However, I disagree with "we know it's possible to travel into the future just by travelling very fast."
From what I understood of that time dilation effect, it's more that you're slowing down things for yourself, so you're not traveling into the future as much as time is continuing as usual, but faster than you see it. It's like saying you time travel by being in suspended animation (which stops you vs. slowing you) and then revived. It may appear to you that you've jumped to the future, but to others not really.
With all due respect of someone who's not as familiar with this, I would still disagree.To others, it would appear that you're from the past. Travelling near light speed and coming back to where you started would indeed bring you to the future.
A tesseract is apparently for representing 4 dimensions that are equivalent. But in special relativity, the time dimension is unlike the 3 spatial dimensions. For that reason, I would not discuss tessaracts in a context of relativity. (if some pros have done it, I am not aware)Yes, I've seen that 4-D tesseract shadow-of-cube in 3D before. I don't really comprehend it. Do any of you? I remember having a math professor tell us that some of her friends could visualize up to 5 or 6 dimensions.
Leaving to come back when everyone and everything is older than the traveller. If that isn't travelling to the future, I don't know what is. But don't take my word for it, here are a few more links if you're interested:With all due respect of someone who's not as familiar with this, I would still disagree.
She has two series I know of: Cunk on Britain (much of which is on YouTube), and the newer Cunk on Earth.That was hilarious!
I've been watching this, very good also. Everything about the Universe is so unbelievable to the extent that anything (theories) is/ are believable.I miss Carl Sagan's Cosmos TV series.
Yes, it is my understanding that Lorentz discovered those factors first (before Einstein) in order to translate the Maxwell's equations from one inertial reference frame to another. However, he didn't realize that the very same factors also show that space and time can be transformed, too. Thus, he did not make the connection to the start of Special Relativity.These are all different ways to explain the Lorentz transformations (Prof. Lorentz hatched these equations first, and then Einstein showed that if the speed of light was a universal constant, then the Lorentz transformations necessarily followed).
I won't say that anything is believable, but certainly there are many proposals based in theory that tax my ability to believe. Yes, the edge of the observable universe is about 13 billion years back in time or our universe is about 13 billion years old. However, the diameter of our universe is on the order of 30 billion light years. How can this be? It is consistent with General Relativity, because our universe is expanding. Within the context of GR some non-material bodies can move faster than the speed of light. The edge of a shadow is listed as one. The "boundary of our universe" is another. So, while the farthest light has been racing toward us for us to see, space is being creating as the universe expands, so that the diameter of our universe is around 30 billion light years.I've been watching this, very good also. Everything about the Universe is so unbelievable to the extent that anything (theories) is/ are believable.
Maxwell had a wave equation for electromagnetic fields, which included a speed. People were used to the speed of a wave being dependent on a medium (sound in air, water waves, violin cords, etc.), so people started looking for a medium for electromagnetic fields (ether). After they failed, Einstein basically thought something like "what if there is in fact no medium and the wave speed is constant and the same for everyone?" Not obvious.Yes, it is my understanding that Lorentz discovered those factors first (before Einstein) in order to translate the Maxwell's equations from one inertial reference frame to another. However, he didn't realize that the very same factors also show that space and time can be transformed, too. Thus, he did not make the connection to the start of Special Relativity.
Maxwell's equations?For what it's worth, I've taught the subject matter of that video (introductory QM) and everything about it sounds great. Using a circular wire (instead of a linear string) to demonstrate standing waves is a great idea. All it's missing is a semester's worth of equations supporting the ideas.
Historically (1700s), d'Alembert used Newton's laws to create a mechanical wave equation, which can express the behavior of a guitar, piano, or violin string, the string in the video, with some adjustments, and sound, with some adjustments.Maxwell's equations?
Are Maxwell's equations a routine part of the modern syllabus?Historically (1700s), d'Alembert used Newton's laws to create a mechanical wave equation, which can express the behavior of a guitar, piano, or violin string, the string in the video, with some adjustments, and sound, with some adjustments.
Then (1800s), Maxwell found symmetry in the known electromagnetic laws by adding some bits, and used the result (now called Maxwell's equations) to create electromagnetic wave equations.
Then (1900s), Bohr and de Broglie thought an electron might be some kind of wave, and Schrodinger sought a wave equation for an electron around a hydrogen atom (the simplest atom). What he found is appropriately called the Schrodinger equation. (Solutions of the Schrodinger equation are the atomic orbitals seen in chemistry classes.)
So historically, yes, Schrodinger's equation is inspired by both d'Alembert's mechanical wave equation and Maxwell's electromagnetic wave equations.
But, Maxwell's electromagnetic wave equations are not strictly required to understand Schrodinger's equation (quantum mechanics). Students first learn to work with the mechanical wave equation. This provides visuals allowing us to better tackle Maxwell's and Shrodinger's more abstract equations later on.
Mathematically, these are all forms of the wave equation, but used for different experimental observables: mechanical amplitude (d'Alembert's), field amplitude (Maxwell's), probability amplitude (Schrodinger's).
Definitely. Not just routine but mandatory. There's no way around them. Newton's, Maxwell's and Shrodinger's are the core of the modern physics syllabus. They neatly tie everything together. Then, people specialize. Physicists explore them in detail, while engineers use what they need to make useful things ASAP.Are Maxwell's equations a routine part of the modern syllabus?
Yes, QM and QFT can be derived from first principles by minimizing the path integral for the langrangian in accordance with calculus of variations.I can remember during my degree having to derive Maxwell's and Shrodinger's equations from first principles.
I think I know what you mean but since the introduction of Planck's constant is arbitrary, it isn't a derivation in the usual sense.Actually schrodingers eqn can be deprived from the Principle of Least Action. It is often introduced to undergrads in a cook book fashion. I have a good book on calculus of variations that shows the derivation.
I'd humbly disagree.To others, it would appear that you're from the past. Travelling near light speed and coming back to where you started would indeed bring you to the future.
Yes.... you return it is the future ...
1. In the year 2000, each of two twins is 30 years old.but they don't see you as a time traveller
That's impossible. (wormholes and quantum effects are for particles and some of their properties, not people.)Now if you can return back to your time ...
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