I'd like to know your interpretation.

In summary: No, it is correct.I think you're forgetting the application of the chain rule.I also think EhsanZ's interpretation is correct, although I do not know what "Hobson's notation" is.I couldn't find it with google, except for in this thread. ;)
  • #1
EhsanZ
11
0
With Hobson's notation:

H=(da/dt)/a

dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2

If ((d2a/dt2)/a) is negative, (dH/dt) is certainly negative.
But if ((d2a/dt2)/a) is positive, (dH/dt) can be positive or negative.

What is your interpretation?
 
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  • #2
dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2

Above is incorrect. Should be:

dH/dt = (d2a/dt2)/a - (da/dt)/a2

Your second term is wrong.
 
  • #3
No, it is correct.
I think you're forgetting the application of the chain rule.

I also think EhsanZ's interpretation is correct, although I do not know what "Hobson's notation" is.
I couldn't find it with google, except for in this thread. ;)
 
  • #4
Actually I think the only thing wrong with second eq. is a lack of superscripting of the 2s:

dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2
 
  • #5
EhsanZ said:
With Hobson's notation:

H=(da/dt)/a

dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2

If ((d2a/dt2)/a) is negative, (dH/dt) is certainly negative.
But if ((d2a/dt2)/a) is positive, (dH/dt) can be positive or negative.

What is your interpretation?

[itex]d^2 a/dt^2 > 0[/itex] and [itex]dH/dt < 0[/itex] means that the expansion of the universe is accelerating while the Hubble constant is decreasing. We think that this is happening today.
I like Serena said:
although I do not know what "Hobson's notation" is.
I couldn't find it with google, except for in this thread. ;)

This (I presume) refers to the notation used in the book General Relativity: An Introduction for Physicists by Hobson, Efstathiou, and Lasenby.

EhsanZ, play around with the spatially flat, matter-only Lemaitre model given on page 406 and in problem 15.23. This a good analytic approximation to our universe.
 
  • #6
George is correct. If you look at the equations dispassionately, it is obvious the result can never be negative.
 
  • #7
I like Serena said:
No, it is correct.
I think you're forgetting the application of the chain rule.

I also think EhsanZ's interpretation is correct, although I do not know what "Hobson's notation" is.
I couldn't find it with google, except for in this thread. ;)
You're right. My bad.
 
  • #8
mathman said:
dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2

Above is incorrect. Should be:

dH/dt = (d2a/dt2)/a - (da/dt)/a2

Your second term is wrong.

No my friend! U made a mistake.
 
  • #9
mathman said:
You're right. My bad.

Doesn't matter! Everybody makes mistakes.:smile:
 
  • #10
I like Serena said:
No, it is correct.
I think you're forgetting the application of the chain rule.

I also think EhsanZ's interpretation is correct, although I do not know what "Hobson's notation" is.
I couldn't find it with google, except for in this thread. ;)

I meant the notation that Hobson had used in his book named "General Relativity: An Introduction for Physicists ".
 
  • #11
BillSaltLake said:
Actually I think the only thing wrong with second eq. is a lack of superscripting of the 2s:

dH/dt = ((d2a/dt2)/a) - ((da/dt)/a)2

Yes, you're right my friend. I should've written it more carefully.
Thanks
 

1. What is the meaning of "interpretation" in this context?

In this context, "interpretation" refers to the way in which someone understands or explains something. It can also refer to the act of translating or making sense of something, such as a text or data.

2. Why is it important to know someone's interpretation?

Knowing someone's interpretation can help us better understand their perspective and reasoning. It allows for effective communication and can lead to a deeper understanding of a topic or situation.

3. How do interpretations differ among individuals?

Interpretations can differ among individuals due to personal experiences, biases, and cultural backgrounds. Different people may also have different levels of knowledge or understanding about a topic, leading to varying interpretations.

4. Can interpretations change over time?

Yes, interpretations can change over time as new information is acquired or as perspectives are altered. As individuals grow and learn, their interpretations may also evolve.

5. How can we determine the accuracy of an interpretation?

The accuracy of an interpretation can be determined by comparing it to evidence and facts. It can also be evaluated based on logical reasoning and consistency. Additionally, seeking multiple perspectives and considering different sources can help assess the accuracy of an interpretation.

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