All of the speed is through space. This analogy also illustrates that an object moving extremely fast through space moves very slowly through time. Hence, an object moving at the speed of light through space experiences no time at all or in other words is frozen in time. And this is a more accurate reason than the reasoning of changing masses. Learn more about can you go faster than light? Particles can be accelerated at nearly the speed of light using electromagnetic fields, magnetic explosions, and wave-particle interactions.
The theory of special relativity explains how space and time are related for objects moving at a constant speed. The idea of relativistic mass of an object was introduced to simplify the concept of relativity. By Don Lincoln, Ph. Let us try to find answers to these questions using the concepts of relativity and spacetime. Also, let us try to debunk some common misconceptions using simple analogies and mathematical equations.
The Concept of Spacetime Spacetime is a more tricky concept. Q: What are the three ways to travel at nearly the speed of light? Q: What is the famous equation of special relativity?
Q: Why was the concept of relativistic mass introduced? All rights reserved. If the effect is real it is difficult to see why it should not be possible to transmit signals into the past by placing the apparatus in a fast-moving frame of reference. Refs: W. Heitmann and G. Nimtz, Phys. A , ; A. Enders and G. E48 , Terence Tao has pointed out that apparent FTL transmission of an audio signal over such a short distance is not very impressive.
The signal takes less than 0. Although this is not what is being done in the above experiments, it does illustrate that the experimenters will need to use a much higher frequency random signal, or transmit over much larger distances, if they are to demonstrate FTL information transfer convincingly.
The likely conclusion is that there is no real FTL communication taking place, and that the effect is another manifestation of the Heisenberg Uncertainty Principle. The Casimir Effect describes the fact that a very small but measurable force exists between two uncharged conducting plates when they are very close together.
A surprising calculation by Scharnhorst suggests that photons travelling across the gap between the plates in the Casimir Effect must go faster than c by a very very small amount at best 1 part in 10 24 for a 1 nanometre gap. It has been suggested that in certain cosmological situations, such as in the vicinity of cosmic strings if they exist, the effect could be much more pronounced.
Even so, further theoretical investigations have shown that, once again, there is no possibility of FTL communication using this effect. Refs: K. Scharnhorst, Physics Letters B , S. Advanced Study. A26 , According to Hubble's Law, two galaxies that are a distance D apart are moving away from each other at a speed HD , where H is Hubble's constant.
Actually, the modern viewpoint describes this situation differently: general relativity takes the galaxies as being at rest relative to one another, while the space between them is expanding.
In that sense, the galaxies are not moving away from each other faster than light; they are not moving away from each other at all! This change of viewpoint is not arbitrary; rather, it's in accord with the different but very fruitful view of the universe that general relativity provides.
So the distance between two objects can be increasing faster than light because of the expansion of the universe, but this does not mean, in fact, that their relative speed is faster than light. As was mentioned above, in special relativity it is possible for two objects to be moving apart by speeds up to twice the speed of light as measured by an observer in a third frame of reference. In general relativity even this limit can be surpassed, but it will not then be possible to observe both objects at the same time.
Again, this is not real faster-than-light travel; it will not help anyone to travel across the galaxy faster than light. All that is happening is that the distance between two objects is increasing faster when taken in some cosmological reference frame. Stand up in a clear space and spin round. It is not too difficult to turn at one revolution each two seconds.
Suppose the Moon is on the horizon. How fast is it spinning round your head? It is about , km away, so the answer is 1. It might sound ridiculous to say that the Moon is going round your head when really it is you who is turning, but according to general relativity all co-ordinate systems are equally valid, including rotating ones.
So isn't the Moon going faster than light? What it comes down to is the fact that velocities in different places cannot be compared directly in general relativity. Notice that the Moon is not overtaking any light in its own locality. The speed of the Moon can only be compared to the speeds of other objects in its own locality. Indeed, the concept of speed is not a very useful one in general relativity, and this makes it difficult to define what "faster than light" means. Even the statement that "the speed of light is constant" is open to interpretation in general relativity.
Einstein himself, on page 76 of his book "Relativity: the Special and the General Theory", wrote that the statement cannot claim unlimited validity. When there is no absolute definition of time and distance it is not so clear how speeds should be determined. Nevertheless, the modern interpretation is that the speed of light is constant in general relativity and this statement is a tautology given that standard units of distance and time are tied together using the speed of light.
The Moon is given to be moving slower than light because it remains within the "future light cone" propagating from its position at any instant. The cases given so far only demonstrate how difficult it is to pin down exactly what we mean by FTL travel or communication. If we do not include things such as moving shadows, then what exactly do we mean by FTL?
In relativity there is no such thing as absolute velocity, only relative velocity; but there is a clear distinction between "world lines" that are "timelike", "lightlike", and "spacelike". By "world line" we mean a curve traced out in the four dimensions of space-time. Such a curve is the set of all events that make up the history of a particle. If a world line is spacelike then it describes something moving faster than light. So there is a clear meaning of what is meant by a "faster-than-light" speed which does not depend on the existence of third-party observers.
But what do we mean by an "object" if we don't want to include shadows? We could define an object to be anything that carries energy, charge, spin, or information; or perhaps just that it must be made of atoms, but there are technical problems in each case. In general relativity energy cannot be localised, so we had better avoid using energy in our definition.
Charge and spin can be localised, but not every object need have charge or spin. Using the concept of information is better but tricky to define, and sending information faster than light is really just FTL communication—not FTL travel. Another difficulty is knowing whether an object seen at A is the same as the one that was earlier seen at B when we claim that it has travelled across the gap faster than light. Could it not be a duplicate?
It could even be argued that FTL communication makes FTL travel possible, because you can send the blueprint for an object FTL as advance information, and then reconstruct the object—although not everyone would accept such teleportation as FTL travel.
The problems of specifying just what we mean by FTL are more difficult in general relativity. A valid form of FTL travel may mean distorting space-time e. There is a distinction between going faster than light locally and getting from A to B faster than light globally.
When a gravitational lens bends the light coming from a distant galaxy asymmetrically, the light coming round the galaxy on one side reaches us later than light that left at the same time and went round the other side. We must avoid a definition of FTL travel that says a particle going from A to B gets there before light that has made the same journey along a lightlike geodesic.
This makes it very difficult, perhaps impossible, to define global FTL travel unambiguously. If you were expecting me to finish this section with a precise definition of what is meant by FTL travel and FTL communication, I am afraid I must disappoint you! The above difficulties are insurmountable. Nonetheless, you will probably recognise the real thing when confronted with it now that I have given some examples of what would not be FTL travel.
When Einstein wrote down his postulates for special relativity, he did not include the statement that you cannot travel faster than light. There is a misconception that it is possible to derive it as a consequence of the postulates he did give. Incidentally, it was Henri Poincare who said "Perhaps we must construct a new mechanics [ It is a consequence of relativity that the energy of a particle of rest mass m moving with speed v is given by. As the speed approaches the speed of light, the particle's energy approaches infinity.
Hence it should be impossible to accelerate an object with rest mass to the speed of light; also, particles with zero rest mass must always move at exactly the speed of light, since otherwise they would have no energy. This is sometimes called the "light speed barrier", but it is very different from the "sound speed barrier".
As an aircraft approaches the speed of sound it starts to feel pressure waves which indicate that it is moving close to the speed of sound, and before the existence and effects of these waves were well understood, they destroyed several aircraft in the mid 20th century; hence the old name of sound "barrier". In fact, with more thrust and the right aerodynamics, an aircraft can certainly pass through the sound barrier.
The situation is different for light. As the light speed barrier is approached in a perfect vacuum there are no such waves according to relativity destructive or otherwise.
Moving at 0. Particles are routinely pushed to these speeds and beyond in accelerators, so the theory is well established. Trying to attain the speed of light in this way is a matter of chasing something that is forever just out of your reach.
This explains why it is not possible to exceed the speed of light by ordinary mechanical means. But it does not in itself rule out FTL travel. It is really just one way in which things cannot be made to go faster than light, rather than a proof that there is no way to do so. Particles are known to decay instantly into other particles which fly off at high speed. A more accurate statement of the principle would be, "nothing can locally travel faster than light.
For instance, if wormholes exist, you could use one to take a shortcut from earth to the North Star. Compared to a bit of light that traveled from earth to the North Star and did not go through the wormhole, you would have been traveling faster.
In other words, you would have reached the North Star first. This is allowed because you never locally exceeded the speed of light.
If a different beam of light was sent from earth to the North Star and did go through the worm hole with you, there is no way you could outrun it. As another example, there are some distant stars in the universe that are moving away from each other at a speed faster than light. This is allowed because it is not a local speed.
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