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/sci/ - Science & Math


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10675802 No.10675802 [Reply] [Original]

F = ma = E = mc^2.
This holds true in any frame of reference.
Discuss.

>> No.10675824

>>10675802
That's just a=c^2 with extra steps.

>> No.10675843

>>10675824
How would you simplfy 1 = 1 = 1 = 1?
You would simply write 1 = 1.
Einstein's equivalence principle is true in any frame of reference.
Even your own mind is a frame of reference independent of the set of all human minds. 0 = x approaching infinity.
But I only know that I know nothing.

>> No.10675850

>>10675802
F certainly does not equal E. Retake high school physics before coming here

>> No.10675864

>>10675850
Prove the contrary without relying on your frame of reference (e.g. everything you learned in high school physics).
I've made falsifiable statements in this thread.
Don't rely on the "burden of proof" meme.

>> No.10675895

>>10675864
Well for one, E = mc^2 is only true for an object at rest, while your equation says a = c^2, which would mean it's not at rest. So it contradicts itself.

>> No.10675921

>>10675864
F=-grad(E)

>> No.10675923

>>10675864
Also, F doesn't equal ma, is equals dp/dt, and >>10675895
Seriously, Gtfo, you're not worth my time

>> No.10675926

>>10675864
[math]F=\frac{dp}{dt}=\gamma ma_{\perp} + \gamma ^3 ma_{\parallel}[/math]
[math]E=\gamma mc^2 = \sqrt{(mc^2)^2 + (pc)^2 }[/math]
[math]\Delta KE = \int F\cdot dx [/math]

>> No.10675972

>>10675864
[eqn] \left[F\right] \;=\; \mathrm M \,\cdot\, \mathrm L \,\cdot\, \mathrm T^{-2} \;\neq\; \mathrm M \,\cdot\, \mathrm L^2 \,\cdot\, \mathrm T^{-2} \;=\; \left[E\right] [/eqn]
Where's my "I was just pretending to be stupid teeheehee"?

>> No.10676075

>>10675802
"a" doesn't have units of "c^2"
ma != mc^2

>> No.10676201

>>10675895
Name an object that is truly "at rest."
"At rest" is an arbitrary limit, inherently implying two objects are in the same frame of reference relative to each other.
If both newtonian physics and the theory or relativity are true (the theory of relativity doesn't disprove the theory of gravity, just, well, generalizes it to include and predict phenomenon related to gravity's affect in curving spacetime)
Obviously, it's more complicated than that (see quantum physics).
Also, you're correct that E=mc^2 is the special case of "mass at rest", which is why F = ma = E = mc^2 is a true statement.
The only thing I'm essentially adding is that "at rest" is an inherently flawed concept.

>> No.10676204

>>10676075
In explicit cases, you're correct.

>> No.10676217

>>10675972
Prove that L1 does not equal L2 unless one first assumes a frame of reference.
If you assume something can be at rest, F = ma follows.
If you assume "at rest" is a consequence of strong gravity, E = mc^2 follows.
It's as if you people haven't even read Newton or Einstein's work, or at the very least didn't understand it.

>> No.10676218

>>10676201
yeah well none of this has any meaning without frame of reference so its all nonsense afaik.

>> No.10676248

>>10676217
>It's as if you people haven't even read Newton or Einstein's work
>dude prove area isnt the same as length
lol
Btw energy is explicitly a scalar quantity and forces are explicitly vector quantities. There's another proof.

>> No.10676249

>>10676218
Research Niels Bohr's correspondence principal.
It's basically states that classical mechanics can be replicated by taking relativity into account, and vice versa.
I'm not even really saying anything new so I don't see what all the fuss is about.

>> No.10676274

>>10676248
How is a scalar (a quantity without direction) unequal to a vector (a quantity with direction) if both "described quantities" are at rest (no discernable movement) in reference to each other?
Obviously, the equation in OP is only true when "at rest" is assumed. That is what Einstein essentially proved was that "at rest" was a fallacious concept and that literally everything in the universe is relative, even things assumed to be independent (such as time, space, and the gravity) were found to actually be intricately related.
I feel as if I'm restating the same thing over and over again to simpletons.
It's simple logic, not rocket science.

>> No.10676308

>>10676248
Prove area isn't the same as length in 1 dimension or zero dimensional space.
Pro tip: you can't.
The "frame of reference" here is your existence in three- dimensional space.
If we even assume two dimensions, our equivalence falls apart.
Because equivalence itself is only necessitated when a "frame of reference" is first assumed.

>> No.10676780

Even the mediums we've had or will have this entire conversation within (English, the current lingua franca, and mathematics, the most rigorous language developed) are fundamentally completely arbitrary ones.
They're both useful though, in this sense, because a large number of the set of living people understand English at some level, and enough people understand mathematics on /sci/ to succinctly argue the contrary.
Anyway, good luck proving three of the greatest human minds in physics (Newton, Einstein, and Bohr) wrong.

>> No.10676991

>>10676274
Dimensional analysis still applies in relativity. Force and energy do not have the same units, so cannot be equated like that. The equation in the OP is false in all reference frames.
However, these equations
>>10675926
where F and a are vector quantities, are true in all reference frames.

>> No.10677321

>>10676991
So, is it impossible for force and energy have the same units?
Moreover, even the concept of units is relative.

>> No.10677424

>>10676991
If we assume force and acceleration are both vector quantities, it's trivial to solve the equation in OP as a true equality.
What proof is there that the equation in OP isn't true in all reference frames as well?
Just that Force and Energy don't always have the same units?
You would be arguing that an incomplete set defines a complete set, which is inherently fallacious.

>> No.10677543

>>10677321
>is it impossible for force and energy have the same units
You ask this like we aren't already sure that force and energy *definitively* have different units
>the concept of units is relative
they aren't
>>10677424
this entire post is nonsense

>> No.10677547

>>10676308
>The "frame of reference" here is your existence in three- dimensional space
>t. doesn't actually know what is meant by "frame of reference" in physics

>> No.10677631

Maybe I should try an example.
Assume, "it's all relative" is a true statement.
It's = a singular something's possesive noun (no limit, meaning there are n terms approaching infinity equivalent to it)
All = infinity (no limit again)
Relative = relative (change is the only constant since relative objects/concepts change relative to other relative objects/concepts).
Therefore, in English, and using mathematical ideals, I've made an argument that 0 = infinity, even simpler, that every limitless concept can be equated to any other limitless concept.
Obviously it's not a "rigorous proof."
I'd never make the mistake of coming to 4chan to do actual work.
This thread is just a thought experiment, essentially.

>> No.10677634

>>10677543
Definitively?

>> No.10677638

>>10677547
Define it for anon then, if you're so great.

>> No.10677678

>>10677634
Yep. Read a fucking book.

>> No.10677684

>>10677638
"In physics, a frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements"

>> No.10677712

>>10677684
Would you agree that frame of reference has no limit, since it's been defined by four limitless terms (coordinate system, standard measurements, and reference points, and unique).

>> No.10677721

>>10677678
No u.

>> No.10677722

>>10677712
No, I dont agree with nonsensical statements.

>> No.10677739

Mods pls ban schizo shit like this on sight

>> No.10677818

>>10677739
Just become a mod and do it yourself.
Relying on the tutelage of others is pathetic.

>> No.10677870

>>10677722
Is it nonsensical because of your own unique frame of reference (a subset of human intelligence, a rather trivial subset of all humans' intelligence which also contains the subset of contemporary scientific consensus) or is it "objectively nonsensical?"
We could argue ad infinitum about relativity, because the frame of reference in this instance is the English language and simple, generally accepted mathematical ideals, two relative concepts per se.
I understand, it's difficult to relate a set that tends to infinity when related to t (only "tending" given the assumption that humananity survives some non-zero quantity and continue to expand their knowledge of reality), because an individual's odds of understanding approaches 0 when related to spacetime.
One can only meaningfully relate things by relating them to a constant, therefore the only true constant is relativity itself.

>> No.10677879

>>10677870
>t. never opened a physics book or taken a physics course in his life

>> No.10678005

>>10677879
No u.

>> No.10678027 [DELETED] 

>>10675802
>not considering dimensions
You wanna know how I know you've never studied physics above high school level?

>> No.10678029

>>10675802 (OP)
>ignoring units
You wanna know how I know you've never studied physics above high school level?

>> No.10678085

Communication aka interaction, that is one common aspect of everything! It allows organized formations on all scales and defines energy aka matter! Intelligence!

That is my conclusion!

>> No.10679051

>>10678029
>misunderstanding what a unit even is.
You wanna know how I know you rely too much on what you learned as child?

>> No.10679056

>>10678085
Did you know that there's a mathematical theory for communication?
It's not even that hard of a read so I'm sure you can do it, champ.