Got into a debate recently

Got into a debate recently.
the jist of it is that theoretically if you have an infinite source of energy would you be able to accelerate an object with mass to the speed of light.
I believe its possible, she doesn't. Ive asked my physics professor and he said i would need to find the rate of change in mass with speed and the rate of change of energy with speed and find which diverges first.
does anyone know how to prove or disprove this mathematically by setting the limit to infinity?

My reasoning as to why this would work is that in relativity gamma can reach infinity as v^2 -> c.
This is not about practicality this is all theoretical.

Other urls found in this thread:

mrelativity.net/MBriefs/Using Integral Calculus for Relativistic Acceleration.htm
twitter.com/NSFWRedditVideo

Well first off you have the wrong equation.

>setting inifinity
>infinite source of energy
this isn't well defined, you're discussing nonsense
what your prof suggested is a way to making this well defined: instead of talking about "infinite", talk about "arbitrarily large" (look at the limit)

the picture is just a picture of gamma so i could post its relevant but not the point of the thread.

i understand that i havent presented this well. What im interested in is gamma tends to zero then Etrans will tend to infinity. My question is is this possible and does anyone have a comprehensive explanation as to how its possible.

Possible to achieve the speed of light? Not unless you had something like negative mass or some shit like that.

with a fixed mass, yeah. it follows from taking the limit in the expression
E = mc^2/gamma - mc^2
given that mc^2 is a positive constant and gamma is positive as well

umm never mind I fucked the equation up. but set it properly and take the limit. I don't really know physics

You may have an infinite amount of energy available, but if you don't also have an infinite amount of power, than you can't accelerate past the speed of light in a finite amount of time.

If by infinite you just mean a source of energy that never runs out, then no, you would never make it all the way.

nonsense
what he's asking is: if I have an arbitrarily large (bigger than any M > 0) amount of energy, then for every d > 0, is it true that I can accelerate past (c-d)? the answer is yes.

Well, if you do what the professor said, you get

mc^2 = E(gamma)/(1-(gamma)
Then dmc^2/d (gamma) gives you
E /(1-gamma) - E (gamma)/(1-gamma)^2

In the limit that v-> c,
You get E - infinity.
This implies that they do converge the same rate.

>i would need to find the rate of change in mass with speed and the rate of change of energy with speed and find which diverges first
I don't know what this is supposed to mean. If it's about relativistic mass, it's bullshit.
Just invert the equation. [math]E=\gamma mc^2 => v=c\sqrt{1-\frac{mc^2}{E}}[/math]
Or something. Now it's obvious as you increase the energy of the object its speed will come closer and closer to [math]c[/math], plot it or something. It's completely pointless to talk about "infinite" energy or whatever, even "theoretically". What you're looking for is limits.

I don't know mucha bout limits, but does anything in physics involving infinite energy doesn't end up with an event horizon eating everything and expanding at the speed of light?

"infinite" anything is badly defined. limits don't talk about infinity, they talk about arbitrarily large amounts exactly in this sense

>umm never mind I fucked the equation up. but set it properly and take the limit. I don't really know physics
this is really helpful could i trouble you to explaining this a bit more?

the proper equation is here take the limit as E->infinity, then mc^2/E goes to 0 (mc^2 is positive, E is positive and very large) and so the right term goes to c.

>nonsense
Brainlet. Put a finite number as the acceleration in the constant acceleration formula and see how long it would take for you to reach c. It is clearly an asymptote on the graph, the only way to reach it is by rounding error, so not physically possible. So having infinite energy doesn't help you if you can't extract infinite energy from it in an instant as well. You need infinite acceleration to overcome c and the only way to do that is with infinite power.

It is probably futile to post this here since I doubt you'd understand it anyway (for simpler it may be), but here it goes: mrelativity.net/MBriefs/Using Integral Calculus for Relativistic Acceleration.htm

im not talking about it being physically possible. This is about whether or not its theoretically possible. Also the link you gave is babyshit maths which is in no way helpful to my question. Please only contribute if you understand the problem to avoid looking like an idiot in future.

I mean it has nothing to do with the question, and muddles the ideas involved. he's asking about the energy needed for the acceleration, not the rate at which it enters the system or is transformed into actual acceleration. it's true that infinite acceleration requires infinite power, just as it's true that grass is green or whatever the fuck else you wanna say. it's just unimportant

>that kid who bugs the professor with his theoretical questions

No, it is not possible. Not even theoretically.
>stop posting numbers! if you don't understand stop posting!!!
So you want me to what? Write a novel explaining why it isn't possible? The way we do physics is with mathematics, you should have come prepared for that when you posted that question. But I'll simplify it for you: suppose you had a device that managed to provide infinite energy and also infinite power to you ship. Okay, now you got an infinite acceleration and an indefinition in your equation. What is your state like after that? Are you going at c? 2c? 3c? infinite? Well, suppose you needed to go at 2c, how much power do you put into your engines? Infinite! Now suppose you need to go at 3c, how much now? Infinite! And so forth. So you don't have a defined physical system anymore. And the cause is obvious: infinite energy doesn't exist, not even in theory, because the theory can't predict it.

nah me and my prof work at the observatory and hes into this sort of stuff.

stop your autistic rant and read the posts. he's talking about asymptotic behavior, not "infinite" stuff. he clarified this early on.

The answer depends on how much are you ready to accept infinity. If "you'll be going at a speed indistinguishable from c, but only after infinite time" is an acceptable answer, that that is that. Otherwise, you'll never reach c.

the question ins about asymptotic behaviour. not "infinity?

>evice that managed to provide infinite energy and also infinite power to you ship. Okay, now you got an infinite acceleration and an indefinition in your equation. What is your state like after that? Are you going at c? 2c? 3c? infinite? Well, suppose you needed to go at 2c, how much power do you put into your engines? Infinite! Now suppose you need to go at 3c, how much now? Infinite! And so forth. So you don't have a defined physical system anymore. And the cause
2c isnt what im talking about, im not talking about exceeding c im talking about reaching c.

>this Amerifat OP posting in third person to give the impression that someone else here really cares about his question and thinks he's not a retard

Stop projecting your insecurities. Also im british and im confused as to why nationality should be a factor in this thread.

Is this satire? You work with your prof at an observatory yet you don't know basic math or physics and pretend putting "theoretical" into your question makes them any coherent.

That said, as the object accelerates, what happens when its Schwarzschild radius exceeds its size?

like i said im a first year physics student. My maths isnt much better than undergrad level. The work i do at the observatory isnt research work. I think you may have misunderstood what i said or missed some of my replies.

Boom lol

Nothing. From its own frame of reference, it's just at rest.
What about from our frame of reference? I don't know. I actually heard two phd students who were tutoring my GR class talking about this, one of which had asked some big shot professor, but I can't remember the answer. Something something it can only form a black hole if you can encapsulate the particle within some finite time frame? Probably way off.

If it's fine in its reference frame, but is under event horizon for external observer, isn't it warp?

No. Just because a limit converges to a value doesn't mean the function actually attains that value. Consider 1/x. This approaches 0 as x goes to infinity, but clearly 1/x is never 0 for any x. As you put more and more energy into the particle, it'll get closer and closer to c, but will never equal it.

Its kind of like we are made of the same stuff as light is made of, just caught in a kind of weird whirlpool, and that is why the relativity stuff works in practise. Thats why time and mass change relative to different frames of ref.