Something I learnt from reddit today.

——————————-

When you point your flashlight at the wall and turn it on, it seems the light ray reaches the wall instantaneously, and so “speed of light for everyone watching” = c = ∞. Or equivalently c⁻¹ = 1/c = 1/∞ = 0.

But careful observation of Nature shows us that in fact: c⁻¹ ≠ 0, c⁻¹ = 1 (or something else if you prefer another unit system, but never 0). Speed of light is finite and the same for everyone watching. Surprising, yes, but it works for really fast things and that’s proven. No biggie.

When you cut a stick in half, then cut the half in half, then get a knife, cut the rest into something even smaller, sharpen the knife, and so on, it feels like you can do this for ever, and with infinite time “it makes sense to have something infinitely small to almost size zero” and we note this idea ħ = 0.

But careful observation of Nature shows us that in fact: ħ ≠ 0, ħ = 1 (or something else if you prefer another unit system, but never 0). It doesn’t make sense to have laws governing something infinitely small. Surprising, yes, but it works for really small things and that’s proven. No biggie.

When a needle falls to the ground, it is pulled down by the gravity from entire Earth (and that’s really really big). But you can pick it up with a tiny magnet. So gravity seems so ridiculously small compared to other forces that in this perspective, we are almost tempted to ignore it as if it didn’t exist: G = 0.

But observation of Nature shows us that it obviously does exist: G ≠ 0, G = 1 (or something else if you prefer another unit system, but never 0).This is not so surprising since you see an apple fall. No biggie.

So we thought that c⁻¹ = 0, ħ = 0 and G = 0, but we now know that c⁻¹ = 1, ħ = 1 and G = 1 and we want one consistent theory starting from there.

The theory behind c⁻¹ = 1, ħ = 0 and G = 0 is called Special Relativity.

The theory behind c⁻¹ = 0, ħ = 1 and G = 0 is called Quantum Mechanics.

The theory behind c⁻¹ = 0, ħ = 0 and G = 1 is called Newton’s law of universal gravitation.

The theory behind c⁻¹ = 1, ħ = 0 and G = 1 is called General Relativity.

Other combinations have different theory names, but the one you asked for was:

The theory behind c⁻¹ = 1, ħ = 1 and G = 0 is called Relativistic Quantum Mechanics.

We have no consistent theory for c⁻¹ = 1, ħ = 1 and G = 1, even though we know it is true. This problem is called “quantization of gravity”. A candidate theory is Loop Quantum Gravity. Another, more famous one is String Theory.

————————

This should keep Postpoc amused for months.

I suspect whoever wrote that needs to look a bit at the idea of limits, especially the idea that lim -> 0 is quite often used in a rather recent idea called calculus.

sibeen said:

I suspect whoever wrote that needs to look a bit at the idea of limits, especially the idea that lim -> 0 is quite often used in a rather recent idea called calculus.

I suspect that whoever wrote the article in the OP is quite aware of limits (and calculus), but didn’t want to scare off people who aren’t familiar with the idea. Or at least, they didn’t want to distract from their main point by preceding it with a lesson on limits.

sibeen said:

I suspect whoever wrote that needs to look a bit at the idea of limits, especially the idea that lim -> 0 is quite often used in a rather recent idea called calculus.

Kids these days! Next they’ll talk about their jmaginary friends.

OCDC said:

sibeen said:

I suspect whoever wrote that needs to look a bit at the idea of limits, especially the idea that lim -> 0 is quite often used in a rather recent idea called calculus.

Kids these days! Next they’ll talk about their jmaginary friends.

That’d be i-friends for all but electrical engineers.

only problem is the string theory guys are yet to actually demonstrate a experimental prediction that is not already demonstrable by either GR or QT

Kingy said:

This should keep Postpoc amused for months.

…….. when ‘months’ = i

Kingy said:

The theory behind c⁻¹ = 1, ħ = 0 and G = 0 is called Special Relativity.

The theory behind c⁻¹ = 0, ħ = 1 and G = 0 is called Quantum Mechanics.

The theory behind c⁻¹ = 0, ħ = 0 and G = 1 is called Newton’s law of universal gravitation.

The theory behind c⁻¹ = 1, ħ = 0 and G = 1 is called General Relativity.

The theory behind c⁻¹ = 1, ħ = 1 and G = 0 is called Relativistic Quantum Mechanics.

We have no consistent theory for c⁻¹ = 1, ħ = 1 and G = 1

Yep, I knew that.

It gets interesting in trying to compute the interior of a white dwarf star. Gravity is needed because it is very dense and held together by gravity. Quantum mechanics is needed because the matter is “degenerate” in a quantum mechanical sense, in the lowest quantum energy state. For large white dwarfs it is supposedly easy to show that particle velocities are approaching very close to the speed of light and hence are relativistic. So you might think that we have no reliable theory of the interiors of white dwarf stars. But that’s wrong, there is a reliable theory, and relativistic quantum mechanics plays a big role.

As a side note, the interior of a neutron star is not well understood, mostly because of the possibility of quantum physics beyond the standard model.