Strange

That is pretty much my point. And that is what I meant when I said you need to know that it is (and how it is) incomplete. The point being that forums get a lot of people trying to support their "personal" theory by using e=mc2 but not realising that, for example, it doesn't apply to photons. (Or trying to apply equations of SR to situations where GR is required. Or ...) In other words, one needs to have an understanding of the meaning of the equations you are using. So we know that the chemistry equation cited earlier doesn't mean that energy is created from nothing (as a dimensional analysis might suggest) but that irrelevant details have been omitted. Maybe what this means is that it may be more important to check that a dimensional analysis says what you expect, rather than being perfectly consistent (if you have decided to omit some things).

In quantum theory there is no distinction between waves and particles. What we call particles are just the quantised amplitudes of waves. Because of the uncertainty principle, there is a possibility for the non-zero energy of the vacuum to reach the level of a pair of virtual particles (for a limited time, as defined by the uncertainty principle). They appear because of the non-zero vacuum energy. They don't contribute extra energy. Also, dark matter is concentrated (e.g. in galaxies) whereas the vacuum energy is the same everywhere.

Quite. As previous examples have shown, being dimensionally consistent is a necessary but not sufficient requirement for an equation to be complete/useful. But if it isn’t dimensionally consistent then we know it is incomplete or wrong. Incomplete can be OK. It can be a useful shortcut, like the chemistry example earlier or e=mc2. As long as you know it is incomplete.

I agree with koti; the important thing is to get them asking questions and then, even more importantly, get them to think about how they could answer the questions. Including the importance of doing a rough calculation to check the validity of an idea (even if you have to guess at the numbers involved - e.g. Fermi estimates). In terms of basic physics concepts that would (at the right time) equip them to do this, I think I would choose: 1. Newton's laws of motion (these can be summarised in one sentence, so I am not counting it as 3 things!) 2. The fact we can separate out vector components of force, motion, etc. -- this amazed me when I learnt it and it still seems remarkable! 3. Newton's law of gravitation These three allow you to solve quite a range of real world problems and discover surprising facts (like, all masses fall at the same rate). 4. The fact that some properties are conserved and that this is related to fundamental symmetries (and point out that this was proved by a woman, as science so often seems dominated by male figures) 5. Point out that all the above are only approximations and that they will find out that the real world is actually more complex and more interesting.

You could read up on the ALPHA project at CERN. They are creating anti-hydrogen to test its properties. http://alpha.web.cern.ch/

But it is totally misrepresenting them. It is like saying "astronomy shows that the planets move. Therefore astrology is correct." For example: Is just nonsense. The behaviour has nothing to do with consciousness.And he has the description of the experiment almost totally backwards. It is not the act of watching that changes the behaviour, but constraining the photon to go through just one slit: this changes the result of the experiment to what you would get if the photon went through one slit (not surprisingly). If you allow the photon to go through both slits, then you get a result consistent with it going through both. The rest is just more of the same misunderstanding/misrepresentation. Edit: cross-posted with koi. Interesting we both picked the same paragraph. I was initially going to pick the drivel about Heisenberg's uncertainty principle. Presumably I changed my mind because koti "observed" the article at the same time!

Pseudoscientific hogwash. With a large side order of Quantum Woo.

I'm quite sure there is no reason you couldn't buy a company and then just wind it up. It would be considered foolish, but I can't see how it could be considered illegal.

Even if true, I fail to see the relevance. An equation would normally use one type of units, and would need to be consistent in those units. An equation converting between units would need conversion factors that maintained dimensional consistency.

I think the key thing they are reporting is that they are effectively able to resolve something smaller than the even horizon (the area where the "lightning" originates).

I found the Mail article pretty confusing. Looking at the abstract of the paper, it doesn’t obviously match the Mail article. This article, despite being apparently being google-translated, seems to make a bit more sense: https://www.sciencedaily.com/releases/2014/11/141110090721.htm The original paper is available here: https://arxiv.org/abs/1412.4936

Your link doesn’t work for me - just takes me to a page full of gossip, lies and hate. But I really wouldn’t rely on the Mail as a source of information on anything. Perhaps you could find a science website (or even a real newspaper) with the info?

It is trivially explained by relative velocity. I’m really not sure why you don’t think this is the case. 1. We observe redshift of light which has not passed through the corona of stars. 2. Can you show, in suitable mathematical detail, that your claimed effect reproduces the observed redshift-distance relation? 3. By claiming this is the cause of redshift you are also claiming GR is wrong. 4. You haven’t explained how we use Doppler shift in terrestrial radar where no corona is involved. Do you mean “not =“? Anyway, gravitational and cosmological redshift are not the same as Doppler.

So you are saying the two sides are not equal in both cases?

But, in both cases, the "=" means that the LHS is equal to the RHS. It is the nature / relationship of the LHS and RHS that defines what the equals sign means. If the convention was to use a different symbol for identity and equality (as is done in some programming languages) then changing the symbol would not (necessarily) turn an equality into an identity; it would just be wrong.

Why would anyone measure height in square metres. (Rhetorical question; no answer required.)

Hyperbolic? Where did that come from?

That is not a function of the equals sign but of the expressions that it is used to show the equality of. The equals sign means “equals” in both cases.

I’m not sure what you mean by “real” but the field is not scalar; ie it has direction.

You said mathematics and applications "are separate and distinct things" But it seems you were mistaken. So you are unable to explain how they are different?

Why would they do that?

It is? So my cousin with a degree in Applied Maths was given a fake degree? In what world is height squared measured in metres?

At least one investment company (Black Rock) has said they will offer investors this choice.

I can't see why not, in principle. A photon (say in the CMB) could continue going through space and missing the hydrogen atoms and stars, which are few and far between. Momentum is transferred from the source to the photon. It doesn't then need to be transferred to something else, does it?

That is not unreasonable: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html Although you could say the field is always there but is zero in the absence of charge.