Actual Infinities

[robvalue]

The problem is with the accuracy of our model in relation to what is actually going on. So our model can be flawed without failing to have anything to do with reality. That's a false dichotomy; time exists as we imagine it, or there is no such thing that could be remotely like "time".

More likely, it's far more complex than we currently realize. For example, we already know from relativity that space and time are intertwined making time more than a simple parameter. I can't get my head around that yet though

[I_am_not_mafia]

Time doesn't pass at all for a photon because nothing can go faster than the speed of light.

So what happens if you send a photon on an infinite journey? Is this actually possible?

Or is this another argument alongside Olber's paradox that allows us to determine that space-time is finite?

Or to put it another way.

If you somehow gained infinite energy to travel at the speed of light then you would seem to arrive instantly at your destination. But if you were on an infinite journey then how could you arrive instantly at a destination that you could never reach?

[robvalue]

In other words, we are trying to see what the carnival staff can easily see, while we're trapped inside the hall of mirrors.

That's right, isn't it?

[I_am_not_mafia]

Oh just realised that it gets worse. According to this page

http://www.askamathematician.com/2013/04...it-travel/

Whenever there’s a “time effect” there’s a “distance effect” as well, and in this case we find that infinite time dilation (no time for photons) goes hand in hand with infinite length contraction (there’s no distance to the destination).

At the speed of light there’s no time to cover any distance, but there’s also no distance to cover.

[Alex K]

Time dilation and length contraction are two aspects of the same thing - that the speed of light remains the same for all observers. We had this example before - if you travel to Andromeda at near the speed of light, seen from the outside, 2 million light years are travelled in 2 million years. From the inside, only a few light years are travelled in a few years time. Both reductions have to be present for the ratio of distance and time, which is near the speed of light, to be the same for both observers.

[robvalue]

Or on the other hand...

[ErGingerbreadMandude]

Does a photon undergo any sort of chemical reaction?
Anyone? Pretty please?

[Alex K]

Does a photon undergo any sort of chemical reaction?
Anyone? Pretty please?

Photons are absorbed and created by electrically charged particles. Chemical reactions on the other hand are the following: atoms get bound to others by electrical forces. Since photons disappear and appear when the undergo reactions, and are not charged in such a way that they could form bound states, the analogy with a chemical reaction is not very accurate.

[I_am_not_mafia]

Time dilation and length contraction are two aspects of the same thing - that the speed of light remains the same for all observers. We had this example before - if you travel to Andromeda at near the speed of light, seen from the outside, 2 million light years are travelled in 2 million years. From the inside, only a few light years are travelled in a few years time. Both reductions have to be present for the ratio of distance and time, which is near the speed of light, to be the same for both observers.

That conversation earlier made me think of this in relation to the concept of 'actual infinities' but I missed the bit about length contraction. Although now that I think about it, I do remember hearing about length contraction before but never really understood it.

Can we use this to argue that 'actual infinities' cannot actually exist because that requires it to be absolute and everything is relative within space-time?

I feel like such an idiot trying to speculate on all of this.

[Alex K]

Time dilation and length contraction are two aspects of the same thing - that the speed of light remains the same for all observers. We had this example before - if you travel to Andromeda at near the speed of light, seen from the outside, 2 million light years are travelled in 2 million years. From the inside, only a few light years are travelled in a few years time. Both reductions have to be present for the ratio of distance and time, which is near the speed of light, to be the same for both observers.

That conversation earlier made me think of this in relation to the concept of 'actual infinities' but I missed the bit about length contraction. Although now that I think about it, I do remember hearing about it before but never really understood it.

Can we use this to argue that 'actual infinities' cannot actually exist because that requires it to be absolute and everything is relative within space-time?

I feel like such an idiot trying to speculate on all of this.

Not everything is relative - the time measured by a clock on its journey from A to B (what is called the proper time) is obviously independent of the observer. But there is a more profound problem - we are assuming special relativity, and indeed in special relativity, all inertial frames are equivalent and there is indeed no absolute time standard. However, in general relativity, and more concretely in the Big Bang cosmology, this is not true any more: if it were, you should in the past have wondered how we can say that the universe is 13.7 billion years old - isn't that an entirely relative statement? No it isn't, because in the actual cosmos out there, we have a special local reference frame, namely that where the cosmic microwave background radiation has the same average frequency in all directions. This is basically the frame in which on average matter in the region is at rest, and this is the frame in which the age measurement applies. The "creation" of radiation and matter after the big bang limits the relativity of space and time to a certain extent because there is one special choice of time axis in which the CMB is maximally isotropic and the stuff in the universe at rest on average.