randombio.com | science notes Thursday, November 2, 2017 ## Why is the speed of light not infinity?Wonky Minkowski diagrams, Rindler frames, and quantum foam, oh myyyy . . . |

n the latest triumph for Einstein's theory of relativity, astronomers had a collective spacegasm last month when they detected gravitational waves from 130 million light years away, close enough to visually identify the source: a kilonova collision of two neutron stars.

As many people noticed, this event, called GW170817^{[1]}, is the strongest
evidence yet that gravity travels at the speed of light *c*. A gamma ray burst
was detected within 1.7 seconds of the GW pulse^{[2]} showing
that gravity and light travel at almost exactly the same speed: at a distance of
40±8 MPc
it means they're the same within 5 parts in 10^{16}, or one part in 2 quadrillion.

Gravitational waves are transverse waves produced by accelerating matter. The effect they have on matter is to alternately compress it in one direction and then the other. This is called a quadrupolar wave, and it is why the LIGO detectors have an L shape.

You can't talk about this without mentioning Einstein. Einstein postulated that the laws of nature, including the speed of light, must be the same for every observer. From this, we are forced to conclude that length, distance, time, space, and mass are no longer constant.

By putting the laws of physics first, Einstein revolutionized our view of the universe,
and empirical evidence showed he was right. Other physicists of his day, notably
Hendrik Lorentz^{[3]}, modified Newton's equations to account for the same results that
motivated Einstein (such as the
Michelson-Morley
result), but as Wolfgang Rindler points out in his book *Relativity: Special, General,
and Cosmological*, these theories were sterile: they might have saved Newtonian
mechanics, but they produced no new physics.

Einstein's theory succeeded because he took his axioms at face value—absolutes, as it were—and followed them to their logical conclusion. So in a sense, the Theory of Relativity really should be called the Theory of Absolutivity.

Space and time are different manifestations of the same thing: spacetime. We still don't fully understand this. Perhaps the biggest mystery is this, as Bernard Schutz put it:

Although ‘time’ and ‘space’ can in some sense be transformed into each other in SR, it is important to realize that we can still talk about ‘future’ and ‘past’ in an invariant manner.

^{[4]}

The question is: why? Also, what? and how? How do we reconcile the fact that the speed of light is the same for all observers with the fact that gravity can propagate through it? Is there a fixed medium or not?

It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed. — Robert B. Laughlin

It's tempting to say it's exactly what you'd expect if the universe were a simulation. If I were programming a simulation of a universe, I might cut corners this way. But it's also possible that relativity is telling us something important about the relationship between observers (or maybe even ‘consciousness’) and time.

A Bing search on this question leads to many explanations: it's because mass increases, or because an infinite amount of energy would be needed to exceed c, or because it would violate causality, or because light would not propagate. These are all true, but they're just re-statements of the question.

Explaining it in terms of causality, for instance, simply means that cause and effect can't occur faster than c. It doesn't explain why.

**Fig. 1** above shows Minkowski's famous diagram of spacetime. It shows how distance
changes depending on your reference frame. Instead of circles, the equidistant lines
of distance 1, 2, etc. become hyperbolas. The dotted lines at 45° show the light
cone of the event at the center, which is to say the direction light would travel.
As the arrows approach 45°, they become longer, which means that travelers at
the speed of light would think they were covering a vast distance
in space in almost no time. (Those *fools*.)

Some people (for example, Schutz) interpret the slope of the arrows to
be the inverse of speed, so any slope less than 45° (into the gray area) is
impossible. Other authors, like Rindler, use a different notation: movement into
the *blue* area is impossible, and real-world particles can only move into the gray
areas. This is what's called a Rindler Frame.

Einstein's theory says that space and time are interconverted in such a way as to keep the distance covered by light in a given period the same. At the speed of light, space and time appear the same. So, if you ask “what is time” you're also asking “what is space.”

As your speed approaches c, the time and space axes measured by a stationary
observer rotate as shown in **Fig. 2**. The t′ and x′ axes remain
symmetrical around the 45° line. They still appear perpendicular to the person
who is moving, but not to someone standing still.

Relativistic effects like length contraction can pose a challenge for quantum gravity. Not even Einstein believed that space is just nothingness. It must be a physical thing in order for light to propagate through it. In loop quantum gravity, space is a quantized physical thing, called a “spin network.” Some physicists theorize that Lorentz contraction, which is the principle that space must contract to keep c constant, must be broken in some way at very small distances.

The concepts in relativity are powerful and can be applied to other phenomena as well. For example, they can help us explain why a charged particle can move in an electric field. But the equations are still only models. Unlike some who make extravagant claims for mathematics being the basis of reality, Rindler is refreshingly honest:

The present result illustrates well the ‘man-made’ character of physical theories. It is really remarkable how the same empirically known orbits can be ‘explained’ by two such utterly different models as Newton's universal gravitation and Einstein's curved spacetime. Nature exhibits neither potentials nor Lorentzian metrics. Yet both these human inventions lend themselves to a description of a large class of observed phenomena.

^{[5]}

So in answer to the original question: the equations and the evidence say so, but nobody really knows why.

1. Abbott BP *et al.* (2017). GW170817: Observation of Gravitational Waves from
a Binary Neutron Star Inspiral.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.161101
The gamma ray burst is called GRB170817A. It originated from a star in NGC 4993,
a galaxy in Hydra; R.A.=13h09m48.1s, Dec.=−23d22m53s

2. Díaz MC *et al.* (2017). Observations of the first electromagnetic counterpart
to a gravitational wave source by the TOROS collaboration. Astrophys J Lett.
arxiv:1710.05844v1.pdf

3. This is the Lorentz Ether Theory, published in 1904, one year before Einstein's famous 1905 paper describing SR.

4. Schutz B (2009). * A First Course in General Relativity, 2nd ed. *, p.14. An
easy to follow but still rigorous textbook with clear explanations. It's highly
recommended; one of the few books on the subject that doesn't warp the space-time
continuum.

5. Rindler W (2006). *Relativity: Special, General, and Cosmological, 2nd ed. *,
p. 190. This is an outstanding book on relativity. It not only explains the equations,
but also their implications, and what evidence supports them.

*nov 02, 2017, 5:55 am; edited nov 03, 2017, 6:39 am*

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