Questioning the Perfect Master on this issue is akin to walking the Planck.
I’m here all week.
Yep, and this is why we say the kelvin is an absolute measure of temperature. But it’s not the only one that’s been used - the Rankine scale is also an absolute temperature scale.
The neat thing about an absolute temperature scale is that it can be directly used in equations related to chemistry and physics. As an example, the thermal voltage in a p-n semiconductor junction (V[sub]T[/sub]) is kT/q, where T is the junction temperature in kelvin.
Hmm does he go into further detail regarding how he arrives at this figure? Because doing a quick back-of-the-envelope, I get something like two orders of magnitude less for typical nucleon binding energies…
The link provided by beowullf. Sorry I wasn’t clear.
Having read Cecils link I have supplementary question; electrons are (as far as anyone knows) elementry particles, but what about protons, neutrons and the like, would they stay intact or would the additional kinetic energy (in the form of heat) overcome the nuclear forces and make them into a quark/gluon plasma? If so at what temperature does this occur?
Would electrons even survive at this temperature? Or woudl they sublimate into energy?
>All I know is that the powers-to-be have decreed absolute zero to be 0 K and the TP of VSMOW water to be 273.16 K. And then they draw a straight line, so to speak.
I think the situation is different from this. There are a variety of scales out there, the Beaufort scale for wind, the How Bad Does It Hurt on a Scale of 1 to 10 scale, the Annoying scale where Dave Letterman is 0 and Tom Arnold is 10, and so forth. A scale provides a means of quantifying when units are poorly defined or there is no clear role of an absolute value. Temperature used to be like this, at least until Amonton (sp?) and maybe through to Kelvin and others.
It is a stronger statement to say you have a unit to measure things and you can tell what zero of those are. That’s the case with all the units of the SI, including kilograms and kelvins. Neither mass nor thermodynamic temperature require a scale. Both are well defined with units. So, neither of them require a statement about what zero means.
It is very easy to measure distance and include the idea of zero in your work. Likewise with kelvins.
A practical means of measuring temperature accurately might better be a scale with points defined in various convenient spots and a polynomial for Pt resistivity. This is a real scale, and it is useful in some situations for practical reasons.
But it is still also true that there are true thermodynamic temperatures that can be stated in kelvins, just as there are true masses that can be stated in kilograms, with no need to invoke scales of any kind.
>matter with a temperature of 2 K has twice as much energy as matter with a temperature of 1 K
Wait, that isn’t right. It is equivalent to saying that the specific heat of any matter is independent of temperature, which is also not true. In fact, specific heats change by large fractions of their value near absolute zero, because of quantum mechanical effects. The number of possible states shrinks rapidly, and it takes very little energy to climb the first K, more to climb the second K, and so forth.
What is true is that the most energy you can tap from heat flowing from a higher temperature to a lower temperature is equal to the amount of heat that flows, multiplied by the temperature difference, then divided by the higher temperature. This is the basis of the definition of thermodynamic temperature in terms of entropy. It’s Kelvin’s insight, for which he is one of only two people with SI fundamental units named for him. It’s part of why he is buried next to Isaac Newton.
Electrons are absolutely stable, under all conditions, and in all contemplated extensions of the current standard model of particle physics. Electric charge is conserved in all known and contemplated interactions, so a particle with charge, if it decays, must decay into at least one other charged particle (plus miscellaneous debris). And mass is also conserved in all known and contemplated interactions, which implies that the sum of masses of a particle’s decay products must be less than or equal to the mass of the initial particle. So for an electron to decay, its decay products would have to include a charged particle with mass less than that of the electron, and no such particle is known to exist. Further, if such a particle did exist, there’s no known explanation for how we could have failed to detect it. So since we don’t detect it, we conclude that it doesn’t exist, and since it doesn’t exist, we conclude that the electron can’t decay.
Napier: As mentioned, NIST considers the absolute/thermodynamic/kelvin scale to be a scale. Lord Kelvin also called it a scale. (Cite.) So I don’t think there’s a problem calling it a “scale.”
As for the value of 273.16 K for the TP of water, it is not a magical number; it is ultimately arbitrary. The values in the Celsius scale (formerly centigrade) were arbitrarily assigned, and Lord Kelvin calculated absolute zero to be -273 °C. He then said absolute zero = 0 K, which put the FP of water around 273 K.
I believe that, at one time, the FP of water was defined to be 0 °C, which meant the TP of water was some weird temperature in the vicinity of 0.009911 °C. It was later decided to make the TP of water the defining temperature, and it was rounded to 0.01 °C (273.16 K). Of course, this meant the FP of water was now a weird temperature (around 0.000089 °C), but for most applications it can be assumed the FP of water is 0 °C. (I may not be entirely correct here on how things historically transpired, but this is a good way to think of it none-the-less.)
In one of his many collections of Fantasy and Science Fiction esseys Asimov mentioned that after writing that article he was contacted by a physicist who tackled the problem. IIRC Asimov said he came up with some really freakin’ huge temp.
As I don’t remember who this fellow was (though a name was given, IIRC), what the answer was, how he came to this answer, or any of the other relavant facts this isn’t really much help. But I was pissed that Expano Mapcase beat me to mentioning this dab of arcania and wanted to at least nip-pik.
So there.
so, to sum things up in layman’s terms, (that would be me on this topic), is it at least theorized that the Planck temperature is the temperature inside a black hole?
Anyone?
Bueller? Bueller?
This is all still bothering hell out of me.
>There isn’t a Kelvin scale.
My statement here is wrong, at least in describing generally accepted usage in all the best places.
>Kelvins are units unto themselves, like inches or grams.
My statement here is correct.
>I disagree. In common usage, “kelvin scale” refers to the thermodynamic temperature scale. NIST also uses this terminology (see this). The ITS-90 is another temperature scale that uses the kelvin as its unit.
Crafter_Man is correct here and in addition provides citations.
Nevertheless, I believe there is an important point about scales and thermodynamic temperatures that actually reflects on the OP’s question at least a little. Yet all sorts of important authorities seem to ignore or confuse this point.
In the measurement of anything, there are several levels of ability to define an expression for the measurement. When it is less possible to define such an expression, you may be forced to use a scale, which is essentially a list of comparisons or rankings and perhaps the instructions for how to put things on the scale in between the comparison or ranking points. Those wind scales for “light gale” and “fresh breeze” and “hurricane” work like this: you compare your observations by the various items listed at each point on the scale.
Any time you hear a statement with “on a scale of # to #”, this is what is going on.
This is a very different state of affairs from when it is possible to fully define an expression of the measurement. In the counting of apples, it has long been possible to use “so many apples” to describe a group of apples. The idea of “an apple” is clear and strong and useable. Measuring something that can be continuously variable, like the length of a rod, adds the idea of noninteger numbers to this concept, and acknowledges the issue of measurement accuracy, but everything is well defined when you say a rod is 22.15 ±0.02 inches long.
So the thing is that in the measurement of temperature it was necessary for a long time to use temperature scales, but this has not been strictly necessary in recent decades, even though it often remains practical to do this. Temperature is a stuff, of which you can have some or none, just like length and mass and electrical current and so forth. We have the idea of “a kelvin” that works like “an inch” or “an apple”. We can talk about thermodynamic temperature without any scale, just like we can talk about length without a scale. We don’t need two or more references. It is obvious what zero kelvins temperature means, as it is obvious what zero inches length means.
The ITS is a scale. It’s been criticized because the “kelvins” it uses are made of rubber, and they stretch a little here and there to accomodate the imperfect accuracy of the fixed point assignments for its various landmarks. But ITS does not define thermodynamic temperature, it only defines a practical scale that tries to imitate thermodynamic temperature while being much easier to actually put to use in physical experiments.
Here is NIST’s page for defining the kelvin. I like this because it is consistent with the distinction between measurements on a scale and the more generally powerful measurement with a unit and no scale. They refer to “the way temperature scales used to be defined” and to the ITS, but they don’t say anyplace that thermodynamic temperatures need scales to be expressed. The fact that they are consistent with this distinction I’m making does not prove that they meant to be or that they recognize such a distinction, but I like to hope that they did.
Unit of thermodynamic temperature (kelvin)
The definition of the unit of thermodynamic temperature was given in substance by the 10th CGPM (1954) which selected the triple point of water as the fundamental fixed point and assigned to it the temperature 273.16 K, so defining the unit. The 13th CGPM (1967) adopted the name kelvin (symbol K) instead of “degree Kelvin” (symbol °K) and defined the unit of thermodynamic temperature as follows:
The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
Because of the way temperature scales used to be defined, it remains common practice to express thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T0 = 273.15 K, the ice point. This temperature difference is called a Celsius temperature, symbol t, and is defined by the quantity equation
t= T- T0.
The unit of Celsius temperature is the degree Celsius, symbol °C, which is by definition equal in magnitude to the kelvin. A difference or interval of temperature may be expressed in kelvins or in degrees Celsius (13th CGPM, 1967). The numerical value of a Celsius temperature t expressed in degrees Celsius is given by
t/°C = T/K - 273.15.
The kelvin and the degree Celsius are also the units of the International Temperature Scale of 1990 (ITS-90) adopted by the CIPM in 1989.
Napier:
I admit I was a bit confused as to your earlier statements, but I think I understand what you’re getting at now. I think what you’re saying is that, theoretically speaking, we really don’t need to assign any numbers to an absolute scale. I agree with this.
One idea is to define an absolute physical parameter strictly on relativistic/ratiometric quantities. We could simply say, for example, that the temperature of Object A is 3.2395621 X the temperature of Object B, and leave it at that. And that the temperature of Object C is 0.832812 X the temperature of Object D, and leave it at that.
Would this work from a practical standpoint? No. As you stated, temperature is an absolute, intrinsic quantity (much like mass), and it would be next to impossible for us to communicate or build things if temperature were defined based upon relativistic relationships between any two objects. A much better idea, then, is for all temperatures to be defined relative to a common object. It really doesn’t matter what the absolute, thermodynamic temperature of the common object is, as long as it never changes and we all use the same thing.
For mass, the common object is cylinder of platinum-iridium located somewhere in France. This is both good and bad. It is good from the standpoint that all mass measurements are referenced to the exact same standard. But it is a pain in the ass to get access to it, which results in very long and complex traceability lineages. Wouldn’t it be nice if any lab could create an economical and sufficiently-accurate 1 kilogram standard in their lab? I seem to recall they’re working on it.
For temperature, obviously, the common object is the TP of VSMOW water. All temperatures are referenced to it. The thermodynamic scale, for example, is simply a ratiometric scale that says, “Object A has a temperature that is 4.65215 X the temperature of the TP of water, and Object B has a temperature that is 0.0322965 X the temperature of the TP of water.” All temperatures are relative to the absolute temperature of the TP of water. The fact that we assign the number 273.16 for the temperature of the TP of water is arbitrary; Lord Kelvin could have assigned it the number 123.456 and everything would have worked out O.K.
And unlike mass, we don’t use a TP water cell located in some forbidden palace in France. For not much money, anyone can buy a TP water cell, and it’s just as good as any other TP cell. (At least that’s the way it is supposed to be. But I’ve read reports that certain manufactures of TP cells are better than others. If you have ten TP cells, and you measure the relative temperatures between each using an SPRT, the cell with the highest temperature will be the most accurate.)
An interesting side note: the temperature of the TP of water can’t be measured. Since its temperature is defined, it is meaningless to talk about measuring it.
Sorry for the long post, but this is a subject I like talking about.
Thank you for the long post, as this is a subject I like talking about too.
The standard kilogram you reference is, I think, used only for comparison with secondary standards that are distributed in, I dunno, 5 or 10 labs around the world. They have these reunions occasionally where they are all compared in the same lab. Unfortunately the master appears to be gaining (I think) relative to the average of all the secondaries. For this and other reasons we are thinking about, they do indeed want to create a more absolute standard. I read an article in Scientific American a couple years ago about this. They are trying to grind beautifully round and precise spheres from crystalline silicon, using the same big grown crystals the semiconductor people use. Since the diameter of the sphere and the crystalline spacing are both distance measurements that can be done pretty accurately, this provides a standard mass. Like you can’t measure the speed of light, or the temperature of TPW (as you point out), if this standard takes over, you won’t be able to measure the atomic weight of silicon.
Although, interestingly, we may hear that it has changed a thousandfold. Atomic weights are given in the cgs system, typically, and not in the SI. But I don’t see why they couldn’t be commonly used in SI.
>I think what you’re saying is that, theoretically speaking, we really don’t need to assign any numbers to an absolute scale.
Yes, this is it. Or, better, we really don’t need to assign any numbers to a scale, we only need to have one unit. You don’t need a scale to measure something that has a unit. “Absolute scale” is a contradiction. Or, at least, should be, if usage were more enlightened.
Theory, properly so called, is completely mute on the subject of the interior of a black hole. Anything we say about the interior of a black hole is at best an extrapolation from theory. That said, extrapolation from classical (i.e., non-quantum, but still relativistic) theory says nothing about the temperature of a black hole, and semiclassical theory says only that a black hole should have a surface temperature that depends on its surface gravity and therefore on its mass (about a millionth of a Kelvin, for stellar-mass black holes). A fully-quantum theory of gravity might predict some higher temperature at or very close to the center of the hole, but that’s just a WAG, since we don’t actually have a theory of quantum gravity yet, and probably won’t for quite a while. And even in that case, you probably wouldn’t get such extreme conditions until you got extremely close to the center: Just inside the horizon, conditions should be very much like those just outside the horizon.
A bit more on absolute measurements of things that have units, as opposed to scale measurements:
There are thermometers that try to measure temperature according to some absolute effect. That is, they measure some response that is proportional to temperature. Proportional - not just linear - some response that must be zero when the temperature is zero.
I know some are based on electronic noise, but a little casting about produced inconclusive hits about Johnson noise and shot noise and other things, without clarifying which of these are known to be strictly proportional to temperature.
But there is a new one out there, discussed briefly on the Scientific American website. Here’s a quote:
“Now physicists have invented an electronic thermometer that ties temperature directly to a fundamental number—namely, the Boltzmann constant, a value related to the kinetic energy of molecules. (The constant is typically abbreviated in high school chemistry as k or kB.) The device centers on the fact that in an array of tunnel junctions—thin, insulating layers sandwiched between electrodes—the electrical conductance can change in a manner directly proportional to the Boltzmann constant multiplied by the temperature.”
http://www.sciam.com/article.cfm?id=a-new-thermometer
There are many automated measurement processes that I think are in effect scale based. For example, if you have a load cell connected to a voltmeter, you can call that a force measurement. But without some independent test of zero force, you can’t guarantee that there is a proportionality.
You can, however, imagine automated measurement processes that are not scale based, though. Photocells generate current from the light falling on them. They are always proportional (until you damage them or something). They are guaranteed to generate zero current when there is zero light. If they ever misbehave this way, we all blow off the SDMB and celebrate the discovery of free energy instead, and screw measurement science. You could use the current to charge a capacitor in a timing circuit, and use a counter to count how many times this cycles. There are no calibration requirements to get this system to work and still guarantee it is giving you a zero signal when there is zero light (I chose the weird capacitor timing and counting method of data acquisition specifically to be able to make this claim, not because it is a popular method).
Temperature has a somewhat tedious history specifically because so much of the work developing its measurement, its nomenclature, its understanding, and all the rest, happened before it was clear there was a real zero with physical significance. Then more of these things happened before anyone figured out with much accuracy where that zero was, relative to the things we had been measuring. It is STILL not the case that there are good (accurate, practical, etc) measurement means that are absolute. While it is easy to construct a mass balance that is inherently correct at zero, and a yardstick, and an ammeter, when somebody creates a thermometer that is inherently correct at zero Scientific American prints a little article about it.
I sometimes teach a class in temperature management, and like to try to talk the victims - I mean, the class - into accepting a distance measurement system where we put the zero at a length of maybe a dime’s diameter, because most measurements of distance measure distances bigger than this, and so it is a more practically useful measurement this way. If you had to measure the diameter of a toothpick, you would get a negative number. As you should guess, I wish temperatures would be measured in kelvins in practice.
Thanks, I didn’t think about charge conservation.
Just a bit of idle googling found this paper, but my maths/particle physics is not good enough to tell whether it has any merit or not. I suspect not as it is a few years old and AFAICT was not published in any actual journal.
I gave it a quick skim. It’s not incorrect, insofar as it is just some guy working through some math, but it is fairly non-compelling. What Mr. Pradhan has done is write the electron as the excited state of a neutrino, which itself would be the bound state of two other particles. The other particles would be very massive and they would be bound by a force mediated by a super massive gauge boson.
My main beefs:
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too many typos (ugh!)
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He is working within a Lorentz invariant gauge theory, which requires charge conservation, yet he is allowing charge non-conservation. He doesn’t give any reason why he can get away with this.
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He gives no reason why his fundamental particles will couple to the photon only when in a bound and excited state. That is, he makes charge this non-fundamental thing, but gives nary a peep on how it arises.
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He calculates that the fundamental particles would have enormous mass, >10[sup]22[/sup] GeV! Assuming these particles were created in the early moments of the universe before they joined up to make electrons and neutrinos, their excess mass-energy would be released upon binding. That’s 10[sup]22[/sup] GeV per electron or neutrino created. I have to imagine that this would leave quite the impression, leading to serious conflicts with data from observational cosmology. (In other words, I’m betting that his theory could be super ruled out already.)
In short, he appears to have spent some time pushing symbols around on a page. He’s not violating any rules in his symbol-pushing, but he’s not doing anything too exciting from a physics point of view (IMHO).
Thanks for the great explanation.
From what you say there seem to be at least 2 reasons why this paper can’t be true, lack of charge conservation and the 10^22GeV energy per neutrino or electron.
One additional question, if you don’t mind though, given that the universe formed form the big bang and was intially composed of energy until about the Planck time when the electrons and quarks/gluons appeared, how was charge conserved in the intial stages? Or is this one of those as yet unanswered questions?