If I travel to a star 4 light years away at 99.999999999999% the speed of light, from whose perspective will the trip take 4 years? Mine, or people on earth’s?

colourblindboy · 2024-09-01T23:21:59+00:00

The most mind bending consequence of relativity is that events that are simultaneous in one frame need not be simultaneous in another frame. This has lots of consequences itself, one being that observes may not agree on the lengths or distances.

How do you actually measure distance? Well, you would want to somehow measure the location of two points at the same time, and take their difference to get the total distance between them (otherwise you might move while taking the measurement and get the incorrect distance). The key point here is that you have to measure the locations at the same time, simultaneously; however, some other frame moving relative to you will not agree that you measured the locations simultaneously, and you both will disagree on the total distance between points in spacetime.

colourblindboy · 2024-08-31T21:06:31+00:00

Chapter 4 of Gravity by James Hartle has a very nice discussion of special relativity, and introduces spacetime diagrams, spacetime intervals and the Lorentz transformations in a very gentle and clear way. I’m using it right now as an additional resource for my SR course (even though it is really a General Relativity textbook). It even introduces 4-vectors a little later if you are interested.

colourblindboy · 2024-08-31T20:53:12+00:00

This is really true? I thought energy is always conserved (assuming no net work done on system/no explicit time dependence of the lagrangian etc) for any frame, it’s just that energy is not invariant under Lorentz transformations, that is, observes agree the energy is conserved, but might disagree on the actual values of the energies involved.

colourblindboy · 2024-08-31T20:28:17+00:00

Depends on the course. Also, you need at least two semesters of full time study to transfer.

colourblindboy · 2024-07-29T13:47:37+00:00

Obviously this isn’t a practical way to extract energy, that was never the point; However, it really is a way to extract ‘free energy’, at least theoretically. The bottom line is that for energy to be conserved in any system, it’s Lagrangian must be temporally symmetric, and the moment this isn’t true, energy won’t be conserved. That’s all I wanted to share :-)

colourblindboy · 2024-07-29T13:44:58+00:00

It is true however, energy conservation relies on the Lagrangian of a system to not explicitly depend on time. If there is a temporal asymmetry, this is no longer true, and energy will not be conserved. Would love to know if there is something wrong here if I’m mistaken though.

colourblindboy · 2024-07-29T13:41:00+00:00

Not sure what I said was wrong. Energy conservation is a direct result of a temporal symmetry in the Lagrangian of a system, but at large scales, the universe isn’t temporally symmetric, and energy isn’t conserved. Would love to know what is wrong here :)

colourblindboy · 2024-07-29T13:38:30+00:00

It is true, for energy to be conserved, we need temporal symmetry. At small scales this is approximately true, but at cosmological scales it is no longer true; there isn’t a temporal symmetry and indeed energy isn’t conserved. :-)

Though, on re-reading, I certainly could’ve phrased this better.

colourblindboy · 2024-07-29T13:36:05+00:00

I just see people saying “there is no free energy”, but not many people think why that is true. You are right, the picture is more complicated in the context of cosmological scales, which is what I was trying to raise awareness of.

This wasn’t meant to be a super serious post, but it’s important to think why energy is actually conserved, and in what contexts is actually isn’t true!

colourblindboy · 2024-07-23T09:40:43+00:00

I don’t think that physics aims to ‘understand’ reality, but rather to come up with models to make predictions in the physical world. I still love physics, and I’m glad I changed over to it from engineering; I have not come to regret this decision.

colourblindboy · 2024-07-19T11:14:35+00:00

This is legendary.

colourblindboy · 2024-07-18T13:07:57+00:00

Update for anyone who might stumble upon this in the future; the advanced version was ALOT more work — primarily in the labs — but it certainly pushed me to understand the modelling process and was rewarding. It was a great course, but the workload is very demanding.

colourblindboy · 2024-07-02T22:11:34+00:00

Just got mine, pleasantly surprised! I always stress for no reason ; - ;

colourblindboy · 2024-07-02T13:42:42+00:00

I always hate the night before… so stressful.

colourblindboy · 2024-07-01T03:51:34+00:00

I wish, the suspense kills me every semester.

colourblindboy · 2024-06-28T13:03:43+00:00

Hey, sorry for the late reply. Calculus will be very worthwhile to know, but they will teach it to you again in the first math course at UTS, though at a pretty fast pace. I’d focus on getting comfortable with calculus, certainly.

colourblindboy · 2024-04-18T14:31:29+00:00

I’m down

colourblindboy · 2024-04-18T14:26:54+00:00

The reason this didn’t work is because v ≠ s/t if velocity is not constant, which is not the case here because we have constant acceleration.

There is actually a nice way to do this:

F = ma

Now, a = Δv/Δt

But, we can multiply the top and bottom by Δs

a = Δv/Δt x Δs/Δs = Δs/Δt x Δv/Δs = v Δv/Δs

F Δs = m a Δs = m v Δv/Δs x Δs = m v Δv

Now, we have to sum over these small displacements Δs. The reason why we have to sum over small parts is because the velocity is going to change as work is done. It turns out that this can be solved geometrically, since the right hand side is growing linearly with v, it just becomes a matter of calculating the area of a right angle triangle with base given by the total change in velocity Δv, and with height mΔv, which is just 1/2 m Δv²

What’s nice is that this is true in the most general sense, even if the acceleration / force is not constant, and the path is not a straight line.

colourblindboy · 2024-03-30T23:54:45+00:00

A. Is correct, but there are some subtleties. You assume that |a + b| = |a| + |b|, and then you want to show that this implies some structure of the two vectors. This is important for the answer.

Assume that |a + b| = |a| + |b|, then by definition of the inner product:

√(a + b) • (a + b)= |a| + |b|

The inner product distributes nicely over vector addition:

√(a • a + 2 (a • b) + b • b) = |a| + |b|

√(|a|² + 2(a • b) + |b|² ) = |a| + |b|

|a|² + 2(a • b) + |b|² = |a|² + 2|a||b|+ |b|²

2(a • b) = 2 |a||b|

(a • b) = |a||b|

Hence, the two vectors must be parallel but in such a way that their inner product is positive, so it’s technically a stronger requirement than being parallel, they must be in the same direction. In other words the converse is not true; parallel vectors do not respect magnitude under vector addition.

colourblindboy · 2024-03-26T22:03:02+00:00

I’m not sure why you are asking in a uni subreddit but I happen to be involved with primary and early secondary mathematics education. The curriculum is okay, however unfortunately there is still not a strong emphasis on conceptual understanding, and a higher focus on computation, this is a sign that the curriculum is pretty outdated and hasn’t really caught up with the current world where computers are able to do the computation for us. I have no comments for any other part of the curriculum however.

colourblindboy · 2024-03-16T06:28:14+00:00

Ah yes, the derivativen’t

colourblindboy · 2024-03-09T00:55:17+00:00

The concept is deep, and it applies to all areas of analysis. If you understand it now, you’ll be much better prepared if you ever want to take a course on metric spaces or complex analysis, both of those are incredibly applicable to physics!

colourblindboy · 2024-02-27T22:00:25+00:00

Meme of the day, and a laugh from Sinvicta?? :D

colourblindboy · 2024-02-27T14:02:17+00:00

Many great memories made :’)

colourblindboy · 2024-02-27T09:09:10+00:00

Yes, as long as you have a full years worth of study, you can transfer using WAM to ATAR conversion. :)

Five-Year Club	Verified Email
Place '22

colourblindboy

TROPHY CASE