# What E=MC^2 means?

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#### bdewoody

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Of course it means energy equals mass times the speed of light squared. But I read that one reason we can't go faster than the speed of light is that as an object approaches the speed of light it starts to convert to energy. But the equation says the speed of light squared which is a whole lot bigger number. So are the reasons for the speed limit somewhere else in Einsteins works?

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#### origin

##### Guest
bdewoody":1ioyo5hf said:
Of course it means energy equals mass times the speed of light squared. But I read that one reason we can't go faster than the speed of light is that as an object approaches the speed of light it starts to convert to energy. But the equation says the speed of light squared which is a whole lot bigger number. So are the reasons for the speed limit somewhere else in Einsteins works?
E=mc^2 simply gives the relationship between mass and energy. If a quantiy of mass is converted to energy this equation will tell how much energy will be produced.

The cosmic speed limit, c is a separate issue. The reason that we cannot go faster than light, or even the speed of light is due to several things. The easiest to see, I think, is that as you approach the speed of light you mass increases. The faster you go the more your mass increases and so you need more energy to continue to increase your speed. The increase in mass is exponential so this means that as you approach very close to the speed of light your mass will increase to the point that there is not enough energy in the universe to get your speed increase any more.

Wikapedia has some very accurate information on the speed of light and special relativity.

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#### Jimmyboy

##### Guest
But would you say that if you had all the known universes energy at your disposal would you be able to make a mass travel at or faster than light..??? it would probebly be yes because that is what happend at the big bang (with the inflation theory).

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#### origin

##### Guest
Jimmyboy":1vq0vsj3 said:
But would you say that if you had all the known universes energy at your disposal would you be able to make a mass travel at or faster than light..???
No.

it would probebly be yes because that is what happend at the big bang (with the inflation theory).
There is nothing about special relativity that would preclude the universe from expanding faster than light - but you cannot travel through space faster than light or even at the speed of light.

Right now there are galaxies that are receding from us at faster than light becasue of the expansion of space, however there nothing traveling through space that is going faster than the speed of light and there is no mass that is traveling at the speed of light.

edited for formating

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#### darkmatter4brains

##### Guest
origin":v84gvx74 said:
The cosmic speed limit, c is a separate issue. The reason that we cannot go faster than light, or even the speed of light is due to several things. The easiest to see, I think, is that as you approach the speed of light you mass increases. The faster you go the more your mass increases and so you need more energy to continue to increase your speed. The increase in mass is exponential so this means that as you approach very close to the speed of light your mass will increase to the point that there is not enough energy in the universe to get your speed increase any more.
The mass increase thing is tricky, though. Your rest mass (your mass as viewed in your frame) stays the same - this is an invariant, it never changes and any other frame can figure out what that is from known information. The mass increase is as observed from other frames that are in motion with respect to you, or at rest with respect to you, like the "lab" frame.

So, if in your frame (which is the one you care about, being on the spaceship and all) your mass seemingly stays the same, why does it take more and more energy to reach the speed of light? One problem is that no matter how close you get to the speed of light (say 0.99999c) you will still see a photon move at C with respect to you. You're literally making no progress.

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#### 5hot6un

##### Guest
bdewoody":17edvc0r said:
Of course it means energy equals mass times the speed of light squared. But I read that one reason we can't go faster than the speed of light is that as an object approaches the speed of light it starts to convert to energy. But the equation says the speed of light squared which is a whole lot bigger number. So are the reasons for the speed limit somewhere else in Einsteins works?
http://www.pbs.org/wgbh/nova/einstein/legacy.html

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#### Jimmyboy

##### Guest
origin":353dd46c said:
There is nothing about special relativity that would preclude the universe from expanding faster than light - but you cannot travel through space faster than light or even at the speed of light.
But there are various theories about the big bang and the early univesre formation where the speed of light is surpassed.
As far as i'm aware the inflation theory is where space itself expanded faster than light, and there is another theory by Joao Magueijo where he states that the speed of light may have been much higher to what it is now (in the order of 60 magnitude). I would have thought this would have all originated from the potential energy of the big bang hence universe

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#### origin

##### Guest
Jimmyboy":3ipawv5m said:
origin":3ipawv5m said:
There is nothing about special relativity that would preclude the universe from expanding faster than light - but you cannot travel through space faster than light or even at the speed of light.
But there are various theories about the big bang and the early univesre formation where the speed of light is surpassed.
As far as i'm aware the inflation theory is where space itself expanded faster than light, and there is another theory by Joao Magueijo where he states that the speed of light may have been much higher to what it is now (in the order of 60 magnitude). I would have thought this would have all originated from the potential energy of the big bang hence universe
Again the expansion of the universe during inflation does not violate the special relativity because nothing is traveling through space at superluminal speeds. There is no known speed limit on the expansion of space.
I personally am very doubtful of the VSL theory, but that is beside the point really. Lets assume the speed of light was 60x faster than it is now - nothing would be able to exceed that speed and no mass could go at that speed, becasue it is still the speed of light!

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#### 5hot6un

##### Guest
darkmatter4brains":3qgewcro said:
The mass increase thing is tricky, though. Your rest mass (your mass as viewed in your frame) stays the same - this is an invariant, it never changes and any other frame can figure out what that is from known information. The mass increase is as observed from other frames that are in motion with respect to you, or at rest with respect to you, like the "lab" frame.

So, if in your frame (which is the one you care about, being on the spaceship and all) your mass seemingly stays the same, why does it take more and more energy to reach the speed of light? One problem is that no matter how close you get to the speed of light (say 0.99999c) you will still see a photon move at C with respect to you. You're literally making no progress.
This really screws my mind up. Light travels (of course) at C. But when you STOP light is when it exhibits mass. Doesn't this defy the physical law you reference about mass increasing with speed?

The whole dual nature of light is mind blowing. When moving at C light has no mass at all. When it strikes my retina it becomes a photon. A particle. Mass.

It reminds me of a thought experiment I once read.

2 people are standing, let's say, 2 light minutes apart. Precisely in between them, 1 light minute from each person, is a light source that is turned off. The light is then flashed on just fast enough to emit a single photon. That photon travels towards both people at the same time. A light minute later, 1 person will see the flash and one will not. The person that received the photon altered the reality of the other person by consuming the photon.

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#### Jerromy

##### Guest
5hot6un":1z31gsls said:
It reminds me of a thought experiment I once read.

2 people are standing, let's say, 2 light minutes apart. Precisely in between them, 1 light minute from each person, is a light source that is turned off. The light is then flashed on just fast enough to emit a single photon. That photon travels towards both people at the same time. A light minute later, 1 person will see the flash and one will not. The person that received the photon altered the reality of the other person by consuming the photon.
Sounds alot like the "spooky action" of quantum entanglement but you cannot "see" a single photon even if your eyes were adjusted to total darkness. Perhaps though one pair could travel apart and whomever "observes" one half of the entangled pair first could alter the other half as to be deemed "unobservable". Could be a method of faster than light communication where the send and receive modes are bits modulated by whichever end detects and therefore alters the pairs first... not quite the power of a Q-bit processor but certainly has potential for instantaneous digital transfer.

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#### marcel_leonard

##### Guest

Admitting that you don't know something is the beginning of understanding. The fact of the matter is we don't know if we can travel the speed of light or not........

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#### origin

##### Guest
5hot6un":2tg4y750 said:
This really screws my mind up. Light travels (of course) at C. But when you STOP light is when it exhibits mass. Doesn't this defy the physical law you reference about mass increasing with speed?

The whole dual nature of light is mind blowing. When moving at C light has no mass at all. When it strikes my retina it becomes a photon. A particle. Mass.
Just a point of clarification here - a photon does not have mass. Just because you can define a photon as a particle - for example with the photoelectric effect, that does not mean that the particle has mass. You should look at a photon as a massless particle.

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#### origin

##### Guest
marcel_leonard":28wlgzar said:

Admitting that you don't know something is the beginning of understanding. The fact of the matter is we don't know if we can travel the speed of light or not........
Yes actually we do know that. The physics is very clear. The experimentation confirms that mass cannot go the speed of light. Hey, I wish Star Wars was a documentary and not Sci Fi movie as much as the next guy but lets not pretend physics is not reality.

Can I 100% guarantee that there will never be some wierd unforseeable breakthrough that allows FTL travel? No. Can I 100% guarantee that there will never be a guy that can flap his arms so fast he can fly? No.

I can, however be pretty darn sure neither one of these things are going to happen.

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#### ramparts

##### Guest
5hot6un":1a6jig3d said:
It reminds me of a thought experiment I once read.

2 people are standing, let's say, 2 light minutes apart. Precisely in between them, 1 light minute from each person, is a light source that is turned off. The light is then flashed on just fast enough to emit a single photon. That photon travels towards both people at the same time. A light minute later, 1 person will see the flash and one will not. The person that received the photon altered the reality of the other person by consuming the photon.
A photon is a particle - think of it like a billiard ball (for now). If I throw a billiard ball at my friend five feet in front of me, will it also hit my friend five feet behind me? Of course not. So if your light source actually just emits one photon, that photon will go in some direction (which probably won't be towards either of your observers). So you'd want to modify this "thought experiment" to say that at least two photons get emitted - one going towards each of your observers.

Anyway, that said, I have no idea what you're getting at here. The person that received the photon altered the other guy's reality? What?

Also, "a light minute later" doesn't make any sense. That's like saying "three miles later"

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#### 5hot6un

##### Guest
ramparts":3ae8vzap said:
A photon is a particle - think of it like a billiard ball (for now). If I throw a billiard ball at my friend five feet in front of me, will it also hit my friend five feet behind me? Of course not. So if your light source actually just emits one photon, that photon will go in some direction (which probably won't be towards either of your observers). So you'd want to modify this "thought experiment" to say that at least two photons get emitted - one going towards each of your observers.

Anyway, that said, I have no idea what you're getting at here. The person that received the photon altered the other guy's reality? What?

Also, "a light minute later" doesn't make any sense. That's like saying "three miles later"
Your billiard ball photon would travel towards both friends but only hit one.

The photon moves as a wave. Like an expanding ripple on a pond. More accurately, like an expanding bubble moving in all directions.

The instant your billiard ball hit friend A, it ceased to be a wave and became a particle. The wave approaching friend B simultaneously ceased to exist. Friend B was about to get hit, but his reality was changed and he was not hit.

And the reality change for friend B happened faster than the speed of light. For if the friends were 2 light minutes apart, it would not take 2 minutes for the wave to cease to exist for friend B. It would happen at exactly the time the photon hit friend A.

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#### ramparts

##### Guest
As I've said in another thread, you have this unusual habit of saying weird things as if they're fact Well, I suppose that's not too unusual around here...

Anyway, I'm happy to discuss this with you and clarify some of your misconceptions, so long as you're willing to listen. I'm honestly not sure what your attitude is here: you ask questions, which is great, but then seem pretty adamantly stuck in your preconceptions.

Photons have direction. They don't just propagate out spherically like ripples and then magically decide to localize when they hit something. Think about a laser, which is just a stream of photons all moving in more or less the same direction. The waves aren't propagating in all directions at once, they're all moving in the same direction.

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#### 5hot6un

##### Guest
ramparts":yxu7v2fv said:
As I've said in another thread, you have this unusual habit of saying weird things as if they're fact Well, I suppose that's not too unusual around here...

Anyway, I'm happy to discuss this with you and clarify some of your misconceptions, so long as you're willing to listen. I'm honestly not sure what your attitude is here: you ask questions, which is great, but then seem pretty adamantly stuck in your preconceptions.

Photons have direction. They don't just propagate out spherically like ripples and then magically decide to localize when they hit something. Think about a laser, which is just a stream of photons all moving in more or less the same direction. The waves aren't propagating in all directions at once, they're all moving in the same direction.
One thing is for sure. My posts rub you the wrong way.

I'm always willing to listen. I may misunderstand what I hear :lol: , but I will listen.

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#### a_lost_packet_

##### Guest
bdewoody":296p2n9q said:
Of course it means energy equals mass times the speed of light squared. But I read that one reason we can't go faster than the speed of light is that as an object approaches the speed of light it starts to convert to energy. But the equation says the speed of light squared which is a whole lot bigger number. So are the reasons for the speed limit somewhere else in Einsteins works?
The best way I've seen it explained goes like this: (An attempt I made on another forum. I'm just a fan of physics, not someone well versed. So, this is just an approximation to demonstrate the ideas surround the reason we can't accelerate a mass-bearing particle (or object) to the speed of light. I'm just quoting this from another post I made so the conversational ref's are to another post, not yours in particular. But, since you're actually talking about accelerating to the speed of light.. well, here's my standard answer.)

"...
You've heard of E=mc2, right? That's Einsteins famous formula. (The amount of energy represented by an object is its mass times the speed of light squared.) Well, we're going to use some ideas that come out of that to explain why something with mass can not travel faster than the speed of light. This means that, in our reality in real space and not in any science fiction book or residing within someone's playful imagination, it is not possible to for anything with mass to travel faster than the speed of light no matter how big of an engine you could ever possibly strap onto it.

An object with any mass has traveling at a velocity (speed) has "momentum." That idea is represented as mv or mass times velocity.

An object's inertia is proportional to its mass. Inertia keeps the object moving in the same direction until some other force is applied which then causes acceleration. That force "adds energy" to the object which increases it's speed, right?

You push things to make them go, the more you push, the faster they go, the more energy they have.

All of this energy is represented as the object's "kinetic energy." That is it's momentum times its velocity divided by two. Which is.. (gotta go to images..)

Now, from that formula, you can also figure out how much energy you would need to accelerate an object at rest with mass (m) into motion of velocity (v). So, if you know those numbers you can plug them in and get a correct answer just like with any other equation.

BUT, that only works with Newton's version of relativity. That doesn't work with Einstein's relativity which is the more exact notion. Newton's works just fine for doing everything from launching rockets into space to throwing a baseball from here to the other side of the Milky Way galaxy... it's just not entirely correct.

There is something called the Lorentz transformation. That appropriately describes the contraction of space and dilation of time in the direction of relative motion under good old Einstein's rules which seem to be exactly appropriate for determining this kind of thing.

In order to translate a Newtonian version of the amount of energy necessary to accelerate an object to the speed of light (look at the first formula) we must include Lorentz's equations and put Einstein's special relativity stamp on it to make it official! Here is the equation:

Notice the similarities with the first equation? See the extra bit? Do you recognize Einstein's famous "E=mc2?" Yup, told ya we would use it! OK, this is where it becomes pretty obvious you can't accelerate anything with mass to the speed of light according to Einstein's relativity which, so far, appears to be entirely correct.

"c" is the speed of light in a vacuum.
"v" is the object's velocity
"m" is the object's mass
"E" is the energy represented

What happens in the equation as the object's velocity approaches the speed of light? See the " v2/c2 " portion in the bottom. Well, it starts to approach 1. What happens when it reaches 1?

When it reaches 1, that would be the object traveling at the speed of light. What happens in the denominator then? 1-1=0, that's what happens!!!!! What does that mean? Well, that means that we'd be dividing by zero, doesn't it? See how the denominator would be zero? Dividing by zeros is bad, mmkay. Very bad.

What happens in that equation if all that gobbity-**** in the denominator is "0" (Zero)? Easy - We get "Infinity" for the answer to E. What does that mean? It means it would take an infinite amount of energy to accelerate an object that has mass to the speed of light.

How much energy is that? Well.. an infinite amount. How do you get an infinite amount of energy? What store sells that in our Universe? What company manufactures infinite energy engines? The answer is, you simply don't obtain it no matter what you do.

No matter what you strap onto a brick, no matter how powerful the engine, no matter what technology you use to push that brick, eventually there will come a point in time where no amount of energy available will be able to accelerate that brick to the speed of light. It's... simply... not... possible.

Of course, things are subject to change. But, it doesn't appear this is one of those things.

(Note: I'm just a fan of physics, not a student of it. So, there are some problems with the equations that, while in no way material to the discussion, a physicist/advanced student/etc may have issue with. But, they're just fine for a general explanation.)..."

The reason I posted this is that the above forumla explanation crystalized the concept for me, personally, when I first came across it. So, I keep duplicating it and bringing it up in conversations like this one so, perhaps, it will help someone else.

(Note: If anyone has any corrections here, their very welcome to note them so I can be sure to, at the very least, give an accurate explanation that is easily understood in the future.)

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#### 5hot6un

##### Guest
a_lost_packet_":18kge17r said:
The best way I've seen it explained goes like this: (An attempt I made on another forum. I'm just a fan of physics, not someone well versed. So, this is just an approximation to demonstrate the ideas surround the reason we can't accelerate a mass-bearing particle (or object) to the speed of light. I'm just quoting this from another post I made so the conversational ref's are to another post, not yours in particular. But, since you're actually talking about accelerating to the speed of light.. well, here's my standard answer.)
Excellent! Thank you for posting this.

What happens when this is applied to the whole universe? I heard that the expansion of the universe will continue until it reaches the speed of light. What will the divide by zero error look like on a universal scale? Is that the big rip?

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#### 5hot6un

##### Guest
More E=MC^2 questions

Question 1:
To give E=MC^2 a perspective that more common people can relate to...
If you could convert 100% of a single H atom to E. How much E would that be, and can it be expressed in watts?

Question 2:
If M warps spacetime. What does E do to to spacetime?

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#### MeteorWayne

##### Guest
Re: More E=MC^2 questions

Shot6un, these are pretty closely related to the other thread, so I'm going to move this question there rather than have a whole bunch of new (there are dozens of old) E=MC2 topics. Hope you understand.

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#### origin

##### Guest
Re: More E=MC^2 questions

5hot6un":iibgexa7 said:
Question 1:
To give E=MC^2 a perspective that more common people can relate to...
If you could convert 100% of a single H atom to E. How much E would that be, and can it be expressed in watts?
It is just a multiplication problem. Get the mass of a proton from wiki and muliply the mass in kg by the speed of light in M/s times the speed of light in m/s. This will give you the energy in joules

There is not a direct convertion to watts because a watt is not energy. The energy would be watt-sec or watt-hr.

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#### origin

##### Guest
5hot6un":17svmloa said:
a_lost_packet_":17svmloa said:
The best way I've seen it explained goes like this: (An attempt I made on another forum. I'm just a fan of physics, not someone well versed. So, this is just an approximation to demonstrate the ideas surround the reason we can't accelerate a mass-bearing particle (or object) to the speed of light. I'm just quoting this from another post I made so the conversational ref's are to another post, not yours in particular. But, since you're actually talking about accelerating to the speed of light.. well, here's my standard answer.)
Excellent! Thank you for posting this.

What happens when this is applied to the whole universe? I heard that the expansion of the universe will continue until it reaches the speed of light. What will the divide by zero error look like on a universal scale? Is that the big rip?
The recession speed of the most distance galaxies is already exceeding the speed of light. There is no rip, there is no problem, we just won't see them anymore. The expansion of the universe is not bound by the speed of light, that is only the speed limit to what is IN the universe.

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#### drwayne

##### Guest
Re: More E=MC^2 questions

One hydrogen atom gives you, approx

1.66x10^-23 * (3 x 10^8)^2

~ 1.5 x 10-10 Joules

per H. Now, you define the rate of H conversions per second, you can get to watts

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#### jgrtmp

##### Guest
The Theory is called Relativity- or how it relates to your reference frame. Can you see faster than the speed of light? Not... Ok, so lets say my reference frame is now accellerated to 0.6 lightspeed, but your a little more high tech than me, so your coming at me with an approach speed of 0.7 ls. The combined closure is 0.6 + 0.7 = 1.3 ls. Neither have broken the speed within their refernce frame, but when referenced to each others frame you won't see the other until they are at about 45-90 Degs from your direction of transit(due to Lorenze contraction). You have Warped each other. Relativity is what it says. It is not a limit....Also the full equation is E = mc^2+c(for Astronomers) or E = mc^2 +K(for physicists where K = kenetic energy of the measured mass)...

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