For all terrestrial phenomena that we have observe so far we have a theory of everything.
In order to put matter into a state where it behaves in such a way that you can tell the difference between two competing theories that describe the world, you have to build the LHC. Anything less than that and the theories all are perfectly good at describing what we see.
I think there is a tendency to misunderstand LHC and it's high energies as somehow being "brute force". High energy really just means small structures. It's better to think of it as the worlds best microscope. LIGO is the worlds best ruler. So we're measuring the world and it's matter to an unfathomable precision and we do not see meaningful divergence between theory and experiment.
We know there is more out there, but it's not stuff we can study on earth. That's the single biggest problem.
We used to make gasoline by heating oil very very hot and separating it. As long as you can keep it away from oxygen we don’t explode.
But now we have catalysts that allow us to get more gas from the same oil, and with less heat. Less energy for a bigger gain.
Big, hot, smashy, explodey things are good for a proof of concept, but for a practical application we want to make them smaller and lower energy (per unit) then scale them up huge (more units) and keep the energy down (magnitude + per unit).
Can you make these particles in a different environment? Can you move some of the embodied energy into a material? Can you reuse that material? All of these are good questions. If we answer them then the next LHC maybe doesn’t have to be an order of magnitude bigger and power hungry in order to see over the next horizon. Maybe 2x would do it.
At issue here is the fact that what physicists need to conduct experiments is not more data, but different data. To study higher energy levels, more energetic particles are needed. Generating more particles at similar energy levels and producing more data is not without value, and has been the work of the last few years at the LHC, but is considered unlikely to turn up surprises since it’s data about particles at a similar energy level to previous runs.
Now that you mention this, would an accelerator in space need walls? Could you make it from a series of big circles (maybe solenoids?) at distances of a million kilometers apart or so? Neptune's orbit is about 15 billion km long, so, you'd need about 15k of such loops. In free fall they would just go around the Sun, so you'd only need to maintain their perfect alignment with some minute adjustments.
Is there some reason to think that the only way to get higher energy collisions is by scaling the accelerators? Is there any possibility that we may be able to get to higher energies with earth-scale experiments?
The limiting factor is the strength of magnetic fields you can achieve. The more momentum the particles have, the stronger a field you need to bend them into a circular orbit. The attainbale strength is determined by material properties and there is nothing to suggest that we can get orders of magnitude improvement here. The improvements have been quite linear for decades, see the figure here:
And you eventually run into rather fundamental problems of tearing your atoms apart with the magnetic field you create. But I am not up to speed on how close we actually are to these limits.
Ultra-high-energy cosmic rays are possible candidate. For example, Oh-My-God particle had energy of a baseball traveling at 100 km/h. 40 million times higher than particle energies of terrestrial accelerators.
For the effort it would be easier to build one around the Earth. Double it up as a driveable highway, rail and electrical infrastructure (and then you can use solar power sold on a global market where one side is always in daylight).
It won't be surprising if we eventually do. A particle accelerator beyond Earth has been often discussed, and recently a paper[0] even sketched such a project for Moon.
Hollywood has vastly overplayed the actual density of asteroid fields. It’s kind of disappointing.
If you build something in a vacuum then you don’t necessarily need a single continuous piece to create a vacuum. If you specced an accelerator a million miles in diameter, the diameter matters from a standpoint of whether we can accelerate the particle sideways fast enough to keep it in the track, but they are also saying they need 3.1 million miles of accelerator hardware. They are implying they can’t lay it out as a crazy straw, but is that because of the lateral acceleration, the interaction between the coils, or the limits of manufacturing?
What if you built a collider in a spherical arrangement, accelerating in three dimensions at once, but 1/3 the diameter? What if the accelerator were broken into sections to dodge asteroids, with a cumulative segment length that added up to the desired total? What if you laid it out like a Spirograph? What if you laid it out like a truncated Spirograph (just bits of the outer circumference)? What if you laid it out like a 3 dimensional truncated Spirograph?
Consider the following:
For all terrestrial phenomena that we have observe so far we have a theory of everything.
In order to put matter into a state where it behaves in such a way that you can tell the difference between two competing theories that describe the world, you have to build the LHC. Anything less than that and the theories all are perfectly good at describing what we see.
I think there is a tendency to misunderstand LHC and it's high energies as somehow being "brute force". High energy really just means small structures. It's better to think of it as the worlds best microscope. LIGO is the worlds best ruler. So we're measuring the world and it's matter to an unfathomable precision and we do not see meaningful divergence between theory and experiment.
We know there is more out there, but it's not stuff we can study on earth. That's the single biggest problem.