More on Gravity

 

                                Blue whale benefits from buoyancy

I have speculated in this blog that it is obvious from the size of the ancient land animals (dinosaurs) indicates that they could not walk the Earth today … most probably because gravity here is much stronger now than in our Earth’s relative infancy .. see: Gravity.

I also speculated that one reason why our gravity has strengthened over the millennia is because time is slowing down (see above reference for reason). Recently, I was reminded of a possible reason for this — Einstein’s postulate that time slows down as our speed increases … see: Physics at Berkeley . 

Now we do know that our universe is expanding after the Big Bang at an accelerating rate. If this is enough to slow down time enough to increase our gravity to cause huge land animals to be unsustainable? This calculation is currently beyond my patience… but it would be an intriguing exercise nevertheless. Maybe someday?

Gravity

 

A while ago on a Zoom call, a discussion came up about gravity. I posited that gravity here on Earth may have strengthened over the millennia ... and offered the fact that huge ancient dinosaurs do no longer ... but actually could no longer walk the earth ... see: More on Gravity.

... nor that ancient flying reptiles could not get airborne today ... see: Pterosaurs (Updated).

I have also speculated elsewhere that a shortening of actual time itself may have affected our gravity. This is because gravity is a measure of acceleration (distance/time^2) ... and if time gets smaller, acceleration (gravity) gets disproportionately larger.

Math Madness

 

The exercise for today is to map the set of all positive integers into the space  between zero one one … using my trusty version of set theory.

Since this space can be described by a set of rational numbers (1/4, 9/77, 17/209, etc. ),  to map the infinite set of integers, we need to set the denominator of all these fractions to infinity.  Then all integers easily map into the numerators of this set of rational numbers … as 1/infinity,  2/infinity, … ip to infinity/infinity  .…  and since any number divided by infinity equals zero … adding up the set of all these rational numbers (equivalent to zero) totals to the number value of one!

Perhaps this paradox can be resolved by positing that  the last number in the above rational number set  (infinity/infinity) is equal to one.  Not very satisfying … but it works.

STAND UP FOR MATHEMATICS!

Photon Mass

 

Does a photon have any mass? Science  says no … yet sunlight is able to propel objects that have solar sails (large surfaces like above) Here is one attempt at an answer from Physlink.com explanation:

“Indeed, photons have no mass. However, they DO have energy and momentum. It turns out that energy and momentum are the requirements that make a solar sail work, not mass.”

However, momentum is defined as “mass times acceleration” and, if photons have no mass, how can they have any momentum?  Also energy is scientifically synonymous with power … whose units are “Newtons times mass” … again this mass thingie.

So, it seems that they have some mass, however tiny, as a requisite for a photon’s ability to push a solar sail (a large thin metallic surface orthogonal to the sun’s rays.)

But things get much more complicated:

There are more issues with photons … one being that they are slightly repelled when they pass by an object of massive gravity.  But, if photons have any mass, wouldn’t they be bent toward the massive object instead of away from it? (I know, I know, Einstein attributes this to a “warp in the space-time continuum”). 

However, black holes have such enormous gravity that light can’t escape them. Does this not suggest that photons have mass?

Signed,

Perplexed

Afterward: Scientists agree that electrons can be comprised of a neutrino and a photon … neither of which has mass  … yet electrons have a very small mass. From whence?

Another afterward:  Curious thought … we see from the above that, if photons have any mass, it is extremely small. And if a photons mass equals its energy … then perhaps it  mass (from e = mc^2) might be equivalent to e/c^2. That would be very very very very  small!

STAND UP FOR PHOTONS!

Fast and Furious

(Originally written in 2011)

Some recent news is shaking up what were assumed scientific absolutes. See: Speed of Light Broken, BBC Article and Roll Over Einstein.  May I suggest that some of the comments in both articles are particularly interesting ... so peruse them too. Now this is pretty heavy stuff which is full of scientific land mines, so I have to watch my step here to keep from being a total doofus ... so please forgive any transgressions. I have written in the past about redefining the speed of light ... since somewhat recently scientists have been able to slow down light (see: Slowing Light) and even stop it entirely! (see: Stopping Light).  So Einstein's absolute notion about light had already been knocked into a cocked hat.  My previous thought on this matter were contained in Speed Limit, Neutrinos and Acceleration of Light.

The Game of Life

(Originally published in my Fletcher's Castoria Blog ... see: Fletcher's Castoria.)

Many, many years ago there evolved a simulation called the “Game of Life.” I think it was first popularized by John Conway in Scientific American magazine (see: Ibiblio Entry). Basically this game consisted of a two-dimensional checkerboard of infinite dimensions in which each cell was either populated or empty. When an initial set of populated cells is created (Garden of Eden condition) with the placement of counters, then a sequence of moves is begun under a rigid set of genetic rules. These rules can change, but Conway’s were (quoted from this article):

1. Survivals. Every counter with two or three neighboring counters survives  for the next generation.
2. Deaths. Each counter with four or more neighbors dies (is removed) from overpopulation. Every counter with one neighbor or none dies from isolation.
3. Births. Each empty cell adjacent to exactly three neighbors--no more, no fewer--is a birth cell. A counter is placed on it at the next move.

When this game was programmed into a computer (I can’t recall for sure, but I think maybe my son and I did such a program on the TRS-80), fascinating patterns were created which often performed spellbinding repetitions.  The game ends with one of three outcomes (again quoted from this magazine): 

[F]ading away completely (from overcrowding or becoming too sparse), settling into a stable configuration that remains unchanged thereafter, or entering an oscillating phase in which they repeat an endless cycle of two or more periods.

 Obviously changing Conway’s genetic rules within this same framework will create different outcomes. You might want to play this game for yourself at one of many Internet sites or download it (Google them). Here is one such on-line site: Kongregate Games .

Now comes the real point of this post … this game-of-life concept has just been brought into the physical world by scientists at Harvard University. They have created simple robots (bots) that can be made cheaply in great numbers and can communicate via infrared signals with one another ... and live by an updated set of rules to form complicated and often life-like learned patterns … see: Wired Magazine Story. Such social behavior often mimics the motion of flocks of birds or schools of fish and obviously may produce remarkable results. Although these Cantab scientists can (I assume) mimic deaths in these bot populations .., they have not yet been able to have them reproduce ... nor allow them to set their own objectives. Once this is accomplished, we may be in for some exciting and maybe even dangerous science-fictional outcomes.

Shazam!

Shazam! was that early television character, Gomer Pyle's exclamation of surprise ... and also the word that the comic book super hero, Captain Marvel, used to change (at the speed of a lightning bolt) his mufti into his orange tights and cape. But, in this case, it is used to describe the incredibly fast speed of quantum interaction ... far faster than the speed of light. As you can read in the following NBC News Story, "entangled" photons (or other atomic particles) exhibit "spooky" interactions (an Einstein term) of their polarizations, even when separated by great distances. The speed of these interactions is as near to instantaneously as can be measured ... and is clearly a puzzlement.

I love to imagine why such things occur. Is this a suggestion of more than four dimensions to our world?  Perhaps the laws of physics are just temporary ... and might change tomorrow?  To me, these are the kind of teasers that keep science moving forward.  When, some years hence, we fully understand how this marvel works, we will have uncovered, in the process, other mysteries even more bizarre. And this really is what makes our animal species unique.  Instead of we humans sighing ... and lounging like a cat in the sunlight, we try to discover an even newer truth ... or disprove an old one. And I think we, in our hearts, understand that we never will understand the ultimate reality.  But that doesn't stop us from this eternal quest.

Momentum

Today's (7/24/2012) New York Times Science section (on the top of page D3) has an article dissecting why certain Pioneer spacecraft have been slowing down more than expected (about 300 miles per year).  After many years and research dollars Slava G. Turyshev has determined that asymmetric heat radiation (photons in the electromagnetic spectrum) from these space probes is the culprit.  Or to quote the article, "The idea that light, of which heat radiation is one form, can carry momentum and thus propulsive force is implicit in the the basic equations of electromagnetism.  A comet's tail, blown by sunlight is one example. [L]ight can be thought of as little particles ... called photons -- that carry energy and momentum."

Now photons, according to any physics book you might read, have no mass.  But the definition of momentum is "mass times velocity" (see: Wikipedia Entry).  Sooo, if photons have no mass, how can they have momentum?  And how are photons (light) bent by gravity as they pass by large stars?  And how can black holes have so much gravity that light (photons) cannot escape?

Somehow, physicists are allowed to have it both ways (kinda like many politicians) ... but I, for one, am still perplexed.

Cosmic Silence

One of my favorite columnists, Charles Krauthammer, has written a thoughtful lament concerning the apparent lack of other sapient civilizations in the universe (see: National Review Article) or at least, if there are such extraterrestials (E.T.s), why we don't hear from them?   Basically, he states that, as we continue to find exo-planets within the habitable zone of "nearby" stars but are yet to see or hear any evidence of any life thereon, this suggests that "advanced civilizations destroy themselves."

I have a slightly different take.  Yes, I do believe, like many renowned scientists, that the laws of probability suggest that there are perhaps many billions (maybe even trillions) of other stars with planets that could and should support life.  However, when one unwinds the spans of time and distances involved in our universe, to me it is not surprising that we have not heard sapient coded message from afar.

Let me explain my logic:

- The universe is approximately 13 billion years old and our earth is about 1/10 of that age ... all back-end loaded.  I would imagine that many of these other theorized exo-planets are either yet to be ... or have been burnt to a crisp when their suns became red giants. Let's estimate that this culling percentage is 50%.  So automatically these billions of stars with habitable exo-planets is cut in half.

- Now, sapient life on our earth has existed for perhaps only a million years ... or 1/13,000 of this earth's existence and scientific advancement sufficient to understand our time and place in the universe has existed for, at most, 100 years ... or 1/130,000,000 of this planets existence.  Let us (optimistically) imagine that this enlightenment age on earth will last for another 13,000 years.  This would result in a sapient window for our planet to be about 1/1,000,000 (one-millionth) of its total existence ... which fraction I suggest should then apply to other exo-planets.  Now these potential billions of habitable exo-planets with enlightened intelligent life is now reduced by 1/2,000,000 (1/2 x 1/1,000,000).

- As for distance spans, our universe is estimated to be 46 billion light years wide.  Now, no communication can travel faster than the speed of light, so assuming that sapient communications was or will be sent out from another exo-planet during our current and predicted future enlightenment age, it must originate within a bubble of 13,000 light years from Earth.  This reduces the number of habitable exo-planets from which we might ever receive a message by another factor of 3.5 million (13 thousand/46 billion).  Or such potential messages from habitable exo-planets with enlightened intelligent life are reduced by a factor of seven trillion (1/2,000,000 x 1/3,500,000)..  Now, assuming we want to get this message within the next 100 years, we then must multiply this fraction by 1/130 (100/13,000) ... resulting in a reduction of the number of eligible communicating exo-planets contacting us within the next 100 years by 910 trillion ... quite a bit larger than even the number of the estimated exo-planets.

-  So, my conclusion is that, even if my calculations are off by one or two orders of magnitude, it is very unlikely that there is an exo-planet from which we might receive an intelligent coded message sometime within the next hundred years.  That is assuming (and this is a huge assumption) that such an exo-planet has a power source large enough to radiate this coded message out over the vast distances of intergalactic space.  This required power source has been estimated to be as large as the energy coming from our sun.  Soooo ... I highly doubt that E.T. will be calling home anytime soon ... and that Charles Krauthammer should find solace in the assumption that our "civilization" could well last for at least another few thousand years without his doom-and-gloom conclusion being justified.