It’s Monday, the first of September, which was “originally” the seventh month, but which is now pushed back to the ninth by the two “caesarean” months.  Speaking of such things, it’s also Labor Day in the US (I’m not sure about other countries) a day on which we celebrate labor by giving most people the day off.  This isn’t quite as perverse as it might sound.  After all, what woman would want to work while in labor?

Ha ha.

Anyway, my workplace is open today, though only for half a day.  It has become more and more common for nearly everything to be open even on huge holidays like New Years and so on, let alone “ordinary” federal holidays.  The reasons are fairly straightforward, and they have nothing to do with any kind of formal, deliberate, corporate conspiracy such as is imagined by so many naïve people on social media.

It’s just the same problem‒or situation‒that leads trees to grow tall when it would make much more sense for them all to stay closer to the ground and not waste so many resources on trunks and xylem and phloem, on getting water and nutrients from the ground up to their highest leaves*.  The trouble is, if all the trees were low but then one variant appeared that was slightly higher, it would have a significant advantage over its species-mates (and other species), so it would be more effective at reproduction, ceteris paribus.  Its offspring would come to dominate, unless and until yet other variants occurred that tended to grow even higher.  And thus the “arms race” would begin.

So in the human world:  if everyone else worked four days a week, but one worker was willing/able to work more days or longer days, especially if for the same or only slightly higher pay, then that worker would have a job advantage, (again, ceteris paribus).  And so competition leads at least some workers to strive to outdo each other to the extent they can, and so on, working for local, individual advantage that inexorably leads to less pleasant outcomes for everyone.  It’s just game theory applied to economics.

Anyway, that wasn’t what I wanted to discuss this morning.  I wanted to discuss two physics-related ideas I’ve had in the last few days.  The later one is just a bit of silly fun, but the other is more interesting to me.

The second one happened this morning (at about 2 am, when I was awake, because of course I was).  I put on a YouTube video of Star Talk in which a string theorist was the guest, and Professor Tyson asked her about the possibility of more than one dimension of time, and she said most such theoretical possibilities fall afoul of paradoxes and trouble with causality.

But it occurred to me, if there were a situation with time travel involving, for instance, the “grandfather paradox”, maybe the fact that preventing one’s grandparents from meeting makes one no longer there to prevent the meeting doesn’t necessarily unravel the universe, but maybe the paths and events correct and change each other in a closed, repetitive loop of time, interfering with each other** until only one, complete resonant spacetime line is there.

It’s analogous to a plucked string*** in which all sorts of vibrations and waves go back and forth between the fixed ends, but most waves/vibrations end up canceling each other out except the ones that fit an even number of times within the confines of the fixed string.  So maybe the actual events of reality could thus only be the ones that are resonant within that spacetime…whatever the hell that might mean.

Anyway, that’s the frivolous question; though it’s a bit fun, it probably doesn’t really have anything to do with our actual world (though it could…remember my thought a bit ago about forces traveling backward and forward in time and interfering until only a fixed number of outcomes resonate****?).

More interesting to me, really, was a question that occurred to me while I was reading Lisa Randall’s Warped Passages, a physics book (of course) and a particularly good one.  It was not really discussing the question that popped into my mind, other than that Professor Randall was reviewing the particles in the Standard Model.

We know that fermions cannot pile up one on another (cannot share quantum states), and that bosons can (e.g., in lasers).  We also know that massless force-carrying bosons such as gluons and photons travel at c, the “speed of light”.  The W+ and W- and Z bosons of the weak force do not because they interact with the Higgs field and so have “rest mass”.

Anyway, that’s not really the point.  The point is that gravitons, the hypothetical force-carrying particle of the gravitational field, are also massless bosons, and gravity travels at the speed of light*****.  But something popped into my head that had never occurred to me before and I’m not sure why:  do gravitons come in different frequencies?

We know that light has a limitless number of possible frequencies, across a very wide range, and that higher frequencies/shorter wavelengths are associated with higher energies per photon.  We also know that all matter radiates photons at a spectrum of frequencies that depends on temperature‒the so-called black body radiation.  Well, we also know that all matter “radiates” gravitons, or at the very least it all interacts with the gravitational field.  What if matter gives out gravitons in a spectrum that depends on total mass?

What would it mean for a graviton to have higher frequency or lower frequency?  Would that entail a stronger (and weaker) gravity?  Or would it correspond to something else entirely?

Of course, I know that gravitational waves are of varying frequencies depending upon the source‒that frequency and intensity (amplitude) increase as, for instance, two mutually orbiting black holes get closer and closer, orbiting faster and faster, before they coalesce.  Is that analogous to them producing large numbers of gravitons of those increasing frequencies?  Or are gravitational waves different types of things than “ordinary” gravitons?  Is ordinary gravity propagated by “virtual gravitons” much as the electromagnetic force is carried by “virtual photons”, which are really just mathematical shorthand for perturbations in the quantum field of electromagnetism?

I suspect that, because we don’t really have anything like a good quantum theory of gravity, there would be few clear answers to my questions about gravitons, but there may be constraints based on what we already know that would make my questions answerable or moot.

I mean, I know that “we” know that gravitons would be spin-2 particles, meaning that to rotate them 180 degrees would leave them unchanged******.  I don’t know how this or other aspects of gravitons would affect possible frequencies, though.  Also, can gravitons be polarized in a manner analogous to light?  I’m not sure whether my graviton questions are sensible or pertinent or utterly off the mark.  If anyone out there is a physicist specializing in such things, please, if you can spare a moment, let me know?

This post has gone on for a long time, I know.  I could meander around much longer on these subjects, probably for pages and pages and pages, but that would be a bit much for a daily blog post, if it isn’t already.  Maybe because it’s a holiday, at least some of you will have the time and interest in reading such thoughts, but I don’t want to push my luck.

However, I welcome any comments on the above subjects if you have an interest, and especially if you have relevant expertise (though I welcome all interested thoughts).

In any case, please try to have a good day.

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*A fascinating physical process that’s only possible because continuous liquids can actually have negative pressures.

**Not in any inappropriate way, just that they interact and waves can cancel out.

***Not a “superstring” or heterotic string or what have you, just for instance a guitar string or a cello string.

****This is not unlike Feynman’s path integral/sum over histories notion, really.

*****We know this is so because there was a neutron star merger detected by LIGO and VIRGO that was quickly looked at using “light” telescopes as well, and the timing matched up (As a silly aside, since gravitons are bosons and could thus in principle share quantum states, one might, in principle, be able to create a coherent beam of them…a GRASER or GASER if you will).

******Spin-1 particles basically return to their identical state if you rotate them 360 degrees.  And for spin ½ particles, you need to rotate them 720 degrees (!) for them to return to their prior configuration.  Once you’ve rotated them 360 degrees they’re kind of the opposite of their prior configuration.  If that’s hard to think about, just imagine traversing a Mobius strip laid out in a “circle”:  once you’ve gone 360 degrees, you’re on the opposite “side” of the strip than that on which you began, and you have to go another 360 degrees (so to speak) to get back where you started.  Neat, huh?