There are two important issues with this goal. First of all, nothing can move faster than light speed. The theory, the special relativity...
There are two important issues with this goal. First of all, nothing can move faster than light speed. The theory, the special relativity shows, and the experiments prove that it is impossible to move faster than light. This is a fundamental principle.
The second problem is that we cannot even reach the speed of light. To reach the speed of light, accelerate until the speed reaches the light's speed is impossible to anything that is made from ordinary matter. As the theory and the experiments show, we would need an infinite amount of energy to accelerate to the light's speed. That is another principle.
Why do we want to do for such an unrealistic thing, to reach what is faster than light? Maybe because of the situation, moving faster than the light, and to catch up on it not as impossible as it looks like. Also, everything related to it is related to the way the universe works. According to our present knowledge, there may be objects in space that are receding faster than the speed of the light from us. Besides, we may not even need to go faster than the light to catch up to them. No, this is not about the hypothetical wormholes. Everything is conventional.
We know our universe is expanding. Edwin Hubble (et al.) noticed, what was already predicted that the astronomical objects are moving away from us. The universe is expanding. Farther the object, greater the receding speed. There is an empirical relation between the distance, and the receding speed, which is called the Hubble constant.
Of course, not everything is moving away from us. The things that are properly bound are not expanding. For example, what is gravitationally bound, like our moon to us, our sun, our galaxy, and our cosmic neighborhood, the local group is gravitationally bound. Even if some parts of this bound system are receding, it caused by local circumstances, not the global universal expansion. However, if we look far enough, we see that everything is moving away from us. It does not mean that we are in the center of something. The distancing is a general rule, everything, that is not bounded by local forces are expanding, going away from each other.
This effect is caused by the Big Bang. In its early stage, the universe was small, maybe infinitely small. We have to be careful with the infinite in the real world, but this aspect does not matter in our subject. The Big Bang happened in the whole, already existing, and non-zero size universe or the whole universe was a point at the time of the Big Bang, or it happened some other way is not concern us now.
The universe, from its initial stage, suddenly became a quickly expanding place. This inflation could come from two sources. First of all, it could come from the effect of the expanding space itself. In the universe's early stage, this kind of expansion was the primary factor in inflation. Later, when matter formed, the universe was in a hot, dense phase. When something is hot and dense, it usually means high pressure. Therefore, the second aspect of the universe's today expansion is the extremely high pressure from its early stages.
Even if both effects are contributed to the expansion of the universe, the effect of the primordial hot temperature and high pressure cannot produce the type of inflation that we experience today. The hot, dense kind of explosion, even if any big, cannot create a non-relativistic speed and the observed pattern of the inflating universe. It can only be a classical effect.
Additionally, matter creates gravity, a universal, unlimited range, attractive (in specific circumstances, gravity could be repulsive, but not in our classically exploding matter case) - let us call it - force. The gravity, with its attractive property, should slow down the expansion from its initial speed. If only the high-pressure explosion effect were present at the Big Bang, we would see that the rate of the expansion is slowing down.
A classical high-pressure explosion would result in a distance independent, slowing down kind of expansion. We do not see that our universe expansion is only a classical explosion process. What we see is that the expansion of the universe is additive. What is farther away, the receding speed is faster in linear proportion. Additionally, looks like the expansion is not even slowing down. The universe seems to be in accelerating inflation.
According to our current knowledge, this kind of expansion can be explained only if space itself is expanding, and the cause of this expansion must be present everywhere to provide the observed effect.
Different effects may cause today's space expansion and the early universe's space expansion. The early universe expanded at a phenomenal rate before the matter formed. Today's universe is expanding in a more gradual way. However, both phases can be satisfyingly described by the expansion of the space itself. If space itself is expanding, its expansion can create a cumulative speed effect. If space is expanding, what is farther away, its receding speed is faster, because of more and more space between them. However, again, the locally and adequately bound objects are not expanding.
Is there a speed limit of this kind of inflation? No. Because space itself is expanding, the things that are in the space are not moving in the classical way to be in the inflating state. The physics of relativity cannot be applied in this case. The expansion of the space, because it is additive, can cause a faster than light speed distancing if there is enough space between the two places.
Very likely that there are objects in our universe that are receding from us faster than the speed of the light. Can we go after them, and reach them? We cannot go faster than the light or even with the speed of the light. However, the answer to this question, to reach those objects or not, is not so obvious.
Why? Because we can move inside the space, we can be in a different location. What if we are going in a direction, where is an object, which receding speed from us is faster than the light? Actually, we can go in any direction to achieve this goal. The chosen object still will be farther than it was before, but the space between us, even if it is expanding, must be less than if we would not move in that direction. From that new place, space creates less expansion effect than from the place where we were before. If we move toward in that direction, the expanding rate and the receding speed will be less and less. Even if the distance between us is growing, the speed of inflation decreases. Eventually, (in a finite time?) we must reach a place where the expansion of the space will be less than the speed of the light between us. As we are going to the direction to that chosen object in the space, the effect of the space-expansion between us is less and less, and the classical movement of the other object will be more and more determinative for the speed between us. Ultimately, if we have enough classical speed compared to the other's speed, we must reach a place from where we can catch the other object.
We can catch something that is distancing faster than light from us. Can we? Is there a paradox somewhere in this thread of thoughts? Is the math, with its infinite series, which limits us to reach? What kind of infinite series is in our universe, if it is the limiting factor? Is it the limiting factor? Is there a limiting factor? If not, then the whole universe is within our limits. Can we have the whole universe?
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