The hard part is to shake off the notion that light is moving through this absolute space stuff. It's difficult because we're used to coordinate systems like maps. You can still use coordinates but they aren't absolute.

Interesting.
As v-->c , t' = infinite.

As t'--> infinite, space seems to shrink? Inverse relation similar to mass vs E

It's ok if this seems hard to think about. It is. Most physics students don't seem to get either, even the one that pass exams.

This idea that the laws of physics are still the same in a 2D universe (like for light) leads to some interesting ideas. If we're brave enough to think movement is only a point of view, that nothing is really moving, we can start thinking about stuff like this:

https://www.wired.co.uk/article/our-universe-is-a-hologram

I hope everyone can see that both the physicist and the muon are correct. We tend to side with the physicist as the correct point of view because we all live on the Earth in a similar inertial frame and majority bias kicks in. If we ask most particles in the universe then our 3D view of the universe would be a minority opinion. It doesn't really matter, only that the same laws of physics (equations) work for everyone.

Like a sawtooth pattern because it's moving across the way for the observer as well as going up and down. It's the difference in distance that each sees that's key. The observer sees a greater distance because they see diagonal lines instead of up and down. But they both see the beam moving at c because everyone agrees c is a constant.

So if c = dist / time, and they both agree c is a constant, they see different times because they see different distances.

It's just a thought experiment so imagine what you like. Imagine the torch was built out of photons. It's the idea that's important, and then you can test it out using experiment irl. At first they flew an atomic clock around the world and compared it with one on the ground and there was a time difference.

hunk wrote:

Interesting. As v-->c , t' = infinite. As t'--> infinite, space seems to shrink? Inverse relation similar to mass vs E

Above is key to understanding the thought experiment. Observed time difference goes to infinite as v-->c.
In other words time slows down for an object as it approaches the speed of c.

So for interstellar travel...if you could travel at speed of light, you would effectively get anywhere instantly as time stops for you?
But for the people waiting for you at different planets time travels 'normally' and it would take you years on their count?

Ok, so we're still at this confused stage. This is good. The best way to learn physics (to my mind) is to teach the history of it, the problems physicists were having at the time with wrestling with these ideas and how those problems were eventually solved. The important thing is that we're thinking deeply about time and space just like they were, and the fact we have to think about these different symmetries from differing points of view was eventually straightened about by Minkowski and his wonderful spacetime diagrams. 

But that's in a bit. For now, as long as we can appreciate that space and time are not the unchanging things we thought they were we'll be ok. And we're going to jump back in time for a bit to Newton's day and talk about Gottfried Wilhelm Leibniz.

Leibniz was truly, staggeringly ahead of his time and his ideas about time and space are only properly appreciated today. You might recognise his name as the the guy that co-discovered calculus (we're going to say discovered instead of invented from now on). He actually discovered it before Newton although Newton took the credit. It's with deep regret that Newton was a bit of a cunt because it put Leibniz's more radical ideas under the radar for 300 yrs.

Leibniz was more mathematical than Newton and viewed space as not existing at all - purely another numeric variable. Newton had just published the Principia and his ideas about absolute space and time, and everyone was so enthralled they all listened to him and he knew it. He was a bully and rubbished any ideas that he didn't agree with. He went out of his way to riducule anyone he saw as a threat.

In this enlightened age of quantum mechanics the ideas of Leibniz are taken more seriously but I'd argue still not seriously enough.



I post this just so we can appreciate that our perceptions are biased and we need to start thinking more mathematically, or to be precise more like Minkowski. We'll look at his diagrams next and it'll cut through the fog somewhat. It was Minkowski that properly defined spacetime, and in a geometric framework where time is considered an axis (dimension) on a graph. From that we can start understanding acceleration and it'll start to come together, just as long as we understand we need to start treating space and time as a mathematical object, and not what we thought they were.

SG might need to rewrite his thread

https://www.theguardian.com/science/2024/mar/09/controversial-new-theory-of-gravity-rules-out-need-for-dark-matter

Can you write next year's section asap please