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#### 爱因斯坦的最大失误

Einstein's Biggest Blunder, Explained

《分钟物理》
In 1915, Albert Einstein published
1915年 阿尔伯特•爱因斯坦发表了
a very important equation

no, not that one,

the one he published didn’t just relate mass and energy

but mass, energy and gravity

this equation replaced the older “Newton’s law of Gravitation,”

which you may be familiar with

and it remains to this day our best description of how gravity works.

Just like how F=ma is a mathematical description

of how the acceleration of an object depends on the forces applied to it.

The Einstein Equation of general relativity relates

the motion of mass and energy (the “T” on the right)

to the curvature of spacetime (the “R’s” on the left).

And Einstein didn’t just pull this equation out of thin air.

it was the natural consequence

of a long and careful consideration of key principles of physics

combined with the advanced mathematics of curved surfaces

and of course , agreement with the experimental observations of the day.

The equation, however, is deceptively simple.

This one single line is in fact an incredibly fancy shorthand

for what’s actually a system

of ten second order partial differential equations

relating mass and energy to the curvature of spacetime

and the R’s themselves are also a shorthand

But the point is this:

after figuring out that these equations matched up with

Newton’s law of gravitation for weak gravitational fields

and after showing that the equations correctly predicted

a previously unexplained anomaly in the orbit of Mercury

Einstein tried to figure out what the equations had to say about the universe as a whole.

Of course, all the matter and energy in the universe is much too complicated

to put into the equations and have any hope of solving them,

but if you zoom out enough,

you can approximate the universe as

having a roughly constant density everywhere and in every direction.

And Einstein was able to solve the equations

for a very simplified universe with constant density everywhere

the ten complicated equations reduced to just two simple ones:

this one says the curvature of space in the universe is proportional to the density

so more stuff in the universe means more curvature of space

and this one says that the density has to be zero.

which would mean there can’t be anything in the universe…

Needless to say, this was a problem.

And it turns out that there are two solutions to the problem

the one Einstein took and the one he didn’t.

he knew (since he had dived deep into the math) that it was

possible to slightly change his original equations

you can just add on a very simple term

without violating any key principles of physics.

There wasn’t much other motivation for adding this term but it doesn’t change anything

about how well the equations match up with Newton’s law when gravity is weak,

or how well they predict the orbit of Mercury or whatever

so maybe it was ok?

And crucially for Einstein,

the new term changes the equation for the density of the universe:

instead of saying “density equals zero,”

it now says “density is proportional to the new term”.

So if the new term was non-zero,

that meant the universe could have stuff in it!

Voila – solution number one

The other solution to how the universe can have stuff in it was this:

don’t assume (as Einstein had) that the universe is static and unchanging.

The general understanding at the time was that the universe didn’t expand or contract

and Einstein had also made a small but unfortunate technical error in his calculations

which appeared to prohibit the possibility of a changing universe

so it’s not surprising that Einstein didn’t see this solution.

But it was there: if you don’t make the mathematical assumption that the universe is static

and you don’t make the technical error Einstein did,

you can find a different valid solution to Einstein’s equations

which physicist Alexander Friedmann did.

Actually he used the version of the equations with the new term

knowing he could always set that term to zero if it wasn’t real.

But the key part is he didn’t assume the universe was static.

Friedmann found that the ten equations again reduced to two:

the first equation now describes

how the change in density of the universe

relates to its change in size:

specifically, it says that if the universe gets bigger, then it gets less dense

which makes sense – stuff’s literally spreading out.

The second equation says that the deceleration of the universe is

proportional to its density minus Einstein’s constant

in other words, the stuff in the universe attracts itself gravitationally

so the universe would have a tendency to pull inwards on itself

slowing any expansion and possibly even contracting.

Unless Einstein’s constant were real and had a value big enough

to balance or overpower the gravitational attraction

So that’s the solution Einstein didn’t see.

Later, once astronomers took sufficiently detailed measurements

it turned out that the universe was indeed expanding:

So Einstein’s equations didn’t appear to have any need for the extra term he had added.

Einstein was reported by physicist George Gamow

to have called it “his biggest blunder”

and while there’s no known documentation

that he ever actually said or wrote those words specifically

there’s plenty of record of him expressing

disdain in other ways:

“远离宇宙项” “我一直很愧疚”
“I found it very ugly,”
“我觉得它很丑陋”
“such a constant appears…unjustified.”
“这个常数看起来…不合理”
And, during Einstein’s lifetime, that was certainly true

– the term did appear unjustified.

However, remember how Friedmann’s equations predicted

that the universe should be attracting itself gravitationally

and so the expansion should be slowing down,

unless Einstein’s constant is real?

Well, in 1998 , decades after Einstein’s death

that the universe’s rate of expansion isn’t constant,

and it isn’t slowing down – it’s getting faster.

And so in a great, ironic twist,

Einstein’s constant does ultimately have a role in describing the universe

though it turns out to be a very different universe from what he had imagined.

If you don’t want to make silly math mistakes like Einstein,

to sharpen and hone your math and science skills.

In fact, Brilliant has a whole interactive course on cosmology
Brilliant上有一套完整的宇宙学互动课程
and within it, a quiz specifically titled “The fate of the Universe”

that was tailor-made for giving you a deeper and longer lasting understanding

than you can possibly gain from simply watching a video

Brilliant also has fun daily challenges,
Brilliant 还有趣味日常挑战
which are bite-sized math and science-puzzles

– like this one about what happens to a thermometer

if you put it in space, and then rotate it.

Does it still read the same temperature? Or hotter or colder?

Brilliant is offering 20% off of a premium subscription
Brilliant会为前200名分钟物理的观众
to the first 200 MinutePhysics viewers to

go to brilliant.org/slash minutephysics

– that lets Brilliant know you came from here,

and gets you full access to all of Brilliant’s courses, puzzles, and daily challenges.

Again, that’s brilliant.org/minutephysics

so that you don’t mess up like Einstein.