IM Egdall

So-called spacetime curvature is the warping of space and time in the presence of matter (and energy). Imagine a place in outer space so far away from all stellar objects that gravity here is essentially zero. Here a clock runs at a certain rate. Now put this same clock in the neighborhood of a stellar object (say the Sun) and it runs slower (compared to clock in zero gravity). And the closer to the Sun, the slower the clock runs. This is time being warped by the mass/energy of the Sun. A ruler in zero gravity marks out a certain distance. Now put this ruler in the neighborhood of the Sun. If placed perpendicular to the Sun, it stretches compared to its length in zero gravity. The closer it gets to the Sun, the more it stretches. This is space being warped by the mass/energy of the Sun. Together this warping of time and space is called spacetime curvature. In the zero gravity location, there is no warping so no spacetime curvature. Here we say that spacetime is flat. And yes, spacetime gets more and more curved (more warping of space and time)) as you get closer to the Sun. The Sun produces a relatively small amount of time and space warp, so spacetime curvature is weak (as you put it) in our solar system. But it is not really flat. There is some curvature, some warping of space and time -- this is what causes the planets to orbit the Sun. Also the warping of space by the Sun affects the diameter of the Sun but not its circumference. So the ratio of the two (as measured from far away) does not equal Pi. If you are trying to compare curvatures, I think the best way to do it is to look at it from the zero gravity location. Start with no curvature there and see how it changes as you get closer to the stellar object (source of curvature).

OK, I'll take a wack at this commonly asked question - why speed of light squared in E = mc^^2? (Without doing the usual mathematical derivation ala Einstein): An object's energy of motion (kinetic energy) is equal to its mass times its velocity squared. This is the Newton physics formula, which works really well for speeds which are small compared to the speed of light. We can see this in a number of physical examples. Einstein discovered that a mass at rest has intrinsic energy- in fact it has the maximum energy it can have. Now tThe speed of light is the maximum speed -- nothing can go faster than the speed of light per Einstein. So the rest energy of an object is its mass times the maximum allowed velocity squared, which is mass the speed of light squared. I think this makes sense. Does it help?

I think Hawking is like Einstein; a pure theoretical physicist. Einstein generally did not work in a lab or do experiments himself. He just worked on his theories in his mind. Of course he also read the work of and talked to other scientists when he could. His method was usually to come up with a mental picture of what is happening, what he called a thought experiment. Then he tried to develop the core pricinples from this mental picture. Finally he tried to come up with the equations which modeled his ideas. This is no doubt a simplification but from what I have read, generally how he worked. Perhaps Hawking works in a similar way.

I don't think so. I've read that the motion of galaxies is actually pretty small. The expansion of the space between galaxies is a far greater effect.

No. All particles travel like waves, including photons.

No, not exactly. The inflationary model says that the universe expanded exponentially just moments after the big bang. It then setted down to a much slower uniform expansion. This uniform expansion is predicted by the theory of general relativity. Then in 1998 examination of supernova data said that this expansion has actually been speeding up for the past 5-7 billion years. No one knows exaclty what is causing this speeding up of the expansion of the universe; so it is called dark energy. In summary: Initlal exponential expansion (over a fraction of a second after big bang) - Inflation theory Subsequent uniform expansion (over billions of years from big bang) - Theory of general relativity Recent increase in the rate of expansion (last 5 - 7 billion years) - Dark energy

Spacetime is flat for the visible universe; that is the part we can see. Objects so far away that their light has not reached us yet are part of the unobservable universe. What the spacetime curvature for the entire universe (observable plus unobservable) is unknown. There is not a question of what the universe is expanding into. Per general relativity, the universe is expanding but it is not expanding into anything. There is nothing beyond the universe for it to expand into. Difficult to conprehend, I know, but this is the current understanding. There is no center of the universe. It looks the same (on a grand scale) no matter where you are located in it.

From what I've read, there are a number of interpretations of what exactly the wavefunction is and what makes it "collapse". I don't think there is a simple answer or even one which is the scientific concensus right now. The math of quantum mechanics works great but the physical interpretation of what it all means is still an argument amongst physicists. I did just read a new book on the subject for the non-expert that I really liked: How to Teach Physics to Your Dog by Chad Orzel. It's all about quantum mechanics and its various interpretations. The Dog stuff is pretty entertaining, and I thought the physics explanations were solid.

Einstein came up with a formula that works for the truck and the beam of light. It is that speed do not simply add or subtract as Newton thought. Take two speeds, the observer's speed is v. The thing the observer is looking at (whether a truck or beam of light or anything else) is w. The combined speed, W is: W = (v +w) / (1 + vw/c^^2) where c is the speed of light. So if a truck is traveling toward you at v= 10m/sec and you are running towards it at w = 1m/sec; then you do not see the truck moving towards you at W = 9m/sec. If you plug in these values for v and w into the formula above, you get a value of W which is very very slightly less than 9 m/sec. (My calculator doe not have anouhg decimal places to do the actual calculation). So the real answer is something like 8.999999999999 m/sec. And for the light beam, v = 300 million m/sec or c and w = 1m/sec. Then W = 300 million m/sec or c . So it all works out!

Two virtual particles (one matter and one anti-matter) appear out of the vacuum for an extremely brief amount of time, determinined by Heisenberg's Uncertainty Principle on energy and time. They collide and annihilate each other. There is significant emperical evidence for this (e.g Lamb shift). Hawking Radiation: The two virtual particles appear at the edge of a black hole event horizon. One of the particles is absorbed into the black hole. The other escapes as a real particle. The absorbed particle has negative energy; the emitted particle has positive energy. As a result, the black hole's mass is reduced by a tiny amount. Eventually, the black hole evaporates. There is no supporting evidence yet for this effect. See: http://en.wikipedia....wking_radiation

A theoretical physicist generates a theory in mathematical terms about how something in nature behaves. She/he makes specific detailed predictions with numbers on the results of certain experiments or observations. When a physicist (preferably someone else) conducts the actual experiment and comes up with measurements which give good agreement with the orignal prediction, then the theory is said to be supported experimentally. This is the process, sort of, but it does not capture the wonder, beauty, and majesty of great discoveries on how our universe works. That, I think, has more to do with the imagination and artistry of the human being(s) involved in the search.

From Freedman & Kaufmann, Universe, Freeman & Co., Sixth Edition, p. 392: " Hydrogen burning in the Sun usually takes place in three energy-releasing steps. (In the first step) two protons fuse to form a hydrogen isotope (nucleus) with one proton and one neutron, a nearly massless neutrino, and a positively charged electron (positron). This positron encounters an ordinary electron, annihilating both particles, and converting them into gamma ray photons." So at least some of the electrons in the Sun's core collide with positrons produced in the fusion process. Their resultant annihilation produces some of the gamma rays which eventually result in the lower energy photons emitted from the Sun's surface as sunlight.

Oy. I know it can be hard to use language to try and describe what is going on, but if there was no time, how could there have been a "before" time?

Objects contract with relative motion along the direction of motion. Perpendicular to the direction of motion, there is no contraction. In between the contraction is a function of I believe the cosine of the angle. The object contracts per the factor: Square root ( 1 - v^^2) where v is relative velocity as a percentage of the speed of light. So for an object which is not moving relative to you, v is zero. So the factor is one and you measure no contraction. If the object is moving at 87% the speed of light, v = 0.87. Here the factor calculates as 0.5. So you measure the object's length in the direction of motion contracted to half what it would be at rest.

As I understand it, virtual particles come in pairs - particle and antiparticle. They exist for a very brief amount of time then annihilate each other and dissapear. So there is no build up; no resultant imbalance of particles.

According to our current understanding (general relativity) there is no center of the universe. The typical analogy is the surface of a balloon. This surface represents our universe. And there is no center to this surface. Now imagine the balloon is expanding. An ant at a particular location on the balloon sees the rest of the balloon surface around it expanding. And any other ant in any other place also sees the rest of the balloon surface expanding from its point of view. So no matter where you are in our universe, you see the rest of the universe expanding from your point of view.

WOW!

Let me try to answer some of this. An atomic nucleus is made up of protons and neutrons. (Except hydrogen which has only a single proton.) Let's take a helium atom for example. It has two protons and two neutrons in its nucleus. Now each proton has positive electrical charge and is in turn made up of three quarks: up, up, down. Their electrical charge is +2/3, +2/3, and -1/3 respectively. So they add up to +1. Each neutron has zero electrical charge and is made up of three quarks: up, down, down. Their electrical charge is +2/3, -1/3, and -1/3. So they add up to 0. Negatively charged electrons are held inside atoms by the net electrical charge of the nucleus. No one know why quarks have electrical charges which come exactly in thirds of the electron charge. The quarks which are inside the nucleus make it different from space around it; which has no real quarks. However virtual quark pairs (and other particle pairs) do pop up out of the vacuum, but they exist for only a very very brief time before they annihilate each other. Yes a nucleus has a definite size and shape. This is really due to their fields. The quarks inside a proton are held together by what is called the strong nuclear force. The same is true for the quarks inside the neutron. And there is some residual of this force which is what holds protons and neutrons together inside the nucleus. I do not think there is a larger concentration of virtual particles (vacuum energy) inside a nucleus than outside. But I am not sure on this. A terrific site to learn all about the basics of atoms, nucleii, protons, neutrons, quarks and a lot more is The Particle Adventure. See link: http://www.particleadventure.org/

Ya, I should have added: To you in the rocket, time is running normally. Why? Because you are traveling in uniform motion (no change in speed or direction). So from your point of view, you and the rocket car are standing still. And you see me moving by you in the opposite direction. This also means that to you see my time running slower than yours. So I see my time running normally and your time running slower. But you see your time running normally and my time running slower. Who is correct? We both are. Time is relative. But say you in your rocket car decide to turn around and return to Earth. Now what? That turn around is key. Your rocket car had to accelerate (change in speed and direction) to turn around. So when you arrive back on Earth, it is you whose time has run slow (compared to me on Earth). Why? Because you experienced acceleration. I did not. (Do you have a headache yet?)

The universal speed of light has nothing to do with how substantial the speeding ship is. Light always travels at the same speed no matter what the speed of the ship. I sympathize with your "I wonder why everyone sees it going 'C' regardless of the traveler's direction or speed". It is a very hard concept to accept. But all kinds of tests, observations, experiments have shown that this is just how light behaves. It reminds me of Feynman's comment, which went something like: Nature doesn't care whether you believe her or not, this is how she behaves. Sure it violates our common sense, but we have to accept what measurements tell us. The reason why we all talk about frame of reference ad nausium is because this conception works! Einstein's great vision of how the world behaves is not accepted by scientists because it is so clever (which it is), but because it gives such accurate predictions.

Oh, I think I get what you are trying to tell me. Krauss is claiming there is a flaw in the old theory (general relativty); so it does not really predict black holes with event horizons as everyone had thought Is this the jist of it?

No. Everything makes sense. I need a more detailed description of the example you have in mind to explain this better. Are "they" two bodies moving relative to each other? And are they moving towards each other so that they intersect at some point in time?

I disagree. As I have said in earlier post, Michelson-Morley experiment failed to find the ether that was believed to be the medium for conducting EM radiation. But it said nothing one way or the other about Einstein's light postulate: the speed of light being constant in all inertial frames. The experiment was done in only one inertial frame (the Earth.) Well an approximately inertial frame. Anyway, the light source and the detectors of that light were at rest with respect to each other. So only one inertial frame. So not a test of Einstein's light postulate.

All this mixing of quantum phsyics and human thought leaves me cold. After all, we humans have only been around what a few hundred thousand years. And the universe is some 13.7 billion years old. What made things work before humans?

Huh? Please give me an example.