I agree that time isn’t a fundamental dimension, rather that it is a consequence of motion, rather than the basis for it. As such, this makes it similar to temperature, rather than space, but that doesn’t make it any less real from our perspective, as anyone who has been burned can tell. What it means is that we are more illusion than time is. To the extent there is some fundamental unity of being, it is as essential basis, rather than ideal form.

For benign unrelated reasons I don’t plan on posting comments for some time, I just want to thank you for your comments

Thanks.

Lawrence B. Crowell

I am not sure how the equipartition theorem comes into this picture.

The number three plays a most interesting role with the triality in group theories, such as the 3 + bar-3 long roots of SU(3) which have some connection to the three families of quarks. The number 5 also comes in with my work in the Steiner group as the representation of a sporadic group. A subgroup of this is S^3xSL_2(7), which is a three sphere with each point identified with a projective map of E_8 onto the Fano plane. So here the numbers 3 and 7 come in, 7 being a favorite number of the bible types. This is a sort of three dimensional Bloch sphere where each point is a set of states given by E_8, with three independent E_8’s required.

There is no intrinsic notion of time in the Wheeler DeWitt equation. The ADM classical constraint equation H = 0 becomes H*Y[g] = 0, and where time enters into the picture it is something the analyst inputs. The lapse functions N are determined by a coordinate condition, analogous to a gauge. One way in which we can do this is to impose a field on the metric g. For that field F we give a wave equation and it is not hard to introduce a phase on the wave functional Y[g, F] so that the W-D equation is extended to

for K_t a Killing vector. Now remember, this field is defined within some scaling or conformal setting. We can just as well chose another field conformally scaled otherwise. This wave equation is perfectly time reverse invariant, even if this “time” is in a sense fake. If we have another metric g’ it has a similar wave functional X[g', F'] and wave equation

Yet covariance requires that K_t =/= K’_t and so we can’t describe a superposition of states, and a path integration over possible states

where S includes NH, is not defined in the usual sense as some parameterization of states in a time ordered sense. There is no single definition of time.

The course graining of these metric configurations leads to an energy uncertainty functional

which describes a coarse graining over many metric configurations. Most of these wave functionals are over metric configuration variables which have no classical description, or in fact have no possible dynamical (diffeomorphic) description. These 4-manifolds are “fake” and this course graining of possible metric configurations, with these as well, introduces this error functional. The Cartan center of E_8 describes the set of possible M^4’s and these “fake” manifolds. This is in part why I think quantum gravity requires the S^3xSL_2(7) \subset M_{24} or more fundamentally M_{24} as a quantum error correction code, which embeds three E_8’s — an E_8xE_8 for the graded heterotic supergravity field theory and the third for this configuration of all possible spacetimes. In the restricted S^3xSL_2(7) this is the Bloch sphere where each point on it is a “vector” in a three space spanned by the Fano planes associated with these three E_8’s. S^3xSL_2(7) has 1440 roots and is itself a formidable challenge, but this represents a best first approach.

So fundamentally there is no such thing as time, or a time which describes the vacua at or “near” the start point of the path integral of the universe. It is hard to avoid tensed language here, and English is very time ordered. Russian might actually be a better language to use. Time is something which obtains on a larger scale as a coarse graining over all possible states with different metric configuration variables.

It is interesting that in our world time is probably the second most feared thing, with the first being death. Of course the two are related in that death is a sort of ultimate deadline. Yet when one thinks about these matters with some depth these worries are put in a proper perspective. Ultimately what we fear the most is an sort of illusion, or a holographic projection.

Lawrence B. Crowell

In QED the cut-off in energy at high energy is permitted because the structure of the theory below the cut-off is self-similar to the physics above. So the cut-off is permitted in a way similar to a Julia set algorithm can cut off the calculation on a certain scale without adulterating the set at a larger scale. The foundational nature of renormalization is encoded in the renormalization group equation,

Why does this sound like some form of fractals all the way through?

hmmmm

hmmm…3 microstates….hmmm

The uncertainty principle is tied to the concept of reactive power in AC electrical theory

Reactive Power (Q):
The power which is exchanged between reactive elements (inductors and capacitors) is called reactive power, Q, and is measured in vars (volt-ampere-reactive) or kilovars. This power does no useful mechanical work, but must be alternately absorbed and supplied by the reactive elements.

another link about this;

http://en.wikipedia.org/wiki/Reactive_power#Real.2C_reactive.2C_and_apparent_power

So in a naive way, you could consider “ZPE” as meaning that the circuitry of the universe is always in an energized state. (pre-energized).

Just interesting.

http://en.wikipedia.org/wiki/Equipartition_theorem

under the section called:

Failure due to quantum effects

Where our equation describes the situation when Z = 3/2

http://en.wikipedia.org/wiki/Equipartition_theorem

under the section called:

Failure due to quantum effects

Where in our equation describes the situation when Z = 3/2

There is a whole lot more I could go on about this, such as the role of conformal groups and dilaton fields, or with zeta functions, and … . But that would take things a bit far afield.

In quantum gravity not every wave function(al) has a configuration variable, which is a geometry or metric, that is a classical space or spacetime. How a classical universe emerges from this is not well understood. So these wave function(al)s over non-classical metrics are in a sense what might be called “un-spaces” or “un-spacetimes.” The spacetime geometries are these strange or “fake” manifolds found in the Uhlenbeck-Donaldson theorems on the moduli for four dimensional spaces. Again, this gets into some very deep mathematics and physics/cosmology it might describe.

Lawrence B. Crowell

http://en.wikipedia.org/wiki/Wien%27s_displacement_law

we find the following equation for a single harmonic oscillator at wikipedia;

http://en.wikipedia.org/wiki/Zero_point_energy

which can be rewritten as;

which is;

and then;

thus;

making

Lawrence, this is a very useful discussion and it is helping me a lot.

From a philosophical standpoint, I really have no preference on how the universe works, other than it should work like the one I’m in.

My current default view of things is to picture the “vacuum energy” or “cosmological constant” as acting like a power source, and black holes act as grounds. (or from a mechanical standpoint, you’d have a boiler or pumping station, and blackholes are the ocean). Sure its a naive toy model, but from a starting point I think its just as good as anything else; sources and sinks.

Anyhow, I also like the analogy that physics is similar to reverse engineering in a lot of ways; and sometimes you have to “break” things to see how they work.

I tend to have a very deep respect for physicists and mathematicians; so I particularly appreciate the time spent discussing these topics. Thanks.

Now about that whole universe thing…

The reason that coastlines, with their jagged edges, don’t have a definite length is because they are examples of fractals. It doesn’t matter how much you magnify a fractal, you always see pretty much the same pattern - in the case of a coastline, another jagged edge. The pattern is the same whatever the scale - fractals are “scale invariant”.

Under scale invariance, matter loses all sense of perspective, and distance is no longer important, says Francesco Sannino of the Niels Bohr Institute in Copenhagen, Denmark, who has also studied unparticles.

This has a remarkable effect on the strength of the force holding unparticles together. Sannino likens it to being able to hear a quiet whisper as easily as a loud yell. “In the normal world, if two people are sitting in different countries and they want to have a conversation, they must use a phone,” he says. “But in a scale-invariant world, even if they were separated by 2000 kilometres they could speak to each other as if separated by just 2 metres.”

These two measurements may be performed instantaneously in a mutual rest frame. Yet no information is communicated from one measurement to the other, for the information obtained in both measurements are identical. Nothing is communicated, but the conservation of angular momentum demands this outcome. This is a relationship between particles that exists independent of any spacetime interval or distance between them.

These are the two relationship systems, and quantum gravity is the area of physics where these two relationship systems are specific examples of a single relationship system.

Could there be some connection here?

In different frames there are different metrics. These two metrics at the same point p will have

but if that point p is extended to another point in the two metrics the result will not be the same. This means that general relativity does not give an absolute definition of points and their distances, but rather can only determine the location of physical bodies with respect to each other. General relativity does not determine the position of bodies with respect to a manifold. This is the fundamental meaning of general covariance. It also suggests that spacetime is really not a physical entity at all, but is more of an auxiliary calculational device. General relativity is fundamentally a theory on the relationship between particles which we describe according to geometry.

Quantum entanglement tells us there is a completely different way in which two particles can be related to each other than by their relative location as given by relativity. This is through quantum entanglement. Two quantum
states may exist in a superposition where one state if up the other is down plus the first down and the second up. This can happen in the decay of a spin 0 particle into two spin 1/2 particles. Angular momentum must be conserved, so the total state is

This state vector is written independent of an spatial or momentum value. The wave function that is defined through space is

.

This can be extended to the domain of special relativity. An optical analogue of this can be obtained with entangled pairs of photons in orthogonal polarization states produced in a parametric down shift by a sapphire crystal.

If two detectors at positions R and -R measures the particle there are two possible outcomes:

These two measurements may be performed instantaneously in a mutual rest frame. Yet no information is communicated from one measurement to the other, for the information obtained in both measurements are identical. Nothing is communicated, but the conservation of angular momentum demands this outcome. This is a relationship between particles that exists independent of any spacetime interval or distance between them.

These are the two relationship systems, and quantum gravity is the area of physics where these two relationship systems are specific examples of a single relationship system.

Lawrence B. Crowell

I suspect that uncertainty principle and the lorentz transformation are fundamentally related.

Also, things like loops and the like in Feynman diagrams are perturbation terms with a summation over their momenta. Just as in calculus summation variables are called dummy variables these loops are really mathematical artifacts, or in a sense dummy variables.

Since the classical variables commute, one could easily rewrite the Hamiltonian for the Hamonic oscillator

as

Since pq = qp classically, all we have added is zero and this is the same Hamiltonian. Now with hbar = 1 if we quantize this Hamiltonian with

the quantized Hamiltonian is

and there is no [a, a^dagger] commutator often interpreted as the zero point energy. The ZPE has been completely removed, there is nothing “funny” or hand waving about this. For this reason often the raising and lowering operators are just “normal ordered” and the ZPE term removed.

What happens with pair creation is that something is coupled to the Harmonic oscillator. The usual equations coupled together are the Dirac equation and the Maxwell equation. The Dirac field acts as a current in the Maxwell equation and the momentum operator in the Dirac equation is put in a gauge invariant form with the EM vector potential. Then things start to get a bit complicated. What does happen is the occurrence of particle pairs that would not obtain if hbar were zero.

The zero point energy is then a very subtle thing, particularly with cosmology. I don’t want to digress into that right now, but there is a whole lot of stuff that goes on, often in published papers, where the ZPE is assumed to be a real “thing.” Instead the cosmological constant is better thought of as a subtle quantum effect of fields coupled to spacetime (analogous to the Dirac equation plus Maxwell equation), or rather better said the gravity field, which results in this term so the cosmology is globally an Einstein space with spacetime curvature proportional to its own metric.

The same is the case with the Heisenberg uncertainty principle and the notion of fluctuations. These are phenomenological results which describe a measurement or the distribution of possible outcomes. The Schordinger wave equation is a perfectly deterministic equation and there is nothing intrinsically stochastic about its time development of a wave. Stochasticity enters into the picture when you try to observe the system, or if the system is coupled to some large classical-like system or one with many modes, and is a tool we use.

Lawrence B. Crowell