Simple. Revoke the Identity Axiom which states A = A. Without it, A != A, and the value of 1 can change to just about anything.
Of course, you don’t have much of a mathematical system if you do this- AFAICT it turns you into a kind of mathematical Fonz who can only assert: “A!” OTOH, if you have a proof of the Identity Axiom I would like to take a look.
Most physicists spend all their time taking the infinities out of equations because they make solutions impossible. Introducing more of them deliberately? Interesting approach, they said as they backed away slowly…
This keeps going around in the same circle. You keep using the word “spacetime” and yet you don’t appreciate the nature of spacetime. It is not 3D space plus time as a property within space. It it were, you could change the speed of c. As c would not be 1. But that isn’t what spacetime is. Spacetime is 4D. Time is not a property of space, it is an additional dimension. We measure this 4D spcae with the same units in all dimensions. You are stuck with measuring space with units of distance and time in a fundamentally different metric. This isn’t spacetime. In your 3D universe there is no simple geometric transformation that unifies motion in both space and time. So you don’t have relativity. The whole point of spacetime is that all 4 dimensions are measured with the same metric. And once you do this c = 1. It cannot have any other value. You can get to 1, buy saying light travels at 3x10[sup]8[/sup]ms[sup]-1[/sup]. But then you have to work out how fast time travels, and it turns out that time travles at 3.3x10[sup]-9[/sup]sm[sup]-1[/sup]. So if you want to work out c in the fundamental units of spacetime, it is 3x10[sup]8[/sup]ms[sup]-1[/sup] / 3.3x10[sup]-9[/sup]sm[sup]-1[/sup] = 1. In spacetime you can measure c in whatever units you like. if you want to know what it is in your 3D space. But if you want to work out what it is in in 4D spacetime you will always end up with 1. Because time travels at the same speed.
Asking what would happen if c changes is no different to asking what would happen is the speed of time changed. They are the same thing. Because they are the same thing
the answer is 1.
Does this mean that light, travelling through 3D space at c, does not move through time at all?
Yes, that’s correct. No time elapses for a photon.
I don’t know how to deal with that. But thanks for a very informative thread everybody!
I understood what you meant by “we are traveling through this 4D thing at a constant speed”. The speed of causality. If you’re stationary, you’re blazing through time. If you’re a photon, there’s nothing left for the time dimension. What I’m suggesting is that the speed of causality does change in certain extreme conditions, e.g. when two gigantic black holes collide, or at the center of a galaxy. Is your faith in 1=1 so strong that this isn’t conceivable?
If I say yes, what happens then? Do you get around to proving this claim using actual mathematics to convince me otherwise?
This was my question too. Three solar masses converted into pure energy? I had been thinking Magnitude 9 earthquake waves in a seriously large volume of space. There must be something about Einstein that I am missing here.
It is that, sensitive as the instruments that detected the gravity waves are, we have a looooong way to go before we even come close to detecting effects anywhere near to Planck-length in degree. The universe has faaaar more depth than we can currently detect- at all. The effect of the gravitational waves seems small because we are as close to deaf as you can get.
But what does that mean? Causality travels in both space and time at the same speed. That speed is unitless. What does it mean for it to have any value other than unity? You have still failed to explain this.
∀x ∊ R: x ≠ 0, x/x = 1 You are somehow suggesting that there is a situation where this isn’t so.
If you think there is, you need to explain what it means.
Step outside natural units for a second. The only way c=1 is if you assume the locally measured speed of a photon is always 299 792 458 m / s. What if the local speed of a photon is 314 159 265 m/s (sorry about the pun) near a huge black hole? This is interesting because then a massive particle could get ejected from its near orbit around a black hole and find itself exceeding the local speed of a photon. What would happen? Infinite mass for an infinitely small time? Could this account for the effects of dark matter?
Missing that the constant “c” and the actual measured speed of photons through a medium is also called “c” but is a different number is one of the most basic mistakes amateurs make.
I’ve advocated that we call Einstein’s Constant capital “C” and the measurement lower case “c”. That might help you overcome your confusion.
No it isn’t, and this is why you are not getting it.
It is all about coordinate transforms. Time and space are intrinsically measured in the same units. We provide a useful for everyday use conversion factor that gets us time and distance as different things.
Look at your definitions.
The speed you measure is 299 792 458 ms[sup]-1[/sup] So, what is a metre? Well it is the distance you get when you measure the speed of light over a defined time. Notice that?
In your warped spacetime, go and measure c. First thing you will need is a length reference. How long is a metre? What is c?
To try to get it, lets make the spacetime much easier. Rather than 4D, lets go with 2D. Try have one dimension of space and one dimension of time. Here are the rules:
[ol]
[li]Get a piece of paper. [/li][li]Draw a horizontal axis and label this time.[/li][li]Draw a vertical axis and label this space.[/li][li]Get a compass, stick a pencil in it and open it out a bit.[/li][li]Stick the pin in the intersection of the time and space axies. Use the pencil end to draw a point, making sure you never draw a point that is to the left of the pin.[/li][li]Repeat 5 as long as you have space to the right.[/li][/ol]
You can otherwise draw any path made up of points so described.
Draw more than one path starting from different points on the space axis.
If two paths intersect the entities represented by the paths affect one another at that time.
Until the paths intersect there is no interaction, and no causality.
Causality is the ability of one entity to affect the other.
That is spacetime. The distance between the pin and the pencil end is c.
You can see causality in action here. (The arc of the compass is your “light cone”)
A vertical path is traveling at c in space, and can be thought of as shining a light onto something.
A horizontal path is simply standing still in space and waiting for time to take you to a point where an entity traveling in space will intersect with you.
I gotta say, right at the time of the discovery, I kinda felt a tingle…
Really? What was the URL of that site? 
I followed your steps, and what I ended up with didn’t look much like the ‘Light cone in 2D space plus a time dimension’ diagram on the ‘Light cone’ page on wikipedia.
Suppose you’re a scientist living near a huge black hole, maybe near the center of a galaxy. You have already determined, like we humans did in the early 20th century, that the speed of a photon is the same, whether the source is moving towards you or away from you. So you decide to measure it’s speed. You come up with 300 142 652 m/s, using technology similar to early 20th century Earth. You then recognize this as a universal constant, and deduce the speed of causality. All of your subsequent observations verify this, so you define this constant as c=1.
How can you be certain this isn’t possible?
It won’t, because you are doing it with freedom to change your speed at every step. And unlike the usual diagrams it is drawn to scale. If you drew a pair of lines from each point to the edges of the allowed circle from which you choose the next point you will have your light cones - it is just that you are only drawing the point where you actually go to affect things next, not the set of all possible points.
There is a mistake in what I wrote, but I assume you worked it out - when you repeat step 5 you start at the last point you drew.
Same question. What is a metre? You can come up with any number you want. But if you want a speed you need two references - a unit of time and a unit of distance. In spacetime these two are the same thing. Because they are the same thing you can define any personal metric you like. Furlongs per fortnight. Oggs per Frobz. But if you measure c, and then work out how to express it, you will always discover that your personal units cancel out. Distance is defined by c and time, or conversely time is defined by c and distance. It doesn’t matter. You can’t define a metre without invoking c. So it is always the same.
To put it more concretely. c = the mutiplicative identity.
It always will.
Again: Identity Axiom repealed. Therefore A != A, such that x/x !=1. “Before” the Big Bang, you don’t need it (the Identity Axiom) anyway, or there isn’t any math to do at that point…