Breaking the Universe's Speed Limit

Amrit,

Congratulations on the article in Physorg:

http://www.physorg.com/news/2011-04-scientists-spacetime-dimension.html

Is c scalable? That's a worthy pursuit. I would like more details about the program for which you were awarded the grant.

A harder question might be what is not scalable. Is pi scalable? I would say no, but the ratio components are scalable. We think we know what is extensible and scalable by looking at networks. So, in this context, is a node scalable and thus emergent? A black hole is definitely scalable and we measure it in terms of star masses. Conserved quantities and invariant forms, constants of nature seem to go in lock step. Scaling an object seems to be the only way to normalize it. The size and shape of. say, a network matters at every node and stage of development. Are there certain nodes that are not scalable? Even when a node desires to limit its scalability could not halt the extensibility around it. The discreteness of the problem becomes elusive: at the very small, the kernel becomes degenerate, vanishing; at the opposite end, accountings must be made for stuff we can only observe indirectly (dark matter and energy). Must one conclude that energy is not scalable but a totality? If c is not a self dual of some ultimate form, is there some other normed space that can be constructed from dark matter and dark energy to give a sort of quantum Hall effect for c being scaleable? What kind of object will this "light" be? It will not be guage invariant if a rank two tensor, so it must be a tensor of higher rank. Where can I learn more details?

LC,

Again, thank you for engaging on this. I fear, however, that because we have not explicitly addressed the paradigm issue which I raised in a previous post we continue, in essence, to talk past one another. This can be corrected, but it will take some effort. I'm willing if you are; I firmly believe it's well worth the candle.

You wrote, "The nature of time is an interesting subject. I don't get very partisan over the issue of time existing, for physics seems not to welcome ontological or existential ideas from the outset, but only suggests these within some theoretical construct."

Let me ask, do you get partisan over the issue of paradigms such as the pre-Copernican vs. the post-Copernican cosmological paradigms? This is the sort of thing I'm talking about here, and I do get partisan over such issues. In this regard, I strongly believe that when you use the word "time" you mean something by it which is very different than what I mean when I use the word "time."

As an example to help clarify this point, please consider the word "day." The word "day" had a very different meaning in the pre-Copernican era than it has now. We no longer think of a day as being the time required for the sun to revolve once around the Earth, but rather as the approximate time it takes for the Earth to rotate once on its axis.

Would it not, therefore, be fruitless to engage in a debate over whether a "day" exists or not? In my opinion, debates about whether "time" exists or not fall into much this same category. Before we can have a fruitful debate about whether something exists or not we need to have a clear and mutual understanding regarding the meaning of the term the existence of which is being debated.

I saw nothing in your previous reply which leads me to believe that you have given serious thought to the different paradigms which I suggested we are using when we think about and talk about the nature of time.

Along these same lines, I also must retract a statement which I made in my post of April 24th (above). In that post I wrote, "I'm not trying to say that either of these paradigms is necessarily more 'correct' than the other, only that they are different and lead to different ways of thinking about the same things, just as there are different ways of interpreting what we're seeing when we look at a Necker cube, for example." That was spoken in error; I do believe that one paradigm for the nature of time is more correct than the other, just as I believe that the post-Copernican paradigm is more correct than the pre-Copernican paradigm. We are not talking about Necker cubes here.

Moreover, I believe that the paradigm which I've spelled out in my various essays (referenced elsewhere) moves forward the longstanding Heraclitean-Parmenidean (essentially "presentism" vs. "eternalism") debate. This debate is not purely academic or metaphysical, by a long shot, any more than are debates about the virtues of pre-Copernican vs. post-Copernican cosmology.

jcns

JCN

Yes, we are the "time mafia" and I am probably the worst of the bunch.`

I was tired of playing with shadows and ghosts. I devised a logical path for the reification of time directly from the requirement of a universe based on (or abiding by) the rule of non-contradiction. The passage of time is now a dynamic and substantial process that follows simple rules of logic which define both existence and causality. The passage of time makes everything and matter can be seen as a form of time replacing time passing by simple logical substitution.

Logic itself requires the ultimate reductionism, that, for the universe to be operational i.e. to work by itself, it has to be made of only one substance.

The "nature of time" is the most wrongly uttered words. The word "nature" calls for a specific aspect of time; what it is by itself, its ontology.

Looks simple and yet, I am the only one in the whole world who seem to be able to fathom this distinction. Everybody else is running around, wanting it all, but not willing let go anything...

Marcel,

Logic says we can't add apples and oranges. This means that logic only allows operations on elements of the same nature. So, an equation like E=mc2 can only be viewed as being logical if/if we realize and accept the fact that every variable and constant on both sides of the equation represent, at the most fundamental level, elements of the same nature and logically computable.

The reductionism in physics has followed our knowledge and has seen a reduction in the number of independent variables: electricity and magnetism, electro-magnetism, mass and energy, space and time etc. but, always gaining in the process the relation that tied them together. But physics limits the amount of reduction we can achieve because we must keep those dimensions around that allow us to do physics... We have to move right into metaphysics in order to effect the final reduction and gain, not one more relation, but the actual logical understanding of the universe. But for this, we have to let go of our reality, just for a moment.

The type of shotgun reductionism that Amrit proposes is about shooting down one important variable without gaining its proper relation to the rest of physics i.e. where it really fits into the big puzzle.

Marcel,

The Parmenidean view is similar in a way to the block universe view of time. The Heraclitean perspective is more in line with the ADM relativity view of time.

Cheers LC

LC,

Thank you for that clarification. I've tended to think of all versions of general relativity as being closely associated with the Parmenidean or block universe view of time, which is the antithesis of the paradigm for time which I've attempted to spell out in my various essays.

The disparity between the Heraclitean and Parmenidean views clearly is *not* an example of a distinction without a difference. The difference between these views (and what this difference means in terms which are meaningful to us as flesh and blood humans) could hardly be more dramatic, just as the difference between pre- and post-Copernican cosmology could hardly be more dramatic. And it is exactly for this reason that I'm puzzled (an immense understatement) that this question of which view is more "correct" has not been settled long before now. Using the more correct paradigm for the nature of time should, at least in principle, allow advances in science not unlike those which were made possible once the post-Copernican cosmology was accepted as being more correct than its predecessor.

I agree with David Deutsch that ". . . one of the most valuable, significant and also useful attributes of human thought generally is its ability to reveal and explain the fabric of reality." (D. Deutsch, 'The Fabric of Reality,' p. 3) Thus far, however, human thought apparently has not succeeded in finally resolving the Heraclitean-Parmenidean debate. This is astounding, in my opinion! And I place much of the blame for this failure directly on the faulty paradigm for the nature of time which has dominated western thinking since prior the advent of physics as a science.

The mainstream, prevailing paradigm for the nature of time has led to many brilliant successes, and this fact has tended to blind us to its less obvious shortcomings, in my opinion. I attempted to spell this out explicitly and as clearly as possible in my essay 'Time: Illusion and Reality.' Going back to the drawing board with a clean sheet of paper and reinventing physics using a different paradigm for the fundamental nature of time understandably is not something which would appeal to many of today's working physicists. And I certainly can't blame anyone for that. If I were more clever I'd give it a go myself, but I fear that the task far exceeds my abilities.

Regards,

jcns

Marcel,

Since Tom insists on questioning every term I use, I keep have to respond by further focusing my argument. I'll post this latest itineration and see if you think it makes sense, as a description of time:

There is only that thermal medium/particle cloud/quantum state.

As the energy/mass/plasma/waves/particles moves around, it changes configuration.

Since it is in a constant state of flux, these configurations are constantly being replaced.

Some areas in which there is greater activity naturally change shape faster than those with slower levels of activity.

Now since we are mobile points of reference, we are also one of those particles moving about. We are moving forward from our individual perspective and the larger situation is changing, so it is quite easy to conflate our sense of motion with this larger change, thus we seem to move from one configuration to the next, in much the same way we move along a path.

The larger reality though, is that our actions are balanced in this larger context, so there is that non-linear reaction to our motion, which compensates for our motion, to maintain the larger equilibrium.

Because there is just this sea of energy and energy is conserved, it is impossible to have sequential configurations co-existing, because they are constituted from the same energy.

So the old configuration fades into what we colloquially refer to as the "past." As all this energy bounces around, the new configurations emerge from this action. Those ranges of probabilities of what might happen as this energy interacts, are what we colloquially refer to as the "future."

So this current configuration emerges out of this action and is replaced by it.

What we colloquially refer to as the "present" doesn't move along some fourth dimension, because it is all that energy/mass particles/waves/thermal medium/cloud of motion that is all that exists.

Thus these moments of configuration emerge from that "future" and recede into that "past."

It is only because we can only exist in that present state, that we sense it as going from past configurations to future ones, but it is not the present which moves, only that it changes shape.

So while we have this subjective sense of "moving" from "past" to "future," the objective reality is that potential becomes actual and is replaced, ie. the future becomes past.

John,

I have great difficulty with the structure, format and content of the text.

What is well understood can be expressed clearly. I am not sure you understand well the idea you are trying to convey.

This appears to be the typical struggle when we mix elements of our reality and element of a real universe as can be deduced from various accepted theories.

1- future, present and past are true in our reality because we have no choice about it, this is the way we think and work. Period. There is no sense in screaming and kicking about it.

2- The real universe is different from our reality and can be inferred/deduced from literal understanding of SR & GR. and applying it to something that exists

in substance.

Again, contradiction and paradox appears when we mix and compare elements from our reality and elements from the real universe.

I am always interested in a theory of time that addresses a specific component of time. I always do it; try to re-formulate it in simple terms ..

The Perception of time I leave to psychologist and neurobiologists and maybe some philosophers etc.

Marcel,

To JCN Smith,

Einstein probably made the biggest push forwards in our understanding of time. He demonstrated with the invariance of light speed that time was interchangeable with space. This is the Lorentz transformation. This extends to general relativity, where now spacetime is in a sense the "field" of gravity. However, something is odd here, for gravitational degrees of freedom are contained in the Weyl tensor. So the field of gravity has physical degrees of freedom in the case of gravity waves where C_{abcd} =/= 0. In the case of a black hole, a stationary observer may watch clocks on objects falling into the black hole slow down to a stop as they asymptote to the horizon. However, this is not a system which interacts with the exterior world by gravitational degrees of freedom in this stationary configuration. An object fall towards a black hole is observed so the frequency of radiation from the body decreases as it red shifts "to infinity," which is the same as watching time slow near the black hole. What does change, or is not entirely static, is the fact that a body approaching a black hole adjusts the mass of a black hole. As a result the stationary (noninteracting) degrees of freedom associated with a black hole changes. This is a sort of gravitational form of the measurement problem.

Time may then be a one dimensional aspect of reality that reflects how gravitational degrees of freedom transform. In that setting time is something akin to a one dimensional communication channel, or a form of transmission line. It is then possible that time is a parameterization of a quantum error correction code for the universe, where the most general form might be the Jordan matrix algebra.

Jacob Bekenstein and Avraham May demonstrated how black holes are one dimensional channels of quantum information back in 2001. Ashoke Sen demonstrated something similar to this. An anti-de Sitter (AdS) spacetime of dimension n is equivalent to a conformal field theory of dimension n-1. The isometries of the AdS spacetime are equivalent to the conformal symmetries of a conformal field theory (CFT) on the boundary. The near horizon condition for a black hole in an AdS spacetime is AdS_2xS^{n-2}, where S^{n-2} is a sphere or dimension n - 2. The AdS_2 is a hyperbolic spacetime with a structure similar to the Escher prints of tessellated disks called circle limits. The boundary of this spacetime is CFT_1, in one dimension, where the isometries of this space are the group of conformal quantum mechanics. The group is the set of diffeomorphisms of the circle (which bounds the AdS_2 disk) and this defines the set of bosonic string states. The AdS_2 is then equivalent to a circle group on CFT_1 ~ S^1xS^0 (where this is a generalization of CFT_n ~ S^1xR^{n-1}) and the S^0 defines two points. These two points turn out to be dual states for the Hartle-Hawking vacuum (HHV). The HHV comes from their seminal paper in 1984 on the wave function of the universe.

The next interesting direction is that Borsten, Duff, Marrani, and Rubens published a paper which illustrates a mathematical correspondence between entanglements in 3 and 4 qubit quantum systems with BPS and extremal black holes respectively. To illustrate this it requires one work in the STU system with radial symmetry. In that case all the Killing isometries of the theory are timelike, and they are defined in one dimension of a moduli space. I have submitted for review a paper which connects this with the AdS theory above with AdS_2 ~ CFT_1, and a coset structure on the AdS constructs the counting of possible microstates on a black hole event horizon. This is a physical partition function, but it is equivalent to a partition function of the integers. This has been one of those unsolved problems in mathematics, which Brunier, Folsom, Kent, and Ono proved in January. This is the mathematics for counting up quantum states on a black hole, or equivalently on the boundary of an AdS spacetime. I have been working up a variant of the proof by Brunier, Folsom, Kent, and Ono, but where the partition function is derived by compactification condition with respect to the correspondence between multi-partite entanglements BPS/extremal black holes.

In the end time is a slippery topic, and how it is interpreted might reflect something of the appropriate field theoretic form of quantum gravity. As a result one has to keep an open mind on the topic, without making prior assumptions about the ontology of time.

Cheers LC

Lawrence,

"Einstein probably made the biggest push forwards in our understanding of time. He demonstrated with the invariance of light speed that time was interchangeable with space. This is the Lorentz transformation"

I think that a finite maximum speed of light gives us the time - space interchangeable relation, not its invariance. The speed of light may change from place to place ... But in any place, the speed of light is the local maximum speed.

For example, the light beam going to the moon and back changes speed a few times but in any point of this travel, it moves at the local maximum speed.

This is because the rate of passage of time varies locally between the Earth and the moon and c=m/s and those seconds don't run the same everywhere. This explains the local invariance; c is always adjusted to the local rate of time and the ratio is invariant. The measured value of c is invariant.

So, my point is that a local maximum speed is not the same thing as the invariance of that maximum speed relative to other various places. This said, it is locally measured as invariant, a constant, because we measure two aspects of the same thing; the local ratio of space-time to the rate of time.

This make sense to you?

Marcel,

Light cones one Earth, the moon and between the two are shifted a very tiny amount. However, given that time differences are ~ 2GM/rc^2 ~ 10^{-10} and that the light travels back and forth in about 2.5 seconds this is a very small effect. It would be on the order of a fundamental time unit of an atomic clock. Differences of this sort which involve the difference between ruler and clock distances are measurable for light or EM radiation passing by the sun have been measured.

LC

Lawrence,

Thank you for the equation. Yes! It is small! But it is there.

Small is relative to something and often to what we want to do.

For the engineer, it could be insignificant. For the scientist, it is small. For the ontologist, it is very significant because it is there, and if it is there, it is part of the understanding of the whole picture.

There are currently billions spent on finding very very small numbers... Gravity probe, gravitational waves detectors etc. In a first instance, we try to demonstrate the presence of something and then we try to measure the magnitude of parameter, more and more precisely.

I take it as a puzzle; every piece has equal importance.

Thanks,

Marcel,

I buttered my bread for a while working out how to synchronize Ce atomic clocks on satellites and the Earth's surface for GPS applications. Those small deviations in the g_{tt} elements δg_{tt} = 10^{-11} as meaning that for every second measured on the Earth surface there is 10^{-10}sec de-synchronization with a clock at 1/2-geosynch where the GPS sats orbit. If I multiply by c = 3x10^{10}cm/sec this implies an error drift of 3mm per second. As a result there are practical ways in which this does materialize.

LC

While the Parmenidean block universe persists within theoretical physics and religions, engineers like me are forced to prefer realism without following jcns who wrote "Heraclitean-Parmenidean (essentially "presentism" vs. "eternalism") debate". I see Einstein's presentism as faulty as the more obviously anticipatory eternalism attributed to Parmenides. Accordingly LC wrote: "The Heraclitean perspective is more in line with the ADM relativity view of time."

The obvious impossibility to analyze genuinely future data led me to the utterly simple but perhaps foundational thesis that while past time is primary an order of realized causalities, time in the sense of something that includes past and future is only a mental construct. Einstein argued: "time is what clocks read". Such (elapsed) time does definitely not include the future Minkowski cone. So future spacetime must not be considered reality.

Eckard

Consider what I wrote earlier about the complementarity between space and time on Apr. 24, 2011 @ 01:21 GMT. This suggests that ΔxΔt = constant between time and coordinates of space. The connection to philosophical or metaphysical issues is that the Parmenidean and Heraclitean perspectives may be related to each other by a noncommutative relationship between coordinates of spacetime, or between time and a spatial coordinate, in an uncertainty principle. The two perspectives may then be related to each other in a similar way that momentum and position are related to each other in the Heisenberg uncertainty principle.

This would work our in an interesting way, for time becomes a one dimensional communication channel for qubits, where this 1-dimensional channel has the geometry given by the AdS_2 ~ CFT_1. The AdS_2 (anti-de Sitter spacetime in 2 dimensions) has a system of isometries which are equivalent to the conformal symmetries of a one dimensional QFT. Further the AdS_2 decomposes from AdS_n for a black hole in that AdS_n and at the region near the BH horizon. The Euclideanized form of the AdS_2 has a tiling representation as seen in the Escher prints called "Circle limit" 1 through 4.

This might then mean the nature of time is far more curious than we have previously thought. I could mean that block time and non-block time (non-time) are quantum complements of each other.

Cheers LC

LC,

I am perhaps the first one who sees argues that both x and t are not as physically real in the sense of measurable as are r and elapsed time t_e. Only The latter have natural zeros. You are perhaps quite right in that both the Parmesidean and what is not quite correctly labeled Heraclitean perspectives are related to each other by a non-commutative relationship. My essay 833 tries to explain why both views are redundant: Obedience of the natural restriction to exclusively positive distance and exclusively realized temporal distance is the key to the commutativity of half-matrices instead of Hermitean symmetry, i.e., instead of Heaviside's split into real and fictitious imaginary part. In order to get most easily understood I remind of distance matrices between cities. If distance between NY and SF is the same as between SF and NY then one merely needs a half-matrix.

Look at Fig. 1 in my 833 essay. Both measurable time t_e and frequency f are always positive. See hyperbolas of the quanta delta t_e times delta f = const.

Don't worry: Frequency corresponds to energy or momentum with respect to the object of concern while elapsed time corresponds to distance from object of concern.

Given I guessed correctly when you wrote: "This would work our in an interesting way" and "I could mean" you meant out instead of our and It instead of I. Nonetheless, I cannot understand you. Doesn't block time contradict human experience? Why is non-block time no time? Didn't I clearly enough explain why the basic notion of time is the only measurable (unilateral and perhaps potentially infinite) elapsed time?

Regards,

Eckard

This is a sort of noncommutative geometry. It is the quantization of geometry, or the field theoretic content that underlies geometry. A for block time being contrary to human experience or intution, those do not really count for much. The non-block time is just a system of spatial geometries which are related to each other by a diffeomorphism group. The notion of time is actually somewhat lost in this picture.

Cheers LC

LC,

"A[s] for block time being contrary to human experience or intution, those do not really count for much. The non-block time is just a system of spatial geometries which are related to each other by a diffeomorphism group. The notion of time is actually somewhat lost in this picture."

Now we're getting into some interesting turf indeed! Regarding whether human experience and intuition count for much, I simultaneously agree with you and disagree with you. Certainly, everyone must agree that human experience and intuition have proven to be extremely fallible. This fact is perfectly illustrated by the pre-Copernican belief that the sun revolves around the Earth.

On the other hand, however, human experience and intuition must count for something, because our empirical observations comprise the very bedrock foundation of science! If we dismiss empirical observations as unimportant (not really counting for much), then what are we left with as the basis for doing science?

I believe most would agree that science is about discovering the "best" explanation (which I take to mean the most useful explanation) for our empirical observations, i.e., for our human experience. The post-Copernican cosmology has proven itself to be more useful than the pre-Copernican cosmology. In the meantime, however, absolutely *nothing* in the universe changed, aside from the way we humans think about and interpret our empirical observations.

I continue to suspect that a similar disconnect is manifesting itself here at FQXi in our discussions about time. Perhaps it is not unlike debates which must have taken place in earlier days between those firmly entrenched in the pre- and post-Copernican views of cosmology, with both sides failing to comprehend what the other was trying to say.

Back to what you were saying above, however, I agree that non-block time is indeed a system of spatial geometries. Whether they are related to each other by a diffeomorphism group or not I can't say off hand, but I agree with you that the notion of time (certainly the conventional notion of time) is indeed actually somewhat lost in this picture.

When paradigms come into conflict, the outcome typically has been decided on the basis of which paradigm is more successful in explaining empirical observations in the least complicated way. Thomas Kuhn's book 'The Structure of Scientific Revolutions' offers a fascinating look at this phenomenon. I suspect that we're witnessing (and participating in) the early stages of just such a conflict of paradigms regarding the fundamental nature of time. As the saying goes, time will tell!

jcns