I feel like this is the point that tomh is missing – the theory of relativity has been shown to be accurate in experiment after experiment, real world situation after real world situation, over and over again. If the formulas were wrong (or, we just ignored the effects of relativity), GPS just wouldn’t work.
@tomh4040, when you were asked for formulas, it wasn’t just for an alternative set of Newtonian formulas – it was a request for a different set of formulas that actually explain the observed universe.
Good example. If a person standing by the train is blowing a whistle, and so is the train, while the train is approaching, both the stander and a person on the train will hear the other person’s whistle have a higher frequency. This is not a paradox
I think that tomh4040 also claimed that the particles in particle accelerators do not gain mass as they become relativistic. It’s hard to tell exactly what the claims are in some of his posts, but I think that was what he said in refutation.
Now, obviously, they don’t “gain mass”, but they do act as though they have more mass. If you multiplied the mass of a particle by its velocity, not taking into account relativity, the energy that you would calculate would be far lower than the actual observed energy in collisions.
If it were just a matter of dumping energy into a particle, and not taking into account the relativistic effects that tomh4040 is discarding, then it would be trivial to accelerate a particle to well beyond the speed of light.
As a 30th century particle with powerful friends, I can start out on earth and then get very close to c, while going to the far side of the galaxy, by application of enormous energy. After accelerating for a while, I am just about to the point where the rest of the trip will be, within the limits of my perception, instantaneous. Except, now, the particle (if I can assume panpsychism here) decides to go in the opposite direction. Won’t this take an enormous amount of energy to decelerate with respect to earth, and then shoot off again in the opposite direction? And won’t that take particle me, from my own point of view, lots of time? Maybe I can just change direction without slowing down with respect to earth, but it seems to me that when you are going very fast and have mass, it is going to take a lot of energy to change direction. Is energy not connected to time here?
I gather that from the point of view of a photon wave, you get everywhere right away. But it feels wrong to me that as I get near c, stuff in the rearview mirror is almost out of reach, but if I ever caught up to my friend the photon, it would be right where we are.
I am only asking for an orthodox physics response here!
It’s more than that. @tomh4040 said that a rocket ship carrying enough fuel can exceed the speed of light. That must be calculable. I was asking for the formula that tells us how much faster than light the rocket will travel and under what circumstances. And since light speed is found in zillions of formulas, I’m asking for the correction to all those formulas to tell us what else would happen if light speed were increased.
And these formulas have to be exact. They cannot be “For all intents and purposes” as he said; you can’t do that even in engineering, let alone theoretical physics.
I’ll just finish off on that note. The point is this has been proven and over and over and over again in particle accelerators, and particle behaviour exactly matches the predictions of special relativity; specifically, the observed lifetime of short-lived particles increases with their relativistic speed, and the kinetic energy of accelerated particles increases exactly as per the graph below, where “speed” is in units of c, so that 1 = the speed of light.
This is indisputable.
For that reason, Newtonian concepts of momentum and kinetic energy are only approximations that have to be discarded when velocity v becomes an appreciable percentage of c.
Thus Newtoniam momentum
p = mv
becomes
p = γm0v
where m0 is the rest mass, and γ is the Lorentz factor 1/(SQRT(1-(v2/c2))
Similarly, the correct formula for kinetic energy when v is sufficiently large for relativistic effects to become evident reduces to:
Ek = (γ-1)m0c2
Note that this simply applies the Lorentz factor to the rest mass, and gives net kinetic energy by subtracting the energy of the rest mass (m0c2). The total relativistic energy of a moving body, the total of rest energy and kinetic energy, is just simply γm0c2. And even more simply, when an object is not moving at all in the observer’s frame of reference, the Lorentz factor is 1 and its total energy is the famous E = mc2.
These – and in particular the phenomenon illustrated in the graph below – are among the most empirically demonstrated facts in all of physics.
And that’s about all there is to say on the matter.
Andy L, Einstein said that these effects are real, not appearances. If they are just appearances, the whole of SRT, and by extension GRT is useless. Your answer is therefore invalid.
Your analogy with the rulers is wrong. Draw a line at 6"on ruler1 and it intersects the other ruler(2) at 7". Draw a line from ruler 2 at 6" and it intersects ruler1 at 5". Don’t just theorise - do it!
It is important to note that, from your perspective, riding along with the near lightspeed particle time seems to pass perfectly normally. Your wristwatch will tick by at 1 second per second…same as it did on earth.
However, the universe will look a lot smaller to you since length contracts. From your perspective the Andromeda galaxy you are travelling towards looks a whole lot closer.
Adding in acceleration (which includes deceleration) complicates things a lot. Indeed, that is what resolves things like the Twin Paradox. For this, though, I am just assuming a constant velocity particle traveling at near light speed. Other posters here will be able to better answer how acceleration complicates things.
But, if you really want to fry your brain, in a manner of speaking everything moves at light speed. Relativity says time and space are not two things but one thing…spacetime. You move through time and you move through space but it is one thing. The faster you move through space the slower you move through time and vice-versa. If we add those two vectors together we always get the same answer. This is why light always seems to travel at the same speed for any observer regardless of their motion.
Which is it - did Einstein discuss this case or not?
Wrong again. Notice the word “perpendicular” and think very carefully about what it means. Then try it. Once you figure out how you got that simple example wrong, we can discuss the difference between “real” and “appearance”
I am glad that you mentioned GPS. It is a falsehood put about by relatavists that it wouldn’t work without relativity being take into account. Relativity plays no part in GPS operation. There is an excellent web site which explains it. It is called a crank web site by relativists, and its address will no doubt be removed by the censors - sorry moderators. http://www.alternativephysics.org/book/GPSmythology.htm
So you keep saying, despite numerous attempts to set you straight. I have to say that the reality is the exact opposite of your statement. Special relativity is beautifully self-consistent and an extremely elegant description of the nature of spacetime.
The very simple formulas I gave upthread are nevertheless sufficient to illustrate how relativistic physics is essentially identical to Newtonian physics for small values of v, and then begins to dramatically depart as v gets closer to c. These have been empirically proven correct many many times. May I suggest that arguing this point incessantly is rather a waste of your time, which you could use instead to try to actually understand the relevant science.
That website doesn’t correctly explain how GPS corrects for relativity. It’s not done by having a perfect clock in your GPS receiver. It’s done by taking relativity into account and adjusting the time on board. Basically, GPS satellites fly around announcing what time it is. Since their position is known, then by calculating the difference in reported time received from each satellite, you know how far you are from each. The receiver gets its time from the satellites themselves.
Or, maybe the time differences are not caused by relativity but by Big Cesium!! If anyone would censor that website, it’s going to be Big Cesium. Don’t mess with Big Cesium!
If I could travel at the speed of light (pretend I can), and length contracts in the direction I am traveling, when I hit light speed will the universe appear as a point, a 1D line or a 2D plane or something else?
