I Couldn't Resist
RE: The speed of light is the highest possible speed in the universe. But how come there is such a thing as the highest possible speed in the universe at all? (Quora)
It was my luck that I happened to see this question in my email; now I’m obliged to provide a different answer to this question. Without any advanced math, I’ll show that the standard model used to answer this question is self-contradictory and paradoxical, thus not completely true.
First let’s acknowledge the question that is begged: “The speed of light is the highest possible speed in the universe.”
This is not true. Even Richard Stevenson admits this in his very detailed response: “The speed of light is only ‘a highest possible speed’ for matter and energy that is already slower than light. If there is matter and energy out there that is already faster than light, then it will always remain faster than light.”
How is this possible? Let’s do a thought experiment.
First, let’s postulate that the speed of light is a given constant. So the speed of light in a vacuum is not only its maximum speed, but also its minimum speed. We know, of course, that for certain reasons it is slower in other media, such as water.
But the speed of light itself is not the same thing as accelerating a mass to approach the speed of light. We will see that a mass cannot be accelerated to the speed of light, not because it requires infinite energy, but because a mass has no known absolute velocity.
Secondly, let’s postulate that there is no absolute rest, and therefore, no absolute velocity. This is in accord with Einstein’s theory of relativity. Velocities are relative — relative to the speed of light. No absolute “zero” velocity can be established anywhere in the known universe. We could even say that the speed of light, c, is the only absolute natural datum to compare velocities.
Furthermore, there is no absolute position. The position of an object is only and always relative to another arbitrary object.
There are consequences to these postulates, if they are true.
The velocity of an object A relative to another object B depends on the observer’s perspective. That is, if B is receding from A at 80% of c from A’s perspective, that is equivalent to saying that A is receding from B at 80% c, from B’s perspective. Neither A nor B have a favored location in the universe, according to the anthropic principle. It is so unlikely that it may as well be impossible that mankind is in the center of the universe.
One can never accelerate a mass from “zero” to any other velocity. One can only accelerate an object in addition to its previous velocity, which is never absolute and never was zero. Here we have our first paradox.
To accelerate a mass to a higher speed requires an addition of velocity v to an unknown velocity u, because the starting speed, u, is only relative to an arbitrary frame of reference. It is somewhat like adding 1 to an unknown x: the result is still x + 1, also unknown. This applies also to the question of accelerating a mass to the speed of light.
It is widely believed that the universe is expanding in all directions. Due to discoveries in radio astronomy, particularly the red-shift of light from distant objects, it appears that this expansion is cumulative, meaning, the farther away the object observed is, the faster it is receding from the observer. It does not matter what direction we look, this is occurring.
Hence, a so-called radio galaxy is moving away from the observer so fast that its radiation signature is shifted down to the radio band. The only explanation of this is that space is expanding for some unknown reason, and that expansion accumulates over distance in a way that appears as acceleration of distant objects. This cumulative recession is not the same thing as expending energy to accelerate a mass.
Now, our thought experiment:
We in the Milky Way Galaxy, M, observe in a certain direction a very distant galaxy, A, receding at 80% the speed of light. Of course, if someone in that galaxy looks back at us, they can legitimately say that it is we who are receding from them at 0.8 c.
So which is it? We can only say that A is moving away at 0.8 c relative to our velocity (which is not absolute), and that it is equally true for B to say that M is moving away from B at 0.8 c. The only difference is an arbitrarily chosen sign. For one, it is 0.8 c, for the other it is -0.8 c.
As Galaxy A moves further and further away from M over perhaps millions of years, its speed relative to M will continue to increase until, measured by M, its relative speed surpasses the speed of light, at which time it will become —and forever remain— invisible to M, because the light from it can never reach our telescopes. Let’s call this M’s light horizon because it is relative to the radius from M within which light can reach M.
Now suppose A points their telescopes away from our direction (MA). What will they see? Whatever else is out there to be seen within their light horizon, which is beyond our light horizon.
Galaxy A has not been ‘accelerated’ to the speed of light; the expansion of space causes this exponential recession. After its disappearance from our sight, A will not be moving faster than the speed of light relative to the speed of light, only relative to observers at M.
The consequence of this is that there is no way to know how far away the ‘edge’ of the universe is—or even if there *is* an edge. We therefore cannot assume that the universe is finite. I don’t. Hence, if we can’t define an edge, we also cannot find a center, and we cannot assume that the universe even has a beginning. All we know is that it is expanding exponentially in all directions and that objects beyond our light horizon are invisible to us (and we are invisible to them).
Finally, let us point our telescopes in the opposite direction of A, to galaxy B, receding from M at 0.7 c. Again, B may correctly say that we are receding from them at 0.7 c.
And at what velocity will we at M say A and B are receding from each other? It is MA+MB = 1.5 c. So yes, although A and B cannot see one another, their relative velocity is 1.5 c. Only M, who can see both, knows this.
This is what is really meant by “If there is matter … out there that is already faster than light, then it will always remain faster than light.”
Of course that’s only relative, not absolute.
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The common analogy likens the galaxies to spots on the surface of a balloon that is being inflated. As the rubber stretches, all the spots move away from each other.
This statement, taken from a current astronomical text, can be found in almost any explanation of the recession of the distant galaxies, either in essentially these same words, or in terms of a three-dimensional analog, such as the one used by Fred Hoyle, in which he compares the galaxies to raisins in a pudding expanding in the oven. It testifies to the general recognition of the fact that the kind of motion typified by the movement of spots on the surface of an expanding balloon is, in some way, different from ordinary motion. This difference has not received any intensive scrutiny in physical thought, and is not given any attention in the textbooks. Indeed, the definition of motion is customarily expressed in terms that specifically exclude the kind of motion that we observe on the balloon surface. The results of the investigation reported in this present work indicate, however, that this special type of motion plays a significant part in many physical phenomena, and that a thorough knowledge of its nature and properties is essential for a full understanding of those phenomena.
As a first step in this direction, a critical analysis of the expanding balloon situation is in order. If the motion of the spots is examined in isolation, without placing the balloon in a reference system, or introducing a reference system into the balloon, which can easily be done conceptually, or if a similar mental picture of the receding galaxies is constructed, there is no way by which the motion of any one spot, or of any one galaxy, can be distinguished from that of any other. The only identifiable change that is taking place is a continuous and uniform increase in the magnitude of the distances between spots, or between galaxies. All spots and all galaxies are moving outward at a constant speed, but they are moving outward in all directions, which means that the motions have no specific directions. Thus the only property of this type of motion is a positive speed magnitude. Such a motion is, by definition, scalar.
With a little further exercise of the imagination, we can make the analogy with the galaxies somewhat closer by replacing the balloon with an expanding three-dimensional object, perhaps some kind of a transparent expanding plastic ball, with visible spots scattered throughout its volume. Here, again, the motion of all spots is simply outward, and unless a reference system is arbitrarily introduced to provide directions, the only property of the motion is its positive (outward) magnitude.
This view of the expanding plastic ball that we derive by mentally abstracting the ball from the local environment, and considering it in isolation, is exactly the same as the view that we get from observation of the distant galaxies. The only thing that we know about the motions of these galaxies is that they are receding from our own galaxy, and presumably from all others, at speeds that increase in direct proportion to the distance, just as the relative speeds of the spots in the interior of the expanding plastic ball obviously do. What we observe, then is a scalar motion of the galaxies, a motion that has no property other than a positive magnitude.
The currently popular view is that the galactic recession results from a gigantic explosion in which the entire contents of the universe were thrown out into space at the speeds now observed. The radially outward motion in all directions is explained as the result of velocity differentials. On this basis, the galaxies in one direction are receding because they are moving faster than the galaxy from which we are observing them. In the opposite direction, the galaxies are presumed to be slower than ours, and we are therefore moving away from them. There is no way by which this kind of a distribution of motions, if it exists, can be distinguished from motion of the type illustrated by the spots in the expanding plastic ball. Regardless of its origin, motion of this kind has no inherent direction. Each identifiable point, or object, is simply moving directly away from all others. Any further characteristics that may be attributed to those motions to fit a theory or explanation of their origin are nof relevant to the existing physical situation.
The type of motion with which we are familiar in everyday life is vectorial. This is motion relative to a fixed reference system. Like scalar motion, it has a magnitude, but it also has a direction in the reference system, and the effect of the motion depends on this direction, as well as on the magnitude of the motion. The difference between the two types of motion can be brought out clearly by consideration of a simple example. Let us assume that a moving point X is located between two points Y and Z on the straight line joining the two points. lf the motion of X is vectorial, and in the direction XY, then the distance XY decreases and the distance XZ increases. But if the motion of X is scalar, as on the surface of the expanding balloon, or in the expanding plastic ball, both XY and XZ increase.
The scalar motions readily accessible to observation are not isolated in the manner of those that we have been considering, but are physically connected to the spatial reference system. This physical coupling supplies the vectorial directions (directions relative to the reference system) that the motions themselves do not possess. The entity that actually enters into physical phenomena is not the scalar motion alone, but this motion plus the coupling to the reference system. In the condition in which it is physically observed, the balloon or plastic ball is connected to a reference system by placing it in that system in such a manner that some point X of the expanding object coincides with a specific point A in the reference system, the reference point, as we will call it, and the outward motion XY of a spot Y coincides with a vectorial direction AB.
The universe as a whole cannot be placed in a reference system, but the same result can be achieved by introducing a system of axes into the universe. The origin of these axes is then the reference point. The Big Bang theory of the origin of the galactic recession introduces a conceptual reference point of this kind, the location of the hypothetical explosion, but leaves the vectorial directions undefined. Thus, aside from being incomplete, and conceptual rather than physical, this Big Bang hypothesis does the same thing as the placement of the balloon in a position in the reference system. It connects a scalar motion with a reference system.
A scalar motion physically coupled to a reference system in this manner may act in essentially the same way as a vectorial motion, in which case it is not currently distinguished from vectorial motion. Alternatively, it may have some quite different characteristics. Current science then does not recognize it as a motion. For an understanding of these hitherto unrecognized types of scalar motions, we will need to examine some of the fundamental facts that are involved.
These pertinent facts are not difficult to ascertain. They have hitherto remained unidentified not because they are hidden or elusive, but because no one has looked for them. This, in turn, has been due to the lack of any clear indication that they might have a significant impact on physical understanding. After all, expanding balloons and plastic balls play no major part in physical activity. It is often asserted that issues in science are investigated for the same reason that men climb mountains—just because they are there to be climbed—but small mountains get scant attention, and seemingly insignificant physical phenomena generally receive the same casual treatment. An attitude of benign neglect is all the more likely to prevail where, as in this instance, some readjustment of thinking is necessary before the existing observational situation can be seen in its true light.
<unquote>
From: The Neglected Facts of Science, by Dewey B. Larson
https://web.archive.org/web/20191122232657/https://library.rstheory.org/books/nfs/01.html
PS: I tried to write a proper vector superscript notation, but it seems impossible.