MigL

You've lost me AJB ( you gotta remember to dumb it down for us ) as I don't see what the fact that 'any combination or product of solutions is also a solution' has to do with it. Am I missing something ?

Also, why is a wave function not technically a wave ? It looks like a wave and can be expanded mathematically as a combination of waves. Do you mean its not a real actual wave or am I again missing something ?

At that time, just after the big bang, there was also sufficient energy to keep quarks from pairing up.

As has been explaned, quark separation energy is finite and much lower than Planck scale energy

( in other words I don't know its exact value but I'm sure you could look it up, if interested ).

Uncharged particles also have antiparticles, and some are their own antiparticles !?!?

Yes, the two original quarks separate. The energy creates a new partner for each of the original two bound quarks. I'm not sure if you can tell, however, as you cannot label the quarks. You may be able to tell from conservation of momentum considerations.

Well, let's see if i can give some examples, questionposer.

Consider the wave equation of an electron. Now a classical wave would be like a bucket with some water in it, if you agitate the water, waves spread out until they hit the siges of the bucket and are reflected.

The electron,o on the other hand, can do something that classical particles and waves cannot. It can 'tunnel' to the outside of a square potential well, and back in again, if it chooses to. We explain this by having the wave overlap the sides of the potential well so that part of it lies outside the well. Now it doesn't make sense to consider that outside part of the wave to be 'part' of an electron since we consider electrons fundamental point particles, and so indivisible. The only available choice is to relate the wave equation to a a probability.

A similiar situation arises in electron scattering off an obstacle. In this case the incident electron wave would produce, upon scattering, several larger ripples or wavelets. Again we cannot conclude that these ripples represent pieces of a broken-apart electron for the same reasons presented in the first example. Again we must conclude that these ripples are related to the differing probability of the incident electron being deflected in that direction.

I realise that the wave function and Shroedinger's equation are not the same, AJB, butit was overlooked for the sake of simplicity.

I wold go so far as to say there is no such thing as information conservation, yet. It is a quantum mechanical concept being applied to the 'classical' theory of GR. Only a quantum gravity theory will provide answers.

Yes, you definitely should learn the math, it really isn't that difficult.

But you should be less concerned with why they are waves, a common state of many physical phenomena, and more concerned with 'what' is waving. Most waves we are familiar with are in a medium such as water, air,etc,or waves of something physical such as electric and magnetic fields. What is waving in Shroedinger's equation however is not really a physical wave, but is somewhat related to a probability wave since the square of the amplitude of the wave at any point, is the probability of finding the particle at that point.

So as you can see it isn't the math, its the concepts of QM which are difficult to wrap your head around.

There is no law that prohibits the destruction of matter!

There is a law that prohibits the destruction of mass/energy, and black holes being good citizens of the universe, dutifully obey this law. They conserve both mass and energy, so there is no need to postulate 'white holes'.

How would regular matter and energy get across these 'tares' ? In 4d space/time they would be a volume and so would be regions of vast void across which light couldn't pass ( like black holes, but emitting gas ?? ).

Your other flight of fancy implies that the 'outside' of the universe is filled with infinite amounts of dark matter. Since dark matter is affected by gravity, it would collapse and crush our embedded universe. And what about the interface between outside and inside the universe ? Along with numerous other problems, too many to mention.

That's usually the problem with spur-of-the-moment hypothesis, not much thought is put into them !!!

Question for you DrR.

You've stated several times now in several different posts that space/time is static and that all space/time events are fixed points on the manifold ( even future events ). Now this is all very well for GR which is a 'classical' theory, since it implies a 'clockwork' determinism, i.e. if you had a big enough computer and could solve all the field equations, you would then know where and when any event would take place.

But just as classical physics was at odds with the emerging field of QM at the turn of the last century, and resulted in the paradigm shift from a deterministic to probabilistic view of reality ( at least at the atomic level ), so will any future quantum gravity theory.

Are you of the opinion that any quantum gravity theory will find these so-called fixed event points on the manifold to be somewhat fluid, or 'smeared-out' and also probabilistic in accordance with the HUP? And if you do why do you keep reiterating the deterministic point of view? Or do you think its too early in the game to call?

basedI know I'll get repremanded again by the good Doctor, but I've never read Thorne, Misner and Wheeler's Gravitation although it is on my to-do list, nor the other book by Choquet-Bruhat. I did try to work my way through Principles of Physical Cosmology by P.J.E. Peebles and found the going tough because I have no background in differential geometry and some books assume a working knowledge of the subject.

I did download a book based on a series of lecture notes by S. Waner called Introduction to Differential Geometry and General Relativity and it only assumes familiarity with college level algebra and calculus, which makes GR a little easier to understand once you have aquired a basic foundation in differential geometry.

Has anyone else read this, and what did you think ?

The Higgs boson does not imbue other particles with mass. It is the Higgs field which may perform this feat of magic through the Higgs mechanism ( look this stuff up ). The Higgs boson is just a manifestation of the field which,just like any other quantum field, produces a carrier boson. The boson, being easier to look for, would therefore, if found, validate the Higgs mechanism.

I believe the principle Seriously Disabled is referring to is the principle of least action developed by Fermat and deMauripitius ( spelling ?? ) and later by LaGrange and Hamilton. The action is basically the sum of the differences between kinetic and potential energy ( Ek-Ep ) and the action is minimised when potential is reduced by increasing kinetic energy. Or as previously stated, things fall down instead of up.

You may be right about reading nonsense...

However I believe math is the tool we use to build models and the physics has to guide you in using this tool. Sometimes the tool and model becomes more complicated than the physics its trying to describe. And ok, maybe some of my examples were questionable ( and although not theories have been put forth many times by members of this forum, which is why I used them as examples of unnecessary complexity ), but it certainly applies to string theory, which, although mathematically consistant, has become extremely complicated and as you say, has made no testable predictions.

They are, supposedly, the building blocks of everything. As such they cannot have structure, and are one dimensional open ended or loops. If they had structure they would be 'made of something', which would then be the building block of everything and not the strings.

The string is under immense tension and, supposedly, vibrates in 10 spatial dimensions. The energy is then, like any other oscillator, proportional to its frequency and amplitude.

Maybe its just my opinion, and I would certainly appreciate your and others' input on the matter, but have extra dimensions become a 'catch-all' for physics problems lately.

Some examples.

String theory in the 80s has a problem. It gets rid of the infinite probabilities that previous quantum field gravity theories had provided, but it has negative probabilities, which also make no sense. The 'solution' is to provide 7 extra spatial dimensions for the strings to vibrate in, and the negative probabilities cancel out. We are left with a 10S+1T dimensional space where each point of the three large spatial dimensions contains a compacted 7 dimensional Calabi-Yau manifold ( hope I'm using the terminology properly ). Has this solved the problem ?

The Many Worlds interpretation of Quantum Theory where the superposition of states of the wave equation is collapsed by observation or any event which 'fixes' the outcome. In this reality or dimension, one state prevails over the other possible states. But in other realities or dimensions each of all other possible states prevail. Shroedinger's cat is alive in this dimension ( I like cats, I have two ), but dead in another dimension. There are infinite other realities and every time a wave function collapses more are 'created'. Does this solve the interpretation problem ?

The time travel problem and closed time-like loops allowed by GR, where a past event is changed to alter a future outcome, such as going back in time to prevent yourself from being born, is interpreted as time branching at that point to create another self-consistant reality or dimension. Extra dimensions are created every time one of these loops is created, not necessarily more spatial dimensions, but the same three spatial dimensions are re-created in a differing time-line, implying at least 2 ( or more ) time dimensions. Has this solved the problem ?

It seems like extra dimensions or realities ( I've used a rather loose definition of dimensions ) are invoked whenever we need a rug to sweep our problems under. We can't test for or verify these extra dimensions or realities so its a convenient way to get rid of problems and forget about them without really solving them.

If this post derails the OP as it has very little to do with it, please feel free to move it.

Didn't watch the video clip, but was rhis 'hi-temp" superconductor levitated by a magnet ?

One property of superconductors is their ability to expel magnetic fields resulting in 'levitation'.

This is one property spurring research to find room temp superconductors. Of course a viable theory of superconductivity would be a great help.

So this dimension in which our space is embedded in, did it begin with the big bang as our space did or was it always there ?

Your 'embedding' diagram deals only with the three spatial dimensions, what about time, does it continue to the 'external dimension ?

I myself don't see how it could since space and time are part of the greater whole, space/time, and as such are linked by GR.

I fear you are adding unnecessary complexity to a subject which certainly doesn't need it. And I believe DrR will tell you that an embedding dimension is not required by GR.

That being said, I believe M theory postulates branes which are embedded in higher dimensional spaces, so we'll just have to wait and see if and how that pans out. And I suppose you can guess my opinion on that.

Don't really understand what you are getting at with the light cones, but I have various objections to the statement

"Can the fabric of space-time be considered, to be 'embedded', in a higher-dimensional 'hyper-space' ?"

I would have to say no.

The energy of photons that cannot escape a black hole is not destroyed, it is added to the black hole.

The speed of light is c in all reference frames, so aphoton travels at c as it exits the event horizon .Unfortunately , by then it has expended all its energy climbing out of the steep gravitational well of the black hole, that its wavelength is red-shifted to infinity. ie zero energy, so nothing actually exits.

S Hawking has an idea similar to yours as an explanation for Hawking radiation. In this case one of the virtual particles that is injested by the event horizon, is actually considered to be travelling backwards in time as it travels up, out of the black hole, it is then scattered by the event horizon into a normal particle moving foreward in time by the event horizon, and continues on its way as Hawking radiation.

This however involves particles with mass not photons.

If we consider the Heisenberg Uncertainty Principle as it relates time and energy, we find that as the time increments get smaller ( more exact ), the allowed energy excursions become larger and larger. In effect, extremely large amounts of energy can be localised in an exceedingly small volume of space for an infinitesimal amount of time. I don't have time to do the math right now, but I believe this could be a limiting factor to infinitely subdividing time increments, and so, may imply a minimum limit.

Without getting into too much detail ( because I'd be in over my head ), the string vibration is just like any oscillation, the requency and amplitude determine the energy and the energy is related to the mass. The problem is that extremely small mass particles like neutrinos or electrons even, are predicted to have zero mass by the theory. And while this may be to a good approximation, it is definitely not accurate. The same is true of massive particles, the masses are only approximate or rounded off. Anyone having a more detailed understanding of string theory mass predictions is welcome to correct me or add to my simple explanation.

I first read about this problem with masses in a popularization ( Brian Green, not Elegant Universe, but his subsequent ), so I don't have a good understanding of it myself.

Sorry my mistake. I remembered a value of about 47GLY but assumed that to be a diameter, so I used a value of 23-24GLY for the radius. You guys are right it should be the higher value for observable universe radius.

I'm no expert in the use of light cones, but are they the right tool to use in this case ??

There is a relative acceleration and speed difference between our galaxy and a galaxy at the edge of our observable universe, but it is due to an expansion of the intervening space, not an actual acceleration or velocity. How does that affect their respective light cones ?

And what about galaxies that lie just outside the observable universe ? Relative to us, they are moving faster than c, how would you represent this with a light cone ?

You guys have drawn a lot of pretty pictures but you haven't proved what I said to be wrong. So I'll repeat...

Starting at a certain distance from us ( 23-24 billion light years comes to mind ) everything in the universe is receding from us at light speed or greater because the separation between our galaxies is growing at or faster than the speed of light. The light we would see from these galaxies is red-shifted to infinity ( infinite wavelength, zero frequency, ie no energy left ), so they are in effect invisible to us. This is what defines the observable universe that is causally connected, any galaxy receding at c or greater is causally disconnected and so has no effect on us.

Your premise that there are galaxies at intermediate distances which can be affected by the causally disconnected galaxies and then pass the effect on to us does not make sense because light speed is finite and the distances cumulative. They still add up to the same total distance and the intervening space still expands by the same amount.

There is a limit to the causally connected observable universe, and it is much smaller than the total universe.