You divided by zero.

You divided by zero. — Banno

That's precisely the point. Infinite speed breaks mathematics and thus the "mathematical" proof.

For light to travel instantaneously, t = 0 for any distance d. The speed of light c would then be d/0 [division by zero. A big no-no]

Also, look at in terms of limits. For c = d/t, for a given distance d, the speed c approaches infinity only if the time t approaches zero.

Is the universe mathematical?

Infinite speed breaks mathematics and thus the "mathematical" proof. — TheMadFool

No, dividing by zero results in an undefined result. The mathematical rule is, don't do it.

Same goes for most of your other threads; don't break the rules and you will have far less trouble talking about what is going on. They are not arbitrary; they set out what can be sensibly stated.

Is the universe mathematical? — TheMadFool

No, but descriptions that use the grammar of maths are useful.

No, dividing by zero results in an undefined result. The mathematical rule is, don't do it. — Banno

That's the point. Division by zero is undefined. Thinking that the speed of light is infinite amounts to dividing by zero. There's no other way for speed to be infinite. And you completely ignored this:

For light to travel instantaneously, t = 0 for any distance d. The speed of light c would then be d/0 [division by zero. A big no-no] — TheMadFool

Same goes for most of your other threads; don't break the rules and you will have far less trouble talking about what is going on. They are not arbitrary; they set out what can be sensibly stated. — Banno

Now you're just making random remarks.

Thinking that the speed of light is infinite amounts to dividing by zero. — TheMadFool

No, poor arithmetic at line three results in division by zero.

Now you're just making random remarks. — TheMadFool

The misuse of

"everything is selfish", — TheMadFool

The contradiction used in

N = This statement can be negated.. — TheMadFool

The confusion of extension and intension in

Nothing is, by definition, not any thing; no thing. — TheMadFool

The failure to acknowledge the consequences of

both affirming and denying a proposition — TheMadFool

.

Should I go on, Zeno? These are all excellent threads; little puzzles to keep us entertained. Thanks.

No, poor arithmetic at line three results in division by zero. — Banno

The division by zero is implied by assuming light travels instantaneously. Instantaneous means time taken = 0. Speed = distance/time and if one claims light travels insatantaneously, it implies c = d/0.

I'm not going to read the other remarks because they're irrelevant.

I read the rest of your remarks and :rofl: :rofl:

The division by zero is implied by assuming light travels instantaneously. — TheMadFool

3. If A = B and B = C then A = C (transitivity of equality)

If 89 km = c * 0 and c * 0 = 89000 km then 89 km = 89000 km ??!! [from 3 above] — TheMadFool

89 km = c * 0
Solve for c: c=89/0

c * 0 = 89000 km
Solve for c: c=89000/0

Nonsense begets nonsense.

I'm fully aware of the division by zero but you seem to be ignoring the fact that it's implied by assuming light travels instantaneously or has infinite speed.

Yes, nonsense begets nonsense but, for better or for worse, it's not my nonsense.

By the way, I'm not as confident as you seem to be about nonsense and how it's somehow an indication or poor thinking or something much worse.

If you plot light speed (c) on a graph [distance (d) on the y-axis and time (t) on the x-axis] you'll get a speed graph that's almost indistinguishable from the y-axis. — TheMadFool

Using what units?

If you plot distance in lightyears and time in years, position over time at the speed of light draws a 45 degree slope.

If you plot miles per hour (which you probably did), you get a much shallower slope.

If you plot kilometers per second, you did a different shallow slope.

If you plot gigaparsecs per femptosecond, you get a much less shallow slope.

The units make all the difference.

If you're concerned with time in hours and distance in miles, then yeah, a beam of light can travel such an absurdly huge number of miles in an hour that for all you (or your personal calculator) care it might as well be infinite

But it's technically not, and measuring in different units shows that.

I'm not as confident as you seem to be about nonsense and how it's somehow an indication or poor thinking or something much worse. — TheMadFool

Not poor thinking - the opposite. When one comes across the sort of contradictions and paradoxes you love, what is one to conclude? What is it that your posts lead to?

For me, it's to go back and look for the mistake.

For you, it seems to be something different - but I'm not sure what.

Merged discussion OP is here.

Using what units?

If you plot distance in lightyears and time in years, position over time at the speed of light draws a 45 degree slope.

If you plot miles per hour (which you probably did), you get a much shallower slope.

If you plot kilometers per second, you did a different shallow slope.

If you plot gigaparsecs per femptosecond, you get a much less shallow slope.

The units make all the difference.

If you're concerned with time in hours and distance in miles, then yeah, a beam of light can travel such an absurdly huge number of miles in an hour that for all you (or your personal calculator) care it might as well be infinite

But it's technically not, and measuring in different units shows that. — Pfhorrest

My only concern with your post has to do with your comment on units being arbitrary, especially you mentioning about how the speed of light could be expressed as 1 lightyear per year. Indeed, units are arbitrary as you so kindly pointed out and with speed of light as 1 lightyear per year it the angle subtended by c would be 45 degrees - very far from my intended target of making this angle as close as possible to 90 degrees.

I did some back of the envelope calculations and here are my findings:

1. 1 lightyear = 9,460,800,000,000 km

2. 1 second = 3.17 * 10^(-8) years = 0.0000000317 years

3. The fastest object, call it x, (other than light) detected in the universe "far beyond the Local Groups" traveling at 1026 km/s and,

1026 km = 5.84 * 10^(-12) = 0.00000000000584 lightyears

So,

1. the space component of object x = 0.00000000000584 lightyears

2. the time component of object x = 0.0000000317 seconds

The angle subtended by worldline of object x = atan( (5.84 * 10^(-12))/(3.17 * 10^(-8)) = 0.0001842271 degrees

Now, cos(0.0001842271) = 1 which implies that the object x's wordline = object x's time component i.e. the object x has no space component. The same argument applies to all objects with speeds less than object x's speed and, in fact, the angle subtended by the speed graphs of other objects to the x-axis (time) would be lesser than that subtended by object x and that would mean that all objects in the universe, except light and probably some particles, are at rest.

This gibes with the speed of light being constant. No matter how fast or in what direction you move, the speed of light will be constant because all objects in the universe are at rest relative to each other [all their worldlines will coincide with the x-axis (time) because the angle subtended by each object's worldline to the x-axis (time) will have a cosine of 1 implying that the worldline is identical to the x-axis (time)] which means the speed of light relative to any object will be a constant. [Proof of why the speed of light is constant??]. Again, I must stress on this being an angular argument.

How can we make sense of the absence of motion as implied by your 1 lightyear per year speed of light? If there's no motion then all objects in the universe must be experiencing pure time as space is out of the equation. Are we, as Martin Heidegger thought, time itself? Food for thought.

If we use normal units for distance (miles/km/m/feet/etc) only light and some particles are found in the extremes where the angle subtended by their speed graphs to the x-axis (time) approaches 90 degrees. Yes, light seems to take a non-zero amount of time to traverse a given distance but, as I said, this isn't about lengths (distances), it's about angles.

In conclusion then (in terms of angles):

1. The speed of light is constant
2. The speed of light is infinite

It makes complete sense if you ask me.

Consider that relative velocity is calculated in terms of addition as in (v1 + v2) if two objects are moving toward each other with velocities v1 and v2 and in terms of subtraction as in (v1 - v2) if two objects are moving away from each other with velocities v1 and v2.

If an object is moving with velocity v1 and measures the veolocity of light coming towards it or is moving away from it, the relative velocity between this object and light would be (c + v1) = (c - v1) = c. The only way this is possible is for c to be infinite: infinity + v1 = infinity - v1 = infinity.

It appears that infinite speed, for some reason I can't figure out, manifests in our universe as 186000 mph/299792 kph or 1 lightyear per year. Go figure!

I'm surprised that people thought the speed of light was not finite because it's relatively easy, using math alone, to prove that all speeds, light's included, has to be finite without doing any experiments at all. — TheMadFool

1) As Banno has pointed out, you can't do this. You can't use infinity as if it's a regular number.

Consider: there is an equation for calculating the sum of the angles of a polygon, and to do that you need to input the number of sides in the polygon: sum_of_angles = number_of_sides * 180

So, based on your logic, we can trivially prove that it's impossible to have a polygon with infinite sides. Because that would allow us to prove that 1 = 2 or whatever.

But we know that there's a polygon with infinite sides: a circle.
OK technically mathematicians do not consider a circle to be a polygon, but it's only for essentially this very reason; that the maths is simpler if we separately handle shapes with finite vs infinite sides. But apart from the number of sides there's clearly no qualitative difference between a hexagon, say, and a circle. Anyway, the main point is, having an equation that would be broken by inputting infinity doesn't tell us anything. All equations are broken by inputting infinity.

2) More specifically on the light speed issue, s = d / t can be considered a crude approximation to Einstein's relativistic equations, that only works for low values of s.

Einstein's equation includes Lorentz contraction and shows that at actual lightspeed, t is indeed zero, even though c is not infinite.

So, ironically, from a photon's eye view, all distances are the same, and part of the OP's premise for saying infinite light speed is impossible is true in reality, even though lightspeed is not infinite!

However, when we're talking about perspectives, it's pretty clear that there is no reason to say it is impossible. For example, a toy cow on my desk might look the same to me as a far away cow in a field. So what? There's no contradiction there.

3) Finally, speaking more empirically, it is possible to reason why light speed is finite.
In our reality, Ole Roemer figured out that lightspeed must be finite from studying the eclipses of Jupiter's moons. But, in a hypothetical reality where we had the equations for electricity and magnetism and still thought light moved infinitely fast, in a single reference frame, we'd find that our equations would tell us that electrical fields and magnets would create infinitely more of each other in a feedback loop.
(The specifics of this are beyond my mathematical ability, but I can link a video if you're interested. Apparently there are a few examples like this in physics, where an infinite light speed (or speed of causality), would break things physically, not just the math).

you can't do this — Mijin

I didn't do anything. Talk to the person who thought that light travelled instantaneously.

But we know that there's a polygon with infinite sides: a circle.
OK technically mathematicians do not consider a circle to be a polygon, but it's only for essentially this very reason; that the maths is simpler if we separately handle shapes with finite vs infinite sides. — Mijin

If the point you're making requires that a circle is a polygon, and mathematicians do not consider a circle to be a polygon, then it really doesn't make your point, does it?

If the point you're making requires that a circle is a polygon, and mathematicians do not consider a circle to be a polygon, then it really doesn't make your point, does it? — Metaphysician Undercover

The point is, the only reason it is not considered a polygon is because it breaks equations like that one.
The OP was saying that, since infinity breaks the speed equation then there cannot be an infinitely fast speed. However, using the same logic, there cannot be an infinitely-sided shape.

Who cares about top speed? How about bringing light speed down to my neighborhood limit! :cool:

Light travels at 38 MPH