- 4188 - TIME - tell the difference in General Relativity? With his theory of General Relativity in 1915, Albert Einstein revolutionized how we think about our universe. Rather than the cosmos simply providing the room for the planets and stars to orbit each other, space and time themselves were now dynamical entities in one ever-evolving expansion with matter and light.
--------------------- 4188 - TIME - tell the difference in General Relativity?
- Einstein's
equations described how stars, galaxies and all other matter curve or warp
space and time. The galaxies and the light rays then travel in this distorted
space-time according to the equation provided by the 18th-century Swiss
mathematician Leonhard Euler.
-
- With the help of
modern telescopes, we can watch this distortion and compare it to the that
scripted by the two giants of science, Einstein and Euler. But can we
differentiate a universe where Einstein's equations were violated from a
universe where Euler's equation were modified? In other words, if what we
observed with telescopes disagreed with what Einstein and Euler prescribed,
would we be able to tell which one of the two was wrong?
-
- You may wonder
why one would want to doubt Einstein or Euler in the first place. After all,
existing observations have beautifully confirmed the validity of their
theories. The reason to put those to the test comes from the fact that our
universe is filled with unknowns.
-
- In the 1930s, the
Swiss-American astrophysicist Fritz Zwicky observed that there was five times
more matter in the universe than we can detect with our telescopes. He called
this new matter "dark matter."
-
- Nearly 100 years
later, we still don't know what dark matter is. We have never detected a particle of dark
matter and we don't know how it moves. It is therefore legitimate to question
if it behaves as ordinary matter and obeys Euler's law. Could it be affected by
other forces and interactions, which would change the Euler equation?
-
- In 1998, two groups
of astrophysicists observed that the expansion of our universe is accelerating,
contrary to the deceleration expected because of the gravitational attraction
between galaxies.
-
- As of today, we
don't know what causes this strange behavior: is it due to the presence of yet
another "dark" substance that has repulsive gravity? Or is it due to
gravity itself, meaning Einstein's predictions of how it behaves over very
large distances would be wrong? Testing Einstein's and Euler's equations is therefore
the logical consequence of the mysteries we face.
-
- Checking if
Einstein's gravity works over the vast distances of the universe has become an
active field of research. Theoreticians propose new ideas for how gravity could
work differently, while astronomers use increasingly advanced facilities to
provide the data needed to test them.
-
- Researchers have
identified a particular "smoking gun" signature of modified gravity
known as the "gravitational slip." General Relativity predicts that
the pathways of light and matter should bend in the same way when traveling
through the same distorted space-time.
-
- This is much like
the fact that different objects fall at the same rate in Earth's gravity (if
the air resistance could be neglected),
something Galileo famously demonstrated from the tower of Pisa. By
comparing the way galaxies fall into gravitational wells to how the light from
these galaxies is deflected by gravitational lensing, one can deduce if they
feel the same gravity.
-
- If we find them to
be different, we would say there was a gravitational slip. Measuring the slip
is one of the main targets of “Euclid”, a wide-angle space telescope launched
by the European Space Agency on a Space-X rocket.
-
- But what if Euclid
found that there was a slip? Could we be certain that it occurs due to a
modification of gravity, or could it also be due to a modification of Euler's
equation? The latter would be different if, for example, the dark matter in the
galaxies were subject to a new force.
-
- Approach this
question from different perspectives one involved developing tests of modified
gravity, while the other investigated the subtle corrections General Relativity
adds to what we measure with galaxy surveys.
-
- Our astronomer's
conclusion despite the common expectation, measuring the gravitational slip
would not allow one to distinguish a modification of Einstein's laws from a
modification of Euler's equation.
-
- One of our key
realizations was that to determine if the measured gravitational slip signals a
breakdown of General Relativity, we would need to measure the velocity of
normal matter when it is not confined to a galaxy. In practice, however, we can
only observe the light from stars that reside in galaxies, and hence move together
with the dark matter.
-
- Telescopes can only
measure the collective motion of a galaxy that contains both normal matter and
dark matter. So, if a galaxy were to fall into a gravitational potential in a
way that was not consistent with our expectations, we would be unable to tell
if it's because the dark matter is doing something, or because gravity was
modified.
-
- There is a new way
to probe the gravitational potential directly through the way it distorts time
via gravitational redshift.
-
- The time kept by a
clock that's on top of a tall mountain is different from that of a clock at the
sea level. These differences are extremely tiny but are, in fact, very
important in the design of satellite navigation systems and cell phone maps.
-
- When the light from
a galaxy escapes the gravitational potential it is falling into, its color
shifts closer to red. This gravitational redshift is solely due to time
distortion. Gravitational lensing, which differs from redshift, is due to both
space and time distortions, as opposed to just time.
-
- We need to have
both “lensing” and “redshift” in order to isolate the “gravitational slip”. It
is this ability to separate the distortion of space and time from the
distortion of time alone that is key to measuring true gravitational slip.
-
- A measurement of
the gravitational redshift is impossible if one cannot easily keep track if a
pair of galaxies swapped their positions. While it's not that hard to tell any
two galaxies measured by a telescope apart, when running a statistical analysis
on a catalog of millions of galaxies, you can quickly lose the ability to
assign any identity to the galaxies; at some point they are all treated as
“points” on the sky.
-
- Techniques have
been developed to split galaxies into different populations and keep track of
swaps between them. In time, new technologies will be able to detect the tiny
effects of gravitational redshift, and consequently distinguish a modification
of Euler's equation for dark matter from a modification of gravity.
-
- Only time will
tell?
-
-
October 14, 2023 TIME
- tell the difference in General
Relativity? 4188
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Sunday, October 15, 2023 ---------------------------------
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