Infinite Speeds

• 77
Hello,

Infinite speeds, this gets pretty interesting. It is not possible for anything with a starting point to move infinitely fast per finite amount of time. As that would imply moving infinite spaces per the given finite amount of time. To move infinite amount of spaces, infinite amount of time is required. But, in that case, the speed of an object would be infinite miles/eternity. But that does not mean it's going very fast, it's speed can be anything in finite amount of time, even 1 mph.
• 1.8k
Because no matter where it's at after travelling, it has not travelled infinite spaces.

Not a good argument. You need not travel an infinite distance to reach infinite speed. Consider any jump discontinuity. For example suppose a particle is moving in the plane according to the rule

f(x) = 0 if x <= 1
f(x) = 1 if x > 1.

In other words it's going left to right along the x-axis, and at x = 0 it jumps up to a height of 1. It's moved a distance of 1 unit up in arbitrarily small time, in other words it has infinite speed. But it only need to hop up one unit. In fact the same example would work if it only hopped up 1/zillionth of a unit. As long as the movement is discontinuous, the "speed" is effectively infinite if you think about it that way.

Note that I'm not commenting on your first assertion, that infinite speed isn't possible. I'm only pointing out that your argument doesn't support that conclusion. You need a better argument.

As far as whether such a thing could happen in the physical world, see quantum tunneling. I googled around to see if quantum tunnelling is regarded as going at infinite speed or exceeding the speed of light, and it seems there's some discussion of this but I didn't have the patience to drill down to a conclusion. Regardless, discontinuous motion does seem to be possible in the physical world and I don't see why this wouldn't count as infinite speed, if only for a moment. I could be wrong about the physics though.
• 77
@fishfry,

• 1.6k
To move infinite amount of spaces, infinite amount of time is required.

Not if you are moving infinitely fast. If your speed is infinite over any amount of time, then you will have moved an infinite distance.

Which is allowed in Newtonian mechanics, for example. You can "always already" move at an infinite speed, or you can accelerate discontinuously, or you can start at rest and continuously accelerate to infinity (in infinite time, of course). The math can bear it, the physics - not so much. By the way, the time-reverse of the latter scenario is one of the ways in which determinism can be violated in a Newtonian universe.
• 135
From our reference frame this is true but from the point of view of a photon of light, this is in fact not the case. It perceives reaching its destination instantaneously and it always travels at speed of c - the speed of light.

This is described by the Lorentz factor, γ

${\displaystyle \gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}={\frac {1}{\sqrt {1-\beta ^{2}}}}={\frac {dt}{d\tau }}}$

Time dilation: The time (∆t′) between two ticks as measured in the frame in which the clock is moving, is longer than the time (∆t) between these ticks as measured in the rest frame of the clock:

${\displaystyle \Delta t'=\gamma \Delta t.}{\displaystyle \Delta t'=\gamma \Delta t.}$

But since γ = ∞ in this case, it simply reduces down to ∞

You may be aware of the analogy from school where a teacher talks about a rocket flying off on a mission. By the time the rocket returns, the astronaut hasn't aged much but everyone else back home has.

For light just think if it in more extreme terms. There is no time elapsing from the point of view of a photon of light but eternity has passed. It feels counterintuitive to think about it, but the inverse of this is that the light doesn't age so to speak. It gets there instantly from its frame of reference. This is where bizarre effects arise such as the EPR paradox. It appears as though we can influence a photon of light from the past. This has been documented in experiments like the delayed choice quantum eraser. In reality, nothing is erased as there is no time passing from the point of view of the photon. The concept of tense doesn't really exist from that reference frame.
• 1.8k
Not if you are moving infinitely fast. If your speed is infinite over any amount of time, then you will have moved an infinite distance.

I already explained that this is false. Did you read my post? Would you be good enough to do so now? You could move a billionth of an inch in zero time and that would be infinite speed but you've only moved a billionth of an inch.
• 1.6k
By "any amount" I do not mean zero, of course - I thought that would be obvious.
• 1.8k
↪fishfry By "any amount" I do not mean zero, of course - I thought that would be obvious.

In the example I gave, the speed is unbounded over "any amount of time" for any interval containing zero as the intervals get small. I see your point but at the time it wasn't obvious. And when someone says "any amount" I take them at their word, zero being an amount. I'm not being cute, that's exactly the case that popped into my head. My pedantic turn of mind. If you'd said, "any nonzero amount of time" I wouldn't have needed to post. Perhaps I should have realized that's what you meant. In some other universe I did. Does the Many Worlds theory absolve us of our sins?

It is not possible for anything with a starting point to move infinitely fast per finite amount of time.

0 is finite. Did you mean to exclude that?

What would you say is the velocity of my function f at the point 0? Well in calculus we would say it doesn't have a velocity because the function's not defined at 0 and it's not differentiable there. But if you take any tiny interval including zero, the particle moves 1 unit up in arbitrarily small intervals of time. So you can make its velocity as large as you want, without bound. That's what infinite means. So I would say it has infinite velocity at zero by that definition. But I admit it could be argued otherwise.
• 6.1k
Does the Many Worlds theory absolve us of our sins?
Absolutely, but everyone else's as well, including those of those who are coming after you. Back to square one.
• 1.8k
Absolutely, but everyone else's as well, including those of those who are coming after you.

How do I get to one of these better worlds?
• 2.1k
To move infinite amount of spaces, infinite amount of time is required.
Under Newtonian mechanics, perhaps. But not in other imaginable, mathematically consistent universes.

I will describe a trajectory with a definite start and end point, incorporating a double jump, that traverses an infinite distance.

The particle traversing the trajectory, which lies in the first quadrant of the two-dimensional, Euclidean, number plane, has position at time t with x coordinate t and y coordinate 1/|t - 0.5|, except at time 0.5 when it has position (0.5, 0).

For time 0 to 1, the particle starts at position (0, 2), at time 0, finishes at position (1, 2) at time 1 - a distance of only 1 unit from the start point, and in between, traverses the infinite lengths of the two hyperbolic arms of the function f(x) = 1/|x - 0.5|, with a zero-duration, cameo visit to the point (0.5, 0) in the middle.
• 1.8k
For time 0 to 1, the particle starts at position (0, 2),

You meant (0, -2) here.

traverses the infinite lengths of the two hyperbolic arms

"I just flew in from infinity and boy are my hyperbolic arms tired!"

Nice example. Finite time, infinite length traversed.
• 112
Einstein's equations show that an object at the speed of light would have both infinite mass and a length of 0.

Also Greater speeds provoke greater weights (Mass).

If you moved at a speed near to the speed of light you would weigh as much as the entire universe weighs. My only suggestion if that should happen might be to try the Robert Adkins weight reducing diet.
• 135
To move infinite amount of spaces, infinite amount of time is required.
Depends on the frame of reference. There are temporal paradoxes to consider with this.

If something is moving at infinite speed - the speed of light - time isn't even ticking from the point of view of a photon. By the time it reaches the other end of the universe, it still hasn't ticked and it never will. You will perceive it move from your frame of reference but while you will have aged quintillions of years or however long it takes, from its pint of view it arrived at the same time it left.

Many experiments have shown this, including the delayed choice quantum eraser. Experimenters have been able to erase a state in a system in the past and effect its future. Well they haven't actually erased of course, that would be nonsense. It's simply that they were able to make a change to a photon of light at one point in our frame of reference, that we perceive as being temporally prior to another change made. But of course for the photon there is no time and so the arrow of time and causality was not violated. Tense is irrelevant when it comes to interfering with a photon in its flight.
From its point of view it gets there the same time it leaves, always.
• 1.8k
If something is moving at infinite speed - the speed of light

Just a quibble. The speed of light is finite. That's the entire point. It's infinite in Newtonian physics. In special relativity the speed of light is finite. That's what makes relativity strange.
• 135
In special relativity the speed of light is finite.

Relativistically speaking yes. It's finite from our frame of reference here on earth, from the frame of a reference of a photon, the clock is not ticking so its difficult to define. I've found that Neil Degrasse Tyson speaks about it just as I see it. When I first saw this video I couldn't stop nodding!

• 2.2k
If something with mass suddenly traveled at the speed of light it would gain infinite mass, but from where? Where does the mass come from? From the perspective of those not traveling that fast the object disappeared but if we were the object we would be infinitely big. But again, how does something in that situation increase its mass? Does it take mass from its environment?

On the purely speculative side, suppose we have a race track that literally goes out forever into the horizon. A hypothetical geometric object goes towards this horizon and miraculously jumps to infinite speed. Since his destination is endless he will never reach it yet his infinity of speed is as infinite as the track. Would this simply tear the fabric of reality of such a situation occurred?
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