Recent content by PAllen

I freeze glass jars with water filled to 2/3 all the time, with no breakage. They are covered, but not securely airtight. So, after freezing, the ice in the jar has gone up higher than the water was, but no breakage if I leave enough space for the expansion. Even if the cover was truly airtight...

Frequently Doppler is used to define mutual rest, by absence of shift. Of course this is just one definition, but it is ONE. It generalizes uniquely and invariantly to any GR situation. Using this definition, then all aspect of SR Doppler carry over quantitatively to GR. You may say that it is...

The issue with this comparison is the at some point we agree there is no baldness. In the case of spectral shifts in GR, all the essential features of Doppler remain: for a given detector at a reception event, every different state of motion at the source event produces a different result, in...

Sure, because in a free fall frame it is primarily Doppler.

Hopefully not beating a dead horse on this, consider any small region in GR. Then there is a class of phenomenon you would consider to be Doppler. Expand the region, starting to discover small differences from SR Doppler due to curvature. At what point do you say there is no Doppler anymore, vs...

Oh come on. All I was saying is that there is a possible way to look at such that the title is right. That doesn't mean your way of looking at it is wrong, or than any title can capture more than a small piece of the whole truth.

But being able to have density decrease everywhere is a very unusual geometric property for an infinite spacetime to have. I would tolerate the description everything everywhere is getting vaster as a metaphor.

It can become vaster per unit of stuff, everywhere. There are different metrics you can put on an infinite spacetime, and only some have this geometric property. The invariant description of the geometric property is that the spacetime admits an everywhere expanding congruence. Thus, for...

And in SR, one ends up being a vector and the other a covector. It can be confusing ...

Hey, Luciano Rezzola is one of my favorite GR researchers! I’ll want to take a close look at these.

One can discuss the topology of limiting surfaces approaching a singularity. In that sense, the topology of the initial big bang singularity for an open universe (either flat or hyperbolic) is R3 meaning ordinary 3-space. This is simply because every isotropic surface that exists in the manifold...

Also, it should be noted that spherically symmetric nonrotating collapse to a BH per general relativity does predict unbounded density for the original matter falling in. This is because, while the singularity can be thought of being the limit of a collapsing hypercylinder, all the original...

But that is part of the measuring device. In the continuum approximation, you can take the limit as charge approaches zero, voltage remaining constant.

One other example is simply that if you charge metal ball or plate with static electricity, then you measure a potential difference (equivalent to voltage) between different points of the space near it, even though there are no electrons existing or flowing at or between those points. This gets...

Yes, I agree with you.