergent property of the universe, then so must be causality.

The other obvious answer is no. If time is a fundamental concept, then so is causality. Causality violation may be an effective sieve that can be used to prune wrong theories.

The other obvious answer is no. If time is a fundamental concept, then so is causality. Causality violation may be an effective sieve that can be used to prune wrong theories.

there is even an approach where time=causality is the only fundamental concept. like the pre-socratic Greek philosophers who said the universe was made of fire (or whatever) in this approach the universe is made of causal ordering = time.

if someone wants to do a keyword search
causal sets
Rafael Sorkin
Faye Dowker
Joe Henson

the idea which maybe sounds a bit eccentric but maybe should be explored as one of several possibilities on the longshot bet it could be right is the idea that

the universe is made of nothing but time
and time = causality itself
and so it can be modeled as a partialorder set, a web, or network, of causality connections
between primitive nodes which are only there for the sake of the connections between them

and so the correct mathematical model of spacetime is made of nothing but a web of pure causality which goes forward in time (because that is what time is) forever branching and rejoining and growing new branches. Sorkin and others can actually derive stuff, like an idea of distance and thus inklings of geometry, from this very spare, lean basis. minimalist qg.

Rafael Sorkin has a new paper in the past couple of months

my apologies, Thomas, if I distracted from your general statement which is a solid mainstream view----causal sets QG takes what you said to an extreme

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The other obvious answer is no. If time is a fundamental concept, then so is causality. Causality violation may be an effective sieve that can be used to prune wrong theories.
There is also a third obvious answer. That time is a fundamental concept, while causality is not. (In fact, this answer seems the most obvious to me.)

the fourth obvious: time is not fundamental
causality is fundamental
time is emergent (from causality)

==============
By way of illustration see this recent article
http://arxiv.org/abs/gr-qc/0703098
Relativity theory does not imply that the future already exists: a counterexample
Rafael D. Sorkin (Perimeter Institute and Syracuse University)
(Submitted on 20 Mar 2007)
Abstract: It is often said that the relativistic fusion of time with space rules out genuine change or 'becoming'. I offer the classical sequential growth models of causal set theory as counterexamples.

in the above article Sorkin mentions several awkward things about time.
a universal time (as from a god's perspective) does not seem to exist.
we need a standard time for QM but there isn't any
if you describe time in the context of a classical SPACETIME then everything is static, the past present and future are all immobilized like a fly in amber, everything that has already happened or will happen exists in a 4D crystalline memory.

well I overstate to get the awkwardness of it across, perhaps its not that bad but there is a kind of inconvenience. if spacetime is complete, then where is the idea of BECOMING?

OK, Sorkin describes a spacetime that has an idea of becoming and that has many different strands of time-evolution.
but this spacetime is not made of time, it is made of causality or causal ordering.

Chronos: neither time nor causality are fundamental
Larson: both are fundamental (and I added the idea that time = causal ordering)
Demy: time is fundamental and causality is not
My take on Sorkin: causality is fundamental and time is not.

marcus said:
Chronos: neither time nor causality are fundamental
Larson: both are fundamental (and I added the idea that time = causal ordering)
Demy: time is fundamental and causality is not
My take on Sorkin: causality is fundamental and time is not.
I think it exhausts all the (obvious) possibilities.
Or does it?

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Demystifier said:
There is also a third obvious answer. That time is a fundamental concept, while causality is not. (In fact, this answer seems the most obvious to me.)
If you want to see what I mean by this, see:
http://arxiv.org/abs/gr-qc/0403121

Cauasality can be invariant of time- therefore it does not matter if Time is fundamental- or even if it 'exists' at all: http://mathworld.wolfram.com/CausalInvariance.html

which is the same as saying that [global] Time cannot be fundamental- and cannot be considered with regurd to a causal system even in principle

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marcus said:
Abstract: It is often said that the relativistic fusion of time with space rules out genuine change or 'becoming'. I offer the classical sequential growth models of causal set theory as counterexamples.[/color]
in the above article Sorkin mentions several awkward things about time.
a universal time (as from a god's perspective) does not seem to exist.
we need a standard time for QM but there isn't any
if you describe time in the context of a classical SPACETIME then everything is static, the past present and future are all immobilized like a fly in amber, everything that has already happened or will happen exists in a 4D crystalline memory.

Sorkin has a universal time in these models, that is counting time. How you turn or twist the beast - unless you want to get stuck in a one observer universe (which only MWI cranks want) - you have to include universal time (and Sorkin has understood that very well).

I'm glad to see that someone else seems to have read the paper.

==quote Sorkin page 4==
... “space developing in time”.
Perhaps a metaphor can bring out the key idea more clearly. Think of the causal set as an idealized growing tree (in the botanical sense, not the combinatorial one). Such a tree grows at the tips of its many branches, and these sites of growth are independent of one another. Perhaps a cluster of two leaves springs up at the tip of one branch (event A) and at the same moment a single leaf unfolds itself at the tip of a second branch (event
B). To a good approximation, the words “at the same moment” make sense for real trees, but we know that they are not strictly accurate, becauseevents A and B occur at different locations and distant simultaneity lacks objective meaning. If the tree were broad enough and the growth fast enough, we really could not say whether event A preceded or followed event B. The same should be true for the causal set. It is “growing at the tips” but not in a synchronized manner with respect to any external time. There is no single “now” that spreads itself over the entire process.

“But wait a minute”, you might object. “Didn’t you just describe the CSG growth process as a succession of births in a definite order, and doesn’t the resulting ranking of the elements of C imply something akin to a distant simultaneity?” The answer to this objection is that a definite birth-order, or an “external time”, did figure in the description I gave, but it is to be regarded as an artifact of the description analogous to one’s choice of coordinates for writing down the Schwarzschild metric. Only insofar as it reflects the intrinsic causal order of the causal set is this auxiliary time objective. The residue is “pure gauge”.
==endquote==

along any separate chain of events or branch, counting steps can be used as time. Causal sets people use that kind of counting a lot. But different chains are not assumed to proceed at the same speed according to a standard time. the "tree" does not grow in tick-tock lockstep. So the illusion that he is incorporating a universal time is "pure gauge", I would say.

an artifact of the means of description, to use his words.

I don't have a special need to discuss Sorkin's paper, so anyone can say whatever they please about it and I shall not wish to argue I simply point out in advance that I may well disagree with others in my understanding of what the paper says. Refer back to this quote from page 4.
Ciao.

marcus said:
I'm glad to see that someone else seems to have read the paper.

==quote Sorkin page 4==
... “space developing in time”.
Perhaps a metaphor can bring out the key idea more clearly. Think of the causal set as an idealized growing tree (in the botanical sense, not the combinatorial one). Such a tree grows at the tips of its many branches, and these sites of growth are independent of one another. Perhaps a cluster of two leaves springs up at the tip of one branch (event A) and at the same moment a single leaf unfolds itself at the tip of a second branch (event
B). To a good approximation, the words “at the same moment” make sense for real trees, but we know that they are not strictly accurate, becauseevents A and B occur at different locations and distant simultaneity lacks objective meaning. If the tree were broad enough and the growth fast enough, we really could not say whether event A preceded or followed event B. The same should be true for the causal set. It is “growing at the tips” but not in a synchronized manner with respect to any external time. There is no single “now” that spreads itself over the entire process.

“But wait a minute”, you might object. “Didn’t you just describe the CSG growth process as a succession of births in a definite order, and doesn’t the resulting ranking of the elements of C imply something akin to a distant simultaneity?” The answer to this objection is that a definite birth-order, or an “external time”, did figure in the description I gave, but it is to be regarded as an artifact of the description analogous to one’s choice of coordinates for writing down the Schwarzschild metric. Only insofar as it reflects the intrinsic causal order of the causal set is this auxiliary time objective. The residue is “pure gauge”.
==endquote==

Funny, I never said the opposite. First, dynamical laws have to be invariant with respect to this universal time, the latter merely serving to include an objective now'' and counting time does exactly that in the CSG models. Actually, the residual gauge invariance is much small than in ordinary gravity where surfaces of equal time can be timelike or null, this is never the case here by definition. Second, albeit the CSG dynamics is stochastic and therefore only statistical properties can be predicted, our universe happens to be one member of this Monte Carlo'' simulations and therefore does posess a definite universal arrow of time (within an ensemble of identical universes resulting frow a different growth process).

marcus said:
But different chains are not assumed to proceed at the same speed according to a standard time. the "tree" does not grow in tick-tock lockstep. So the illusion that he is incorporating a universal time is "pure gauge", I would say.
Strictly speaking, the notion of speed with respect to universal time is not an observable quantity, but I assume you merely want to say that the timelike distance between two successive chains is in general a function of the points on the chain. But there is a definite difference between GR and the causet CSG dynamics: the latter singles out by construction one particular time gauge ! Now, if you think this is artificial somehow, I urge you to rewrite the theory such that this does not occur (quite impossible as you realize after a few moments).

Btw Marcus : no-one uses the word universal time as you just described it.

Bye

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I suspect time and causality [and entropy, for that matter] are different manifestations of the same underlying principle. Separating one from the other is like separating siamese twins conjoined at the brain stem, only harder. For all practical purposes, I think they are fundamental in our universe. On a deeper level, they may well be emergent, but no observables to test that hypothesis appear possible. The notion of universal time is intriguish. Could this be the 'Dark Time" a University of Central Lancashire scientist claims to have found experimental evidence for in this article?:

http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-3040.1995.tb00201.x?journalCode=pce

If time is motion, can you "get away" with time? Imagine a closed box, away in space very far from any other body, in which no information from the outside world can be accessed. If all particles inside the box are kept at a fixed relative location among themselves and to the box walls, then does time stand still? One of course would have to impose a balancing force so as to keep the relative distances of particles fixed (otherwise they would eventually atract each other due to their relative gravitational interactions). The presence of the balancing force, however, would be an indication that, once released, particles would move, so eventually one would not be able to get away with time, and hence time would manifestly exist, even tought in some kind of potential or latent form.

Now, if you set the box as small as you wish, then when you approach the Planck scale, spacetime geometry starts to fluctuate quantum mechanically (if the spacetime foam framework is correct), so you are no longer able to keep a fixed distance between particles anyway. But what would be the notion of time, then?

Suppose DSR is right, then you have a minimum length scale (e.g. the Planck length) in which all micro-observers would agree about. Let all particles inside the box fix their relative distances as the minimum invariant scale or length. Notice that there is an assumption that the minimum length scale is an invariant and does not fluctuate. That is, would one here again be able to add a prescribed balancing force, under such a situation? Or, better yet, would one really *need* a balancing force at all? If not, would one be able to make time stand still then?

Christine

Dear chrisitine,

First of all you should distinguish clock time (being the result of a physical process) as periodic motion, and universal time as the parameter with respect to which this motion should be expressed (this distinction is unfortunately only somewhat made in GR). All other times in our laws of nature are clocktime : the time in Newtonian physics, Special and General Relativity. It is just so that in Newtonian physics and special relativity a gauge fixing of the universal time has been made (identifying it with physical clocktime of the prefferred class of observers).

Universal time cannot be banned from our laws (and never stops), unless you are prepared to go on the relational tour and describe the universe with respect to one observer (and by taking as time that observer's clocktime).

Careful

Careful said:
Universal time cannot be banned from our laws (and never stops), unless you are prepared to go on the relational tour and describe the universe with respect to one observer (and by taking as time that observer's clocktime).

A single-observer description is exactly what is needed to get around the present stalemate. This is no more (and no less) solipsistic than expanding a function in a Taylor series.

Note that the Taylor coefficients do not only depend on the function being expanded, but also on the base point, i.e. the observer's position. One can of course change the base point, and the coefficients must transform accordingly, but it does not make sense to consider more than one base point at a time. So by passing from field to Taylor data, we pick out a single observer.

Remarkably, this seems to resolve all the conceptual problems in quantum gravity, cf the last section of http://www.arxiv.org/abs/hep-th/0701164 . Careful may also note that the most glaring defects in my previous attempts (overcounting for the harmonic oscillator, no inner product) have been eliminated.

A single-observer description is exactly what is needed to get around the present stalemate. This is no more (and no less) solipsistic than expanding a function in a Taylor series.
I agree that it is a possibility, but it is too undemocratic to take one physical clock as a classical entity and study an identical clock as a quantum mechanical object relative to the first one. What one needs to do is to reformulate QM with respect to universal time and develop the relational picture from there : the braking of symmetry between clock1 and clock2 (which does not occur in the classical theory) can at best be an effective picture.

Careful said:
it is too undemocratic to take one physical clock as a classical entity and study an identical clock as a quantum mechanical object relative to the first one.

No, the parameter along the observer's trajectory is not a physical clock. A point-like observer moves along a one-dimensional curve, which can always be parametrized in some way. However, the parameter is not physical, since a group of reparametrizations act on it. It does define a sense of causality, since a continuous reparametrization cannot reorder points on a curve.

At any rate, the important thing about this modification is that it is either right or wrong. Since it gives rise to new diff and gauge anomalies, it is not merely a matter of interpretation.

No, the parameter along the observer's trajectory is not a physical clock. A point-like observer moves along a one-dimensional curve, which can always be parametrized in some way. However, the parameter is not physical, since a group of reparametrizations act on it. It does define a sense of causality, since a continuous reparametrization cannot reorder points on a curve.

At any rate, the important thing about this modification is that it is either right or wrong. Since it gives rise to new diff and gauge anomalies, it is not merely a matter of interpretation.
I was speaking about another approach where you can write physical observables in terms of A(tau), where tau is eigentime along the curve and then perform a quantisation with tau as the time parameter. I am aware that your theory does not suffer from this, but such symmetry braking occurs already at the classical level in the Starodubtsev Freidel approach where matter is generated by Wilson loops braking diffeomorphism symmetry upon the worldline (except for reparametrization invariance along the worline) - but again this is not the same thing.

However my point remains, it is undemocratic to break diffeo invariance on your preferred worldline and maintain it anywhere else (at least, I guess that this was the case in your theory).

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Careful said:
it is undemocratic to break diffeo invariance on your preferred worldline and maintain it anywhere else (at least, I guess that this was the case in your theory).

This is like saying that you break rotational invariance by constructing well-defined representations of SU(2). The need to quantize the observer's trajectory is forced upon us precisely by the representation theory of the diffeomorphism algebra.

B. The time misconception

Suppose that our universe is indeed some form of computation.
A common misconception in the universe simulation
literature is that our physical notion of a onedimensional
time must then necessarily be equated with
the step-by-step one-dimensional flow of the computation...
The temptation to equate time steps with computational
steps is understandable, given that both form a
one-dimensional sequence where (at least for the nonquantum
case) the next step is determined by the current
state. However, this temptation stems from an outdated
classical description of physics: there is generically no
natural and well-defined global time variable in general
relativity, and even less so in quantum gravity where time
emerges as an approximate semiclassical property of certain
perspective time with computer time is unwarranted even
within the context of classical physics. The rate of time
flow perceived by an observer in the simulated universe
is completely independent of the rate at which a computer
runs the simulation... Moreover, as emphasized by Einstein, it is
arguably more natural to view our universe not from the
frog perspective as a 3-dimensional space where things
happen, but from the bird perspective as a 4-dimensional
spacetime that merely is. There should therefore be no
need for the computer to compute anything at all — it
could simply store all the 4-dimensional data, i.e., encode
all properties of the mathematical structure that is our
universe. Individual time slices could then be read out
sequentially if desired, and the “simulated” world should
still feel as real to its inhabitants as in the case where
only 3-dimensional data is stored and evolved

max tegmark http://arxiv.org/abs/0704.0646

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This is like saying that you break rotational invariance by constructing well-defined representations of SU(2). The need to quantize the observer's trajectory is forced upon us precisely by the representation theory of the diffeomorphism algebra.
In ordinary physics, I break rotational invariance any time I add some massive particle (this comment goes specifically about the breaking of GC on *one* worldline). Concerning diffeomorphism invariance : I don't want any initial (since they are first class) constraints at all, the latter merely express that my mathematical language is containing excess bagage. Indeed, if we do observations, we always think in terms of imaginary straight lines. Now if light is somehow bending, you may think of that as light traveling on straight lines in a curved geometry, or as light not traveling on straight lines at all. Both viewpoints are I think equivalent (the latter giving rise to a gauge theory on Minkowski). Now, if in the latter approach you know how to distillate the beables (for example strings) - just like we know how to do this in gauge theory - then we are in business. I don't argue that general covariance is incorrect, just that my theory does not need to be *manifestly* covariant, just as I don't want any manifest gauge covariance in some SU(N) gauge theory.

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SetAI, thanks for noting that passage from Tegmark. I will highlight a part that seems especially relevant from my standpoint:

However, this temptation stems from an outdated
classical description of physics: there is generically no
natural and well-defined global time variable in general
relativity
, and even less so in quantum gravity where time
emerges as an approximate semiclassical property of certain
“clock” subsystems... The rate of time
flow perceived by an observer in the simulated universe
is completely independent of the rate at which a computer
runs the simulation...

But notice that if you exclude black holes or other extreme curvature there is an approximate universal time in cosmology as measured by an observer anywhere in the universe who is at rest with respect to the CMB.
One reason we get puzzled sometimes may simply be because we confuse General Theory of Relativity with the actual universe we live in.

Tegmark makes good points here though!

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marcus said:
SetAI, thanks for noting that passage from Tegmark. I will highlight a part that seems especially relevant from my standpoint:

However, this temptation stems from an outdated
classical description of physics: there is generically no
natural and well-defined global time variable in general
relativity
, and even less so in quantum gravity where time
emerges as an approximate semiclassical property of certain
“clock” subsystems... The rate of time
flow perceived by an observer in the simulated universe
is completely independent of the rate at which a computer
runs the simulation...

But notice that if you exclude black holes or other extreme curvature there is an approximate universal time in cosmology as measured by an observer anywhere in the universe who is at rest with respect to the CMB.
One reason we get puzzled sometimes may simply be because we confuse General Theory of Relativity with the actual universe we live in.

Tegmark makes good points here though!
Well yeh, there is no natural global *physical* time function (unless you build some cosmic restframe from dust or something like that - K. Kuchar has worked on that), but it doesn't exclude a global ontological time''. Even Einstein's theory contains such notion of time (there we call it coordinate time) : but if you are convinced this is a mathematical artifact, I dare you to reformulate the theory so that only *observables* are included in its very formulation. Cynically enough (since all AE worshippers are more blind -as is usually the case for worshippers - than the master himself), Einstein realized this point very much as well as the related problems concerning a local conserved energy momentum current in GR. Friends of his, including Nathan Rosen, invented therefore the so called bi metric theories...

Careful

Belief systems are a problem. It is wise to question all assumptions. I think that is precisely what Einstein attempted to do - and did it better than anyone else in history. A universe without observables is - fantasy.

Chronos said:
Belief systems are a problem. It is wise to question all assumptions. I think that is precisely what Einstein attempted to do - and did it better than anyone else in history. A universe without observables is - fantasy.
Euh, who said something about a universe *without* observables, I was merely speaking about (not wanting) a *classical* universe with *nothing but* observables. Now, I you want to shoot hidden variable theories containing more unobservable hidden variables than observable ones, you might want to go to the QM forum.

It is fairly apparent that cosmic clocks were ticking away long before humans came along and coined the term 'time' to assign it measurable properties. In a universe governed by cause and effect, time is literally of the essence. I am content [at times even insistent] with a description of the universe that includes nothing but observables as facts in evidence. In other words, I deeply suspect QM is more fundamentally flawed than GR. No denying that it works at many levels, but . . .

## What is the Planck scale?

The Planck scale is the unit of measurement used in quantum mechanics to describe the smallest possible length, time, and energy scales in the universe. It is defined as 1.616 × 10^-35 meters or about 10^-44 seconds.

## How does causality work at the Planck scale?

At the Planck scale, the fundamental laws of physics break down and traditional concepts such as causality may not apply. This is because the fabric of spacetime becomes highly curved and quantum effects become dominant.

## Can causality be violated at the Planck scale?

It is currently unknown whether causality can be violated at the Planck scale. Some theories, such as loop quantum gravity, suggest that causality may still hold at this scale, while other theories, such as string theory, propose the possibility of effects preceding their causes.

## Are there any experiments that can test causality at the Planck scale?

Due to the extreme conditions at the Planck scale, it is currently impossible to conduct experiments to directly test causality. However, scientists can use mathematical and theoretical models to make predictions and test the validity of different theories.

## What are the implications of causality being violated at the Planck scale?

If causality is violated at the Planck scale, it could have profound implications for our understanding of the universe and the laws of physics. It could potentially lead to a revision of fundamental principles and a new understanding of how the universe operates at its most fundamental level.