IM Egdall

Thank you for the explanation and links. So very close to time zero of the big bang, the time co-ordinate became a space co-ordinate. like inside a black hole, Thus per general relativity, there is no time "before" the big bang. However, since general relativity breaks down at time zero, there may be something more going on here. A quantum gravity theory may some day give us a more definitive answer. (Hope I got this right.)

Yes, I understand that general relativity breaks down at time zero. But when going backwards towards the big bang does time (per Hawking) become a 4th dimension of space? And how?

Per string theory, the space dimensions beyond the standard three are curled up so small that we are not aware of them. It's like a wire between two telephone poles. From far away, ithe wire looks like a line of one dimension. But up close, you can see that ithe wire has thickness; it's really cylindrical, so has other space dimensions.

Just read Hawking and Mllodinow's new book The Grand Design. Very interesting. Although I thought it was way too short, and didn't go into concepts in nearly enough detail. For example, it says that per general relativity: Due to the immense density of the very early universe and thus its stupendous spacetime curvature, time was a 4th dimension of space! As the universe expanded (and its density and spacetime curvature became less), tIme itself was formed out of this 4th space dimension . So based on this, there was no time before the big bang. Can anyone tell me something about how this works? I have read that inside a black hole, time and space switch roles due to the intense spacetime curavture, but this is the first time I've read about time becoming space in the very early universe. How?

An antiparticle has identical mass but opposite electric charge than its corresponding particle. For example: An electron has a charge of -1. Its corresponding anti-particle, called the positron, has an electric charge of +1. A proton, of electric charge +1, has a corresponding particle, the anti-proton of charge +1. The photon, with an electric charge of 0, is its own antiparticle. According to the big bang theory, just after the universe began, the extremely hot, dense cosmos was filled with equal amounts of matter and antimatter. But if for every particle there would have been a corresponding antiparticle; they would have eventually collided , resulting in the destruction of all matter and antimatter in the universe! Physicists theorize that there must have been a very slight excess of matter over antimatter immediately after the big bang. Based on rough estimates of the number of photons in the microwave background and the number of protons and neutrons in the universe today, scientists estimate that for every billion antiparticles, there must have been a billion plus one ordinary particles, leaving a single particle per billion to survive after annihilation. This single surviving ordinary particle per billion is what makes up our universe today. (The reason for this asymmetry is a subject of ongoing research.) When an electrically charged particle collides with its antiparticle, they annihilate each other, and give off energy. The mass of the initial particle pair is converted to energy in the process, via E=MC2. The reverse is also true; energy particles (given enough energy) can convert to mass particles. Both these processes are commonly seen today in particle accelerator experiments

Huh?

Regarding the photon, I think Einstein's light postulate is important to consider here. No matter what reference frame you choose, the photon is still traveling at the speed of light. In other words, no matter how fast you are going, the photon always goes at speed c (in a vacuum) with respect to you. Consider a reference frame traveling at c. Now look at a photon from this reference frame. It still sees that photon traveling at c! No matter what reference frame you chose, the photon is not stationary. So that it possesses a frequency/wavelength is not a contradiction. I believe a graviton also fits within Einstein's light postulate. I think anything traveling at speed c does. Thus no matter what refererence frame you chose, the graviton is always traveling at speed c with respect to you.

So it isn't that simple. You have to consider momenergy per the equation you give. And one would have to choose the apple at rest just before it begins falling as the frame of reference. So E=mc^2 applies for the apple in that r.f. But where to go from there? To figure this out, do we need Einstein's field equations? This would be way beyond my capabilities. Is there anyone out there who can help?

I just got Hawking's book, so I am interested in this discussion. I know that in Quantum Mechanics there is this vacuum energy I think its called. And according to the Uncertainty Principle, a particle and its anti-particle spontaneously rise up out of nothing; that is out of the vacuum of "empty" space, then annihilate each other, and disappear. One particle has positive energy and one has negative energy, so their annihilation results in a return to zero energy. The time of existence for these virtual particles is determined by their mass/energy by the Uncertainty Principle, where the uncertainty in mass/energy times the uncertainty in time is always greater than or equal to Planck's constant divided by 4 Pi c^2. That's why they exist for such very short time periods. So what does this have to do with M-theory and gravity? Does anyone out there know if the rise of virtual particles out of empty space is the basis for Hawking's creation of universes. And again, where does gravity come in, as proposed by M-theory?

Good question! I looked up the reference again (Nigel Caulder, Einstein's Universe, p. 82-83.) and it says: "Atoms, atomic clocks and light all vibrate slowly in regions of stronger gravity. Because of the link between energy and frequency, they possess less energy than they would in space, a long way from the source of gravity. An apple consists of atoms and possesses less energy when lying on the ground than it has when on the tree. Its rest-energy, in the sense of Einstein's equation E = mc^2 is reduced." Caulder points out that the quantity which remains unchanged in general relativity is actually "the scalar product of the tangent vector with the Killing vector". So I took E=mc^2 and tried to apply it to your question. Let E be the rest energy Rearranging E=mc^2, we get m = E/c^2. As you note, the change in energy near the earth's surface is mgh So substituting gives mgh = E/c^2 gh = Egh / c^2 As you also note, the slowing of time near the earth's surface is this same gh/c^2 factor. Is it this simple?

I find the explanation in Nigel Caulder's book, Einstein's Universe helpful in explaining how general relativity works. Maybe it is a simplification, but I think it gives a real feeling for the concept. Take an apple falling towards the surface of the Earth for example. The Earth's mass/energy causes the space around it to stretch (iin the radial direction). And this stretching gets greater and greater as the apple approaches the ground. The apple just released from a tree moves in the direct of stretching space. Now the Earth's mass/energy also affects time. It makes time run slower and slower as the apple approaches the ground. This means that (from the point of view or reference frame of a far away observer) a clock will run slower and slower the closer it gets to the Earth. So as the apple moves ,all its atoms and molecules slow down more and more. To make up for this reduced internal energy of motion, the apple accelerates. In other words, it goes faster and faster towards the ground so its overall energy of motion makes up for this reduced internal energy of motion. In this way, the law of energy conservation is maintained. In summary: - an apple falls towards the ground (rather than upward or sideways or in other direction) because of the stretching of space as it approaches the ground; and - the apple accelerates as it moves downward due to the slowing of time and to obey conservation of energy.

The big bang, if it were visible, would be both behind and in front of this galaxy. As I understand it, cosmological models tell us that the big bang is not at a specific location. It occurred here, there and everywhere in the universe. Wild, huh! Think of the expanding balloon analogy. The SURFACE of the balloon represents our universe. So where is the center of this surface? There is no center.

I find the following link helpful in trying to understand the relationship between the age of the universe and the "visible" universe we can see. I think it relates to the discussion: http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN

See if this helps. As I understand it, per quantum field theory, a particle (photon, electron,etc.) spreads out as it travels from place to place like a wave; but is detected only in a single location like a particle. What does the traveling? The so-called wave function; which represents the probability of finding the particle at a certain place and time. So in the double-slit experiment, a single particle's wave function goes through both slits! This causes interference. But the electron shows up (is detected) at only one location on the photographic film. (This is called the collapse of the wave function). Repeating with many particles, we see the interference pattern on the film. Take a look at the following animation: http://phet.colorado...ve-interference

I don't think the last statement is quite correct. Einstein's original 1905 field equations of general relativty predict that a universe with matter/energy could not be static. In other words, the universe had to be expanding or contracting. But prevaliing belief was that the universe is static. So he added a fudge factor, his cosmological constant, in 1907 to model a static universe. In the 1920's, Hubble discovered the existence of other galaxies and that in general the further away they are, the more they are red-shifted. And Lemaitre and Friedmann independently modeled the expansion of the universe using Einstein's original equations ( no cosmological constant). But per these models, all very distant objects are not moving away from us; it is space itself between galaxies which is expanding. And also please note that there is no "dark energy" in these models of our universe. In 1998 physicists discovered that this expansion of space is accelerating! The term "dark energy" is used to account for the unknown cause of this acceleration. It is modeled by adding back a cosmological constant into Einstein's equations. So Einstein's original equations predict the expansion of the universe. An added dark energy term is needed to model the observed acceleration of this expansion.

Excellent point. So the change in motion of the box due to emission of the photon would affect the determination of time. I think that's it. Thanks.

I find that the most understandable explanation of what goes on in the various frames of reference in the twins paradox is to consider the effects of time dilation and the Dopper Effect. I suggest you look at the link below. My link and click on: Its Relative Archives The Twins Paradox (Sorry but a direct link is having problems for some reason) Hope this helps.

In 1930, Einstein made a famous argument against Heisenberg's Uncertainty Principle. Imagine a box with a photon inside and an opening covered by a shutter. When a timer attached to a clock activates the shutter, the photon escapes from the box. So we could in principle acurately time when the photon is emitted from the box. Now this box is also suspended by a spring so that we can weigh the box before and after the photon is emitted. So, Einstein supposedly argued, we can determine the mass difference in the box. And by E=mc2 the energy of the photon. So we now know both the time of photon emission and the photon's energy to arbitrary accuracy. But this is a violation of Heisenberg's Uncertainty Principle. Bohr came up with a counter-argument. When the photon is emitted, the change in mass of the box causes it to rise on its springs. But due to gravitational time dilation, time runs a tiny bit faster at this higher altitude. Bohr calculated that this induces just the uncertainty in the clock's rate to satisfy the Uncertainty Principle. Borh and Quantum Mechanics wins! A diagram of this is in: http://en.wikipedia....instein_debates (under Second Debate). So here's my question. What if we conduct this thought experiment in outer space so far from any stellar objects that gravity is effectively zero? Here we use an Inertial Balance to measure the mass of the photon box before and after the photon is emitted. An Inertial Balance has the photon box suspended between two springs attached to fixed walls. You push the box to one side and let it go. It will then oscillate back and forth between the two springs. The frequency of oscillation of the box is a function of the spring constants and the mass of the box. See attachment: Inertial Balance Figure.ppt (The same concept is used to measure the mass of astronauts in space) The difference in frequency of oscillation of the box before and after the photon is emitted gives us the change in mass of the box and hence the photon's energy. And since there is no gravity (spacetime curvature), there is no gravitational time dilation effect. Thus now the time of emission of the photon as recorded on the clock is known to arbitrary accuracy. So we now know both the photon's energy and time of emission to arbitrary accuracy; violating the Uncertainty Principle! What is wrong with this argument? Perhaps there is no exactly zero gravity location at the Planck level. Or perhaps the Inertial Balance and its supports themselves provide a source of gravity? Do virtual particles have an effect? I'd like to hear any thoughts on this idea.

Real basic stuff on quantum mechanics, general relativity, and string theory (hope it helps): What is now called the "Standard Theory" of quantum mechanics describes the behavior of all known phenomena in our universe, with one exception; gravity. Quantum electroweak theory covers the electromagnetic force and the weak force. Quantum chromodynamics covers the nuclear (strong) force. The odd man out is gravity. However, modern attempts at a unified theory which includes the three quantum forces and gravity have proven most formidable. The predictions of general relativity, like all classical physics theories, are "deterministic'. This means that if we know a particle's current location (where it is) and its velocity (where it is headed and at what speed); we can determine exactly where it will be at any time in the future (assuming no outside influences). And in principle, we can do this to arbitrary accuracy. But the Uncertainty Principle of quantum mechanics tells us that we cannot know a single particle's position and velocity to arbitrary accuracy. Per the Uncertainty Principle, the more accurately we know a particle's position, the less accurately we can know its velocity (momentum). And vice-versa! The "Holy Grail" of theoretical physics research today is the unification of quantum mechanics and general relativity under a single construct; termed "quantum gravity." There are a number of approaches; string or M-theory is the most active. Some of the major predictions of string theory include: 1) the overall universe of universes (the "bulk") is made up of 11 dimensions, 10 spatial and 1 time. 2) Our local universe is a "3-brane". There are other branes of various dimensions. 3) All fundamental particles are 1-branes or strings of a finite one-dimensional size: 10-33 cm. (In quantum mechanics, fundamental particles like quarks are modeled as points having zero dimensions, so they are infinitely small.) The finite size of the string model puts a limit on quantum jitters (vacuum fluctuations), a key to incorporation of relativity spacetime considerations. 4) For every known quantum mechanics standard model particle, there is a new corresponding supersymmetric particle or "sparticle" which has a spin that is different by ½ unit. 5) The four forces of nature (electromagnetic, strong nuclear, weak nuclear, and gravity) are all the same force. Moments after the big bang, as the universe cooled and expanded this force split off in stages into the four separate forces. 6) All matter and force particles except gravitons are open strings. Endpoints of these open strings stick to branes, like the 3-brane of our universe. Thus they are trapped within certain regions. 7) Gravitons are closed strings. Thus they are free to roam throughout our 3-brane universe, and free to leave it! Gravitons leak into other branes and the bulk. This explains why gravity appears weaker that the other three force. 8) The Cyclic Cosmological Model - We are living within a three-brane that collides with a nearby parallel 3-brane every few trillion years (in higher dimensional space). The "bang" from this collision initiates each new cosmological cycle. (Ref: B. Greene, The Elegant Universe, Part IV) Science fiction or science fact? Nobody knows. Now some 40 years old; string theory is still very much a work in progress. Since its beginnings in the 1970's, literally thousands of physicists have worked on it. There has been great progress, especially in the mathematics; yet no single definitive version of string theory has emerged.

Thanks for your clear explanation. I see your point that flat curvature is still curvature. But, boy, the way Einstein states it can be misleading.

You are on to something here. In spacetime physics, mass, energy, and momentum are combined into a single four-dimensional vector called "momenergy". Since this vector is in spacetime, it has a time component, and three space components. Energy is the time component, and momentum is the space component (actually three space momentum components for x, y, and z). And mass is the magnitude of this 4-vector. The magnitude or mass is given by: Mass2 = energy2 - momentum2 And the beauty of this construcnt is that the mass is invariant with uniform motion (just like the spacetime interval). So the energy component and momentum component of the momenergy vector change with relative motion, but the mass stays the same. This means that if you are moving with respect to me, you measure a different value for the energy and momntum of a certain paticle than I do. But we both measure the same mass for the particle. For example, if we choose a new reference frame where the particle’s motion through space is increased, then the particle’s energy will increase due to more energy of motion. The particle’s momentum will increase as well. But the difference between the squares of the energy and momentum will remain the same as in the original frame of reference. The square root of this difference is the particle’s mass. An excellent description of momenergy is given in Spacetime Physics by Taylor and Wheeler. It is a wonderful book, and you don't need a PhD in physics to understand it.

Thanks for your insights. I understand (or think I do) the dynamic nature of spacetime. However, I still have an issue. You say a solution to Einstein's equations are possible with a universe empty of matter and energy. I don't doubt you. But I am still wrestling with Einstein's words: On the basis of the general theory of relativity . . . space as opposed to 'what fills space' . . . has no separate existence . . . If we imagine the gravitational field, i.e. the functions gab to be removed, there does not remain a (flat) space, but absolutely nothing . . . there is no such thing as an empty space, i.e. a space without a (gravitational) field. If there is no matter/energy, then there is no gravitional field. And according to what Einstein is saying here, then there is no space. Your thoughts?

I realize that some new theory of quantum gravity may give us a new way of looking at "before" the big bang. But for now, we have to use the theory validated by empirical evidence; general relativity. I base "no matter/energy means no spacetime" on general relativity and the words of physicist John Stachel as well as Einstein. I believe I am correct. Please let me know what you think. Spacetime does not claim existence on its own, but only as a structural quality of the (gravitational) field. - Albert Einstein The Ricci Tensor and the Ricci scalar depend only on the Metric Tensor (in a complicated, non-linear way). So you can write the left-side of Einstein's field equations totally in terms of the Metric tensor. Thus spacetime curvature and how it changes is solely represented by the Metric Tensor. The Metric Tensor serves two functions; the ten g's represent both the gravitational field, and the underlying spacetime co-ordinates.[ii] Einstein realized that since the ten g's determine the underlying spacetime background, the so-called "metrical structure" of spacetime; then if there are no mass/energies, then there is no metric and there is no spacetime! In Einstein construct, the gravitational field "must be determined before the points of spacetime (events) have any physical properties! In more formal language "the points of the spacetime manifold," writes Stachel, "only derive their physical individuation from the metric (gravitational) field,"[iv] This means you can't just start with a flat spacetime, then add the matter and energy and see how spacetime curves. There is no spacetime; no spacetime co-ordinates, no metric before you add the matter and energy.[v] On the basis of the general theory of relativity . . . space as opposed to 'what fills space' . . . has no separate existence . . . If we imagine the gravitational field, i.e. the functions gab to be removed, there does not remain a (flat) space, but absolutely nothing . . . there is no such thing as an empty space, i.e. a space without a (gravitational) field. - Albert Einstein[viii] (i) Einstein (1952). As cited in John Stachel, Einstein from 'B' to 'Z', p. 297. [ii] Stachel, p. 294. [iii] Stachel, p. 297-298. [iv] Stachel, p. 304. [v] ""In non-generally covariant theories, the structure of spacetime is given a priori." writes Stachel. "But in the generally covariant theory of general relativity, the gravitational field (i.e. the presence of mass/energy) produces the structure of spacetime." Thus spacetime events are defined with respect to a unique gravitational field. If there is no mass/energy, gravitational field; then there are no events! Stachel, p. 297 [vi] Stachel, p. 295-296. [vii] As cited in Stachel, p. 297. [viii] Einstein (1952). As cited in Stachel p. 297.<BR clear=all>

In addition to giving us a remarkably accurate model of gravity, Einstein's field equations provide an equally remarkable insight into the very existence of space and time. Per his gravitational field equations, if you remove all the matter and energy from the universe, you are left with no space, no time, no spacetime, no events in spacetime. You are left with nothing at all! This has a deep meaning in the Big Bang theory. Per the theory, space and time in our universe began at the moment of the Big Bang. Thus before the Big Bang, before the existence of matter and energy, there was no space and no time. So under this construct, it makes no sense to ask what happened before the Big Bang; there was no "before" before the big bang!

To me the key is "prediction." A true prediction is one which says that if you do a certain test or observation that has never been done before, you will get a specifc value for a certain measurement. The big bang theory is generally accepted by physicists as the best theory of the creation and evolution of the universe because of all its successful predictions. For example the big bang theory predicted the existence and temperature of the cosmic microwave background many years before its discovery. Yes, the big bang theory tells us nothing about time zero itself, or what "caused" the big bang in the first place. But any new theory which claims to do so must make predictions that can be tested. Without these predictions and the future evidence if their validity, the theory has no supporting evidence. The thing that bothers me about a religious theory trying to explain the "cause" of the big bang is that it doesn't even try to make any predictions that can be used test that theory. So how can we know scientifically if it has any merit? A person can believe his/her religious point of view based on faith, but please don't call it science.