Is there an absolutely upper limit for temperature?

I would have to check my old physics books but I think I remember that you actually get negative absolute temperatures if you go through what could be called infinitely hot temperatures.

Check this paper if you can:

http://www.springerlink.com/content/j45862lt261g3q34/

And this thread:

http://www.advancedphysics.org/forum/showthread.php?t=1213

"negative absolute temperatures"

Now that is something to really blow you mind!

I had an unusual web site on screen a few months back. IIRC 10^-15 was said to be the smallest and 10^15 the largest of anything.

On that basis my WAG is 10^15 deg. K.

Hi SS,

I may be something like √(-1)º K or todays temp is 32iº K. Weird huh?

Anyway, how does a negative absolute temperature (if one exists) impact the highest possible temperature?

-John

It appears that from both ends of the scale, temperature (range) is a hyperbolic function. A step of 10^-6 ° at 10^-4 ° K is a very great interval. A step from 10⁴ ° to 10⁶ ° is not much. 10^-7 from 10^-6 is as significant as 10⁶ to 10⁷. Should we ever reach 10^-30, we will probably be starting to understand 10³⁰. Significance plotted against power of 10 appears to be a more linear relationship.

RichH

I read that about negative kelvin temperatures in Resnick & Halliday, but they just mention it and don't give any explanation.

However, I have found this nice article:

going below absolute zero

The coldest temperature that can conceivably be reached is absolute zero, or zero degrees on the Kelvin scale. Negative temperatures on the Kelvin scale are said to be impossible, however nature seems to have a way to reach down below absolute zero. Once it gets there though is when the really interesting stuff happens.....

temperature

Temperature is understood by most people to be a way of measuring hotness or coldness. There are three scales to determine temperature: Fahrenheit, Celsius, and Kelvin. Fahrenheit and Celsius are relative scales which means they define temperatures based on reference points. These reference points just happen to be the boiling and freezing points of water. The Kelvin scale, however, is based on Charles's law for gases. Charles's law for gases states that the volume of gases is proportional to temperature. When a graph is plotted of volumes of gases versus temperature, no volume is ever negative. This implies that no temperature (on the Kelvin scale) is ever negative. This can be said due to the proportionality of the temperature-volume relationship and that no volume of gas in reality can ever be negative.

The kinetic molecular theory states that the kinetic energy of gases depends on their temperature. With lower temperatures, gases have less energies, therefore, having slower motion. However, all energy can never be removed from a system which is another reason why it is thought that temperatures can never be zero on the Kelvin scale.

molecular energy distribution

Every molecule possesses some amount of energy. Imagine a system where the molecules have only two choices for energy states: excited or ground. An example that we will also use later is a magnetic field. In a magnetic field the molecules align with the field so that they are in the ground state, or the molecules align opposite the field in an excited state. Those molecules that align in opposition of the magnetic field require more energy to exist in this higher energy state. The Boltzmann distribution law is a law that is used to determine the energy levels of molecules. It also determines the number of molecules in each energy state. The equation derived from this law says that as temperature increases there is more energy available which, in turn, increases the ratio of excited state molecules to ground state molecules. According to this equation, as the temperature gets closer to absolute zero, the ratio also approaches zero. This is because, at absolute zero, there is no energy to distribute to the molecules. This results in all of the molecules going to the ground state. Alternatively, as the temperature goes to infinity, the ratio approaches one. The molecules are distributed equally to the excited and ground states.

population inversions

However, there are conditions when there is enough energy absorption that the excited state molecules outnumber the ground state molecules. This is where we recall our example of the magnetic field. Suppose there existed ten molecules in a system. Eight of them existed at the ground state and two were in the excited state. If the magnetic field was suddenly switched, for an instant, the eight ground state molecules were in the excited state and the two excited state molecules were in the ground state. This is called a population inversion.

A formula derived from the formula that earlier determined the ratio of ground to excited state molecules can calculate the temperature of a system based on the populations of the energy levels. It says that if the ratio exceeds one (equilibrium of excited state molecules and ground state molecules), then the absolute temperature is negative. A temperature below absolute zero!

Manipulation of an equation that determines total energy for a molecular system reveals that the molecules below absolute zero have much more energy the those above absolute zero. This means, if you recall the laws from above, that the molecules below absolute zero are actually hotter than those above absolute zero!

reality of negative kelvin

Upon first guess, most people would think that to get below absolute zero, you would need to go from positive to zero then down to negative. However, paradoxically, negative absolute temperatures can only be obtained through infinite temperatures (as the temperature goes to infinity, the ratio gets closer to one, and by inverting the population, the ratio goes above one). Population inversions really do happen in everyday life. They are the basis for lasers, in which the numbers of excited molecules outway those in the ground state. Therefore, lasers share properties with molecules below absolute zero. The concept of negative absolute temperatures has been verified using the magnetic field example.

Ordinary means will not measure negative absolute temperatures. It takes something abstract to measure something abstract. That abstract measuring tool is mathematics. Mathematics takes the world from these abstract viewpoints and uncovers all the hidden mysteries and meanings the universe has to offer.

Correction to your sig:

Those who can, parent, those who can't, created OHSA.

RichH

Shhhhhhhhh! OSHA is watching.

Damn. I wanted to reply, but I sprained my typing finger on the last post.

An oddity in this process is the apparent requirement of the "population" ratio to be nearing 1, so that the inversion produces a population ration of greater than 1.

Two faults exist with this premise to my mind. The P/R is said to approach 1 at an infinite temperature. That would indicate the impossibility of ever getting even half of the molecules/atoms/bosuns to an excited state. Half of the hydrogen in the suns core is at a temperature of absolute 0 K? It would appear that all matter must, in their theory, be either aligned or counter-aligned to a magnetic field. A magnetic field is a half (directional) singular dimensional vector. That would be the equivalent to saying that the jets of a quasar must either point to Bolingbrook or directly away. The infinite number of points in a one-dimensional line are a class of infinity less than the number of points on a plane, and still another class away from the points in a 3-d space, and still another from that space in time. Or is there a minimum increment in time itself that would remove that class?

Second, if inversion when P/R is nearly one becomes greater than 1, what happens when a population at 550 K is inverted, with it's P/R of maybe 0.1? Your inverted P/R would be 10. Would that be hotter or colder than 0 K or 10³² K?

It would appear that there is an ignored discontinuity when the math is created that is dependent upon P/R approaching 1 for an inversion to result in negative K. Either an inversion is effective regardless of the P/R, or the old math is again proving that 1=2.

Figures don't lie.

RichH

Ah... I get it. As t↑, after a point, molecules are removed, until that population is replaced with a population of disassociated atoms, which gives way to richHelectrons and nuclei, and then bosuns, quarks, mesons, and finally a wave-form energy only. Odd. That would remove the concept of a one of two state requirement in the inversion theory.

Ohhh.. Maybe I don't get it.

You must work with statistical distributions here. I guess your problem is "not seeing the solid because you focus on atoms". Yes, more than half of the particles of the sun are in ground state. So what? There is no possible way to select each particle on ground state, you have to work with the whole sun. Check any text on statistical thermodynamics. All the molecules vibrate at different speeds but your interest is the integral average.

I give you a point on the inversion with a P/R of 0.1 I would have to check the formulae to see how the calculations are done. I suspect they work with a certain probability distribution and invert this function to come up with a new probability distribution for P/R > 0.5 that they call "negative kelvin".

Another way to work would be to just define a prob distribution that goes from 0 to 1, but that would have a discontinuity since P/R = 0.5 is imposible to attain.

So how does Bell's curve jive with a 2=state system? Which is where I see the inversion process falling apart. Yes, some bosuns at the suns corewill have momentarily given their all before the next interaction comes along, and would conceivably, and conceptually, have a total ground state, for the briefest increment of time. Another few probably reach near 1 Tev. Between are billions each at a trillion differing states. If thre reduction to a 2-state system is needed to describe the model such that the inversion has the desired effect, that is reductum ad rediculum. Even a laser is based on the excitation of a large percentage of the population above the mean sate of particles not electricly excited. i doubt that lasing would occur in a CO₂ environment of say 1° K. Any energy applied would result in an intermediate state producing heat until the population reached some minimum temperature. As I recall, He lasers only work at very low temperatures, beyond which they no longer lase. I'm not sure what they do, but lasing stops at some maximum temp for He.

I thought the problem with ruby lasers was a maximum power level without excessive heat. I understood that the wonder of CO₂ lasers was room temperature lasing.

None of these square with the concept of reduction to a 2-state system to make inversion result in a negative value.

Magnetic alignment has been used for decades to extract heat from sub-degree materials.

So would a negative K material draw energy from , or transfer to, a micro-degree K well, would the -K material heat of cool and what would happen to the micro-degree?

The last concept I recall of "inversion" through infinity waas the very early concept of a closed, curved universe. Look or travel far enough in any direction and you would see the back of your head, or run into it, That's grown much more comprehensible and useable without the infinite connection to both ways. Maybe this can lead to the next step, also.

RichH

Wouldnt the upper limit occur when all atoms (nuclei) had been pulled apart?

Hi Guest,

You said: "Wouldnt the upper limit occur when all atoms (nuclei) had been pulled apart?"

What does the thermometer read when this occurs?

What does the thermometer read when this occurs?

I think the thermometer has melted by then....D'oh !

Unlike Wile E. Coyote who is continually defeated by his own gadgets, often obtained through a fictitious mail-order company called "ACME", my thermometer will not melt thank you. it's made of "photonic" glass and it did not come from "ACME"! (actually, I borrowed it from photonicgirl, but I'll return it soon Jules).

-J²

I loved roadrunner when I was a kid

I did, too, and I hope that love didn't end yesterday.

richh

Non-caps is littlerichard

Love never dies, only you don't see it here anymore.

This may happen as low as five to six thousand Kelvin with the formation of plasma.

We already spectro-analysed regions of the sun's Corona with some twelve to fourteen million K.

I aw something recently about this.

While there is no absolute temp limit,

the highest temp to ever occur was at the first instant of the big bang,

where all the the mass of the universe was concentrated into the PLank volume.

I dont remember exactly, but it was something like 10 ^ 31 K, Ouch!

What puzzles me is why all of the particles at that time

didnt fuse into lots more heavy elements.

Thats what stars / super novae do? Hmmm . . .

There was know particals. There was only energy. Later when the universe cooled off and the matter condensed and formed matter.

Alzie wonders: "What puzzles me is why all of the particles at that time didn't fuse into lots more heavy elements."

-----

The early Universe was simply too hot for particles to fuse. Too hot for the right particles that might constitute heavy elements to even exist.

But what'll really bake your noodle is this: why the Universe didn't collapse into a black hole during the roughly 10⁷ Planck Times between the first and second symmetry breaks? The first symmetry break occured approx one PT after the Big Bang, when gravity split off from the superforce. Until the second symmetry break, gravity dominated the scene, Inflation had not yet begun, and the Universe was still small enough for the mutual gravitation from all parts of the tiny Universe to be felt everywhere. So why didn't it all collapse in one black hole? Some speculate that many smaller black holes might have been produced during this epoch, but then why didn't they immediately coalesce into a single larger one? They could all still "feel" each other, gravity-wise, and so what stopped them from merging? Remember, Inflation during this epoch had not yet started, so everything in the nascent Universe was well "in touch" with everything else, gravity included. Assuming gravitational effects propagate at the speed of light, something else was preventing total collapse. But what?

Let's play (if you indulge me) with some basic assumptions, and see where it may lead to:

Heat, is equivalent to kinetic energy of particles. This movement, although erratic or irregular in vectorial terms, still result with some mean velocity, dependant on the particle's mass. Velocity, a particle's velocity, has a definite upper limit.

Well then, would it thus make sense to assume, given all the above, that temperature, being particle's velocity of a sort, has an absolute upper limit?

My bet would be a hesitant "yes"...

Then what is the temperature of a positron in the interaction with gamma rays and the super c speeds attributable as in the proximity of Co⁶⁰?

RichH

Hi again Rich,

I think Yuval's point is well taken. Please explain further about super c speeds and Co60.

-John²

Cobalt⁶⁰ has a strong gamma ray degradation. In the near vicinity of a mass, many e⁺/e^- pairs are produced apparently without regard as to where either may have originated, although their point of origin appears to be identical. The electron moves out of the picture, while the positron travels until it meets an electron, whereupon the positron and the new electron collide and mutually annhilating. One proposal many years ago, involved interaction between an electron and a gamma ray, resulting in the electron being accelerated to above c velocity. this super-spped electron, through its own instability, would release the excess energy as a gamma ray, and be decelerated to sub c velocity.

As a result of this apparent interaction of an electron electron/positron pair and a pair of gamma rays, was presumed to be a single electron, which upon reaction with the original gamma ray, and achieving super c, reached it's end "collision" before leaving it's creation point. The natural decay of the c+ electron reporduced an electron, at the point of the pair production, and the release of the gamma ray energy as the same energy gamma ray. Gamma rays don't track, so the e⁺ and e^- are all that are visible. An electron absorbs a gamma ray, and becomes a positron. The positron travels a short distance, and releases a gamma ray, and leaves as a sub c electron. Because the electron reached its decay before its creation, the net appearance would be the creation of the pair from nothing. Prior to that, a positron and an electron collided, disappearing.

Or was the positron/electron pair merely a case of quantum mechanics creating a random bit of material from nothing?

RichH, a nearly perfect vacuum.

This is some fascinating stuff.

Nice of you to mention, and elaborate on.

NoSciFi writes: "...One proposal many years ago, involved interaction between an electron and a gamma ray, resulting in the electron being accelerated to above c velocity."

-----

The interaction between an electron and a gamma ray will not accelerate an electron to a velocity in excess of c. No matter how you accelerate an electron, Special Relativity tells us that you would have to impart an infinite amount of energy to the particle to even reach c, let alone surpass it. The most energetic gamma rays observed to date have energies in the 10 TeV (trillion electron volts) range. Were such a gamma ray to impart all of its energy to an electron, the electron's relativistic mass would still be less than 1.8 x 10^-23 kg, corresponding to a velocity less that of c.

Einstein's Special Relativity tells us exactly what happens to a particle's mass as its velocity approaches c:

M = γm, where

M is the particle's relativistic mass,

m is the particle's rest mass, and

γ (gamma) is the ubiquitous Lorentz factor, shorthand for

Here v is the particle's velocity and c is, of course, the speed of light. Clearly as v --> c, γ --> ∞. If you re-arrange the terms above, you can derive v from M, given the particle's relativistic mass and its rest mass. For an electron, the rest mass is 9.109 3897 (54) x 10^–31 kg.

Forgetting electrons for the moment, consider the most energetic particles known: cosmic rays ("rays" being a misnomer). Cosmic rays are energetic baryons or atomic nuclei which have been accelerated to extremely high energies. Cosmic rays having energies in excess of 10²⁰ eV have been observed. Consider for a moment a single proton having the kinetic energy of a baseball travelling in excess of 100 MPH! Still, these particles travel at less than the speed of light.

Here's a quote from Wiki:

The Feynman-Stueckelberg interpretation

By considering the propagation of the negative energy modes of the electron field backward in time, Richard Feynman reached a pictorial understanding of the fact that the particle and antiparticle have equal mass m and spin J but opposite charges q. This allowed him to rewrite perturbation theory precisely in the form of diagrams, called Feynman diagrams, of particles propagating back and forth in time. This technique now is the most widespread method of computing amplitudes in quantum field theory.

This picture was independently developed by Ernst Stueckelberg, and has been called the Feynman-Stueckelberg interpretation of antiparticles.

Sometimes I'd like to reformat my memory.

RichH

The question I believe, was "Is there a limit", not "what should be the calculated limit of a given case". I tried to make a humble attempt to look at the question from a fundamental, principal take.

- Was your question rhetorical?

- If so, can you define this case in terms of velocity?

- If so, is it finite?

Hi Yuval,

That was, of course, my original question. I was thinking along the same lines as you in that temperature is simply a scale that defines the relative velocity of particles, which I assumed were confined by c as the limit of the scale. However, if there are, in fact, super c particles as Rich has indicated, then the scale may actually tend toward infinity. What's the final verdict, limit or no limit?

-J²

It was also mentioned somewhere here on CR4, could be by one of our physics buffs, be it Europium or Jorrie, I cannot recall now, that during a stage of inflation following the initial Big-Bang, the summing velocity of relativistic particles 'riding' the inflation wave, should theoretically move beyond C, not to mention Einstein's idea of Tachions, so for me, my bet of "yes" to your questions, is hesitant.

I'm as curious as the next in-line...

- Don't you just love physics?

Dear Yuval,

As you pointed out, the particle's temperature is a function of the particle's kinetic energy which, in turn, is a function of velocity. Velocity does have c as an upper limit, but as the velocity increases toward c, the particle's mass tends toward infinity. As the mass and the velocity both contribute to the particle's energy, that energy tends toward infinity as the velocity tends toward c. Hence, the temperature of the particle, which is related to its energy, also tends toward infinity. Of course, the foregoing ignores restrictions QM and General Relativity place on the particle's maximum energy...

As the particle's energy increases, it's equivalent (Compton) wavelength decreases. If the particle's wavelength should reach the Planck Length, it's relativistic mass would be such that the particle would collapse into its own black hole and vanish forever. One implication of all this is that it makes it impossible to measure objects smaller than one Planck Length.

Wouldn't the upper limit of temperature occur when each particle was moving at the speed of light?

Therefore... Maybe the upper temperature might be different for different elements and compounds? (Different bonding forces between particles).

All a bit academic, really, isn't it? I mean, we all complain when there's a heat wave for a few days of around 40 degrees Celsius. at 40 Million Celsius would all the moaning stop?

My texts on cryogenics simply say there is no concievable upper limit to temperature, only a lower limit that can never be reached.

I find it interesting that about the only thing man has been able to beat nature at is low temperature. We have not produced higher temperatures, brighter light sources, more massive structures etc. etc. However, the lowest natural temperature is that of the cosmic background radiation left over from the Big Bang (2.7 Kelvin) while we routinely reach temperatures in the milliKelvin range with off the shelf cryocoolers.

Hint: Temperature can also be expressed in terms of electron-volts, or eV, which allows us to gauge the equivalent "temperature" of particles accelerated to relativistic velocities.

1 degree kelvin= 8.621738 X10^-5 eV
= 0.0862 meV
= 0.695 cm^-1

So, just for fun, compute the equivalent temperature of a 1.0 TeV electron. What is it's wavelength at this energy (from the accelerator's standpoint)? What is it's mass? What are these values for an electron which is moving at 0.9999999999c? Don't neglect Einstein's mass/energy equivalence relation.

Hmmm... not exactly my field, but; going back to the original Q> "I would like to know what others think about the possibility of an upper temperature limit. Is there one?"

I seem to recall, while reading about the Rodman smoothbore cannons at Ft Jefferson (Dry Tortugas), that the fellow who 'perfected' the rifling techique (it had actually been used as far back as the 1500's) developed an astonishing hypothesis. We know there is an upper limit to the temperature achievable by combustion ... as well as from multitudes of chemical reactions and toying with atomic forces ... but, that hypothesis that was developed back in civil war days stated that there is NO upper limit to the temperatures achievable by friction. It seems that I have committed this to memory as an aphorism, or even a veritable axiom. Can any of our enlightened physicists either corroborate, clarify, demystify, or debunk this age-old hypothesis please?

Share what you know, learn what you don't...

Hi ndt,

The following excerpt from this may be what you're referring to:

"Rumford had observed the frictional heat generated by boring cannon at the arsenal in Munich. Rumford immersed a cannon barrel in water and arranged for a specially blunted boring tool. He showed that the water could be boiled within roughly two and a half hours and that the supply of frictional heat was seemingly inexhaustible. Rumford confirmed that no physical change had taken place in the material of the cannon by comparing the specific heats of the material machined away and that remaining were the same.

Rumford argued that the seemingly indefinite generation of heat was incompatible with the caloric theory. He contended that the only thing communicated to the barrel was motion.

Rumford made no attempt to further quantify the heat generated or to measure the mechanical equivalent of heat."

Regards,

-John

Dear NDT,

The kinetic energy of a particle can be expressed in a multitude of ways, including temperature, but what ultimately happens is that as the energy density passes various thresholds, the energy results in the production of elementary particles. Real ones and/or virtual (transient) ones. The answer to your question lies in the realm of quantum mechanics. Energy, or more specifically, energy density, cannot increase without bound without resulting in the production of particles.

Take, for instance, the electric field intensity/electric-field density very near an electron. So far as physicists have been able to tell, the electron does not have a "size." It is, for all practical purposes, infinitely small (QM has something to say about minimum size, as well, but we're not going there right now). As one approaches the "center of charge" of an electron (this, too, has problems, thanks to the Uncertainty Principle), the field density continues to increase. If the electron is infinitely small, then "at" the electron, the field density would be infinite. But it is not. Rather, the region where the electron seems to be is embedded in a boiling sea of virtual particles continually flickering in and out of existence. This curious property of the Universe limits the field density near an electron to finite values (values which "flicker" as well) no matter how close you get.

The Universe doesn't seem to allow infinite energy densities. Even the unimaginably hot inferno that was the Big Bang did not have an infinite energy density. It's temperature, though incredibly high, was finite. Quantum Mechanics simply doesn't allow such infinities. You always end up with particle production. And the more energy you pour into a system to increase its temperature, the more particles that are produced.

So, yes, there is an absolute upper limit on temperature. I'd sit down and calculate it for you, but I'm just too friggin' lazy to bother with that right now. Wait til after my mid-afternoon nap.

Is this sufficiently opaque?

Excellent post europium.

One thing that bothers me is that you said "The Universe doesn't seem to allow infinite energy densities". What about in a black hole? I know there's lots of speculation about what might go on there but even so, doesn't current thinking suggest that gravity approaches infinity within the beast. If it does, then doesn't that imply that mass also approaches infinity? And if it does, then, since mass and energy are interchangeable, energy would also approach infinity. Where am I going wrong here?

-John

The mass "inside" a black hole (what exactly is meant by "inside" a black hole is a bit iffy, as the physics near a singularity go a little wacko) remains constant.

Let's say some binary star Out There somewhere dumps material onto its massive companion until the companion exceeds the Chandrasekhar Limit and collapses into a black hole. The mass the companion had at that point (assuming none is blown off during the collapse, which is almost never the case, plus barring other incidental problems that cause mass loss) will still be there. The first star will still orbit pretty much the same as it did before its companion's collapse, the gravitational field it feels from the companion will be pretty much the same, but instead of orbiting a bright, glowing star, it's now dancing around a big black drain in the sky. The companion's mass has not increased to infinity, but the mass density and the gravitational energy density are both attempting to do exactly that.

Whether the companion's mass density actually does increase to infinity is anyone's guess. My opinion (and it is just that: an opinion) is that it does not.

Think about Hawking Radiation: particle pairs are produced just inside the event horizon of a black hole. Following the Uncertainty Principle, there is a small but finite probability that occasionally one of the pair will find itself outside the event horizon without having actually passed "through" it (call it "tunneling," if you will) and will zip off into space, go into orbit around the BH, or whatever, but not re-enter the event horizon. These particle pairs are produced as a result of the gravitational energy density at the point of their creation. The higher the energy density, the more particles that are produced. One of the pair escapes only by virtue of its proximity to the event horizon. But I believe that well within the EH the same thing is happening, except that both particles are still trapped inside. Hence the net mass of the BH doesn't change.

But in a manner similar to the case of the electron in my earlier post, the particle production near the singularity increases the closer you get to the singularity. These particles will get sucked into the singularity (I assume, given the conditions there) or annihilate each other (they're usually particle/antiparticle pairs), but other particles are produced to replace them just as quickly and in a continual process. I would imagine, then, that the singularity itself may be surrounded by a roiling "cloud" of virtual particles, similar to that in the immediate neighborhood of an electron. These particles would effectively distribute the mass of the singularity over the volume of the cloud and, consequently, would prevent the mass density near the singularity from ever assuming infinite values. But I must point out that much of this is speculation. As one approaches a singularity, Physics itself falls apart. It's hard to build a good model with a broken toolbox.

Very interesting. I now need to digest this and try to get my head around it before making a feeble reply.

About your last statement though, the toolbox is not broken, it's just incomplete. We still need a couple of good vector wrenches, a singularity micrometer and a few more good precision tools (not Craftsman though). I'm sure we'll get there soon enough.

Hi europium,

Here's an interesting excerpt from a paper by Martin Bojowald of Penn State:

"The idea that the universe erupted with a Big Bang explosion has been a big barrier in scientific attempts to understand the origin of our expanding universe, although the Big Bang long has been considered by physicists to be the best model. As described by Einstein's Theory of General Relativity, the origin of the Big Bang is a mathematically nonsensical state -- a "singularity" of zero volume that nevertheless contained infinite density and infinitely large energy. Now, however, Bojowald and other physicists at Penn State are exploring territory unknown even to Einstein -- the time before the Big Bang -- using a mathematical time machine called Loop Quantum Gravity. This theory, which combines Einstein's Theory of General Relativity with equations of quantum physics that did not exist in Einstein's day, is the first mathematical description to systematically establish the existence of the Big Bounce and to deduce properties of the earlier universe from which our own may have sprung. For scientists, the Big Bounce opens a crack in the barrier that was the Big Bang".

However he goes on to say "Scientists using this theory to trace our universe backward in time have found that its beginning point had a minimum volume that is not zero and a maximum energy that is not infinite. As a result of these limits, the theory's equations continue to produce valid mathematical results past the point of the classical Big Bang, giving scientists a window into the time before the Big Bounce".

Read more of it here.

Regards,

-John

Interesting read. Thanks!

Bojowald is correct about the "singularity" at the moment of the Big Bang being non-sensical when viewed from the broader perspective of QM and its ubiquitous Uncertainty Principle. Even apart from Bojowald's theory, the phrase 'at the moment of' is meaningless for values of t less than one Planck Time. For a Universe smaller than one Planck Length the concept of 'smaller than' likewise becomes meaningless. That the Universe at (loosely speaking) the moment of the Big Bang did not assume zero volume and infinite density is not news.

<flame>

What is so amazing (to me, at least) in discussions of black-hole physics (particularly in the popular press) is the continued insistence on a singularity at the center of a non-rotating black hole. (Yes, this is related to our discussion.) For instance, the same author might discuss, on the one hand, Hawking Radiation and the mechanisms that produce it and, on the other, utter some inane blurbage about the zero-volume, infinite-density "singularity" at a BH's center (somehow neglecting pair production that just might be (like, is) going on deep within the event horizon and the implications of that), then go on about the Big Bang not starting out as a singularity, thanks to QM, whilst piously invoking Heisenberg, Planck, Wheeler and the rest of the QM gang to justify that conclusion. Doesn't a person's knowledge of one area transfer to another, closely-related area? I don't get it. Maybe it's just me.

</flame>

That being said, Bojowald's model looks to be pretty cool. Thanks again.

The "big bounce" would require several several conflicts with the original singularity, whatever it's size or density. A bounce is a Newtonian concept, a response to inertia. Inertia implies both mass and a force either wiped out in, or non-existant at the time of the big whatever.

Unless something was outside of the event horizon, which could now be dark matter and dark energy, crumbs left behind, but not included in, the big....

I succeed in the concept of the big whatever only by comparing that to fitting such large concepts into my small mind, and watching the resultant confusion begin the expansive explosion I'm left with.

RichH

Hi Rich,

It's my impression that Bojowald, et. al. are using "bounce" sort of metaphorically, as in one universe contacts, the new one expands, etc. Personally, I don't believe that folks at that level of study, physics, math, etc. would not have taken Newtonian concepts into consideration.

What with my, sometimes, wild imagination I find it absolutely fascinating that we are mathematically where we are, i.e., at the point where we're actually extrapolating events back beyond what science has, up until recently, considered the "beginning" of everything. The possibilities are downright excitin' podner!

-John²

"Sufficiently opaque...?" Absolutely! "...as the energy density passes various thresholds, the energy results in the production of elementary particles..." This resounds of "maybe there's something there", with respect to the new particles of matter (1 particle per hundred thousand cubic kilometers or so) being created as our universe expands. Still digesting "The Fabric of the Cosmos", I remain politely skeptical now of any talk that seems to be too rigidly adherent-to either Q-M or Einsteinium physics (he himself admitted those mistakes of which he became aware ... what of those about which he did *not* become aware?!). ?When did the electron quit exhibiting a mass approximately 1/1800th of a single proton? I can't seem to keep up!

Love the avatar... and your explanation for same. Would appreciate if I could elicit your thoughts pertaining to a conundrum that I've fallen-into ~ a rubik's cube relating to "penetration" of the spectrum's varying wavelengths (thru air and/or water), and how the eye/brain combination actually "sees" colors. Appropriate for this venue, or another...(?)

Sorry about the opacity. I'm only a journeyman quantum grease monkey trying to expound on a subject best left to the masters.

NDT writes: "This resounds of "maybe there's something there", with respect to the new particles of matter (1 particle per hundred thousand cubic kilometers or so) being created as our universe expands."

Virtual particles are being created (and annihilated) continually and everywhere. Better (or worse) yet, down at the Planck Scale spacetime itself is a real zoo. Physicist John Archibald Wheeler calls the stuff at those scales quantum foam. This property of spacetime has nothing directly to do with the expansion of the Universe (as far as anyone knows).

NDT writes: "I remain politely skeptical now of any talk that seems to be too rigidly adherent-to either Q-M or Einsteinium physics (he himself admitted those mistakes of which he became aware ... what of those about which he did *not* become aware?!)."

Skepticism (as distinct from cynicism¹) is healthy. Skepticism of quantum mechanics is healthy, too, in spite of its being the most successful scientific theory in history. QM has a lot going for it. A whole lot. Tomorrow someone may discover a serious flaw with it and we'll do with QM as has been done throughout scientific history: either modify the theory to accommodate the new data, or trash it altogether in favor of a better theory. But until then, QM is the best we have for what we've got, quantum-wise. Like, if someone offers me a Lamborghini Countach, you can be damn sure I won't opt for a bicycle. Until then, I'll ride my bike - and keep my eyes open.

NDT writes: "When did the electron quit exhibiting a mass approximately 1/1800th of a single proton?"

Nowhere did I mention anything about the electron's mass.

(Note 1: My ex-girlfriend was a cynic. A cynic is someone who, when she smells flowers, looks around for a coffin.)

Apologies if I read more into it (or, (?) took-away from it?) in your statement:

"the electron does not have a "size." It is, for all practical purposes, infinitely small..."

As with everything else that I read pertaining to such subjects, I should have gone back 2-or-3 times, asking myself" "How else can this be interpreted?"

Your "Member Statement" says that your field of study is light. "In what context(s)", if I might ask? (You didn't address my allusion to the conundrum that I'm trying to wring-out...)

NDT writes: "As with everything else that I read pertaining to such subjects, I should have gone back 2-or-3 times, asking myself" "How else can this be interpreted?""

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Are you in the mood, perhaps, for a whimsical analogy? No matter how hard you smash a cookie (the energy you put into the system), all you'll get is crumbs (particle production).

NDT writes: "...relating to "penetration" of the spectrum's varying wavelengths (thru air and/or water)..."

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Probably a topic for a separate thread, IMO.

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NDT writes: "...and how the eye/brain combination actually "sees" colors."

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I'm afraid you've got me there. I'm not very knowledgeable about the physiology of color perception. My son is color-blind, however, and it's interesting to see how he perceives colors differently than I do. For example, when he was a young child, we happened to be admiring some flowers while taking a walk. There were some flowers that were pure scarlet, and some that were distinctly orange. To him, they were the same color except that the orange ones were a lighter shade of orange. This was the first inkling I had that he might be color-blind.

Go to hell and find out.

Sorry, my fiance forgot to log in.

I inquired further, and she said, "Yes. If (and only if) you repent."