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General Physics: Speed of Light

How do we know that light travels at this speed? And how can something be affected by gravity if it has no mass, as with light? If something has no mass, how could it affect us?
The speed of light has been measured often and very accurately, going back to as early as 1675, and using a variety of techniques. We know what it is, and we know that theories predict it correctly. As far as us not being affected by something with no mass, this is untrue. Your body is sensitive to light (massless), you feel heat (infrared energy), the nuclei in your body interact with xrays and gamma rays (all massless). Dr. Louis Barbier
I am researching the possibility of finding a theory to show that the speed of light is not constant. Where should I search?
The first thing you should do is get your PhD in physics, specializing in General Relativity. General Relativity has MANY observations (precession of Mercury's orbit, slowing down of binary pulsars, etc., etc., etc.) that your theory would have to explain as well or better before anyone else would even consider it. It will take years to learn and understand all the complexities. Many extremely intelligent people have tried and no one has even come close. I'm not saying it's impossible, and many of us hope that a loophole will eventually be found, but don't think it will be easy. Dr. Eric Christian (April 2000)

Is there is any data about variations in "c", the speed of light, such as the effect of nearby mass?
The presence of mass doesn't change the speed of light. Mass can change the energy of light (gravitational redshift) and bend it, but the speed is still "c". The speed of light is slower in material than it is in a vacuum. The "index of refraction" of a material is the ratio between "c" and the speed of light in that material. For example, glass has an index of refraction of about 1.5, meaning that light travels at only about 2/3 the speed it travels in a vacuum. Dr. Eric Christian

I read that the speed of light (186,000 miles per second) was slowed to 38 miles per hour. Is this true?
This is, in fact, true, but it was accomplished "by
passing light through an unusual system  an ultracold gas of sodium
atoms bathed in laser light." 186,000 mps is the speed of light in a
vacuum. Read a good explanation of this recent accomplishment at the
Jupiter
Scientific site. Beth Barbier
Don't temperatures of this sort (50billionths of a degree above absolute zero) exist naturally in deep space, or is the "coldest" temp we have equal to the background microwave 3K radiation? Wouldn't an environment that has so little atomic action (little movement when supercold) present less opportunity for a photon to hit and scatter and lose energy? What happens to spacetime when light goes so slowly?
The 3K background radiation sets the "coldest" temperature in the Universe. It takes work to make anything colder, and that doesn't really happen naturally. The index of refraction is determined by how a material responds to electromagnetic waves, it is not a scattering process. And the supercold atoms just don't respond quickly. Spacetime is determined by the speed of light in vacuum, not the local speed of light and so isn't affected. Dr. Eric Christian (May 2000)

What is the significance of the speed of light in relation to the conversion of mass to energy in E=mc^{2}? It is a constant, but why that particular constant?
E=mc^{2} comes out of the equations of General Relativity. Why is it exactly c^{2}? I guess it says something fundamental about the relationship between mass, energy, and the speed of light, but that's just the way the universe is. Dr. Eric Christian

Would it be possible to spin an object (as an airplane propeller spins) to approach the speed of light? Is there a formula that I could use to calculate the needed RPM and diameter of a large rod that would approach the speed of light at the tip of the rod?
If I had a rod that was 100 feet in length and spun it that fast, what would happen to this rod? What kind of gravitational forces would be experienced by someone riding on the tip of this rod?
This is indeed an example that has been discussed quite a lot. Unfortunately, the speed of light barrier cannot be overcome with tricks. It doesn't matter whether an object that is flying straight is approaching the speed of light or the tip of a rotating object. The result is the same: no object with mass (when it is at rest) can reach or exceed the speed of light. Classically you would compute the speed v at the tip of your rod as v = 2*pi*f*r where f is the rotation frequency in rotations/second (multiply this number by 60 to get it in rotations/minute or RPM) and r is the length of your rod from the center to the tip. The 2*pi is needed because the motion is on a circle. Now you could put a number in for r and calculate which value you need for f to reach the speed of light c. However, this formula becomes invalid when v approaches c, as the time elapsed for the tip of the rod and the length of the circle change for high speeds. What physically prevents the rod from reaching the speed of light is the fact that according to Einstein's theory (and this can be measured!) the increasing kinetic energy of the rod (i.e. its energy of motion) is equivalent to an increasing mass. Thus the rod becomes heavier and heavier the faster it rotates, with the tip of the rod approaching infinite mass as it approaches the speed of light. Of course, infinite mass cannot be accelerated further. In other words, instead of further accelerating the rod you just increase its mass. As far as your second question goes: Suppose we could accelerate a rod with 30 m length (your 100 feet) to reach the speed of light at the tip, this would create an enormous centripetal force, i.e. the force that is necessary to keep the tip on a circle (pulling it constantly inward away from the straight path that it wants to go otherwise). This force would turn out to reach approx. 10^{12} times, or one trillion times, the gravitational pull on the Earth's surface. No known material is strong enough to withstand such an enormous force. During their training, astronauts are subjected to, at most, 10 times the Earth's gravitation. Dr. Eberhard Moebius (March 2004)

Why is it that nothing may go faster than the speed of light? I have also heard that they once got an electron to travel faster than the speed of light in a particle accelerator. Can you confirm or deny this?
Our current understanding of the laws of physics say that nothing can go faster than the speed of light, and that objects with mass cannot even get up to the speed of light (it requires an infinite amount of energy). They have never gotten an electron to go faster than the speed of light (see above). The fastest electrons from an accelerator go about .999999 times the speed of light.
Is it not possible to bend space?
Matter can bend space, but to bend space enough to get light years away quickly, again takes near infinite amounts of mass and energy. There is no way we currently know of to get around the speedoflight limitation, although many of us hope that a loophole will eventually be found.
What if you had a rigid (nonbending) steel rod that was, say 187,000 miles long? If you pushed on one end of it, wouldn't the other end have to move instantaneously, thereby transmitting motion faster than light speed?
It is impossible to have a bar that is perfectly rigid. There is a sound speed through materials that limits the response to motion. Pushing the rod at one end would only set up a compression wave that would travel down the rod at this sound speed, which is much less than the speed of light. Remember that what is happening is that you are putting a force on just a few atoms, which then move closer to the next layer of atoms, which are repelled by the first layer and are accelerated away (which takes a finite amount of time) and so on. For most of what we do, the sound speed is fast enough that we don't notice it, but it is always there. Dr. Eric Christian
How about this: You are in a spaceship traveling at the speed of light. You are sitting in a chair holding a flashlight  you shine that flashlight towards a nearby wall directly in front of you while you are facing the direction of movement. You will see the light, correct? Because relative to you the light is traveling at c. Now to someone standing motionless outside the spaceship looking in  technically, if they see the light, it would be traveling at twice the speed of light, but from what I understand, nothing can go faster than the speed of light. I understand that no matter the speed of the viewer of the light it is always at the same speed c. I want to know if this were to happen even though it is impossible, right now  would we get a "light boom" comparable to a sonic boom? How about if you are facing opposite the direction the light travels? Now the photons are traveling at the speed of light, but the spaceship is also traveling at c, so what would happen?
First off, there is no evidence that a spaceship can travel at the speed of light. It would take an infinite amount of energy. Plus, time would stop for you, so you couldn't do the experiment. But let's say the spaceship was moving at 0.9 c. The important thing to realize is that distance and time are not fixed quantities (which is why Einstein's theories are called relativity  distance and time are relative). The person outside the spaceship measures a shorter distance between your chair and the wall (relativistic contraction) and also measures a different time from when the flashlight turns on to when the light hits the wall (time dilation). If he divides the two, he'll get the speed as c, as will you on the ship. But the quantities you both measure to calculate c will be different. Dr. Eric Christian

Back in 2000, I read on the CNN website that scientists had done an experiment that broke the Universe's speed limit. Is this true?
You question has been answered well by our sister
site, Imagine the Universe! See their page on the recent
faster than light experiment. Beth Barbier (May 2005)

Please explain Cerenkov radiation. I've read the definition: "an optical shock wave traveling faster than the speed of light in its own medium", but I don't understand it. What medium are we talking about, and how can anything travel faster than c?
Every transparent material has an index of refraction, that is the ratio of the speed of light in vacuum to the speed of light in that material. So light travels through air slightly slower (~ .9997 c) than in vacuum and only 2/3 c in glass (index of refraction = 1.5 for glass). If a electrically charged particle enters a material moving faster than the local speed of light (any particle > .667 c in glass for example), then the electromagnetic field, due to its electric charge, can't keep up with its own motion, and an electromagnetic wake is created, which manifests itself as photons, or Cerenkov (or Cherenkov) light. Dr. Eric Christian (May 2000)

I have been taught that as matter approaches the speed of light, time slows down for that object. I was wondering if there is a linear formula for calculating the amount of time passing for an object traveling at the speed of light, compared to an object sitting on Earth (i.e. if an object travels at 186,000 miles/sec for one year, how much time will pass on Earth)?
The standard equation for "time dilation" is that the time passing on Earth will equal the time on the object * 1/sqrt(1((v*v)/(c*c))), where v is the velocity of the object and c is the speed of light. At v=c this goes to infinity, or in other words, time would stop for an object moving at the speed of light. This is not a problem because objects can't go at the speed of light  it would take an infinite amount of energy (and their mass would also become infinite). Dr. Eric Christian
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