Question about Speed of Light and Relativity

[WestAir]

Sorry westair, got my degree nearly 10 years ago and don't remember anything about that. To be honest I'm not sure what you are asking, can you reference an article or be more specific?

Speed is determined by distance x time. In this case, meters x seconds. The plank length, too, is a distance. The difference here is that you can't crunch any information smaller than the plank length - so something that's moved 0.1 Plank Lengths is in the exact same physical position as something that has moved 0.6 Plank Lengths. There's no difference. There is a similar variable for time; if it takes you "the age of the universe" to move 1 meter, then you've moved 1 meter as of today. If it takes you "longer than the age of the universe" to move 1 meter - well you've yet to move 1 meter.

The thought experiment here is that there is a physical, non-infinite energy requirement for an proton to travel 10 plank lengths in 10.5 plank times. However, because you can't fractionate the plank length, both the proton and a photon will have traveled the same physical distance. The thought experiment can be dragged even deeper. Pretend both a proton and a photon began their journey during the birth of the Universe. If the protons speed is slower than a photon by 1 plank length x the age of the universe plus one second, then up until now, it's kept pace with a photon - it's traveled at C, which is impossible, but will become possible in the future when it begins to lose the race.

How can that be without breaking the rules? Surely the energy requirements needed to accelerate the proton to this speed are calculable, and surely some Oh My God particle has been traveling at this speed somewhere. It's NOT traveling at the speed of light, but because of the existence of the Plank Scale, it should appear to be.

Edited October 2, 2013 by WestAir

[Oops]

Its about spacetime. Not space and time. To Einstein it was the one thing. When you cannot logically grasp the relative change, just bend spacetime and it folds right into your lap. Beautiful.

[Beowolf]

WestAir, since energy as well as spacetime is quantized wouldn't the energy required to give that proton such a velocity involve terms like "infinity minus less than a single quanta"? Which would make it really impossible, which would resolve your paradox.

Just guessing, obviously.

[-Velocity-]

How can that be without breaking the rules? Surely the energy requirements needed to accelerate the proton to this speed are calculable, and surely some Oh My God particle has been traveling at this speed somewhere. It's NOT traveling at the speed of light, but because of the existence of the Plank Scale, it should appear to be.

It takes an infinite amount of energy to accelerate a particle with non-zero rest mass up to the speed of light. What you are talking about would require such a tremendous expenditure of energy into a single particle that I assure you, no such particle exists in the universe. It would probably have the energy of like a, AT LEAST a large hydrogen bomb, maybe something closer to a supernova, packed into a single particle. There is just no way, natural or otherwise, to focus that kind of energy into a single particle. I tried to calculate the amount of energy involved, but my computer is simply not capable of calculating down to that many decimal places. Maybe MATLAB could, but I doubt it.

[-Velocity-]

WestAir, I might also note that you're trying to take a QM approach to Relativity (Plank Length is a QM concept), and as we know, the two do not coexist peacefully yet. So it may be that no one truly knows the answer anyway.

Anyway, I figured out a way to do the calculation, and it turns out, if my numbers are right the particle would have an energy of something like 3x10^20 J. That is over 1500 times the energy of the largest hydrogen bomb ever tested. It's equivalent to 3600 kg of mass. I have to wonder whether that is enough mass, packed into the size of a proton, for the particle to collapse into a mini black hole. If so, would it? From the frame of reference of the particle, its mass doesn't increase, or does it? From our frame of reference, it should, and it might collapse under its own gravity. I'm not sure how this is resolved, I've never thought about the mass increase at relativistic velocities much. If it did collapse, it would rapidly dissolve in a burst of Hawking radiation.

Finally, note that your hypothetical particle is over 6x10^18 times more energetic than the most energetic cosmic ray EVER detected. Such a thing does not exist in this universe, you can be sure of that.

Edit: Just to make sure we're on the same page, this is the speed I assumed for the proton:

One plank length behind a photon after the photon and proton had traveled 15 billion light years.

That's about one part in about 10^61 less than the speed of light. I had a hard time doing the calculation till I wrote it out and realized that (1 - (1-10^-61)^2)^0.5 could be simplified to (2*10^-61)^0.5.

Edited October 4, 2013 by |Velocity|

[WestAir]

|Velocity|

You hit my thought experiment right on. I had assumed the proton could be an OH MY GOD particle, but if it's 6x10^18 more powerful than the one that frightened us decades ago, I'm obviously mistaken!

It might be that the QM approach to relativity is what makes this experiment fail, or maybe it's simply because the proton would be massive enough to fall within its own event horizon. [Does the mass increase caused by acceleration even affect the object locally from its perspective? Or would it just have an event horizon to an outside observer but not itself? How can that even be explained?]

I'm extremely intrigued by these questions. I just wish I had the answers.

Edit: It sounds like, if QM and Relativity could be assumed to flesh out evenly with this experiment, that 3x10^20 Joules is the single energy requirement below a value of infinity [today], and adding more energy would do nothing to accelerate the proton further [until the future when spacetime expands further]. It also means that the energy required to reach "a quanta below infinity" changes based on the distance being measured, and you can only reach true infinity with a distance of infinity.

Edited October 4, 2013 by WestAir

[-Velocity-]

[Does the mass increase caused by acceleration even affect the object locally from its perspective? Or would it just have an event horizon to an outside observer but not itself? How can that even be explained?]

Yea, I'd like to know this too. Actually come to think of it, even if it DID collapse into a mini black hole, the time dilation caused by moving that fast would be so extreme that the black hole would probably NOT evaporate very quickly at all.

Edited October 4, 2013 by |Velocity|