studiot

These were just examples, there are many shapes of wiggly lines. But I beg to differ that these are unimportant. If the lines represent energy what about the local maximum of activation energy ? And if we move to multivariable situations what about saddle points/ Are there any maximum / minimum points there? This represents a whole vital part of Physics.

This may be your thread, but your latest post moves the goalposts. Before you can discuss time in universes we are not in, you have to prove that the time in these universes is the same as time in out universe. Difficult since we have not yet arrived at a definition of time in our universe.

Nah, Trumps has a new infallible strategy for reelection. Appoint Alexander Lukashenko as campaign manager.

As regards local v global I have The plot of y = - x2 has a global maximum, but no minimum. The plot of y = x3 - x2 has no global maximum or minimum, but has a local maximum and local minimum.

Yes see your doctor. There are some parasites which lay eggs that hatch and burrow out to lay more eggs that hatch and burrow............ Thus there is a time interval between appearances. But this is not a medical diagnosis site so I repeat the ScienceForums prescription See your doctor.

Let us go back to the conditions you specified in the beginning of this thread. I am assuming a spherical earth to take advantage of symmetry. So the tunnel has two ends, both open to the atmousphere at r = R. The pressure at both ends must be equal and equal to the pressure of the atmousphere at the surface of the Earth. If they were not equal then air would move along the tunnel to make them equal. If they were not equal to the atmouspheric pressure then air would move into or out of the tunnel until they were equal. This pressure is denoted PR So you have one value for PR, given by the integral from r = R to r = the edge of space given by the conventional formula for the atmouspheric column above any point of the surface. You can choose a constant gravity and density or assume some meteorological function to get this figure. You get a second value for PR by developing a formula for gravity inside the Earth, which must equal the first value, as already noted. So you can form an equation between these two for your answer.

Which is more complicated than what I said, but OK it will do. I can see that The pilot does (can't) measure 'the universe' he can only measure the distance to something that is moving relative to him Remember all movement is relative. Movement without a reference point is meaningless. His frame includes his ship and the whole rest of 'the universe'. Here is an alternative look at the problem. Let us suppose that when he is travelling at full speed, he passes by an object exactly 1 m long when it is at rest in his frame. What will he see ? He will see an incredibly foreshortened object, many many orders of magnitude smaller than 1m, which he can measure as he passes by first the back, then the front and knowing his speed relative to the object he can recover the 1m rest length, if his super computer onboard is better than wolfram alpha. Now scale that up to the whole universe. Does this help?

OK so be it. So you have the volume of the 'reservoir' available to each well. You are given the density, porosity (phi if I am not mistaken) and specific heat of the rock and injected fluid. So you can do a "heat gained by fluid = heat lost by rock" calculation to establ;ish Tprod, which I assume is the eqyilibrium temperature produced. Thus you can substitute into the first equation (HIP) given. Where do you think the permeability comes into things ? You need to show some working, we don't do the calculations for you, but might help you check them.

Thanks for the replies and the support. Here's a couple of thoughts to add If a function vanishes at some points i.e. is zero, does that make it local or non-local at these points?

Well, Liz, there's your answer Your book is too basic. Get a more advanced one.

This thread was inspired by comments from Markus Hanke about how important 'local' is. So if some effect is either local or non local what does these mean ? For instance how big a region does a local effect affect ? Does it make any difference whether we are talking galaxy sized, or microbe sized ? Is there any relationship between the size of the region and the effect? Similarly if something is not local (non-local ?) what is then affected ? I have in mind that a non local effect may be distributed without affecting the whole universe. And also the difference between extrinsic and intrinsic properties.

Huh? So what. The muon will decay in a few microseconds, even though nothing changes in the meantime. So obviously time passes with no change. Indeed, but it is worse than that because different observers (including the muon) will measure that amount of time differently. How does that work with quantisation? One observer's quantum is another's 1/3 or 0.3 recurring forever quantum ?

You haven't shown why this claim of yours is true, (or why you ignored my example that shows it to be false) Good response to my second query to Drumbo over this. +1 I know of no evidence that space is quantised. Although there is much speculation and discussion about that question in Physics, nothing has definitely shown this. In any event time itself is not quantised in Relativity theory.

I don't see the connection. Further the idea of no change over time can be very important. Take some Uranium atoms and watch them for several hours (days). Will there be a change and is no change significant?

Are you sure of these three figures ? A well every kilometre on a strip that narrow?

Neither of these ideas make any sense to me. Do you have any supporting evidence?

Yes indeed that is our spacetime. But space, having three axes had left hand and right hand. Or alternatively if we have angular coordinates, clockwise and anticlockwise. Time on the other hand cannot supprt this behaviour on a single axis. But I do wonder (and this is pure speculation) if the 'arrow of time' has something to do with this (I won't use the word connection since Markus has already bagged another meaning for this word) but that is what I mean.

Well there's electric charge / polarity There's chirality / eg handedness of the spatial axes. There properties to do with matter/antimatter. Perhaps temperature. But we are supposed to be singling out time for discussion in this thread.

So we are back to what I said a page or two ago. If we are going to be able to define time we will have to do so in terms of the properties it possesses and the effects it bestows on other inhabitants of the manifold or receives from them.

Ok finite universe. Your problem is that you are not specific enough " it is just a matter of to speed up close enough to c to contract it to 1 m" spedd yes, but speed relative to what ????? So I picked a 'what' as the start point. Why left ? Well if you circumnavigate a finite universe you will arrive at your start point travelling from the opposite direction. Again for specifity I picked left and right. It could have been down and up or up and down or whatever. So we have a spaceship travelling fast round the universe. But this is relative which means it could just as well have been the universe travelling past the ship. And it is that which the pilot observes. He does not observe his own travel as he is stationary in his own frame.

It sounds like you're referring to the spacetime as 'the universe' and others are referring to all the moving stuff in it as the universe? If all the stuff was moving, the pilot would measure it as length-contracted. Thank you, yes my text was unclear small wonder Strange was puzzled too. +1 Hopefully I have corrected this in my immediately previous post.

Mass is not a function of the coordinate system, or the manifold.

I neither agree nor disagree with you maths I just can't follow it. What do you mean by the definite integral of the product of two constants, from the limits zero to a constant R, with respect to an variable r ?

So you have read my comments, even though you did not respond to them. I think you are mixing up referential systems. You are asking from the point of view of the pilot so consider what he sees. Although you have not answered my question as to what is his velocity in an otherwise isolated universe let us further allow one referential point as a starting point. The pilot sees the rest of the universe (the reference starting point) receeding away from him to the left at this incredible speed. In his frame he is stationary. If the manifold is finite but closed he then sees the reference point approaching at incredible speed from the right a very short time later. If (as i am inclined towards) the universe is infinite of course he never sees the reference point return and the maths has a division by zero error. So as far as the pilot and his spaceship are concerned the rest of the universe is smaller than his ship and makes a circuit around it. So what ? Where is the paradox ? By his measurement the total size of the universe must be 10 m plus 1 m.

I hope I carefully avoided saying there was but I am waiting until we can help Michel develop his thoughts, which are often highly rational, if not formally expressed. We should all help each other improve the expression of our thoughts. Joigus picked me up on something a few posts back, for which I was (am) grateful.