A mass “in” a moving train is heavier but there is no way the embankment frame can falsify or prove it.
I take it no one has heard of falsifiability in relativity – at least in this forum.
This is a serious observation. Are there are no physicists here that can address falsifiability in the embankment frame?
Let me break it down.
The mass in a moving train is heavier in the embankment frame. Can the embankment frame measure this to prove or disprove it?
The older model of Special Relativity had something called relativistic mass which was a tensor; you couldn’t just say it got heavier, you had to say in what direction it got heavier. By the time I was earning my doctorate in experimental particle physics, mass of particles was represented as a scalar in the 4-vecctor describing its motion in the accelerator. So the embankment frame simply has to observe the speed and direction of the train.
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Plus it predicts the trajectories and behaviors of particles travelling at high speeds in accelerators experiments.
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How does the embankment frame see mass increase? I asked if he can measure it. If it were to inflate, seeing would have helped.
PS: Mass of an object changes on motion regardless of what you call it. It’s not Newtonian mass in Relativity, neither in GR nor in SR.
The mass of an elementary particle in special relativity is modeled as an invariant scalar. Every electron ever created has the same mass in every inertial frame. You would not observe it on a train track, obviously, so maybe that was my bad example. (But the sun beating down on it would change its energy, and therefore its mass, m=E/c2.)
A composite object, like a helium molecule, can absorb or release internal energy. These objects would change their trajectory in a magnetic field if they got ‘hotter’ or ‘colder’, thus changing their energy and momentum which would be observable. I’m trying to keep it understandable, but NM, SR, and GR are mathematical models, each with a sphere of applicability. It really is what you call it. You can use the obsolete notation has a mass value for each of three dimensions, but I’d be very surprised if any working physicist would publish a peer-reviewed paper with it. It is like the difference between the old astronomy with epicycles and the Newtonian with gravitation. Both models usefully prediction planetary motion, but Newton’s method is more intuitive and so much less work.
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If a stationary electron is in a moving train,how do you “measure” the heavier electron that the embankment frame predicts? Do you use a weight machine? And if you do what would it measure? It would measure the weight as in the train frame which is fine. But the embankment frame predicts a heavier electron. How do you measure this? I’m saying you can’t. Hence falsifiability is violated in the embankment frame.
Here is what I would do: determine how fast the train is moving first. Assume I weighed the train at rest. From that weight (measured in newtons) I infer the mass (in grams). That is what they called rest mass a hundred years ago. Now we physicists just say mass (m).
The moving train has momentum (p) and (kinetic) energy (E). Using optical devices, I can measure the velocity (v). Using the mass (m) I can then calculate p. Then I can dig out an old textbook and calculate this 3-dimensional vector thing that the ancients called relativistic mass (rm).
Seriously, all measurements involve some agreement on how to do it and what it means. The rm of anything can only be inferred from some agreed upon indirect measurement. Even after you have it, it has little value. The variables that go into designing elementary particle experiments are E, p, and m.
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When I was a university professor, I received self-published books from authors who believed they had falsified Special Relativity (SR). My working definition: “A theory is falsifiable if and only if you can conceive of evidence that would tell against it.” SR is indeed falsifiable, witness the many experimental tests that could have tended to disprove it. That is what makes SR a valid scientific idea; it can be tested. These authors had conceived of possible observations, which, if true, would have told against SR. Unfortunately, those observations had failed to appear over and over when the experiments were performed correctly.
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How do you as a person in the embankment frame “prove” or “disprove” or “measure” that an electron is “heavier” for the embankment person and “less heavy” for the person inside the train?
I can tell that you’re a retired professor.
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Google’s Gemini answered the question better than I did. Here is the unedited AI response, which I elicited today:
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Me: Really a historical question: is the concept of relativistic mass still used by physicists?
AI:
No, the concept of relativistic mass is largely obsolete and is no longer used by the vast majority of professional physicists.
1, 2\] Modern physics has abandoned it in favor of a single, invariant concept: **rest mass** (now simply referred to as **mass**, \\(m\\)). \[2
While the idea that “mass increases with velocity” (\(m_{rel} = \gamma m_0\)) was popularized in early textbooks and pop-science media to help explain why objects cannot accelerate past the speed of light, it introduces severe conceptual problems in advanced physics. [1, 2]
Why Relativistic Mass Was Phased Out
- Directional Ambiguity: In relativity, force and acceleration are not always parallel. If an object is moving close to the speed of light, it requires more force to accelerate it along its direction of motion (“longitudinal mass”) than it does perpendicular to its motion (“transverse mass”). Having a mass that changes depending on which direction you push an object is mathematically clumsy.
- Redundancy with Energy: The concept of relativistic mass is effectively just total energy divided by the speed of light squared (\(m_{rel} = E/c^2\)). [2] Because it mirrors energy exactly, physicists realized it is redundant and unnecessarily redefines a fundamental property of matter. [2]
- Four-Vectors and Spacetime: In Einstein’s mature formulation of spacetime (using four-vectors), mass is defined as an “invariant scalar”—a property that stays completely identical regardless of who is looking at it or how fast they are moving. [2]
What Physicists Use Instead
Today, the relationship between mass, momentum (\(p\)), and energy (\(E\)) is expressed through the standard relativistic energy equation:
\(E^{2}=(pc)^{2}+(mc)^{2}\)
In this modern framework, mass (\(m\)) is a permanent, invariant property of the particle (like its electrical charge). [2] When an object speeds up, its momentum and energy increase, not its mass. [2]
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Yep! The YouTube video I linked covered that all pretty nicely too, walking people through the equations and what they mean.
There is a nice tie-in to your field about how the concepts are integrated in particle detection.
A splendid explanation!
If something becomes inconvenient you cannot walk back a theory but abandon it and adopt a new theory. Stephen Hawking believed in old relativity but you don’t because you move the goal post. (Look up the idiom if you don”t understand it. AI maybe unnecessary for this.)
Even if you move the goal post e=mc^2 says mass increase is real.
Still the embankment frame cannot measure or prove or disprove the mass increase with old relativity or new relativity or with e=m.
Are you going to move the goal posts again? You’re playing football with science.
Watch the video. If you still don’t get it, don’t worry about it.
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Does a moving mass gain weight via e = mc^2?