Can one theoretically travel faster than light relativistically?

[tomh4040]

Francis, I am asking the same question because I am not getting an answer, for the most part, just evasions. I am told I am not using reference frames for instance. The question does not need them. The answer might need them. I have been told that one clock appears to run slower than the other, but that is not what Einstein said. He said they were real effects. Therefore clock A runs slower than clock B while clock B runs slower than clock A. This is not possible. The question therefore stands unanswered.

Tom Hollings

[Francis_Vaughan]

Seriously, your argument is this.

1. Special Relativity says that the two clocks both see one another as slower.
2. If Special Relativity is false this is impossible.
3. I don’t believe in Special Relativity.
4. It is thus impossible.
5. Thus Special Relativity is false.

You can’t just keep cycling around this stupid loop of ill formed logic. Basically you refuse to consider that special relativity might be right, and just keep yelling - it is impossible. Understand that Special Relativity is about the nature of time, and it absolutely allows for the clocks to both see one another as slow.

One is reminded of a famous quote.
Mr Spock - His pattern indicates two dimensional thinking.

@tomh4040

I am told I am not using reference frames for instance. The question does not need them.

Really. It does not need them? You are asking about special relativity and you don’t need to consider reference frames? You are going to have to justify that in excruciating depth. Reminder, clocks A and B are moving at different speeds, they are by definition in different reference frames.

@tomh4040

This is not possible.

Why. You refuse to answer why. Why do you refuse?

[k9bfriender]

@tomh4040

I am not using a third reference frame, I don’t know what makes you say that.

I say that because that is the only way that your question actually makes any sense.

Thought experiment for you. You and I are standing next to each other. You start moving north at 15 mph, I start moving east at 20mph. Which one of us is further from the other? Which one of us is moving away from the other faster?

That is the question that you are asking, and demanding an answer for. As my question to you involves only newtonian mechanics, and simple math, it should be easy for you to answer.

You may say that this question is nonsensical, but your question is simply nonsensical, as nonsensical as asking which one of us is further away from the other, or which one of is moving away faster from the other.

Tell you what, with your clocks, tell me which is further from the other, and/or which is moving away from the other faster, and I’ll tell you which one is ticking more slowly.

@tomh4040

I want to know according to the rules of relativity which clock is running slow, and why that one.

Running slow(ly), compared to what?

A little bit contrary to what some have said, there is a more or less unique reference frame. It’s not special or privileged, but it is at least one that everyone (within a galaxy, anyway) could theoretically agree upon. And that is being at rest WRT to the CMB.

If you are measuring the clocks WRT that reference frame, or your own for that matter, then your question makes sense and can be answered. If you are only measuring between the two, then it makes as much sense as asking which one is further from the other, or which is moving faster than the other.

So, are you invoking a third reference frame, or are you simply demanding an answer to a nonsensical question? If the former, great, you’ve learned something. If the latter, then you will never learn anything, and will be stuck with the inferior and incorrect knowledge that will never serve you in any way other than to annoy those around you.

[wolfpup]

@Mangetout

The trouble with the small/far away analogy is that there exists the temptation to invoke a privileged referenced frame in which we can measure that neither cow is actually small.

But that’s just the trouble with analogies - they are by definition different from the thing they try to explain, and nobody should expect that the analogy holds when extended beyond the stated constraints.

Of course. The purpose of my intentionally very silly cow analogy was just to show how trivially silly this objection to relativistic time dilation was. To wit,

@tomh4040

Suppose the relative velocity is 161,000 miles a second. Then, according to the theory, the time according to one clock (A, say) between the readings 1.0 and 2.0 o’clock of B is 2 hrs., so that A works twice as fast as B.

Correct, from the frame of reference of “A”.

@tomh4040

But, similarly, the theory requires that the time according to B between the readings 1.0 and 2.0 o’clock of A is 2 hrs., so that B works twice as fast as A.

Correct, from the frame of reference of “B”.

@tomh4040

These results are clearly contradictory.

Wrong. There is no possible frame of reference in which this alleged “contradiction” would be observed. If you claim there is, please describe it. How is it moving relative to the two clocks?

[Mangetout]

I’m predicting next we’re going to have ‘but that’s impossible! When I walk to the shops, my clocks don’t change!’

[Mangetout]

Despite what I said earlier about analogies, let’s try this one:

Me and my friend are standing on a vast, level, smooth, featureless plain on planet Earth - we agree to walk away from each other, occasionally looking backwards to check on each others’ progress. We have walkie-talkies and powerful binoculars.

After a long while walking, I observe that my friend is only visible from the waist up - he’s walked down over the curve of the earth and from where I’m standing, he’s clearly in position that is downhill from me.
I call him on the radio to let him know about this and he argues “No, I’m on the level and you have gone over the curve of the Earth, and you are standing in a position that is downhill from me”

Which one of us is actually lower?

[Chronos]

If we’re going with analogies, the rulers-at-an-angle one really is the best, since it’s the closest you can get to the twin paradox without involving that counterintuitive minus sign in the metric. The relationship between the two rulers isn’t just “like” a Lorentz transformation-- It actually is a Lorentz transformation.

[Andy_L]

Unfortunately, our current interlocutor seems allergic to the ruler analogy

[Half_Man_Half_Wit]

@tomh4040

Therefore clock A runs slower than clock B while clock B runs slower than clock A. This is not possible.

Perhaps if analogies don’t help, let’s try pictures! Suppose the denizens of Plato’s cave have only ever seen shadows on the wall. Of these, they can take two measurements: height and width.

In the image, Arrow A₁ has a height of 6, and a width of 1, while A₂ has a height of 8 and a width of 7. A₂ therefore has a greater height than A₁. Furthermore, the cave-dwellers hold the following to be true:

Of two objects of unequal height, one (and only one) is always higher than the other.

But now suppose, perhaps due to some looseness of the restraints, one caveperson finds out that they can tilt their head to some degree. To their astonishment, they will find that now, all of a sudden, the heights and widths of objects—thought heretofore constants by all of cavepeople science—begin to change! Moreover, if they tilt their head far enough, the relative heights of objects may change, too—what was of greater height before, now is of lesser!

Now, arrow A₁ has a height of (about) 4.3, while A₂ has a height of 2.5. Thus, now, A₁ is higher than A₂!

Then, suppose they try to tell their spelunked compatriots of their findings. One pipes up, and says—“If what you say is true, then this would mean that arrow A₁ is shorter than A₂, and A₂ is shorter than A₁. But this is not possible.”

This is the argument you’re making. This is also why everybody is telling you that you’re assuming a third frame of reference: it is the case that in one particular frame (that is, at one particular tilt of the head), arrow A₁ can’t be both shorter and longer than A₂. But the claim that is being made is that there is one frame (i. e. head-tilt) where A₁ is shorter than A₂, and another where things are the other way around—which is trivially possible.

The problem is that we, and the cave-people, are used to thinking of two parts of a unified quantity—width and height as parts of total length in the caver’s example, and time and space as parts of the space-time interval—as separate quantities; but they’re not, but rather, they’re intermixed by a particular transformation (a rotation for the cavites, a Lorentz transformation for us). Total length, for the caveys, is invariant; space-time interval for us. But neither time nor distance / length are, on their own.

[Francis_Vaughan]

The problem is deeper.
Relativity deniers won’t accept special relativity as an act of faith.

The argument we have above is:

1. I don’t accept special relativity is true.
2. Therefore I don’t need to consider different frames of reference.
3. I calculated what special relativity says, even though those calculations implicitly include two frames of reference.
4. I demand that you interpret those results in a system that does not use different frames of reference, ie interpret special relativity in a system that contradicts special relativity.

so:

1. Demands that you provide a contradiction.
2. Assumes that relativity is both true and not true.
3. Claims anything you say proves that relativity is false.
4. Therefore assumption that relativity is false is true, and the argument is valid.

I am suspecting that somewhere out there there in the Internet there is a clickbait meme that goes along the lines of “Special relativity proponents can’t answer this simple question!”

It really is a problem when the education system spits out people who have such poor logic skills. This is everyday living level of survival logic.

[LiterateRaven]

Long time reader, though almost never comment. I am incredibly impressed with the mutual respect shown. On many of the other threads (and I am not referring to the pit), this would have devolved very early.
Respect for the patience shown.
Also, as someone without an advanced Math’s degree (Mech Eng but no further), I am impressed with the willingness to explain complicated concepts in ways that laymen can approach.

The two angled ruler analogy was where it clicked for me. The answer to the question is that the effect is ‘real’ from each reference frame. That is what Einstein seems to mean.

On the other hand, from a single reference frame, lets say Earth, if both objects are moving in opposite directions from us, the one moving faster will have the clock that is slower. The other has the clock that is faster. Done.
They are not both faster than the other when measured from earth.

Francis, excellent. Andy, great analogy. Tom, I appreciate the perseverance.

[tomh4040]

The favourite trick of relativists again HMHW. It is my question (or rather prof Dingle’s) which I want answering. Answer it any way you want, use reference frames or not as you see fit. I have been accused of ignoring RFs, but the question does not require them - the answer may do.

Tom Hollings

[Mangetout]

The question has been answered a dozen times already in just this thread. You just don’t like the answer.

[Francis_Vaughan]

@tomh4040

I have been accused of ignoring RFs, but the question does not require them - the answer may do.

If you go back to your initial question, where you didn’t provide calculations of the effect, you may pose the question without RFs, but you are asking for an answer in terms of special relativity. By definition special relativity requires reference frames if any question involves elements that are moving at different velocities. That is what special relativity is. So asking what special relativity provides as an answer requires that you admit the use of different reference frames. Dismissing an answer that includes reference frames as invalid, not answering the question, or impossible, is simply demanding an answer about special relativity that is explicitly demanding that the answer does not include special relativity. The question is thus internally inconsistent and a non-question.

Demanding that the answer is what is “really” happening is tainted in exactly the same way. You are implicitly defining “real” as something that cannot include special relativity. So you are again creating a contradiction in your won question and it becomes a non-question.

You can’t come to questions about special relativity with the mindset that it is ab-initio invalid. Ask a question about the nature of special relativity, fine, but accept that the answer must, by definition, be cast in terms of that theory. You can’t simply dismiss the answer as invalid or impossible simply because you don’t like, or can’t comprehend, the answer you are getting. And that is what has been happening so far.

[tomh4040]

Two points LR. You said :- “The two angled ruler analogy was where it clicked for me. The answer to the question is that the effect is ‘real’ from each reference frame. That is what Einstein seems to mean.”.Einstein said these effects were or are real. You have cited an example with three reference frames, the question had implicitly only two, and Einstein never used three.
You have also done the relativist trick of changing the question to one of your own. Not allowed. Answer the question posed.
Tom Hollings.

[Francis_Vaughan]

@tomh4040

You have cited an example with three reference frames, the question had implicitly only two, and Einstein never used three.
You have also done the relativist trick of changing the question to one of your own. Not allowed. Answer the question posed.

He did. He added the third reference frame as an afterthought. The discussion about the Earth reference frame is nothing to do with your question, but just an idle observation made after answering your question.

[Andy_L]

@LiterateRaven

Andy, great analogy.

Thanks. The analogy is not unique to me of course.

[tomh4040]

I’m ashamed of you Francis, here we were having a (possibly heated) conversation/discussion, when you start throwing in assumptions and getting very close to ad hominem attacks. However I will answer.
Point 1 - I agree.
2. True. The question doesn’t need them, although two clocks in uniform translation implies two RFs. However the answer may need them.
3. Nonsense, that is for you to do.
4 Nonsense. I have said that the answer can use two RFs.
Tom.

[Francis_Vaughan]

@tomh4040

However I will answer.
Point 1 - I agree.

If you want to progress you need to at least be open to the idea that it is valid.

2. True. The question doesn’t need them, although two clocks in uniform translation implies two RFs. However the answer may need them.

As I point out, it they are moving at different directions special relativity demands that we consider a reference frame for each element. Whilst you can pose the question without naming the RFs, if you invoke SR, you have implicitly agreed that they will be used.

3. Nonsense, that is for you to do.

This was in reference to your question where you posed ready calculated results.

4 Nonsense. I have said that the answer can use two RFs.

Excellent.
In the first reference frame (that of clock A) clock B appears to run slow.
In the second reference frame (that of clock B) clock A appears to run slow.

Exactly what we have been saying. Seems you should be happy with the answer now.

[tomh4040]

Francis, “seems to run slow” is not actually running slow. Einstein said these effects were real. Therefore according to the theory, clock A runs slower than clock B and clock B runs slower than clock A. That is a contradiction.

Tom.