Energy/Mass transitioning from finite to infinite amounts

[Cody Richeson]

E=MC², if I understand it correctly, tells us that an object would need an infinite amount of energy and mass in order to travel at light speed, which is why particle accelerators can only travel at 99.99999 or so percent of the speed of light. With this in mind I have a couple of questions:

1) Why would you need an infinite amount of mass and energy in order to travel at a finite speed?

2) Why is it that the amount of energy and mass required to travel at 99.99999% of C is finite, but suddenly becomes infinite at 100% C? If the percentage was 99.9 followed by a billion decimals of 9, the energy and mass would obviously still be a finite number. What accounts for this sudden transition into infinity?

 

[mathman]

Look at the formula for Lorentz transformation. When v is close to the speed of light the mass is 1 divided by a very small number. The limit of the denominator as the speed goes to the speed of light is zero.

http://galileo.phys.virginia.edu/classes/252/energy_p_reln.html

 

[Cody Richeson]

Unfortunately, I'm not educated enough to understand the math in the link you posted. Is there possibly a laymen explanation, or is it impossible to answer my questions without evoking complex formulas? What if the value were 99.9% of C, with the decimal place extending a gogol gogolplexes? Now, I am speaking purely out of ignorance, but could you conceivably take it even further, and have the value be 99.9% with the decimal place extending to infinity, like an irrational number? Would that even matter?

 

[mathman]

The key term is γ=√(1 - (v/c)²). When v < c, γ is a small positive number. When v = c, γ is zero. When you divide by γ you will get a large positive number for v < c, but infinity for v = c.

 

[Cody Richeson]

Well, I guess that's your name is mathman.

 

[soothsayer]

Cody, Energy asymptotically aproaches infinity as velocity approaches c. That is to say that velocity approaches c slower and slower the closer it gets, while Energy increases faster and faster and faster. You can see this behaviour in graph in the link mathman posted. Calculus tells us that energy increases without bound as velocity approaches c. You are picturing this function as a linear one, with some sort of discontinuity at v = c but this is not the case.

 

[flinky]

looking at the link and the graph mathman posted. what would be the most likely realistic speed a spaceship could reach? looking at the graph it looks to me it is either going to be 0.5 the speed of light or around 0.8 to 0.9.

 

[pervect]

Well, I guess that's your name is mathman.

If you're interested in questions like the ones you just asked, unfortunately in order to understand the answers you will undoubtedly need some math.

The amount of math needed isn't great, it is just high school algebra. If you're not out of high school yet, you may need to wait a bit and take the appropriate classes before you can answer the questions you are asking in any detail.

If you are in high school, I would really encourage you to study the math. It's something that can be learned!

I've seen what I refer to "math phobia", an unreasoning fear of math and an unreasoning conviction that even simple math is "beyond ones abilities". IT always makes me sad, and. I really believe that most such fears are unjustified. The fear itself seems to be the biggest obstacle to learning. Without the fear element, the learning requires time and effort and perhaps a bit of patience, but nothing more.

 

[soothsayer]

I've seen what I refer to "math phobia", an unreasoning fear of math and an unreasoning conviction that even simple math is "beyond ones abilities". IT always makes me sad, and. I really believe that most such fears are unjustified. The fear itself seems to be the biggest obstacle to learning. Without the fear element, the learning requires time and effort and perhaps a bit of patience, but nothing more.

Agree 100%. It seems 99% of the people I know are not only disinterested in math, but are totally freaked out by it. I'm not sure how that's come about in our culture.

Cody Richeson, I'd mirror what pervect said. The math required to understand the Lorentz factor is fairly basic, and not difficult to learn. Look up what an asymptote is, if you're fuzzy on the concept. This is exactly what the Lorentz factor is. I would also look up the equation for the Lorentz factor, how it's used in special relativistic equations and just spend some time plugging in numbers and see what happens. Investigate the behavior of the equation as velocity goes to c. If you are patient with it, I think you'll gain a much better understanding of WHY energy is said to be infinite when a massive object reaches the speed of light.

 

[soothsayer]

looking at the link and the graph mathman posted. what would be the most likely realistic speed a spaceship could reach? looking at the graph it looks to me it is either going to be 0.5 the speed of light or around 0.8 to 0.9.

The fastest speeds we've achieved with spacecraft so far have been maybe .0001c. anywhere near .8c would require tremendous amounts of energy and would make free hydrogen in space very hazardous to the spacecraft . Honestly, without something like a warp drive, I don't see spaceships ever reaching a point where relativistic effects even become that pronounced.

 

[Cody Richeson]

In response to the "math phobia" issue, I don't believe that I'm beyond the ability to learn some of the math behind the scientific concepts I'm interested in, but what must be understood is that there are certain subjects, mathematical or not, which are so difficult to learn that the frustration and panic they cause can be mentally exhausting. For instance, I failed pre-algebra at least three times in high school (never passed it), failed geometry twice, failed college astronomy, barely passed rudimentary college physics and failed basic algebra twice in college (I was only able to pass by cheating thanks to my girlfriend). There were times when I literally had to lie down, stricken with fear, depression and physical pain (in the form of moderate to severe headaches) from trying to do basic math. When I see formulas for scientific concepts, I instantly panic and become very uncomfortable, and have not figured out how to get past it. The phobia is not as unreasonable as it may seem.

 

[soothsayer]

Well, Cody, I hope you can work past your fear of mathematics one day. I myself was not super fond of math until I got into college and started doing a lot of calculus, and I saw the beauty in it. It's a wonderful subject and the natural language of physics. It's hard to learn physics in any capacity unless you have a grip on the math, I'm afraid, but this graph should, hopefully, clearly demonstrate why energy does not "all of a sudden" become infinite at v=c. Asymptotes were a little difficult for me to grasp when I was first studying them, but just know that this trend to infinity at a finite x value is ubiquitous in math and sound in physics, and is integral to much of special relativity.

 

[harrylin]

E=MC², if I understand it correctly, tells us that an object would need an infinite amount of energy and mass in order to travel at light speed

That's inexact, and may make a correct understanding difficult. Better:
An object would need an infinite amount of energy in order to attain an infinite amount of relativistic mass (inertia); this would happen at light speed.

1) Why would you need an infinite amount of [STRIKE]mass and[/STRIKE] energy in order to travel at a finite speed?

Nobody really knows what is going on inside matter when you accelerate it. However, matter has electromagnetic wave properties, and such waves propagate at c. It also behaves more and more like radiation (light) at high speed; it cannot become more light-like than light.

2) Why is it that the amount of energy [STRIKE]and mass [/STRIKE]required to travel at 99.99999% of C is finite, but suddenly becomes infinite at 100% C? If the percentage was 99.9 followed by a billion decimals of 9, the energy and mass would obviously still be a finite number. What accounts for this sudden transition into infinity?

As illustrated in the last graph (post #12), it's not a "sudden transition". Instead, increasingly more energy must be pumped into get it closer to 100% of c. This energy comes free as heat when it crashes into a wall.

 

[flinky]

hypothetically speaking - if a spaceship was to accelerate to 99.9% the speed of light, then turned off it's engines so it wasn't accelerating anymore but still traveling at 99.9% the speed of light and then a spaceman with a jet pack left the spaceship and accelerated away could he or she achieve the speed of light? or does everything inside the spaceship have a near infinite energy/mass?

 

[soothsayer]

hypothetically speaking - if a spaceship was to accelerate to 99.9% the speed of light, then turned off it's engines so it wasn't accelerating anymore but still traveling at 99.9% the speed of light and then a spaceman with a jet pack left the spaceship and accelerated away could he or she achieve the speed of light? or does everything inside the spaceship have a near infinite energy/mass?

No, he cannot. You cannot simply add velocities, so if the spaceship were traveling 99.9% the speed of light, and the astronaut were traveling 0.1% the speed of light relative to it, the resulting velocity of the astronaut would NOT be c in any reference frame, even in frames flying by at, say, 99% the speed of light the opposite direction. You must do a Lorentz velocity transform. Physics at the everyday level allow us to simply add v₁ and v² to get v³, as given by Galilean transformations, but this does NOT hold up in the relativistic limit.

 

[soothsayer]

Also, harrylin, that's for crossing out "mass" in the OP's text. That always bugs me. XD