Speed of light, a Question, a Thought; Why and How?

Science and Technology
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I had a related question regarding the speed that I asked a physicist once. I wanted to know whether the speed of light includes spacial expansion or exclusive of it. (?) I can link you to his response but first want to see how others might answer this one. I’m not sure his response was completely satisfactory but it is a real question that has to be considered.

That is, for some speed/displacement, ‘x’ and the rate of linear expanstion, ‘e’, which of these three possibilities are true, and why?

(1) c = x + e
(2) c = x - e
(3) Some other explanation. If you think this one, what would you propose?

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I’m not sure that the two are related. AFAIK, expansion is a metric function whereas c is a physical limit.

Metric space

In mathematics, a metric space is a set together with a metric on the set. The metric is a function that defines a concept of distance between any two members of the set, which are usually called points. The metric satisfies a few simple properties.

Informally:

the distance from {\displaystyle A}A to {\displaystyle B}B is zero if and only if {\displaystyle A}A and {\displaystyle B}B are the same point,
the distance between two distinct points is positive,
the distance from {\displaystyle A}A to {\displaystyle B}B is the same as the distance from {\displaystyle B}B to {\displaystyle A}A, and
the distance from {\displaystyle A}A to {\displaystyle B}B is less than or equal to the distance from {\displaystyle A}A to {\displaystyle B}B via any third point {\displaystyle C}C.
Metric space - Wikipedia

Speed of Light (c)

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is defined as 299792458 metres per second (approximately 300000 km/s, or 186000 mi/s).[Note 3]

It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1⁄299792458 second.[Note 4][3] According to special relativity, c is the upper limit for the speed at which conventional matter, energy or any signal carrying information can travel through space.
Speed of light - Wikipedia

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I do not follow at all. “Metric space” merely seems like a standard based upon the geometry one uses. Although those non-Euclidean geometries are useful for the ease of some descriptions, like how Einstein needed a means to formulate something to define a spherical field (a metric that might describe the set of radial distance points from a mass used to define the strength of gravity. I find that many seem to overcomplicate the descriptions by jumping to advanced maths prior to establishing the logic needed to first define the theories intuitively.

Spacial expansion is inferred as real distance being added to space, …new points being added. So the relevance of e has to have a linear meaning based on some added distance per unit time that is real or the whole concept of expansion is a form of religious interpretation of the doppler effect of light. We use differences in velocity at apparently equal Euclidean distances when we look out at the stars, not the models’ means to make the math easier to describe when using an alternate geometry.

There is a ‘rate of expansion’ that is ‘linear’ and represents a segement of added space between us and the distant object from our perspective. The change in velocities we infer by the doppler effect of light to be ‘expansion’ can only mean that as things are further out, an increase of finite distance is added between a given unit of linear measure, like a meter. As such, my question is asking if the distance ct includes the finite addition of distance et or if ct is distinct from it and that et should require being added for each unit distance in the same time.

I just used c and e as velocities assuming it is understood these are distances per unit time. Sorry if that was not spelled out. They have the same unit of time here and so can be thought of algebraically as t(c + e) or t(c - e) as distances rather than velocities.

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(3) The speed of light has nothing to do with the expansion of space. c=c

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I did not imply that the speed of light is dependent upon expansion but that the expansion rate has to be either added, subtracted, or have some other mathematical relationship with respect to it.

If they were not, then you’d have to assume the apparent distance of objects are unrelated to the doppler shift in the spectra of light and thus equal to the actual distance. The doppler shift implies that what we see at distance D is actually an illusion due to the expansion rate and so is further than merely the distance that can be measured in terms of lightspeed.

Ignore the speed of light if this is confusing you. Instead, turn it into what distance it represents in a time unit, like a second. The distance is what counts or, as I initially worded it, the comparable rates as real distances in some unit of time. Certainly if a wave of light stretches due to expansion, a given period of that wavelength goes from a shorter one to a longer one. The difference of these two represents the additional space being added. And since all light waves travel at a constant speed, then the distance light travels in a given time of say a billion years ignoring expansion, this is much less than the actual distance inclusive of expansion.

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I think the standard answer to your question is that if space expands everything expands with it. The common example is that if we mark the length of a meter on the surface of a large balloon and then pump up the ballon to twice the original size the length of a meter also increases and so any measurement on the surface of the ballon using the meter marked on the surface of the balloon won’t change.

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Of course it has everything to do with the expansion of space. It is only because we insist that light speed is constant throughout the universe that expansion is deduced from red shift.

Expansion cannot be measured; it is a conclusion base on the premise that light speed is constant. If we were to accept the premise that the size of the universe is constant we would have to conclude that red shift shows us that light speed decreases over large distances.

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The specific speed of light has nothing to do with the expansion of space.

11 d later, rather than driving it.

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The example of using a balloon does not mean that matter expands with space. It is meant to help visualize how the space surrounding matter expands but that the relative positions of galaxies to each other remains the same. While I take issue with the Big Bang interpretation’s assumption of a fixed quantity of matter and energy as ‘popped’ into existence (where the original insult that gave “big bang” its name), it is the space that is ‘added’. This is why it is assumed that at the singularity was dense.

It is measured or it lacks meaning. It is called the Hubble constant.

See: Measuring the Universe’s Expansion Rate

I responded to this above but didn’t quote you directly. Did you miss this?

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Sorry. No I did read it.

Just a few corollaries:

The speed of light is constant in (any constant medium like the vacuum of) space.
Spacetime is acceleratingly expanding omnidirectionally at every point (if not fuelled by inexplicably increasing dark energy, then we haven’t even that faintest idea).
This has no effect whatsoever on the speed of light for any observer.
If an observer shines a light, the rate of expansion of spacetime, along its spatial dimensions over time, of increase of distance, along the light’s path cannot increase the light’s velocity, only its frequency: The light must be acceleratingly blue shifted.
The expansion of the universe is a function of the big bang of the now mainly vacuum of space and the accelerating omnidirectional expansion of the spacetime spatial dimensions over the time dimension (including cosmic inflation) that space fills.
The only things that change are distances, proper and comoving, between light emitters. And the frequency of the light.

I don’t understand c = x +/- e. What is x the rate of displacement of? And how is c a function of e in any regard?

The increasing speed of a receding galaxy from an observer at t1 is x + e1 <= c, with a red shift for each speed, x’s being constant, e’s accelerating, when it can no longer be observed at t2, x + e2 > c

But what do I know? : )

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Thank you.

From What Actually Expands In An Expanding Universe? - YouTube

“What Actually Expands in an Expanding Universe” by Veritasium, I understand it as he spells it out other than that I never interpreted the error he seems to assume is shared by some when they interpret the expansion of the wavelength as implying that matter expands too. So I understand all of this.

What he shows as a wave being stretched cannot apply to matter is obvious to me and what I responded to Write4U about the expansion as not including matter. [That was the same error that Veritas was mentioning as the common mistaken.] So taking that description of only the wave expanding, the difference between the stretched wave after say 1 second minus the wave at time zero is what I understand as the distance due to expansion in one second as a linear distance in line with the direction of the wave. That explains the extra space.

Now, when we initially measure the speed of light, the unit distance, ct, includes et, so that xt + et = ct, where x is the actual speed of light ideally with no expansion [So (et = 0)]. So in that ideal case, x = c. We assumed this before discovering expansion.

But because we discovered space as expanding later, we should have to go back and treat et as included in the original measure of ct, correct? So what I am not sure is whether we adjusted c to reflect the speed with respect to no expansion or if we adjusted it to reflect the included expansion correctly?

If we didn’t alter the original measure, then c = x + e. Only if we readjusted it with respect to expansion in one second, then we ‘fixed’ it so that x = c once again. Then we have no further use of x.

Do you understand the problem expressed this way? The physicist I initially asked confused my intepretation of the question. I never went back to ask given I only discovered his response about two years after I asked.

[Your last response mistook me too but in a different way.]

If you are not sure, I can try reasking another physicist later.

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In our Universe today, the light arriving from a distant galaxy is shifted into the red because the Universe is expanding. The expansion rate was greater in the past, and for this, more distant objects appear to be receding even more quickly than a naive extrapolation of the expansion rate would indicate: this is because our Universe doesn’t simply contain matter and radiation, but dark energy as well.

The way the expansion rate changes over time is determined by what your Universe is made up of. For the first few thousand years after the Big Bang, radiation dominated.

For billions of years after that, matter dominated. And today, it’s dark energy. But before the Big Bang, space expanded at an exponential, enormous rate, which stretched the Universe flat and gave it uniform properties everywhere. This was during the period of cosmic inflation.

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Exponential expansion means that rather than having the expansion rate slow as time goes on, at having distant points recede from one another at ever slower speeds, the expansion rate doesn’t drop at all. As a result, distant locations — as time goes on incrementally — get twice as far away, then four times, eight, sixteen, thirty-two, etc.

Because the expansion is not just exponential but also incredibly rapid, “doubling” happens on timescale of around 10-35 seconds. Meaning, by time 10-34 seconds have passed, the Universe is around 1000 times its initial size; by time 10-33 seconds have passed, the Universe is around 1030 (or 100010) times its initial size; by time 10-32 seconds have passed, the Universe is around 10300 times its initial size, and so on. Exponential isn’t so powerful because it’s fast; it’s so powerful because it’s relentless.

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![This diagram shows, to scale, how spacetime evolves/expands in equal time increments if your… [+]

Universe is dominated by matter, radiation, or the energy inherent to space itself, with the latter corresponding to cosmic inflation. Inflation causes space to expand exponentially, which can very quickly result in any pre-existing curved or non-smooth space appearing indistinguishable from flat, and drives any two non-coincident particles apart extraordinarily rapidly.]

If two particles are created very close to one another during this inflationary state, they still have to obey the laws of special relativity: they can only move relative to one another at speeds less than (or equal to, if they’re massless) the speed of light. But the space between them is free to expand at whatever rate the Universe dictates.

If that means you’d extrapolate their relative speed to be greater than the speed of light by combining the effects of relative motion (special relativity) with expanding space (general relativity), there’s nothing forbidding that. You’d simply be mistaken for attributing the entirety of the apparent cosmic motion to special relativity. And you don’t even need to go to an inflationary state to run into that problem.
In a region just 1/32,000,000th of the sky, we’ve found 5,500 identifiable galaxies, all owing to the Hubble Space Telescope. Hundreds of the most distant ones seen here are already unreachable, even at the speed of light, due to the relentless expansion of space.]

If you take a look at the galaxies in our Universe today, the ones that lie beyond about 15 billion light years already appear to be receding from us faster than the speed of light. If you got into a spaceship today and took off towards them at the speed of light, you’d never reach them.

The expansion of the Universe teaches us that the rate that the fabric of space is stretching is greater than the distance we can cover even at light speed; the distance between us and them increases by more than a light year with each year that goes by. Beyond a critical distance in the Universe, all the galaxies that reside there are already forever out of reach.

There is no theoretical bound on the expansion rate because it itself isn’t a speed, but rather a property of the Universe that’s determined by the amount of energy in it. Today, that rate is around 70 km/s/Mpc, but during inflation, it was likely some 1050 times higher.

Within the observable Universe (yellow circle), there are approximately 2 trillion galaxies.... [+] Galaxies more than about a third of the way to the boundary of what we can observe can never be reached due to the Universe's expansion, leaving only 3% of the Universe's volume open to human exploration.
Within the observable Universe (yellow circle), there are approximately 2 trillion galaxies.... [+] Galaxies more than about a third of the way to the boundary of what we can observe can never be reached due to the Universe's expansion, leaving only 3% of the Universe's volume open to human exploration.960×814 187 KB

Within the observable Universe (yellow circle), there are approximately 2 trillion galaxies… [+]

WIKIMEDIA COMMONS USERS AZCOLVIN 429 AND FRÉDÉRIC MICHEL / E. SIEGEL

In an inflationary Universe, any two particles, beyond a tiny fraction of a second, will see the other one recede from them at speeds appearing to be faster-than-light. But the reason for this isn’t because the particles themselves are moving, but rather because the space between them is expanding.

Once the particles are no longer at the same location in both space and time, they can start to experience the general relativistic effects of an expanding Universe, which — during inflation — quickly dominates the special relativistic effects of their individual motions.

It’s only when we forget about general relativity and the expansion of space, and instead attribute the entirety of a distant particle’s motion to special relativity, that we trick ourselves into believing it travels faster-than-light. The Universe itself, however, is not static. Realizing that is easy. Understanding how that works is the hard part.

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I don’t know where you get c = x + e from. For me c = c in all frames of reference. It’s not derived from anything, it’s measured.

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We discovered the constant of the speed of light before we discovered expansion. Since the expansion rate has such an imperceptible value except on large scales, it may seem trivial to redefine the speed of light. But we understand this kind of acceptance in error with respect to using classical Newtonian physics as sufficiently valid for practical considerations too.

But once we know that the actual Newtonian formulations are actually imprecise because it ignored a fixed maximum speed to everything in space, the rational thing is to use the new forumulas including the Lorentz transformations for precision. If any constants were derived using Newtoninan formulas, then any constants not updated when placed in the new formulation would be off, right?

So the old measure of ‘c’ to me is what my ‘x’ stands for in the ideal case that space does not expand. I hear you asserting that it doesn’t differ but think this is an error. This does not mean that the speed of light changes within the same frames of reference because the time changes as perceived by all the matter that measures the light too changes. When space expands, it also alters the particular wavelengh from its original ‘speed’ with respect to non-expanding space if placed ideally side by side, even though we cannot actually do this in practice. That is why the apparent distance of an object at greater distances is actually greater and greater in real distance the further out things appear.

For an extreme example, lets say that a source sent out not light but a gamma cosmic ray that locally cannot be measured when it is originally created and sent out. When far enough, it would stretch and shift into the light spectra range becoming what appears as ‘light’ at a great distance observer. {This example is similar to the light emitted rays that gets shifted into radio ranges as the cosmic background observations except that I am starting this example using a higher-than-light-spectra wave that becomes shifted into the light-range.]

We would not necessarily have a noticable pattern of the spectra of light because it is red-shifted. The characteristics would be distinct of a gamma ray spectra of the particular waves sent, whatever that may be. As such, we begin with a source of radiation that may not even be detectible if we were at the source and so it would appear that something went from a MEASURE of zero speed (since it is unmeasurable) to a MEASURE matching the speed of light when received.

I used this relative example to show logically that the difference of apparent speed of ‘nothing’ to ‘something’, with the understanding that they are the same speed, means that the total expansion distance is very great in comparison to the distance light travelled if there were no expansion at all. Yet they have the same real time with respect to any fixed inertial frame.

Thus (Actual Distance)/ Time is greater then (Ideal Distance of Non-expanding Space)/Time. The (Actual Distance)/Time is c as defined with expansion, but is not equal to c as defined ideally without expansion.

This proves that the two values are different and so some adjustment of the old constant has to exist. I assume that someone recognizes this but do not know if this adjustment occurred or if they kept the old constant but used some other invented constant using the original constantto define this.

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I have always liked this illustration that clearly shows the wavelike structure of the universe and that the wavelength of spacetime is growing longer and flatter, until at some point in the future the wavelength becomes flat and universal expansion stops?

Is the universe ringing like a crystal glass?

“The new finding suggests that the universe has slowed down and speeded up, not just once, but seven times in the last 13.8 billion years, on average emulating dark matter in the process,” said Mead. “The ringing has been decaying and is now very small — much like striking a crystal glass and hearing it ring down.”

Count the waves!

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Figure 2. Image credit: NASA.

…more

1 Like
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There is neither evidence nor requirement for c not to be c in any circumstance. Unless wiki knows otherwise and you know the link.

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@martin-peter-clarke

I’ll ask someone else. I’m not getting properly understood by the question.

[edit: the director ‘at’ martin above. I’m still adjusting to this software’s features.]

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That does bring up a question. There must be something that restricts a photon from travelling at infinite speed. Remember a photon reaches its speed instantaneously as it has no mass that needs acceleration.

IMO, it is the Higgs field that restricts a photon to c, at which point it acquires mass.

However during the inflationary epoch, for an instant, the universe (and everything in it was expanding (moving) at FTL into a totally “permittive” condition (nothingness).

So, perhaps the question can be rephrased to, “can a photon move at greater than c in a non-restrictive environment?”

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Higgs feels right. For now. But light has no mass at c. At all. Zero. The nothingness is still there. And it was spacetime that was expanding FTL.

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I know and that is the problem.
a) light does acquire energetic mass at c, because spacetime has “fields”
b) light occurs “inside” spacetime and is a result of field disturbance.
c) spacetime expands (inflates) at FTL

This presents a paradox.

conclusion : spacetime is expanding (inflating) faster than light can travel inside it but does not acquire energetic mass itself because it is apparently expanding in a totally permittive nothingness.

question: at what point do fields develop and do fields occupy all of spacetime?