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How is energy conserved when length contracts?


captcass

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To be fair, natural units are a thing. But I can't see how that it is at all relevant. Captcass seems to be complaining that he used natural units when he shouldn't have. And we didn't spot it. Or something. (In natural units it would just reduce to "l * E = 1/2".)

The OP claimed that "length and energy are related: l * E = ħ / 2". The units wouldn't make any difference to the truth or otherwise of this statement. And it still looks bogus to me (it is not dimensionally consistent, apart from anything else).

On 01/03/2018 at 7:36 PM, captcass said:

Heisenberg's uncertainty principle tells us that ...

[math]\sigma_{x}\sigma_{p} \geq \frac{\hbar}{2}[/math]

For position and momentum.

Length and energy are not related in this way.

Edited by Strange
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13 minutes ago, Strange said:

To be fair, natural units are a thing. But I can't see how that it is at all relevant. Captcass seems to be complaining that he used natural units when he shouldn't have. And we didn't spot it. Or something. (In natural units it would just reduce to "l * E = 1/2".)

The OP claimed that "length and energy are related: l * E = ħ / 2". The units wouldn't make any difference to the truth or otherwise of this statement. And it still looks bogus to me (it is not dimensionally consistent, apart from anything else).

Why would anyone use natural units for c and hbar and then convert back? I don’t understand...might as well use the units I proposed above if we are to convert back anyway.

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25 minutes ago, koti said:

Why would anyone use natural units for c and hbar and then convert back?

Apparently I have been way overestimating you folk. Natural units are used to simplify calculations by dropping out terms by making them = 1. It eliminates a lot of infinities and Pi factors from the calculations. When the final result is achieved, to find the actual result, you factor those elements back in. In particle physics they make h-bar and c = 1.

https://en.wikipedia.org/wiki/Natural_units

http://www.phys.ufl.edu/~avery/course/4390/f2015/lectures/natural_units.pdf

 

 

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2 hours ago, captcass said:

This was in my original question. Without re-reading it all, I don't believe anyone noticed (as I didn't when I posted it, duh) that it is in "natural units". To find the answer in the correct units, the c and h-bar elements have to added back in.

I think this would have been the correct reply to my question.

Oh, it was noticed. But since it's wrong, it doesn't matter.

How about showing your work? Derive the expression.

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34 minutes ago, captcass said:

Natural units are used to simplify calculations by dropping out terms by making them = 1. It eliminates a lot of infinities and Pi factors from the calculations. When the final result is achieved, to find the actual result, you factor those elements back in. In particle physics they make h-bar and c = 1.

If you really think all that complexity is necessary when multiplying two numbers, I feel sorry for you ...

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2 hours ago, Strange said:

To be fair, natural units are a thing. But I can't see how that it is at all relevant. Captcass seems to be complaining that he used natural units when he shouldn't have

It is relevant because I was asking about the relationship of energy and length when I found the relationship in a particle physics book. The proper answer is that there is no recognized relationship between length and energy. The relationship is only used when doing computations using natural units......

That's it for me here.

BiBi

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4 minutes ago, captcass said:

The proper answer is that there is no recognized relationship between length and energy. The relationship is only used when doing computations using natural units......

If there is no relationship why would it be used?

It doesn’t make any sense. 

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9 hours ago, captcass said:

It is relevant because I was asking about the relationship of energy and length when I found the relationship in a particle physics book. The proper answer is that there is no recognized relationship between length and energy. The relationship is only used when doing computations using natural units......

That's it for me here.

BiBi

BS 

Natural units don't let you arbitrarily put the constants back in. You might use E = m for convenience, but you can't then arbitrarily plug an hbar into the equation and claim there is meaning to it. If you "found" a relationship in a particle physics book I'm guessing there was context to it that you are not including (like it was a scaling factor, rather than equality) 

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27 minutes ago, swansont said:

Then show your work, as I've already asked.

Lol. I have no idea what you are asking for here. I started this thread with a simple question asking for clarification. I did this because, even though it was right in front of me, I missed that it was in natural units. There is no math here. There is no derivation. I am not making any claims here. I just wanted your folks' help in clarifying, which no one really did. Strange came closest when he said, " Note that this refers to wavelength, not length in general. But your question still applies. "

So......there are no bones to pick here.

Thanks.

BiBi

 

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10 minutes ago, captcass said:

I am not making any claims here.

You claimed that "length and energy are related: l * E = ħ / 2"

This is obviously wrong. And has nothing to do with the uncertainty principle.

10 minutes ago, captcass said:

I missed that it was in natural units

You still haven't explained how that is relevant. Your claim is wrong in any units.

10 minutes ago, captcass said:

There is no math here. There is no derivation.

And that is the problem. You are posting unsubstantiated nonsense.

10 minutes ago, captcass said:

Strange came closest when he said, " Note that this refers to wavelength, not length in general.

There is a relationship between energy and wavelength, but it is not the one you claim. 

Edited by Strange
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1 minute ago, Strange said:

You claimed that "length and energy are related:

lol. I did not claim this.

I asked you folks for clarification about what I found in the particle physics book, that is all.

2 minutes ago, Strange said:

There is a relationship between energy and wavelength, but it is not the one you claim. 

I am NOT claiming anything! I understand the relationship between energy and wavelength! My question had nothing to do with that aspect. It was based on my own misunderstanding on what I read.

This thread is dead and I am moving on. Thanks for your time......

 

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30 minutes ago, captcass said:

lol. I did not claim this.

"Heisenberg's uncertainty principle tells us that length and energy are related: l * E = ħ / 2 and using natural units where c = 1= ħ, we can deduce that   2*10-16 m = 1 / GeV."

This is literally the first sentence of your OP. (emphasis added)

If you can't derive it, or have no math to show, then where did you read it?

 

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1 hour ago, swansont said:

This is literally the first sentence of your OP.

That is literally what I found in the book and asked you folks for clarification on. Hello?

I will not be responding to any more of these.....

 

I provided the link to the book early on. I haven't the time for this......IT WAS A MISUNDERSTANDING ON MY PART TO BEGIN WITH!. Geeze!

OK. Here it is again:

https://books.google.com/books?id=SW3FCwAAQBAJ&pg=PA49&lpg=PA49&dq=1.782662×10−36+kg&source=bl&ots=17y_BtXxUY&sig=DCfJ6RQ8drGjYwW8zGOxQsgDjt8&hl=en&sa=X&ved=0ahUKEwjV47qBsMnZAhUS9WMKHd0mATwQ6AEIPTAC#v=onepage&q=1.782662×10−36 kg&f=false

Here is a link to the book. The applicable section is on page #49

Have fun with it. I now understand it so I am done with it.......

BiBi

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15 minutes ago, captcass said:

That is literally what I found in the book and asked you folks for clarification on. Hello?

I missed that.

But I see what is going on. The author is in error. It has nothing to do with the HUP.

If you set hbar*c = 1, you get the relationship that 1m equates to 2 x 10^16 / GeV

(3 x 10^8m/s) * (4.15 x 10^-15 eV-s/2π) = 2 x 10^-7 eV-m

It is simply a byproduct of natural units.  

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1 hour ago, swansont said:

It is simply a byproduct of natural units.  

Thank You! That is what I have been saying. I didn't see that before I asked the question.

The author does not show how he derives it from HUP,  but I took him at his word, as odd as it also seemed to me.....

OK. Now I think the thread is done....yes?

Thanks for your time, folks.

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14 hours ago, captcass said:

Thank You! That is what I have been saying. I didn't see that before I asked the question.

It's not something that has physical meaning, though. It's simply a conversion factor.

14 hours ago, captcass said:

The author does not show how he derives it from HUP,  but I took him at his word, as odd as it also seemed to me.....

It was not derived from the HUP. The author erred in claiming that.

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