Replies to post #44 on Extraterrestrial

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Got a pic of one of those wormholes? Wait... here's one.

How's your French? http://www.astrosurf.org/lombry/trou-de-ver-wormhole.htm

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The Speed of Light Q & A

WHENEVER WE MENTION THE SPEED OF LIGHT in the pages of Scientific American, readers send us questions. Here we try to lay a few perennial puzzles to rest.

1. I read that charged particles traveling faster than light emit Cerenkov radiation--but how can anything go faster than light? Isn't it supposed to be the universal speed limit?

2. What is the speed of light?

3. Why is c a speed limit anyway?

4. Aren't there quantum effects that propagate instantaneously and therefore faster than c?

5. Weren't there experiments recently that sent light itself faster than c?

6. Doesn't Hubble's Law imply that galaxies far enough away are receding from us faster than the speed of light?

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1. I read that charged particles traveling faster than light emit Cerenkov radiation--but how can anything go faster than light? Isn't it supposed to be the universal speed limit?

This goes to the heart of much confusion about the speed of light. "The speed of light" has two quite distinct meanings. One is "the speed at which light travels," and that speed varies depending on the medium: fastest in a vacuum, a tiny bit slower in air, two thirds as fast in glass.

The second meaning, the universe's speed limit, is phrased more carefully as "the speed of light in a vacuum" and is given its own symbol: c. The velocity c seems to be an absolute, unchanging quantity. The speed at which light travels through a vacuum is only one of c's manifestations, however. We call c the speed of light only because of the historical accident that scientists first encountered c in its role as the velocity of light and other electromagnetic waves. Some physicists advocate renaming c "Einstein's constant."

When we distinguish these two speeds of light, the conditions for Cerenkov radiation are no puzzle. In water, light travels at about 0.75 c. Particles can go faster than that through water without breaking the speed limit of 1.00 c.

2. What is the speed of light?

c is exactly 299,792,458 meters per second.

2a. Exactly? How can it be a whole number?

Some metrological sleight of hand is at work: nowadays the meter is defined as the distance light travels in a vacuum in 1/299,792,458 of a second. Metrologists define the meter that way because doing so results in a quantity that is more precise and more convenient to reproduce than the alternatives. The definition of a second is based on an atomic frequency that can be reproduced and measured to an accuracy of about 2 parts in 1015, which is thousands of times more precise than the meter could be defined using a direct length measurement.

3. Why is c a speed limit anyway?

This relates to the real importance of c: it defines a fundamental relation between space and time. A distance of 299,792,458 meters is equivalent to a time interval of one second. This is one of the messages of Einstein's theory of special relativity: space and time are different aspects of a single entity called spacetime. Omitting the vestigial hyphen from "space-time" emphasizes that this "spacetime" is conceptually something new and not merely the old space stapled to the old time.

In spacetime, if one can travel faster than c, one can devise ways to travel through time into the past. Time travel would unleash logical paradoxes of cause and effect, which convinces many physicists that such travel (and even transmission of information faster than c) must be impossible. This is perhaps the most fundamental reason for believing c to be an absolute speed limit, but there are other reasons or clues to support the idea.

The laws of special relativity make it impossible to accelerate an object beyond c. As the object's speed approaches c, its mass increases. If you keep on applying a force to make the object go faster, more and more of the energy that you transfer to the object goes into increasing its mass (the old E=mc2). Because of the object's greater mass, the force you apply increases the object's speed more slowly. The object's speed becomes incrementally closer to c without ever quite reaching it. Achieving c would take infinite energy.

However, that reasoning only rules out the possibility of accelerating objects continuously from below c to above c. One can postulate the existence of elementary particles that always travel faster than c. These particles, called tachyons, would have fundamental properties unlike those of familiar particles such as electrons. For example, tachyons would gain mass as they were slowed down closer and closer to c. Conversely, their energy would decrease as they sped up, reaching a minimum at infinite velocity--which would be as accessible to a tachyon as zero velocity is to an ordinary particle. The mass of a tachyon would be imaginary, in the sense of imaginary numbers and the square root of minus one.

Such tachyons are not a part of the standard model of particle physics (which accurately describes almost all particle physics experiments to date) or the standard model's most plausible extensions.

In the end, the idea that c is a speed limit is supported empirically by the lack of evidence of any physical object or signal traveling faster than c.

4. Aren't there quantum effects that propagate instantaneously and therefore travel faster than c?

The classic example of such a phenomenon is what Einstein famously called spooky action at a distance. Two particles, say A and B, are "entangled" (meaning their quantum states are intrinsically linked or blended together) and separated by a large distance. A measurement performed on particle B will always give results consistent with the results of a corresponding measurement performed on A--even if there has not been time for anything physical (such as a signal, or a propagating wave of some sort) to travel between A and B to force the measurement results to agree. Naively, it looks as if some sort of information must have traveled faster than c between the particles, and that the effect could be used to transmit information that rapidly. Instead, however, the random nature of the individual quantum measurement results makes it impossible to use this effect to transmit information faster than c. The accepted explanation is not in terms of anything traveling faster than c, but is related to the "nonlocal" nature of quantum mechanics: the two entangled particles do not have well-defined individual states; all that is well-defined is their combined state, which is not localized in one place.

5. Weren't there experiments recently that sent light itself faster than c?

Yes, last year a group at the NEC Research Institute in Princeton, NJ, performed this feat by sending pulses of light through a cell of gas irradiated with laser beams. See our September 2000 issue for a more complete report. Similar experiments actually date back to 1982. The key here is that a pulse of light has many different velocities associated with it. Some of those velocities can be greater than c without violating special relativity.

One description of what happens in the NEC experiment is that the front portion of their light pulse is amplified, which makes it appear as if the peak of the pulse has been shifted forward. The velocity based on the location of the peak is greater than c. (Actually it's worse than that: the velocity is negative, meaning the peak exits the far side of the experiment's gas cell before it enters the near side.) Yet it seems clear that no energy has moved faster than c: the extra energy at the front of the pulse is presumably added from the laser-excited gas.

In addition, the system cannot be used to send information faster than c. In a preprint posted in January, the NEC group and collaborators take into account quantum fluctuations that their system necessarily adds to each pulse. They prove theoretically that these fluctuations make it impossible for someone waiting downstream with a photon detector to know that an individual pulse is arriving any sooner than they would if it the pulse had simply traveled through a vacuum at speed c all the way.

One other point is worth noting with the NEC experiment. The pulses of light that they used were about a kilometer long. The brief period of travel "faster than c" shifted those pulses forward about 20 meters, a mere 2 percent of the pulse length.

6. Doesn't Hubble's Law imply that galaxies far enough away are receding from us faster than the speed of light?

Yes. Hubble's Law, v = Hd, tells us that a galaxy that is d megaparsecs away from us will be receding at velocity v. And if we take the current best measurement of Hubble's constant H (72 kilometers per second per megaparsec), simple algebra predicts that galaxies 4.2 gigaparsecs (4.2x109 parsecs) away are receding at velocity c. More distant galaxies recede faster than c. This indeed violates special relativity--but that's not a problem because over such cosmological distances general relativity applies. Special relativity assumes that spacetime is flat and not expanding, while general relativity happily deals with a curved, expanding spacetime.

In general relativity the speed limit c only applies locally: One cannot have a particle traveling faster than c relative to another particle that is nearby. To compare velocities over very large distances in a curved, expanding universe requires some sophisticated mathematics. It is no longer as simple as measuring a distance and seeing how fast the distance changes.

Let's say galaxy Omega is 5 gigaparsecs away. The distance between us and galaxy Omega will be increasing at a rate faster than c. But that is because the spacetime between us and galaxy Omega is itself stretching and becoming larger at that rate, not because galaxy Omega is exceeding the speed of light in its local part of spacetime. This description may sound like doubletalk, but it is grounded in well-defined mathematics of curved spacetimes.

If we could build a telescope to see across 4.2 gigaparsecs what would we see? We can't see that far. The galaxies that we see a billion light years away appear to us today as they were a billion years ago. Before our telescope "reaches" 4.2 gigaparsecs, what we can see runs so far back in time that we hit the Big Bang, or more precisely, we hit the first moment at which light began traveling freely through space. In a sense we can already "see" that far: that oldest and farthest traveling light is none other than the cosmic microwave background.

This answer has also glossed over details such as the changing rate of expansion of the universe over the aeons, which modifies the simple law v = Hd, but the principles remain the same.

--Graham P. Collins, staff writer and editor

http://www.physics.hku.hk/~tboyce/sf/topics/lightfreeze/0701haubox1.html#hubble_law

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Beam me up, Scotty.

Quantum Teleportation http://www.crystalinks.com/teleportation.html