Somewhere between holding on and letting go

In Special Relativity, it is assumed that the speed of light is invariable, such that light always moves at the same speed regardless of who’s observing it. This assumption has led to the prediction of time dilation, that time in a reference frame that is moving in relation to the observer must be slower. Using this understanding, physicists have predicted a variety of differences between clocks that apparently prove that the theory of Special Relativity is true.

Using similar reasoning to that which is used to predict time dilation, however, a completely opposite prediction could be made: time advancement. That is, as an object moves through space at a high velocity, the time in that reference frame should advance farther than in the observer’s reference frame. This effect is mathematically necessitated by the fact that two clocks that are in sync in one reference frame will not be in sync in a reference frame that is moving at a high velocity. Since one of the clocks will be faster than the other, an observer that moves from one clock to the other should move from one time frame to another time frame. It happens to be (in accordance with the direction of the velocity) that the difference in time frames will always be such that the new time frame will be faster than the old one. In other words, as an observer moves at a high velocity from one clock to another, he must also move through time at a rate equal to the difference between the clocks (which will always be farther forward in time).

The effect of time advancement is not taken into account in any of the predictions that supposedly prove that Special Relativity is true. Time advancement is a mathematically legitimate prediction, just as legitimate as time dilation, and yet it contradicts the evidence. An observer should not predict that a clock moving at a high velocity will end up slower than his own, he should predict that the moving clock will end up faster.

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Time advancement, like time dilation, is necessitated by the assumption that the speed of light is invariable. The rate at which a moving object advances through time can be derived from the difference in time frames between two ends of an object of some length (x) moving through space at some velocity (v) relative to an observer. The difference in time frames between the two ends of the object is equal to the difference between:

• t1 — the time it takes for light to reach the end of the object moving toward the light source, and 
• t2 — the time it takes for light to reach the end of the object moving away from the light source,

where the source of light begins exactly halfway between the two ends (x/2). At low velocities, the difference between t1 and t2 is insignificant; at high velocities, though, the difference can be very large.

The length of time it takes for light to travel any given distance is equal to the distance traveled divided by the speed of light (t = d/c). So, if the ends of the object were not moving in relation to the observer, the time it takes to reach each end would be equal to half the length of the object divided by the speed of light (t = (x/2)/c). [The distance traveled can also be represented as the time it takes to travel the distance times the velocity of traveler (x = tv).] However, since the ends of the object in question are moving, the time that the light takes to reach one of the ends must equal half the length of the object (x/2) divided by the speed of light minus the velocity of the end of the object in relation to the light source (c-v). Since one end is moving toward the light source, it must be represented as a velocity in the negative direction (-v), whereas the other end that is moving away from the light source must be represented as a velocity in the positive direction (+v). Therefore:

• t1 = (x/2)/(c+v) = (tv/2)/(c+v) = (tv/2c)/(1+v/c)
• t2 = (x/2)/(c-v) = (tv/2)/(c-v) = (tv/2c)/(1-v/c)
• t1-t2 = (tv/2c)*(1/(1+v/c)-1/(1-v/c))

Using these calculations, t1 minus t2 represents the difference in time between the two ends of the object in the observer’s reference frame. However, according to time dilation, everything in the moving object’s reference frame changes at a slower rate. So, in order to calculate the actual difference between the two ends of the object, the entire difference must be factored for time dilation (t’ = t*sqrt(1-v^2/c^2)). [α = sqrt(1-v^2/c^2).] Therefore:

• t1-t2  = α(tv/2c)*(1/(1+v/c)-1/(1-v/c))

The Upsilon Factor

The traditional formula for predicting the time in a moving reference frame is solely dependent on time dilation. The effect of time dilation in a moving reference frame is: t’ = t*sqrt(1-v^2/c^2), or t’ = tα.

The effect of time advancement in a moving reference is: t1-t2 =  α(tv/2c)*(1/(1+v/c)-1/(1-v/c)), or t1-t2 = tυ, or tυ = α(tv/2c)*(1/(1+v/c)-1/(1-v/c)). With a bit of algebra, tυ = α(tv/2c)*(1/(1+v/c)-1/(1-v/c)) can be simplified to υ = (v^2/c^2)/sqrt(1-v^2/c^2).

In order to account for both time dilation and time advancement, these factors should be added together to yeild the total difference in time between a clock in the observer’s reference frame and a clock in a moving reference frame. The effect of time dilation and time advancement in a moving reference frame is: t’ = tα+tυ.

Interestingly, α+υ = γ, the Lorentz Factor (1/sqrt(1-v^2/c^2)). Since α = 1/γ, this also means that υ = γ-(1/γ). More importantly, the total effect of time dilation and time advancement together is: t’ = tγ. In other words, a clock that is traveling at a high velocity relative to the observer should end up faster than a clock in the observer’s reference frame (not slower).

Time dilation is mathematically necessary when the speed of light is invariable. The effect of time dilation is such that the rate of time in a moving reference frame (R’) must be slower than in the observer’s reference frame (R). This is because in a moving reference frame, a ray of light will travel a shorter distance than it does in the observer’s reference frame. If the light ray travels a shorter distance and yet is moving at the same speed, the time it takes to travel that distance must also be shorter. Physicists have reasoned that in order for the total time to be shorter, the rate of time must be slower.

The rate of time in a moving reference frame (t’) can be derived using simple trigonometry (shown above), recognizing that all of the velocities involved (one path of light in two different reference frames, and one velocity to describe the difference in reference frames) form a triangle. Understanding this, it is easy to understand how as the velocity between reference frames increases, so does the difference in lengths that must be traversed by the ray of light in different reference frames (as v increases, the greater the difference between c and c’). Also, if we believe that this kind of triangle necessarily describes reality, nothing can travel faster than the speed of light (because v cannot be greater than c).

According to the theory of relativity, time can travel at different rates, lengths can have different measurements, and events can happen at different times, all based on how fast things are moving in relation to one another. Commonly, it is asked, ‘which reference frame is right?’ or, ‘what is the actuality?’ Physicists usually respond by saying that this question is meaningless, and that there is no right answer.

That is a very strange, unscientific, and generally useless response to give. Nonetheless, according to the theory of relativity, it seems to be the only legitimate answer that could be given. In response, the following thought experiment investigates what would happen if the physical predictions of relativity were measured. Ultimately, it seems that the question is not meaningless, and it may be the case that the theory of relativity is simply wrong (or incomplete).

The Setup

Imagine there are two synchronized clocks (C1 & C2) and a light bulb, which are all stationary in Reference Frame A (RF:A). The clocks are on opposite sides of the bulb, the exact same distance (D) away. On each clock is a sensor that stops the clock when it detects light.

Now imagine there’s a plane flying by, parallel to the path of the light rays to the clocks, at a very high velocity (V). The reference frame of the pilot is Reference Frame B (RF:B).

Predictions of Relativity

In RF:A (stationary clocks and light bulb), when the light bulb is turned on, the clocks should stop at the exact same time (T). The light travels the same distance, and light always travels at the same speed (c), so the light from the light bulb should reach each sensor at the same time. So, an observer in RF:A would predict, according to the theory of relativity, that the clocks will read identical times. It doesn’t matter when the light is turned on, the clocks should stop at the same time.

In RF:B (perspective of pilot), however, the story is a little different. After the light bulb is turned on, it will take some amount of time before the light rays reach the sensors to stop the clocks; because, although light travels really fucking fast, it cannot travel from one point to another instantaneously. Since, in RF:B, the clocks are moving at some velocity (V’), by the time the light rays travel to the clocks C1 will have moved closer to the origin of the light ray and C2 will have moved away from it. In other words, the distance that the light ray must travel to reach C1 will be shorter than to C2. And, since in relativity the speed of light is invariant, it must take a shorter amount of time for a light ray to reach C1 than to reach C2. So, an observer in RF:B would predict, according to the theory of relativity, that the clocks will read different times. And, once again, it does not matter when the light bulb is turned on, the clocks should stop at different times.

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downtotumbolia

On your relativity stuff: well, surely the theory of relativity is not true for every physical system. For example, at the microscopic level, the theory does not hold. A single evidence for that is the fact that subatomic particles are said to travel faster them the speed of light (quantum entanglement and the like). So the theory isn’t ”true”, because it can’t explain every physical system. But I guess you know that. Thing is, physicists view it through a different light.

When a theory is accepted by the scientific community, it is so because it explains some set of phenomena and/or can make accurate predictions about some physical system. That is true for relativity, notably so to the General ToR. It doesn’t mean it is absolutely true, or that it explains every aspects of objective reality. So.. By the time a theory does not work for a certain system, physicists discard that theory and elaborate another that can explain it, even if it is not in concordance with previous ones.

So.. I’m sorry if I didn’t understand the discussion you’re trying to raise here, but to me it is very simple: a theory is true until it can’t explain certain phenomena. From then on the theory is merely a valid model for a few phenomena, but not objectively true for all others. I’d say physicists would call it the utility principle, haha.

I think you make a good point about the utility of a theory; however, I also think it’s important for scientists to recognize the difference between a theory that makes some good predictions and one that makes consistently good predictions. I have doubts about the theory of relativity to the extent that I do not believe it can make consistently good predictions, mostly because it tends to make contradictory predictions. I will soon be posting some thought experiments that make this point clear.

Ultimately, I think the theory of relativity is false, or there are some deeper insights into our physical reality that I don’t yet understand. I am raising my concerns about the theory because I like science, and I want to be able to truly understand the natural world, but there are more questions to be answered before that is possible. And I’m not just going to take anyone’s word for it.

For the purpose of investigating the theory of relativity through thought experiments, these are some of the basic facts that have led to its development, and which will be considered in deriving contradictions.

Luminiferous Aether

When there is a disturbance in a medium such as water or air, it tends to create ripples in the medium. It has been observed that the speed of these ripples, the rate at which they move away from the source of the disturbance, depends not on the speed of the source but the rest-state of the medium. So no matter how fast a boat moves across the surface of water, the waves it creates will always move at the same speed.

Light is an electromagnetic wave. When an electric field is in flux a magnetic field is created as a byproduct, and when a magnetic field is in flux an electric field is created as a byproduct. The result of these fields constantly propagating one another is an electromagnetic wave. Because of its wave properties, scientists of the nineteenth century believed that light and other electromagnetic waves also moved through some kind of medium, sometimes called “luminiferous aether,” or more generally “aether.”

In 1887, Michelson & Morley used a light source, a light detector, and a series of mirrors in attempt to provide evidence of the existence of aether. The light in their experiment, however, did not behave how they predicted, and the evidence they gathered was logically inconsistent with the theory of luminiferous aether. Light did not behave like waves on the surface of water, and the assumption that there is some medium through which light must move was abandoned.

Relativity

In order to explain the data, Einstein proposed a radical new theory, known as the theory of relativity. The key component to this theory is that the speed of light is invariant; in other words, any observer, in any reference frame, will measure any light to travel through space at approximately 3.0 * 10^8 m/s (299,792,458 meters per second).

This theory has a number of interesting consequences. The first of which is time dilation. Imagine you have a light source and a mirror, placed a distance, D, away from each other. When you turn on the light, it travels from the source to the mirror, D, and then back to the source, for a total distance of 2 D. Whatever time it takes to travel this distance will be the time in your reference frame, T. So the light travels 2 D per T, or 2 D/T. Imagine now that the light and the mirror are on a ship moving at a very high velocity. Since the source of light and the mirror are moving, the round trip from the light source to the mirror and back to the light source must cover greater distance, D’ > D. If the speed of light is assumed to be invariant, the light must have more time to travel the necessary distance in your reference frame than it does in the first reference frame (in which the light source and the mirror are stationary). In other words, time must travel slower in the reference frame of the moving light source and mirror, in relation to how fast they are travelling, T’ > T. So, if the round trip of the light were measured, both reference frames would get the same result, because 2 D/T = 2 D’/T’. It is this reasoning that leads to the prediction of time dilation (which can be calculated using the Lorentz transformations).

In addition to time dilation, the theory of relativity also necessitates length contraction (objects that move very fast must have smaller lengths than when they are at rest) and the relativity of simultaneity (events that happen at the same time in one reference frame may not happen at the same time in another).

Evidence

There is a body of evidence that, in the eyes of many, serves as proof that the theory of relativity is true. In a variety of ways, the predictions of the theory have been empirically verified. It should be noted, however, that in order to make legitimate predictions the theory must be internally coherent. If the theory leads to contradictory predictions, there is no evidence that can verify the theory. Therefore, if the theory leads to contradictory predictions, the empirical evidence is irrelevant. It should be noted that, although the theory of relativity makes some predictions that have been verified, there might be a better theory to explain the evidence that has been gathered.

What if the scientific community has just as poor of reasons for believing in Special Relativity as religious communities have for believing in the word of God? What if people have failed to properly question the evidence? It wouldn’t be the first time.

We call him a genius, they called them prophets.

Take nothing on faith. Worship no one.