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/sci/ - Science & Math


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2566166 No.2566166 [Reply] [Original]

AS-level physics student here, probably easy question for you guys to answer, but here goes.

So, I've heard that E=mc^2 is not totally true, and that the full equation is E^2=m^2c^4 + p^2c^2, and that E=mc^2 is found by assuming p=0 and taking the root of each side of the equation.

But yeah, that left me thinking... are there not actually four possible equations that can be simplified to two?

E^2=m^c^4
ergo E=mc^2
or E=-mc^2
or -E=mc^2
or -E=-mc^2

(-E=-mc^2) = (E=mc^2)
and (E=-mc^2) = (-E=mc^2)

So yeah... does E not equal both mc^2 AND -mc^2. So we get negative energy. What's negative energy? Explanations please!

>> No.2566168

pic unrelated

>> No.2566200

You often encounter many solutions in a physical problem, of which only a few make "physical sense"
This is nothing surprising and new, the solutions which make no sense are simply discarded

>> No.2566214

I see... but what is the logical reason for discarding them? Simply because they don't fit in with our own perceptions of reality can't be a good enough reason, can it?

>> No.2566222

energy is not a physical thing, it's a sort of concept, right, so it doesn't really matter if it's negative or not, it just depends on your reference frame

>> No.2566235

>>2566222

Are you saying that energy is just the same as negative energy? So (E=mc^2) = (E=-mc^2)? Why is that? Energy is a scalar, not a vector, so you can't simply say that negative energy is just energy in a different direction or something...

>> No.2566237

>>2566214
sure they can

take for example the equation for position with constant acceleration in one dimension

x = x0 + v0t + 1/2at^2

let's say we are watching an apple fall from the sky

at a certain point, it's gonna hit the ground, and any values that we get for x as we put in higher and higher values of t past the point at which it hit the ground are going to be erroneous because they don't make any physical sense

>> No.2566245

>>2566235
Saying there is not such thing. Just like you don't have negative distance or negative speed

>> No.2566247

>>2566235
well okay, but how exactly would you get negative energy in the first place, even if we were to say E = -mc^2

where does the negative sign come from, physically? I think this is the point the guy was trying to make with the physical sense idea. It doesn't make physical sense for there to be a negative sign there, so we ignore it

>> No.2566256

>>2566235

he is saying you need to discard the negative energy the same way you would discard a false Mathematical solution that doesn't fit reality in basic physics.

that said, i do think there is such a thing as negative energy, or at least that gravity cancels energy and we basically live in a zero energy universe.

this however (if im not mistaken) is just a theory and i doubt it has anything to do with what you did.

>> No.2566264
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2566264

>>2566235
Negative energy doesn't mean anything. It's like saying -5km, it's just still the same length as 5km.

If you really want your brain to explode start thinking about imaginary solutions to that equation.

>> No.2566265

>>2566247

This is probably my answer. The mathematics only produces negative energy if we have negative mass in the first place, which (as far as I know?) doesn't exist.

>> No.2566284

Yeah but there is no such thing as negative mass, negative velocity or even negative energy.
Mathematically speaking, there would be 4 equations but physics eliminates the ones physically impossible.

>> No.2566295

>>2566284
> no such thing as negative velocity.
go learn some physics brah

>> No.2566298

>>2566166
what is p and why do we assume it is zero?

>> No.2566313

>>2566298
p is momentum and it can be assumed to be zero if the object in question is at rest

>> No.2566352

>there is no such thing as negative mass
says who?

I'm still not convinced that it's logical to discard mathematical ideas just because they don't make sense to us...

>> No.2566357

>>2566166
This line of thinking has been historically seen as motivation for 'negative energy' states that were seen to represent antimatter.
As in:
http://en.wikipedia.org/wiki/Dirac_sea

>> No.2566362

>>2566352
has there ever been negative mass? what would negative mass mean? It doesn't mean anything in the way that we have defined mass. We didn't find a big textbook that told us what mass was, we have defined it. And we have defined it in such a way that to have negative mass does not make physical sense.

>> No.2566380

>>2566362

>what would negative mass mean?

a) instead of resisting force, negative mass will increase the force applied on it.
or at least that's the reverse of the definition of mass.
b) that we need to get the mass relay up and get ready for the reapers.

>> No.2566390

>>2566380
yeah, you see, that doesn't make any sense

if you had some object of mass -m with force F acting on it then the acceleration would be -a, it would accelerate in the opposite direction of the force.

For example, I have a crate with negative mass, I push on it with force F and it accelerates... into me. You see how this just doesn't work?

>> No.2566400

>>2566390
If it weren't for that, you'd also have the problem that an object which increases the forces exerted on it would accelerate indefinitely, violating the conservation of energy.
Then again, you'd also have negative kinetic energy...

>> No.2566404

>>2566357

now that is interesting... very interesting. So Dirac used the idea of negative energy to discover antimatter? I suppose that doesn't really prove the existence of negative energy, but it's an interesting idea...

>>2566362

So are you saying that we cannot have negative mass because mass is defined as being positive?

>> No.2566405

How can you have a negative magnitude?

>> No.2566410

>>2566390

You're right in that it seems ridiculous and doesn't appear to fit in with reality... But I'm not sure I agree that that is a valid reason to dismiss the idea.

>> No.2566412

>>2566400
>>2566390

i didn't say it's real.
i just said that's what it would be if it was real...
that a very silly thing to say now that i think about it.

>> No.2566415

>>2566405
What's mod (sqrt -1) equal to ?

>> No.2566422

>>2566415
hurr durr, -1.

>> No.2566427

>>2566404
yes. It's a scalar value, scalar values are always positive

>> No.2566435

>>2566415
1

>> No.2566441

>>2566410
why not?

"Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: For it can contain nothing but sophistry and illusion. "

>> No.2566445

>E=-mc^2
>or -E=mc^2

They're the same equation.

>> No.2566449

>>2566427 It's a scalar value, scalar values are always positive
Oh shut up.

>> No.2566460

>>2566445

You misquoted me.

>(E=-mc^2) = (-E=mc^2)
>does E not equal both mc^2 AND -mc^2?

>>2566441

We don't know that it doesn't contain "experimental reasoning concerning matter of fact and existence," it just appears not to.