Breaking the Universe's Speed Limit

SR is applicable for objects in space and not for the expansion of space itself.

The standard model of cosmology indicates that galaxies which have a red-shift of 1,5, their wavelength of light equals 150% of the one we measure in the laboratory, move away from us at the speed of light.

Right now we know of about 10.000 galaxies with a red-shift greater as 1,5. these objects are moving away from us at a recession speed faster as the speed of light.

The cosmic background radiation has covered a much longer road, its cosmological red shift is about 1100 !!!. So when the hot plasma that radiated the waves that we observe today, it is probable that it (relatively) moved away from us at a speed of 50 times the speed of light. The emitted photon has its local speed of light, so it looses distance compared with its origin (like someone trying to go up on a fast moving down staircase ) here we meet the Hubble Constant .

The Hubble constant right now is 70Km/sec/Mpc (one Mpc=3.262.000light years). In this view also the speed of light is variable and without its limit as indicated by Einstein. It would be interesting also to read the essay of Peter Jackson : 2020 Vision. A Model of Discretion in Space (Is reality digital or analog Contest)

When the above is applicable then the visible Universe should be much greater as the 13,6 milliard years that we are talking of now.

I think this article has excellent timing considering the previous FQXI article was about real-time physics. Does John Donoghue postulate that time emerges from the microcosm of the quantum world? If these particles in the early universe are interacting and converging to a constant value for the speed of light then does that mean time had not yet emerged? If we keep time do Donoghue's ideas no longer work? Why is that last row of the Rubik's cube take an hour to solve when the first two rows can be solved in a few minutes?

I apologize if these questions seem puerile but please remember I am outsider to this community. I think a conceptual precis comparing and contrasting the big ideas for real time and emergent time would help me.

Hi dear Robert,

How are you it was time, but where were you?

rationalization's revoltion.....

Steve

For this article

it's interesting.I admit that the light limit is a problem for future travel inside our universal.The gravitational waves are relevant.Now of course we could find others linear speeds more important above the gauge of light and even without the light.The light is for the perception and like a fuel.It exists probably others linearities, but of course it's for the future.Can we find now, is it important to invest now, is it rational....

The gravitational waves are rlevant in all case.If you take some binar system with stars ,as pulsars, their rotations are improtant.We take the orbital period ,the time of arrival of signals,and the phasis of the orbital of the pulsar and the position and the topology spherical.The waves are under the general relativity , insert the volumes of spheres and the evolution linked witht the speeds of rotations orbitals and spinals see maxwell for the distribution of velocities and the cooling since the hypothetical BB,the rule of spheres become so important and the volumes also considering the entropic evolution.The cinetic momments are purelly correlated and the orbitals momments also, in logic of spherization repecting the cooling,we see the effect of mass and light...now considering the volumes for BH we see the pure relativity if we understand the 4D space time and the distribution of velocities of these spheres, quantics and cosmologics.The gravitational waves are correlated but we see only the light gauge constant.In logic of distribution and with the evolutive volumes, we can find others linearities more important.perhaps the extrapolation of Taylor eissberg can help.The dr Corda and his very relevant works can find very relevant roads if we consider the spherical 3D waves and the pure ditribution of velocities of rotations.The volumes are a key and seem so essential as all thermodynamical links.

Regards

Steve

If the space expands with a speed faster than that of light then it will be torn apart into causally unconnected regions. However, gravity may have to travel faster than light in order to maintain the integrity of the universe.

Excuse the typo in my initial comment.

My question is a serious and sincere scientific question.

Is there any way to test Prof. Donoghue's ideas via predictions that are prior, feasible, quantitative, non-adjustable, and unique to those ideas?

Or not?

Speculation is fine and useful in the initial stages of theory development, but a scientific theory must eventually lead to definitive predictions, or it is not testable and therefore not science.

Robert L. Oldershaw

http://www3.amherst.edu/~rloldershaw

Discrete Scale Relativity; Fractal Cosmology

Hi Robert,

I see possible overlap between your ideas and John Donoghue's. Are you and John collegues at Amherst? Suppose that our Classical Scale is defined on the large-scale side by the Speed of Light Scale limit, on the small-scale side by Planck's Scale limit, and has complexergy of ~10^41 (Dirac's Large Number).

A greater Scale (say the Cosmic Scale?) may have complexergy of ~10^123 (and thus the origin of the "Cosmological Constant" of 10^(-123)). I haven't read your ideas closely, but don't you have a scale number of order this number's square root ~3 x 10^61?

The greatest scale may be an infinite Multiverse (and our Observable Universe is but a fragment of fractal dust). OK - this scale isn't testable, but 10^(-123) deserves questioning. Is 10^123 dependant on a Cosmic Scale number, or is it Dirac's Large Number cubed (3 spatial dimensions)? What if Dark Energy is "leakage" from a greater Cosmic Scale?

Now to connect your ideas with John's:

A greater (say Cosmic) Scale should have a greater speed limit. I suspect that these different scales interact with Spacetime in such a manner as to "pinch off" Spacetime in certain extremes. Near the Black Hole "singularity", Spacetime rearranges into a Buckyball or toroidal lattice geometry because "Infinity" cannot exist in a Finite Observable Universe (we are Scale-limited from "Infinity"). On the outer edges of our Observable Universe, we may have a graphene-like lattice of Spacetime separating our Classical Scale and the greater Cosmic Scale. If Quantum Gravity exists in this Cosmic Scale with a greater speed limit, then it could be transferred holographically across this "graphene-like boundary" as an effective "Spacetime Curvature".

Have Fun!

Dr. Cosmic Ray

At the risk of coming across as "old-fashioned" and/or of belaboring what should be obvious, it seems worthwhile at the outset of this (or any) discussion to ensure that all participants in the discussion share a common understanding of the terminology involved. Would it be safe to assume that the term "speed" as use in this article (and related discussion) is defined in the standard way, i.e., as being a ratio of some distance per some unit of time?

If the answer to the above question is yes, then is it also safe to assume that the definition of time being used is the so-called "operational definition of time," i.e., "time is that which is measured by clocks"? And then would it be safe to further assume that a clock is defined as being "a device which measures time"?

If so, let the discussion proceed. If not, please clarify how the terms being discussed here differ from the above. Thank you.

jcns

Dear JCNS,

The assumption of Scale Invariance and/or Scale Relativity set fundamental length scales upon which everything else could be based. The awkward fact is that multiple scales exist, and therefore, multiple definitions may be required.

We need to look at important dimensionless numbers for clues about Scale behavior. A couple of very relavant dimensionless numbers are the inverse fine-structure constant: 137, and Dirac's Large Number: 10^41.

Perhaps John and Robert could explain their definitions.

Have Fun!

Dr. Cosmic Ray

Hi Robert,

I doublechecked your ideas. OK - You expect Lambda = 1.7 x 10^58, which isn't exactly the inverse square root of the Cosmological Constant ~ 3 x 10^61, but in the grand scheme of scale building, it sounds related to me. It is mathematically improbable and philosophically illogical to expect fine-tuning on the order of 10^60 (or 10^120 or 10^40) - THIS MUST BE REAL PHYSICS! They "invented" Supersymmetry to solve the Weak-GUT Hierachy Problem and that is only 16 orders of magnitude of fine-tuning - How can they ignore such extreme fine-tuning?

What do you think of my 2011 FQXi essay?

Have Fun!

Dr. Cosmic Ray

The idea that time does not exist and the speed of light varies, might be complementary to a situation where space does not exist but time does. In a noncommutative coordinate geometric setting this might then recover the constancy of the speed of light.

Cheers LC

LC,

Wait, please; you're making my little head hurt. This is exactly why I asked (somewhere above) for clarification of the terminology being used here. As I understand the conventional use of the word "speed," it is defined to be a ratio of some distance per some unit of time. But if you then propose that ". . . time does not exist and the speed of light varies. . . ." (as you appear to have done) how do you determine speed without time? I fear that perhaps I'm too easily confused by what should be very simple concepts? Please explain. Thank you.

jcns

Not to rain on any parades, but yesterday morning I received my latest Phys Rev Lett in the mail. The following quote from Physical Review Letters 106, #131802 (1 April 2011) tend to agree with my C-field predictions on SUSY:

In the first LHC search for supersymmetry, "no excess above the Standard Model background expectation is observed"

and

"These ATLAS results exceed previous limits set by other experiments."

Edwin Eugene Klingman

Quantum gravity depends upon inertial and gravitational equivalency in keeping with space that is made equally larger and smaller in keeping therewith. This balances attraction and repulsion, as the space is BOTH flattened/contracted and stretched/expanded in a balanced fashion.

Look at the ground and your feet. Gravity is key to distance in/of space.

I already proved this in/as dream experience. The center of the body is the linked origination and generation of our experience.

You all are repeatedly going about the unification of physics in the wrong manner.

DREAMS COMBINE AND INCLUDE OPPOSITES.

Hi Edwin,

If we are going to talk about Atlas, have you heard the rumor on this diphoton bump with effective mass of 115 GeV?

Have Fun!

Ray,

Yes I have. What do you think it is?

Edwin Eugene Klingman

Hi Edwin,

It is where SUSY phenomenologists expect the Light SUSY Higgs. The strength of the diphoton signal is so strong that it doesn't look like a Standard Model Higgs. I suppose it could be a composite Techni-pion that provides a Goldstone origin of mass, but Technicolor has other problems that probably requires SUSY as a solution. The graph at the top of page 30 in this old paper with my colleagues and me shows how a relatively light-weight Light Higgs could exist, while m_1/2 (and most gaugino masses - most Neutralinos and Charginos) remain quite massive. This implies that we need to look closely for the Light Stop Squark.

The Tevatron has not confirmed this observation, although LEP had gotten to the edge of this region a decade ago, and thought they were on the edge of seeing something. The "leaking" of this paper did not follow protocol, and may or may not stand after the other couple of thousand LHC researchers "sign off".

I guess data and time will tell...

Have Fun!

The argument involves quantum uncertainty between different coordinates. Principally this is between time and position. Suppose there is a theory that time does not exist. All that exist with some geometric content is space. Suppose there is another theory where only time exists, but not space. It might then be that these two theories are complementary sets. They are complementary in the same way that position and momentum are complementary in standard quantum mechanics. If you read my article here on FQXI I indicate (though the calculations are not presented in detail as they are formidable) how light cones and Heisenberg groups emerge from a single structure. I will try to indicate how this works from more elementary considerations.

In 1930 there was a famous Solvay conference where Einstein and Bohr sparred over the reality of quantum mechanics. Einstein was convinced of reality and locality and argued staunchly for an incompleteness of quantum mechanics. Quantum theory could only be made complete if there are some hidden variables that underlay the probabilistic, nonlocal quirky aspects of quantum mechanics. At the 1930 Solvay conference Einstein proposed an interesting thought experiment. Einstein considered a device which consisted of a box with a door in one of its walls controlled by a clock. The box contains radiation, similar to a high-Q cavity in laser optics. The door opens for some brief period of time $t$, which is known to the experimenter. The loss of one photon with energy $E~=~\hbar\omega$ reduces the mass of the box-clock system by m = E/c^2, which is weighed. Einstein argued that knowledge of $t$ and the change in weight provides an arbitrarily accurate measurement of both energy and time which may violate the Heisenberg uncertainty principle ΔEΔt ~ ħ.

Bohr realized that the weight of the device is made by the displacement of a scale in spacetime. The clock's new position in the gravity field of the Earth, or any other mass, will change the clock rate by gravitational time dilation as measured from some distant point the experimenter is located. The temporal metric term for a spherical gravity field is 1 - 2GM/rc^2, where a displacement by some δr means the change in the metric term is ~ (GM/c^2r^2)δr. Hence the clock's time intervals T is measured to change by a factor

T --> T sqrt{(1 - 2GM/c^2)δr/r^2} ~ T(1 - GMδr/r^2c^2),

so the clock appears to tick slower. This changes the time span the clock keeps the door on the box open to release a photon. Assume that the uncertainty in the momentum is given by the Δp ~ ħΔr < TgΔm, where g = GM/r^2. Similarly the uncertainty in time is found as Δ T = (Tg/c^2)δr. From this ΔT > ħ/Δmc^2 is obtained and the Heisenberg uncertainty relation ΔTΔE > ħ. This demands a Fourier transformation between position and momentum, as well as time and energy.

Consider an example with the Schwarzschild metric terms. The metric change is then ~ 1x10^{-12}m^{-1}δr, which for δr = 10^{-3}m is around 10^{-15}. Thus for a open door time interval of 10^{-2}sec, the time uncertainty is around Δ t ~ 10^{-17}sec. The uncertainty in the energy is further ħΔω, where by Fourier reasoning Δω ~ 10^{17}. Hence the Heisenberg uncertainty is ΔEΔt ~ ħ.

This argument by Bohr is one of those things which I find myself re-reading. This argument by Bohr is in my opinion on of these spectacular brilliant events in physics.

This holds in some part to the quantum level with gravity, even if we do not fully understand quantum gravity. Consider the clock in Einstein's box as a black hole with mass m. The quantum periodicity of this black hole is given by some multiple of Planck masses. For a black hole of integer number n of Planck masses the time it takes a photon to travel across the event horizon is t ~ Gm/c^3 = nT_p, which are considered as the time intervals of the clock. The uncertainty in time the door to the box remains open is

ΔT ~ Tg/c(δr - GM/c^2),

as measured by a distant observer. Similarly the change in the energy is given by E_2/E_1 = sqrt{(1 - 2M/r_1)/(1 - 2M/r_2)}, which gives an energy uncertainty of

ΔE ~ (ħ/T_1)g/c^2(δr - GM/c^2)^{-1}.

Consequently the Heisenberg uncertainty principle still holds ΔEΔT ~ ħ. Thus general relativity beyond the Newtonian limit preserves the Heisenberg uncertainty principle. It is interesting to note in the Newtonian limit this leads to a spread of frequencies Δω ~ sqrt{c^5/Għ}, which is the Planck frequency.

The uncertainty in the ΔE ~ ħ/Δ t does have a funny situation, where if the energy is Δ E is larger than the Planck mass there is the occurrence of an event horizon. The horizon has a radius R ~ 2GΔE/c^4, which is the uncertainty in the radial position R = Δr associated with the energy fluctuation. Putting this together with the Planckian uncertainty in the Einstein box we then have

ΔrΔt ~ (2Għ)/c^4 = L^2_{Planck}/c.

So this argument can be pushed to understand the nature of noncommutative coordinates in quantum gravity.

So these arguments concerned with the existence of time are interesting in some sense. I have not been a particular partisan in either say, where Fotoni argues time exists, but not space. Of course space and time are really just holographic manifestations from strings and Dp-branes, which means space and time have no degrees of freedom of their own. However, it does seem that it is possible that space and time are complements in a quantum mechanical sense within quantum gravity. The speed of light is something which emerges from this parabolic group structure I work with which derives Heisenberg groups and light cones.

Cheers LC

LC,

Thank you very much for your excellent reply to my question. You have explained this as clearly as I could have asked or hoped, and your answer is very logical, indeed. Moreover, I'm certainly not in any position to pick an argument with anything you've spelled out here.

That said, however, I'd like to clarify what I see as being probably the primary reason why some of us who are part of what I've come to think of as "the FQXi Time Mafia" seem to be talking past one another when it comes to discussing these things. That reason is, in my opinion, that we are coming at the topic of time from two rather dramatically different paradigms regarding the fundamental nature of time. These different paradigms naturally lead to different ways of interpreting the same empirical observations.

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.

One paradigm for the nature of time, the mainstream, prevailing paradigm, which is a key component in the foundation of modern physics, including especially special and general relativity, is most succinctly summarized, in my opinion, by what has been called the operational definition of time, i.e., time is that which is measured by clocks. Taking this view as a starting point, everything else which is taken as orthodox thinking about physics follows logically and consistently (certainly for the most part, at least).

The other paradigm is the one which I've attempted to spell out in purely qualitative terms in several essays such as those here and here. I don't even know what to call this paradigm. Perhaps it could be called a relational paradigm for time? In a nutshell, it holds that particular times correspond with, and are identically equivalent to, particular configurations of the universe. This view takes clocks to be specific subsets of an evolving universe; in this view, the special role given to clocks in the mainstream paradigm is viewed with skepticism. Far from being a magic bullet for resolving all of the outstanding conundrums of modern physics (see Lee Smolin's 'The Trouble With Physics,' for example), this paradigm raises a host of knotty problems and questions of its own, and I have answers to none of them.

I do not know how to describe this "relational paradigm" in a more rigorous fashion, but it is possible that another, far more clever, person, Joy Christian, has made a stab at this in an essay here. I would not presume to speak for Mr. Christian on this point; it is possible that he would totally and vehemently disagree with me.

Regardless, thank you for engaging seriously on this topic, LC.

Regards,

jcns

J.C.N. Smith,

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. We have some issues with reality in a quantum mechanical content, in particular with nonlocality and a local definition of reality. Time and space though are not impacted by this. However, it is likely that quantum gravity will have implications along these lines. Julian Barbour is pretty much into the notion that time does not exist. This is based largely on the Wheeler DeWitt equation HΨ[g] = 0, which is a quantum version of the Hamiltonian constraint in ADM relativity.

I could well enough imagine presenting how time exists, but space does not. We could presume there is some one dimensional space, a line or curve, and there is a fibration on that space by a three dimensional space. This internal space is a symmetry of the dynamics of this one dimensional parameterized space we label as time. This then connects to relativity when we consider the metric line element

ds^2 = -c^2dt^2 g_{ij}dx^idx^j,

where mixed time-space metric components are not included. We have here two notions of time. The first is the proper time τ = s/c, which is the invariant of relativity. The other time is a coordinate time t, which is not an invariant.

The obvious question to ask is whether ds is real. We can multiply it by mc^2 and define an action according to the extremal principle of the proper interval

S = mc∫ds,

which appears real in some sense. It has units of action, or angular momentum, which is a measurable quantity. Yet there is something a bit troublesome about all of this. How does the observer on this world line actually measure this interval? A clock is employed which must have some system of oscillations, such as a spring. Yet this is measuring the invariant interval according to something carried on that world line that deviates from the world line. Hence some sort of nongeodesic motion is being used to define or measure an interval along a geodesic path. Of course I am thinking primarily of a mechanical clock, but an atomic one still appears to hold for an EM field must be applied to knock electrons in the Ce atoms.

This Lagrangian is measured according to something which is not invariant. So we might then consider that action as dS = pdq - Hdt. Now we have some Hamiltonian, which might include a part for the dynamics of the clock. Hamiltonians must be specified on some Cauchy surface of data with a coordinate time direction. Yet this has gotten us into some funny issue, for to define an invariant interval it appears that we need a coordinate defined clock.

So far we have some identification of Hdt, or the square of this, with the c^2dt^2 in the interval above. We then have that the bare action term ∫pdq is identified with

∫pdq = mc sqrt{g_{ij}dx^idx^j}.

So we have a bare action given by our fibration, but we also have some constraint, where H acts as a Lagrange multiplier. So we then have our one dimensional curve defined in a spacetime, where the space is the space of fibration and the Lagrange multiplier determines the symmetry of that fibration which is the Lorentz group.

Now to make things curious, we could imagine this picture as dual in some ways to the picture where time does not exist, but space does. The duality might then have a noncommutative coordinate geometric content in quantum gravity.

The acceleration can be found by a number of means. F = ma with the Newtonian law of gravity and the centripetal acceleration a = v^2/r,

mv^2/r = -GMm/r^2.

This gives v = sqrt{GM/r}, which is v = 29.5km/s or v = 2.95x10^4m/s, for the mass of the sun and r = 1.5x10^8km. The acceleration is then 5.8m/s^2.

As I indicated I think there is some noncommutative geometric issue with the nature of space and time in quantum gravity. This will be a noncommutative geometry that is more general than the Kahler geometry of geometric quantization. That extends the pseudo-complex symplectic structure of classical mechanics into a complex structure with a Hermitian complentarity between conjugate variables. A simplectic group with z_i = (q_i, p_i} (index notation implied) obeys dz_i/dt = Ω_{ij}z_j. In quantum mechanics this is generalized to a commutation system, and the symplectic 2-form implies an operator valued Hamiltonian. However, this is not the most general system possible. This may be extended to in noncommutative geometry with more general Usp(n) groups. A unitary Lie structure can give rise to commutators [q_i, q_j] = ħω_{ij}, which are necessary in string theory with uncertainty principles involving transverse and longitudinal string modes ΔX^ΔX^- ~ L_s = 4πsqrt{α'}, α' = string parameter and L_s the string length. Noncommutative geometry is then a setting for complementarity principles.