No objection to that. I just wanted to emphasize that at the (near) singularity of the big bang the laws of gravity as we know them (GR) alone are not enough. We will also have to take QM into account. For this there is just a little research required. If a final theory will be strings or LQG or whatever is just not known yet.
Only in a thought experiment and if you fell into a big black hole and were able to manipulate the external boundary conditions beforehand.
In practice the most powerful radar ranging kit on the planet, Arecibo so far cannot quite do Saturn's moon Titan. So unless you are closer to the inner surface of the event horizon than that distance and able to deploy planetary scale marker objects you are not going to see much.
Light doesn't have a visible path through space unless it is scattered or reflected by objects in its path. Typically in visible laser labs they have a smoking spill or dry ice smoke to show visitors light paths (it used to be easier in the days when everyone smoked)
I have seen someone light a cigarette off a 10W argon laser.
In our own universe we cannot see back past the surface of last scattering where the universe became transparent to EM radiation so you have no hope at all of seeing any "exterior" that might be present.
It was never quite a true singularity in the first place. Either that or for reasons that are to do with quantum mechanics the absolute mathematical singularities in current theories are prohibited or unstable. Only when we have a more complete description of the physics will it become clear what the answer is. Testing them will be tricky.
Not necessarily. Gravity looks like it was pretty much the same right back to the instant of creation the big problem arises when the radius of the proto universe becomes too small for our theories to handle.
It is arguably a generalised rotation if the operations are normalised in the right way. Design of FFTs have inspired some physics researchers to investigate Clifford algebras and other esoteric mathematics in an attempt to simplify some notation and gain new insights into phenomena.
I think the singularity in classical GR at the centre of a BH is sufficiently pathological to resist all attempts at analytic continuation. Unlike the apparent singularity at the event horizon which can be eliminated by a judicious choice of coordinates.
By the time it is valid the mass distribution is a static (no spinning) mass M in the middle of a sphere of influence.
Oh yes. There are some fantastic simulations the first successful ones being done by the gang of four. They got the Gruber prize for it in 2011
When they started out the mass of neutrinos had just been shown to be non-zero so they tried hot dark matter first and ended up with nothing like the right thing. Then they tried cold dark matter and got a lot closer. The best simulations today using the observed mixture of the present universe are absolutely stunning.
One of the places it crops up rather nicely is in SQUIDs and Josephson junctions where the voltage step is quantised by increments of mangetic flux as current is increased. It is a rather pleasing staircase.
My supervision partner (an experimentalist) did this elegant test as one of his his part II practical experiments.
I think the problem is that common sense just doesn't work at all when you go to the very small or the very fast. We didn't evolve with the ability to handle situations so far removed from our daily reality.
Don't hold your breath for that one!
Yes, those pages also contain a fair bit of obfuscation. For example, it is said that magnetic flux is quantized in steps of h/2e. That's misleading. Magnetic flux can take any value. It's the SQUID that confines the flux inside its loop to multiples of h/2e. It has to exert some effort to obtain that, which is manifest by the appearance of a DC voltage between the halves. This voltage traces out a periodic sine over a flux change of h/2e. It's easy to measure flux changes much smaller than h/2e by looking at that voltage.
Also, this works well for flux values close to zero. The periodicity progressively disappears when the flux grows. SQUIDs usually have feedback coils to keep the nett flux at zero.
I'm fine with calling h/2e a flux quantum, but it's wrong to pretend that flux can only be an integer multiple of that value. That is true only inside the SQUID.
Jeroen Belleman
Sure. Fractional derivatives are another example.
Cheers
Phil Hobbs
Sounds to me like you are agreeing with me.
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