quantum gravity

The strange beauty of Planck units

by
Supercharging' Atoms with X-ray Laser

What does it mean to say that the speed of light is 1?

We know the speed of light in the vacuum of space to be 299,792,458 m/s – or about 300,000 km/s. It’s a quantity of speed that’s very hard to visualise with the human brain. In fact, it’s so fast as to practically be instantaneous for the human experience. In some contexts it might be reassuring to remember the 300,000 km/s figure, such as when you’re a theoretical physicist working on quantum physics problems and you need to remember that reality is often (but not always) local, meaning that when a force appears to to transmit its effects on its surroundings really rapidly, the transmission is still limited by the speed of light. (‘Not always’ because quantum entanglement appears to break this rule.)

Another way to understand the speed of light is as an expression of proportionality. If another entity, which we’ll call X, can move at best at 150,000 km/s in the vacuum of space, we can say the speed of light is 2x the speed of X in this medium. Let’s say that instead of km/s we adopt a unit of speed called kb/s, where b stands for bloop: 1 bloop = 79 km. So the speed of light in vacuum becomes 3,797 kb/s and the speed of X in vacuum becomes 1,898.5 kb/s. The proportionality between the two entities – the speeds of light and X in vacuum – you’ll notice is still 2x.

Let’s change things up a bit more, to expressing the speed of light as the nth power of 2. n = 18 comes closest for light and n = 17 for X. (The exact answer in each case would be log s/log 2, where s is the speed of each entity.) The constant of proportionality is not even close to 2 in this case. The reason is that we switched from linear units to logarithmic units.

This example shows how even our SI units – which allow us to make sense of how much a mile is relative to a kilometre and how much a solar year is in terms of seconds, and thus standardise our sense of various dimensions – aren’t universally standard. The SI units have been defined keeping the human experience of reality in mind – as opposed to, say, those of tardigrades or blue whales.

As it happens, when you’re a theoretical physicist, the human experience isn’t very helpful as you’re trying to understand the vast scales on which gravity operates and the infinitesimal realm of quantum phenomena. Instead, physicists set aside their physical experiences and turned to the universal physical constants: numbers whose values are constant in space and time, and which together control the physical properties of our universe.

By combining only four universal physical constants, the German physicist Max Planck found in 1899 that he could express certain values of length, mass, time and temperature in units related to the human experience. Put another way, these are the smallest distance, mass, duration and temperature values that we can express using the constants of our universe. These are:

  • G, the gravitational constant (roughly speaking, defines the strength of the gravitational force between two massive bodies)
  • c, the speed of light in vacuum
  • h, the Planck constant (the constant of proportionality between a photon’s energy and frequency)
  • kB, the Boltzmann constant (the constant of proportionality between the average kinetic energy of a group of particles and the temperature of the group)

Based on Planck’s idea and calculations, physicists have been able to determine the following:

Credit: Planck units/Wikipedia

(Note here that the Planck constant, h, has been replaced with the reduced Planck constant ħ, which is h divided by 2π.)

When the speed of light is expressed in these Planck units, it comes out to a value of 1 (i.e. 1 times 1.616255×10−35 m per 5.391247×10−44 s). The same goes for the values of the gravitational constant, the Boltzmann constant and the reduced Planck constant.

Remember that units are expressions of proportionality. Because the Planck units are all expressed in terms of universal physical constants, they give us a better sense of what is and isn’t proportionate. To borrow Frank Wilczek’s example, we know that the binding energy due to gravity contributes only ~0.000000000000000000000000000000000000003% of a proton’s mass; the rest comes from its constituent particles and their energy fields. Why this enormous disparity? We don’t know. More importantly, which entity has the onus of providing an explanation for why it’s so out of proportion: gravity or the proton’s mass?

The answer is in the Planck units, in which the value of the gravitational constant G is the desired 1, whereas the proton’s mass is the one out of proportion – a ridiculously small 10-19 (approx.). So the onus is on the proton to explain why it’s so light, rather than on gravity to explain why it acts so feebly on the proton.

More broadly, the Planck units define our universe’s “truly fundamental” units. All other units – of length, mass, time, temperature, etc. – ought to be expressible in terms of the Planck units. If they can’t be, physicists will take that as a sign that their calculations are incomplete, wrong or that there’s a part of physics that they haven’t discovered yet. The use of Planck units can reveal such sources of tension.

For example, since our current theories of physics are founded on the universal physical constants, the theories can’t describe reality beyond the scale described by the Planck units. This is why we don’t really know what happened in the first 10-43 seconds after the Big Bang (and for that matter any events that happen for a duration shorter than this), how matter behaves beyond the Planck temperature or what gravity feels like at distances shorter than 10-35 m.

In fact, just like how gravity dominates the human experience of reality while quantum physics dominates the microscopic experience, physicists expect that theories of quantum gravity (like string theory) will dominate the experience of reality at the Planck length. What will this reality look like? We don’t know, but we know that it’s a good question.

Other helpful sources:

Jayant Narlikar’s pseudo-defence of Darwin

by

Jayant Narlikar, the noted astrophysicist and emeritus professor at the Inter-University Centre for Astronomy and Astrophysics, Pune, recently wrote an op-ed in The Hindu titled ‘Science should have the last word’. There’s probably a tinge of sanctimoniousness there, echoing the belief many scientists I’ve met have that science will answer everything, often blithely oblivious to politics and culture. But I’m sure Narlikar is not one of them.

Nonetheless, the piece IMO was good and not great because what Narlikar has written has been written in the recent past by many others, with different words. It was good because the piece’s author was Narlikar. His position on the subject is now in the public domain where it needs to be if only so others can now bank on his authority to stand up for science themselves.

Speaking of authority: there is a gaffe in the piece that its fans – and The Hindu‘s op-ed desk – appear to have glazed over. If they didn’t, it’s possible that Narlikar asked for his piece to be published without edits, and which could have either been further proof of sanctimoniousness or, of course, distrust of journalists. He writes:

Recently, there was a claim made in India that the Darwinian theory of evolution is incorrect and should not be taught in schools. In the field of science, the sole criterion for the survival of a theory is that it must explain all observed phenomena in its domain. For the present, Darwin’s theory is the best such theory but it is not perfect and leaves many questions unanswered. This is because the origin of life on earth is still unexplained by science. However, till there is a breakthrough on this, or some alternative idea gets scientific support, the Darwinian theory is the only one that should continue to be taught in schools.

@avinashtn, @thattai and @rsidd120 got the problems with this excerpt, particularly the part in bold, just right in a short Twitter exchange, beginning with this tweet (please click-through to Twitter to see all the replies):

https://twitter.com/avinashtn/status/964883532144304128

Gist: the origin of life is different from the evolution of life.

But even if they were the same, as Narlikar conveniently assumes in his piece, something else should have stopped him. That something else is also what is specifically interesting for me. Sample what Narlikar said next and then the final line from the excerpt above:

For the present, Darwin’s theory is the best such theory but it is not perfect and leaves many questions unanswered. … However, till there is a breakthrough on this, or some alternative idea gets scientific support, the Darwinian theory is the only one that should continue to be taught in schools.

Darwin’s theory of evolution got many things right, continues to, so there is a sizeable chunk in the domain of evolutionary biology where it remains both applicable and necessary. However, it is confusing that Narlikar believes that, should some explanations for some phenomena thus far not understood arise, Darwin’s theories as a whole could become obsolete. But why? It is futile to expect a scientific theory to be able to account for “all observed phenomena in its domain”. Such a thing is virtually impossible given the levels of specialisation scientists have been able to achieve in various fields. For example, an evolutionary biologist might know how migratory birds evolved but still not be able to explain how some birds are thought to use quantum entanglement with Earth’s magnetic field to navigate.

The example Mukund Thattai provides is fitting. The Navier-Stokes equations are used to describe fluid dynamics. However, scientists have been studying fluids in a variety of contexts, from two-dimensional vortices in liquid helium to gas outflow around active galactic nuclei. It is only in some of these contexts that the Navier-Stokes equations are applicable; that they are not entirely useful in others doesn’t render the equations themselves useless.

Additionally, this is where Narlikar’s choice of words in his op-ed becomes more curious. He must be aware that his own branch of study, quantum cosmology, has thin but unmistakable roots in a principle conceived in the 1910s by Niels Bohr, with many implications for what he says about Darwin’s theories.

Within the boundaries of physics, the principle of correspondence states that at larger scales, the predictions of quantum mechanics must agree with those of classical mechanics. It is an elegant idea because it acknowledges the validity of classical, a.k.a. Newtonian, mechanics when applied at a scale where the effects of gravity begin to dominate the effects of subatomic forces. In its statement, the principle does not say that classical mechanics is useless because it can’t explain quantum phenomena. Instead, it says that (1) the two mechanics each have their respective domain of applicability and (2) the newer one must be resemble the older one when applied to the scale at which the older one is relevant.

Of course, while scientists have been able to satisfy the principle of correspondence in some areas of physics, an overarching understanding of gravity as a quantum phenomenon has remained elusive. If such a theory of ‘quantum gravity’ were to exist, its complicated equations would have to be able to resemble Newton’s equations and the laws of motion at larger scales.

But exploring the quantum nature of spacetime is extraordinarily difficult. It requires scientists to probe really small distances and really high energies. While lab equipment has been setup to meet this goal partway, it has been clear for some time that it might be easier to learn from powerful cosmic objects like blackholes.

And Narlikar has done just that, among other things, in his career as a theoretical astrophysicist.

I don’t imagine he would say that classical mechanics is useless because it can’t explain the quantum, or that quantum mechanics is useless because it can’t be used to make sense of the classical. More importantly, should a theory of quantum gravity come to be, should we discard the use of classical mechanics all-together? No.

In the same vein: should we continue to teach Darwin’s theories for lack of a better option or because it is scientific, useful and, through the fossil record, demonstrable? And if, in the future, an overarching theory of evolution comes along with the capacity to subsume Darwin’s, his ideas will still be valid in their respective jurisdictions.

As Thattai says, “Expertise in one part of science does not automatically confer authority in other areas.” Doesn’t this sound familiar?

Featured image credit: sipa/pixabay.