Relative strengths of the fundamental forces

[Pasta]

@colonial

I am not real happy about the discrepancy.

Such discrepancies are inevitable in these tables because there really isn’t any way to condense the “strength of the forces” down to single numbers like that. These are effective numbers in “typical” scenarios, for arbitrary choices of “typical”.

For instance, the electromagnetic force and the weak force are actually the same force. They only appear different because an aspect of the unified “electroweak” force is frozen out at today’s typical energies due to the Higgs mechanism giving substantial mass to two of the three physical force-carrying bosons. If you heated up some material to, say, 10[sup]16[/sup] K, what we call the “electomagnetic” and “weak” forces would be about the same strength.

The strong force is also very situation dependent, exhibiting of note asymptotic freedom. The strong force gets very weak for two closely confined strongly charged (“colored”) particles like quarks. For instance, the quarks inside a proton behave nearly as if they are free quarks. However, if you try to remove one, perhaps by smashing into it with another particle, the strong force holding the quarks together gets very strong very quickly as separation begins.

In practice, then, one picks “typical” particles interacting with “typical” energies and puts some order-of-magnitude numbers together. Since the Coulomb and gravitational forces have a familiar functional form for everyday scenarios, one can just pick protons or electrons or whatever and take the ratio of the forces. For EM vs. weak, one might compare the interaction probabilities for electron-electron collisions versus electron-neutrino collisions at some arbitrary collision energy. More likely for such tables, though, one might just note that the ratio of the forces at low energy will be approximately the square of the ratio of the energy scale of the interaction to the mass of the relevant gauge boson (e.g., the Z boson). At 1 GeV (high for “everyday”, but not too high for some relevant behaviors like particle decay), one gets (1 GeV / ~90 GeV)[sup]2[/sup] ~= 0.0001. So, if you choose to set the EM force at 1/137 in a table, then the weak force would end up at ~10[sup]-6[/sup] in this approach. The strong force might be introduced by looking at the ratio of lifetimes for a prototypical strongly decaying particle to a similar weakly decaying particle.

Anyway, yes, these tables are somewhat arbitrary, though not without pedagogical value. However, even with current theory, any two of the three Standard Model forces can be made to have the same strength by choosing your situation appropriately. It is an active area of theoretical research to determine if there is a more generalized theory – a “grand unified” theory – for which all three of these forces end up being the same underlying force, just with three different low-energy manifestations. (Getting gravity to join such a theory is another task entirely.)

[colonial]

First of all, it would have been best if Mr. Pasta had perused my 2nd cite (in post #15) before replying,
since much of what he says is discussed there.

@Pasta

Such discrepancies are inevitable in these tables because there really isn’t any way to condense the “strength of the forces” down to single numbers like that. These are effective numbers in “typical” scenarios, for arbitrary choices of “typical”.

Second, my original cite (in post #8) was written by a Cal Tech PhD, and if he is comfortable with
condensing the strength of the forces down to single numbers, then so am I. I just wish he and
the author of the 2nd cite would get together, come to an agreement, and make some appropriate edits.

@Pasta

For instance, the electromagnetic force and the weak force are actually the same force. They only appear different because an aspect of the unified “electroweak” force is frozen out at today’s typical energies due to the Higgs mechanism giving substantial mass to two of the three physical force-carrying bosons. If you heated up some material to, say, 10[sup]16[/sup] K, what we call the “electomagnetic” and “weak” forces would be about the same strength.

I know-- it is one of the (few) things I recall from Steven Weinberg’s excellent book
Dreams of a Final Theory. Weinberg, as you are aware, was a corecipient of a Nobel Prize
(with HS/college classmate Sheldon Glashow and the Pakistani scientist Abdus-Salam) for
contributing to the theoretical discovery of electroweak.

I am not sure how the early combination of the two forces in questions provides anything
OP relevant, although mentioning it here may provide others with an awareness of the SDMB
poster’s impressive store of knowledge.

@Pasta

The strong force is also very situation dependent, exhibiting of note asymptotic freedom. The strong force gets very weak for two closely confined strongly charged (“colored”) particles like quarks. For instance, the quarks inside a proton behave nearly as if they are free quarks. However, if you try to remove one, perhaps by smashing into it with another particle, the strong force holding the quarks together gets very strong very quickly as separation begins.

Addressed in 2nd cite.

@Pasta

In practice, then, one picks “typical” particles interacting with “typical” energies and puts some order-of-magnitude numbers together.

What do you mean by “order of magnitude?” The numbers derived are accurate to very much better
than an order of magnitude, if that is what you mean. In particular, the number for the electromagnetic force,
aka the Fine Structure Constant, is quite precise, isn’t it?

@Pasta

Since the Coulomb and gravitational forces have a familiar functional form for everyday scenarios, one can just pick protons or electrons or whatever and take the ratio of the forces. For EM vs. weak, one might compare the interaction probabilities for electron-electron collisions versus electron-neutrino collisions at some arbitrary collision energy. More likely for such tables, though, one might just note that the ratio of the forces at low energy will be approximately the square of the ratio of the energy scale of the interaction to the mass of the relevant gauge boson (e.g., the Z boson). At 1 GeV (high for “everyday”, but not too high for some relevant behaviors like particle decay), one gets (1 GeV / ~90 GeV)[sup]2[/sup] ~= 0.0001. So, if you choose to set the EM force at 1/137 in a table, then the weak force would end up at ~10[sup]-6[/sup] in this approach. The strong force might be introduced by looking at the ratio of lifetimes for a prototypical strongly decaying particle to a similar weakly decaying particle.

Why don’t you take a look at my 2nd cite and then take it from there?

@Pasta

Anyway, yes, these tables are somewhat arbitrary, though not without pedagogical value. However, even with current theory, any two of the three Standard Model forces can be made to have the same strength by choosing your situation appropriately. It is an active area of theoretical research to determine if there is a more generalized theory – a “grand unified” theory – for which all three of these forces end up being the same underlying force, just with three different low-energy manifestations. (Getting gravity to join such a theory is another task entirely.)

Not OP relevant.

[Pasta]

@colonial

First of all, it would have been best if Mr. Pasta had perused my 2nd cite (in post #15) before replying, since much of what he says is discussed there.

You seem to be saying that my post agrees with your cite (which I see it does). So, I don’t see where the defensive tone is coming from. Your cite even gives an explicit (if only an effective) expression for how the strong coupling constant varies with energy, implying straightaway that, indeed, there isn’t a single number that characterizes the strength of the force.

Second, my original cite (in post #8) was written by a Cal Tech PhD, and if he is comfortable with condensing the strength of the forces down to single numbers, then so am I.

While Eric Weisstein did happen to get a PhD in astronomy, the website you cite provides a broad-brush picture of science and math to lay audiences, and as I mentioned, such “strength of forces” tables are not without pedagogical value in such contexts. However, it remains true that such tables are somewhat arbitrary reductions of the much more complex framework underneath, and this arbitrariness is exactly the reason for the discrepancy you originally asked about and that I was addressing.

I am not sure how the early combination of the two forces in questions provides anything OP relevant, although mentioning it here may provide others with an awareness of the SDMB poster’s impressive store of knowledge

I was replying to your explicit request for explanation in Post 15:

@colonial

Maybe one of the board technical specialists will show up and provide some clarification.

I wasn’t answering the OP, I was answering you (although you do not seem pleased with the answer). The fact that these forces are the same force in the underlying theory is tremendously relevant to explaining why the tables are not uniquely defined.

What do you mean by “order of magnitude?”

I mean just that: the strengths are reported in these tables to an order of magnitude. Your first cite gives the numbers (in decreasing order) as 1, 10[sup]-3[/sup], 10[sup]-16[/sup], 10[sup]-41[/sup]. These are the very definition of order of magnitude (i.e., a power of ten is given, but no numerical coefficients). The other cite does the same except that it normalizes everything to a particular pre-defined unitless constant, namely the fine-structure constant.

Why don’t you take a look at my 2nd cite and then take it from there?

Note sure what you mean here. You did ask for clarification on the discrepancy, right? Your 2nd cite itself discusses the arbitrary choices made when constructing the table it shows.

[Cheshire_Human]

@Washoe

:smack:. I just now caught this. You guys are slipping—I should have been branded the village idiot by now and the yo’ momma jokes should be flying.

This is GQ. We’re not allowed to insult you or your mother.

[colonial]

@Pasta

You seem to be saying that my post agrees with your cite (which I see it does). So, I don’t see where the defensive tone is coming from. Your cite even gives an explicit (if only an effective) expression for how the strong coupling constant varies with energy, implying straightaway that, indeed, there isn’t a single number that characterizes the strength of the force…

I do not know what you mean by “defensive”, but what I meant to convey
was frustration at your having neglected the citations I went to the trouble
of looking up. I take it you have no objection to the numbers provided by
the 2nd cite. However, I still have no idea where the first cite obtained its
numbers, and why they differ.

@Pasta

…I mean just that: the strengths are reported in these tables to an order of magnitude…

1/137 is not an order of magnitude (power of 10, exponontial) expression,
which was one source of confusion.

[Pasta]

@colonial

I take it you have no objection to the numbers provided by the 2nd cite. However, I still have no idea where the first cite obtained its
numbers, and why they differ.

I have no objection to those numbers. Most of my earlier post was aimed as conveying the idea that you shouldn’t expect the numbers to match, due to the nuances I attempted to describe. For the two tables you link to, one explains some of the arbitrary choices made, while the other does not. But it’s a bit like asking “What are the relative ratios of the number of people that live in a house versus a city versus a state?” No one would worry if one person said that the relative sizes were 10[sup]-6[/sup]:10[sup]-1[/sup]:1 and another said 10[sup]-5[/sup]:10[sup]-2[/sup]:1. Both order-of-magnitude tables are useful if the audience doesn’t know anything about “cities” and “houses” and “states”. But from such tables alone, you can’t work out exactly what assumptions went into them, although you can make your own version to see that they all end up in same ballpark and/or to see what pitfalls are present.

So, too, with these strength-of-force tables. The second cite puts in the fine structure constant as an explicit entry because of its historical importance, but it’s a bit misleading, as it suggests that such numbers can be defined rigorously.

For the particular ratios, consider EM:weak, for which the first cite gives 10[sup]13[/sup] and the second gives 10[sup]4[/sup]. If I were to take the decay of strange-quark-bearing baryons as an (arbitrary) benchmark for weak decay, as your second cite does, then I’ll get about 10[sup]4[/sup]. (The corresponding energy scale is a few hundreds of MeV to a GeV, which leads to a weak propagator factor of roughly (1 GeV / 80 GeV)^2 = 10[sup]-4[/sup].) If I were to use instead the energy scale of tritium decay (tens of keV), then I would get 10[sup]-13[/sup]. But even these are far from the only approaches to getting numbers into the table, as there are countless physical systems that could make for sensible benchmarks. For grav:EM, one could look at the forces between two protons or two electrons or one of each or anything else. In fact, a hydrogen atom wouldn’t be an unreasonble system to base gravity, EM, and weak ratios on for such a table, as it’s a simple system that everyone is familiar with. But since the weak force doesn’t have historical ties to atomic physics, people don’t usually do that.