Reword this. Does run slower as seen from each reference frame.
The words “appears” and “seems” are not interchangeable in this context. By doing so, you have attempted to change the answer given to be one that you can disagree with.
Yes, in one reference frame, clock A runs faster than clock B. In another reference frame, clock B runs faster than clock A.
In fact, there’d be many reference frames in which clock A runs faster than B, and many where clock B runs faster than A.
There’d be a smaller number, but still quite a few, reference frames in which both are running at the same speed.
No there isn’t. Only if you can find a single reference frame where clock A is running faster than B, while clock B runs faster than A is there a contradiction.
Can you identify this reference frame?
Yeah, the words “appears” and “seems” implies a third and/or preferred frame of reference despite any protestations to the contrary.
Bit sloppy, mathematically.
How about: “as observed by”.
That is what I intended by “appears.”
We’re assuming that clocks always run at 1 second per second in their own reference frame. Clocks will always appear/be observed to/seem to run faster or slower to observers in other reference frames. It’s baked into the concept of relativity.
The objection by Tom ignores the reality of relativity.
While in the same RF, the clocks must run at the same speed. When in different RFs, they appear to run at different speeds. Note - they do not actually run at different speeds.
You are bantering semantics : appear = come into sight or become noticeable. Seems = give the impression of. They seem pretty close to me. Or if you prefer, They appear pretty close to me.
Tom.
To someone in another RF, they do. That’s the whole point. Observations = reality.
This is false. Extremely short-lived particles in particle accelerators moving at high speed last longer than they should from our stationary reference frame. A particle with a half second half life at rest will have a half life that’s longer than a half second from our reference frame when zipping around a particle accelerator.
Relativity is more than just time dilation. It makes many predictions. Every time scientists try a new experiment to test Einstein, they wind up with results that agree completely and exactly.
Three Experiments That Show Relativity Is Real
Optical Clocks
The best-known effect of relativity is probably the slowing of time by motion. An observer watching a clock of some sort go past will see that clock “ticking” more slowly than an identical clock at rest with respect to the observer. This goes both ways, as well-- a second observer traveling along with the moving clock will look back and see the first observer’s clock in the lab “ticking” too slowly. …My favorite test, though, is at the low speed end, using ultra-precise atomic clocks based on aluminum ions. … Dave Wineland’s group at NIST has built two nearly identical clocks of this type, and comparing the two clearly shows the relativistic effect of motion at human speed.
When they compare the rate at which the moving ion “ticks” to the rate at which the stationary clock “ticks,” they find a small difference. Their measurements, shown in the graph above, agree beautifully with the prediction of special relativity.
They can do something even cooler with their two identical clocks, though: they can raise one to a slightly higher elevation than the other. General relativity predicts that gravity also affects time, and that a clock near a massive object like the Earth will “tick” more slowly than one at higher elevation. They placed one of their optical tables on hydraulic jacks and boosted it above the other by about a foot (33cm, if you want SI units), and clearly see the difference in repeated measurements:
Visible Astronomy
Einstein was really catapulted to international fame after the Eddington eclipse expedition of 1919 verified his prediction for the bending of light by gravity.Observing such “gravitational lensing” would require a really fortuitous alignment of objects on the sky, but the universe is “vastly, hugely, mind-bogglingly big,” in the immortal words of Douglas Adams, and such alignments do, in fact, exist.
Radio Astronomy
Such a system of huge, rapidly moving objects ought to produce gravitational waves, a stretching and compression of spacetime predicted by Einstein’s general relativity. These gravitational waves, in turn, should carry off some energy, causing the orbit of the pulsar to decay over time, as the two pulsars spiral together toward an eventual collision. Observations over a period of many years, shown in the graph above, agree beautifully with the prediction of general relativity for how the orbit ought to change due to this energy loss. These observations earned Hulse and Taylor the 1993 Nobel Prize in Physics.
If three conceptually separate types of confirmation, including the one we’ve been talking about here, have been made and agreed upon by international bodies, then your theory must either agree with relativity (whether you understand that it does or not) or give observably different results in a measurement. If not the former, then what results does your theory predict and what experiments have been done that shows those results?
Yeah, but never mind that for now. The answer has been given many times in this thread; you don’t understand it—which is perfectly OK, obviously. It is a deeply counterintuitive result. Hence, I’m trying to figure out where we loose you—thus my scenario above. So let’s take Dingle’s question:
My conclusion is that the theory must be false, since it demands that each of two clocks works faster than the other, which is impossible. Otherwise, something must determine which clock really works the faster.
Let’s adapt it to the cave-scenario:
My conclusion is that the theory must be false, since it demands that each of two arrows has a greater height than the other, which is impossible. Otherwise, something must determine which arrow really is higher.
What would you tell somebody who made the above remark in relation to the cave-setting? This is an honest, good-faith question, by the way—I’m genuinely interested in your reply.
Me, I would say that height (and width) are only meaningful given a certain ‘head-tilt’, a certain orientation of the axes. Given such an orientation, they’re perfectly objective, real quantities; without one, however, it makes no sense to speak of either—just in the same way that it makes no sense to speak of the color of ‘the car’, without specifying whether you’re talking about Smith’s or Jones’ car. You wouldn’t say that a statement like ‘Smith’s car is blue, while Jones’ car is red’ is contradictory, since ‘the car’ can’t be both blue and red—‘the car’ is simply an underspecified term with no unique point of reference.
Likewise, when one speaks of ‘the height of the arrow’, one isn’t really referring to anything in particular—the arrow has no unique height, no ‘the height’, it has a height in a given orientation (of the head / the axes). Without specifying that orientation, any reference to the arrow’s height is meaningless.
Hence, saying ‘each of the two arrows has a greater height than the other’, is already meaningless—it’s not actually talking about any well-defined quantity. Meaningful would be a statement of the form: “In this orientation of the axes, A1 has a greater height than A2, while in that orientation, A2 has a greater height”. And given each of these orientations, each arrow’s height is a perfectly well-defined, real quantity—but without a specification of the orienation, there simply is no meaning to speaking about each arrow’s height.
What do you think of the above? Does this make sense to you? Or would you hold, with Cave-Dingle, that ‘something must determine which arrow really is higher’?
It is foundational to special relativity, and empirically verified many times, that there is no such thing as absolute motion or absolute time. Measurements of velocity and time crucially depend on the frames of reference involved. No concept of time or motion can be meaningfully discussed except with respect to a specified frame of reference. Your question has been answered many times: each clock runs slow with respect to the other’s frame of reference. My question to you, however, was never answered: in what frame of reference would the two clocks be observed to be “contradictory”? (There is no such reference frame, hence there is no contradiction.)
They absolutely DO run at different speeds from any frame of reference where they are moving at different speeds. Proof: extended decay time of short-lived particles in particle accelerators. Also, the twin paradox for non-symmetrical frames.
I’m no longer going to bother arguing with Tom about the clock question since the answer has been given to him more than a dozen times in several different ways and he just keeps repeating the same nonsense. But I was curious about this, and though there probably is such a clickbait meme somewhere, the clock “impossibility” example that Tom keeps quoting is taken word for word from the book Science at the Crossroads, by the crackpot Herbert Dingle. Dingle had an interesting history of contrarian thinking even before he retired and turned his energies to trying to refute special relativity, which he did in ways that were not only uninformed and illogical, but sometimes self-contradictory. He initially denied that the twin paradox could possibly be true, and wrote a letter to the editor of Nature to that effect. On receipt of a barrage of critical responses from actual physicists, he then changed his mind, but alas, not for the better. He decided, instead, to double down and declare that all of special relativity must be false, thus following in the footsteps of a handful of other philosophers and scientists who, in what should have been their golden years of retirement, appeared to descend into a kind of combative senility, like Freeman Dyson taking up the mantle of climate change denial.
Unable to get any of his thinking published, Dingle continued writing letters to the editor and eventually, in frustration, produced the above-mentioned book. He rejected all criticism of the book and of his views, eventually developing the paranoid delusion that the whole of the scientific world was against him, saying “a proof that Einstein’s special theory of relativity is false has been advanced; and ignored, evaded, suppressed and, indeed, treated in every possible way except that of answering it, by the whole scientific world.” He also began warning of some unspecified “calamity” from “modern atomic experiments” due to their reliance on the principles of relativity.
In short, Dingle was a classic crackpot. The distinguished quantum physicist and Nobel laureate Max Born described him with typical understatement: “Dingle’s objections are just a matter of superficial formulation and confusion.”
Here’s another wacky analogy (much less physics-oriented):
Mark and Mary are about 5 and live with their Mom. They don’t get out much (Covid), but occasionally do hear their Mom referred to by her name, Marge. So naturally, they think of “Mom” as a synonym for Marge. Marge shows them a picture of her sister, Anna, and tells them often, “This is your aunt Anna.” Then the big day comes - their aunt visits, with her own children, Andy and Alice, who are just about the same age as Mark and Mary.
The children get into a big argument though, because Mark and Mary call Anna, “aunt” when as far as Andy and Alice are concerned, Anna is “Mom” and Marge is “aunt”. Fortunately, they eventually figure out that “Mom” and “aunt” are relative (hah!) terms. Marge is not absolutely “Mom” - she’s a mom from Mark and Mary’s frame of reference - and an aunt from Andy and Alice’s frame of reference.
Likewise, the rate of a clock and length of an object are terms with no absolute meaning - they have meaning only relative to a frame of reference.
They do, in fact, run at different speeds, unless you happen to be in a reference frame in which their relative velocity is the same to you.
From the point of view of clock A, clock A always runs at one second per second.
From the point of view of clock B, clock B always runs at one second per second.
From the point of view of clock A, clock B runs slow.
From the point of view of clock B, clock runs slow.
Perform the experiment with spacecraft able to accelerate to huge speeds. Fit the spacecraft with powerful radios. Have astronauts talk to one another whilst travelling a speed. Each will conclude that something is weird in the other spacecraft. It doesn’t get more actual than this.
However Actually is a relative thing. There are multiple actuals.
Since there is no privileged observer there is no such thing as a one true actual truth. A bland statement such as “this is not actually true” can only mean that from the reference frame of the person making that statement it is not observed to be true. It is not meaningful to talk about anything else. There is no overarching base reality that this statement can be made in. (The overarching base reality when considering SR is spacetime. Spacetime, as a basic reality of how it works, does not divide space and time into distinct realities. The reality is simply that clock A and clock B are both travelling through spacetime at one second per second. This never varies. Each reference frame is a line in spacetime. Those lines are the rulers in the 2D examples provided. You can make overarching true statements about the spacetime properties of components, but you can’t make overarching statements that are universally true about a subset of spacetime. You can’t divide time out from space.)
So how might we resolve this? The question continues to be asked in a different form. “Which of the two clocks is the slower?” Now clearly this is an attempt to come up with some other form of contradiction, but tells us how to perform another useful experiment.
Bring the two clocks back together again and directly compare them in the same reference frame.
It ceases to be a question of multiple viewpoints or multiple reference frames. We can agree that no matter what reference frame you might be in, if the two clocks are compared whilst residing in the same reference frame there becomes a clear result. If special relativity still predicts that clock A is slower than clock B, and clock B is slower than clock A, everyone would agree that an impossible contradiction exists. If SR predicts that the two clocks are the same, then we might reasonably suggest that the result is inconclusive at best, and nothing supports the truth of SR over any other theory. So still bad for SR.
But SR doesn’t predict either of these. What it does predict is (depending on the exact manner in which the clocks are brought together) that the two clocks will be running at the same speed when measured side by side (boring) but also that one clock will be behind the other in displayed time (not boring).
That is a solid prediction, one that isn’t an illusion, and moreover one that can be tested right now and delivers a clear and irrefutable answer. This is of course the twin paradox.
Now Einstein was quite clear about this. the effect is real, and he quite clearly did say this. It is in his original paper (the one I linked to above.)
A well known test of the phenomenon.
We measure in reality that time dilation does occur. It isn’t a matter of semantics. The best known example is the lifetime of particles in accelerators. Particles travelling down an accelerator can travel vastly further down the line before decaying than they should be able to. Moreover, the predictions of special relativity match the observed change in lifetime. This is important. Not only do the particles live longer, but SR predicts correctly just by how much. It is a quantitative and testable prediction.
Now you might come up with some other handwaving reason as to why particles live longer than they should when at rest, but your reason must provide testable predictions, so that they can be compared with reality and checked. And those predictions need to match reality.
For those still reading this thread because they enjoy learning new things, and haven’t extensively studied relativity, here’s a fun short video that taught me, only today, that deriving E=mc^2 from SRT is way easier than I thought.
Honestly, I kinda like these threads where there is someone who is rather stubborn, as out comes dozens of explanations and analogies and resources that allow my to understand the ideas being discussed better.
I feel for those who feel as though they are banging their heads against a wall, but if it makes them feel any better, it is not just the obstinate who read these threads.
I totally agree with that. Thank you to everyone in this thread who has taken a stab at explanation. It’s helped my understanding of Special Relativity, even if it hasn’t gotten through to the specific poster those explanations were aimed at.
I don’t disagree, it’s just that 10 years ago a rotating cast of SDMB posters started banging their heads against this exact same wall, and kept on banging for 7 months before everyone was fed up and let tomh4040 “have the last word”.
That was the thread in which Tom demonstrated that he didn’t understand acceleration even in the Newtonian context
I don’t think anybody is under the illusion of actually being able to change the minds of the obstinate. In my own armchair psychology, I think these sorts of opinions actually become part of a person’s sense of identity—identity being who you are and, more importantly, who everybody else isn’t; so anything about you that serves to exclude large swaths of the rest of the population, like being the only one to know what’s wrong with relativity, yields lots of signal there. But then, each argument against that opinion becomes a threat to that identity, an attack on the self—and then, it isn’t a battle fought on the fields of rational discussion anymore. This is also why it typically isn’t stupidity, or ignorance, or a lack of critical thinking skills that’s the culprit—on the contrary, upholding such a contrarian view, even only to the satisfaction of oneself, often takes a great deal of intelligence and skill at compartmentalizing the parts that don’t fit together so that they don’t grate upon one another.
But I still think it’s interesting to figure out the points where people diverge, the constructions they use to shield their opinions from having to revise them and thus, potentially face the consequence of having their carefully constructed identity collapse back into the rubble of the undifferentiated masses. I think it tells us more about our own everyday thought processes than we usually like to admit—because in the end, we’re all doing the same sort of thing, even if not necessarily on the same scale.