I Why is there a universal speed limit, c, and why is it what it is?

[nitsuj]

bobc2 "WHY does an observer's 3-D cross-section view (the X1 axis) of the 4-D universe continually rotate so as to eventually converge on the 4th dimension (X4 axis)?"

That is some writing worthy of publishing. Just tickles my brain lol

Some annimation of that happening would be wicked.

 

[CosmicVoyager]

@bobc2

I should have replied the first time to say thanks and that I find it difficult to convert the graph into visualizing what is happening in 3D. What I would like to see is an animation of a photon in a 3D grid, or an illustration with 2D representing 3D and 3D representing time. You seem to be saying the universe is changing shape, which it obviously cannot be doing since it would require the universe to simultaneously have different shapes for every particle moving at a different speed. That is a direct contradiction.

 

[bobc2]

@bobc2

I should have replied the first time to say thanks and that I find it difficult to convert the graph into visualizing what is happening in 3D. What I would like to see is an animation of a photon in a 3D grid, or an illustration with 2D representing 3D and 3D representing time.

Let me think about that and see if I can figure out a way to do a better job of communicating.

You seem to be saying the universe is changing shape, which it obviously cannot be doing since it would require the universe to simultaneously have different shapes for every particle moving at a different speed. That is a direct contradiction.

I think I fully agree with you. But, I must be cardful that we are talking about the same universe. When I think of the universe not changing shape, I'm picturing the 4-dimensional universe. But, with the so-called "block universe" model the observers experience a continuous sequence of new cross-sections of the 4-dimensional universe. And this does mean that observers moving at different speeds would, at any instant of time, be "living" in different 3-D universes. And that would certainly be contradictory if it were not for a model that feature a 4-dimensional universe populated with 4-dimensional objects (including the 4-dimensional bodies of the observers). I really hesitate to carry the description much further for a number of reasons, but can if you wish. But the 4-D picture is pretty much as shown in the earlier sketches. After a while I'll throw up one more graphic to make the picture a little more complete.

 

[nitsuj]

Let me think about that and see if I can figure out a way to do a better job of communicating.

I think dalespam and bobc2 should become friends. :)

 

[CosmicVoyager]

I think I fully agree with you. But, I must be cardful that we are talking about the same universe. When I think of the universe not changing shape, I'm picturing the 4-dimensional universe. But, with the so-called "block universe" model the observers experience a continuous sequence of new cross-sections of the 4-dimensional universe. And this does mean that observers moving at different speeds would, at any instant of time, be "living" in different 3-D universes. And that would certainly be contradictory if it were not for a model that feature a 4-dimensional universe populated with 4-dimensional objects (including the 4-dimensional bodies of the observers)..

If time is one of those dimensions,and each particle is a cross section, wouldn't that require 5 dimensions? Because with only 4 the fourth has to be either the sequence of cross sections which would still require an additional dimension for time, or the fourth be time and no cross sections for each particle?

 

[bobc2]

If time is one of those dimensions,and each particle is a cross section, wouldn't that require 5 dimensions? Because with only 4 the fourth has to be either the sequence of cross sections which would still require an additional dimension for time, or the fourth be time and no cross sections for each particle?

In this model you don't need a dimension for time. I am considering only spatial dimensions as containing 4-dimensional objects. We refer to time as a parameter. Below is a sequence of sketches that attempts to clarify that idea. The toughest aspect of this model to wrap your mind around is the part that has an observer moving along the 4th spatial dimension at the speed of light. In lower left sketch, C, I've shown a solid curved bar object with two ends fixed in the ground. Perhaps it is night time (to make the illustration easier). A beam of light is focused on the bar, and the light source is moved in just the right way to make the light spot move along the length of the curved beam at a constant speed along the beam (speed tangent to the beam). Time is used as a parameter--we can tell what time it is at each point along the beam that the light spot passes. That is, we could actually mark off time values along the beam that records the time at which the light spot passed each point on the beam. The bar really extends along a 3-dimensional path, and we could obviously establish a spatial coordinate along the beam--we could use the regular X1, X2 coordinates (ground surface), but then use the path of the beam as the X3 coordinate. So, now we have three spatial coordinates, but we are using time as a parameter to keep track of where the light spot is along the beam, i.e., along the X3 coordinate. The reference to the 4th dimension as a time dimension, in my view, is a misnomer. I and many other physicists believe that the 4th dimension should be regarded as a purely spatial dimension (just like our curved bar X3 dimension in 3-D), but having a distance relation along the bar to parametric time.

So, the universe is actually 4-spatial dimensions, and time is something, associated somehow with consciousness. Just like the light spot moved along the 3-D curved beam, some aspect of observers (we don't know exactly what) moves like the light spot along the 4th dimension of the 4-D objects, and we use time as a parameter to locate our observational positions along the 4th dimension of observer body structures. Of course the body structures cannot move. They are static 4-dimensional objects--they don't move any more so than the 3-D curved bar anchored to the ground (just the light spot moves, and perhaps just some aspect of mind moves). (More later if you wish--but I'm afraid I am way too long winded.)

 

[CosmicVoyager]

IIn this model you don't need a dimension for time. I am considering only spatial dimensions as containing 4-dimensional objects. We refer to time as a parameter. Below is a sequence of sketches that attempts to clarify that idea.

Four spatial dimensions?! Now *that* changes everything! Someone was telling me something like this before but they were saying time was one one the dimensions. I knew it could not be done with just 3 spatial dimensions! Let me think about this.

 

[CosmicVoyager]

@bobc2

Figure d is showing the fourth dimension to be time. It shows the big bang in one direction and the big crunch in the other. I thought there were going o be four dimension plus time. I'm back to the problem of where are the cross sections. How is there one for every particle? A cross section is 3D, right? And a series of 3D cross sections is 4D. So I don't see how there is a cross section for every particle. Each particle would only exist at one point in time. One 3D cross section per moment throughout the history of the universe.

 

[OnlyMe]

The speed limit is a consequence of what? Is what we know to be the speed limit the result of measurements? Or is it a logical problem that can be figured out in a thought experiment?

I just dropped in on this forum today. It seems several of the posts I read kind of skated around a direct answer. Mostly because other than in theory or hypotheses, no one really knows why c is a velocity limit.

That said... The speed of light as a speed limit most likely is a consequence of Einstein's (AE) 1905 paper (On the electrodynamics of moving bodies) introducing special relativity. And was drawn from connecting a the work of a number of others.

Piece 1. Earlier that year AE published a paper on Brownian motion, an argument in support of the existence of atoms. The idea of atoms had been around for a long time but his paper essentially crystalized the concept. Aside from electrons, no other subatomic particles were known at the time.

Piece 2. In the first or second paragraph of his paper introducing special relativity, he mentioned failed experiments to discover the motion of the Earth relative to the light medium, an assumed reference to the Michelson & Morley experiments and then later essentially discarded the concept of the ether completely.

Piece 3. There had been experimental evidence establishing the velocity of light in a variety of mediums -- solid, liquid, gaseous and vacuum. The speed of light in vacuum was in close agreement with the work of Maxwell, on electrodynamics.

Piece 4. In the first section of that paper, Kinemetical Part, Part 1. Definition of Simultaneity, he asserts, "In agreement with experience we further assume the quantity 2AB/(t'-t)=c, to be a universal constant--the velocity of light in empty space."

conclusion: Empty space and a vacuum, the abscence of atoms, were assumed to be equivalent. No ether and with no knowledge of anything other than atoms, empty space was a vacuum. The speed of light in a vacuum is c. The speed of light in empty space is c.

Nothing has been observed to have a greater velocity than c. The speed limit aspect most likely came much later and probably from interpretations of the E=mc^2 formula, which suggest that it requires an infinite amount of energy to accelerate an object having mass to the speed of light.

The above give at least one answer to how c came to be accepted as a limiting velocity. It still does not say why.

 

[Dmitry67]

Relativity theory suggests we all travel thru the continuum at the equivalent of c. This suggests that what we measure as "the relative velocity between material entity" is the result of unparallel speed-c velocity vectors thru the continuum. If parallel, then they are at rest with each other.

It is a result of our spacetime being (locally)pseudoeuclidean (+++-)
So the original question falls into the same category as 'Why there are 3 (macroscopic) space dimesions?'

 

[bobc2]

@bobc2

Figure d is showing the fourth dimension to be time. It shows the big bang in one direction and the big crunch in the other. I thought there were going o be four dimension plus time. I'm back to the problem of where are the cross sections. How is there one for every particle? A cross section is 3D, right? And a series of 3D cross sections is 4D. So I don't see how there is a cross section for every particle. Each particle would only exist at one point in time. One 3D cross section per moment throughout the history of the universe.

No. Figure D is showing a 4-dimensional universe. The whole universe is all there, all four dimensions of it, frozen in time. You see the 4th dimension coordinate labled X4--that's the direction of the 4th spatial dimension. I label one instant of time as "NOW." But, remember time is just a parameter used to mark off points along the 4th dimension as the yellow spot on the diagram moves along the static 4-dimensional world line at the speed of light. Time is something perceived by that yellow dot as it moves along the 4th spatial dimension (just like the example of the light spot moving on the curved beam in the earlier sketch).

We use phrases like, "The big bang happened at the creation of the universe." That satisfies our stubbornly persistent subjective conscious feeling that things happen. That derives from our conscious experience--again associated with the yellow spot moving along our bundle of neuron fibers that are stretched out for billions of miles along the 4th dimension--as though the mind is watching a movie as it moves along the sequence of 3-D images presented by the 4-D neurons.

I hate to have to present things in this way, because there are some very unpleasant discussions that are evoked--and some even more unpleasant implications coming out of this kind of picture. But, once this picture is grasped, it hopefully helps crystallize some of the fundamental issues of special relativity. And it leads ultimately to "why" questions beyond the realm of physics. A great physicist who passed away a number of years ago, Bryce DeWitt (Univ of North Carolina and Univ Texas), made the statement in a "Physics Today" article that, "...there is much more to reality than physics."

 

[Dmitry67]

I know another great physicist, Max Tegmark, who is alive, and his famous MUH program. When I first read it I was shoked and for 2 weeks was not able to think about anything else.

He has an opposite view - that on the very fundamental level, there are just equations, and the size of how he calls it "word baggage" is exactly 0.

For me he was able to asnwer all "Why" questions here:
http://arxiv.org/abs/0704.0646

 

[Dale]

Nice reference. Particularly "if there is an isomorphism between a mathematical structure and another structure, then they are one and the same. If our external physical reality is isomorphic to a mathematical structure, it therefore fits the definition of being a mathematical structure."

The lack of word baggage would, of course, necessarily exclude word questions, which I like.

 

[Dmitry67]

There is a second interesting part in the same article.
Say, we have TOE equations with no "word baggage"
Max asks "But WHY these equations, not another?" or "What burns fire in these particular equations?" and answers them starting from p16.

 

[Calrid]

There is a second interesting part in the same article.
Say, we have TOE equations with no "word baggage"
Max asks "But WHY these equations, not another?" or "What burns fire in these particular equations?" and answers them starting from p16.

The debate about maths being the underlying structure of reality and reality being the underlying structure of maths is an interesting one, ie does maths have an existence in and of itself or is it an abstraction. But I'm not sure it is going to be resolved in physics or maths by this paper. I'll have to take a look later. I personally see mathematical models as an approximation of reality that has some lower bound where it is accepted as being close enough so that there is no distinction. But meh whatever floats your metaphysical boat.

The only baggage I can see is faulty assumptions, maths or English or Swahili is beside the point.

 

[bobc2]

I know another great physicist, Max Tegmark, who is alive, and his famous MUH program. When I first read it I was shoked and for 2 weeks was not able to think about anything else.

He has an opposite view - that on the very fundamental level, there are just equations, and the size of how he calls it "word baggage" is exactly 0.

For me he was able to asnwer all "Why" questions here:
http://arxiv.org/abs/0704.0646

Yes. I've studied his ideas. And he has developed a remarkable concept with solid rationale. I particularly admire him for his guts in laying it out there (MIT of all places) in an environment not suited for out-of-mainstream avant garde stuff. He has taken some heavy incoming from some in the physics community at times.

I'm personally still carrying the "baggage" but still very much admire his work. Thanks for calling attention to him, Dmitry67. I think your admiration and excitement over his ideas is well placed. Once you buy into his reality, then you've answered lots of "why" questions.

 

[nitsuj]

lol, you mean to say the Cohen brothers have it right?

Morpheus: Unfortunately, no one can be told what the Matrix is. You have to see it for yourself.

 

[Dmitry67]

bobc2, I am happy we are on the same page.

May be you have heard about... well, I even don't know what to google.

There are dimensionless parameters of the standard model. (and also density of Dark Matter and Energy). What happens if we change these parameters? Will life be possible or not? If not, what will be the weakest link in a chain (galaxy formation, stellar evolution, planet formation, chemistry, existence of self-replicating molecules etc)? That work of different scientists will help us to draw a ‘map’ of the ‘island of life-friendliness’ of the Universe. The questions I am interested are:

How big is that island?
Are we in the center or closer to the ‘seashore’?
Are the any other separate ‘islands of life-friendliness’? (may be based on another chemistry)?

 

[bobc2]

DaleSpam is right.
But just 2 cents.
Science is capable of answering "Why" questions (only to some extent) - using the Anthropic principle

http://en.wikipedia.org/wiki/Anthropic_principle

Remember your earlier Anthropic Principle link? There are so many examples of properties and conditions in the universe that defy expectations, but are absolutely necessary for life.

My favorite example is the highly unlikely circumstance of an obscure excited state of the Carbon 12 nucleus having just the magically correct resonance that provided a way to synthesis of the normal Carbon 12 configuration (there would be no way to synthesize the remaining periodic table without first synthesizing Carbon 12--it is the bridge from He and Be to the rest of the elements) . But Be-8 could only combine with He-4 if the resulting Carbon nucleus matched the combined energy--only possible if there existed an excited state of C12 (analagous to an isomer) that matched the Be-He combination.

The story told by Simon Singh in his book, "Big Bang" about how Fred Hoyle speculated that there had to be a special excited state with just the right energy is priceles! Hoyle calculated the required resonance and pestered William Fowler at Cal Tech mercilessly until he agreed to run an experiment in search of the resonance--Fowler couldn't believe it was right where Hoyle predicted it (7.65 MeV more energy than the normal C12 state). But what an enormous unlikely but fortunate outcome for life that nature prepared that special configuration of the Carbon nucleus.

 

[SeventhSigma]

Too lazy to read this thread so I am very sorry if I am repeating anyone.

I would assume c is what it is because of, partly, the anthropic principle. In our particular universe, everything is structured in such a way (composed of atoms/quarks/electrons/particles/etc) under certain laws with various constants such that c is a mathematical eventuality and necessary condition arising from relativistic symmetries of space and time.

For instance, E = mc^2 is really just a form of conversion. We write it this way because we've defined energy/mass/speeds in various metrics. Let's just hold the speed of light c to equal 1 in natural units (which is to say, instead of defining c as 300,000 of something else of value 1, let's just define c as our fundamental unit of 1 to begin with). Then we simply see that E = m only we're discussing both E and m in different units.

The real question isn't so much "why is c equal to 300 km per second" but why is E = m in the first place. Understanding this can help explain the relative ratios of how everything in our universe relates, which in turn helps to explain why c has the value it does relative to other things.

IMO, when it comes to our cosmos, it all comes down to the ratios and conversions inherent in our universal properties. Given certain ratios/conversations necessary to sustain a stable, functional universe with working laws, the mathematics and values/properties of other phenomena emerge as necessary conditions/eventualities.

 

[LeeJeffries]

Yes, I mean what is holding the light back. It is like an invisible hand jumps up in front of things at c and stops them from going faster.

I suspect my paradigm might be completely wrong and I need to shift, in which case I need why it is wrong explained. It seems the same as if I were adding more and more to an object to increase it's mass, then suddenly the mass stopped increasing, and I think "What the heck is going on?"

The Ether ;)

 

[nitsuj]

For instance, E = mc^2 (i edited this part for my sake) We write it this way because we've defined energy/mass/speeds in various metrics. Let's just hold the speed of light c to equal 1 in natural units (which is to say, instead of defining c as 300,000 of something else of value 1, let's just define c as our fundamental unit of 1 to begin with). Then we simply see that E = m only we're discussing both E and m in different units.

I like trying to understand things, can you please explain to me what "just hold the speed of light c to equal 1 in natural units" means? And how then E = mc^2 can be changed to E=m?

Why are you taking the C part out of that equation you called a "conversion"?
E=M is wrong, it's E= mc^2. it "converts" to a little mass equates to a lot of energy, and vice versa. The "various metrics" thing you mentioned is crucial. If you index C to equal 1, it won't change the relationship that a little mass equates to a lot of energy.

http://www.1728.com/einstein.htm has a calculator at the bottom. You enter mass, select the UoM you used for mass, and it tell you the amount of energy it has in various UoM. Never do you see "C".

"The real question isn't so much "why is c equal to 300 km per second"" your right, its why does "time"(which I also assume to mean space) stop at 300k km/s, that's what the "c" part of the equation is doing.

 

[LeeJeffries]

I like trying to understand things, can you please explain to me what "just hold the speed of light c to equal 1 in natural units" means? And how then E = mc^2 can be changed to E=m?

Why are you taking the C part out of that equation you called a "conversion"?
E=M is wrong, it's E= mc^2. it "converts" to a little mass equates to a lot of energy, and vice versa. The "various metrics" thing you mentioned is crucial. If you index C to equal 1, it won't change the relationship that a little mass equates to a lot of energy.

http://www.1728.com/einstein.htm has a calculator at the bottom. You enter mass, select the UoM you used for mass, and it tell you the amount of energy it has in various UoM. Never do you see "C".

To demonstrate that C is a conversion factor

 

[SeventhSigma]

I like trying to understand things, can you please explain to me what "just hold the speed of light c to equal 1 in natural units" means? And how then E = mc^2 can be changed to E=m?

Why are you taking the C part out of that equation you called a "conversion"?
E=M is wrong, it's E= mc^2. it "converts" to a little mass equates to a lot of energy, and vice versa. The "various metrics" thing you mentioned is crucial. If you index C to equal 1, it won't change the relationship that a little mass equates to a lot of energy.

From http://en.wikipedia.org/wiki/Mass–energy_equivalence

[The formula is dimensionally consistent and does not depend on any specific system of measurement units. For example, in many systems of natural units, the speed (scalar) of light is set equal to 1 ('distance'/'time'), and the formula becomes the identity E = m'('distance'2/'time'2)'; hence the term "mass–energy equivalence" ]

Natural units are basically ways to redefine your unit scales. Instead of saying that the speed of light is 300,000 km/s, you might just say that it's equal to 1 light-second per second (a light-second is a unit of distance, and a second is a unit of time, and we know distance/time is a rate). It's basically redefining the speed of light from one distance/time metric to another, only instead of using 300,000, we use 1. The idea is to change the units so that we can simplify certain relations.

So when we set c = 1, we more clearly see that E = m, or that the rest energy of a particle in Planck energy units is equal to the rest mass of a particle in Planck mass units. The important thing to keep in mind is that energy and mass are seen as different forms of the same thing and are proportional to each other to the tune of the maximum speed anything can move in our universe (light, gravity's effects, etc).

We see c in so many equations in the same way we see pi everywhere. It's like asking why pi is equal to 3.14159 etc. It is because of the nature of the circle. Circumference over diameter equals pi. Saying "Let's make pi equal to 5 instead of 3.14" is like saying "Let's make c equal to 200,000 km/s instead of 300,000 km/s." If we set pi to be something else, then we're really not talking about a circle anymore because there's no way we can get 5 if we divide circumference by diameter.

Similarly, c is equal to c because if it were anything else, the nature of our universe wouldn't exist as it is now.

 

[nitsuj]

To demonstrate that C is a conversion factor

Umm, no it was for me to demonstrate that SeventhSigma can use the calculator and assume that "c" is 1. the formula still shows a little mass is a lot of energy. It takes the 'ratio' of all three (opps, four) measurements (energy, mass, distance, time).

My opening in that post "I like trying to understand things, can you please explain to me what "just hold the speed of light c to equal 1 in natural units" means?" should prove difficult as speed is two measurements, not 1.

 

[SeventhSigma]

You have to assume SOMETHING is 1 at some point. We always measure something in terms of something else. You can say c = 300,000 km/s, but then you have to ask what a meter is equal to. A few hundred years ago it was suggested to make the meter equal to one ten-millionth of the length of the distance from the Equator to the North Pole. TEN millionth because we're accustomed to the decimal system (because we have ten fingers) and an Earth distance because it's something "applicable to all" and this ratio gives us something workable on human scales.

Either way we're still calling the meter "1." Changing c to equal "1" is just another way of redefining our units. It can help us better understand certain physical relationships. In this case, energy-mass equivalence. Saying c equals 1 is a way to define it as a standard tautological unit where c = the distance that light goes in one unit of time.

 

[nitsuj]

Natural units are basically ways to redefine your unit scales. Instead of saying that the speed of light is 300,000 km/s, you might just say that it's equal to 1 light-second per second.

Wow, I actualy never understood what "c" is. 300,000km/s is very definitive. I thought it was a measure of speed.

 

[SeventhSigma]

It's actually something like 299,792,458 m/s in a vacuum but it's just easier to say 300,000 km/s

 

[harrylin]

Why on Earth would you say that? [..]

I explained it immediately below by means of a quote by Newton about the purpose of his work - didn't you see it? The asterix is even in your quote of what I wrote...
Here it is again but now with emphasis by me:

[..]
* But how we are to collect the true motions from their causes, effects, and apparent differences; and, vice versa, how from the motions, either true or apparent, we may come to the knowledge of their causes and effects, shall be explained more at large in the following tract. For to this end it was that I composed it.

An important aspect of answering "why" is "the knowledge of causes and effects"; that's much more than "the mathematical model X correctly predicts".

 

[nitsuj]

We see c in so many equations in the same way we see pi everywhere. It's like asking why pi is equal to 3.14159 etc. It is because of the nature of the circle. Circumference over diameter equals pi. Saying "Let's make pi equal to 5 instead of 3.14" is like saying "Let's make c equal to 200,000 km/s instead of 300,000 km/s." If we set pi to be something else, then we're really not talking about a circle anymore because there's no way we can get 5 if we divide circumference by diameter.

After you setting me straight with what "c" actualy is, I see how perfect your annalogy to pi is. They're almost siblings :)

 

[pip1974]

CosmicVoyager. I have a thought experiment relating to your original question that I thought I'd share with you. You started wondering what it was that stopped the object, or spaceship or whatever it is accelerating as it approached the speed of light. The answer is nothing!
Here goes...
Imagine one day the people of Earth get a message from an alien spaceship that is hurtling towards us at 0.75c. It says that they are on a huge generational starship, and if we wanted to we could send a spaceship on an intercepting course, dock with their planet sized spaceship and join them.
So, we make necessary preparations and do exactly as they suggested.
Don't worry about the details so much - it's a colourful story - but the important point is that we are now on a huge planet sized spaceship that is moving at 0.75c relative to Earth, with our own spaceship, also capable of accelerating to 0.75 safely docked there.
Once there we watch the Sun rush away from us at 0.75c as we begin our new lives, having a whale of a time finding out all about the alien civilisation and lounging on the beaches by the shore of the lovely artificial oceans. We call it "Earth Two"!
Now here we are, on our new home in space, very different from but as comfortable as our old home, Earth, and of course just as valid as a frame of reference! We can play ping pong there in exactly the same way that we could on Earth! We can also look at the stars at artificial night-time and look upon similar constellations as we did on Earth with equal wonder.
Now after some time, we, the band of intrepid Earthlings, settle down and have families. And eventually we grow old and die, but our families go on. Then one day a group of our descendants decide upon a curious course of action. They decide to get back in the old spaceship and set off. Now they just happen to choose a course which is the exact opposite direction to our old Earth. They don't care - they don't want to go back there. To them it's just an obscure planet orbiting a distant star that happens to be moving away from us at 0.75c.
So they set off in the spaceship, and after a few months find themselves going at 0.75c relative to New Earth.
Now, as I said, they'd forgotten about Earth and the Sun, but if they had spared it a thought, they'd notice that that system was speeding away from them at a very high speed approaching the speed of light and definitely not at 1.5c as the uninitiated might expect.
If they'd thought to check before they set off they'd have observed Old Earth flying away at 0.75c when they were still stationary relative to New Earth. Then if they’d kept looking as they approached 0.75c relative to New Earth they’d see the acceleration relative to Old Earth slow down. The velocity relative to Old Earth would approach but never exceed the speed of light, even as the velocity relative to New Earth continues to increase.
Now the interesting thing here is, the whole slightly unnecessary bit in the middle of this story where our intrepid explorers settled on the alien star ship was exactly that - a bit unnecessary! The Earth explorer's ship (which I've decided runs by scooping up interstellar hydrogen atoms by the way) can actually carry on accelerating indefinitely as far as the crew are concerned without any need for a stay on a friendly alien star ship world. Their speed relative to their origin will carry on increasing, but never reach the speed of light. The engines will be working just as before, life on board ship will be much the same, but they will observe the acceleration relative to the origin decrease. At any point they can shut off the engines and just fly on through space for a bit, decide on a new frame of reference, then turn on the engines again and start accelerating towards the speed of light away from a new fixed point on the same heading. If they look back and start measuring their velocity according to the old reference frame again, they'll still be getting nowhere fast, but they'll be whizzing away from the new point! The two frames of reference are equally valid, just like the two reference frames that see me sitting fairly still in front of my monitor, and hurtling around the Sun at 100,000 km/h.
The point is, at no stage does God come along with a speed limit sign telling you to slow down because you are approaching the universal speed limit, things just aren't ever going to be moving away from you faster than that limit, no matter how long and hard you or they run for.
Phew!
I enjoyed writing about that. I hope you enjoy having a think about it!
By the way, before anyone jumps on it, I realize this doesn't answer your original question but perhaps gives you another way of visualising the consequences of there being a speed limit that you may find useful. And one final note just in case people are thinking that somehow I'm claiming that the spaceship will be going faster than the speed of light - it won't be - OK! If the explorers always had it in mind to get somewhere, a star, let's say, the spaceship would never be traveling towards that star at the speed of light (and the light from the star they are heading towards would still always be traveling to the peepers of the people on board at the speed of light!)
As for why! Well, I still think that's an interesting question :)

 

[Dale]

I explained it immediately below by means of a quote by Newton about the purpose of his work - didn't you see it? The asterix is even in your quote of what I wrote...
Here it is again but now with emphasis by me:


An important aspect of answering "why" is "the knowledge of causes and effects"; that's much more than "the mathematical model X correctly predicts".

If some parts of your mathematical model have a relationship to each other that we expect from causes and effects then you have modeled cause and effect and accomplished the goal of Newton as I understand it, which is a scientific goal. I don't think that he was asking "why" his laws worked, and that statement that you quoted doesn't seem to indicate that either.

I think you are really undervaluing the mathematical models here. Cause and effect is a relationship that can certainly be captured mathematically, and in fact is an important feature of the modern concept of spacetime.

 

[SeventhSigma]

I think the OP is asking why c is 300,000 km/s and not, say, 200,000 km/s and why it's an absolute limit at all (i.e. why isn't light instantaneous?).

I don't know the answer, but I am trying to say that it's likely a similar analogy to circles and pi. Pi is a ratio between two properties of an object that is defined in a particular way. In other words, a circle has pi as a necessary condition. Changing pi means you are no longer talking about a circle.

I figure our reality is much the same way. Our universe is to c as a circle is to pi. I just don't know how you'd derive c based on everything else.

 

[nitsuj]

I think the OP is asking why c is 300,000 km/s and not, say, 200,000 km/s and why it's an absolute limit at all (i.e. why isn't light instantaneous?).

I don't know the answer, but I am trying to say that it's likely a similar analogy to circles and pi. Pi is a ratio between two properties of an object that is defined in a particular way. In other words, a circle has pi as a necessary condition. Changing pi means you are no longer talking about a circle.

I figure our reality is much the same way. Our universe is to c as a circle is to pi. I just don't know how you'd derive c based on everything else.

That annalogy, is perfect. I have been in awe today absorbing the idea of "c". what's speed calculated without time? "c" lol what a trip


"I just don't know how you'd derive c based on everything else" I thought you've intentialy said it already, with...

"Instead of saying that the speed of light is 300,000 km/s, you might just say that it's equal to 1 light-second per second"


"everything else" moves around relative to each other, and that is seen as time. measure the fastest (known) thing amongst everything else, and cross your fingers that it's a property of spacetime and not of the fastest (known) thing amongst everything else. I'd bet dollars to dimes that if the fastest (known) thing amongst everything else wasn't a property of spacetime that "c" would have come about later then it did (truism).

How it actualy came about is much much different(im sure you know), but it is a wonderful coincidence in hindsight.

 

[nitsuj]

Greetings,

Why is there a c? Why is there a speed limit to the universe? Why is there a limit to how quickly a cause can follow an effect at distance? Why is there a "causality constant"?

What is(are) the limiting factor(s) that make it what is? The speed limit is a consequence of what? Is what we know to be the speed limit the result of measurements? Or is it a logical problem that can be figured out in a thought experiment?

What was God thinking? lol

Thanks

It took a lot of thinking but I got it.

Because it's the fastest. That's my final answer. Nice and circular. :)

 

[Rap]

I think the OP is asking why c is 300,000 km/s and not, say, 200,000 km/s

If you are asking why the number is 3e8 m/s rather than 2e8m/s, the answer to this question is anthropomorphic. The question is essentially "why is the meter the length that it is?" and "why is the second the length that it is?". Change the value of the meter or the second, and the number changes*. The meter was chosen as a length easily comprehensible to humans - about the distance between outstreched arms. The second was chosen as a time interval easily comprehensible to humans - about a heartbeat. The numerical value for the speed of light follows. I bet if we contact an alien race and knew their size and metabolic rate, we could make a good estimate of what their fundamental length and time interval were, and what numerical value they assigned to the speed of light in terms of those length and time units.

If you are asking why it has the speed it has, this is an improper question. The nature of the universe is described by the values of the fundamental dimensionless constants (i.e the fine structure constant, the gravitational coupling constant, mass ratios of elementary particles, etc.). If you double the speed of light, but adjust other fundamental constants (e.g. Planck's constant, mass of electron, etc.) so that the fundamental dimensionless constants remain the same, you will be living in a universe that is identical to this one. The length of the meter and second will change, but if you redefine the meter and second anthropomorphically, absolutely everything will be the same.

A proper question is why is the ratio of the speed of light to some other velocity equal to whatever it is? For example, a valid question is "why is the speed of light so fast (compared to anthropomorphic speeds - e.g. 1 meter per second)?". This is a more interesting question, and can be discussed.

*I know, c is now defined as a constant value which, along with cesium radiation defines the meter and second, but those numbers were chosen to be close to meters and seconds that were otherwise defined.

 

[Dale]

Excellent post, Rap.

 

[SeventhSigma]

Rap: That post honestly frustrates me because it makes me feel like you missed what I mentioned above (basically saying the same thing). Nobody is arguing about the labeling of the units. We've defined a meter in an arbitrary fashion and a second in an arbitrary fashion, and we know the speed of light is 3 * 10^8 times as fast. The question is why that particular ratio exists and why it isn't smaller or larger.'

Asking why it has the speed that it has is not an improper question in the sense that I am asking it in the context of ratios, much like how I equated this question to the circle / pi argument earlier. Yes, if you adjust EVERYTHING by the same relative scalar, we won't notice any difference. We're not talking about this, however. We're talking about why everything has the ratios to each other as they do. When we ask "why 300,000 km/s and not 200,000 km/s," we're implicitly discussing ratios in this case and not the labels.

 

[Dmitry67]

There is no ratio. space and time are the same. They should be measured in the same units. So when you use natural units, c appears to be equal 1.

c = 1.

 

[SeventhSigma]

It doesn't explain why there's a cap on how high c can go, however.

 

[Rap]

Rap: That post honestly frustrates me because it makes me feel like you missed what I mentioned above (basically saying the same thing). Nobody is arguing about the labeling of the units. We've defined a meter in an arbitrary fashion and a second in an arbitrary fashion, and we know the speed of light is 3 * 10^8 times as fast. The question is why that particular ratio exists and why it isn't smaller or larger.'

Ok, that would be addressed by the third paragraph in my post, that says "A proper question is why is the ratio of the speed of light to some other velocity equal to whatever it is? For example, a valid question is "why is the speed of light so fast (compared to anthropomorphic speeds - e.g. 1 meter per second)?". Your example is "why is the ratio of the speed of light to our anthropomorphically defined standard velocity (1 meter per second) equal to 3e8?" - the same type of question, and its a valid and interesting question.

Asking why it has the speed that it has is not an improper question in the sense that I am asking it in the context of ratios, much like how I equated this question to the circle / pi argument earlier. Yes, if you adjust EVERYTHING by the same relative scalar, we won't notice any difference. We're not talking about this, however. We're talking about why everything has the ratios to each other as they do. When we ask "why 300,000 km/s and not 200,000 km/s," we're implicitly discussing ratios in this case and not the labels.

Ok, yes, as I said, framed this way, this is a valid and interesting question. But note that you don't want to multiply the fundamental dimensionless constants by the same scalar. The fine structure constant is \alpha=e^2/\epsilon_0 h c. If you multiply c by 2, \epsilon_0 by 1, h by 8 and e by 4, you will have the same fine structure constant. If you multiply everything by 2, you will not have the same fine structure constant. It is valid to ask why the fine structure constant has the value it has, but the point I was making is that it is not valid to ask why the speed of light is what it is without referencing it to some other speed, or length/time. And you have done this, so your question is a good one.

About answering that question - that gets into biology. Life forms are constrained by the chemistry of life. Nerve impulses only allow life forms to react to external stimuli on the time scale of fractions of a second. Our eyes must be large compared to the predominant wavelengths emitted by the sun. Single cells must be larger than a certain size in order to accommodate all the chemical reactions necessary for life, and humans, being multicellular animals, must be orders of magnitude larger. Are life forms larger than the dinosaurs reaching some sort of upper bound on the size of multicellular organisms, in the sense that they are at some evolutionary disadvantage? I don't know, maybe. All of these factors put constraints on the size of the meter and second, assuming that the meter and second are defined anthropomorphically. I don't know the full answer, but I think it is and interesting and complicated question.

 

[SeventhSigma]

Sorry -- that's what I meant by relative scalars. Not so much everything by the same number in itself but just everything by the same relative ratios. In other words, keeping the numerators and denominators the same no matter where we look. It's basically no different from multiplying everything by 1.

Regarding the evolution argument, there's an upper limit because of the types of structures required to support weight (for instance, large creatures like King Kong would collapse under their own weight because as you increase, say, the diameter of the thickness of a leg, the strength of this cross-section is proportional to that section's surface area whereas the weight is proportional to volume, so eventually it's not sustainable). However, these limits are in place because of the relative strengths of forces. There's a reason why, for instance, our brains did not evolve as smaller structures on a quantum scale. The nature of the constants ultimately guide complex chemistry and physics and therefore the kind of life we'd expect to see in its extreme expressions.

In other words, if the constants were tweaked in various ways, we'd expect to see different expressions of reality. The question is how much leeway these constants have. It'd be like popping into a complex 3D computer game and tweaking various constant variables and then running the game to see what happens. Odds are things wouldn't play quite right or wouldn't play at all if some logical rule winds up being violated.

The thing that depresses me is the notion that we may never know what "causes the constants." If I were a being inside the game Halo, then it doesn't matter how hard I pry into that environment -- I will never be able to see the code that underlies my program, nor would I ever be able to see anything outside the program/TV/etc. I can't tear into a rock and see the internal polygon code and texturing algorithms. I can certainly model my reality based on what I observe, but it doesn't tell us the driving factors that serve as the underpinnings to the reality itself.

That's what the anthropic principle tries to address by saying "If it were any different, reality wouldn't be here to begin with -- so the fact that we're even able to make these observations means that conditions must be correct for observation to occur." A bit tautological, but important.

 

[Dmitry67]

The thing that depresses me is the notion that we may never know what "causes the constants."

The fundamental constants are, contrary to how they are called, are not constants at all. In Planks units,

G = h = c = 1.

However, you can vary other dimensionless numbers, which are called 'the parameters of the Standard Model'.

They are here:
http://en.wikipedia.org/wiki/Standard_Model#Construction_of_the_Standard_Model_Lagrangian
On the right side of the page

(Masses are given in GeV units, but they are actually dimensionless (and very small) numbers in Planks units)

 

[Dmitry67]

P.S.
You can express "c" in a non-antrophic way, for example, why light passes N carbon atom sizes during a half life of a neutron?

The answer will be a function of the parameters of the Standard Model.

 

[SeventhSigma]

Yes, we can always redefine the label, but the question is the nature of the ratios involved in the structure of the framework that defines our universe. Again, we're *not* talking about labels or scales. We could define pi = 1 if we wanted to -- but we're really after the answer "pi is the result of dividing the circle's circumference by the diameter and we can prove this based on the definition of a circle." Similarly, we're trying to ask why these constants have the implications that they do by understanding the relationships between different components.

The question is what the nature of the relationships are. This isn't the same as saying "Well we know what c is because we know p and therefore E/c as well as hf/c as well as h/lambda," etc -- it's asking why these relationships exist the way that they do to begin with.

The way I approach this problem is, ultimately, under the assumption that our universe is inherently something mathematical. I posit that the nature of existence itself requires certain logical constructs to be in place for the concept of "existence" and therefore those logical constraints are mathematical in their build and ultimately give way to the structure of the universe.

 

[nitsuj]

It doesn't explain why there's a cap on how high c can go, however.

In what sense is 300,000km/s a cap? You taught me that it is not a measure of speed.

300,000km/s is "off" and not 300,000km/s is "on"

 

[SeventhSigma]

It's a cap in the sense that if we define a meter in an arbitrary way and time in an arbitrary way, we can therefore define speed in an arbitrary way. The speed of light is not infinite and therefore there is an upper bound to it that we can describe with our arbitrary definitions of speed. Again, the question is not about labels but the relative ratios.

 

[Dale]

Yes, we can always redefine the label, but the question is the nature of the ratios involved in the structure of the framework that defines our universe.

Rap and Dimitry67's point is only that those ratios (the ones that define the structure of our universe) are always dimensionless constants like the fine structure constant and not dimensionful constants like c.

http://math.ucr.edu/home/baez/constants.html

 

[Dmitry67]

SeventhSigma, what is a nature of ratio between WIDTH and HEIGHT?

 

[SeventhSigma]

A ratio can be anything. But some ratios are bound by constraints. For instance, again, I bring up the circle analogy. A circle is a concept such that it has two properties which we can define as circumference and diameter. The division of these two result in pi, a "constant" bound by constraints resultant from the mathematical implications of what a circumference and diameter are.

Similarly, I make the analogy that the speed of light is likely another such eventuality of something bound by mathematical constraints based on the nature of the universe's structure. The question is what the explanation behind that particular ratio/relationship is.

Rap and Dimitry67's point is only that those ratios (the ones that define the structure of our universe) are always dimensionless constants like the fine structure constant and not dimensionful constants like c.

http://math.ucr.edu/home/baez/constants.html

Right, we're in agreement there.