A number that fascinates physicists
cosmosmagazine.com
cosmosmagazine.com
The last part of the article, however, is still quite intriguing. Nobody would expect any of the 3 components of alpha to change, unless somehow the measurements can be affected by the medium (as the speed of light depends on that).
I think invoking the Anthropic principle only makes sense if we can demonstrate that there are a number of other "places" with varying "conditions". For such a selection bias to occur there needs to be a population to actually select from. For example, the Anthropic principle makes sense regarding the composition of the earth because we know that there are a large number of planets with a distribution of orbits and masses around a distribution of stars. Of course we will be on a planet that supports life as we know it.
To invoke the anthropic principle regarding a constant would imply — to me, at least — that there would need to be a number of universes with different constants. Or different regions of this universe where the constant would vary.
If there truly is only a single universe, and the constant is not changing in time or space, then it would seem we did actually just happen to get lucky.
Edit: of course, at this point we can't say definitely either way about our universe. We don't know if ours is one among many, or if its the solitary universe in existence. We also, clearly, have uncertainty about how constant this constant actually is.
H&H spend a lot of time comparing themselves to the approach of selecting an initial values surface in the early universe and marching it forward; they more or less do the same but flip the direction of the arrow of time and arrive at a superposed state. Re-flipping the arrow of time leads to relic fields like the CMB carrying evidence for the superposition.
Essentially this is just taking time-reversibility of local microscopic physics seriously (great), and absorbing the difference in degrees of freedom in macroscopic physics into a superposition (uh, ok). The problem of setting up a values surface remains pretty much the same. "Fine tuning" is just a way of saying that the system is sensitive to the values it evolves from (or to).
I'm not really convinced that that a present-day spacelike hypersurface is easier to write down than an early-time initial values surface.
ArXiv version: http://arxiv.org/abs/hep-th/0602091
Thanks for the link, though! I'll get studying.
I think this entire discussion is sensitive to exactly what one means by "The Anthropic Principle". If one's definition of the Anthropic Principle in this context simply means that an observed universe will be consistent with a universe that can be observed, then I find it to be trivially true and applicable to a single universe scenario.
I subscribe to a definition of the anthropic principle that invokes selection bias as its core mechanism. I think that, in order to have a selection bias, one needs to actually be selecting from a population. Hence my assertion that you need a multi-verse (with different constants in each universe) or a constant that is variable in space or time [2].
The difference, to me, is this:
If you are selecting from a population the Anthropic Principle can actually help explain why a value is what it is. Under our understanding of planetary bodies, we often invoke the Anthropic Principle to explain why the earth falls in the habitable-zone. Earth falls in the habitable-zone because — we think — life is most likely to arise on a planet in that zone.
However, if you are not selecting from a population, I don't find that the Anthropic Principle explains why a value is what it is. In the scenario where there is only a single value, I think the Anthropic Principle simply demonstrates that that particular value must support life.
Put another way, if all planets we observed were the exact same distance from their star as Earth [1], then we couldn't use the Anthropic Principle to explain why Earth is that particular distance from the sun. We would have to find other astronomical reasons to explain why planets form at that specific distance from a star. In this single-distance scenario the only thing the Anthropic Principle actually does for us is confirm that such a distance supports life.
[1] Well, not distance per se, but placed such that they received the same amount of stellar energy in their orbits.
[2] This final sentence of the introduction of the Anthropic Principle also makes some reference to this saying: "Most often such arguments draw upon some notion of the multiverse for there to be a statistical population of universes to select from and from which selection bias (our observance of only this universe, compatible with life) could occur."
It is "trivially" true in a sense. It's a tautology. But it's still useful for thinking about things. I think it applies just as well to a single universe or a multiverse, because even with a single universe you can at least hypothesize about other ways the single universe could behave.
> However, if you are not selecting from a population, I don't find that the Anthropic Principle explains why a value is what it is. In the scenario where there is only a single value, I think the Anthropic Principle simply demonstrates that that particular value must support life.
It might not answer the extremely broad and ill-defined question "why" to your satisfaction, but I find it fairly satisfying. If things were another way, then I wouldn't be observing the universe because I wouldn't exist. So it's not strange that the universe is this way, given that I exist.
If there is only one value, the universe can't "plan" or "choose" a value that is conducive to life, and so pointing to its suitability for life is a teleological argument-- it explains a cause (the value of the constant) in terms of its effect (the eventual existence of life). That's backwards and circular-- causes come before effects.
That is, the anthropic principle doesn't try to "explain" why a constant takes a value. It just notes that the conditional property of us observing that value (given that we exist) is 1, regardless of what the unconditional property might be (or even whether it's variable to begin with).
Edit: It's hard to come up with a good analogy because obviously I don't have that "perfect" language at my disposal. But for example, a triangle fundamentally has 3 angles. We can imagine polygons with more angles, but it doesn't make sense to imagine a triangle with any other number of angles. If "the whole universe" were synonymous with "triangle", the notion of "universe with 4 angles" would be absurd. The ideal description would not even allow for that possibility.
There are a couple challenges to these measurements, though. Sean Carrol presents a theoretical challenge in his blog post "The Fine Structure Constant is Probably Constant"[1]. Chad Orzel has a more observational critique of the results in "Why I’m Skeptical About the Changing Fine-Structure Constant" [2].
To be fair, these critiques are from 2010 and Webb, et al. has published several papers since these critiques were made. I haven't seen updated debate or discussion over Webb, et al's findings. Still, I would think we have some potential evidence that the constant may vary, but I don't think this evidence is near conclusive yet.
[1] http://www.preposterousuniverse.com/blog/2010/10/18/the-fine...
[2] http://scienceblogs.com/principles/2010/09/14/httpksjtracker...
The Anthropic Principle is usually invoked to explain why two very large dimensionless numbers, i.e. the inverse gravitational "fine structure constant" (which is assumed to be constant), and the age of the universe measured in atomic units (which increases with time), are both very close to 10^40. It is suggested that, for intelligent life to evolve and measure them, the two numbers must be roughly equal, and other dimensionless numbers, such as the electromagnetic fine structure constant, must similarly have values within a narrow range. And this in turn has led some people to believe it's the deliberate action of a creator, or that there are numerous other universes whose constants have different values, and almost all are devoid of life.
Fine-tuned Universe: https://en.wikipedia.org/wiki/Fine-tuned_Universe
However, if we apply this Anthropic Principle to planetary orbits, we could conclude that planetary orbits are roughly circular because, if they were (for example) very long rectangles (or some other random shape), we wouldn't be around to observe their shape.
Of course, no one believes that. It is accepted that Celestial Mechanics, based on Newton's Law of Gravity, (which can be derived from the more accurate General Theory of Relativity), adequately explains why planetary orbits are roughly circular.
An alternative explanation is that we simply haven't worked out all the physical laws. For example, the force of gravity could become weaker as the universe gets older or less dense (or, expressed in different units, gravity remains constant but elementary particles get lighter). Dirac, and later a few others including myself, modified Einstein's equations in an attempt to explain this coincidence.
Dirac large numbers hypothesis: https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis
Another argument against fine tuning is the Inverse gambler's fallacy: https://en.wikipedia.org/wiki/Inverse_gambler's_fallacy
In other words, things are the way they are because we wouldn't be able to fall in love, dance to the music and enjoy life, if things were otherwise.
Thinking too much about why, distracts from the now. Mystery is what makes life worth living. And hiding ourselves from our self is what makes discovery possible.
If reality is a computer simulation, then proving that is a bit redundant in my opinion.
However, I think it can be proven but once it is, what will there be to know?
If reality is a computer simulation I can think of a multitude of other questions about reality:
- Can we communicate "outside" of the simulation?
- Is the simulation a product of intelligence that is intentionally running the simulation? Or is it a mere by-product of a higher-order universe?
- By studying the simulation in great enough detail, is there anything we can learn about the "outside" universe?
- Is the "outside" simulation a turing machine? Can it compute a higher class of computational problems?
- Are the simulations infinite? Is the "outside" also a simulation? Is it simulations all the way down — or all the way up? Is there a "real" reality?
- If its simulations all the way down, how did the first simulation get started?
- If there is a "real" reality we get to start all of science over at square one studying this new reality.
This is a rough initial list, but I'm sure there's an endless number of questions to be asked and answered about reality even if we prove its a simulation.
Consider the broader philosophical implications of what I wrote. And proving it was a simulation would explain all those questions you proposed.
I have asked some of the smartest people I know about this topic, and no one seems to know.
It would be awesome if someone reading this thread knew something unique about it and emailed me. That's my only motivation.
I may well have missed the point, though if I have done so because you purposely wrote obtusely then I have no real interest in attempting to decode your writing. I wish you luck in your ventures, and hope someone with more time and ability than I discovers your writings and sends you the e-mail you desire.
No they don't. For instance, a simple aspect ratio measures how something is wide relative to how it is long. It has no units.
This here desk I have here is about 1.7 times as long as it is wide. No inches or centimeters required.
There isn't anything amazing or mystical about a unitless quantity.
Now for a piece that's more interesting. The fine-structure constant (alpha) is the coupling constant that sets the strength of electromagnetism. This means that its value is the thing that matters in the equation: e^2/\hbar c. Each of the other values is a derived quantity. Further, to speak a bit loosely, only changes in alpha matter -- in the sense that if the speed of light (c) changes, but the other constants (e and \hbar) change in a way that keeps alpha the same, then you wouldn't be able to tell with an experiment that anything has changed.
Contrast this situation w/ a change in alpha -- a table-top experiment would be able to detect the change (given that it's large enough, and we have methods of measuring changes on year-time scales that are a few parts in ~10^-18 (Rosenband, 2008)), as it would mean that physics has changed in a fundamental way.
http://phys.columbia.edu/~millis/1900/readings/Science-2008-...
\alpha(\mu = M_Z) is about 128. But m_0(photon), h, and e are the same at both energy scales (we can determine the numerical values experimentally). To the best of our ability to measure, none of them (including, if we ignore the main posting, \alpha_em) varies anywhere in a background fixed by the isometry group of SR (where we find c as the sole free parameter, corresponding to the speed of a particle where m_0(particle) = 0).
So I'm having trouble understanding your assertion that "Alpha is the fundamental physical constant: c, e and \hbar are the derived quantities" (in your other comment, but also reflected in your second paragraph above).
I think we both totally agree that varying \alpha_em at different points in space or time leads to a mess.
But you are using units. Your unit is the width of your desk. If it were a different width but the same length, your measurement would be different.
Note that the aspect ratio lets us say things like: "these two desks have the same aspect ratio".
The "desk widths" interpretation of aspect ratio precludes this useful sentence from having semantics.
The aspect ratio 1.7 has a life of its own, independently of that desk.
You do need radians, but that's not a unit in the same way a 'meter' is, you don't need any kind of reference to know how much, say, 1 pi radians is. For most intents and purposes angles are unitless.
See root comment. I do not have to specify the units that I used when I quote the aspect ratio, or the method that I used.
I think the confusion is in actually measuring these things. Scientists use dimensionless numbers all the time, but you have to directly measure quantities with units to indirectly get the dimensionless quantity.
1. Standardised. 2. Defined by a numerical relationship to observable physical constants, like c, by definition.
Desk widths aren't a scientific unit. You can only measure the ratio of width to height by reference to a standard unit like the metre, which in turn is based on a constant observable quantity - the distance travelled by light in one second.
You can pick your derived units using any relationship to c - like the distance travelled in 3.2 seconds. But that's still a derived unit, not a fundamental observable unit.
And ratios are dimensionless because they stay the same whatever derived unit system you choose, as long as it's consistent.
/nitpick
Another point that throws me off is the Vulcan scientist part. They would need to be using the same numerical base in order to get that number. There might be some base-less representations of numbers, but they are usually restricted to representing integer numbers. The constant could still be represented by a fraction, but there would be no math-neutral way of saying "hey, this here is a fraction/division".
To give one example, my piece of US Letter paper is 93.5 in^2 in area. One side is 8.5 in long. If I divide these, I find that 93.5 in^2 / 8.5 in = 11 in. Is that eleven inches a ratio or a quantity?
How did you measure your desk in order to compute its length/width ratio?
I am not convinced they determined the ratio of his table's length and width without first measuring those quantities in some unit.
The units involved in the aspect ratio disappear because they are divided out. After that, we don't have to (in fact, must not) cite any units when giving the aspect ratio.
Of course, both the quantity and the associated error come from previous measurements.
If this sort of thing interests you, I'd encourage you to look at the quantum metrology triangle. Frequency, resistance, and current are all currently related to a josephson voltage standard, the quantum hall resistance, and the current generated by a single electron transistor. This allows us to standardize all these back to a frequency. Length can be related to frequency by wavelength of light. Everything has been related back to frequency. Basically the only thing not referred back to something absolute is mass, which I think is still referred back to a mass standard, which is a physical thing stored in a vault.
Okay well more than you ever wanted to know.
Consider two voltage sources that you want to measure the ratio of. Place one source on one arm of a resistor, and the other through a pulse width modulator, (ideal) low pass filter with a cutoff frequency much lower than the pulse width modulator frequency, and then attach this to the other lead of the resistor. Turn on the voltage sources and adjust the pulse width modulator until the resistor doesn't heat up. You could place it in a cup of water and monitor the temperature. Remember we're free to push up the current in this thought experiment
i would like an example of an experiment that directly measures a dimensionless quantity without inferring it from direct measurements of dimensional quantities. it's just a curiosity.
Suppose some rectangle is visible at a distance. We can use parallax angles from our vantage point to estimate its aspect ratio.
We have no idea how long or wide that rectangle is because we don't know how far away it is.
(Indeed, we don't even know whether it is a rectangle, or whether it is some quadrilateral that appears as a rectangle under perspective.)
Either that, or i'm misinterpreting your first sentence.
> Now for a piece that's more interesting. The fine-structure constant (alpha) is the coupling constant that sets the strength of electromagnetism. This means that its value is the thing that matters in the equation: e^2/\hbar c. Each of the other values is a derived quantity. Further, to speak a bit loosely, only changes in alpha matter -- in the sense that if the speed of light (c) changes, but the other constants (e and \hbar) change in a way that keeps alpha the same, then you wouldn't be able to tell with an experiment that anything has changed.
> Contrast this situation w/ a change in alpha -- a table-top experiment would be able to detect the change (given that it's large enough, and we have methods of measuring changes on year-time scales that are a few parts in ~10^-18 (Rosenband, 2008)), as it would mean that physics has changed in a fundamental way.
> http://phys.columbia.edu/~millis/1900/readings/Science-2008-...
Alpha could be different in different galaxies. It will not vary in a galaxy but maybe vary between galaxies. This is not clear, most likely not. It has much to do with the early stages of galaxy crystallization which could be the same for all galaxies.
It has a geometrical underlying principle in BSM-SG. c is also derived, e more or less, not so sure with h, guess you could.
Most of the 'constants' from the standard model are derived in BSM-SG, there are only very few underlying constants.
This surprises me. I would have thought pi, the ratio of any circle's circumference to its diameter, is a much better known example of a pure number.
Everyone is so fancy. One, two, three, and even zero are pretty well known, even outside physics.
[0] why I don't feel uncomfortable disclosing this here
I prefer their earlier slide deck for gory details (it's mostly based on King et al 2012).
https://www.eso.org/sci/meetings/2012/ESOat50/Presentations/...
See especially the "Really?" slide (p 27).
(The previous "What if it's correct?" slide undersells the impact to the standard cosmology of a violation of isotropy and the consequent erosion of the "must be homogenous at scales > 250 Mly" part of the cosmological principle. Also, "what if atomic physics is really obviously different only very slightly outside the horizon?" feels like a declaration of war against the Copernican principle with precious little evidence, and against pretty good theory that has other lines of evidence backing it (cf. Carroll @ http://www.preposterousuniverse.com/blog/2010/10/18/the-fine... who points to Banks, Dine & Douglas @ http://arxiv.org/abs/hep-ph/0112059 who in turn point to other work that shows that you probably can't vary \alpha without varying other constants like the m_e and QCD coupling).
I mean "growing evidence" in the sense that it wasn't even questioned before, and some very early-stage experiments have asked the question.
I agree with you that it's still _way_ to early to be making any conclusions, and it all may wash away as the experiments improve.
This is much more natural when working with frequencies instead of using cycles.
Yes, this constant arises prolifically when looking at the atomic "fine structure", which modifies the usual hydrogen energies to includes interactions between an electron's spin and its orbit (the un-modified ones only include the kinetic energy of the reduced electron-proton and the electric potential energy). There are further interactions that can be added, eg the hyperfine interaction which includes the spin-spin interaction between the proton in the nucleus and the orbiting electron.
And if you use Planck units where hbar=c=G=1, you can do many things easily, for example denote the potential of an electron at distance r as just alpha/r (without all those other pesky constants embedded in Gauss's law).
I don't know the detailed history, but in practice the fact that it's an inverse is essentially because it's most important role is as part of an expansion like a Taylor series. The standard method for calculating lots of observable effects gives an answer with the form
X = X_0 + \alphaX_1 + \alpha^2X_2/2! + ...
http://www.amazon.com/Basic-Structures-Matter-Supergravitati...
2.9.6.B Fine structure constant as embedded feature of the twisted prisms
12.A.5.3. Hypothesis of embedded fine structure constant in the lower level structures of matter organization
It gets derived later to: α_c = 2 ⁄ [ ( n^2 + 2/2 )^1⁄2 + n ] = 7.29735194 × 10–3
where n =137 results in a very accurate value of α. It is important to understand that the fine matter constant has it's origin in a geometrical organization of the prisms. A very low level building block of matter in the BSM-SG model. It is 1/6th the size of a neutrino (neutral or positive flavor) - those 2 neutrinos are composed of 6 prisms of either large or small prisms an rectangular geometry j but the prisms is itself a very large structure compared with the ultimate building blocks, the fundamental particles.
The prism itself is quite complex in it's internal structure but there is a very logical explanation for its existence. On the first level of organization or you could see it as the first crystallized structure is the Primary Tetrahedron. You basically take a bunch of Fundamental Particles - just very, very small balls, and create a tetrahedron with same length sides out of it.
Very simplified explanation: This tetrahedron has a very complex vibrational mode - like every layer of our physical world. You end up basically with 2 overlaying vibrational modes, where you need n cycles of the small cycle to result in one cycle of the larger one. Alpha is the Energy relation of those cycles. Through alpha, you end up with 2 Energies in the prims, CP and TP.
Alpha is very fascinating feature as it is basically the driving force of most of the complex behavior of nature, it is everywhere in the BSM-SG model.
Funny side-node: In the BSM model, the cosmological redshift is not of Doppler kind (also no space expansion) and you can find the fine matter constant in the periodicity of the red-shift.
https://en.wikipedia.org/wiki/Redshift_quantization
Please note, that you have to do a proper Doppler correction in the BSM model if you measure galaxies. It also explains the Lyman-Alpha-Forest phenomena very well.
From the standard model perspective: I have no clue what it could be, like most constants.
The fine structure constant is physically pure.
I highlight text on the internet as I read it, but this page moves all over the place when I do! And on NYT it jumps around to different articles as I'm reading. Makes it impossible for me to consume the text on these pages.
/rant