MigL

I was a bit of a 'gear-head' in my younger days... The only reason higher octane fuel produces more horsepower is because it can take advantage of higher initial timing, or how many degrees before top-dead-center the spark can fire the fuel-air mixture. Alternately it allows a higher compression ratio or turbo/super charging. This puts the explosion/expansion at a more advantageous position to produce power and other cylinders waste less. It does this by reducing the speed that the flame front travels through the air-fuel mixture, in effect by being LESS explosive. That pinging you hear at wide-open-throttle while going up-hill in high gear is pre-ignition. The flame front explodes too fast and slams against the aluminum piston dome. It can actually blow a hole in it, ruining your engine. Believe it or not, in North America the highest octane consumer gasoline at a rating of 94 is obtained by mixing up to 20 % methanol with gasoline . And some higher performing vehicles have pre-ignition detection. If a sensor detects the pinging vibration, the computerized ignition lowers the initial timing to eliminate it. Still, a lot of high performance vehicles, especially turbocharged or supercharged, require the use of 91 or higher octane.

One could argue that human aggression is instinctive. We are after all, animals. One could them make the argument that religion, which came even earlier than societal structure, is what curbed our instinctive nature, It taught us to 'play nice' with each other against our baser instincts. In other words ( if you are religious and believe that sort of thing ), it gave us a 'soul'.

And none of that addresses the concerns I raised. I'm not saying the choice should be one way or another, just that with advancements in medical tech, some women, or, all women are going to be disadvantaged. You'll have women with the testosterone level of men making it unfair for other women, or you'll have to disqualify women with man-level testosterone. You can't have it both ways. I'm glad Its the Olympic Committee's problem.

Thanks for the concern DrP, but it was a rhetorical question. Both of the named individuals are evil villains out to rule the world.

Any introductory textbooks you can recommend, AJB, to get a better grip on fibre bundle treatment of fields ? Assume a working knowledge of diff. geometry and just a basic understanding of topology/group theory.

Any theory of 'Quantum gravity' has to reduce to quantum mechanics at the low-energy, small scale limit and general relativity at the large scale limit.

Quantum fluctuations are by definition, not localized in space or time. You have heard of the HUP, haven't you?

Then you have a choice to make... Be fair to her in particular. Or be fair to women in general. Does 'the good of the many outweigh the good of a few' ?

She looks like she might have one. She blurs the distinction between man and woman. Either you consider naturally elevated testosterone levels just another physical ability ( like strength, endurance, co-ordination, etc ), and get rid of the men's and women's classes, and hardly any women will ever win an event. Or, you set an upper boundary for natural testosterone levels in women athletes, because right now, she has an unfair advantage over other ( normal ? ) women. And no 'normal' women will ever win an event. Instead of supplying athletes synthetic steroids and other performance enhancing drugs, Russian doctors will start enhancing testosterone producing glands, and suppressing androgen producing glands in women athletes when they approach puberty, so that you have basically males with female genitalia. Either way is unfair to a 'normal' woman whose testosterone level falls between the 5 and 95 % Gaussian.

Starting a pool. This thread gets closed in less than 15 posts.

There seems to be some conflict here. Are you guys of differing religions ? ( sorry, I'm trying to lighten things up, and couldn't help myself )

Remember the definition of a field ? A scalar value, vector or tensor associated with each point in space. A field, say a vector field like the EM field, is defined on a differentiable manifold, and belongs to a certain symmetry group, U(1). The tangent vector at each point would then be called the tangent bundle, for example. And, it can be used to perform operations on the manifold. So in answer to your question, none of those pictures represent the EM or gravitational field. And no, I'm not really sure about all the above, so we'll have to wait on AJB

In the two lowest pics of the Cylinder and Mobius, notice the vertical lines with arrowheads pointing up ? Those would be equivalent to fibres. Notice what happens in transforming the cylindrical manifold to the Mobius manifold; about halfway around the circumference of the cylinder, the fibres are flipped so that the arrowhead is pointing down, and this results in the Mobius. At least that is my (very limited ) understanding.

Keeping in mind that I haven't had my 'eureka' moment yet, where fibre bundles actually make sense to me... In the example AJB gives. If you consider a tube, and attach a 'fibre' at various points along the circumference, oriented towards the openings at each end of the tube, then you can transform the simple tube to a Mobius simply by flipping the fibres halfway around the circumference. The 'fibres' are a convenient way to manipulate the action on a global topological manifold. I wouldn't mind a new thread where AJB, if time permits as he must be extremely busy at the moment, could give us all a tutorial on the subject.

No. If the 'units' of your co-ordinate system just expanded, you'd never be able to tell expansion is going on. The number of units between events actually increases. And it can then be counteracted by local gravity.

EM waves have two mediums ????? They don't even have one ! You didn't read that in my post. Re-read it. Otherwise, why would you jump to that conclusion ?

What change are you talking about Michel ? A metric is simply the distance between two points. In 4d flat ( Minkowsky ) space-time it is simply the extension of Pythagoras to 3 spatial dimensions plus time, given by dS^2. In curved, GR, the multipliers of the Pythagoras terms are not unitary anymore because of curvature. But in either case you need geometry to have separation, S.

So we've made Mike happy with... 'Space-time is the medium for gravitational waves' and we can finally move on. But space-time, or rather its curvature, IS gravity. So Mike has finally agreed that the gravitational field IS the 'medium' for gravitational waves. Just as he seems happy with the EM field is the 'medium' for EM waves. IOW gravitational and EM waves are their 'own medium', or alternately, don't need a 'medium'. Which for the rest of us ( less tenacious ) was established 35 pages ago

You need to have geometry to have a metric. If you're considering a singularity, you have no geometry. So what exactly is the metric measuring Michel ?

As mentioned before. As you run time backwards, the universe shrinks. If it stops shrinking at a size where quantum effects are negligible, then you have geometry ( space-time ), so you can talk about 'now' or 'before' meaningfully. If it shrinks past that point, nobody knows, as we don't have a quantum gravity theory to describe that kind of space-time. It could be a totally different kind of geometry ( or none at all ), like J.A. Wheeler's quantum foam, or quantized, discrete space-time of LQG, or 11 dimensional branes in the bulk of SS theory. And so, no-one knows what this implies for a discussion of time and sequence. If it shrinks down to singular size then there cannot be geometry and therefore, no space-time. In effect, you are then 'north of the north pole'.

I believe I may have used the coin example of entangled particles a long time ago... Take a coin and slice it in half, such that one half has heads showing and the other has tails showing. Seal each half in an envelope and then give one to DrP and the other to DrmDoc ( the two doctors ). Neither one knows the state of the coin in his envelope, it could be either heads or tails. But as soon as either one opens his envelope ( and collapses the wave function ), he immediately knows the state of the other coin held by the other doctor. Even though one is in the US and the other is in the UK. And no actual information has been transmitted.

Even a hot, dense initial state will have a size, and so, geometry and space-time. All parts of this initial universe will need to be in causal contact to ensure isotropy and homogeneity. That is one of the reasons for postulating inflation. You will of course still have quantum fluctuations to provide the 'seeds' for future structure. If the initial universe is small enough however, such that quantum effects don't allow for geometry, or if its actually a singularity with no geometry, then of course there cannot be space-time. And if there is no time, how do you define a universal 'now' ?

You know, Airbrush, that Mussolini quote is a variation of Milton, in Paradise Lost "Better to reign in Hell than serve in Heaven". Somebody should investigate this. There are too many similarities between Lucifer, the Anti-Christ, and D. Trump. ( yu know I'm just being sarcastic now, although... )

Why don't we just check the scoreboard... Number of people killed in NON-RELIGIOUS wars over the last century: Optimistic estimate about 80 million. Pessimistic estimate, about 120 million. These are wars where the combatants share a common religion but different culture/ideals. And I've only considered WW1, WW2 and Korea. So what's the death toll for all the bloodshed RELIGIOUS wars have caused ( in even the last thousand years ) ?

Sorry String Junky, I was in a hurry this morning and didn't re-read my post. You're right it was rarther confusing. Meant to say if velocities match, then same frame. If velocities don't match, so that one frame is moving with respect to the other, and one can be considered at rest, then different frames.