IM Egdall

Here's what I think I undertstand: Newton's bucket: a bucket of water is made to spin. The water rises up at the edge of the bucket. Looking at it per general relativity (GR) from two frames of reference: (1) Ground reference frame - Bucket spins and makes water form concave surfrace. (2) Bucket reference frame - From bucket's point-of-view, it is stationary and rest of universe is spinning. But if bucket at rest, what makes the water surface concave? General relativity says: the rotation of the rest of the universe causes the water to become concave in case 2. This is due to frame dragging. Imagine a massive rotating object, a huge hollow sphere (a shell) with the water bucket at its center. Since the particles which make up the sphere are moving, and moving particles have momentum, which are a source of gravity per GR -- spacetime inside (and outside) the hollow sphere is dragged by this rotational motion. So the space inside the sphere starts spinning in the same direction. This in turn causes the water surface in the "stationary" bucket to form a concave shape. And calculations show that for a shell mass/energy on par with that contained in the universe, the frame dragging produces the same concave water surface as when the universe is stationary and the bucket is rotating. Here's what I don't understand: If there were no other mass/energy in the universe, per GR the water would still become concave. But In the bucket reference frame, it is at rest. With no mass/energy in the rest of the universe, there would be no frame-dragging effect. Right? So what makes the water become concave? What am I missing?

I disagree with Wikipedia here. The language of scientists is too imprecise to lend itself to strict definitions. The use of the terms "Law" and"Theory" are arbitrary. A scientific theory can be one with no compelling evidence to support it (like string theory) -- or one with volumes of evidence supporting it (like quantum theory or the theory of general relativity). Unfortunately, physicists use the same word "theory" for both cases. So what makes a "theory" a "law"? Again it is arbitrary. There is no meeting of physicists or committee of experts which decides to promote a theory to a law. It is just a matter of convention. Saying Newton's Law of Gravity is really no different than saying Newton's theory of gravity. And per Einstein's theory of gravity (general relativity), Newton's gravity theory is only an approximation for when 1) motions are small compared to the speed of light, and 2) gravity is "weak". (A stellar object whose escape velocity is small compared to the speed of light is considered a source of weak gravity.) So why do we call it Newton's Law of gravity? Just habit from our history.

I agree that time is not a subjective human phenomenon. But it is relative. How an observer measures how fast time passes on a clock depends on the observer's motion relative to that clock. The reason we agree on time's measurement in our everyday lives is because our everyday speeds relative to each other are such a small percentage of the speed of light. Light travels at about 670 million miles an hour in a vacuum. So even commercial airplane speeds (about 550 miles an hour relative to the Earth) are less than a millonth the speed of light. Einstein's formula on the rate of time's passage and relative motion is the so-called Lorentz factor or the square root of (1 - v^^2). Here v is relative velocity as a percentage of the speed of light. A v of a millionth the speed of light results in an extremely small factor for a change in the rate of time's passage. So we don't notice it. But it is real -- and measurable with ultra-high accuracy clocks. If in some future age, people regularly travel in spaceships at hundreds of millions of miles an hour, they would know from first-hand experience that time is relative.

To try and answer aimforthehead's original question, in relativity there are two effects on the passage of time. Let's use GPS satellites as a simplified example: Special relativity. Atomic clocks on board the satellites run slower than clocks on Earth by about 7 thousand nanoseconds per day. This is due to their motion relative to the Earth (time dilation). General relativity. Satellite atomic clocks run faster than Earth clocks by about 45 thousand nanoseconds per day. This is becuase they are further away from Earth -- the source of the gravity. (gravitational time dilation). Now 45 minus 7 is 38. This means that taken together, the two relativity effects produce a net gain of about 38 thousand nanoseconds per day in the timing of satellite clocks (compared to clocks on the ground). See link: http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

From what I have read, for a "flat" universe with a cosmological constant -- as long as dark energy continues to exist in the same amount in the future (a big assumption since we don't know what it is -- the universe will eventually expand to the point where all but the closest galaxies will recede from us faster than the speed of light, making them impossible to see. Then stars will eventualy run out of nuclear fuel and go dim. The universe will be filled with dead stars and cold planets. Random collisons will eventually drive many stars to lower galactic orbits. As they circle black holes at the galactic center, they will give off stronger and stronger gravitational waves. Over time this loss in energy will drive stars closer and closer to black holes, to be eventually absorbed. Galaxies will then consist of enormous black holes surrounded by dead stars. But there is hope (sort of). According to Stephen Hawking's theory, these black holes will eventually evaporate. In the final moments, they will become white holes "pumping new matter into the universe in unpredictable ways." So at least theoretically, our universe may continue to exist in some strange way. But, as others have said, predictions on the future of the universe are very much a work in progress and highly speculative at best. Quote: R. A. Freedman, W. J. Kaufmann III, Universe, 6th Edition, p. 661

Imagine a tiny ant on the surface of a big ball. To that ant, the very small part of the surface he can see looks pretty flat. On the surface of the huge Earth, we are like that ant. The Earth is round. It is just that up close on the surface, us tiny humans see only a very small part of it, so it appears pretty flat. If you could rise up into the air and look back at the Earth, you'd see more and more of it as you go up. It looks pretty flat at first. But as you go up higher and higher, you start to notice it curves. And even higher. you start to see it is really the shape of a ball. Keep searching and learning -- good luck.

I totally agree, especially with respect to string theory, which is highly speculative. No compelling evidence to date supports (or contradicts) it. I thought you were saying that inflation theory is also highly speculative. Perhaps I misunderstood.

I thought iinflation answered the Big Bang theory's horizon and flatness problem. And per Greene's book, its predictions agree with CMB anisotropy. I understand inflation theory is still "a work in progress," as Greene put it. But saying it is mere speculation seems a bit too strong here. And virtual particles also have supporting evidence like Lamb shift. Your thoughts please.

This is talking not about velocity through space but velocity through spacetime. This is called the 4-velocity because it is the velocity over three space and one time dimension. When you calculate this velocity, you find it always equals the speed of light c or 299,792,458 km/s. Motion through time only: Say you are sitting in a chair. You are at rest with respect to that chair. But time is going by. So in the chair reference frame, you are moving only through time. And in this frame of reference, time is going by as fast at it can. Why? There is no time dilation when you are at rest. Motion through time and space: When you move with respect to that chair, you are now moving though time and space. Time is going by and you are moving though space. But there is time dilation now. In fact, the faster you move though space, the slower your time runs (with respect to time in the chair reference frame). So time and space kind of balance out. The more through space the less though time. The net result is the same velocity though spacetime. Motion though space only: Now light travels at the speed of light c with respect to that chair reference frame. And at c, time dilation is maxed out. That is motion though time is zero. So a photon of light travels through space only. At what speed does a photon travel through space? At speed c. So actually, the whole thing balances for motion through spacetime. No motion through space means all motion through time (no time dilation). Some motion through space means less motion through time ( time dilation). All motion through space means no motion through time (max. time dilation). Since the space and time velocities balance out, they are all the same velocity through spacetime. And the velocity for motion though space only is the speed of light c. Therefore it is the same speed of light c for all motions through spacetime. So when you are sitting in that chair, with respect to the chair, you are going at the speed of light (though spacetime)! I think this is not easy to absorb at first, but I found that thinking about it over time, it helped me understand why all motion through spacetime is at the speed of light. (Edited for spelling)

Here's what Einstein said about the existence of space: "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.' REF: Einstein (1952). As cited in John Stachel, Einstein from "B" to "Z", p. 297.

Just posted a picture to my last blog. Thanks for the help!

I just read in Relativity for the Questioning Mind by Daniel Styer, 2011, p. 92 that "no electron at CERN has traveled as fast as or faster than light"(no surprise here). "The maximum speed achieved so far is 0.999 999 999 997 c."

Hmmm. If you could look at the world from the point-of-view of a photon, it is at rest and everything else is moving at the speed of light. Soooo . . . for time: to the photon, time is standing still. The Lorentz factor for time dilation is sqrt (1 - v^2/c^2). For v = c, the Lorentz factor equals zero! So, for example, the photon travels from the Sun to the Earth instantaneously -- actually it is at rest at the Sun and the Earth travels to it instantly. for space: to the photon, all distances are contracted to zero. (Same Lorentz factor is zero for length contraction.) So the photon at the Sun sees the distance to the Earth as zero. No time. No space. So I guess I don't see why your argument is just about time. But it is interesting. And didn't Einstein say something about if no matter/energy, then no time and space. (But even a no matter/energy universe can still have non-zero curvature (gravity). -- I need help here! And I think you can't consider something at the speed of light as a legitimate frame of reference because the reciprocal Lorentz factor is a divide by zero or infinity. The math blows up. Other thoughts, people?

I read in Brian Green's The Fabric of the Cosmos that inflation "created" the matter and energy particles that exist today. Per quantum mechanics, in "empty" space, virtual particles pop into existence in matter/ antimatter pairs. They then collide and annihilate each other. Per Greene, inflation just after the big bang expanded space at such a stupendous rate that it separated virtual particles before they could find each other and annihilate. Thus they became real particles. Did I get this right? Comments please.

Thanks for the earlier info. I'm getting better at this blogging stuff. Two more questions, please: How do I insert a picture from my computer to one of my existing blog articles? How do I add keywords, so my blog gets more hits?

YA, good point. I should have been more rigorous. I am assuming that everything inside the vehicle is at rest with respect to everything else inside the vehicle. So all things inside the vehicle are moving along with the vehicle at the same speed and in the same direction as the vehicle. So with this assumption, all things inside the vehicle are in the same frame. Oh, and I don't think of the wheels as "inside" the vehicle. In my mental construct, they are outside the vehicle in contact with the road.

It helps me to substitute "in a frame" to "inside a vehicle". So in a frame in uniform motion is inside a vehicle in uniform motion. In an accelerating frame is inside an accelerating vehicle. Inertial frames are frames in uniform motion. The tricky part is that, for uniform motion, any other "vehicle" moving at the same speed and in the same direction as the original vehicle is in the same inertial frame. All objects moving at that speed and direction are in that inertial frame. See if the following link helps: www.youtube.com/watch?v=ZSmz2XAjl1E

You gotta think on terms of relative motion. Say you are travelling at a constant speed of 87 percent the speed of light (and going in a constant direction) relative to me. So you are in what's called uniform motion, i.e. no change in speed or direction. But per Einstein's Principle of Relativity, from your point-of-view, you are at rest and I am moving at 87 percent the speed of light. So for a velocity v of 0.87, according to the Lorentz Factor, you observe my time running two times slower than yours. The Lorentz factor is the square root of (1 - v^2) where v is velocity as a fraction of the speed of light . Now what if you are in uniform motion at a v of 99.5 percent the speed of light relative to me? Then per the Lorentz factor, you see my time running ten times slower than your time. And if you go at 99.999 percent the speed of light, you see my time running 224 times slower than yours. So the closer your speed gets to the speed of light, the slower you see my time running. At the speed of light (v equals 1), the Lorentz factor is 0. So if you could travel at the speed of light, you would see my time running infinitely slower than yours. This can be interpreted as you seeing my time as STANDING STILL. But nothing with mass can travel at the speed of light. And the experts say that a reference frame traveling at the speed of light (like a photon) does not constitute a legitimate inertial (unifrom motion) reference frame -- I think because we have to divide by zero and get infinity. And, oh by the way, no matter what uniform speed you travel at relative to me, you observe your time running normally and my time running slower. AND I see my time running normally and your time running slower. Time is relative.

This net zero energy idea refers to a "flat" universe - that is one in which the overall spacetime curvature is zero. And yes, our observtions say the universe is "Flat". But this applies only to the so-called "observable universe', the part of the universe we can see. The observable universe is, to quote Wikipedia, "the galaxies and other matter that we can in principle observe from Earth in the present day, because light (or other signals) from those objects has had time to reach us since the beginning of the cosmological expansion." Is the rest of the universe we cannot see also "flat"? From what I read, this is a matter of debate amongst the experts. Comments?

Please give us more details on your question. In the meantime, I'll try to help. As I understand it, a reference frame refers to a co-ordinate system. Think of three long wooden pointers assembled so they are all perpendicular. They are all attached to a central point. One pointer points up, one points to the right, and one points towards you. This represents an x,y, z co-ordinate system for the three dimensions of space. Now let's put a clock at the center of this contraption. Now we have a space and time co-ordinate system. We can measure a location in space of an event relative to the center of this "co-ordinate system" in the three axes, x, y, and z. We can also measure the time duration from event to event using our clock (assuming this contraption is in uniform motion - no change in speed or direction - and there is no gravity). We can think of this as an "inertial" reference frame. Say you are in a car moving along a highway at 60 miles an hour going north. Your car is in uniform motion. You could imagine the above contraption inside your car. It represents an inertial reference frame because of its uniform motion. (And for all practical purposes, the gravitational field is uniform). Any change in speed and/or change in direction, is what physicists call acceleration. If your car accelerates, it no longer represents an inertial reference frame. It represents an accelerating reference frame. Imagine two cars moving at the same constant speed and in the same constant direction. They are in the same inertial reference frame. All objects moving at the same speed and in the same direction are in the same inertial frame But if we include gravity, the issue is more complicated. Say that you have two cars - one in Miami and one say in LA. Together they do not represent an inertial reference frame, even if they are going at the same speed and direction. Why? Because their respective gravitational fields are pointing in different directions. The gravity in both locations is approximately pointing towards the center of the Earth. If you visualize a globe, you'll see that the two gravity direction arrows are not parallel. So only locally, each car represents an inertial frame, but together globally the two cars do not. This is a bit of a simplification, but I hope it helps visualize "frames". Please let me know.

Ah, with all due respect, science doesn't work that way. You don't just propose some new theory and then say there is no evidence to say it is not possible. You have to propose a new theory and make specific new predictions. When these new predictions are shown to be correct by new experiments, measurements, observations --- then your new theory gets the attention of scientists. The burden of "proof" is on you to show the validity of your idea, not on the rest of us to show that it is impossible. marksmodernphysics.com

An object in uniform motion will stay in uniform motion, unless it is acted upon by an outside force. That is the Law of Inertia. The key here is uniform motion, where the speed of the object and the direction of the object do not change. So an inertial frame of reference is one that is in uniform motion. As soon as some outside force makes the object change speed and/or direction, it is no longer in uniform motion -- it is accelerating. (In physics, any change in speed or direction is defined as acceleration.) So once an object changes speed and/or direction, it is no longer in an inertial reference frame. Hope this helps.

I think Chris said it correctly. The only aspect of the laws of physics that tells us why the arrow of time in our universe is in the forward direction is the second law of thermodynamics. And the universe is evolving to higher and higher entropy. Wikipedia quote:"second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and explains the phenomenon of irreversibility in nature. The second law declares the impossibility of machines that generate usable energy from the abundant internal energy of nature by processes called perpetual motion of the second kind." I suggest reading Brian Greene's wonderful book, The Fabic of the Cosmos. It tells the entropy/arrow of time story in plain English.

If matter and anti-matter collide, they produce energy. LIke an electron colliding with an anti-electron (positron) -- they can annihilate each other and produce photon. But what about virtual particles (so-called vacuum energy)? Here a particle and its anti-particle appear spontaneously out of the the vacuum, annihilate each other, and dissappear. So why don't they produce energy (photons) like real particles? Because one of the virtual particles has positive energy and one has negative energy. So they cancel each other's energy out.

1. As timo said, all photons travel at the same speed in a vacuum; about 670 million miles per hour. 2. Photons are a form of energy, and per Einstein's E=mc^2, energy (such as a photon) has weight and produces a graviational field just like mass does. A photon is a massless particle. Its energy is proportional to its frequency (the higher the frequency the greater the energy). 3. Per modern physics, that is quantum mechanics, light (photons) behaves like a wave and like a particle.. So do electrons, quarks, neutrinos, atoms, and molecules! They all travel from place to place all spread out like a wave. We see this in the interference pattern they produce in a number of experiments, such as the famous double-slit experiment. But a photon, electron, etc. is detected in only a single location like a particle.