A Self-Gravitational Upper Bound on Localized Energy

Edwin,

In your Mar.7,2013 @ 18:30 GMT reply to Rob you write, "describe energy as h/T". Please help me get this 'buzzing phrase' out of my mind. What does it mean? You ask why I ask? Because in The Thermodynamics in Planck's Law I derive the duration of time required for an 'accumulation of energy' h to occur is given by h/kT. So how does this relate to "energy as h/T" ?

Constantinos

Jonathan is correct. Heisenbeg uncertainty does not refer to a system's information content. If such were true, we would know with certainty the point where quantum phenomena become classical.

Tom

Thanks John,

I think the camera analogy is rather appropriate here. There is always a question about what you are trying to capture or emphasize. Is sharpness of focus on the subject more important, or is the depth of field paramount because we need to see the background to establish context? Is sharpness of time definition of greatest value, as when determining the winner of a race, or do do you want to preserve the blur of motion for artistic effect, and leave the shutter open longer?

Some phenomena are too faint to photograph without a long exposure, and others are too swift for anything but the shortest exposure possible. So you correctly point out that even a single observation involves a trade-off of sorts. I'll have to think more on this.

Regards,

Jonathan

Rob, Jonathan, all,

I believe part of the problem is 'whose?' uncertainty principle we're discussing. The above arguments seem to assume there is AN uncertainty principle. I suspect (without going to the trouble to prove it) that both Rob and Jonathan can find a reputable text or paper that supports very closely their own interpretation. So, without arguing about what THE uncertainty principle says, I believe the issue is 1) the informational approach, largely based on Fourier analysis, that Rob describes and 2) the fact that the order of measurement *does* determine the outcomes in the cases of interest, when the measurements interact with the system under consideration to a degree that changes the system. This is the significance of "weak measurement". (Jonathan, thanks for the link to Physics World. It shows the same 'wave function measurement' diagram that is on the first page of my FQXI essay, "The Nature of the Wave Function", and I provide 3 references to such articles.)

Rob, I had the same problem with Kauffmann's 'mandatory' phraseology, and yet I believe that this is the perspective of most quantum field theorists, "the most successful theory ever". My own goal is not to dismiss it as a stupid misinterpretation but to try to understand the physical essence of what's going on. I was in a discussion night before last with a very bright physicist who was singing the theme song, "but our intuitions did not evolve to understand quantum reality, yada-yada-yada. That's what Bohr, claimed, and is the basis of the Copenhagen interpretation, yet the weak measurements clearly show, as stated in Jonathan's Physics World link: "But it is striking that the average result of such a measurement will yield exactly what common sense would have suggested."

I began my above comment by stating my belief that 'quantum action' is the fundamental reality of our universe, more fundamental than momentum, energy, what have you, as there is no universal measure of momentum, or of energy, but Planck's constant IS the universal measure of action. Action has units of mass*length-squared*inverse-time (MLL/T), but it is the product of these terms that is constant, not the terms themselves, the mass, the length, or the time. Thus when one analyzes energy over very short durations, the constant is divided by time, and if there are no limits on the time interval, the energy heads toward infinity. I don't believe this happens, but neither do I believe that there is a "shortest time" in the universe, so the question is what to believe about physical reality. I think most quantum field theorists agree with Kauffmann's wording. For this reason I was happy to see his 'self-gravitating' approach as a possible self-limiting solution to the 'problem'. I do not believe in the physical reality of infinity, so when the math seems to imply infinity, I look for the point or mechanism at and by which it breaks down. Kauffmann may have found one.

Rob, while I agree with your information-based analysis, and with your FM examples, there is still a physical aspect that is interaction-based in the sense that measurement of quantum 'objects' interacts with, interferes with, and changes what is being observed. That's why weak measurement theory and approach is so significant.

Constantinos, I am speaking of action as the fundamental unit of the universe. We speak of momentum and energy because our minds find it easier to grasp these, since everyday experience does not illuminate units of action. Yet quantum theory began with Planck's discovery that action allowed him to match the data when all else failed, and quantum theory is intertwined with action every step of the way, from variational principles, to uncertainty principles, to spin, Bohr orbits, you name it. There appears to be no meaningful physics between zero action and a Planck unit of action, hence nothing to 'accumulate'. When you refer to h/kT you are working with the thermodynamic relation based on statistical ensembles (indicated by your use of the Boltzmann constant, k) and temperature T, which is a measure of average energy. Averages, of course, are NOT limited to integral multiples of h, as they are mathematical, not physical. The statistics show that the averaging scale factor, 1/kT, is useful in probability in terms of units of h, which is multiplied by a frequency to get the energy that is then compared to the average energy. The T in h/T is not temperature but time, and refers to what one gets when one tries to separate time from energy in a world built around quantum action. I hope this clarifies it somewhat.

Best,

Edwin Eugene Klingman

I'd like to recap here, one of Edwin's comments above..

Steven Kauffmann "is talking about the interaction of gravity with energy (including the energy of the gravitational field.) But more specifically he is saying that localized energy -- such as the 'virtual' particles of infinite energy that appear in QED -- will have a mass equivalence that generates its own gravitational field, and this field, if energy is to be conserved, will not be 'extra' energy added to the situation but will be energy of the particle that is effectively 'converted' to gravitational energy."

This has the effect of restoring the sense of physical realism to our picture of the world. I think Kauffmann would agree with Rob that the infinities arising from the point particle assumption plus QFT do not appear to be a physically realistic possibility, and this may be part of why he sought a reason things could be resolved otherwise.

Have Fun,

Jonathan

Jonathan,

There is complexity in simplicity and simplicity in complexity.

Edwin,

I was mistaking the T in your h/T as temperature and not time. Thanks for clarifying. Consider the following in response to your comments.

1) Physical reality is 'manifested' (observed, measured) at or above Planck's constant h.

2) Physical reality exists the same but 'unmanifested' (not measurable or observable) below h

3) Planck's constant though considered as minimal 'action' can also be thought as minimal 'accumulation of energy' (the time-integral of energy -- what in my formulation is the prime physis 'quantity eta') that can be observed or measured.

4) Though E(average)=kT is a statistical derivation, the same equation can be derived without any statistical thermodynamics, as is the case in my formulation. In this non-statistical formulation, h/kT is the duration of time required for an 'accumulation of energy' (quantity eta) h to occur or manifest.

5) If in h/T the T is 'time', what 'time'? If this time T is the 'duration of time for h to occur', then h/T would be 'average energy' according to my results. Is that the reference made in "energy as h/T" in your comment? That is indeed very interesting and fitting my formulation!

6) Indeed the most basic 'physical reality' is 'action'. This is the 'quantity eta' in my formulation. In terms of this 'quantity eta' all other physical quantities can be defined and basic laws of physics can be mathematically derived.

See my chapter The Thermodynamics in Planck's Law for all of the above.

Best,

Constantinos

Edwin,

"weak measurement" - a new name for an old concept? Increase the signal-to-noise ratio, by measuring a large number of identical entities, perform "post selection" by basing the final computation on the detectors (within a filter-bank) with the highest SNR. This is what a filter-bank, of FM detectors, tuned to different center frequencies accomplishes. This is what I discussed in my FQXI essay. The basic idea is older than I am, and I'm retired. The article I published in "EDN", twenty years ago, showed how Gaussian windows could be combined with Fast Fourier Transforms (FFT), to perform this very efficiently. The "weak measurement" is the Gaussian window, that has a wider bandwidth than those used by the "strong measurement", narrow bandwidth "uncertainty principle" filter-bank. "Post selection" consists of only using the filters with the highest amplitude, to derive the final frequency estimate.

Rob McEachern

Constantinos,

I am familiar with your mathematical approach, and admire it very much, as I've said several times in comments on your essay blog. I realize that your 'eta' is 'action'. You say: "If in h/T the T is 'time', what 'time'? If this time T is the 'duration of time for h to occur', then h/T would be 'average energy' according to my results." I agree that thermodynamically it may be 'equivalent' to your formulation. But for a single event "average energy" doesn't have a well defined meaning. I think I understand statistical phenomena - I tend to focus on the more fundamental events and/or entities, and try to understand them. The answer to "what time" is somewhat artificial, and is a result of trying to break action into 'energy' * 'time'. You could call it the "time to accumulate" enough energy for the action to occur, but I don't really believe that the universe works like that, just as I don't believe the universe "computes its next step (or state)". When we break a unified whole into pieces, we can say a number of things about the pieces, but what we say and the pieces themselves may be fictitious.

Rob, I would not argue with anything you say. There are very few ideas that do not a recycle an older idea from a different context. But for quantum theory, suffering from a century of Bohr, and half a century of Bell, weak measurements are big deal, and I'm excited about it.

Best,

Edwin Eugene Klingman

Edwin,

I understand the dilemma understanding my results using statistics. For example, you write "for a single event 'average energy' doesn't have a well defined meaning".

If you consider 'average energy' to be of an ensemble of many events, than clearly this would not apply to a single event. But 'average energy' can also be equivalently thought as 'accumulation / time'. In this sense, there is no need to consider an ensemble of events in order to define 'average energy'. This is how I am using the term.

Another example along the same lines is defining 'temperature of radiation'. Clearly, the way temperature is currently defined in statistical thermodynamics (as the 'average kinetic energy of moving particles') this concept also would not make sense for radiation.

I have defined 'temperature' in such a way that it does not depend on 'moving particles'. And I am able to get the same results and equations as with statistical thermodynamics. Furthermore, this approach enables us to make sense of Planck's constant as being that constant 'accumulation of energy' used as standard to define (in this way) the Kelvin temperature scale. So there is no mystery why Planck's constant exists and what it actually means. Mystery resolved!

Best,

Constantinos

Stephen

"It now remains to puzzle out what conceivable "real world" physics could relate to the mathematical abstraction of the quantum fields' bounding radius r...The universe' cosmological redshift...appears to serve as the "containment" for all that we can hope to survey. Therefore a not altogether implausible crude estimate of the quantum fields' "bounding radius" r ought to be given by the age of the universe times the speed of light".

But light is merely the physical phenomenon which enables sentient organisms to be aware of the existential reality, in one particular form (the subsequent processing of the received physical input being irrelevant to the physics of the circumstance). With the evolution of the recipient sensory system (eg sight), light has acquired the functional role of providing an independent representation of what occurred, because it is created by interaction with what occurred. So, apart from not being reality, the precise nature of that interaction, and possibly with different forms of whatever constitutes reality, needs to be understood, so that reality can be discerned. There can be no presumption, and probably no actual likelihood, that the physical effect know as light provides a completely comprehensive and/or accurate representation of the existential sequence.

Paul

Edwin,

"But for quantum theory, suffering from a century of Bohr, and half a century of Bell, weak measurements are big deal, and I'm excited about it."

As I have said previously, it is unfortunate that QM was discovered a generation before communications and information theory. If it had been the other way around, physics would have been quite different, with a much better Theory of Measurement. Weak Measurement is a start, but they are still thinking in terms of wave-functions. The sooner they realize that the concept of a wave-function is an unnecessary crutch, the sooner they will be able to move forward; the whole problem ought to be framed in terms of the "post selection" detection process, the filter-bank, rather than some supposed, traveling wave-function. The former is the only thing that is real, and observable.

Rob McEachern

In the two slit experiment, two measurements are being taken; By the slits and the photon detector. One shows waves, the other points. The first is traveling, the second is stopped/absorbed. So the energy is spread out when traveling, but contracted when absorbed. Doesn't this basic relation of expansion/contraction play out across many of the issues, such as the inverse relation between cosmic expansion and gravity. Mass is the product of contraction of energy and radiation expands when released, rather than still traveling as point particles. What would hold light to a point when it is unbounded, since it has no internal structure?

Rob,

You write, "The sooner they[physicists] realize that the concept of a wave-function is an unnecessary crutch, the sooner they will be able to move forward".

I couldn't agree with you more! In my own work (see, The Thermodynamics in Planck's Law) the prime physis quantity 'eta' (the time-integral of energy, h is such example) is the starting point of my formulation. In terms of it, other physical quantities like energy, momentum, force etc. can be defined. And basic law of Physics can be derived as mathematical identities.

I show the 'quantity eta' relates to the wave-function psi. This gives a physical meaning to the wave-function as the space-time distribution of the 'quantity eta'. In this sense, the wave-function need not be thought as a 'wave'! While Schrodinger's Equations can be thoughts as defining 'energy' and 'momentum' operators. And not the other way around!

Best,

Constantinos

Constantinos,

A normal wave is the effect of energy transmitted through a medium. Now the reason light is no longer thought of as a wave is there is no medium, but what if light is the medium and waves are simply perturbations of it? Think of water flowing around rocks and the rippling effects. So when light goes through the slits, the resulting wave patterns are due to the interaction with the obstacles, rather than a primary form for the light. Same for how it is absorbed by the photon detector, as an effect of the absorption mechanics of the material.

This goes to the issue of whether reality is only what can be measured, or is measurement inherently limited by the interactive features of what is being measured and the form of the measurement device.

Overlooking the necessary limitations of measurement doesn't seem very scientific. To be most effective, the limits of our tools need to be as understood and appreciated, as their advantages.

John,

Of course! See my fqxi essays and my chapter, The Thermodynamics in Planck's Law for my thoughts on this. But I feel the fundamental underlying physical 'medium' may not be energy but rather the 'quantity eta' in my papers. This is the 'time-integral of energy'. Planck's constant h is such a quantity. And the 'wave-function' is the space-time distribution of 'eta'. So for me, the fundamental 'stuff' of Nature is not energy or mass or force. But rather 'eta', and the space-time distribution of 'eta' as expressed by the wave-function psi. What we are able to measure and observe (energy, momentum, force, temperature, etc.) are derivative physical quantities. Observable and measurable effects, as it were.

Constantinos

Constantinos,

I re-read your essay, and I still do not completely agree with you. My own theory predicts the existence of a constant of action, including the units MLL/T, but it does not tell me what the value of the constant is. Your work does not predict the value either. Nor does anyone else. Thus there is something physical beyond the math. When someone can show that the math implies the actual constants of nature, including their values, I will reconsider my opposition to a math-based universe. By the way, the field equation that describes the behavior of the C-field is a vector identity also. I would not expect a continuum-based universe to violate calculus identities, but to generally obey them. But math is generally not constrained as is nature, so math can produce results that do not necessarily have a physical counterpart.

Rob, you and I agree on the relevance of information theory, but I disagree that "the wave function is an unnecessary crutch." My own theory is based on the reality of the field that is induced by the particle (Bell was right in this point!) and, having recently become enamoured of Mathematica, I am hopeful of soon having more quantitative results to augment my many qualitative results. But I've followed enough of your comments, with which I am in general agreement, to know that I'm not going to change your mind about this, or Constantinos either, so I'm going back to work on Mathematica now. Thanks for the stimulating exchanges.

To everyone else I would say that Jonathan's links to Kauffmann and to the weak measurement writeup are well worth following.

Have Fun,

Edwin Eugene Klingman

Constantinos,

Glancing through and only going by the title but if its called; The Thermodynamics in Planks Law, why is temperature derivative and time elemental? You say time is variable, wouldn't that make it a derivative of the process of measurement as well?

Edwin,

I agree. The Universe is not the same as Mathematics. But I only argue basic law of physics can and should be mathematical identities. And leave open the question of physical constants.

As mathematical identities, laws of physics would only apply if all of the premises are known to be true. And if these are true, then clearly the conclusion must also be true. The math would be misapplied only when we are not certain our premises are true. I see that to be the work of physicists to determine.

Thus, for example, we know the Pythagorean Theorem to be true for points on a Euclidean space. Were we to apply the formula to calculate the distance between two points and discover our calculations do not agree with our experimental measurements, then we would know we are in a non-Euclidean space (assuming we are not making experimental errors).

By having all physical laws formulated as mathematical identities, we shift the emphasis from our equations (models) fitting our data to using the data to determine if our premises (postulates) to a mathematical identity (model) are true.

Constantinos