|
||||||
|
|
|||||
 |
Okay if time dilation means that someone in a space ship that is moving faster than me has a slower moving clock then I do (according to the time reference of myself) then what about his point of view? If he thinks he's going at a velocity of 0 according to himself, then I should be moving at a speed greater than him and for that reason should be experiencing a slower time passage then he is. Well if this goes on for a while, who ages faster (i.e. who has the faster clock)? |
 |
It is important to realize that it really is the case that each of these people measures the other's clock as running slowly. So who is really running slowly? So long as both remain within their fixed inertial reference frames, the answer is relative and always the other guy. Ah, you say, what if they meet up again sometime? But they will never meet again if they remain in their inertial reference frames: inertial motion means linear, constant velocity travel, and straight lines meet only once. But what if they accelerate, or what if space is curved so they do meet again? In that case you can always compute how much proper time will have elapsed for each person. The result when acceleration must be considered is no longer as simple as the comparison between two inertial frames, but there need not be reciprocity between general accelerated (or curved spacetime) frames. Hence one or the other observer will be younger, and the answer is unequivocal. |
|
I thought that things shrinking (length contraction) was an optical illusion. But the text says that it is not. If not, then how does something shrink? |
|
Time dilation and length contraction are not just optical illusions, but neither do they represent a physical contraction. These effects are the result of a measurement from a given inertial frame that is performed on body moving with respect to that frame. We assume that the measurements always take into account the finite travel time of light. Consider two observers moving relative to one another. You have no difficulty with the idea of their velocities being relative - each thinks the other is "really moving." In SR, time intervals and space intervals are also relative. You don't shrink or see your own clock run slow. The other observer sees your clocks slow and meter sticks contracted from his frame. Similarly you will observe his clocks slow and meters sticks short from your frame. The time dilation and length contraction are inherent properties of the way measurements must be performed in spacetime. Note: It is a complicated question to ponder how things would appear visually if they were moving close to the speed of light. It is necessary to trace light rays carefully to determine what would actually impinge on your retina. |
|
If we go near the speed of light we have weird effects, time slowing, lengths contracting to zero. But light doesn't. Why isn't light subject to relativity? |
|
Light is certainly subject to relativity. Light has zero rest mass, and relativity says that anything with zero rest mass always has to go at the speed of light along lightlike trajectories in spacetime. If you want to be anthropomorphic about it, a photon doesn't experience the passage of time. To it, it is everywhere at once. |
|
If a person traveling to Alpha Cen near the speed of light sees their clock running "normally" shouldn't it take him longer to reach Alpha Cen than the Earth person would believe? |
|
No. The distance to Alpha Cen is length contracted, so even though the clock is running normally it doesn't take so long to get there. |
|
I'm confused about travelling to Alpha Centauri in less than 4 years on the traveller's clock. Is this due only to length contraction. Contraction of what? The "space" between Earth and Alpha Cen? What frame is that space in? Where does time dilation fit into this situation? |
|
In the frame of the traveler, the distance between the Earth and Alpha Centrauri is length contracted. As a concrete example, suppose the spaceship is moving with a boost factor of 10 relative to the Earth. The Earth-based observer would say that the spaceship clock is running slow by a factor of 10 so it takes only 0.4 years on the spaceship clock for it to reach Alpha Cen. The spaceship, on the other hand, observes its clock to run normally but sees the Earth and Alpha Cen whipping past at a boost factor of 10, causing the distance between them to be length contracted in such an amount that it takes 0.4 years between the time the Earth passes the window until Alpha Cen appears. Both observers agree on the amount of time required for the journey in the frame of the traveler, but in one case the effect is due to time dilation and in the other, length contraction. |
|
All the details of special relativity, like time dilation and length contraction, are applicable in inertial reference frames. How does relativity apply in non-inertial reference frames? |
|
Newton's Laws were formulated for inertial frames, but they work in noninertial frames so long as one adds terms to account for the accelerated frame (e.g., "fictitious" or inertial forces). The same is true for relativity. Length contraction and time dilation also occur in noninertial frames; things are just a bit more complicated. And noninertial reference frames are not equivalent to inertial reference frames, so the principle of reciprocity does not apply. (E.g. in the Twin Paradox the traveling twin is noninertial and is younger at the end of the journey; there is no symmetry between the twins.) General relativity provides the formalism to deal with all frames, including inertial, noninertial, and even curved spacetimes. |
|
If light doesn't move through a medium (the ether) how does it have a measurable speed? |
|
Set up a bulb. Pace off a distance. Set up a receiver. Set up sophisticated timing apparatus. You can measure the time it takes light to travel from the bulb to the receiver. Divide by the distance. There is your speed. |
|
What makes the speed of light so special anyway? |
|
Anything that has zero rest mass must travel at the speed of light. Photons carry the electromagnetic force and have zero rest mass. Now what is so special about this maximum speed? In the relativistic point of view, time and space intervals derive their meaning from interactions and physical processes which involve forces. For example, two particles interacting electromagnetically by the exchange of photon. This could happen at some maximum finite speed (which must be the same for all frames by the relativity principle), or at an infinite speed. In our universe it happens at a finite speed. Let's speculate for a moment. Would it be possible to have a universe where interactions took place at an infinite speed? Every particle in the universe would immediately interact with every other particle. Everything would have to be fixed into some grand equilibrium. It doesn't seem to me that it would then be possible to have such a universe evolve in time. |
|
If the speed of light is the same in all frames, why does light travel in water at a speed less than c? |
|
The speed of light in vacuum is the same in all frames. When light travels through water it is interacting with the water. These interactions reduce the net speed through the water. |
|
I have learned that the phase velocity of transverse electric waves can be greater than the speed of light in some media. How can this be? How much of scientific law is based on the idea that c is the fastest speed at which anything can travel? |
|
The phase velocity refers to the velocity one gets by multiplying the wavelength times the frequency of a wave. It is the propagation speed of a particular wavelength component of a general wave. However, the rate at which the energy in a wave pulse propagates is the group velocity. This is also the speed at which information can be carried by a wave pulse. The group velocity is always less than c. Certain velocities can exceed c but nothing physical (information, energy etc.) can be transported faster than c. In answer to the second part of the question, all of physical law is grounded in the principles of relativity as postulated by Einstein. It may be difficult to accept or understand, but modern technology (computers, video, internet) is based on relativity. |
|
Copyright © 2005 John F. Hawley |