In 1915, Albert Einstein published
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.
就像F = ma一样
The Einstein Equation of general relativity relates
the motion of mass and energy (the “T” on the right)
将质量 能量的运动（右侧的“ T”）
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.
Einstein’s solution was this:
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
具体来说 如果宇宙变大 密度就会减小
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
换言之 宇宙中的物质因万有引力 而自我吸引
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:
“away with the cosmological term” ,“I always had a bad conscience”
“I found it very ugly,”
“such a constant appears…unjustified.”
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
astronomers made the surprising discovery
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.
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最后 有了Brilliant/ Minutephysics
so that you don’t mess up like Einstein.