Suppose you are walking through an airport at a steady 2 mph. You get onto a slideway that's also moving 2 mph. You're now moving 4 mph.
Nope. Your speed is 3.999999999999999964 mph. That's about 4 minus one-quadrillionth of a mile per hour.
Welcome to our universe.
Citation required.
Velocities through space don't add. They only seem to do so at low speeds.
See L. Epstein's book, "Relativity Visualized".
You just have to account for inflation.
Actually velocities in space time do add. Instead of just adding 3 component velocity vectors, you need to add 4 component vectors where the fourth component is time based. The shift in time is what makes the a 3 component vectors no longer add arithmatically.
Take a high school physics class.
Wouldn't that depend on whether the high school physics class covers special relativity?
I'm not sure high school physics gets to that particular one.
Einstein, A. On the electrodynamics of moving bodies, Annalen Phys. 17 (1905) 891-921.
You can read here:
https://users.physics.ox.ac.uk/~rtaylor/teaching/specrel.pdf
You can find what you are looking for in section 5.
Jackson's "Classical Electrodyanamics" has a chapter on the "Special Theory of Relativity" which I always found enlightening. It does require a basic knowledge of vector calculas.
Oh yeah, that's one of the classics. A must-have on anyone's shelf.
next up... bell's theorem
I dunno, I was always taught that I should round up after 16 decimal places
What's weird about this? If I add a liter of methyl alcohol to a liter of water, the volume of the resultant is not two liters. And I've certainly never heard anyone claim on the strength of this observation that the universe is weird.
Well, under Newtonian physics you would be going 4 MPH, right? So, the methyl alcohol thing isn't really relevant.
But I agree with lower-case -- wait till you google 'Bell's theorem' or EPR Paradox. Special relativity is a little counterintuitive but falls out pretty naturally if you recognize like Albert did that the laws of physics, including the speed of light, is the same in all reference frames.
But Bell's theorem just isn't intuitive, period.
This is why I'm convinced we must be living in a simulation. These kind of weird behaviors just can't be explained any other way. It's just because certain instructions in the simulation conflict with other instructions. Voila!! Nonsensical rules result.
Yes, well so long as the simulation doesn't try to execute the Halt and Catch Fire instruction... https://en.wikipedia.org/wiki/Halt_and_Catch_Fire_(computing)
The laws of physics aren't nonsensical. They are counterintuitive unless you understand that the rules that we assume should apply are really just a very good approximation that holds only at relatively low velocities and near to only relatively small masses. Those aren't the same thing.
Or alternatively, the simulation was designed for low velocities and relatively small masses, and it's only when we conceive of situations that were not envisioned in the simulation do we get these non-intuitive results.
Would you like to hear how this also explains the Schrodinger's cat paradox?
The laws of physics are only counterintuitive because we don't routinely travel near the speed of light. Our apes' brain evolved in a reality where only relatively low velocities (and weak gravitational fields) are routinely experienced. Newton's laws are just a special case of Einstein's theory for when velocities are small compared to the speed of light.
This is the stupidest explanation for the stupidest concept I've seen in a long time.
Just because you don't understand things doesn't mean the answer is something unprovable and really dumb.
Worse, it's a solution which adds complexity without adding detail.
'The universe unfolds following these rules' being changed to 'a computer/god/etc did it' doesn't explain the rules or and steps, it just adds one, 'how did the computer/god/etc get there?'
The same could be said for pre-Daltonian chemistry. Or the fact that no matter what optical system you used, you could not create an area of focus hotter than the source was a mystery before the development of thermodynamics.
Bell's theorem is not exactly intuitive, I grant. But that's primarily because of all the machinery -- including definitions -- that you have to build before you can get to the point that you can ask meaningful questions on this subject. For myself, all it means is that these days my position, to the extent I have any, is that I am inclined towards superdeterminism. Primarily because the Many-Worlds crowd has gotten so obnoxious of late.
I once got into a serious argument with a very smart engineer when I tried to explain you couldn't achieve a temperature hotter than the surface of the sun with a magnifying glass, even one that was miles in diameter. Thermodynmics is perhaps the most basic of natural laws, and it saws thermal energy flows from a hotter body to a cooler one, not vice versa.
Of interest but far beyond my level of detailed understanding is the recent revelation that both quantum mechanics and general relativity are necessary to explain why certain types of black holes don't violate thermodynamics and information theory.
That's... not quite right.
It assumes the surface is the same, single point.
But if you took light from the other side of the object and light from this side of the object, and those weren't points which were shared in space, you'd exceed the source.
because they're different sources. 'The sun' is actual a surface larger than our planet.
Of course, the square-law of light being transmitted would also break this far before thermodynamics entered the picture.
But that's why you can surround something with lamps or lasers and get higher (or lower) temperatures.
All I care about is that people who are standing on the slideway move to one side and not stand in the middle blocking all of us habitually late hyperactive travelers trying frantically to get to our designated gate. 🙂
Or those of us who want to get to a seat instead of standing around!
Why is the speed increased if you and the slideway are going at the same rate?
I guess you are still walking at the same rate with respect to the slideway. Kevin doesn't make that clear.
As akapneogy says, you are walking at 2mph relative to the walkway you are standing on, and the walkway is advancing at 2mph relative to the corridor.
That's not as weird as the fact that when you stepped on the moving walkway, you and everything on your body (including the CPU in your phone) started running slower, and will speed back up when you walk off the far end. (Any resulting discrepancy in the phone's timekeeping will be erased the next time the phone synchronizes with the network.)
What’s really crazy is I think we now have atomic clocks that are precise enough to measure this. Atomic clocks are precise enough to measure changes in time at slightly different elevations due to the change of gravity.
Indeed, the clocks on GPS satellites have to contend with both special relativity, because they're moving so fast, and general relativity, because they're in a weaker gravitational field.
What's really crazy is that the distance over which the time dilation has been measured is about 1 cm. That's insane, and means measuring time to something like one part in 10^19.
One way to think of it is that you are always traveling through 'spacetime' at a constant velocity. If you aren't moving through space, the velocity is all through time. As you start moving in space, your velocity through time decreases to keep the total velocity the same so time slows. If you move at the speed of light, there's no velocity left to move through time.
The speed of light should be faster. Much faster.
Technically, what you want to change is the fine-structure constant.
Yeah, that's been a hobbyhorse of mine for years. I bring it up every Thanksgiving, but all the people at the table pretend that they didn't hear me - for some reason.
So 2+2=/4. I fcking knew it!
Relative to what? Relative to the slidewalk, you are going 2 mph. Relative to you, you aren't moving at all but the airport is going backwards at 3.999999......
My speed is closer to 0 mph. What gives?
Wait... which end of the walkway was I supposed to start at?
Kevin shows his absolute disdain for significant figures because if he turned in an answer other than 4 any physics teacher would mark it wrong.
This is my favorite. Yes!
Yes, but your flight will still be delayed.
haha
And now, how long would that moving walkway have to be (those messages warning you it is about to end never call it a "slideway"...) and for how long would you have to walk before you were more than 1 minute away from where you expected to be assuming you were going 4 miles per hour? ...
No, your speed as you perceive it is 4mph. Everyone else who's not walking on the conveyor belt is moving at 2.000000000000000036 mph.
"SLIDEWAY?" Is that what the kids today are calling them instead of moving sidwalks? BTW in the UK they are "travelators."
First, we must idealize the walkway with respect to a sphere rotating and revolving about a point that is moving around another point at roughly 200 km/sec...
Bugger all.
https://youtu.be/buqtdpuZxvk