Questions and Answers about General Physics

1. IS THERE SUCH A THING AS "NON-MOTION" .... and if there is (and you were at a non-moving place) WHAT WOULD YOU SEE AROUND YOU???

  You'll always be moving with respect to something.  Even if you could somehow be unmoving yourself, stars and gas and dust have their own movements.

  However, if what you're asking is whether there is a special "average" motion of the universe, yes there is.  As the universe expands, at any given place there is a movement you could make such that you are as stationary as possible.  The way you could tell is a little tricky.  When the universe began in a Big Bang, it was hot and dense.  About 500,000 years after the Big Bang, the universe became mainly transparent to radiation, so we can see radiation from that time (this is called the cosmic background radiation).  It is from everywhere in the sky equally, because it happened at a *time*, not a specific *place* (sorry if that's confusing).  Have you heard of the Doppler shift?  If you hear a siren coming towards you the pitch is high; going away from you the pitch is low.  Similarly with light: moving towards it makes it seem higher energy (bluer), whereas moving away from it makes it seem lower energy (redder).

  So, if you aren't in the "rest" frame, but are moving one way or the other, part of the cosmic background seems hotter (bluer) than the other.  That's the case with us.  We are moving in one direction at about 600 kilometers per second.  So, there is a "best rest" frame, but we'd still see stuff moving.

Cole Miller

2. What your opinion is on the idea of you living in a glass bubble where time around you is going at 10000 years per second and you live forever.  In your opinion would you see around you in the universe in a period of 1000000000000000  years?

I'm not sure about the glass bubble :) :), but one could imagine living very near (but outside!) a black hole.  The strong warping of space and time would mean that although everything about you would seem normal to you, things from outside would appear to move really fast (i.e., people talking to you would be high-pitched and talk fast!). In such a situation you would see things going at an accelerated rate. You wouldn't appear to yourself to live any longer than normal, but if you were really close to the event horizon of a black hole you would be able to see stars evolve and die, things like that.

  Whether you could see all the way around the universe depends on whether the universe will expand forever or not.  If it will, then light can not make it all the way around the universe, so no.  If, on the other hand, the universe eventually stops expanding and begins to collapse, it would be possible to see around the universe.  We're not sure which of the fates our universe will go through, yet.

Cole Miller

3. I was wondering if there is a chance that something does travel faster than the speed of light? If there is, how would we detect something like that and what would it be like?

Nothing can travel faster than the speed of light in a vacuum (e.g. outer space). But that is not the end of the story! The speed of light is slightly slower when it passes through a denser medium such as water or air. This is what causes "refraction" or the bending of light rays (e.g. a straight drinking straw placed in a glass of water appears to be bent). This means that really fast particles can be traveling faster than the speed of light in, e.g., air or water, and still be traveling slower than the speed of light in a vacuum. So how could we detect such particles? Well, it turns out that if a particle is moving faster than the speed of light in a dense medium it creates what is known as "Cherenkov radiation", basically a shower or light -- a bit like the sonic boom you get when something travels faster than the speed of sound. This light can then be observed.

Andy Young

4. What is time?

To a physicist, time is not a concept but one of the four, fundamental measurable (that's important) quantities that describe all physical systems and processes. The other three are length, mass, and electric charge.  All the other quantities you may have heard of (weight, angular momentum, electric current, magnetic fields, energy, force....) are combinations of these four.

Time happens to be the one we can measure most precisely.  So precisely, in fact, that lengths are actually defined in terms of the time it takes light (in a vacuum) to travel that distance.  Even the quartz crystal in a cheap watch measures time more accurately (to a part in one million or thereabouts) than anyone can now measure masses.

I suspect your underlying question is really more like "why do we live in a 4-dimensional space time, and could there be other universes in which there are more or fewer than 3 space and 1 time dimension; could we or anybody life in such a universe?"  Physicists and astronomers have actually been thinking about these issues for many decades, perhaps more in the last few years. Of course, our way of "thinking" about something normally involves writing down equations and applying them to the problem we happen to be interested in.

This topic was discussed a good deal at a meeting in Cambridge (England) that I attended last year.  I will try to summarize some of the results (some are new, some not). a. if space has fewer than 3 extensive (meaning you can walk around in them) dimensions, you cannot have any kind of complex circuit, whether it is your blood stream, a pentium chip, or even just the connection of everybody's houses to electricity, water, and gas b. if space has more than 3 extensive dimensions, then forces like gravity and electromagnetism (forces derivable from a potential,  a physicist would say) do not result in any stable orbits.  Thus you could not have planets orbiting around stars, and probably not atoms made of electrons "orbiting" nuclei.

The latter objection does not apply if the extra space dimensions are "compactified" (that is, curled up so that neither you nor anything even as tiny as an atom can move around in them), and several modern approaches to trying to understand the particles and forces of physics involve this sort of higher-dimension space.  In one variant, gravity (and only gravity of the 4 forces) is allowed to leak a little tiny bit into a 4th or 5th spatial dimension, and this helps to explain both the current expansion of the universe and how the structures we see first begin to form soon after the expansion started.

C. if there is more than one time dimension, then there is no causality. I think this is even harder to imagine than the idea of being able to walk around in a 4th spatial dimension.  Events to do not occur in any order; no event can be associate with any other as cause or effect; change seems to have no meaning; and so forth.  Some science fiction writers have tried to explore this, not, I think, very successfully.  It is, anyhow, a safe bet that if there are space-times with 2 or more time-like dimensions, nothing in them is self aware.

I guess I need to provide a quick and dirty definition of time-like and space-like.  Within the framework of general relativity (which works very well for every context where we can test it), if two events are separated by a time-like interval, you can travel from one to another and be present at both.  If two events are separated by a space-like interval, you cannot get from one to the other before it is over.

For what it is worth, inside the horizon of a general relativistic black hole, the time and space coordinates switch signs, implying that you might be able to move freely in time, but can travel only one direction, at one speed, in space (toward the center of the black hole, in fact).

Anyhow, the bottom line is that time to a physicist, astronomer, cosmologist, etc. is not at all an abstract concept, but a very concrete quantity that we measure day in and day out, often with very great accuracy.

A final word about general relativity - it passes every test we have ever been able to throw at it, and must nevertheless still be wrong (because it is not a quantum mechanical theory and cannot be made into one).  Many people have tried to find more complete theories (that would act like GR in the contexts where we have already tested it, but would act like quantum theories in other contexts).  Extra dimensions, in either space or time or both are one of many directions people have looked for such more complete theories.  One of the important results is that two or more extensible time dimensions yield a non-causal (acausal) universe, and you would not want to live there.

Virginia Trimble

5. I'm finding it difficult to find laws of physics that support the theory that we can't go faster then the speed of light, which would go with my belief that it's not only possible but quite probable. I base this upon the fact that the root word in "relativity" is relative, meaning that the faster you travel away from an object the more apparent time relative to you and the object slows down. So if you were to go the speed of light the apparent time between yourself and the object would stop. This would also work inversely for the object you're heading towards.        That wasn't much of a question, but I would greatly appreciate any incites or correction to my understanding. Again I thank you for your time.

Actually, it's a very good question, and the answer that Einstein came up with generated a whole new branch of theoretical physics. Einstein wrote an excellent introduction to relativity, aimed at the general public with a high school education, back in 1920. The English translation is excellent and the book is still being published. What I'm going to summarize below comes directly from there. If you'd like to read it yourself - and I highly recommend this - the title is "Relativity: The Special and the General Theory, A Clear Explanation that Anyone Can Understand", by Albert Einstein, translated by R.W. Lawson, from Crown Publishers, Inc. (New York). So, here we go...

First, we need to get a few definitions out of the way: The law of inertia states that a body will remain at rest or continue in uniform, straight-line motion (that is, not speeding up, slowing down or rotating) unless it is subjected to an outside force.

1. In order to determine the state of motion of a body, you have to have some reference frame. (We use the fixed stars as a reference from for many things, for example.)  If you have a reference frame K, and bodies within that frame follow the law of inertia, then we call that a Galilean coordinate system.

2. If K is a Galilean coordinate system, and K' is a coordinate system which is moving in uniform, straight-line motion with respect to K, then K' is also a Galilean system (and the law of inertia holds).

3. The Principle of Relativity states that if K and K' are both Galilean coordinate systems, then all natural phenomena behave precisely the same in K as in K'.

With me so far?  OK, that last statement, the Principle of Relativity (I'll call it "PR" from now on to save typing), means that rules don't change just because you're moving. This has been demonstrated to be true many, many times, and good thing too. If relative motion affected the laws of physics, then you'd have to worry about things like where the Earth is in its orbit, or where you happen to be standing on it, before you could figure out things like velocity or acceleration.

Starting with these definitions and observations, Einstein began a thought exercise. He contemplated a long, straight rail line, and a rather long train traveling at a constant speed along that line. Someone standing on the ground beside the railway is in one Galilean frame of reference, K; while another person standing on the moving train is in another Galilean system, K'.  We know that physical laws must behave the same for both people. Here's where the fun begins.

Imagine the man on the ground observing the passenger in the train. The passenger is walking in the same direction as the train, also with a constant velocity. Classical mechanics states that in order to determine the velocity of the passenger with respect to the observer on the ground (call that velocity W), you merely add the velocity of the train, v, and the velocity of the passenger with respect to the train, w. That is:

            W = v + w

Seems simple, yes?  Well, there's a problem.  Light is a natural phenomenon. The speed of light in a vacuum is a constant 300,000 km/s (called 'c'). Many experiments have been done which demonstrate incontrovertibly that the speed of light does NOT depend on the speed of the body which emits that light. It is truly constant, regardless of relative motion.

[Side note: When a light-emitting body, like a star or galaxy, is moving very quickly either towards or away from us we see a change in the WAVELENGTH of the light that reaches us, but regardless of the color the light itself always travels at c.]

But if c is constant regardless of relative motion, what about the passenger on the train carrying a flashlight?  Obviously for the passenger the light leaving his flashlight travels at c. But - and this is the important part - the observer standing on the ground sees the light leaving the flashlight moving at c as well, NOT v + c, as classical mechanics would predict. So it looked to physicists like either the PR was invalid, or c was not constant.  But repeated experiments showed that both were, in fact, true. This is exactly the sort of conflict that keeps physicists up nights. Einstein's breakthrough was in realizing that there are some implicit assumptions in classical mechanics.  Specifically, classical mechanics assumes that both space (that is, the distance between two points attached to a rigid body) and time are invariant.  Einstein started with the two things that had been proved true by experiment (c and the PR), allowed the others to fall by the wayside, and followed the logic to see where it would lead.

He started by imagining three points on the stationary railway line: A and B, which are far away from each other, and C which lies halfway in between. At the point C we place our observer standing on the ground, and we have a second observer standing on the moving train. The standing observer sees lightning strike the rails at points A and B simultaneously, as the observer on the train also passes point C. Does the observer on the train also see simultaneous flashes?

In fact, he doesn't. Because the speed of light is finite and invariant, and because he is moving toward point B, he sees the flash from point B before the flash from A - so for him the events are NOT simultaneous, despite the fact that he passes point C at the same time that observer A sees simultaneous flashes.

Einstein used this simple thought exercise to demonstrate that both time and space are altered for the moving observer with respect to the standing one. The math involved is actually rather simple.  Here's the result:

In classical mechanics, coordinates in the K frame can be transformed into coordinates in the K' from using the Galilean transformation equations:

  x' = x-vt      z' = z

  y' = y         t' = t

These are the equations that lead to the velocity addition problem when c is invariant. Einstein found that by following the results of his logical argument, the transformation consistent with PR is actually the Lorenz transformation:

 x' = (x-vt)/sqrt(1-(v^2/c^2))        [ ^ = exponentiation ]

 y' = y

 z' = z

 t' = (t-(vx/c^2))/sqrt(1-(v^2/c^2))

 Note that when v is much, much smaller than c, you get the Galilean transformation equations as a good approximation. The accuracy of these equations has been demonstrated by experiments, most notably by Fizeau, who measured the speed of light in moving fluids (the speed of light through any particular medium is a physical invariant). The Lorenz transformations actually were developed by Lorenz in studying electrodynamics (light is an electromagnetic phenomenon) before Einstein started contemplating trains and lightning.

This just leaves one more step to the answer to your question. As you may know, the kinetic energy (that is, the energy of motion) of a mass 'm' is given by the equation: K.E. = (mv^2)/2.  But this equation is from classical mechanics.  By applying the Lorenz transformation equations we get the expression consistent with the principle of relativity:

            K.E. = (mc^2)/sqrt(1-(v^2/c^2))

Now we apply a little more logic:

 1. It is impossible for any single body to have infinite kinetic energy.

 2. In the K.E. equation above, the closer v gets to c, the closer the denominator gets to zero.

 3. If the denominator were ever to reach zero, then the mass would have infinite K.E., which is impossible (by #1).  Therefore, it is impossible for any body with non-zero mass to accelerate to the speed of light.

And there, finally, you have it. The equations of classical mechanics are very good approximations for most things on Earth, because very few macro- scopic experiments approach a significant fraction of the speed of light. The classical equations are simpler, so they're the ones you learn in high school and see in most science classes.  But once you do start to approach the speed of light, the old familiar equations like "F = ma" and "d = at^2+vt" are no longer accurate enough. That's when you start seeing relativistic effects, including the absolute speed limit: c. Hope I've managed to make sense. Good luck with finals!

-Anne Raugh

6. According to Einstein, anything that can travel the speed of light will have a doubled mass. If we were able to achieve the speed of light and somehow harness it's mass, couldn't we duplicate this mass and put it on either end of a black hole and be able to travel through its tunnel?

If you were to observe some object of mass traveling at some speed that is less than the speed of light, you would measure a mass that is larger than the mass you would measure if the object were simply sitting still on your table.  The greater the speed with which the object moves, the larger the mass you would measure for it.  If you looked at the equation that relates the mass to its speed, you would notice that if you plugged in the value of the speed of light for the object, you would obtain an infinite mass.   In a real-life experiment, however, this can't happen.  Think of Newton's second law which says that F=ma where F is the force acting on an object of mass m and a is the acceleration that the object undergoes as a result of that force.  In order to get my object of mass m to travel at faster and faster speeds, I must accelerate it.  But, if the mass m continues to increase so that the ma increases, the force F must increase as well.   Therefore, as my mass increases in speed, it increases in mass, and the force F must increase.  At some point it is no longer physically possible to provide a large enough force to continue to accelerate the object and the object is limited to a speed that is less than that of light.  The final part of your question is not clear to me.  I don't see how you are attempting to use this mass to travel through a black hole.  The extra mass that is generated when an object is moving fast is used in accelerators whereby subatomic particles are accelerated to large speeds and smashed into one another to study the properties of that extra mass.  If I haven't addressed your question fully, feel free to reformulate it.

David Garofalo

7. I was wondering what were to happen if an astronaut were to shoot a gun on the moon and the bullet were to travel through space without hitting anything what would happen to it?  Would it just continue to travel through space and if there is an end to the universe what would happen then?   Also, do we know that there is an end to the universe and if so how could that be possible?  What would be beyond that?

I am a graduate student in the astronomy department at the University of Maryland. An average bullet has a speed of .625 miles/sec - the escape velocity from the moon is almost 2.5 times that. The bullet would not escape the gravity of the moon. If you had a particularly powerful gun and the bullet escaped the gravity of the moon the bullet would not escape from the gravity of the sun (the escape velocity from the sun is about 26 mi/sec). The bullet you fired from the moon would end up orbiting the sun.

The size of the universe is not well defined but the universe does not have an edge the way that the surface of a balloon does not have an edge. One of the things that is difficult about studying the universe is that we can only see a small portion of it defined by the speed of light times the age of the universe. But the universe is larger than the portion we can observe.

Zoe Malka Leinhardt

8. Although we have talked about both Einstein's Theory of Relativity and time dilation, I don't quite understand how each works and how they relate to one another.  Would you please explain these theories?

Einstein actually published two "Theories of Relativity".  The first, published in 1905, was his Special Theory of Relativity which dealt with motion with regards to electricity, magnetism, and light.  In 1915, he released a General Theory of Relativity, which extended Special Relativity to deal with gravity.  I'm going to stick with Special Relativity, which is all that is needed to talk time dilation.

The idea behind relativity dates before Einstein came along. Essentially, relativity says that if you conduct an experiment on a rocket ship on the ground and the exact same experiment with the rocket ship moving in a straight line at a constant speed, the results you obtain will be exactly the same!  This also means that there is no experiment that can be done (in the rocket ship) that would tell a person whether the rocket ship is on the ground or moving.  In fact, if you are in one rocket ship and you see another one coming towards you, you won't be able to tell whether you're still and it's moving towards you, or it's still and you're moving towards it (or whether you're moving towards each other, etc etc).

Now one of the things about Einstein's Theory that makes it so revolutionary is that time (and distance) is no longer an absolute!  This is really a result from experiments that showed there is a "universal speed limit" (the speed of light)!  Nothing we know of can travel faster than it and nothing with mass can get to it.  Why does the speed of light being constant make a difference?  Suppose there is a flight of stairs and an escalator.  You can run 2 meters/sec down stairs, and the escalator is moving 2 meters/sec downwards.  Doing quick math, this means that if you use the escalator, you'll move at 4 meters/sec, right?  Well, not according to Einstein!

The problem is this ... if nothing can get to the speed of light, then suppose you have a rocket ship going half the speed of light, and decide to shine a light from inside the rocket ship.  Using conventional wisdom of just adding speeds together, someone from the ground would see the light moving at 1.5 times the speed of light!  But this contradicts what scientists have seen (ie - we can't get anything past the speed of light!).  So Einstein had to rework the conventional wisdom and figure out how to "add" speeds in such a way that no sum would ever be greater than the speed of light.

Now we get to time dilation.  Because Einstein needed to figure out how to "add" speeds together to keep the speed of light "speed limit", what he realized is that time and distance are not absolute.  If you're moving, time runs SLOWER (and your length gets SHORTER).  If you're on the ground with an atomic clock, and your friend hops on a space ship going near the speed of light with an identical atomic clock, when you friend gets back, the time on her clock will be SIGNIFICANTLY less than the time on your clock.

Of course, now you're thinking back about what we said about relativity ... you're on the ground, your friend is in the ship.  But thinking relativistically, how can we be sure that the ship is not still and the whole earth is moving??  If this is the case, why doesn't your clock run slow and your friend's run fast?  Doesn't this violate the whole idea of relativity?  Herein lies the catch - relativity holds once you are at a constant velocity, but someone needs to ACCELERATE to that constant velocity!  Whoever is doing the acceleration to get to the constant velocity is the one that has the slow clock (since relativity does NOT hold for accelerating objects).

Chul gwon

9. Asked about the time measurements used on Earth, and whether some kind of universal time measurement could be developed for use outside our solar system.

Our measurements of time are indeed based on solar system phenomenon. The basic unit of our time is the day, which is the time it takes for the Earth to rotate once on its axis.  Other measurements are the month, which is based on the lunar cycle, and the year, which is the time for one orbit of the Earth around the sun.  The reason we adopted these measures is because they are convenient for use in our every day lives.

Eventually, we will send spacemen to Mars, and when we do, they are likely to adopt a Martian day for their working schedule.  The Martian day is 40 minutes longer than the Earth day, and if they used an Earth clock, the sun would rise at a different time every day.  This would make it much more difficult to keep track of time than if they used a Mars day for their time measurement.  (In fact, the scientists working on the Mars rover mission are working on Martian time, so they go to work 40 minutes later each day, to stay synchronized with the Mars day.  This messes up their Earth days, but they arrive at work in time for sunrise on Mars every day.)

On Venus, the day is 243 Earth days, so it would not be practical to use the Venusian day as the time base.  In that case, they may still work on Earth time, simply because that is what the body is accustomed to.  Or they may use Mars time, or any other time system that they might find convenient.  Though it is likely to be around 24 hours, simply because that is what humans are used to.  (The Venus example ignores the fact that the temperatures on Venus are hot enough to melt lead, so people are not likely to land there any time soon.)

Someday, we might travel outside of our solar system, but right now we don't know what time measurements would make sense, because we have no measurements of extra-solar planet rotation.  Again, we would probably adopt something around 24 hours, if possible, but it may depend on circumstances.

In general, it makes some sense to adapt the time measurement to the local conditions if possible, and if it is not possible, then a system would be defined somehow, based on other considerations.  Someday, it might make sense to create a universal time system for use anywhere in the solar system (and beyond).  However, until there is a compelling reason to create this universal time system, we are likely to simply use whatever is convenient for a given situation.

Cole Miller

10. I would like to know if you think it will ever be possibly to accelerate something to a speed greater than that of light. I now that right now we probably can't get anywhere near C , but if we had better technology and a better understanding of the universe do you think it would be possible.

The simple answer is no: nothing with mass can ever achieve the speed of light, much less exceed it. When accelerating a massive object (even just an electron!) to relativistic speeds (i.e. >= 0.1c), relativistic effects start coming into play.  For example, the object would get shorter along its direction of motion, as well as heavier altogether.  This doesn't just appear to happen, it actually occurs as a byproduct of special relativity!  So to accelerate a massive object all the way to c, you'd need to apply an infinite amount of energy because it just keeps getting heavier and heavier as you approach c.

However, Einstein (and others) did find that the equations of general relativity allow, mathematically, for the existence of "wormholes."  These are like tunnels through the fabric of spacetime, or like connecting a black hole to a "white hole," where matter would get sucked in on one end and spit back out elsewhere.  Since a black hole effectively rips spacetime, one could theoretically find such a wormhole, enter it, and circumvent the need to travel at speeds less than c by reappearing somewhere else in our universe (or perhaps another!) at a distance greater than that which light could travel in that time.  Unfortunately the wormhole would only exist for an extremely short period of time, if such things physically exist, so the odds of sending something through are slim to none.  But who knows... perhaps future generations of cosmic explorers will find wormholes and discover ways of harnessing their abilities to make space travel much more efficient!

-Laura Brenneman,

11. A). It seems to me that even time should pass as light is traveling. How can time stop when light is still traveling a distance if time and space exist together?

B). If an object is traveling at the speed of light can it slow down? If it can, does that also imply that it can speed up and go faster than the speed of light?

A). What relativity tells you is that time passes slower when you travel faster compare to the time in a stationary system.  In your case, when you see the light travel in light speed, you see time passes as well; therefore, you conclude that time does not stop.  But what you see is YOUR TIME that doesn't slow down.  If someone can stand on a light beam and travel with it, you, as an observer from outside, would find him experience no time.

B). An object can be slowed down if you apply force to against its motion. An object can also speed up, but only up to the light speed. Relativity tells you the amount energy you need to speed things up increase when the speed approaches the light speed.  You will need infinite amount of energy to get objects very close the light speed.

Kimberly Nielson

12. We learned that if a clock is in motion in relation to our reference frame, then we perceive time for that clock to be moving more slowly than time is moving for us.  However, from the clock's point of view, we are moving.  Does it appear, from the clock's point of view, that time is passing more slowly for us then time is passing for it?  Is this a contradiction?  Can frames of reference really be compared in this way? Or is the problem in the way I am measuring time, is seconds (observed object) per seconds (perceived by observer)?

Relativity is always a challenge because it requires that you abandon "common-sense" concepts based on your everyday experience. Relativity is all about pushing physics to its limits, at which point the rules we're used to that govern the world around us break down.

In your particular example, you are correct: both observers will see time slow down for the other.  This is the nature of relativity -- all motion is relative.  The mutual time dilation is a direct consequence of Einstein's postulate that the speed of light is the same for all observers.

So although from one point of view, we (as the observer) appear to be in a stationary frame of reference, from the other (the clock) we appear to be moving.  This symmetry means there is no special (absolute) frame of reference.

Prof. Derek Richardson

13. While online with a friend about a year ago we got into an argument over his thesis statement. He was trying to tell me that it would be possible to create a room that was in two dimensions at once. And that anything in that room would have properties of both. I argued that any item in that kind of situation would be pulled completely into one of the dimensions.

It may be necessary to clarify what you're speaking about when you mention "dimensions".  In simple terms, a "coordinate" (such as x, y, z) each represent a "dimension".  So a piece of taut string would be a 1-dimensional object, since one coordinate is sufficient to describe all the points on the object (of course, we must neglect thickness of the string).  A piece of paper would be a 2-dimensional object, since we need x, y coordinates to define all the points on it _uniquely_.

I'm a little fuzzy on what you mean by "room", but I'm going to try to take a guess.  Physically, if we look at big objects and ignore really small scales (similar to ignoring the thickness of the string and calling it a 1-d object), we currently live in a 3-dimensional world (x, y, z).   You can also throw in time as a 4th dimension, but let's just worry about the spatial dimensions.  Current theories predict that there is an additional "extended" spatial dimension that is parallel to ours.   Putting this into an analogy, it would be as if you lived on a 2-d sheet of paper, and you were only permitted to look in the x, y directions (physical laws would insure that you couldn't cheat and look in the z direction).  Then right above that sheet, there was another sheet with people also only able to look at their x, y directions.  Above that, there would be an infinite number of sheets.  The extended 4th spatial dimension can be looked upon similarly ... parallel 3-d universes that cannot see each other because the physical laws do not currently allow it.  So my guess is that you're wondering if we can have some 3-dimensional space that can occupy two of these 3-d universes simultaneously.

To answer this, if you think about the whole idea of a dimension, it is to define _unique_ points in space.  Adding a dimension means that you need more information to describe each point in a specified space.  Since this is typically very difficult to picture in 3-dimensions, let's think about it first in 1-D and use that to develop intuition.  So if you start with a string, and lay another one next to it, each string can be defined with a single x-coordinate, but you now need another coordinate (a y-coordinate) to differentiate between string 1 and string 2.  So supposing you take a pen and draw a point on string 1, a mark is not going to suddenly appear on the string 2 because the two strings represent two unique 1-d objects.   Similarly in our 3-d space, if you construct a "room"  in our world, there's no reason that the same room will be constructed in the parallel 3-d space.

Where it becomes tricky is that in the above-mentioned theories, there are actual points where these parallel universes "touch".  To go into specifics about how or why this can occur is beyond my knowledge, but it is believed that things such as "wormholes" in our universe may indeed be points where our 3-d space "touches" points in another parallel 3-d space.   In this case, it is possible to have points that are common to both 3-d spaces.  So you can figuratively have a "room" in both spaces, but it's not really a macroscopic physical space.

There is one caveat to all of this, of course.  The ideas presented in the aforementioned theories are not fact.  They are still developing and while many assume they must be true, nothing has been proven experimentally yet (so it's still possible that it could all be a thought-experiment and none of it is true).  But in the framework of these theories, I believe this is what you were asking.  Let me know if I've misunderstood what you were getting at.

Chul Gwon

14. I figured out that if you manipulate the equation you form a derivative stating that the change in time of the observer with respect to the change in time of the moving object is the square root of the quantity one minus the velocity squared divided by the speed of light squared. The first question I have is if you were to integrate the equation what would you get and the second is what variable would you integrate.

The relation you are referring to is from the Special Theory of Relativity, which is for objects that are in inertial reference frames (constant velocity, no acceleration).  Since this is the case, all of the terms in the square root of your factor are constant (velocity must be constant between your reference frames, and the speed of light is a constant).  So if you're starting with the differential times of the observer and moving object, integration over the times will just tell you the relation between the time that passes for the observer and the time that passes for the moving object.

Also, important to note, the relation you've mentioned should say the "one over the square root of ...".  Moving clocks always run slow.  To develop an intuition about this, I would consider reading Chapter 1 of "Mr. Tompkins in Wonderland" by George Gamow.  Truly amazing book that allows you to develop some intuition about these concepts without the equations.  Once you have the intuition, it helps to remember which direction the gamma factor is supposed to go.

Chul Gwon

15. I understand that time is relative to the speed of light, but I don't understand how mass can become infinitely massive, yet infinitely light. (These are my words.) Mathematically, that becomes n/0, which is impossible. How exactly does that work?

To begin, I'm not sure what you mean when you say that "time is relative to the speed of light".  Time recorded on a clock depends on the state of motion of that clock and in this sense you can say that time is relative to the state of motion.  The way the rate of ticking of a clock depends on the state of motion is such that a measurement of the speed of light will give a value c (remember that to get a speed, you need to measure a time).  This value c is the value you would get if you measured the speed of light using another clock that runs differently from the previous one. In other words, Regardless of the different ways in which time runs on different clocks, all measurements of the speed of light give the same value.

Then you go on to say that "mass can become infinitely massive, yet infinitely light."  The only way I can make sense of what you are saying here is to assume you are referring to the fact that a massive object gets more massive as it speeds up, infinitely massive as it approaches the speed of light; this idea is then compared to the notion that anything moving at the speed of light must have zero mass such as light.  There is no incompatibility in these statements.  When you act on a massive object to speed it up, you must accelerate it.  By looking at Newton's second law,

                      F = ma

you see that the greater the mass 'm' becomes as the speed of the mass increases, the less the acceleration 'a' produced if the force 'F' is constant.  What you would find is that as the acceleration decreased; the mass 'm' would get closer and closer to a given speed 'v' which is less than the speed of light.  Therefore, the only way to get it to go faster would be to increase the force 'F'.  Now we can repeat the process above and we will find that with the new force applied, the object's mass increases further and the new acceleration will decrease from its starting value of F/m where 'm' is the mass of the object as it approached the speed 'v'.  We end up getting the same thing, namely an increase in the mass but approaching a new speed 'v_new' that is greater than 'v' but is still smaller than the speed of light.  In short, you would have to apply an infinite force to get the mass to reach the speed of light.  The impossibility of this is just the statement that no massive object can reach the speed of light because it would require applying an infinite force to an infinite mass.  Therefore, massive objects do not travel at the speed of light; only massless ones do.

David Garofalo

16. Why can't light go any faster than the speed of light when a flashlight is turned on inside a moving box-car?

The reason we are intuitively led to thinking that shining a beam of light on a moving train results in the beam going faster than a beam that is shined on the ground, is that we think of the motion of the beam with respect to what is referred to as absolute space.  The train is moving with respect to this absolute space and so the extra speed of the beam with respect to the train must be added to the speed of the train to get a greater speed with respect to absolute space.  Theorists deduced and experimentalists confirmed, that this background space with respect to which all motion can be identified, does not exist.  In short, the absence of this fixed background implies that speed, motion, and changes in general, is something that occurs between the objects themselves that are moving.  In what sense, then, are we to understand the notion of speed with respect to other objects and not with respect to a fixed background space?  The speed of something is just the ratio of a difference or change in distance and a difference or change in time.  But precisely because there is no notion of a fixed background space, this difference or change in space is not an absolute quantity.  The non-absolute character of this quantity makes it dependent on the state of motion of the person that measures this quantity.  It couldn't be any other way if we abandon the notion of a fixed absolute space with respect to which any difference or change in space is the same for everyone that measures this change in space.

Theorists have also deduced and experimentalists have also confirmed that time as well is not an absolute quantity.  The rate at which time flows is not the same for all clocks but it too, like a measurement of space, depends on the state of motion of the clock.  From the viewpoint of an absolute space and an absolute time, the speed of the light beam on the train can be measured to travel at the speed of the train plus the speed of the beam on the train.  Let's call this speed change in space/change in time.  But because the change in space and the change in time are not absolute quantities, you can imagine that there are people whose state of motion is such that the ratio change in space/change in time is not the same.  It is precisely because of the lack of an absolute space and an absolute time that the ratio of changes in space over changes in time for the motion of light, comes out to be the same regardless of the person doing the measurement.  In other words, the way in which space and time change as the speed of the observer changes, is such that the ratio of change in space over change in time for the motion of LIGHT gives the same answer for all observers.  When you consider the speed of some object that is moving on the train that is NOT light, as measured by the person that is on the ground, this quantity will be different than the speed measured by someone on the train but it still is not just a simple addition of the speed of the object on the train plus the speed of the train.

In fact, this is your question in part 2 so I answer it more completely in the next paragraph.  The fundamental point, then, is that measurements of space and time depend on the state of motion of the observer with respect to other observers, and all measurements of speed will differ from those of Newton's theory where space is a fixed absolute thing and time flows equally on all clocks.  One of the main difficulties in understanding these ideas is the fact that we have no mental image of something we call space that is not fixed, out there, independent of the point of view of the observer.

David Garofalo

17. If person A and person B were in an open box-car moving at 75 km/h and person A threw a ball to person B at 100 km/h, what would the speed of the ball register as if person C was standing on the ground outside the box-car with a radar gun?

If person A threw the ball in the same direction as the open box car is moving, you would you would calculate using Newton's theory that the ball would be traveling at 175 km/hour which is just the sum of the speed of the ball plus the speed of the box car.  If you did the calculation using relativity, you would get a value that is a bit less than 175 km/hour.  The speeds you used in this example are so small compared to the speed of light that both the Newtonian value and the relativistic value of the speed of the ball as measured by person C would be almost the same.  This is the reason why relativity was not discovered experimentally.  Let's imagine, instead, that the box car is traveling at half the speed of light and the ball is thrown at half the speed of light. Then the speed of the ball as measured by person C would be 2/3 of the speed of light.  The incorrect addition of speeds that you would use in Newtonian theory would give a speed measured by person C to be equal to the speed of light so there is a large difference in the two values. Finally let's imagine that the train was traveling at any speed you want between zero and the speed of light and the ball is thrown at the speed of light (i.e. it is actually a photon of light that is emitted from person A toward person B).  In this case the measured value as recorded by person C would be the speed of light.  All I did to get these results is to use the so-called Lorentz transformations that you probably have seen in your physics textbook for motion along the x-direction.  These transformations allow me to calculate speeds as measured by different observers for whom changes in space and time are different.

David Garofalo

18. Recently I read the Astronomy magazine about the SS 433 star that blueshifts and redshifts and the stars gas is time dilated it also says that the star also has a Doppler effect. Does this mean that Einstein’s theory of special relativity is correct?

Thanks for asking!  In a sense, it's really the other way around: because we know based on laboratory experiments that special relativity works to high precision, we can look at an object such as SS 433 and interpret what we see based on our understanding of special relativity. That is, when we see gobs of matter coming off in a certain way, or see the spectrum highly redshifted or blueshifted, we can use special relativity to figure out how fast it is moving, and in which direction.

There are cases in which one can use astronomical observations to try to understand basic physics.  For example, observations of the expanding universe have suggested that there is something called "dark energy" that wasn't suspected before, and people are trying to understand why this might exist.  Also, looking at black holes can tell us whether the extreme predictions of Einstein's *general* theory of relativity are correct.  I tend to think about such things in my research, because I think it's cool to go to the extreme!

Cole Miller

19. Is there evidence for more then 3 dimensions? If there is, how would that work in space?

As you know, we often consider time to be the fourth dimension, but I think you were asking about extra spatial dimensions.

People have suggested that there are others.  In particular, the leading candidate for a "unified theory" that explains all physics in a single context, is something called "superstring theory", and it does indeed suggest that there are other dimensions.  In the standard version of this idea those extra dimensions are all very small in extent (on the order of 10^{-34} centimeters!), but some people have proposed that some of those dimensions could be more extended, perhaps on the order of microns.

At this stage, these are only hypothetical ideas.  Mind you, they involve beautiful mathematics and have many aesthetically appealing qualities, but no *experimental* evidence exists for them.  In fact, these are challenging enough mathematically that it could be quite some time before predictions can be made that are comparable to experiments or observations.  Therefore, what I would say is that maybe there is "evidence" in the sense of these ideas being appealing, but there is no "evidence" in the usual sense of the word.  Still, though, it is fun and intellectually productive to pursue these concepts!

Cole Miller

20. A) what would happen to an object that travels faster than the speed of light?

Let's think about what happens to objects that travel at speeds slower than the speed of light first.  There are three things that are affected when an object starts moving: time, mass, and length.

The first effect is called time dilation.  A clock that is moving experiences time at a slower rate than a clock that is stationary. This effect has been measured by scientists.  In one experiment in 1975, a clock on an airplane flying around the Earth for 15 hours was compared to a clock on the ground.  The airplane clock was 6 billionths of a second slower than the clock on the ground.  That's because the airplane clock was moving.

The faster an object moves, the slower its clock runs.  If an object could move at the speed of light, its clock would seem to stop moving completely.  We've run into our first problem with traveling as fast as the speed of light: if an object could move that fast, time would slow down to a stop for it.  How could it get anywhere if it time isn't running to let it get there?

Time is not the only thing affected by moving.  An object in motion has slightly more mass than when it is at rest.  The faster an object moves, the larger its mass gets.  If the object could move at the speed of light, its mass would be infinite.  This is another way of understanding that moving as fast or faster than the speed of light is impossible.  How could any object have infinite mass?  That would be like having more mass in one object than there is in the whole rest of the universe.  Where would that mass come from?

The size of an object is also affected by motion.  The faster an object is moving, the shorter it seems to get.  An object that was moving at the speed of light would have no length at all.  Also, from the discussion above, it would have infinite mass.  How could we have any object with infinite mass in zero space?  Even a black hole has FINITE mass in zero space -- we can measure the masses of black holes by how their gravity affects nearby objects.

These ideas mean that traveling faster than the speed of light is impossible.  Because of that, we really can't answer the question of what happens to an object that moves faster than the speed of light. We also can't say whether or not we could see an object traveling faster than the speed of light, since it's not possible.


I may sound like a party pooper, saying that traveling faster than the speed of light is impossible.  While no object can travel at the speed of light or faster, there are some theoretical ways to take shortcuts. We have no way to test these kinds of theories yet, and they are pretty mind-boggling to try to understand.

One theory is that there are more physical dimensions than just our three dimensions of length, width, and depth.  If that were the case, we might be able to make a tunnel through another dimension and pop out some place really far away in just a short amount of time.  These other dimensions are sometimes called hyperspace.

Since it's hard to picture extra dimensions, here's an analogy to think about.  Suppose that you wanted to travel from Idaho to Australia.  Normally, you would have to take a plane and fly in a circle around the Earth to Australia.  That's a long plane ride!  It would be a much shorter trip if you could just travel through a tunnel through the center of the Earth -- a more direct route.

The theoretical idea of hyperspace is that we could travel through a tunnel in another dimension and in a short time travel somewhere that's light-years away.  However, this idea is still untested.  The laws of physics as we know them don't say it's impossible, but no experiments have yet shown that it is possible.

B)  How do we know that it's impossible to travel faster than the speed of light?

As I discussed in the previous question, scientists have measured the effects of time dilation, mass increase, and length contraction of objects that are moving quickly.  Just extrapolating those ideas to what would happen to an object moving at a speed of light gives good evidence that it's impossible.

However, a theory is not conclusive; it must be tested.  Scientists have tried to make sub-atomic particles travel at the speed of light. To do this, they use particle accelerators.  Particle accelerators accelerate sub-atomic particles to very high speeds.  The very first particle accelerators didn't have much trouble accelerating particles to 99% of the speed of light.  Scientists wanted to go even faster, of course.  Newer and better particle accelerators have been built. However, no matter how good the technology in the accelerator or how much energy is put into the acceleration, the particles have never been able to travel at the speed of light.  The closest they have gotten is about 99.99999% of the speed of light, and no faster. This makes sense:  by the time a particle is going at 99.99999% of the speed of light, its mass is almost infinite.  It would take an infinite amount of energy to push that particle a little harder to make it travel even faster.  We can't do it!

C)  Light travels differently in space than on Earth, so does it travel differently in other galaxies than here on Earth?

Light does in fact travel different in space than on Earth. That's because in space, light travels in a vacuum (areas with no matter in them), but on Earth light must travel through some type of material: air, water, glass, or other objects.

Light travels at different speeds in materials depending on their density.  The denser a material is, the slower light travels.  This is similar to how you might run along a beach and into the ocean:  you can run fast through the air when you're on the beach, but when you start running into the water, you have to slow down.

The fastest light can travel is when the material its traveling through has the lowest density.  That would be in a vacuum, where there's no material at all:  the density is zero!  The speed of light traveling through a vacuum is what we call "the speed of light", which is 2.9979245 x 10^8 m/s.  We usually round this to 3 x 10^8 m/s. What's the speed of light in other materials?       air:  99.97% of speed of light in vacuum       water:  75% of speed of light in vacuum       glass:  62% of speed of light in vacuum       diamond:  41% of speed of light in vacuum

Even in diamond, the speed of light is 41% of 3 x 10^8 m/s, which is 1.2 x 10^8 m/s, or 275 million miles per hour.  That's still really, really fast!

Consequently, we understand that the speed of light is different in different materials because of the density of the material.  There's nothing special about our galaxy that causes light to travel at a specific speed.  We expect light to travel at the same speed in a vacuum no matter where that vacuum is located.

Melissa Hayes-Gehrke

21. If there are 2 parallel dimensions is it possible that as a person you could enter into the other dimension without knowing that you have done so?  Or is that not a possibility because we could not enter into another dimension?

This is a tricky one, and the answer could be yes or no depending on what is meant.

First, consider the familiar situation of three dimensions in space. You always inhabit all three dimensions (you can't flatten yourself into a plane!).  Also note that there is no unique definition of which dimension is which: if you talk about "the first dimension", "the second dimension", and "the third dimension", people won't know what you mean because these could be any combination of up/down, left/right, and back/front.  Therefore, you can't say how much of any particular dimension you inhabit, just that you are three-dimensional. Said another way, you can't say that you have "entered" one dimension or another, because you always inhabit all three dimensions.

Now let's consider one interpretation that people have discussed. In this idea, rather than space being three-dimensional as we're used to, space has more dimensions (maybe ten total, maybe more). However, most of those dimensions are really tiny, as in far, far, smaller than even the size of a proton.  In this interpretation, you would already inhabit all of those extra dimensions, but you wouldn't be aware of it and it wouldn't have any impact, because the sizes are all tiny.  Therefore, in the same sense as above, you would say that you are ten-dimensional, and you can't "enter" any particular dimension because you always inhabit all ten dimensions.

However, since this is a frontier subject, people have suggested other ideas as well.  In particular, there has been discussion that rather that having continuous dimensions (where you can go from any point in space to any other point in space without leaving the space), you have separate "membranes", usually called just "branes".  Imagine having a number of sheets of paper, and ants that are forced to live on a single sheet.  For our purposes, the ants are living in a two dimensional world.  If the sheets of paper are far enough apart from each other, then ants can never go from one sheet to another. For practical purposes, then, the sheets represent separate universes to the ants.  If two sheets get really close to each other, though, the ants might notice some big changes to their universe.

The analogy in our case is that people have considered separate "branes" with extra dimensions that move around and mostly don't interact with each other.  Gravity is supposed to act from one brane to another but other forces can't make the jump.  When two branes get close to each other they can collide, and some people have suggested that this is what leads to an event like the Big Bang.  Hey, what can I tell you; this is frontier stuff and pretty speculative, but the researchers in this field obviously have a lot of fun!

Cole Miller

22. I have come to understand that time is not a single line going in one direction, but is in fact a branching off of sorts like a tree. Am i right in thinking that this is a theory in astronomy, and if it is, is it a popular one, or more of an abstract one? And also, does time branch off for every single possiblilty down to the smallest atom, such as there could be another one of me that is exactly the same except for a slight change in an atom of, say my hand?

Those are profound questions! I can think of two things you might be referring to, and both are definitely abstract ideas:

1. Consequences of an infinite universe

Max Tegmark had an article in Scientific American that talked about what might happen if the universe were infinite. He considers different categories, including universes with the same physical laws as ours, and universes with potentially totally different laws. There are some bizarre conclusions, such as that if the universe is infinite and all the laws are the same, there will be some other universe with someone exactly like you having lived exactly your life! There will also, as you say, be a universe where everything is exactly the same except for a tiny change.

2. The "many worlds" interpretation of quantum mechanics

In quantum mechanics, there are events that cannot be predicted at all, even in principle. For example, if you measure the position of an electron, you can't know it exactly; there will always be some uncertainty. This is confirmed experimentally. However, how should we interpret this? In the "many worlds" interpretation (which is possible but not favored by most people), every time there is a choice between possibilities, completely new universes are produced such that every possibility happens in at least one universe. In that sense, there is an extraordinarily large (but finite) number of universes, and new ones are being generated all the time.

How seriously should you take these? Not terribly. The point is that although these things are possible, in the sense that they do not violate experiments or observations, no experiments or observations support them either. To my mind, then, they fall into the realm of fun speculation but don't change my world view at the moment :).

Nice questions!

Cole Miller

23. The question I have is, why is light affected by gravity if it has no mass?

This is an excellent question. It actually leads to more fundamental questions such as "Does light have mass?", or "What is mass?"

Simply speaking, by "mass", we usually mean "rest mass". And by "light has no mass", we implicitly mean light has no "rest mass". On the other hand, light does have energy and momentum. The energy of light is characterized by its color, or its frequency/wavelength. The bluer the light is, the more energy it encapsulates in a unit of light (physicists call it "photon"). According to Einstein's famous formula E=mc^2, anything with mass has energy, and anything with energy has mass. In this sense, light does have mass, which is referred to as "relativistic mass", as oppose to "rest mass". It's then easy to understand why light is still affected by gravity from the point of view of traditional Newtonian concepts.

But Special Relativity (SR) has to speak now because Newtonian system is far from enough to understand the behavior of light. SR says that light has to travel at a constant speed in vacuum in any reference frame. So gravity affects light in a different way from how it affects ordinary things like you and me. It doesn't change the speed of light, but it either changes the direction of light, or changes the energy of light. When light goes away from a massive body such as a star or a black hole, its losses energy, and its color gets redder and redder. This is called gravitational redshift. The sunlight we see on the Earth is redder than it just comes out from the Sun, although the change is only a factor of two parts of a million.

So far we are trying to answer this question from a semi-traditional physics. The answer from a pure General Relativity (GR) point of view would be that everything has to travel along the shortest path in 4-dimentional space-time regardless of their mass (here I mean rest mass). This is why light is also affected because nothing in the space-time can survive. In an empty space where there is no gravity, the shortest path to go from one point to another (thinking about 4-D points with 3 space coordinates and 1 time coordinate) is to travel along a straight line at a constant speed, or stay rest. Gravity distorts space-time so that the shortest 4-D distance is no longer a straight line in the 3-D space we see, and the speed is no longer constant. This is what we see as, for example, free fall or ballistic trajectory. For light, the change of its direction under gravity also reflects the distortion of 3-D space, and the change of its color under gravity reflects the distortion of the time dimension.

Jianyang Li

24. In one of our recent lessons we talked about time travel. I find it a very interesting subject and i think i understand the basic concept of it. I understand that if you travel faster than light, you pass the light that has already hit you, therefore you see things that you have already seen. But, if you are traveling away from one light source, you are traveling towards another light source. I am curious if you would be traveling backward in time in one direction, and forward in time in the opposite direction.

Time travel is a tricky concept and fraught with so many conceptual difficulties that many people, including a number of very famous physicists, believe it is not possible, but let's take your question about time travel and think it through a bit.

First, it is not necessarily true that if you are "traveling" away from one light source you are traveling toward another. A simple counter example is to imagine that you are on the surface of a balloon, and the balloon is being inflated. If you look around you, everything is moving away and there isn't anything you are moving toward (in fact, you could get paranoid). I put "traveling" in quotes because the example with the balloon is not the sort of traveling that agrees with your everyday experience, but rather characteristic of the expansion of space itself. In much the same way, if you were to travel backward in time you aren't really traveling forward from anything.

Some people believe that if time travel is possible, it may only be possible to go forward in time, not in backward. One reason is called the Grandfather paradox. This is the notion that you can't travel backward in time because then you do something intentionally or unintentionally that might interfere with the birth of your father or mother (for example by killing your grandfather) and if you had done that, then you wouldn't exist in the future to come back and make sure you didn't happen. If you go forward in time, you don't have that paradox.

For another point of view, here is a reference to an interview with Carl Sagan about time travel. Dr. Sagan explains some of the issues surrounding time travel, including the grandfather paradox and the connection between time travel and traveling near the speed of light.

Best Regards,

-- Jeff Livas

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