Monthly Archives: April 2016

Why America needs a Trump candidacy

Most of my coworkers are Latinos – most of those are El Salvadoran.  So when we went out for lunch one day, it was only a matter of time before they found out I was leaning towards Trump.

Needless to say, it got awkward at first.  First came the comments about his disparaging attacks on Latinos.  Then his comments about Muslims.  But after I wasn’t knuckling other to either one, since I honestly think both charges are bullshit, the silence led one of them to make an illuminating comment:

“Of course we need to have laws.”

We need to have laws.  Indeed.  That’s the crux of the Trump candidacy, and it’s the crux of the European electoral tumult.

I’ve been in politics a long time – since my naive days of Jerry Brown’s 1992 presidential campaign.  I can say that the primaries are a brainstorming session for both parties – they let any comers shoot off any strange and unformed ideas they have, and see what sticks with the voters.  It’s only towards the end of the primaries, heading into the convention, that they decide it’s time to close down the session and rally around a candidate they feel represents them.

Only sometimes it doesn’t quite work as planned.  Like this year.  This year has been a real popular backlash against ruling class policy – that of abolishing all immigration law, and allowing anybody on earth to move anywhere they want.   We may have our “illegal immigrant” problem here at home (I’ll get to that in a bit).  But it’s nothing compared to the brilliant EU loophole of allowing “refugee” status to people in any one country and then letting them in through that back door into any other country in Europe.

As Douglas Murray puts it “‘imagine there’s no countries’?  We don’t have to imagine it, we’re seeing the real consequences of getting rid of borders, and that’s people blowing themselves up in the heart of Paris.”

It’s no stretch to say this is deliberate policy.  And part of that policy is to smear anyone who criticises the scrapping of immigration law and borders as a bigot.  This is happening both in European and American governments, both Democrat and Republican parties.

And that’s why when Trump comes in and says things like “build that wall” or “seal the borders” it’s a signal that he supports something THEY CANNOT ALLOW TO HAPPEN.

The remarks themselves aren’t even worth scrutinizing that much.  In a brainstorming session, one wants provocative remarks like this, because they spur thought, reaction, debate.  Nevermind if they’re unworkable or offensive, we have plenty of time to take those comments, see the direction they’re going in, and hammer them out into workable policy.

Like the “ban all Muslims” remark.  Nevermind that they twisted what he said.  Nevermind that there’s no way to ban based on religion.  But there are bans based on country of origin.  It’s not that hard to go from one to the other, and we did it to Iran after their hijackings.

But back to the American issue of immigration.  If I make one point, it’s this.  It’s okay to demand immigration be made legal.  It’s okay to make sure those immigrating here legally can do so more easily than those who don’t.  It’s okay to demand that those who pose a terrorism risk aren’t allowed in.  The more voters who make these demands are made to feel like bigots, the more they will rally and solidify behind a man like Trump.

It’s in everyone’s interests that everyone in this country is here legally.  The fact is, someone who is here working illegally is someone who is working with no rights.  Are there issues with this?  Of course.  That’s a whole separate article.

But nobody’s saying “kick out all the Mexicans” or “Mexicans are criminals”.  Those are just slanders.  Trump’s main remark, time and again, is that we can’t just ignore our own laws and let people pour over without any record.

That’s a great starting point.  If we’re short on workers, nobody has a problem with liberalizing immigration law.  As my coworkers told me, and I suspected, poor Latin Americans can’t immigrate legally to USA.  Only the rich can.  Well, that’s a problem.  And we can change that.  With laws.  Not by ignoring laws and ridiculing those that have a problem with it.

It’s no secret that America’s a nation of immigrants.  My coworkers relay to me their parents’ stories of escaping violence and poverty to seek a better life in America, and honestly, it doesn’t sound too different from anybody else’s story.  That’s why nobody’s doing themselves any favors by claiming the Trump campaign anti-immigrant.  Because those who’ve been paying attention to Trump’s remarks realize it’s a “pro-law” campaign.

Because America is a nation of immigrants, but it’s also a nation of laws.  And one doesn’t trump the other.

You can travel faster than light speed

“And I think it’s gonna be a long, long time
‘Til touchdown brings me ’round again to find
I’m not the man they think I am at home” – Rocket Man by Elton John

A misconception exists in Einstein’s famous equations – that there’s some absolute speed limit where we couldn’t possibly travel to the stars any faster than light speed.  It’s actually false. Well, to everyone we knew out on Earth, they’ll be long gone by the time we come back to regale them with our tales.  But to us and our crew on the SS Enterprise, well we could explore half the galaxy in one lifetime, with the right warp drive (which is entirely another issue).

First, the Twins Paradox – and the hidden paradox within.  The focus of the twins paradox is how one twin flying to a distant star and back will barely age, while their counterpart back here on Earth has aged several decades.

Okay, do you see what I’m talking about yet?  Here’s another hint.  Do you think they were hanging out on their spaceship all those years enjoying some fountain of youth?  No – they literally took that amount of time to travel back and forth.  While years and years passed on Earth, only a few days or months passed on the spaceship.

And that, to me, is the far more interesting paradox.  Let’s take our favorite star, Alpha Centauri, hanging out four light years away.  I’ll leave my brother off at home, and take off on my high speed rocket at near the speed of light, so it takes nine earth years to go there and back.  But my brother and I, being rather perceptive people, don’t just notice that he aged and I didn’t.  When we compare clocks, literally only a year passed for me, while nine years passed for my brother.

Wait.  How can that happen?  How could I have travelled to Alpha Centauri and back, something light would do in nine years, in only a year?  Did I mysteriously break the speed of light?  And if so, how did I do that?

Well, yes and no.  What the absolute speed of light says is that no object can reach the speed of light relative to another object.  That’s why it appears to my brother to take me this long.

But what happens to me?  The answer is another twin – time dilation’s lesser known twin, space dilation.  As my ship accelerates past Earth into sublight speed, it’s not just time that shrinks to nothing, space also shrinks to nothing.  The distance I have to travel to get to Alpha Centauri now shrinks from four light years to only half a light year.


The Lorentz transformation – how spacetime dilates with relative velocity.

And yes, the shrinkage is exactly the same.  It’s called the Lorentz transformation and is why Einstein called it spacetime and not just time or space.  Both time and space dilate equally according to gamma.  This is what allows a photon (ray of light) to appear to travel the same speed relative to everyone looking at it.

Here’s another fun way of looking at it.  As we said above, accelerating a spaceship to that speed is well out of our technology, and that’s the real issue of space travel.  But we regularly accelerate particles to quite near light speed in our accelerators.  So let’s pretend this particle is a spaceship and see how long it would take for it to get to, say, the center of our galaxy (25k light years away).

Fortunately my favorite website has a great example – just as it throws up its hands in at the implication that we’re permanently Earthbound.

Difficulty of acceleration

The fun part is, right below it they talk about the problems with variable mass – implying problems in general.

Saves just a second for you landlubbing Earth dwellers, maybe.  But let’s see how the world looks from the perspective of that electron.  By the Lorentz transformation, space and time dilate by a factor of about 60 for the first electron, and about 11,000 for the second one.  A good way to understand gamma is you’re going gamma times the distance in one gammath (1/gamma) the time.

Essentially, that first electron is going 60 times the distance in 1/60th the time.  So spacetime has dilated to 3600 times what it was used to back at rest – particle 1 is going 3600 times the speed of light of its old frame of reference.  Particle 2?  It’s going 121 MILLION times the speed of light of its old frame of reference.

Translation?  Particle 1 could get to the center of the Milky Way galaxy in about seven years.  Particle 2 could get there in a little under two weeks.

Of course we’ll never see the news of either of these guys travels.  We would have to wait here at rest for 50,000 years for them to return.  Entire civilizations, entire species will have come and gone by then.  But that’s not for rocketmen to ponder.

When you think about it, fiction portrays it rather accurately. The stars imploding on the ship are a good portrayal of how space would dilate.

When you think about it, fiction portrays it rather accurately. The stars imploding on the ship are a good portrayal of how space would dilate.


The event horizon – a cosmic mirage

Black holes – or more specifically, their event horizon – are a cosmic mirage.  Not much different from a rainbow.  Oh, they’re real alright, I’m not talking about leprechauns with the pot of gold at the end, but the way we experience them is totally different from the thing itself.  There is no such thing as “falling though the event horizon” because the “event horizon” is precisely only our experience of it.

Contradictions in last episode

The interesting thing about scientific inquiry is you’re never satisfied with your answers.  Answers always lead to contradictions, things that don’t make sense, new questions.  I had answered how something can accelerate to light speed in a black hole’s pull.  But what if it doesn’t?  What if some daring astronomer constantly decelerates himself as he comes closer and closer to the event horizon, constantly making sure he’s both aiming for dead center, and making a nice slow descent?

Now you could counter by saying that if you didn’t let yourself freefall, the G forces would tear you to shreds.  But here comes the complicating factor.  Supermassive black holes exist which have relatively weak gravitational force at the event horizon.  A black hole with a radius of about one light year, for example, would have a gravitation at its event horizon equivalent to here on Earth’s surface (aka 1G).

Not so coincidentally, if you were to accelerate for about a year at 1G, you would reach what I call nominal light speed – which is your actual speed if you accelerated to light speed in a simplified Newtonian universe  That just happens to be 0.618c (0.618 the speed of light) – which is exactly the proportion of the golden rectangle (?) – but we’ll save this tidbit for later.  The question right now is how is such weak gravity at an event horizon even possible?  Aren’t black holes supposed to spaghettify us and tear us into subatomic shreds and stuff?

What’s an event horizon doing with such, well, EARTHLY gravity?

Wait, what?

Yes, that’s right.  radius accelSupermassive black holes have very low gravity at their event horizon.  It’s a simple formula, really.  The radius of the event horizon is the inverse of its acceleration – i.e. gravity.  r*a is the same for each and every black hole.

I could do some extra wizardry to show you the math, but you have the internet for that.  Small black holes pull really hard on that photon to whip it in a circle.  Large black holes can take their sweet time.  And here’s the fun part – if you were to free-fall into a black hole radius accel integral– ANY black hole – from somewhere outside its influence, you’d accelerate to the speed of light.  Ve = velocity at event horizon = c (speed of light).

But the twisted logic that happens at that event horizon remains the same.

A lesson on geodesics

Well, how do we wrap our minds around that?

black hole geometry

The non-euclidean geometry (geodesics) of a black hole, as discussed in our previous post

For that we have to delve into the world of geodesics.  And first in that, a beef.  I don’t like the term “geodesics.” It conjures up hippy domes in the middle of the desert.  I prefer the term “non-Euclidean geometry”.  It easily tells us we’ve left the familiar world of ancient geometers with their simple circles and triangles on a flat surface, and are falling down the rabbit-hole (so to speak) of curved spaces and planes.

And that’s what we need to know to understand a blackhole.  It’s how we can picture Einstein’s theory of relativity.  If you’ll recall from my last post, this 3D well describes the spacetime around a black hole – how it curves down into an infinite well.

There’s a few things going on in that diagram, so we’ll try to take it a bit at a time.

The thing to remember about this well is, it’s not like gravity is pulling everything down it.  It mainly describes how light, a massless particle that always travels in a perfectly straight line, can still seem to bend.

Now there’s difference in the specifics of how light and massive entities  fall towards a gravitational center.  But what’s the same is the acceleration.  Here on Earth, we are constantly accelerating towards it at 9.8m/s2.  And light is no different.

Even though it travels in a straight line.

And that’s my second beef with “geodesics”  – the definition of a straight line as the closest distance between two “local” (i.e. “close”) points.  That’s a bit of a copout, like saying “well we’re reducing this to a map”.  I prefer the term “no sideways pull”.

plane aileron

The (air)plane rotates, twisting the (geometric)plane it’s on, and then lifts into a turn. Get it?

But let’s go back to our analogy of the plane from last chapter.  There’s rudderless planes out there.  By just rotating the plane with ailerons, and using the elevators in back, you can turn every which way without ever having sideways pull.  Just rotate the plane, and go up or down.

So if you look at what makes the plane “turn without turning”, the factor here is “which way is up”.  As it rotates, it changes that “upwards” direction, and then goes up or down in that upwards direction.

And BTW, this works equally for spaceships in zero gravity.  So gravity has nothing to do with which way is up.  In more complicated math, it’s called “orthogonal” which is defined as the perpendicular to the plane.  This allows us to pile on more dimensions.

But we’re here to discuss black holes, not study math.  So let’s translate this “upness” into black holes.  earth v supermassiveCompare Earth’s gravitation of a beam of light – a1 – and compare it with a REALLY massive black hole, whose acceleration near the event horizon is less than at Earth’s surface.

As a light beam approaches earth, it enters Earth’s gravity, changing its “upness” and starts to “curve” around Earth.  What causes the curve is the “upness changing”.

Now, compare that to a supermassive black hole.  By the time you’re near the event horizon (as seen by this incredibly drawn cut-out) you’re practically vertical.  But there’s not much “upness” left to change.  You’re just being whipped around in what seems like a flat surface, in a very large cylinder, “upness” pointing directly into the middle.

Any way you look at it, it’s the speed of light

The problem though, with such small scale cutouts, is they conveniently leave out just how far we’ve come to get to this “vertical space” in the supermassive black hole.  As I hinted earlier, before we get to this spot in a supermassive black hole, we’d have been freefalling literally for years and years.

But what if we decided not to freefall?  What if we got some theoretical rocket thrusters and slowed down our descent, so we avoided being anywhere near the speed of light at the event horizon?

Einstein’s Theory of Gravitation

The answer is it doesn’t matter.  Because how would you do that?  You would manually accelerate yourself in this gravitational field.  If you did the same manual acceleration outside a gravitational field (i.e. deep space), you would go from 0 to light speed.  So no matter what your behavior is around the event horizon – hovering, freefalling, or some combination of the two (i.e. orbiting) – you’d be at near light speed.

This is what Einstein is talking about, that we experience a spacetime dilation in a gravitational field, even if we’re hovering/standing/using rocket thrusters.  The spacetime dilation is basically equal to the sum of acceleration from deep space to whatever surface you’re at.

Back to where we started

Which takes us back to the incredible shrinking black hole, except this time we take it a step further.  In the last post, we talked about the fact that a black hole shrinks away from any object approaching it.  But just how?  We don’t want to just WATCH something fall into a black hole, we want to KNOW what it’s like.  We want to BE whatever it is that falls in.

Well, considering we nixed any realistic possibility of crossing the event horizon with strange tricks, let’s pretend  we’re freefalling directly to a black hole’s heart.  And orbits are boring.  We want to go straight in.  So we have this craft that doesn’t try to resist gravity, and doesn’t let us slip to the right or left.  And we’ll start well outside a nice supermassive black hole, about 1 light year diameter.

The best way to picture this is pretend we’re falling in a Newtonian universe, and at periodic intervals, we’ll recalibrate to allow for how spacetime changed around us.  Don’t worry, if someone gives us flak for this, just tell them delta apporoaches zero.  If it doesn’t shut them up, send them my way.

If you were to freefall to what you think is the event horizon, you’d hit what you’d think was light speed in a Newtonian universe – i.e. “nominal light speed”, or to put it another way, Newtonian velocity = momentum divided by mass = light speed (v=p/m=c).  So let’s take our new bearings.

Distance to center is still r.

Actual relativistic speed is now ?c (~.618c).

At ?c, distances shrink to ??.  So the radius of the new black hole is r*??.

Time also dilates to ?(1+?) for those outside of you, but we don’t care about them, so that’s kind of irrelevant.

Recalibrate your instruments for your new reality, and freefall AGAIN to “nominal light speed” – the speed you’d reach at the new event horizon at r*??.

Distance to center is now r*??.

Except now you’re at ?c compared to where you were before, or basically, your momentum doubled from your starting point.  You’re at  ?c compared to your last point.  Or, to put It another way, Newtonian velocity is twice the speed of light (p/m=2c).

New event horizon is now r*?.

freefall graph

While “light speed” is maximum, momentum is infinite. Here’s how momentum compares to the relative size of an event horizon. You would even out where the event horizon was ?? times the distance from the singularity as you are.

And so on, in the grand progression of the golden rectangle.  The ultimate equation is that y=r*a/ ?0.5(x-1) . Where y is your Newtonian velocity (momentum/mass) and x is the radius of the black hole.

Here, you know what?  Let’s draw a graph.

Notice there’s no time here.  Acceleration is whatever it is to get you to the light speed you’d reach at event horizon.

How far down do you want to go?  How much can your imaginary ship take?  How infinitely fast do you want to go?  How far do you want to escape those boring confines of flat spacetime and see the universe from the perspective of the infinite?

That is what it’s like to fall down that well.