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Someone asked a question the other day that made me realise that there seems to be a parallel between the Heisenberg uncertainty principle (HUP) and Noether's theorem. For example, one conjugate pair of variables in the HUP is energy and time. While in Noether's theorem, the conservation of energy is related to time symmetry. Another conjugate pair is momentum and position. And the conservation of momentum is related to spatial translation symmetry. I assume this is not just a coincidence. So is there a deeper reason? Is Noether's theorem the reason why these are conjugate pairs?

Huummm… Noether's Theorem doesn't really relate position and momentum, or time and energy. It simply states that every differentiable symmetry ( time and translation )of the action ( integral over time of the Lagrangian ) has a conserved current ( energy and momentum ). I'd put it down to coincidence. But if someone can show a relation, I'd be very interested in hearing about it. ( good question, Strange )

Mass and energy are equivalent. They are both properties of "things" (in the most general sense). Energy is a property. But I suppose the one property it has is that it is conserved. One definition of energy is simply that it is a bookkeeping device, a conserved property of systems.

Which is consistent with the lack of certainty about how many kids he has. The problem is that he seems to think with them. What caused that estrangement was largely Boris lying about them while pretending to be a journalist. There really isn't much difference between the EU and the UK. But there's a lot of lies about the EU.

We can disable the Diplomacy Filters, but then the popup says things like, "Scratching Itchy Area" and "Screaming at Neighbor" and "Having Another Whiskey". We THOUGHT we were doing you a favor....

Thank you for the reply. B-T does include time implicitly in that it the unfolding process does not destroy each copy as it is made so they must exist simultaneously. How about my glass of water?

Because non-mathematical human language is imprecise

I saw a cartoon of a guy who said he made a solar powered device that extracted CO2 from the air and produced building material as a by product. The guy he was talking to asked to see it. The first guy pointed at a tree. The problem is finding land where we could plant them.

There is a big push for carbon capture and storage technologies, but so far AFAIK there is no real option that is more sustainable than alternatives (such as use of plants for carbon storage). The most efficient methods include capture at point of emission, which could have some use to mitigate industrial release. Some, are already in use for quite some time (at least the capture part, storage is a bit more iffy). In industrial use methods such diethanolamine treatment or selexol are in use, but they are not generally not feasible post-emission. There are efforts to push monoethanolamine capture as means to do that, but I am not sure how sustainable that method is. Last thing I hear was a rather mixed bag.

You understand it wrong. It has nothing to do with light reaching you more slowly. While we do use light in examples dealing with time dilation, this is just a convenience as using light makes the examples clearer. But light itself has nothing to do with the reason for time time dilation. These examples are just highlighting something much more fundamental about the very nature of time and space in our universe. Basically, If we are in motion with respect to each other, we simply do not measure time and space the same. 1 sec for you is not 1sec for me, and one meter for you might not be 1 meter for me. We will not even agree as to whether given events are simultaneous to each other or not. Relativity forces us to accept that the idea of universal time, where one sec is the same for everyone, just doesn't apply in our universe.

+1 Perfect logic requires the right assumptions, and we can't be absolutely sure about the ones we have taken on.

The big bang had a beginning. The question is what was before the big bang? And what is beyond the range of the big bang?

Fire. I like my food cooked.

Nonsense.

Alright, assuming I start taking out parts of my brain, when do I become unconscious? When I take out the brain stem. But can I prove that I do not become a different person as soon as I take out the first chunk? No I cannot in terms of Evil Demon theory. But that is in no way stopping me from achieving immortality with the dream groups though. This is what observation is based on, we use our best estimate. Could an Evil Demon alter our senses to see the result of an experiment? Sure there could be, is that going to stop me from publishing my paper, probably not

height - width - depth - 3d - all spheres are 3d

No - a sphere has a border.

You want to explain how a basketball is 2d?

All spheres are 3d - look it up in a dictionary - unless you live in fantasyland.