Is E=MC² the optimal description of nature?

[Frogton]

Einstein's 1905 derivation of E=MC² involved a thought-experiment using photons to derive a Lorentz factor equation and (ignoring higher powers in the Taylor expansion) comparing that equation to the classical Kinetic Energy Equation.

This is actually the only valid method of deriving E=MC², other methods such as the one involving a photon in a box, are merely examples of 'petitio principii', something Herbert Ives wrongly criticised Einstein's 1905 derivation for. Indeed Ives' own attempt at a derivation was an example of 'petitio principii', as well as containing a mathematical error.

The problem with a derivation involving the classical Kinetic Energy Equation, is that KE=½MV² is not just an incomplete description of nature, but an equation that is only accurate at low-speed.

Since it is the season of goodwill to all men, I wondered whether I might be able to speculate that the Frogton Universal Force Law is actually a better description of nature than E=MC²?

The Frogton Universal Force Law leads to the integral equation F=(M+FʃV.dT)V/T, with V integrated between T=0 and T=T. I know what V is in terms of the variable T and the constants F and M, but does anybody know how to go about solving such integral equations other than by guessing?

[swansont]

41 minutes ago, Frogton said:

Einstein's 1905 derivation of E=MC² involved a thought-experiment using photons to derive a Lorentz factor equation and (ignoring higher powers in the Taylor expansion) comparing that equation to the classical Kinetic Energy Equation.

This is actually the only valid method of deriving E=MC², other methods such as the one involving a photon in a box, are merely examples of 'petitio principii', something Herbert Ives wrongly criticised Einstein's 1905 derivation for. Indeed Ives' own attempt at a derivation was an example of 'petitio principii', as well as containing a mathematical error.

The problem with a derivation involving the classical Kinetic Energy Equation, is that KE=½MV² is not just an incomplete description of nature, but an equation that is only accurate at low-speed.

So use the exact equation. The derivation doesn’t actually rely on the approximation, IIRC

 

Quote

Since it is the season of goodwill to all men, I wondered whether I might be able to speculate that the Frogton Universal Force Law is actually a better description of nature than E=MC²?

If you comply with the guidelines (provide evidence, etc.), go ahead.

Quote

The Frogton Universal Force Law leads to the integral equation F=(M+FʃV.dT)V/T, with V integrated between T=0 and T=T. I know what V is in terms of the variable T and the constants F and M, but does anybody know how to go about solving such integral equations other than by guessing?

What are these variables? Mass, force and velocity? What if there’s no force, or the object is at rest? What does this have to do with mass-energy equivalence?

 

 

[joigus]

43 minutes ago, Frogton said:

The Frogton Universal Force Law leads to the integral equation F=(M+FʃV.dT)V/T, with V integrated between T=0 and T=T. I know what V is in terms of the variable T and the constants F and M, but does anybody know how to go about solving such integral equations other than by guessing?

Swansont's points well taken. Also:

That's not an integral equation. There's extensive work in mathematics about how to solve integral equations.

In what variable? Do you mean,

\[ F\left(t\right)=\left[M+F\left(t\right)\int_{0}^{t}v\left(t'\right)dt'\right]\frac{v\left(t\right)}{t} \]

as an equation for \( v \)? But \( F \) depends on position.

What happens at \( t=0 \)?

[Frogton]

20 hours ago, swansont said:

So use the exact equation. The derivation doesn’t actually rely on the approximation, IIRC

If you believe that Einstein's derivation was wrong, please can you point out where he erred, and how you would correct his paper.

20 hours ago, swansont said:

What are these variables? Mass, force and velocity? What if there’s no force, or the object is at rest? What does this have to do with mass-energy equivalence?

Sorry, I should have rearranged the equation to FT=(M+FʃV.dT)V, that way it would have been clear that if F=0, then however long the force is applied for, V will be 0; and also that when T=0, V=0.

20 hours ago, joigus said:

That's not an integral equation. There's extensive work in mathematics about how to solve integral equations.

In what variable? Do you mean,

 

F(t)=[M+F(t)∫t0v(t′)dt′]v(t)t

My derivation was based on a constant force, F is not a function of T, so some of the extra Ts you added are not needed.

The solution I am looking for is V expressed in terms of T, F, and M (the constant rest-mass). An explanation of the customary notation would be interesting, but mostly I was interested in seeing the equation solved.

[joigus]

1 hour ago, Frogton said:

My derivation was based on a constant force, F is not a function of T,

Then it definitely isn't "the optimal description of Nature."

The equation is also dimensionally inconsistent.

1 hour ago, Frogton said:

and also that when T=0, V=0.

Then you have an indetermination of the kind \( 0/0 \).

It still has nothing to do with \( E = mc^2 \).

Solving it is not difficult, but it makes no physical sense.

Edited December 26, 2020 by joigus

[swansont]

1 hour ago, Frogton said:

If you believe that Einstein's derivation was wrong, please can you point out where he erred, and how you would correct his paper.

I don’t see how you concluded that I had a problem. I was commenting on your objection that he used an approximation.

 

Quote

FT=(M+FʃV.dT)V

How did you derive this equation? How do you reconcile the units of the integrated part of the equation with the other terms?

[joigus]

13 hours ago, Frogton said:

My derivation was based [...]

Wait a minute. That's right. What derivation?

Edited December 27, 2020 by joigus

[joigus]

More comments:

In special relativity it doesn't make sense to talk about a constant force. It's a constant 4-force what plays the role of a "constant push."

In those conditions, velocity doesn't grow indefinitely; it tends to a limit, the speed of light in vacuum. It's called hyperbolic motion.

Also, you should clarify whether you mean coordinate time or proper time.

 

[Frogton]

On 12/26/2020 at 9:09 PM, joigus said:

Then it definitely isn't "the optimal description of Nature."  The equation is also dimensionally inconsistent.  Then you have an indetermination of the kind 0/0  It still has nothing to do with E=mc2 .  Solving it is not difficult, but it makes no physical sense.

 

8 hours ago, joigus said:

More comments: In special relativity it doesn't make sense to talk about a constant force. It's a constant 4-force what plays the role of a "constant push."  In those conditions, velocity doesn't grow indefinitely; it tends to a limit, the speed of light in vacuum. It's called hyperbolic motion.  Also, you should clarify whether you mean coordinate time or proper time.

 

11 hours ago, joigus said:

Wait a minute. That's right. What derivation?

So you've made desperate attempts to disprove my derivation without knowing what it involved. Is your philosophy “all new truths start as heresies”, so any heresy against special relativity needs to be suppressed to stop it being acknowledged as a truth?

 

On 12/26/2020 at 9:09 PM, joigus said:

Then you have an indetermination of the kind 0/0 .

So you are unable write a equation for dropping a ball from stationary because at T=0, V=0?

On 12/26/2020 at 10:07 PM, swansont said:

I don’t see how you concluded that I had a problem. I was commenting on your objection that he used an approximation.

You are confusing me with Max Planck. What I said was that Einstein's derivation was “the only valid method of deriving E=MC²”, and that it is E=MC² itself that is inexact.

I cannot work out if you think Einstein's 1905 derivation is 'both right and wrong' or 'neither right nor wrong'. Is it possible for you to open the box and reveal all?

[joigus]

14 minutes ago, Frogton said:

So you are unable write a equation for dropping a ball from stationary because at T=0, V=0?

Oh, boy. You are so mathematically illiterate this is gonna take some time...

Edit: Ok. I'm sorry. I take it back. So what's your problem. You have a magic trick to divide 0 by 0? There is a "magic" trick, but you haven't set up the problem properly. Seems like you're clueless. Are you clueless about these things?

When t goes to zero (in the denominator), the numerator goes to zero for at least three reasons: the integration range shrinks to zero, the integrand goes to v(0), which is zero, the v factor outside the integral is zero. So it's zero divided by zero.

Your eq. has nothing to do with dropping a ball. It's a different eq. of motion.

14 minutes ago, Frogton said:

So you've made desperate attempts to disprove my derivation without knowing what it involved.

I can't disprove your derivation for the very simple reason that you haven't shown any.

Edit: You don't know what hyperbolic motion is, do you? Otherwise you couldn't possibly be asking such dumb questions.

Why don't you just ask?

Edited December 27, 2020 by joigus

[studiot]

21 minutes ago, Frogton said:

What I said was that Einstein's derivation was “the only valid method of deriving E=MC²”, and that it is E=MC² itself that is inexact.

Yes you may have done, but did you give a proper reference ?

Are you referring to the 1905 paper

Ist Die Tragheit eines Korpers von seinem Energehalt abhangig ?   :  Annalen der Physik 17, 1905

(Translated means   -  Does the inertia of a body depend on its energy content ?)

Which is a short paper that ends with the conclusion

Quote

Einstein

If a body gives off energy L in the form of radiation, its mass diminishes by L/c²

 

Or are you referring to section 10 of the 1905 paper on Special Relativity  - The electrodynamics paper  ?

Which section is entitled (translated) Dynamics of the slowly accelerated electron.

Edited December 27, 2020 by studiot

[joigus]

29 minutes ago, Frogton said:

You are confusing me with Max Planck.

The similarities are uncanny. But I don't think he is.

[swansont]

1 hour ago, Frogton said:

So you've made desperate attempts to disprove my derivation without knowing what it involved. Is your philosophy “all new truths start as heresies”, so any heresy against special relativity needs to be suppressed to stop it being acknowledged as a truth?

No, he noted that you have not provided a derivation. 

 

Quote

You are confusing me with Max Planck.

I am very much not.

 

Quote

What I said was that Einstein's derivation was “the only valid method of deriving E=MC²”, and that it is E=MC² itself that is inexact.

I cannot work out if you think Einstein's 1905 derivation is 'both right and wrong' or 'neither right nor wrong'. Is it possible for you to open the box and reveal all?

You seem to be reading a lot into what I said, which was that you could use an exact expression rather than merely retaining the first term for KE. You identified this as a problem. Kindly stop projecting this on me. This is your thread.

Perhaps you could address the issues I raised: providing the derivation of your equation, and explaining how the units are consistent.

[Markus Hanke]

11 hours ago, Frogton said:

Is your philosophy “all new truths start as heresies”, so any heresy against special relativity needs to be suppressed to stop it being acknowledged as a truth?

I think his is a philosophy of acknowledging the overwhelming experimental and observational evidence for the validity of SR within its domain of applicability. Anyone who comes along and claims that SR isn't a valid model will thus have some serious explaining to do. Because of this sheer amount of observational evidence, claims to the contrary will generally be dismissed pretty much by default, on the simple principle that extraordinary claims require extraordinary evidence - it's thus your responsibility to show yourself right, not ours to show you wrong. And if you don't mind me saying so, for the case of SR your evidence will need to be exceptionally extraordinary indeed, given how well-tested and verified a model this is. This means you need to show that your own model can replicate all the results of SR, can function as a local approximation to GR, and can make verifiable predictions that standard theory can't.

I dare say you will find this hard to do.

[joigus]

10 hours ago, Frogton said:

Is your philosophy “all new truths start as heresies”, so any heresy against special relativity needs to be suppressed to stop it being acknowledged as a truth?

You completely missed Huxley's meaning. Now why doesn't that surprise me.

When a new theory is born implying a shift in the way we think about certain problems, most people are still so comfortable with the previous one that they contemplate the new ideas as "heresy." When the new theory finally becomes well established, people grow used to it, to the point that it becomes a common tool. Most of the scientific community accommodates to a new comfort zone. To the point that what previously was a heresy becomes now a "superstition."

The words "heresy" and "superstition" are not to be taken literally, of course. That's called a simile (if, e.g., you use the word "like" or "as") or a metaphor (if you identify the analogous terms.)

[Frogton]

On 12/27/2020 at 10:40 PM, studiot said:

Are you referring to the 1905 paper

Ist Die Tragheit eines Korpers von seinem Energehalt abhangig ?   :  Annalen der Physik 17, 1905

(Translated means   -  Does the inertia of a body depend on its energy content ?)

Yes. That is what I want to discuss. Unfortunately my thread has been hijacked by Jogius with a torrent of meaningless nonsense, irrelevant jargon and personal abuse.

On 12/27/2020 at 11:30 PM, swansont said:

Perhaps you could address the issues I raised: providing the derivation of your equation, and explaining how the units are consistent.

My equation is dimensionally inconsistent but agrees with experiment. It was introduced merely as a mathematical challenge which nobody has yet accepted. Jogius has racked all 3 corners of his brain in a desperate attempt to prove me wrong, and has just come up with utter nonsense, yet you immediately found the one valid criticism. I was tempted to compliment you by saying that you are clearly many orders of magnitude cleverer than Jogius, but then I realised that is not much of a compliment.

On 12/27/2020 at 11:30 PM, swansont said:

You seem to be reading a lot into what I said,

I am just trying to get you to express a clear opinion about E=MC², so I can give you an argument. It seems that we are both trying to play a game of cat and mouse, but making no progress because we both insist on being the cat.

14 hours ago, Markus Hanke said:

I think his is a philosophy

I don't think Jogius has any real interest in learning or teaching physics, he just needs to convince people that he is amazingly clever. But using Feynman's analogy, he is doing this by reciting the names of various birds in different languages, when in reality he cannot tell a snow-goose from a mongoose. In the words of the greatest philosopher, he is sick of self-love. I am hoping that if I ignore him, he will go away, but it seems he is so convinced I am a heretic that he will not rest till he sees me burnt at the stake.

14 hours ago, Markus Hanke said:

 Anyone who comes along and claims that SR isn't a valid model will thus have some serious explaining to do. Because of this sheer amount of observational evidence .................I dare say you will find this hard to do.

Actually I am the biggest fan of the principle of relativity and the Lorentz transformations, but E=MC² is not one of the Lorentz transformations. What I object to is those narrow-minded bigots who insist that if people do not use the politically correct special relativity jargon, then that means they are scientifically wrong.

[joigus]

6 minutes ago, Frogton said:

Yes. That is what I want to discuss. Unfortunately my thread has been hijacked by Jogius [...]

Boy, that was hilarious!!! +1

[swansont]

2 minutes ago, Frogton said:

 My equation is dimensionally inconsistent but agrees with experiment.

I don’t see how it can, since it’s flawed. Units matter.

2 minutes ago, Frogton said:

I am just trying to get you to express a clear opinion about E=MC², so I can give you an argument. It seems that we are both trying to play a game of cat and mouse, but making no progress because we both insist on being the cat.

I think you have a fundamental misunderstanding of what’s going on here. You have proposed some alternative physics, and need to defend it by providing evidence. You say your equation agrees with experiment but you waste effort by complaining about abuse and making insults.

Where is this evidence?

 

2 minutes ago, Frogton said:

Actually I am the biggest fan of the principle of relativity and the Lorentz transformations, but E=MC² is not one of the Lorentz transformations. What I object to is those narrow-minded bigots who insist that if people do not use the politically correct special relativity jargon, then that means they are scientifically wrong.

Equations with inconsistent units is enough to be scientifically wrong. The rest of this is distraction from discussion. 

[Markus Hanke]

9 hours ago, Frogton said:

Actually I am the biggest fan of the principle of relativity and the Lorentz transformations, but E=MC² is not one of the Lorentz transformations.

First of all, this particular relation is valid only for massive particles at rest (p=0); it’s the limit case of the full energy-momentum relation

\[E^2=m^2c^4+c^2p^2\]

This relation follows from the fact that the inner product of the 4-momentum with itself (i.e. its Minkowski norm) is an invariant:

\[\eta _{\alpha \beta } p^{\alpha } p^{\beta } =m^{2} c^{2}\]

So the validity of the energy-momentum relation is a direct result of the transformation properties of the 4-momentum under Lorentz transformations. Since you have already stated that Lorentz invariance is indeed a given, you can’t then go on and dispute the energy-momentum relation, especially not if you try to replace it with an expression that is dimensionally inconsistent and not itself Lorentz-invariant.

 

Edited December 29, 2020 by Markus Hanke

[studiot]

11 hours ago, Frogton said:

On 12/27/2020 at 10:40 PM, studiot said:

Are you referring to the 1905 paper

Ist Die Tragheit eines Korpers von seinem Energehalt abhangig ?   :  Annalen der Physik 17, 1905

(Translated means   -  Does the inertia of a body depend on its energy content ?)

Yes. That is what I want to discuss. Unfortunately my thread has been hijacked by Jogius with a torrent of meaningless nonsense, irrelevant jargon and personal abuse.

Thank you for your answer.

Have you read this paper ? It is only 3 pages long.

 

However I cannot see a link between this first part of your opening post and thread title.

On 12/25/2020 at 11:26 PM, Frogton said:

Is E=MC² the optimal description of nature?

Einstein's 1905 derivation of E=MC² involved a thought-experiment using photons to derive a Lorentz factor equation and (ignoring higher powers in the Taylor expansion) comparing that equation to the classical Kinetic Energy Equation.

This is actually the only valid method of deriving E=MC², other methods such as the one involving a photon in a box, are merely examples of 'petitio principii', something Herbert Ives wrongly criticised Einstein's 1905 derivation for. Indeed Ives' own attempt at a derivation was an example of 'petitio principii', as well as containing a mathematical error.

 

and the second

 

On 12/25/2020 at 11:26 PM, Frogton said:

The problem with a derivation involving the classical Kinetic Energy Equation, is that KE=½MV² is not just an incomplete description of nature, but an equation that is only accurate at low-speed.

Since it is the season of goodwill to all men, I wondered whether I might be able to speculate that the Frogton Universal Force Law is actually a better description of nature than E=MC²?

The Frogton Universal Force Law leads to the integral equation F=(M+FʃV.dT)V/T, with V integrated between T=0 and T=T. I know what V is in terms of the variable T and the constants F and M, but does anybody know how to go about solving such integral equations other than by guessing?

 

I was hopingyou might explain this in some detail ?

In particular I am puzzled that you have introduced an expression involving 'Force' and 'Time' when the reference does not mention force or time anywhere.

I am further puzzled by your notation.

What exactly do you mean by

[math]F\left( {\int {V.dT} } \right)[/math]

?

Are you intending an inner or dot product ?

How does this work with a vector and a scalar ?

What physical quantity do you think it represents ?

 

The only real agreement between Einstein and yourself seems to be that in both the 1905 papers Einstein was working with 3 dimensional vectors as you appear to be.
Of course, in 1905, four-vectors had yet to be introduced in Physics.

[joigus]

Ok. If you're done discussing me, we can talk some physics.

You still haven't addressed my question: Is your T proper time of coordinate time?

Proper time is time in the non-inertial reference frame co-moving with the particle.

Coordinate time is time as measured from an observer sitting somewhere and not subject to forces.

The solving of the problem is very different.

Also, the constant force is constant 4-force? (the derivative of 4-momentum with respect to proper time)

If so, the solution of your "horrible" equation is trivial --as calculus is concerned--. I have solved it and I get a cubic in v, with coefficients depending on t. Assuming that's proper time.

It doesn't look completely out of whack (it reminds me of solutions of hyperbolic motion), but you obviously have made some relevant conceptual mistake, that's why you're getting inconsistent units.

Hyperbolic motion is the closest you can get in special relativity to uniformly accelerated motion. It's not exactly as I said, a constant 4-force. A constant 4-force seems to be what you're implying.

I just want to know where the hell you have "derived" your equation from.

Related to @studiot's comments: I am assuming everything is collinear and you don't mean a dot product.

I also recommend you read carefully @Markus Hanke's comments.

Instead of going into a tantrum, try to interact with the users. It's all I can say.

But, as long as you got personal, just a couple more things:

I've read Feynman's Lectures since I was 16, What do You Care what Other People Think too. Also, I can tell a jay from a tit, from a robin, from an avocet, from a gannet, etc. Not all of them, but just one blob of colour and in some cases I can distinguish two very close species one from one another, male from female, and one-year immature seagulls from adults. So yes, as an amateur ornithologist, I can tell. In other cases, apparently different species are grouped under same name because they happen to be male and female of the same. So names do help. Names are a useful mental tool. So Feynman was wrong about that one. But he was a genius. He turned other people crazy by insisting on his own names and notations, though.

And a last thing: As to self-loving narcissism, how about coming up with a silly equation and naming it "the Frogton Universal Force Law"?

[Frogton]

On 12/29/2020 at 12:32 AM, joigus said:

Boy, that was hilarious!!! +1

Thanks. It is fantastic to have finally found somebody who appreciates my sense of humour.

On 12/29/2020 at 1:31 PM, joigus said:

And a last thing: As to self-loving narcissism, how about coming up with a silly equation and naming it "the Frogton Universal Force Law"?

What a pity you spoilt your post by reverting to type at the end. Also a shame that you are not an etymologist, because then you could have ascertained the origin of the name Isaac Frogton, and reached the opposite conclusion.

On 12/29/2020 at 1:31 PM, joigus said:

I've read Feynman's Lectures since I was 16,

Have you found many errors?

On 12/29/2020 at 1:31 PM, joigus said:

I have solved it and I get a cubic in v, with coefficients depending on t. Assuming that's proper time.

If you could share your solution that would be very interesting.

On 12/29/2020 at 12:38 AM, swansont said:

Equations with inconsistent units is enough to be scientifically wrong. The rest of this is distraction from discussion. 

“Dimensionally inconsistent” was not a good choice of words, as by definition it implies in-correctness. I should have confined myself to giving you your due for spotting the issue with so little to go on.

There may be some dark corner of your mind panicking about the catastrophic possibility that the Frogton Universal Force Law might be correct, but the title of the thread is “Is E=MC² the optimal description of nature?”

On 12/29/2020 at 9:43 AM, Markus Hanke said:

First of all, this particular relation is valid only for massive particles at rest (p=0); it’s the limit case of the full energy-momentum relationE2=m2c4+c2p2

Thank you for rushing in where Swansont feared to tread, with that monstrous equation. But you are doing what I object to, by trying to impress with jargon.

To demonstrate that you understand nature, and are not just repeating what you have read, derive that equation, explain how it relates to E=MC², and reveal the true meaning of 'petitio principii'.

On 12/29/2020 at 12:23 PM, studiot said:

Are you intending an inner or dot product ?

No.  I do not know why I put a dot there, but to my untrained eye it looks neater.

You need to consider just the first 3 paragraphs of my post together, and say what you disagree with. I do not have unlimited time to reply to everything.

[Bufofrog]

1 hour ago, Frogton said:

"Dimensionally inconsistent” was not a good choice of words, as by definition it implies in-correctness.

Dimensionally inconsistent does mean it's wrong.

1 hour ago, Frogton said:

There may be some dark corner of your mind panicking about the catastrophic possibility that the Frogton Universal Force Law might be correct,

No one is panicking, there is just mild curiosity about how you came up with such a terribly wrong equation. 

[joigus]

1 hour ago, Frogton said:

What a pity you spoilt your post by reverting to type at the end. Also a shame that you are not an etymologist, because then you could have ascertained the origin of the name Isaac Frogton, and reached the opposite conclusion.

What a goblet of nonsense!

1 hour ago, Frogton said:

Have you found many errors?

No. But people have. I remember a conversation with J.M.R. Parrondo years ago. I loved Feynman's work, but he didn't seem to find it so fascinating, for some reason. He was busy finding flaws in it. Apparently he found one in the chapter on thermodynamics and the ratchet, and that's what led him to Parrondo's paradox. My take on it is that even in error, Feynman was incredibly inspiring.

Edited December 30, 2020 by joigus

[studiot]

2 hours ago, Frogton said:

On 12/29/2020 at 12:23 PM, studiot said:

Are you intending an inner or dot product ?

No.  I do not know why I put a dot there, but to my untrained eye it looks neater.

You need to consider just the first 3 paragraphs of my post together, and say what you disagree with. I do not have unlimited time to reply to everything.

I asked for clarification, I can't agree or disagree as Idon't know what you are talking about

So  this is a wind up then.

Thank you for confirming that and wasting my valuable time.