Can one theoretically travel faster than light relativistically?

Factual Questions
223

@tomh4040, can you address the fact that particles with short half lives moving at high speeds have longer half lives when measured from a different reference frame?

I’m sitting next to a particle accelerator and I have a pile of stuff with a half life of 0.1 seconds. I measure the stuff, and it indeed has a half life of a second. Then, I get that stuff moving really fast in the accelerator, and now I measure that it has a longer half life, in fact, longer by the amount predicted by the theory of relativity. Why do you think that is?

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I mean, we are living under a particle accelerator. Cosmic rays produce muons that would never make it anywhere near the surface to be detected if it were not for time dilation.

Detect a muon produced by cosmic rays on the surface, and you have proven relativity.

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I thought that was due to length contraction, but googling around, I’m apparently wrong. So, sure! Although the “alternative” physics site claims that’s it’s not due to relativity for some reason or another.

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Depends on the reference frame. In the earth reference frame, those muons get to the surface because their half-life clocks are running slow. In the muon reference frame, their clocks are fine - but the Earth’s surface is just closer than we think it is.

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Oh, that’s cool. This has been a most informative thread.

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You might find this interesting
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html

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Relativity is full of situations like that, where two observers agree on the bottom line (like whether the muons reach the surface or not), but disagree on the details of why. Another famous example is that observers in different reference frames can attribute the same effect to either electric or magnetic fields, a fact known since Maxwell (and which in fact is what inspired Einstein to come up with his theory of relativity).

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Wolfpup. The clocks do not have to be brought together to decide whether according to the theory of relativity, clock A is running faster than clock B, or whether clock B is running faster than clock A . Einstein said that these effects were and are real, so which clock is running slow, and why that one? You can invoke reference frames in your answer if you want to, the question does not need to explicitly mention them. You seem to insist on it though, so here it is. Two exactly similar clocks, A and B, are in uniform relative motion. The reference frames are implicit. I will make it explicit. There are two reference frames.

Tom.

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That’s true, they don’t. Bringing them together, however, clearly demonstrates the twin paradox, an important notion in relativity which shows that time dilation is truly “real” by the fact that one of the clocks has aged less than the other, namely the one that was switching reference frames.

No, there are an infinite number of reference frames. The one you choose determines how you see the clocks. The frames in which A is at rest, and the other one where B is at rest, are two useful ones for illustrative purposes. You could also imagine a reference frame where A and B are moving away from you in opposite directions at the same relative speed. From that one, both clocks are running at the same speed, although slower than in your own reference frame.

Again, for about the thousandth time, describe what reference frame you’re in – how you see the motion of the clocks – and then I can tell you which one is seen to run slower. If you don’t specify a reference frame, the question is meaningless. This is trivially obvious, so I will not discuss this further.

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Wolfpup, then as you acknowledge that my statement is true, answer the question as put.

Tom.

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Jesus H. Christ, man, again? Really? :roll_eyes:

I quote:

234

Can you please address the short-lived particles that live longer when moving at high speed?

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At least he was polite enough to tell me that he wasn’t going to read my answers to his questions anymore.

236

Seriously, you are not evening being the slightest bit sensible here.

You are demanding an answer in a Galilean world for a Relativistic question.

The manner in which you refuse to provide a reference frame for your question renders it meaningless in special relativity. You seem to be incapable of understanding this.

You ask a question of special relativity. You claim to understand special relativity. Everything in special relativity is with respect to a reference frame. Including questions. There are no meaningful questions that do not specify the reference frame.

Your question is:

  • In a relativistic universe I have two clocks moving at different velocities.
  • Can you tell me in a Galilean universe which one is running slower according to special relativity?

You can’t just switch universes mid stream.

Now sure, you think you live in a Galilean universe, and don’t seem to be able to comprehend that this might not actually be real. Yet you demand answers in it, and keep asserting that Einstein said the effects are real. But clearly, you are expecting that Einstein is claiming that the effect is real in a Galilean universe. Which he did not.

If you think you are posing a clever argument that proves special relativity is internally inconsistent you have failed. The question and answer can only be posed and evaluated in the same universe.

  • In a Galilean universe the clocks run at the same speed.
  • In a Galilean universe there is a universal time.

However:

  • In a relativistic universe the clocks run at different speeds according to the reference frame of the observer.
  • As special case of these reference frames, the clocks are slow relative to one another.
  • In a relativistic universe, unless you specify the reference frame a question is posed in, the question is incomplete and meaningless.

Now do us the polite thing, and when you pose a question, be clear about the question you are asking. If you are asking the question about special relativity, interpret the answer with respect to a relativistic universe, and stop implicitly moving the goalposts and shifting back to a Galilean universe to protest the impossibility.

The Galilean universe is a simple structure useful for simplified physics, physics of low energies, low speeds, and short times. It is very useful for this. But it isn’t real. It is a convenient illusion. When Einstein says an effect is real he isn’t talking about it being real in this simplified universe. He is talking about it being real in the actual real universe. Special relativity is itself a simplification of general relativity, but the effects we are asking about are not impacted by the simplification.

If your mind rejects the idea of a relativistic universe, well fine. That doesn’t make it any less true. Nor does stamping your feet and crying make the universe Galilean. Experimental evidence is quite clear. So far despite a century of ever more stringent testing, not a single crack has been found.

A Galilean universe has been comprehensively debunked. That is just life. It isn’t real, and objections to reality posed in a Galilean universe, are simply wrong.

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Actually, this isn’t true. There are a lot of things in relativity, called invariants, that don’t depend on reference frame. And most actual work in relativity is done using those invariants. The trick is just to find a way to frame questions in terms of those invariant quantities, instead of in terms of frame-dependent quantities.

Time, for instance, is a frame-dependent quantity. But what’s called “proper time” (which is actually the same thing as “proper distance”, or more generally “proper interval”) is not frame-dependent, and so it’s a lot easier to work with.

And in fact, this business of some quantities being frame-dependent and others being invariant isn’t even new to Einstein’s theory. The same thing happens in Galilean relativity. It’s just a matter of which quantities are the invariant ones that changes.

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Tony Rothman wrote an article on Einstein in the Nov.-Dec. issue of American Scientist. One paragraph is relevant here.

Physicists occasionally get mail, too. The most popular topics are “Einstein was wrong”; “Einstein was a fraud”; “Attached find my unified field theory correcting Einstein.” Sometimes UPS delivers the proposals as entire crates of self-published books on why relativity is incorrect. Those of us who receive such submissions tend to file them under “Prophets and Cosmic Visionaries” or “Delete,” or we may silently excuse ourselves by forwarding the submissions of one author to another, and vice versa, allowing them to debate matters intelligently among themselves.

BTW, Tom, why haven’t you answered any of the many questions I’ve politely asked?

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That’s a real time saver, in any reference frame.

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Yeah, I do know that. I was debating with myself whether to go down that path or not. I probably should have been a bit clearer but it was written in haste.

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FWIW quantum tunneling may be superluminal. That’s a long way from a rocket going over light speed but recent experiments suggest it is possible at least at the quantum level.

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You have to be really careful when you’re defining speeds of waves, including quantum mechanical waves. Wavefronts often travel faster than the information they carry.