# Reconciling Constant Speed of Light & Relativity

• Sturk200
In summary: To determine v, we would calculate c-x/t. But in this case c-x/t is not always going to be equal to x, because v will be different than the speed of light in our frame. So we would have to compare the results of our calculation for different velocities and states of motion to see which one gives us the result we were looking for. In other words, we would have to do a calculation for every possible velocity and state of motion
Sturk200
If the speed of light is constant regardless of the state of motion of the source, then doesn't this imply that it is possible to calculate the velocity of a reference frame by measuring the time it takes for light to traverse some known distance in that frame. For instance if our frame is moving in the positive x direction with velocity v and a pulse of light is emitted from the origin, shouldn't it be possible to calculate v by considering the time it takes for the pulse to reach some position x? The actual distance traveled by the light beam will be the measured distance x plus the amount our reference frame has traveled in the requisite time it took for the light to reach x. In maths, ct=x+vt, and therefore v=c-x/t, where x is the apparent distance traveled by the light as measured in our reference frame, t is the amount of time it took for the light to make that trip, and v is the velocity of our reference frame. In sum, since the speed of light is constant, the amount of time it takes for light to travel some fixed distance will depend on one variable only, and that is the state of motion of the frame in which the time is measured, and thus it should be possible to deduce the state of motion of a reference frame, simply by measuring how long it takes for light to travel a fixed distance. My question is, doesn't something have to be wrong here, since according to relativity it should be impossible for an inertial observer to deduce his own state of motion by observing local phenomena?

Our frame is moving with velocity v relative to what?

our frame is moving in the positive x direction with velocity v

There is no absolute velocity, so the phrase has no meaning.

axmls said:
Our frame is moving with velocity v relative to what?
mathman said:
There is no absolute velocity, so the phrase has no meaning.

Let's define a reference frame such that ct=x. That is, so that when we emit a light pulse from the origin and measure the time it takes for that pulse to reach a position x, the product of the known speed of light and the time will be precisely equal to x. Can we do that and then define v w/r/t this newly defined frame?

Sturk200 said:
Let's define a reference frame such that ct=x. That is, so that when we emit a light pulse from the origin and measure the time it takes for that pulse to reach a position x, the product of the known speed of light and the time will be precisely equal to x. Can we do that and then define v w/r/t this newly defined frame?
This will be true in every frame, whatever their relative state of motion, and whatever the speed of sources in each frame. That was the key finding leading to SR (starting well before Einstein) - that the speed of light is the same independent of emitter speed in a frame, and is the same for frames moving relative to each other.

PeterDonis
PAllen said:
This will be true in every frame, whatever their relative state of motion, and whatever the speed of sources in each frame. That was the key finding leading to SR (starting well before Einstein) - that the speed of light is the same independent of emitter speed in a frame, and is the same for frames moving relative to each other.

Maybe I'm not being clear. Take a ruler and set it in motion in the positive x direction. Imagine that we are in the rest frame of the ruler. Now emit a pulse of light from the left end of the ruler and time how long it takes for the pulse to reach the ten inches mark. If the ruler is not moving at all relative to the ideal frame I tried to set up, then the time it takes for the light to hit the mark will be exactly 10 inches/c, because the light will actually have had to travel only ten inches. But if the ruler is moving, as we supposed, and if it's moving awfully fast too, then it will take a longer time for the light to reach the ten inches mark, because (1) it has farther to travel and (2) the speed of light is independent of the state of motion of the source. Now the difficulty I am having is this, if it takes longer for light to travel ten inches in my frame when my frame is moving in the direction in which light is emitted, then can't I deduce my state of motion from this extra time?

To illustrate more clearly, consider the comparison to a tennis ball in classical relativity. If I am traveling at constant velocity and fire a tennis ball at ten mph, it will always take the same of time to travel ten inches, no matter how fast I'm going or what direction I'm going in -- and this is because my state of motion imparts a velocity to the tennis ball, providing it with the means of traversing any extra distance created by my motion with no added time. Of course, when we are dealing with light there is no such effect, and my velocity will change how long it takes for light to travel ten inches in my frame.

Sturk200 said:
Maybe I'm not being clear. Take a ruler and set it in motion in the positive x direction. Imagine that we are in the rest frame of the ruler. Now emit a pulse of light from the left end of the ruler and time how long it takes for the pulse to reach the ten inches mark. If the ruler is not moving at all relative to the ideal frame I tried to set up, then the time it takes for the light to hit the mark will be exactly 10 inches/c, because the light will actually have had to travel only ten inches. But if the ruler is moving, as we supposed, and if it's moving awfully fast too, then it will take a longer time for the light to reach the ten inches mark, because (1) it has farther to travel and (2) the speed of light is independent of the state of motion of the source.
This is false, pure and simple. The rest of your difficulty follows from this. Pick 10 such rulers moving at different speeds. In frame in which each ruler is at rest, it will still take the same time to reach the 10 inch mark. Pick any combination of emitter motions and ruler motions, and every ruler will measure light from every emitter to be going at the same speed.

PAllen said:
This is false, pure and simple. The rest of your difficulty follows from this. Pick 10 such rulers moving at different speeds. In frame in which each ruler is at rest, it will still take the same time to reach the 10 inch mark. Pick any combination of emitter motions and ruler motions, and every ruler will measure light from every emitter to be going at the same speed.

Interesting. I guess my confusion is more basic than I thought. So then would the following be correct?

We place a light detector in the center of a ruler and two light sources, one on either end of the ruler, each facing the detector in the center. When we place the ruler at rest, on a table, the light detector registers simultaneous pulses every five seconds. Now we give the ruler a large constant velocity along the axis of its length. Will the light pulses still be registered as simultaneous?

Sturk200 said:
My question is, doesn't something have to be wrong here, since according to relativity it should be impossible for an inertial observer to deduce his own state of motion by observing local phenomena?
So the basis of relativity (in traditional derivations) are the two postulates. The first is the principle of relativity, which implies that you cannot measure an absolute velocity, and the second is the invariance of c.

Relativity starts from these two postulates and then proceeds to derive the Lorentz transformation which describes the relationships between distances and times as measured relative to different inertial reference frames.

It turns out that, in order to avoid the type of measurement you suggest, different frames will disagree on the distances and times involved.

Sturk200 said:
We place a light detector in the center of a ruler and two light sources, one on either end of the ruler, each facing the detector in the center. When we place the ruler at rest, on a table, the light detector registers simultaneous pulses every five seconds. Now we give the ruler a large constant velocity along the axis of its length. Will the light pulses still be registered as simultaneous?

Don't forget relativity of simultaneity - it's important.

If the two sources flash simultaneously in a frame in which the ruler is at rest, they will not flash simultaneously (that's relativity of simultaneity at work - don't forget it) in a frame in which the ruler is not at rest. The difference (along with length contraction) will be just enough to make up for the different distances traveled from source to detector so that the flashes reach the detector together no matter which frame you choose.

Did I mention the importance of rememembering relativity of simultaneity?

harrylin
Sturk200 said:
if the ruler is moving, as we supposed, and if it's moving awfully fast too, then it will take a longer time for the light to reach the ten inches mark, because (1) it has farther to travel

No, it doesn't. The ruler is length contracted. Once you take that into account, you find, as PAllen said, that ##ct = x## holds in every inertial frame.

controlfreak
Sturk200 said:
Interesting. I guess my confusion is more basic than I thought. So then would the following be correct?

We place a light detector in the center of a ruler and two light sources, one on either end of the ruler, each facing the detector in the center. When we place the ruler at rest, on a table, the light detector registers simultaneous pulses every five seconds. Now we give the ruler a large constant velocity along the axis of its length. Will the light pulses still be registered as simultaneous?

Yes if you are traveling with the ruler, but not to us who remained behind.

Sturk200 said:
If the speed of light is constant regardless of the state of motion of the source, then doesn't this imply that it is possible to calculate the velocity of a reference frame by measuring the time it takes for light to traverse some known distance in that frame. [..] My question is, doesn't something have to be wrong here, since according to relativity it should be impossible for an inertial observer to deduce his own state of motion by observing local phenomena?
That is exactly what led to "special relativity":

"We will raise [..] the “Principle of Relativity” to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory [..]" (emphasis mine).
- https://www.fourmilab.ch/etexts/einstein/specrel/www/

Others here already mentioned the main elements of the solution.

1977ub said:
Yes if you are traveling with the ruler, but not to us who remained behind.

A bit of clarification here. The pulses will arrive simultaneously at the detector according to both frames, They will not however be emitted simultaneously in both frames.

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## 1. What is the constant speed of light and how does it relate to relativity?

The constant speed of light, denoted by the letter c, is a fundamental physical constant that represents the speed at which all electromagnetic radiation travels in a vacuum. This includes visible light, radio waves, and X-rays. In Einstein's theory of relativity, the speed of light is considered to be a universal constant and a fundamental limit for the speed at which any physical object can travel. This means that no material object can ever reach or exceed the speed of light.

## 2. How does the constant speed of light affect our understanding of time and space?

According to Einstein's theory of relativity, the constant speed of light has significant implications for our understanding of time and space. It states that the laws of physics are the same for all observers, regardless of their relative motion. This means that time and space are not absolute, but rather are relative and dependent on the observer's frame of reference. This is why time can appear to pass differently for different observers, and why objects can appear to be different sizes depending on the observer's perspective.

## 3. Can anything travel faster than the speed of light?

No, according to our current understanding of physics, nothing can travel faster than the speed of light. As mentioned before, the speed of light is considered to be a fundamental limit for the speed at which any physical object can travel. This is because as an object approaches the speed of light, its mass increases infinitely, making it impossible to accelerate any further. This concept is known as the theory of special relativity.

## 4. How does the constant speed of light reconcile with the concept of time dilation?

Time dilation is a phenomenon predicted by Einstein's theory of relativity, which states that time passes at different rates for objects in different frames of reference. This means that a clock on a spaceship traveling at high speeds will appear to tick slower than a clock on Earth. However, this does not violate the constant speed of light because the speed of light is constant for all observers, regardless of their relative motion. This means that the rate at which time appears to pass may differ for different observers, but the speed of light remains the same.

## 5. How has the constant speed of light affected our understanding of the universe?

The constant speed of light has had a profound impact on our understanding of the universe. It has led to the development of the theory of relativity, which has revolutionized our understanding of space, time, and gravity. It has also played a crucial role in the development of modern physics and has helped us explain various phenomena such as time dilation, length contraction, and the equivalence of mass and energy. Without the concept of the constant speed of light, our understanding of the universe would be vastly different.

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