# Why is the speed of light independent of a frame of reference?

I understand the Michelson–Morley experiment and its result; but what I don't know yet is the REASON.
Example:
A torch in free space is moving at a velocity [v] w.r.t me. Considering the material nature of light, shouldn't the speed of photons emitted from the torch be [v+c] w.r.t ME?
According to the experiment, it's not so.
I know how relativistic velocities are formulated (Lorentz transformation, Einstein's Addition, etc.). But all these calculations are based on the accepted norm that light speed in invariant. WHY? What's the scientific explanation of this (if any)? Is it still a mystery?

I've seen other posts regarding the speed of light, but couldn't go through them all. So, apologies if this topic already exists.

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Ich
"Why" is hard to answer, if you expect something tangible. Like the name of the responsible god.
One can prove from relatively basic axioms/postulates that there must be an invariant velocity, which is the maximum velocity also. This velocity could be infinite, then you'd get Newtonian mechanics. But it happens to be finite. Don't know why.
Light simply goes as fast as possible, as it has no mass. That's why the speed of light is the invariant speed.

jtbell
Mentor
In physics, the answers to all "why?" questions have more "why?" questions lurking behind them.

For example, one answer to "why is the speed of light invariant?" is "because spacetime has Lorentz symmetry." But that simply begs the question, "why does spacetime have Lorentz symmetry?" Nobody knows, at least not yet. Maybe someday someone will come up with an answer "X" that becomes generally accepted. But then everybody will ask, "But why is X?"

Doesn't somebody have some ideas about how light stays at c in different frames? Or is it just a given?

The speed c, distance over time, is the tangent of the furthest angle from both the space and time orthogonal basis vectors. The 45 degree angle.

Since these basis vectors transform in a way that they collapse in on each other, this tangent never changes in any set of coordinates (reference frame).

See attached picture.

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The speed c, distance over time, is the tangent of the furthest angle from both the space and time orthogonal basis vectors. The 45 degree angle.

Since these basis vectors transform in a way that they collapse in on each other, this tangent never changes in any set of coordinates (reference frame).

See attached picture.
Greetings,

It seems like you have an explanation, but I don't quite understand it

Could you elaborate?

Thanks

Speed is distance over time and distance and time are not constant.

Time for example, is a measurement of the motion of some reference object. Some people use pendulums, the sun, digital clocks, computers, etc. All these objects are one and the same, another object in motion.

This means time is once again a measurement of distance over time itself. So distance over distance over time means time is relative based on your reference object's reference frame (relative velocity).

So when you accelerate from one reference frame to the other (increase your relative velocity) the measurement of the speed of light, distance over relative time, will be exactly the same.

Time is something defined by humans, not a physical thing, and it is simply the comparison of objects that move. Because of this it is relative, and because there is nothing to use as a reference object that moves faster than the speed of light, the relative time will never allow any reference object (clock) to measure light moving any faster than c from any reference frame.

The number c itself has no special meaning, it is just a conversion factor. For another alien race the number c would be a different number based on their decision of units for measuring space and time. In proper units c = 1 and one unit of space is roughly 300 million meters.

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So this still leaves the reason behind the invariance of c, a mystery. I guess it's better to leave it that way.. for now.
Another question: Is there any solid experimental evidence to prove that mass increases with velocity or the phenomenon of time dilation?

jtbell
Mentor
Check out the sticky thread at the top of this forum: "FAQ: Experimental Basis of Special Relativity."

It is not a mystery, c is exactly the tangent of the 45 degree angle between the space and time basis vectors (which is always 1 y/x), any transformation will leave this tangent the same. After completing a special relativity course (which can be done in a 1 day cram) it can be fully understood. The big factor is that speed is a derivative of space.

There needs to be a sticky explaining the difference between "why" and "how" as questions addressed to physics, and what physics actually attempts to answer.

Questions like why is c the number that it is,
and why do charges accelerate each other,
and why is the mass of a proton the number that it is,
might not have an exact answer.

but with the question of why is the speed of light the same in all reference frames, it can be answered and has been since 1905.

bcrowell
Staff Emeritus
Gold Member
FAQ: Why is the speed of light the same in all frames of reference?

The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you have to define what you think would be satisfying. If you ask Euclid why the Pythagorean theorem is true, he'll show you a proof based on his five postulates. But it's also possible to form a logically equivalent system by replacing his parallel postulate with one that asserts the Pythagorean theorem to be true; in this case, we would say that the reason the "parallel theorem" is true is that we can prove it based on the "Pythagorean postulate."

Einstein's original 1905 postulates for special relativity went like this:

P1 - "The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion."

P2 - "Any ray of light moves in the 'stationary' system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body."

From the modern point of view, it was a mistake for Einstein to single out light for special treatment, and we imagine that the mistake was made because in 1905 the electromagnetic field was the only known fundamental field. Really, relativity is about space and time, not light. We could therefore replace P2 with:

P2* - "There exists a velocity c such that when something has that velocity, all observers agree on it."

And finally, there are completely different systems of axioms that are logically equivalent to Einstein's, and that do not take the frame-independence of c as a postulate (Rindler 1979).

For someone who likes axioms P1+P2, the frame-independence of the speed of light is a postulate, so it can't be proved. The reason we pick it as a postulate is that it appears to be true based on observations such as the Michelson-Morley experiment.

If we prefer P1+P2* instead, then we actually don't know whether the speed of light is frame-independent. What we do know is that the empirical upper bound on the mass of the photon is extremely small (Lakes 1998), and we can prove that massless particles must move at the universal velocity c.

In a system such as Rindler's, the existence of a universal velocity c is proved rather than assumed, and the behavior of photons is related empirically to c in the same way as for P1+P2*. We then have a satisfying answer to the "why" question, which is that the existence of a universal speed c is a property of spacetime that must exist because spacetime has certain properties (basically, it has some symmetries, and it doesn't have universal simultaneity).

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

Bokonon1verse5
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A torch in free space is moving at a velocity [v] w.r.t me. Considering the material nature of light, shouldn't the speed of photons emitted from the torch be [v+c] w.r.t ME?
...
If your question is about what is different between relativity theory and Newtonian/Galilean physics that allows something (not travelling with infinite velocity) to be measured as having the same velocity in any reference frame, then I can perhaps offer a physically satisfying answer in terms of LET. If on the other hand your question is about why is the universe the way it is, then one possible answer is the anthropic principle.

c is exactly the tangent of the 45 degree angle between the space and time basis vectors
But this is again experimentally shown isn't it? Is there any available derivation?

@bcrowell
empirical upper bound on the mass of the photon is extremely small
But this again is experimental right?

And I'm sorry but my knowledge in this field is yet shallow, so you lost me on the universal simultaneity thingy.

Also, what I inferred from you post is that a particle cannot be accelerated to light speed with such high a force due to some unexplained barriers of spacetime which are it's property.
But consider an universe in which there exists only one body and even if it's traveling at a velocity larger than c, we wouldn't know because there's nothing else to compare it to. So we can assume as well that the body is at rest, so the phenomenon is feasible. But in reality it's not. So does that mean that a body can not be accelerated to light speed but it can well be traveling at light speed (or maybe a large fraction of it) by default?

But this is again experimentally shown isn't it? Is there any available derivation?
It is just a consequence of our choice of axes. We usually choose the time axis to be perpendicular to the space axis with two dimensions supressed. The space axis units are chosen to be one meter and the time axis units are chosen to be one light meter. With this choice of axes the light path referred to these axes bisects the angle between these axes, that is forty five degrees to both axes.

Whatever the speed of light happened to be we could always set up the axes so that the light path makes such an angle with the axes.

Matheinste.

As a simpleton I would state that all we know is that c is constant, is measurable by various means and, so far, has held up under all observations (now, I am referring to 30,000,000 m/sec in a vacuum - light does slow down when it passes though a medium such as water or oil.)

It seems to logically fit into other observations about the so-called "tangent" as described above as well other "symmetries" of which I have no clue how they were derived, but actually, t is an observed "assumption."

To wit - geometry as taught in high school is Euclidean, and all the assumptions or postulates were just that - the most basic elements of this geometry so far never disproven. Along comes non-Euclidean geometry which forces a change in basics (for example, parallel lines do meet in a finite distance. This helps in the understanding of General Relativity, which Einstein and Hilbert "derived” (and Eddington demonstrated in 1919 and the Aussies did in 1922-3.)

Look at the parable of the two travelers who live in a two-dimensional world but that two dimensions is the surface of a sphere. As they move "north" they approach each other as if there were a "force" of attraction. Their unstoppable move "north" is the result of the unstoppable and ever persistent advance of time which extends the world lines. The worldlines should be straight in two dimensions but because the two dimensions are on a sphere, the world lines bend towards each other which means acceleration or force.

Likewise with c - the speed of light. It is possible that we are a speck on some greater system in which c "holds its own" at 30M m/sec. It is possible that this could change, too. After all, Newton was right with the world as he knew it. His speed, time, distance formulas, to use the British phrase, were "spot on." But the observable world as he knew it and as common sense tells us was merely a speck on a greater "reality" which Maxwell, Lorentz , Einstein, Hilbert and Eddington uncovered.

TCS
I understand the Michelson–Morley experiment and its result; but what I don't know yet is the REASON.
Example:
A torch in free space is moving at a velocity [v] w.r.t me. Considering the material nature of light, shouldn't the speed of photons emitted from the torch be [v+c] w.r.t ME?
According to the experiment, it's not so.
I know how relativistic velocities are formulated (Lorentz transformation, Einstein's Addition, etc.). But all these calculations are based on the accepted norm that light speed in invariant. WHY? What's the scientific explanation of this (if any)? Is it still a mystery?

I've seen other posts regarding the speed of light, but couldn't go through them all. So, apologies if this topic already exists.
Because all reference frames are the same. If the speed of light varied according to reference frame then there would have to be some ultimate reference frame.

Newton was right with the world as he knew it. His speed, time, distance formulas, to use the British phrase, were "spot on." But the observable world as he knew it and as common sense tells us was merely a speck on a greater "reality" which Maxwell, Lorentz , Einstein, Hilbert and Eddington uncovered.
I know what you mean. I understand the concept of higher dimensions and other realms of our universe (beyond our perception), but honestly, seems I need to study deeper to get it clear.

Because all reference frames are the same. If the speed of light varied according to reference frame then there would have to be some ultimate reference frame.
Well light has to originate somewhere, what if I let that 'somewhere' be the reference object (say, the sun).

@bcrowell What I inferred from you post is that a particle cannot be accelerated to light speed with such high a force due to some unexplained barriers of spacetime which are it's property.
But consider an universe in which there exists only one body and even if it's traveling at a velocity larger than c, we wouldn't know because there's nothing else to compare it to. So we can assume as well that the body is at rest, so the phenomenon is feasible. But in reality it's not. So does that mean that a body can not be accelerated to light speed but it can well be traveling at light speed (or maybe a large fraction of it) by default?

I guess that the all frames of relativity is the only one multi-einsteinself frame.
so that relativity is einstein one man show so that c is always c.
I think so.

Both statements work for predictions, but are unlikely to be the whole story. Spacetime is a model which conforms well to reality (usually), and the QM vacuum is the same for "empty" space. These are just current theories which are useful for application and furthering the quest for better and more descriptive theories. I don't think that people accept either of the premises you mention, they accept the theories which describe the observed behavior, and wait or search for better theories.
Isn't this somewhat a semantic distinction? Spacetime (geometric), QM quantum field and spacetime "fabric" all describe a space that has qualities.
Is not just nothingness, pure vacuum.

Einstein said roughly,,, Space has no existence outside of matter.

This can be interpreted as; space is brought into existence as an emergent consequence of matter. It could still have actual qualities as a background for the behavior and motion of matter and EM propagation.

I agree that space must be filled with waves, EM , Gravity (either as propagated "gravitons " or as a geometric reality) etc. That this alone constitutes a background of sorts , with possible consequences , besides what ever emergant or intrinsic properties it might possibly have.

Isn't this somewhat a semantic distinction? Spacetime (geometric), QM quantum field and spacetime "fabric" all describe a space that has qualities.
Is not just nothingness, pure vacuum.

Einstein said roughly,,, Space has no existence outside of matter.

This can be interpreted as; space is brought into existence as an emergent consequence of matter. It could still have actual qualities as a background for the behavior and motion of matter and EM propagation.

I agree that space must be filled with waves, EM , Gravity (either as propagated "gravitons " or as a geometric reality) etc. That this alone constitutes a background of sorts , with possible consequences , besides what ever emergant or intrinsic properties it might possibly have.
This sounds a bit like an argument for an Ether...

TCS
This sounds a bit like an argument for an Ether...
I'm not against an "ether" as long as you are really careful about how you define it. If you define the ether as having a zero velocity for all observers and if you say that all particles are distributed throughtout the entire universe and the thickness of the ether is the sum of the the thicknesses of all particles at the spot, then I would accept the existence of a type of ether. Although such an ether wouldn't have the qualites of the 19th century ether and you couldn't think of it as the oscilatory medium of em waves in the 19th century sense.

However, you would want to think of the ether as expanding with time so that the particles would have a Minkowski (hyberbolic in time) type metric and the expansion as being constrained by the thickness of the ether so that the particles would have a GR type metric (the local degree of hyberbolicity would be determined by the energy density)..

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I'm not against an "ether" as long as you are really careful about how you define it. If you define the ether as having a zero velocity for all observers and if you say that all particles are distributed throughtout the entire universe and the thickness of the ether is the sum of the the thicknesses of all particles at the spot, then I would accept the existence of a type of ether. Although such an ether wouldn't have the qualites of the 19th century ether and you couldn't think of it as the oscilatory medium of em waves in the 19th century sense.

However, you would want to think of the ether as expanding with time so that the particles would have a Minkowski (hyberbolic in time) type metric and the expansion as being constrained by the thickness of the ether so that the particles would have a GR type metric (the degree of hyberbolicity would be determined by the energy density)..
It must also be undetectable.

Matheinste.