## Do Physics Equations Disprove the Speed of Light as a Constant?

• 450
For the mathematically inclined, does the following manipulation of equations suggest that quantized matter lacks a speed limit traditionally gauged as the velocity of light?

(*Amended with the correct Planck's constant units in a following post, so you may want to skip this and go directly to that one. The change does not alter the final equation.)

1.
The units of Planck's constant are joule seconds or meters per kilogram per second. This essentially amounts to distance multiplied by mass and time, which I'll call "dmt".

2.
Wavelength equals Planck's constant divided by mass and velocity, which can be written as w=dmt/mv.

If we cancel mass, then translate the remaining variables into meters and seconds for the sake of demonstration, we get w=meters*second/(meters/second). This translates into seconds squared, which I'll call time (t) squared.

3.
Force equals mass times acceleration, F=ma, and energy equals mass times the squared speed of light, E=mc(squared).

If we solve for mass and then equate, we get F/a=E/c(squared), and cross multiplying yields Ea=Fc(squared).

If we again translate distance and time quantities into meters per second, we get:
E*m/s(squared)=F*meters(squared)/second(squared).

If we cancel terms, energy equals force multiplied by distance, E=Fd, which can be translated into energy equals mass multiplied by acceleration and distance, or E=mad (lol).

4.
Frequency equals energy divided by Planck's constant, f=E/P. P=dmt, and E=mad, so f=mad/dmt.

If we cancel mass and distance, f=a/t remains. Substituting meters and seconds again, we get
f=meters/seconds(squared)/seconds, which translates into meters/second(cubed) or distance divided by time(cubed), d/t(cubed).

5.
If we multiply w=t(squared) by t, we get wt=t(cubed). If we solve the frequency equation for t(cubed), we get d/f. This yields wt=d/f.

In this scenario, time has been completely disjuncted from distance, which seems to imply the absence of a velocity constant, whether of light or any kind. So are values of time, distance, frequency and wavelength completely without intrinsic parameterization in the context of current physics? Do basic equations intimate an absence of dimensional constants, whether of space, rate or acceleration?
• 6.5k
The units of Planck's constant are joule seconds or meters per kilogram per second.
Per second squared.

J = (Kg)(m^2)/s^2

That is, J = (kg)(m^2)(s^-2)

I get the s-squared. I do not get why the the m is squared. To anyone explaining it, please KIS.
• 450
Whoops!, substitute via distance rather than time and you get the same final equation: wt=d/f. I got the units of Planck's constant incorrect - m(squared) kg / s, but doesn't change the result with appropriate cancelling.
• 1.6k
The very premise of this exercise is utterly clueless. Physics equations don't prove, much less disprove the assumptions that were built into them.

Wavelength equals Planck's constant divided by mass and velocity, which can be written as w=dmt/mv.

If we cancel mass, then translate the remaining variables into meters and seconds for the sake of demonstration, we get w=meters*second/(meters/second). This translates into seconds squared, which I'll call time (t) squared.

LOL. So you got the wrong units for length, right in step 2. This is where one would go back to look for the mistake, but no, you forge ahead...
• 450

Snarkiness as anticipated lol I corrected the Planck's constant value, yielding d(squared)*m/t. It still works: d=w, d=acceleration*time/f. The assumption is usually made that the speed of light is a constant maximum, which this shows can only be justified empirically if at all, not in principle. The equations don't support it. I recall reading that Einstein himself never claimed the speed of light as an absolute maximum anyways, but I've demonstrated that it is radically hypothetical based on fundamental equations. You can quote me on that!
• 405
The equations of special relativity entail that nothing can accelerate up to or beyond the speed of light, taken as the constant c, since the logical consequence would be a division by zero. Einstein was clear about that. This says nothing, of course, about the possibility of the existence or non existence of things that travel at speeds above c, it just rules out those things having accelerated to those speeds from sublight speeds. Einstein was always clear that fixing c as a constant for all frames of reference was an assumption, and one that would be finally justified by empirical results, as it has been numerous times. Dimensional analysis has a role in physics, of course, but as far as I'm aware it's just a basic tool to avoid simple errors, and to use if for that, you need to get the dimensions right from the beginning.
• 450
This says nothing, of course, about the possibility of the existence or non existence of things that travel at speeds above c, it just rules out those things having accelerated to those speeds from sublight speeds. Einstein was always clear that fixing c as a constant for all frames of reference was an assumption, and one that would be finally justified by empirical results, as it has been numerous times. Dimensional analysis has a role in physics, of course, but as far as I'm aware it's just a basic tool to avoid simple errors, and to use if for that, you need to get the dimensions right from the beginning.

What's conceptually interesting to me about the wt=d/f formula is that the perceptual and structural unity of intuitive spatiotemporality is completely dissolved, with both space and time being equivalent to something like pressure, temperature and volume in Boyle's gas law equation (PV=nRT): purely definitions of emergent properties in substance, and only real by analogy with macroscopic structure.

If you think of spacetime as not the fabric of reality but instead a pair of descriptive variables only real by analogy, this suggests that motion is not essentially either spatial or temporal, though it is hard to imagine logically. Space and time are direct and inverse correlations that don't exceed the constraints of modeling formulas in which they are utilized, not in any way essences.

If motion is fundamentally supraspatiotemporal, it seems plausible that light can be part of a large spectrum that extends in the direction of more rapid speeds, while the acceleration of massive bodies towards light speed constitutes a very narrow range of material occurrence. Velocity and acceleration as we have thus far measured them could be like a sliver of the motion spectrum. Atomic orbital shifts in response to photon/electron interactions might occur faster than light, advanced waves may propagate such that slower events are affected by backwards in time causal reactions, quantum entanglement becomes explicable, and the existence of tachyons may be not improbable.
• 1.2k
Please return to metaphysics. The real deal is a challenge.
• 450
Please return to metaphysics. The real deal is a challenge.

I wonder if physicists and mathematicians popularize their ideas just to set the public up for a mocking lol You dismiss my analysis just because I didn't utilize decimals? We all can comprehend the basic concepts of physics without a calculator. I've taken calculus and quantitative chemical analysis, I know some stuff.
• 1.2k
You dismiss my analysis just because I didn't utilize decimals?

Not a decimal person myself. But equations do not determine reality.
• 8.5k
The equations of special relativity entail that nothing can accelerate up to or beyond the speed of light, taken as the constant c, since the logical consequence would be a division by zero.

What about the effects of spatial expansion? When spatial expansion increases as time passes, and things start speeding away from each other faster than the speed of light, does this not qualify as acceleration?
• 450
But equations do not determine reality.

I think my equation might be getting at something relatively fundamental though, at least in the context of current physics. Does wt=d/f imply that time dilation is directly proportional to distance or dimensional extension and inversely proportional to wavelength and frequency, while distance is directly proportional to wavelength and inversely proportional to frequency or energy?

Is the classical scale categorically disjuncted from the quantum scale because of time dilation? Is energy directly proportional to time contraction?
• 1.2k
Sorry. Can't follow what you are trying to say.
• 450

Subatomic phenomena of the quantum scale as traditionally construed might behave so differently than objects at the classical scale because of an exponentially compressed distance accompanied by likewise contracted time, giving them almost instantaneous rates. The more energy that is contained in a system at the quantum scale, the more time contracted its causal effects, all else being equal. The sun generates relatively non-time contracted effects because most of its energy is dissipated into kinetic energy of the classical scale. Brains by contrast, with the elaborate quantum machinery of their unique biochemistry, are like quantum suns, radiating entanglement effects on a large scale while overriding classical time dilation. Maybe this accounts for the introspective perceptions which lead to a panpsychist impression of the way consciousness works, the "all is mind" illusion.
• 1.2k
Brains by contrast, with the elaborate quantum machinery of their unique biochemistry, are like quantum suns, radiating entanglement effects on a large scale while overriding classical time dilation.

A reference in this regard would be nice. I know very little about the quantum world.
• 450
A reference in this regard would be nice. I know very little about the quantum world.

Try reading three threads I posted awhile back at this site to get a feel for the concepts, which seem to be unprecedented:

Qualia and Quantum Mechanics
Qualia and Quantum Mechanics, The Sequel
Qualia and Quantum Mechanics, the Reality Possibly
• 1.2k
If I had more interest in this subject I might do just that. It may be unprecedented but the word "qualia" dampens my enthusiasm. Good luck, though.
• 450

Uniting spirituality, psychology and physics, how can your interest flag?
• 450
To expand upon this for those whom it may concern:

According to this equation, wt=d/f, time is completely unlike a constant, but rather a conditional variable, inversely correlated with wavelength and frequency, and directly correlated with distance. This means that, all else being equal, increasing frequency (energy) causes time contraction, and decreasing distances faster than energy (per what units?) decreases will cause time contraction as well.

In electromagnetic radiation, wavelength and frequency are inversely correlated in a linear relationship, so the d/t or rate value stays effectively stable, leading to the famed constant speed of light across all of its wavelengths. But in an atom, frequency is more like energy concentration and wavelength a configuration of these energy concentrations, together varying in an extremely nonlinear way as obviously manifest by the heterogeneity of atomic structure. Distances are also nonlinear since a peak of the wave function or equivalently the core of a wavicle’s position is much smaller in diameter than the entire range encompassing its less probable and thus less concentrated locations.

Vast difference between quantum and classical phenomena can be explained by the deep disjunct between subatomic and macroatomic scales. The subatomic scale contains all the energy of the classical scale, but the relatively tiny diameter of its highest probability concentrations compared to the total probability wave means that a huge time contraction is in effect, making the relative motions of subatomic matter almost instantaneous. This can be contrasted with the greater continuity of macroatomic to macroscopically Earthlike scales that produces dynamics of classical physics.

A solar system has similarly large disjuncts between stars, planets and what surrounds them, causing a time contraction which makes their movements coordinated in an effectively instantaneous way.

What insights can we gain from the fact that increases in energy at constant distance will result in time contraction? If subatomic wavicle cores contain almost as much energy as the macroatomic structures they comprise, this means that time contraction is not simply a nanoscale phenomenon but permeates nature. Earthlike matter consists of dual timescales: a quantum layer in which the interactions of high energy wavicles are time contracted enough to happen almost instantaneously even on the macroscopic scale, while the classical layer is time dilated such that events unfold much more slowly by comparison.

Causation at the quantum scale happens almost instantaneously, and the elapsed time is faster the more high energy the matter is. Some of the highest energy matter on Earth is electricity, for it is made up of maximally compacted electrons. This high energy means that it conveys quantum entanglement effects more robustly than probably any alternate form of Earthbound matter.

The brain with its one hundred trillion synaptic connections is an extremely powerful electric field, and so radiates quantum causation like an electron differential or electrical potential sun, seemingly entangled with surrounding matter in an instantaneous way that defies the laws of classical physics. This can perhaps explain the mystical experiences such as synchronicity that many have, and the philosophical doctrine of “all is mind” which we see surfacing throughout history.
• 1.2k
You know, you sound very authoritative in all this, but I don't have the knowledge to engage you, and I don't know if you actually know what you are talking about. But I give you the benefit of the doubt. It would be good if kenosha kid or another real physicists would comment.
• 450
It would be good if kenosha kid or another real physicists would comment.

That's what I'm hoping for. Gotta get all my variables accurately correlated, this is a challenge. Its all derived from deep thinking about books by renowned physicists, so I'm not b.s.ing you.
• 450
An amended version of the OP's proof using the correct Planck's constant units. This also yields wt=d/f.

1.
The units of Planck's constant are joule seconds or (meters^squared) * kilograms / seconds. This essentially amounts to distance squared multiplied by mass and divided by time, which I'll call
"(d^squared)m/t".

2.
Wavelength equals Planck's constant divided by mass and velocity, which can be written as
w=((d^squared)m/t)/mv.

If we cancel mass, then translate the remaining variables into meters and seconds for the sake of demonstration, we get w=((meters^squared)/second)/(meters/second). This translates into meters or distance (d).

3.
Force equals mass times acceleration, F=ma, and energy equals mass times the squared speed of light, E=m(c^squared).

If we solve for mass and then equate, F/a=E/(c^squared), and cross multiplying yields Ea=F(c^squared).

If we again translate distance and time quantities into meters per second, we get:
E*m/(s^squared)=F*(meters^squared)/(seconds^squared).

Cancel terms and energy equals force multiplied by distance, E=Fd, which can be translated into energy equals mass multiplied by acceleration and distance, or E=mad.

4.
Frequency equals energy divided by Planck's constant, f=E/P. P=(d^squared)*m/t, and E=mad, so f=mad/(d^squared)m/t.

If we cancel mass and distance, f=at/d remains, which can be translated into d=at/f. Substituting meters and seconds again, we get d=meters/(seconds^squared)*seconds/f, which translates into (meters/second)/f or d=d/ft: ft must equal 1, perhaps in conjunction with as of yet unspecified variables, which at any rate is an intermediate step in this context so that the complications can be disregarded.

5.
d=w and d=d/ft, yielding wt=d/f.

For those knowledgeable about physics, what is the significance of ft=1? It seems that as energy increases, time contraction occurs, and if the energy increase is nonlinear by whatever measure, time will contract nonlinearly, perhaps exponentially. Maybe a constant would be necessary to scale this properly. Distance and wavelength probably need to be defined with more precision, even though the equation in this crude form does capture the essence of correlations being considered.

Maybe w/t=df is a valid equation also, from a different perspective? Does w/d have to equal 1, and if so what are the implications?.
• 405
Nothing, or more strictly no object, can accelerate beyond the speed of light, including galaxies, and that is according to both special and general relativity. Galaxies far far away from us appear to be receding at speeds greater than the speed of light, this is true, but, according the physics I was taught anyway, which of course may one day be superceded, this is a function of at least two parameters, the velocity of the galaxy and the expansion rate of space. However, space is not a thing that has a velocity: an expansion rate is not measured in metres per second, but in metres per second per relative distance, it has the same units as frequency, not velocity.
• 112
To answer your actual question in the OP....

No, equations to not tend to prove anything. Equations merely try to describe what is observed.

They may provide a theoretical explanation at best, but the only thing which acts as proof is evidence and examples in the real world.

The two basic examples which break the principle that the speed of light is the fastest speed that anything can travel are:-

1 - the size of the universe, which on current estimates is more than 98bn light years across - and therefore more than 4 times the widest spread that could be achieved by an exploding singularity at the speed of light.

2 - the faster than light experiments conducted by Nicolas Gisin across lake Geneva which demonstrated that particles of light travelling away from each other in opposite directions (twice the speed of light) were still able to communicate instantly - (or technically, at least 10,000 times the speed of light).

The fact that your equations can't cope with this means that they are not proof of reality.
• 405

1 Doesn't really break the "no object faster than the speed of light" principle: as per my post above, the speed that galaxies appear to be receding at is a function of both the velocity of the galaxy which is sublight and the expansion rate of space, which is not a speed at all.

2 New one to me, I'll have to look it up. Is it yet another case where QM and relativity clash?
• 156

Force equals mass times acceleration, F=ma, and energy equals mass times the squared speed of light, E=m(c^squared).

If we solve for mass and then equate, F/a=E/(c^squared), and cross multiplying yields Ea=F(c^squared).

This is terribly unprincipled. F=MA is a Newtonian approximation, that disintegrates in special-relativistic (or for that matter, general-relativistic) contexts - from which the latter formulation stems. You can't interchange the two, without discounting the argument of relativistic mass (which is inextricably associated with the work encompassed by a body). F = dp/dt, with an updated Lorentz factor, may be an appropriate substitute. Physics isn't so exoteric, such that it lends itself to a mindless coalescence of equations, with an approach bereft of a priori significance.

https://qr.ae/pGX0v5

If motion is fundamentally supraspatiotemporal, it seems plausible that light can be part of a large spectrum that extends in the direction of more rapid speeds, while the acceleration of massive bodies towards light speed constitutes a very narrow range of material occurrence.

What, on Earth, is 'supraspatiotemporal'?

For those knowledgeable about physics, what is the significance of ft=1? It seems that as energy increases, time contraction occurs, and if the energy increase is nonlinear by whatever measure, time will contract nonlinearly, perhaps exponentially. Maybe a constant would be necessary to scale this properly. Distance and wavelength probably need to be defined with more precision, even though the equation in this crude form does capture the essence of correlations being considered.

Time contraction, in special-relativistic contexts, is engendered by a local constancy of the speed of light in (presumed) Minkowski Spaces; that is to say, c remains intractable to inertial reference frames.
You can't passively adhere to that idea, whilst simultaneously espousing tachyons - or variable lightspeeds.

Try reading three threads I posted awhile back at this site to get a feel for the concepts, which seem to be unprecedented:

Qualia and Quantum Mechanics
Qualia and Quantum Mechanics, The Sequel
Qualia and Quantum Mechanics, the Reality Possibly

Why is it, that there seems to exist an unrelenting fixation on integrating QM with metaphysical ideas? Quantum Mechanics is the hallmark of Mathematical Physics; it entails Wavefunction Collapses, Hilbert Spaces, PDFs, Dirac Matrices and Path Integrals; Qualia, on the contrary, pertains to human consciousness. In what fictitious universe, are the two intertwined with one another?

Causation at the quantum scale happens almost instantaneously, and the elapsed time is faster the more high energy the matter is. Some of the highest energy matter on Earth is electricity, for it is made up of maximally compacted electrons. This high energy means that it conveys quantum entanglement effects more robustly than probably any alternate form of Earthbound matter.

The brain with its one hundred trillion synaptic connections is an extremely powerful electric field, and so radiates quantum causation like an electron differential or electrical potential sun, seemingly entangled with surrounding matter in an instantaneous way that defies the laws of classical physics. This can perhaps explain the mystical experiences such as synchronicity that many have, and the philosophical doctrine of “all is mind” which we see surfacing throughout history.

With all due respect, are you not being dishonest to yourself? You're sermonizing in a manner quintessential of fraudulent proponents of Quantum Mysticism, such as Deepak Chopra. What does the term 'quantum causation' convey, precisely? Why would you bring 'synchronicity', to the fore? What's an 'electron differential'? I'm not a Physicist, but you're demonstrating an utter apathy, to the overarching subject that you're sourcing fragmentary ideas from.

Vast difference between quantum and classical phenomena can be explained by the deep disjunct between subatomic and macroatomic scales. The subatomic scale contains all the energy of the classical scale, but the relatively tiny diameter of its highest probability concentrations compared to the total probability wave means that a huge time contraction is in effect, making the relative motions of subatomic matter almost instantaneous. This can be contrasted with the greater continuity of macroatomic to macroscopically Earthlike scales that produces dynamics of classical physics.

Are you referring, in part, to the probabilistic nature of Schrodinger's Wavefunction? If so, can you elucidate the nature of the time contraction you're interpreting? For instance, are the notions of 'energy' you've readily apprehended, conceptually attached to the Hamiltonian Operators and Time-Evolution of a model particle? What formalism are you construing them in, from a mathematical perspective?

If you're undertaking an epistemic pursuit inside a rarefied framework (Physics inclusive), then do so in a manner that is adherent, and respectful of that framework. If you don't, you appeal neither to the scientific method - nor a purely nonscientific one. You're entrapped instead, in a pseudoscientific paradigm.

1 Doesn't really break the "no object faster than the speed of light" principle: as per my post above, the speed that galaxies appear to be receding at is a function of both the velocity of the galaxy which is sublight and the expansion rate of space, which is not a speed at all.

That's an exemplary clarification - and simultaneously what I was pensive over, having read the comment. Universal expansion isn't characterized by a velocity; it's empirically derived by an (approximately) linear gradient mapping of the Hubble Constant, onto observed recessionary velocities against their distances from Earth.

You know, you sound very authoritative in all this, but I don't have the knowledge to engage you, and I don't know if you actually know what you are talking about. But I give you the benefit of the doubt. It would be good if kenosha kid or another real physicists would comment.

That's an affirmative stance, but is it necessarily wise to accord a benefit of doubt, prior to witnessing an even partial demonstration of an argument's veracity?
• 1.2k
That's an affirmative stance, but is it necessarily wise to accord a benefit of doubt, prior to witnessing an even partial demonstration of an argument's veracity?

The benefit of doubt in the context of babble is inconsequential.
• 6.5k
1 - the size of the universe, which on current estimates is more than 98bn light years across - and therefore more than 4 times the widest spread that could be achieved by an exploding singularity at the speed of light.
\
Pretty good Youtube video on this, here.
https://www.youtube.com/watch?v=vIJTwYOZrGU
• 112

Hi Both

the video which Tim provided is, I think, flawed, because it mixes concepts and ignores the basics.

Firstly, the guy talks about space expanding, when space is probably not expanding - but the objects within it are just spreading out. That is an important difference. (If space were truly expanding, the objects within it would also be expanding/swelling - and they're not).

Secondly, he layers 'Dark Energy' on top, (when it is no more than a concept that is not proven, and just a theoretical way to plug a gap in our understanding based on the strengthening redshift of galaxies - which can be interpreted in other ways). He then says that the combination increases the spread beyond what it was before.

The overall effect is still that things had to travel faster than the speed of light to get from the Big Bang point, to the extremities of what we can see and theorize about in the universe, in absolute terms. Nobody knows how big the Universe is because we can't see its outer limits (if indeed, there are any).

I could add that the notion of curved space has also been largely disproven by the 9 year results of the WMAP programme which concluded, (with a small margin of error), that the dimensional lines are straight and therefore that space is potentially infinite.

I feel that the best way to think about things is that the most distant objects we can see are in a place where they existed 13billion years ago, not the present day. We are also in the middle of the expansion, and because we are surrounded by material evenly on all sides, it is logical to assume that if there was a Big Bang, (which also seems likely), that the material emitted before us came out faster than us, and the material that came out after us, was travelling more slowly.

That being the case, if you try to argue that the speed of light is the maximum that anything could go (also just a theory), then we are still faced with the dilemma that the universe shouldn't be more than 27.4 billon light years across, no matter what.
• 6.5k
the video which Tim provided is, I think, flawed, because it mixes concepts and ignores the basics.
You think is flawed? All that can mean is that you think it's flawed. Is it flawed? Do you know? Did you pay any attention to it? What flaws? What does it ignore?

when space is probably not expanding - but the objects within it are just spreading out
Oh, citation/reference/evidence please?
• 156

Oh, citation/reference/evidence please?

We don't reside in a world, that confers any value to evidence anymore. I'm not denigrating anyone, but @Gary Enfield is adhering to a nonstandard interpretation, without disconfirming the specifics of its antithesis (on which there exists an empirical consensus: Hubble's Law).

The overall effect is still that things had to travel faster than the speed of light to get from the Big Bang point, to the extremities of what we can see and theorize about in the universe, in absolute terms. Nobody knows how big the Universe is because we can't see its outer limits (if indeed, there are any).

C remains insurmountable, solely under the following prerequisites (I may be mistaken, but this is a canonical interpretation):

If a massive body were to traverse alongside a beam of light, on a flat space-time fabric (the intuitive analog of a four-dimensional Pseudo-Riemannian manifold), then it'd be unable - with any degree of acceleration, to surpass that beam. If there exist crevasses or protrusions within that manifold, such as a metric tensor defining a traversable Einstein-Rosen bridge, a massive body might be able to encompass an otherwise spacelike distance, that a beam of light would cease to trace on a flattened variant of the continuum.

Space-time fabrics, nonetheless, are tractable - if they expand, they necessarily elongate the relative distances between any two bodies on them. @jkg20 delineated this idea, earlier; you can't characterize space, with a normative velocity. I hope you'll attribute any degree of credence to a (reverified) Wikipedia article on the construct (insofar as you won't be incorrigible, or obstinate):

https://en.wikipedia.org/wiki/Expansion_of_the_universe

The benefit of doubt in the context of babble is inconsequential.

I'm sorry; I didn't quite grasp this - can you elaborate on what you meant?
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