Time Dilation, Mass-Energy Equivalence: Implications for Time Passage

[PhyCurious]

TL;DR Summary

Given the principle of time dilation and the fact that matter and energy are one and the same, what does that tell us objectively about the passage of time?

I'm an amateur physics enthusiast, and there is a question that's been in the back of my mind for some time that I haven't been able to answer on my own, and haven't gotten a satisfactory answer elsewhere. First, I want to define a couple of terms and make sure my understanding isn't breaking down there before diving into my question on the implication.

First is the concept of time dilation. When an object / person / particle is traveling at an extremely high velocity or is near a massive gravitational object, they experience time dilation relative to an outside observer. E.g., me and my twin brother are on earth, I travel in a rocket at the speed of light for one light-year, and return to Earth at the same velocity, I experienced the trip as having been instant, but my twin brother is now two years older. Is this generally the correct understanding?

Next is the concept of mass-energy equivalence expressed in Einstein's famous equation, that mass is energy. So effectively, any piece of matter (an object with mass), is nothing but energy and simply condensed down so far that it appears solid to us as an observer in spacetime. I struggle to think of energy outside of electricity, so it's difficult for me to conceptualize it outside of that, but even thinking of a single atom, the component parts (protons, neutrons, and electrons, breaking it down even further into quarks and leptons) are moving around a central locus in spacetime (which appears classically as the nucleus. Again, please correct me here if I'm wrong.

If both of these definitions are correct, it seems to me that all of us as observers are really just energy traveling at light speed at an atomic or subatomic level. Does that mean that, as physical objects, we are not experiencing time, but rather just feel we are experiencing time as higher level observers? Or to put it another way, from the relativistic frame of my own experience, I experience time, but there is no objective experience of time? Or perhaps another way, time is a property I experience as an observer (my own subjective experience) but not a fundamental part of the universe?

This seems to be the implication given that the universe has been expanding out from the big bang, and all the mass / energy in the universe emerged from that event and has been traveling at the speed of light since. We experience time as the increase in entropy, but the reality of the universe simply is, and that experience is the result of our current relativistic frame.

When I google "Time is an illusion", I get a lot about Carlo Rovelli, of which I've read a decent amount (although not his book The Order of Time, just a synopsis so far), but I don't really get a definitive answer. I would love any input at all to help me better understand this quandary. Thank you!

 

[PeterDonis]

I travel in a rocket at the speed of light

You can't travel at the speed of light. But you can travel at a speed very close to that of light, relative to your stay-at-home twin brother, and make the time you experience very small compared to his.

any piece of matter (an object with mass), is nothing but energy and simply condensed down so far that it appears solid to us as an observer in spacetime

Not really. Energy is a property of matter, but it's not the same thing as matter.

even thinking of a single atom, the component parts (protons, neutrons, and electrons, breaking it down even further into quarks and leptons) are moving around a central locus in spacetime (which appears classically as the nucleus.

No. Atoms and subatomic particles are quantum objects and can't be usefully viewed in the classical way you are describing here.

If both of these definitions are correct

They aren't, so the rest of your post is based on false premises.

Also, please review the PF rules on personal speculation, which the rest of your post, starting with the above quoted phrase, is.

When I google "Time is an illusion", I get a lot about Carlo Rovelli, of which I've read a decent amount (although not his book The Order of Time, just a synopsis so far), but I don't really get a definitive answer.

That's because there isn't one. Nobody really knows "what time is". Various physicists have various speculations, but that's all they are, speculations. We don't have any way of testing any of them by experiment.

 

[Dale]

Is this generally the correct understanding?

It is not too far off. Typically we would call the twin paradox phenomenon differential aging to distinguish it from time dilation since differential aging is frame invariant but time dilation is frame dependent.

More explicitly and generically time dilation is the ratio between proper time and coordinate time. Since it involves coordinate time it is coordinate dependent. If you are moving fast in my coordinates then your clock is slower than my coordinate time, but since you are not using my coordinates it makes no difference to you.

This isn’t really a correction since as I said above you are not too far off. It is just a bit of next-step information for you.

mass is energy. So effectively, any piece of matter (an object with mass), is nothing but energy and simply condensed down so far that it appears solid to us as an observer in spacetime

Mass is not energy, but mass has energy. The relationship between mass and energy is $$m^2 c^2=E^2/c^2-p^2$$ So if you have something with $m>0$ then you know that $E>0$ also. So mass has energy, but if $p\ne 0$ then they are not proportional.

 

[DEvens]

Reading posts of this nature is a challenge to staying within the rules. You should try to avoid writing long "wordy" explanations. You need to have very precise definitions and explanations. Using analogy to argue is slippery at best and drastically misleading at worst.

Just one example: You present time dilation as a premise. But its' not. It's a result that arises from the axioms of relativity. This approach is very sloppy. It leads you to posit time dilation without bringing along all the other machinery and methods of relativity. Which then has a huge tendency to mislead you into thinking you understand the nature of time dilation, and how it fits into the body of physics that relativity affects. But you don't, since the conclusions you jump to are not even wrong.

This little essay you have written would be very much at home in a post-modernist philosophy department. But it's really very sloppy for physics.

 

[PhyCurious]

That's why I posted here asking the question. I start the question off saying I'm an amateur, I would just like to learn more about physics. I wasn't trying to present time dilation as a premise - it's just a relativistic effect that was relevant to the question I have. Could you please point out what I'm saying that isn't correct?

 

[PeterDonis]

Could you please point out what I'm saying that isn't correct?

I already did that in post #2.

 

[PhyCurious]

Thank you for the clarification on time dilation, that makes a lot of sense.

Mass is not energy, but mass has energy.

Can you expand on this a little bit? Perhaps a more specific question could be, what is energy in this context? Is there a way for a lay-person to understand or conceptualize it? I have always basically thought of it that mass is a store of energy, which I have called "condensed energy" elsewhere, although I think that's not particularly accurate either. Thanks in advance!

 

[PhyCurious]

Not really. Energy is a property of matter, but it's not the same thing as matter.

No. Atoms and subatomic particles are quantum objects and can't be usefully viewed in the classical way you are describing here.

Can you please help me understand these two things?

Energy is a property of matter, as is mass. Mass and energy are equivalent for an object at rest (or in anyone particular frame of reference). So what is matter besides an object that occupies space and has mass and energy as properties? It strikes me as circular so I'm sure I must just be missing something.

I would think that fundamental particles would qualify as matter, but if we can only understand them as quantum objects, then that means they are described by the wave function, which is its own rabbit hole.

 

[PhyCurious]

I already did that in post #2.

Hi Peter, your criticism of how I described time dilation seemed to be targeted at the language I used to describe it rather than a misunderstanding of the concept itself. It seemed to me like I should have just said "near the speed of light" rather than "at the speed of light" to resolve that particular issue.

My understanding is that any object with mass can't be accelerated to the speed of light because it would require too much energy inputs, which is why only massless objects (can we call them that) such as photos travel at the speed of light.

I put a disclaimer in at the beginning that I'm an amateur; I just find this stuff fascinating but because I'm no longer in school, I have no other outlets to ask these types of questions.

 

[PeterDonis]

Energy is a property of matter, as is mass.

Yes, but a property of matter is not a "thing". It's a property. You seem to be thinking of energy and mass as things. They're not. Matter is the thing.

what is matter besides an object that occupies space and has mass and energy as properties?

"Matter" is a shorthand term we use for stuff that is made of fermions--leptons and quarks. We use "radiation" (sometimes the term "energy" is used, but that's not really correct) as a shorthand for stuff that is made of gauge bosons--stuff like light and other EM radiation. These things that matter and radiation are made of--leptons, quarks, gauge bosons--are fundamental objects in the Standard Model of particle physics, which is the best model we currently have of everything except gravity. That's the best answer we currently have.

"Occupies space" is not a bad heuristic, but it should not be taken too far. All of the things I referred to just now--leptons, quarks, and gauge bosons--are quantum objects, which means that they are nothing like anything you are used to thinking about. So you have to be very careful not to visualize them the way you would visualize the ordinary everyday objects you're used to.

It strikes me as circular so I'm sure I must just be missing something.

See above. The definition I gave above is not circular. The Standard Model is not defined in terms of "mass" and "energy". Those are emergent properties that don't appear anywhere in the fundamental equations.

I would think that fundamental particles would qualify as matter, but if we can only understand them as quantum objects, then that means they are described by the wave function, which is its own rabbit hole.

Yes. See above.

It seemed to me like I should have just said "near the speed of light" rather than "at the speed of light" to resolve that particular issue.

Yes, that would do it.

My understanding is that any object with mass can't be accelerated to the speed of light because it would require too much energy inputs, which is why only massless objects (can we call them that) such as photos travel at the speed of light.

Yes, that's basically correct. We do indeed refer to things like photons as "massless"; that's basically shorthand for "always travels at the speed of light".

 

[PhyCurious]

This is helpful, thank you! I'm trying to wrap my head around these subatomic particles, I appreciate the help.

 

[PeterDonis]

You're welcome!

 

[Dale]

Perhaps a more specific question could be, what is energy in this context?

Energy is the conserved quantity associated with time-translation symmetry. The laws of physics are the same today as they were yesterday, so by Noether’s theorem there is an associated conserved quantity which we call energy.

Is there a way for a lay-person to understand or conceptualize it?

If you are familiar with vectors then there is a fairly simple way to conceptualize this.

Ordinary Newtonian mechanics uses vectors with 3 components (x,y,z). In relativity time and space mix together in a way so that it makes sense to use vectors with four components (t,x,y,z). Time and space are closely related in this manner so we join them in one structure called spacetime.

Now, if you continue with this way you find that energy and momentum naturally join together in the same way so you get a four-vector that contains energy in the time component and momentum in the space components (E,px,py,pz).

Now, as with all vectors you can define a magnitude, although it is a slightly different formula than the Pythagorean theorem for four-vectors. When you do so you find that the mass is the magnitude of the energy-momentum vector.

So mass is not the same as energy for the same reason that the magnitude of a vector is not the same as a component or the same reason that the hypotenuse is not the same as the side of a right triangle.

 

[Mister T]

Energy is a property of matter, as is mass.

That depends on your definition of matter. Some people call photons matter, but individual photons have no mass.

Mass and energy are equivalent for an object at rest (or in anyone particular frame of reference).

Mass and rest energy are equivalent.

So what is matter besides an object that occupies space and has mass and energy as properties? It strikes me as circular so I'm sure I must just be missing something.

You are mixing up the phenomena with the phenomenology. Matter is the phenomenon. Assigning properties like mass and energy to matter are a part of the phenomenology.

 

[PhyCurious]

I'm hanging by a thread here but I think this makes sense. I'll keep digging based on the info provided here to try and understand it better. Thanks!