This discussion board is a place to discuss our Daily Challenges and the math and science
related to those challenges. Explanations are more than just a solution — they should
explain the steps and thinking strategies that you used to obtain the solution. Comments
should further the discussion of math and science.
When posting on Brilliant:
Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.
Markdown
Appears as
*italics* or _italics_
italics
**bold** or __bold__
bold
- bulleted - list
bulleted
list
1. numbered 2. list
numbered
list
Note: you must add a full line of space before and after lists for them to show up correctly
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
Math
Appears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3
2×3
2^{34}
234
a_{i-1}
ai−1
\frac{2}{3}
32
\sqrt{2}
2
\sum_{i=1}^3
∑i=13
\sin \theta
sinθ
\boxed{123}
123
Comments
well, it depends on the chosen refference point, but for a given refference point , does it vary between frames?
well that depends on the force law that defines it,
but how about this, if we have a electromagnetic situation, surely it depends on frame of observation
magnetic field in one frame is electric field in another, and hence the potential too must vary, as the contribution of electric field too the total field changes
but, i do not think there is any other situation, what is the solution?
First let us talk about gravitational potential energy..!!
If We talk about slow speeds then mass is nearly invariant and so does gravitational force and therefore potential energy is invariant for Newtonian physics. Gravitational potential energy between point masses depends upon their mass and their relative distance. the distance between the masses and mass of the masses will remain same for slow speed and thus all the frames will say the same potential energy if they take the same zero potential energy configuration.
But if we talk about relativistic speeds then mass increases length contracts thus gravitational potential energy may vary and so does the kinetic energy..!!
Similarly in different frame electric field and magnetic field are different therefor electrostatic potential energy is frame dependent as well charge is though invariant but electric field is variant of frame of reference..!!
yes sir, however i have read that newtonian expression doesnt hold for gravity in relativity , so substituting γm for m does not suffice, but yes the potential depends on frame
Well, i think I derived my thought from the following (may be flawed) thought experiment.
Let v1 be the velocity of the sytem in Frame 1. Let's say that the velocity of the object is v2 in another frame of reference. If v1 is not equal to v2 (and thus kinetic energies are not equal). If total energy is conserved, then Gravitational Potential Energy may be unequal. And therefore that makes it frame dependent. Can you correct me Sir?
Now I am trying to take help of Special Theory of Relativity which I learnt in 7th grade....
@Swapnil Das
–
Energy is conserved, not invariant, so you cant say that
(conserved means it is conserved in all inertial frames as long as you stick to one,
invariant means that it may not be conserved but it will not change from frame to frame at any given instant (like mass) ( it is both conserved and invariant in newtonian mechanics)(only invariant in SR))
@Swapnil Das
–
also, one thing, in SR, some may disagree that mass is invariant
actually it is a matter of definition
some define mo as rest mass and moving mass as γmo , for them , mass is not invariant and momentum and energy is given by mv and mc2
whereas i and many others think its better to define a fixed mass m and instead change the momentum and energy expressions as γmv and γmc2
this is more convenient as you dont have to put the word rest every time you say mass
however, another reason is that the mass changes in inelastic collisions as well (heat lost in newtonian collisions builds up as mass in SR) , and hence instead of having to define mass as a quantity that changes in both inelastic collisions and motion
it is simpler to define a fixed mass that only changes in inelastic collisions, and alter the expressions for momentum and energy instead
so for us, mass is an invariant but not necessarily conserved in a collision
@Mvs Saketh
–
Basically mass and energy are two different forms of one thing and they are inter convertable and in any situation the sum of mass and energy is conserved!!
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*or_italics_**bold**or__bold__paragraph 1
paragraph 2
[example link](https://brilliant.org)> This is a quote# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"\(...\)or\[...\]to ensure proper formatting.2 \times 32^{34}a_{i-1}\frac{2}{3}\sqrt{2}\sum_{i=1}^3\sin \theta\boxed{123}Comments
well, it depends on the chosen refference point, but for a given refference point , does it vary between frames?
well that depends on the force law that defines it,
but how about this, if we have a electromagnetic situation, surely it depends on frame of observation
magnetic field in one frame is electric field in another, and hence the potential too must vary, as the contribution of electric field too the total field changes
but, i do not think there is any other situation, what is the solution?
First let us talk about gravitational potential energy..!! If We talk about slow speeds then mass is nearly invariant and so does gravitational force and therefore potential energy is invariant for Newtonian physics. Gravitational potential energy between point masses depends upon their mass and their relative distance. the distance between the masses and mass of the masses will remain same for slow speed and thus all the frames will say the same potential energy if they take the same zero potential energy configuration. But if we talk about relativistic speeds then mass increases length contracts thus gravitational potential energy may vary and so does the kinetic energy..!!
Similarly in different frame electric field and magnetic field are different therefor electrostatic potential energy is frame dependent as well charge is though invariant but electric field is variant of frame of reference..!!
Log in to reply
yes sir, however i have read that newtonian expression doesnt hold for gravity in relativity , so substituting γm for m does not suffice, but yes the potential depends on frame
thanks for this question , it was enlightening
Yes , potential energy is frame dependent.
Log in to reply
What about gravitational potential energy?? is it also frame dependent?
Log in to reply
Oh, now it makes me really confused!
Well, i think I derived my thought from the following (may be flawed) thought experiment.
Let v1 be the velocity of the sytem in Frame 1. Let's say that the velocity of the object is v2 in another frame of reference. If v1 is not equal to v2 (and thus kinetic energies are not equal). If total energy is conserved, then Gravitational Potential Energy may be unequal. And therefore that makes it frame dependent. Can you correct me Sir?
Now I am trying to take help of Special Theory of Relativity which I learnt in 7th grade....
@Rohit Gupta
Log in to reply
Energy is conserved, not invariant, so you cant say that
(conserved means it is conserved in all inertial frames as long as you stick to one,
invariant means that it may not be conserved but it will not change from frame to frame at any given instant (like mass) ( it is both conserved and invariant in newtonian mechanics)(only invariant in SR))
Log in to reply
Oh, Thanks for correction.
Log in to reply
also, one thing, in SR, some may disagree that mass is invariant
actually it is a matter of definition
some define mo as rest mass and moving mass as γmo , for them , mass is not invariant and momentum and energy is given by mv and mc2
whereas i and many others think its better to define a fixed mass m and instead change the momentum and energy expressions as γmv and γmc2
this is more convenient as you dont have to put the word rest every time you say mass
however, another reason is that the mass changes in inelastic collisions as well (heat lost in newtonian collisions builds up as mass in SR) , and hence instead of having to define mass as a quantity that changes in both inelastic collisions and motion
it is simpler to define a fixed mass that only changes in inelastic collisions, and alter the expressions for momentum and energy instead
so for us, mass is an invariant but not necessarily conserved in a collision
Log in to reply
Basically mass and energy are two different forms of one thing and they are inter convertable and in any situation the sum of mass and energy is conserved!!
I think gravitational potential energy is not frame dependent in normal conditions.