You were absolutely adamant that this was impossible earlier in the thread. The interaction between particles is mediated by electromagnetics, and that travels at the speed of light you said, and thus it is impossible to create an accelerator using electromagnetic forces that can make a particle go faster than light. You were quite clear that this is why we never see accelerators make particles go faster than light.
The simple logical fallacies that permeate all these relativity-denial arguments never cease to amaze me. The two statements quoted above are in direct contradiction. This argument is no different from the one that says if you have a spaceship traveling close to light speed which then fires a rocket that is itself capable of traveling a substantial fraction of light speed, then “obviously” the rocket will exceed the speed of light, since “obviously” velocities are additive. QED.
Here again is the Lorentz factor which applies to all relativistic phenomena like length contraction, time dilation, momentum, and kinetic energy:
\LARGE\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}
What happens to the value of the Lorentz factor as v approaches c? What is its value when v = c? What about when v > c?
You guys are missing the lede.
I’m trying to get Tom to answer direct questions, which of course he can’t so he never does, so I was being polite.
If I were being impolite, I might wonder why someone who is not a relativist and thinks that relativity is wrong is quoting a source that assures us that the [imaginary] behavior being referenced definitely does not violate SR [special relativity] and starts by using SR to explain what [nonsensical] behavior an electron will exhibit.
If I were even less polite, I would go to that source and link to the page labeled Faster Than Light Behavior. That page touches on all the things talked about here, including the muons. It says:
I would like to use this experiment as evidence of the existence of FTL speeds. The argument runs as follows:
- Muons moving at 0.995 c had an observed half life 10 times greater than muons at rest.
- This exactly corresponds to the prediction of SR that they should experience a time dilation of factor 10 at that speed, and this proves time dilation has occurred.
- However time dilation is impossible because there are no fixed frames of reference and it is not possible to say which muons are ‘at rest’ and which are ‘in motion’. See this earlier chapter for a full explanation.
- Therefore the most likely explanation for the observed degree of decay is that the calculation of speed was wrong and the muons were in fact travelling ten times the speed of light .
- Thus the muon experiment proves FTL travel.
A finer example of circular reasoning would be difficult to find outside of a merry-go-round.
At this point I’m basically treading a line between having fun with this and providing actual useful information for other readers. I don’t expect TomH to ever answer serious questions or admit to comprehending anything.
The point of providing the Lorentz factor yet again (this time formatted with MathJax so it’s crystal-clear) is that it’s a very succinct way of conveying the empirically proven consequences of relativity. The answers to my last two rhetorical questions, of course, are that when v = c the Lorentz factor becomes undefined – it’s a divide-by-zero error, and if v exceeds c, the corresponding Lorentz factor involves an imaginary number. Thus either the math is wrong (and a century of scientific observations demonstrate that the math is exactly right) or one must conclude that those conditions are physically impossible.
The real implications of relativity theory are mind-bendingly strange, but that turns out to be because the nature of space and time, the nature of simultaneity and causality, are also mind-bendingly strange and non-intuitive. Relativity deniers appear to lack the imagination to acknowledge the empirical facts, which is why their relativity-denying explanations are always so mundane and unimaginative that they could be demolished by a bright 12-year-old. As a matter of fact a group of high school students a while ago demonstrated the reality of the Lorentz transformation (not that it needed to be demonstrated, but it was a cool science project) in a beautiful collaboration with CERN, which briefly made available to them the most powerful particle accelerator in the world to conduct their little science project. What a great way to inspire future scientists!
While I’m here and still have the patience, here’s another analogy directly relevant to the two-clock argument. Say I throw a baseball at 30 mph. This speed can be demonstrated by observing distance traveled, clocked by a radar gun, and felt by the impact in a catcher’s mitt. There is no doubt about the “real” speed.
But say I throw the same ball inside a train that is moving at 70 mph. How fast is the ball “really” traveling now? By all the criteria previously mentioned (and by the relativistic principle of Lorentz invariance) it’s still moving at 30 mph. The radar in the train car confirms it, and so does the catcher traveling with me, standing at the other end of the car.
But to an observer standing in a cow pasture as the train goes by, the ball can be measured as traveling at 100 mph (if it’s thrown in the direction the train is moving). So what is its “real” velocity? By the example above, it would seem to be 30 mph. But suppose the pitcher is now on the roof of the car, and throws it forward. He ducks, because there is an underpass coming up. Ignoring air resistance, that ball will smash into the underpass at fully 100 mph.
How about that? The ball is simultaneously traveling at 30 mph and also at 100 mph, which is impossible. My brain hurts just thinking about it.
Exactly. We should run a sweep on how many posts it takes for him to revert to “but that is impossible.” as the core argument.
This does underline the fundamental problem the Galilean adherent’s viewpoint has. They cannot grok the idea that time is treated in the same geometric framework as space, and that spacetime is an actual real thing. Their reality is the dualistic space with things happening in time, and despite continual claims that they understand relativity and have worked out the flaws, they have clearly never understood relativity. All the geometric examples earlier slide past uncomprehended.
This is probably a flaw in some of the arguments we have presented. We have assumed that the idea that space and time must be treated together is understood, and thus the geometric understanding of Lorentz transforms is grasped as a valid thing.
Tom just quotes the Lorentz forms randomly, sometimes claiming their validity in an isolated case, and denying they can ever be valid in others. It makes a good example to the curious reader of the incoherent arguments that come from the alternate physics crowd. The entire alternatephysics web site is an amazing morass of handwaving, and totally misunderstood physics. The entire chapter on GPS contains so many errors and misunderstandings of how GPS works, errors that one wonders if the author bothered to research anything at all.
I’m also trying to get Tom to answer questions. I don’t actually think it’s worth trying to discuss relativity directly, as that’s not even the problem - it would be a problem further along the line, but there are more fundamental issues confounding this discussion; they are:
- The question of how the universe can legitimately contain two or more apparently contradictory observational viewpoints which are real, and in fact still consistent.
- The matter of contaminating the logic of a thought experiment about reference frames by inadvertently injecting an additional one that is not defined.
Well, slightly less, due to relativistic effects…
Francis, this quote is true :-"…it is impossible to create an accelerator using electromagnetic forces that can make a particle go faster than light…"
That is a correct but unqualified statement because I thought it was understood what was meant. An EM force cannot push a particle past light speed with respect to the origin of that force. Re-read my analogy with the ice hockey players, but have each one move at eg 10 mph faster than the player behind him. That will give you the general picture.
Particle A has a force field which repels particle B. Particle B cannot exceed light speed (300,000,000 m/s) with respect to particle A so the maximum speed can be assumed to be 299,0000,000 m/s WRT particle A. Particle B has a force field which repels particle C to 299,000,000 m/s. Particle C cannot exceed light speed WRT particle B, but WRT particle A, its speed is 598,000,000 . Please don’t tell me about relative addition of velocities.
Tom.
Look, I drop an apple and it falls to the ground. Here’s where I demonstrate that it’s because of electromagnetic forces. Please don’t tell me about gravity.
No the statements are not contradictory. Yes your rocket analogy is correct.
Apply the Lorentz transformations to the reference frame where the force originates, and v will never approach c .
Please show us the experimental evidence that a speed of 598,000,000 m/s occurs.
OK, this is getting boring now because you’re going around in circles, steadfastly ignoring attempts to educate you, ignoring valid questions, and repeating the same nonsense over and over again.
The general picture I get is that you still don’t understand how particle accelerators work, despite having had it explained to you about three times. There are no miniature hockey players swinging at protons or other subatomic particles in an accelerator; in fact, nothing is moving at all except the particles themselves, propelled by precisely timed oscillating electromagnetic fields. This virtual wave can move at any arbitrary “speed” faster than light, since neither matter nor information is being transferred. It’s equivalent to having a string of Christmas tree lights strung between here and Mars, preprogrammed so that the flashes appear to be moving faster than light.
Your understanding of particle accelerators, and hence your analogy, is nonsensical. Ironically, a bunch of high school students in the UK understood it far better than you, and won a competition to get access to the CERN accelerator to demonstrate the reality of the Lorentz transformation, and its inherent proof that no material substance can move at or faster than the speed of light, because it leads to mathematical impossibilities.
The statements are absolutely contradictory. The series of multiple electrons is just an intentional obfuscation by whoever invented this silly thought experiment. It doesn’t matter if C is moving at less than light speed relative to B; if it’s moving faster than light with respect to A, or its point of origin – which is the whole point of what this sorry little tale is supposed to “prove” – then it has violated relativity; that is, it can no longer be described by a Lorentz transformation, and hence is physically impossible.
As @Francis_Vaughan previously said, you seem to like to quote the Lorentz transformation more or less at random, whenever it seems to suit you, despite the fact that this one formula alone completely invalidates absolutely everything you’ve been saying from the very beginning of this thread. In this case, “where the force originates” is at the rocket motor, which is moving and accelerating along with the ship. So of course v will never approach c; v will in fact always be a constant, zero. Or the speed of the rocket exhaust if you use that as a frame of reference. The v that is relevant is the one observed from a frame of reference where the rocket is seen to be accelerating under a constant thrust, and we can observe what happens when the observed v begins to approach c. The Lorentz factor tells us exactly what happens.
I’m saddened that tom never came back to discuss the particles’ half-lives in accelerators.
Has he run off again?
I don’t know - let’s measure how fast his clock is going.
Clever.
I like it. 
This thread may have exceeded his own half-life.
Wolfpup, OK, this is getting boring now because you’re going around in circles, steadfastly ignoring attempts to educate you, ignoring valid questions, and repeating the same nonsense over and over again (this is to all, not just to Wolfpup).
Tom Hollings
Speaking of ignoring valid questions, I’m still waiting on your response to my question about particles in an accelerator.
And once you’ve responded to RitterSport, would you update your webpage with your understanding of the train/lightning-thought experiment now that I’ve explained to you that simultaneity within either inertial reference frame isn’t a relevant issue?