# National Aeronautics and Space Administration

## Library of Past Questions

Space-Time

### Can you recommend web sites that discuss space time? (Submitted January 06, 1997)

The Question

My daughter needs URL pointers to help her understand the subject of space time. Are you able to recommend any? Thanks!

Spacetime is a fascinating topic to physicists and astronomers. It all began in 1905 when Albert Einstein published the Special Theory of Relativity, which showed that space and time are both altered near the speed of light. To an observer, distances (space) appear to contract and clocks tick more slowly. Later, Einstein revolutionized the way we think of gravity. General Relativity states that gravity arises when mass warps spacetime; it's not a force acting at a distance.

The spacetime around massive compact objects like neutron stars and black holes is so warped that surprising distortions occur. A couple of examples are available on the World Wide Web. Try:

I think these links will be a good start for you and and your daughter.

Have fun,
for Imagine the Universe!

Question ID: 970106d

### Have General Relativity and Special Relativity been proven? (Submitted March 27, 1998)

The Question

I would like to know if it is true, that the theory of relativity has been proven by some scientists, who made satellite experiments?

What was there discovery and how did they prove it?

This topic is fairly broad, so let me try to narrow it a little. "Relativity" is a rather general term that encompasses both special and general relativity. The former encompasses effects such as the changes in physical properties of objects with speeds approaching that of light, whereas the latter includes effects having to do with the bending of "spacetime" by massive bodies. There is no one experiment which "proves" relativity, and yet so many experiments have provided consistency with the "theories", that most scientists accept them as being extremely accurate in their descriptions of reality.

"Special Relativity": The strongest direct evidence comes probably from particle accelerators, in which subatomic particles such as electrons and positrons are accelerated to within a few inches per second of the speed of light. We can observe very clearly and accurately the changes in, for instance, the apparent masses of the particles. They are observed to increase dramatically, and in fact new and much heavier particles can be created by making counter-rotating beams of, say, electrons and positrons, collide head-on with each other. Special relativity has played a key role in the design and operation of particle accelerators for many decades.

"General Relativity": There have been a variety of experiments over the years which have supported general relativity in ever more detail. I would say the culmination was the awarding of the 1993 Nobel Prize in Physics to Russell Hulse and Joe Taylor for the discovery of the binary pulsar 1913+16. This binary star system consists of two neutron stars which are orbiting about their common center of mass about every 7.75 hrs. Over time, they are spiraling in toward each other, due to loss of energy via "gravitational radiation" - a prediction of general relativity. Other general relativistic effects are observed, such as the "precession of the periastron". That is to say, the stars are in elliptical orbits, and the "long direction" of each ellipse is precessing with respect to a distant observer. This effect is about 4 degrees per year. (In comparison, for Mercury going around the Sun, it is about 44 seconds of arc per century.)

There are a host of other experiments which confirm different aspects of both special and general relativity. I view those just mentioned as among the strongest examples.

J.K. Cannizzo

Question ID: 980327b

### What evidence is there that supports the theory of curved space? (Submitted June 10, 1997)

The Question

What evidence is there that supports the theory of curved space? What does General Relativity predict about the shape of space-time near a large mass (eg, a star)?

There has been experimental evidence for the curvature of spacetime by a massive object since the early part of this century (1922), when observers set out to test the predictions of general relativity. During a solar eclipse, they realized, the light from stars in the same general area of the sky as the Sun are visible during the day. If light from these stars is affected by the curvature of spacetime due to the Sun's mass, then this would be measurable as a deflection (or a change in location) of the star's position on the sky. The stars closer to the position of the Sun in the sky would suffer a larger deflection; in general the deflection would be proportion to the stars distance from the Sun's location on the sky. This effect was observed for 15 stars during the solar eclipse of 1922 in Western Australia, and was interpreted as observational verification of the predictions of general relativity. General relativity predicts that spherical masses deform spacetime in much the same way a lead ball would deform the surface of a rubber sheet. It is this deformation that causes the planets to orbit the Sun, and the Moon to orbit the Earth. In fact, all orbital motion is the result of bodies being affected by the curvature of the spacetime in which they move.

Since that time, astronomers have observed other instances of the curvature of spacetime near massive objects. One example is the deflection of radio waves from quasars which are occulted by the Sun every year (such as 3C 279). Another is the growing collection of gravitational lenses. A gravitational lens occurs when the light from a very distant object (often a quasar) is bent by a closer massive object (such as a galaxy) into *multiple* images. Some very impressive images of gravitational lenses have been taken. See, for example the Astronomy Picture of the Day:

Regards,

Question ID: 970610

### Is gravity just warped space-time? (Submitted April 07, 2006)

The Question

General relativity explains gravitation without using the force of gravity by postulating that mass curves space-time. Why would a curved space-time accelerate me towards the earth?

Thanks for your excellent question. This is not really an easy question to answer in a few sentences. We'll give you a brief answer here and then recommend you to better websites for more details. As you already know, matter tells spacetime how to curve and curved spacetime, then, tells matter how to move. The idea of acceleration and how it relates to gravity comes from Einstein's Equivalence Principle, which states that you cannot tell the difference between a gravitational field and an equivalent uniform acceleration. So that objects in free fall under gravity all accelerate by the same amount, or in other words, they move the same way as if there was no gravity (ie weightlessness). So what seems to be the result of gravity is really the result of curved spacetime. Since spacetime is curved around massive objects, the Earth is merely traveling along the shortest path in curved spacetime, which has the same appearance as if the Sun were pulling on the Earth due to gravity. Einstein used a simple gedanken experiment using light to illustrate his ideas. We recommend the following websites to follow this gedanken experiment and understand General Relativity better:

Hope this helps,
Georgia & Mike

Question ID: 060407a

Traveling at Light Speed

### Why is it not possible to travel at the speed of light? (Submitted May 12, 1998)

The Question

Why is it not possible to travel at the speed of light?

According to Special Relativity the total energy of an object increases as its speed increases and approaches infinity as the object's speed approaches the speed of light. This means that it would take an infinite amount of energy to accelerate an object to the speed of light.

Damian Audley

Question ID: 980512a

### Can you answer my question about energy, space travelers, and relativity? (Submitted May 16, 1997)

The Question

A Space traveler is under constant acceleration, ignore for a moment the propulsion unit or fuel requirements. As the traveler approaches the Speed Of light, "The way I understand it " the hull of the ship would be undergoing tremendous stresses, High Energy Photons would be bombarding the ship at an ever increasing energy level. While behind the ship, light would be shifting into the infrared.

Light from the approaching Red Giant would be shifted into the Gamma Ray region.

Time would be coming to a standstill. The Ship would be attaining great mass.

That the Speed of Light the occupant would be seared by "All Radiation " "All Energy " "All Mass " and be at "All Time ". Is this basically the correct idea?

If it is, the other question is: Speed is linked to Time and Mass/Gravity, so it leads me to think there is some sort of "agent " such as "air molecules in a planetary atmosphere " that is getting compressed or otherwise affected. As though a fabric is being stretched.

I understand that we live on the edge/surface of an expanding "Soap Bubble ", the Past being at the nonexistent center while the future being what we are expanding into. Have I got it right so far?

The observer which keeps constant acceleration will not feel any stresses other than the normal when he approaches the speed of light. stresses are caused by acceleration, not velocity and since the acceleration is constant there will be no more stresses when the velocity is large or small.

It is true there will be a blueshift of all forward coming photons and if one wants to compute that, yes there will be stresses from their interaction with the space ship. Other than that, in as much as the observer does not interact with the outside he should feel as comfortable as when he sits in his office.

The power requirements of course become humongous because of the amount of fuel necessary to approach the speed of light arbitrarily close. One can compute at which point the mass of the fuel required to keep the ship accelerating becomes so high that its self gravity would cause it to collapse as a black hole. Of course the observer (assumed human) would have been crushed long before due to the intense gravitational field of his own ship.

Yes, your picture of the expanding universe is (we believe) basically correct if we assume that the universe is indeed closed. if it is open then the soap bubble analogy does not hold and one would have to consider a different kind of hypersurface which extends to infinity.

Jim Lochner

Question ID: 970516e

### Does anyone have an analysis of time dilation that I could read? (Submitted July 01, 1997)

The Question

Time dilation is at least several times stated to be a function of acceleration rather than velocity. The Lorentz transformations do not deal with acceleration, just velocity. I started to calculate the time dilation effect of mass and velocity as functions of energy in the system. I wonder if anyone has an analysis I can read. My math stops short of tensor calculus, but I can usually comprehend other's work.

Time dilation is a function of velocity. It is a function of the relative velocity of two inertial reference frames. However, to get from one reference frame to another, you have to change your velocity, you have to accelerate.

In the twin paradox, Romulus stays home on Earth, while Remus travels at a good fraction of lightspeed to Alpha Centauri, then turns around and comes back. When they get back together again, they find that Remus is younger than Romulus. However, during the out bound leg of the flight, Remus sees Romulus aging more slowly than him, and during the return leg, Remus also sees Romulus aging more slowly than him. Since Remus always sees Romulus aging more slowly, how did Romulus get to be older? (Romulus always sees Remus aging more slowly, so he has no reason to be surprised.)

The explanation is that when Remus turns around and comes back, he shifts from a frame where Romulus is younger than Remus, to a frame where Romulus is older. It is this changing of frames, rather than the physical effects of acceleration, that results in Remus ending up younger than his stay-at-home twin.

Understanding this type of explanation makes it easier to understand the confusing explanations often found in books.

Tom Bridgman and David Palmer

Question ID: 970701a2

### Has time dilation been detected in controlled experiments? (Submitted February 25, 2005)

The Question

Has the time dilatation been prooven in any experiments? If so how?

Effects of the right magnitude have been measured to be consistent with time dilation to within measurement uncertainty. These are not definitive proofs of the theory but strong indications that the theory is correct. One experiment has been to fly atomic clocks in planes around the Earth in opposite directions. The difference in time between the two clocks after the flights was consistent with those predicted by time dilation. Furthermore muons, sub-atomic particles created in the upper atmosphere by cosmic rays, are unstable and fall apart after a short period of time. However because they move close to the speed of light, their lifetimes are longer, at least as seen by us on the Earth's surface. This extended life, is also consistent with the prediction of time dilation.

with regards,
Martin Still & Jay Cummings

Question ID: 050225a

### What is the Twin Paradox in Special Relativity and how is it resolved? (Submitted November 09, 1997)

The Question

I once heard a "story" about two twins, one of whom went on a rocketship to a nearby star while the other stayed behind. When the errant twin returned, his earth-bound twin had aged considerably while he had not. What determines which of the twins ages the most?

Yes, you are correct, this is the classic "Twin Paradox" and it is a product of special relativity.

The short answer is that one twin stays in a an inertial reference frame, while the other doesn't. The twin that stays in an inertial frame ages more.

Here are some more details: Einstein's theory of relativity assumes two things:

* The laws of physics are the same in all inertial reference frames
* The speed of light is always the same regardless of reference frame

This is counter-intuitive, but it has been verified over and over by experiment. To see why it is counter-intuitive imagine two trains, each going 60 mph one going North and the other one South.
Case 1: In the reference frame of the ground, each has a speed of 60 mph.
Case 2: In the reference frame of the northbound train, the northbound train is still, but the southbound train is going 120 mph.
Case 2: In the reference frame of the southbound train, the southbound train is still, but the northbound train is going 120 mph.

On the other hand, the light from each train's headlamp is moving at exactly the speed of light, no matter who measures. Not c+60mph or c-60mph, just plain c. (where c is the speed of light)

Once you make this assumption, then the other things that you usually expect to be constant have to change. Quantities such as lengths and times that are often constant independent of the observer's reference frame must change to keep the speed of light the same in each reference frame.

If the trains were moving close to the speed of light, the people in each train would see their own train as normal, but looking out the window at the other train, or the earth, they would see clocks moving slow and everything a little shorter (in the direction of motion).

In the case of the twin paradox, the assumption is that the person gets in a ship and then is in this different reference frame. At some point he turns around, thus switching reference frames again, and when he gets back home he now is back in reference frame of the Earth. Depending on how fast the ship went, much less time elapsed for him then his twin brother who stayed at home. This will be shorter by a factor of:

sqrt( 1 - (v/c)^2 ) : where v = speed and c = speed of light

There is one catch, how does his ship accelerate to this fast speed and then turn around? It not only takes an enormous amount of energy, but if it is going to be comfortable for the astronaut it cannot accelerate faster than a "g" or so.

You can find even more details in the Physics FAQ at:

Jonathan Keohane

Question ID: 971109a

The Behavior of Light

### Do photons have mass ? (Submitted July 31, 1996)

The Question

Do photons have mass? Because the equations E=mc2, and E=hf, imply that m=hf/c2 . Is it so?

No, photons do not have mass, but they do have momentum. The proper, general equation to use is E2 = m2c4 + p2c2 So in the case of a photon, m=0 so E = pc or p = E/c. On the other hand, for a particle with mass m at rest (i.e., p = 0), you get back the famous E = mc2.

This equation often enters theoretical work in X-ray and Gamma-ray astrophysics, for example in Compton scattering where photons are treated as particles colliding with electrons.

Andy Ptak

Question ID: 960731

### If photons have no mass, how are they affected by gravity? (Submitted November 02, 1996)

The Question

This questions has been bugging me and my chemistry class. Does light have mass? Most people would think not but here's why I argue against it. Even though light does not effect anything it its path like a solid object, it is affected by gravity. Anything that has mass is affected by gravity. Why do I say that light has mass? Well, If a black holes gravity field is so strong that light cannot escape itself, light must have mass? Am I right? Everyone argues against it.

These are interesting issues that you bring up. Whether or not light (or more accurately photons, the indivisible units in which light can be emitted or absorbed) has mass, and how it is affected by gravity, puzzled scientists for many, many years. Figuring it all out is what made Albert Einstein famous. Bear with me and I'll try to explain both the theory and the observation.

Back in the 1700s, scientists were still struggling to understand which theory of light was correct: was it composed of particles or was it made of waves? Under the theory that light is waves, it was not clear how it would respond to gravity. But if light was composed of particles, it would be expected that they would be affected by gravity in the same way apples and planets are. This expectation grew when it was discovered that light did not travel infinitely fast, but with a finite measurable velocity.

Armed with these facts, a paper was published in 1783 by John Michell, in which he pointed out that a sufficiently massive compact star would possess a strong enough gravitational field that light could not escape --- any light emitted from the star's surface would be dragged back by the star's gravity before it could get very far. The French scientist Laplace came to a similar conclusion at roughly the same time.

Not much was done over the next hundred years or so with the ideas of Michell and Laplace. This was mostly true because during that time, the wave theory of light became the more accepted one. And no one understood how light, as a wave, could be affected by gravity.

Enter Albert Einstein. In 1915 he proposed the theory of general relativity. General relativity explained, in a consistent way, how gravity affects light. We now knew that while photons have no mass, they do possess momentum (so your statement about light not affecting matter is incorrect). We also knew that photons are affected by gravitational fields not because photons have mass, but because gravitational fields (in particular, strong gravitational fields) change the shape of space-time. The photons are responding to the curvature in space-time, not directly to the gravitational field. Space-time is the four-dimensional "space" we live in -- there are 3 spatial dimensions (think of X,Y, and Z) and one time dimension.

Let us relate this to light traveling near a star. The strong gravitational field of the star changes the paths of light rays in space-time from what they would have been had the star not been present. Specifically, the path of the light is bent slightly inward toward the surface of the star. We see this effect all the time when we observe distant stars in our Universe. As a star contracts, the gravitational field at its surface gets stronger, thus bending the light more. This makes it more and more difficult for light from the star to escape, thus it appears to us that the star is dimmer. Eventually, if the star shrinks to a certain critical radius, the gravitational field at the surface becomes so strong that the path of the light is bent so severely inward so that it returns to the star itself. The light can no longer escape. According to the theory of relativity, nothing can travel faster than light. Thus, if light cannot escape, neither can anything else. Everything is dragged back by the gravitational field. We call the region of space for which this condition is true a "black hole" (a term first coined by American scientist John Wheeler in 1969).

Now, being scientists, we do not just accept theories like general relativity or conclusions like photons have no mass. We constantly test them, trying to definitively prove or disprove. So far, general relativity has withstood every test. And try as we might, we can measure no mass for the photon. We can just put upper limits on what mass it can have. These upper limits are determined by the sensitivity of the experiment we are using to try to "weigh the photon". The last number I saw was that a photon, if it has any mass at all, must be less than 4 x 10-48 grams. For comparison, the electron has a mass of 9 x 10-28 grams.

Hope this answers the questions that you and your Chemistry class have.

Good luck,
Laura Whitlock.

Question ID: 961102

### If I were traveling at the speed of light, and turned on a flashlight, would it illuminate my console, or will the light "stall"? (Submitted January 02, 1997)

The Question

I looked all over but, this is the only place I found that may answer two questions of mine.

1. If I were traveling at the speed of light (out in space), and turned on a flashlight (facing forward), would it illuminate my console or will the light "stall"? Also, could I illuminate a target outside, if I turned on my headlights?
2. I believe this is the same question, just in a different setting. If I shot a bullet that travels at 600 ft/sec, and my car is speeding at the 600 ft/sec, would the bullet fly out of the barrel? Can the bullet actually accelerate to 1200 ft/sec?
Not only would I greatly appreciate the answers, I would really like to know a good place to learn this type of physics (like books, WEB, etc..)

Thanx!!!

These are very good questions, and thinking about questions like these motivated Einstein to develop his Theory of Relativity. It will be easier to answer the second question first. In that case, the bullet would accelerate to 1200 ft/s relative to the ground. The reason is that the force of the gunpowder explosion increases the velocity of the bullet by 600 ft/s relative to the gun. If the gun happens to be traveling at 600 ft/s relative to the ground, then the final speed of the bullet relative to the ground will be 1200 ft/s. Keep in mind that essentially all speeds are relative to something else. For example, the Earth is rotating and moving around the Sun, so you are moving through space even when you are "at rest" relative to the ground.

I said "essentially" because there is one exception... the speed of light is always the same (specifically, 300000 km/s) to all observers , regardless of the speed of the observer or the light emitter (in this case, the flashlight). This is not very intuitive, as I hope the bullet explanation was. So even if you are traveling at 150000 km/s, a beam of light would still pass you going 300000 km/s or approach you going 300000 km/s. What happens is that as you travel faster and approach the speed of light, distances shorten and time slows down so that light still travels at 300000 km/s relative to you. This is not just a theory... these effects have been observed in experiments. According to Einstein's equations, it is impossible for anything with mass to reach the speed of light. So the answer to the first question is that you couldn't be traveling at the speed of light, but even if you were traveling at close to the speed of light, you would still be able to illuminate your console and shine a light on a target outside. The speed of a bullet is negligible compared to the speed of light, so in that case we don't have to worry about these effects.

A good general-level book on these topics is Einstein's Universe by Nigel Calder.

Andy Ptak
for the Ask an Astrophysicist team

Question ID: 970102c

### In gravitational lensing, why do off-centered objects appear as multiple images instead of ellipses? (Submitted November 13, 1997)

The Question

I saw a reference to this subject on The Imagine the Universe! site, but I'm afraid I just don't get it. The example given stated that if a massive object (such as a galaxy) lay directly between us and another object (such as a quasar) then the light from that quasar would be bent around the massive object to form a ring. That part makes sense. However, if the massive object is not in a direct line between us and the object being lensed, then two or more identical images of the object would appear around the massive object (like Einstein's cross). I just don't understand why this is the case. Why would it not form an ellipse? What focuses the light to two, or four points?

Vague answer: It has to do with optics, the cardinality of points versus lines, and symmetry arguments.

Assume, for the sake of argument, that off-center objects behind the lens were imaged as ellipses. Suppose that two objects were (in actual, rather than apparent position) in directions e.g.,
a) 1 degree north of the lens and
b) 1 degree east of the lens
You would expect that the two ellipses that formed would be the same size and shape, but rotated with respect to each other. They would therefore cross in at least two places.

Since light is reversible in simple optical systems like this one, imagine a ray of light traveling from your eye towards one of the points where the ellipses appear to cross. By reversibility, that ray has to hit object a), since it is going towards a's image. It also has to hit b), since it is going towards b's image. Since simple optics (without half-silvered mirrors and the like) does not allow rays to split, this is impossible.

Since the assumption that the image would be elliptical leads to an impossible result, that assumption must be wrong. (This is the 'reduction ad absurdum' technique).

I'm not a mathematician, but it is probably provable that any mapping of all points in real_space to lines in image_space leads to crossings of the image lines, and therefore is optically impossible. However, that does not mean that you can't map points to multiple point images.

David Palmer

Question ID: 971113e

### Why is the velocity of light the max speed despite its dependence on the permeability and dielectric constants? (Submitted June 11, 1997)

The Question

Why is the velocity of light the max speed despite its dependence on the permeability and dielectric constants?

The speed of light in a given medium does indeed depend on the permeability and dielectric constants. As you likely know together these form the index of refraction n = (epsilon * mu).5 In turn the index of refraction determines the velocity by v = c/n. The values of mu and epsilon for all known materials is greater than the value in a vacuum, so the speed of light has a maximum value in a vacuum. The precise reason why the values for mu and epsilon are smaller in media rather than a vacuum is a little outside of astrophysics and is more under the domain of materials science or solid state physics.

A brief historical sketch of the speed of light and its measured value starts in 1675 with the astronomer Roemer, who noticed an unexplained difference in the transit times of the moons of Jupiter. What he saw was, depending on the time of year, the moons of Jupiter would pass in front of the planet at a time that was slightly off the predicted time, with the offsets up to about 16 minutes. Since the orbits of the moons can be assumed to be quite regular, Roemer correctly attributed the difference to the variable distance that the light must travel before we observe the transits. When the Earth is closer in its orbit to Jupiter the light must travel less of a distance than when the Earth is on the opposite side of its orbit. Roemer had a good estimate of the diameter of Earth's orbit, and he deduced a reasonable value for the speed of light. Measurements of the speed of light improved, and Foucault conducted one in 1846 which used rapidly rotating mirrors on hills that were separated by several miles. When James Clerk Maxwell was working on his theory of electromagnetic radiation, he realized that electromagnetic waves were actually predicted by this theory. Their velocity, in terms of electromagnetic constants, was so close to the measured value of the speed of light that he immediately inferred that light was therefore an electromagnetic wave.

Regards,

Question ID: 970611d

### What do recent "faster than light" experiments imply for relativity? (Submitted May 30, 2000)

The Question

It seems that Einstein's theory that the speed of light is a constant (c) may be in jeopardy. Several physicists have claimed to have caused light to travel at speeds 300 times the normal speed of light. If their research proves accurate, what would that do to Einstein's theories and our perception on the evolution of the universe? With this knowledge, surely space travel for man (and other life forms which may have discovered this thousands of years ago) could take the possibility of galactic space travel out of science fiction and into the realm of what we could only dream and write about.

First, a clarification: the speed of light in vacuum has always been observed to be constant (c) --- this is not Einstein's invention, but rather the fact on which he based his theories of relativity.

On the other hand, physicists have always known that the speeds of light in gas, liquid, and solids (air, water, glass etc.) depend on the material composition. This is the domain of optics; the consensus of those who know these recent experiments think that they are exciting new developments in optics, which however does not contradict relativity. I.e., faster than light travel still firmly belongs in science fiction, unfortunately.

If you have a Java-enabled browser, check out:

This applet lets you wee how a feature apparently moving faster than c can created from a superposition of waves of different frequencies, all traveling at or below c; and it also let you see for yourself that this cannot be used to send a signal faster than c.

Best wishes,

Koji Mukai, David Palmer, Kevin Boyce & Bram Boroson

Question ID: 000530b

### Are gravitational lenes achromatic? (Submitted November 14, 2001)

The Question

According to an answer to a previous question ( http://imagine.gsfc.nasa.gov/ask_astro/relativity.html#961102) photons do not respond directly to a gravitational field. Instead, they respond to the curvature in space-time, caused by the gravitational field.

If photons respond to the curvature in space-time, I would expect this curvature to be the same for all wavelengths of light. Is there any experimental evidence for this, so, does blue light follow the same path as red light in a gravitational field?

Yes, you are right. According to Dr. Gregory Bothun of the Department of Physics, University of Oregon
( http://nedwww.ipac.caltech.edu/level5/Bothun2/Bothun4_6_6.html):

"Gravitational lensing is achromatic. There is no equivalent to the index of refraction for a normal lens as the behavior of light passing through curved space time is independent of its wavelength. This is the unique signature of gravitational lensing as the cause of the variability of the light output of a distant star." This is a fundamental property of general relativity and no violations have been measured. Some theories of quantum gravity do predict a small wavelength dependence at short wavelengths. This effect has not been seen either.

Hans Krimm for "Ask an Astrophysicist"

Question ID: 011114a

Energy-Mass Conversion

### What does E=mc2 mean? (Submitted March 26, 1997)

The Question

What does E=mc2 mean?

E=mc2 is a version of Einstein's famous Relativity equation. Specifically, it means that Energy is equal to Mass times the speed of light squared. In essence, it states that there is an equivalence between mass and energy. This simple statement has many profound implications... such as no object with mass can ever go faster than the speed of light!

Here are some references (some more advanced than others..)

Rosser, W. G. V. (William Geraint Vaughan). - Introductory special relativity. - London : Taylor & Francis, 1991. - 0850668387

My personal favorites are:

Taylor, Edwin F. (Edwin Floriman). - Spacetime physics : introduction to special relativity / Edwin F. Taylor, Jo. - 2nd ed. - New York : W.H. Freeman, 1992. - 0716723263

and:

Feynman, Richard P., Richard Phillips, 1918-1988. - The Feynman lectures on physics. - Vol. 1: [mainly mechanics, radiation and. - Reading (Mass.); London : Addison-Wesley, 1964. - x1574051

Hope this helps,

Laura Whitlock and Tim Kallman

Question ID: 970326a4

### Why is it impossible, at this point in time, to convert energy into matter? (Submitted July 24, 1997)

The Question

Why is it impossible, at this point in time, to convert energy into matter?

It happens all the time. Particle accelerators convert energy into subatomic particles, for example by colliding electrons and positrons. Some of the kinetic energy in the collision goes into creating new particles.

It's not possible, however, to collect these newly created particles and assemble them into atoms, molecules and bigger (less microscopic) structures that we associate with 'matter' in our daily life. This is partly because in a technical sense, you cannot just create matter out of energy: there are various 'conservation laws' of electric charges, the number of leptons (electron-like particles) etc., which means that you can only create matter / anti-matter pairs out of energy. Anti-matter, however, has the unfortunate tendency to combine with matter and turn itself back into energy. Even though physicists have managed to safely trap a small amount of anti-matter using magnetic fields, this is not easy to do.

Also, Einstein's equation, Energy = Mass x the square of the velocity of light, tells you that it takes a huge amount of energy to create matter in this way. The big accelerator at Fermilab can be a significant drain on the electricity grid in and around the city of Chicago, and it has produced very little matter.

Koji Mukai, with David Palmer, Andy Ptak and Paul Butterworth

Question ID: 970724a

Gravity

### How fast do gravity waves travel? (Submitted September 05, 1998)

The Question

I am a first-year college student and I have a questions about gravity. Is it known how fast gravity waves travel?

Gravitational waves, just like photons, are waves that travel at the speed of light. However, even now, astronomers can not detect them directly, but can observe their effect on the bodies emitting them.

Gravitational waves are believed to be emitted close to compact stars, like a neutron star or a black hole. Just as ripples spread away from a stone tossed into a pond, so gravitational waves spread across space, bending it up and down. Two scientists at the University of Massachusetts, Taylor and Hulse, were able to prove their existence from observing a binary system of pulsars. They proved that gravitational waves do exist and were awarded the 1993 Nobel prize in Physics.

David Palmer & Samar Safi-Harb

Question ID: 980905b

### Could distant spacecrafts be used for gravity wave detection? (Submitted January 03, 2010)

The Question

Why can't we use the signals received from distant spacecrafts to look for gravity waves?

Wouldn't their transmissions show spatial or temporal based shifts when the time-space from transmitter to receiver is expanded or contracted by gravity waves?

The reason is that the amplitude of gravitational wave is tiny:

Using 10-20 as the representative amplitude, and using a baseline of 30 astronomical units (roughly the distance to Neptune, say), we need to measure the displacement by 4.5x10-8 m. That's the size of a molecule.

The clocks on spacecrafts we have launched are nowhere near accurate enough to measure such a tiny displacement, whatever techniques we might want to apply. The transmitter on these spacecrafts are nowhere near stable in frequency to allow measurements at such a demanding level.

That's why the proposed LISA mission is so technically challenging, and the same goes for ground-based detectors such as LIGO.
http://lisa.nasa.gov/

Hope this helps,
Koji & Barb

Question ID: 100103a

### How does antimatter react to gravity of normal matter? (Submitted May 31, 2000)

The Question

I have a question that I could not find in your archive: How does anti matter react to the gravity of normal matter? Are there experiments? (I could imagine anti neutrons in the earth field, but I don't know anything.)

There is a popular level summary in the Usenet Physics FAQ:

The one argument that I like is by Schiff: Eotovos' famous experiments have established the equivalence principle, that the ratio of gravitational to inertial mass is identical in different materials. Mass of these "normal" materials include contributions from virtual positrons which are constantly created and destroyed (along with virtual electrons), and the virtual positron contribution is different in different materials (more in higher Z elements). Thus, the Eotovos experiments prove that the virtual positrons react to gravity the same way ordinary matter does.

Well, are there direct experiments using real antimatter? Not yet, at least nothing conclusive, but there may well be one (or more) in the near future. CERN's ATHENA (AnTHydrogEN Apparatus) group hope to perform precision tests of WEP (weak Equivalence Principle) using trapped antihydrogen atoms, and they probably are not the only group pursuing this goal. ATHENA's public information page:

have many links that you may find interesting; in particular, there are several papers in the "Proceedings of Intl. Workshop on antimatter gravity and antihydrogen spectroscopy" with intriguing titles/abstracts.

Best wishes,

Koji Mukai & Bram Boroson

Question ID: 000531a

Relativity and Quantum Physics

### What is a graviton? (Submitted March 19, 1998)

The Question

What is the graviton?

In quantum theory, force is mediated by an exchange of virtual particles. Although general relativity is a classical, not a quantum, theory, we expect that gravity is also mediated by a particle. We call this the graviton.

Best wishes,
Koji Mukai

Question ID: 980319b

### If gravity is just warped space, why do we need gravitons? [Follow-up to above] (Submitted December 17, 2007)

The Question

General relativity tells us that mass warps spacetime and spacetime "tells" mass/energy how to move. If this is so, then why do we need gravitons (since gravity is an effect, not the cause)?

Thank you for your question. Indeed, from the point of view of pure general relativity theory, there is no need for such a thing as gravitons. However, in quantum field theory all fundamental forces are mediated by the exchange of (virtual) particles (massless particles in the case of long-range forces). Therefore, if the conjecture that all of the forces of nature are unified at some energy scale is correct, one must also be able to describe gravity in these terms. Presumably, in this far-from-completed ultimate theory, the exchange of gravitons and the curvature of spacetime would emerge as equivalent ways of describing the same phenomenon.

-- Michael Loewenstein and David Chuss

Question ID: 071217a

### What are the experimental difficulties in 'discovering' gravitons? (Submitted June 08, 1997)

The Question

Force carrying particles for electromagnetic radiation, the weak/strong nuclear forces and gravity have been either discovered or postulated. What are the experimental difficulties in "discovering" gravitons?

There is a strong analogy between the photon and the graviton. EM forces are propagated by virtual photons, and of course we detect 'real' photons in the form of (classical) EM radiation. Similarly, since the graviton must be massless (since gravity has an infinite range), the graviton can only be 'detected' analogously to the way that the photon is detected, i.e., in the detection of 'classical' gravity waves. Part of the idea of unification theory is that at high enough energies all four forces 'merge', and can be propagated by the same particle (i.e., this has been shown to be the case for the EM and weak interaction, and hence they are often referred to collectively as the electro-weak interaction). But I think you would need a particle accelerator bigger than the size of the Earth to get to energies high enough for all of the forces to be unified.

Andy Ptak

Question ID: 970608

### Does Quantum Uncertainty apply in Relativistic effects? (Submitted October 05, 2000)

The Question

I was taught that the Uncertainty Principle disallows the measurement of any quantity exactly. I was also taught that this property manifests itself in all of nature and not just in our lack of measuring sophistication.

On the other hand, Einstein's Theory of Relativity uses quantities such as mass, energy and time as quantities of exact definition (certainties) and not as statistical averages of the probabilities given by the Quantum Theory.

My question is, while at our human level of observation, the uncertainty in particle velocity/position is extremely negligible, wouldn't these uncertainties have fundamental effects at relativistic frames of references?

Surely the probabilistic nature of these quantities (mass, energy, time) would have fundamental impact when dealing with Relativity!

That is a very good question.

First we should probably clarify the Uncertainty Principle (UP). This has to do with the possibility of measuring "conjugate pairs" of variables simultaneously --- these include momentum and position, time and energy --- any pair whose product has the dimensions of "action" (the dimensions of Planck's constant), as such measuring mass doesn't fall under the UP.

You are correct, quantum mechanics (as opposed to quantum field theory) is an instantaneous model, which violates causality. If you try to make it "covariant," even in flat space-time, you quickly run into the need to introduce additional particles and pair creation/annihilation to take up negative-energy states. If you don't, you find that your theory predicts every particle is an infinite source of energy and there are no ground states.

The "standard" quantum field theory (QFT) approach is an attempt to fix this problem. You can also apply QFT in curved space-time, but that isn't often necessary, except near black holes. What you can't do (yet) is quantum gravity, where space-time isn't just curved, but has spin-2 particle carriers.

In situations where both general Relativity and quantum uncertainty are important (e.g., the Big Bang before the Planck time), important things that we do not understand completely must be happening. E.g., we don't know the initial conditions for inflation, and have to assume something "generic" and make appeals to Occam's Razor.

Hope this helps,

Michael Gross, Mark Kowitt and Michael Arida

Question ID: 001005a

Hypothetical Questions

### Will humans ever be able to time travel? (Submitted March 26, 1997)

The Question

Can humans go back or forward in time ( in the future )? If yes then how?

An interesting question....can humans travel back and forward in time. I presume that you are asking about travel in time like you see on television or in the movies. But let me take a more scientific (if simplified) approach.

The laws of science do not distinguish between the forward and backward directions of time -- yet they do distinguish the past from the future (time increases as disorder increases). There are some solutions to the equations of General Relativity which would allow for travel back and forth in time....(1) would require that you move faster than the speed of light, but we know that this cannot be done; (2) would require space-time to be very warped and a sort of "tunnel" between two space-time points to be present (called a "wormhole"). Such tunnels would not last long enough on their own for anyone to travel through them (unless the traveler discovered some way or built some machine which would keep the tunnel open). There are all sorts of other conditions which would have to be imposed on space-time in order for human beings to travel into the past. All of these conditions tend to conspire against time travel being more than a theoretical possibility. But, as of 1997, our understanding of physics causes the possibility of time travel to remain an open question. NOTE: What I have said here is related to big objects like humans...and my comments do not necessarily apply to very small (subatomic) objects.

Hope this helps,

Laura Whitlock

Question ID: 970326a3

### How can one prove the existence of tachyons and once proven, can they be implemented for space travel? (Submitted June 12, 1997)

The Question

My question comes as a result from reading "About Time" by Paul Davies. In it he talks of time travel and other such things. How can one prove the existence of tachyons and once it is proven, can they be implemented for space travel like in Star Trek (i.e. faster than light space travel)?

Probably two of my favorite popular level treatments of the possible technological implications of tachyons are:

"Future Magic: How Today's Science Fiction Will Become Tomorrow's Reality" by Dr. Robert L. Forward, Avon Book, 1988.

and

"Faster Than Light: Superluminal Loopholes in Physics" by Dr. Nick Herbert, Plume Books, 1988.

Personally, I think Bob Forward's is the better of the two.

As to proving the existence of tachyons, one basically has to discover a particle interaction which can *only* be explained by the presence of one or more tachyons. Some theoreticians argue that if tachyons exist, the universe could be filled with them but they interact so weakly with ordinary matter that we can't detect them. Physicists have searched through some experimental records and so far none of the high-energy accelerator labs have detected an interaction which can *only* be explained by tachyons. This means that tachyons must be far more weakly interacting than neutrinos. If they do exist, tachyons would be extremely difficult to utilize under our current understanding of physics.

You could travel faster than light if you could turn yourself (and your starship) into a tachyon. However, special relativity indicates that if you did this, you could travel back in time and violate causality - the idea that causes must precede their effects. You could wind up in the "Grandfather Paradox": What if you go back in time and kill your grandfather before your father is born? But if you're never born, how could you go back and kill your grandfather?

There seems to be a lot of bogus science on the Web surrounding the subject of tachyons. A number of companies seem to like the name in their product so be careful what you read.

Tom Bridgman
CGRO Science Support Center

Question ID: 970612b

### Could you explain the relativity of theoretical travel through a worm hole? (Submitted September 02, 1997)

The Question

My husband and I both have Applied Physics degrees and studied the theory of relativity in college. We went to see "Contact" the other day in which Jodi Foster discovers plans for a space transport. The theory of relativity states that a person in space will age less than a person on earth; in other words, time moves slower in space, relative to earth.

In this movie, based on Carl Sagan's book, Foster's trans- port capsule drops through a gyroscope-like accelerator and is enclosed for approximately a half a second. Her experience is that she travels through a series of "worm holes" and is gone for about 18 hours. Her recording device recorded 18 hours of static in spite or her only being out of reach for a split second. This story line is backwards to Einstein's theory of relativity.

Our question for you is: could you please explain the theoretical "worm holes" and if they would account for the longer time spent in space relative to the time that passed on earth.

I am sorry that I didn't make contact with you sooner, however your question spurred a flood of diverse comments from our Ask an Astrophysicist Team. I will not inundate you with the raw data, however I will attempt to put them together into some sort of answer. So here it goes:

I did not see the movie Contact, but from what you said, I would agree with you that the movie got the relativity wrong. I do not know if the plot device had Jodi Foster's character fly away fast (thus accelerating greatly to start, stop and turn around) or if she went close to a black hole (thus entering a very strong gravitational field) or both. Either way the effect is basically the same -- time appears to slow down from the point of view of someone in an inertial reference frame. So, I agree, the clock should have shown less time than the observers from the mother-ship (or however the story went) would have seen.

On the other hand, strange gravitational field structures can do strange things. This was pointed out by one member of my team who wrote:

From: David Palmer

Worm holes can be time machines as well as space machines. Thus you can go through a series of wormholes and end up wherever and whenever the wormholes are set up to take you (within limits).

Carl Sagan, when writing Contact, asked Kip Thorne (one of the world's leading relativists) how to transport a person to distant stars, have her come back to find that no time had passed on Earth (which is in both the book and the movie).

From this question, Kip Thorne revitalized the whole modern field of the study of wormholes, a field which had lain dormant for a few decades until Thorne figured out how to make a wormhole people could actually travel through.

A good book on wormholes is:
Black holes and Timewarps, Einstein's Outrageous Legacy, Kip Thorne, ISBN 0393312763

In addition, another member of our team wrote a really nice letter in response, which I will include verbatim here.

Thank you for writing us with your question about the crucial plot element in the movie (and novel) 'Contact' with regards to an observed time difference. Although it is realized in slightly different ways in the novel and the movie, the essential point that, to Earth observers, nothing happened while the cosmonauts (there were several in the book rather than just Dr. Arroway in the movie) traveled for some time and arrived at a destination which they were also at for some time. I don't recall the time they thought they were gone in the book (the danger of borrowing books from friends is you can't go back and check details five years later!), but certainly it was comparable to the movie's depiction of eighteen hours. In both cases, it is a crucial plot. Considering that Dr. Sagan is a knowledgeable and accomplished astronomer, my own reaction without resorting to equations is to assume he has something quite specific and physically correct in mind.

You are, however, correct about the interpretation of relativity. The essential concept is that objects in motion with respect to each other will observe different time frames. This was measured experimentally some years ago when two identical high-precision atomic clocks were synchronized and then one was flown on a high-speed plane and the synchronization of the clocks checked. The flying clock observed less time had passed in exact accordance with relativity (though the difference is very minor: pilots are not getting a significant boost on life by their choice of profession!). There are a number of other types of high speed clocks which so the same temporal effects (relativistic muons generated at the top of the Earth's atmosphere by cosmic ray collisions can be observed at the surface of the Earth, even though their decay life time is so short they should not be observed save for the time dilation effect they experience due to their near-light-speed velocity). Thus if the idea of relativistic motion was intended in 'Contact', your point is correct: a speeding Dr. Arroway (and recording gadgets she might be carrying) would record less time as passing than observers on Earth.

However, the plot element which allows Dr. Arroway to travel to distant destinations in the Galaxy is not a speeding spaceship, but something that bears a strong resemblance to some modern physics ideas about worm holes. Worm holes are hypothesized as possible consequences of certain well-regarded contemporary high energy physics theories. There is a good deal of literature on the subject of worm holes, including some very readable resources such as Steven Hawking's 'A Brief History of Time' and Lawrence Krauss' 'The Physics of Star Trek' (which addresses the theory behind the worm hole used in Deep Space Nine). Temporal flow in a worm hole need not necessarily match that outside the worm hole, although I must admit worm hole theory is well outside my field of study. Thus it might be possible for considerable time to pass in the worm hole while less observed time occurs external to it. Thus the Contact plot might seem to be intact scientifically.

Or maybe not: Ellie Arroway also talks to a projection/simulation of her father at the terminus of the worm hole network that brought her there. This was not in the worm hole and appreciable time passed while she was there, so unless the worm hole actually functioned as a short-range time machine sending her back to a time perhaps eighteen hours earlier, the same problem of time remains. One very weak speculation on this point might be that this is what happened. Some physics does seem to actually allow the possibility of time travel. Perhaps this is what Dr. Sagan had in mind. It should be noted that he was heavily involved in the production of the movie and it was in post-production editing prior to his death. His wife, who is also well versed in science, also worked very closely with the movie production. I (personally) suspect that Dr. Sagan did have some very specific physics ideas in mind to explain, or at least make possible, the temporal paradox you noted.

Alas, ultimately, though, the movie and novel are interesting pieces of entertainment. Some contortions might make the physics of the plot work, but at the same time: 1/ The canyon at the end of the movie in which Ellie Arroway dangles her feet with VLA in the background exists... but it is several hundred miles away from the VLA, and 2/ There is no straight road in front of the U.S. Capitol also depicted near the end of 'Contact'. Now THAT'S a physics error!

Jesse Allen

Thank you again for you insightful question that gave us something fun to think about and debate.

Sincerely,

Jonathan Keohane
for the entire Ask an Astrophysicist team

Question ID: 970902c

 Do you have a question that isn't answered in our archive?
 We do not answer homework questions. term paper or research paper questions. questions asking for science fair project ideas. questions that can be answered by doing a web search (see How to Search the Web) questions unrelated to space-based astrophysics. Special Guidelines for Teachers