# Space is "Entangled", says Leonard Susskind

• A
In the following youtube video, at 1:10:15, is he saying that space itself is "entangled" by means of the virtual particles of the vacuum energy being entangled? It sounds like this is one of the main points he is trying to make in the video. But if this is so, then isn't he saying that space itself is made of virtual particles, particles that transverse distances of space?

I know some here really hate the idea of virtual particles and think of them as just a popular euphemism for the entities of quantum field theory. But I have to wonder how whole fields can be entangled. I thought only particles could be entangled.

MathematicalPhysicist
Gold Member
That what happens when you are doing theoretical physics too long, you stop differentiating between what is virtual and what is real...:-)

ISamson and Demystifier
atyy
One way to think about it is that we get slightly different theories at different energy scales. The energy scale is a continuous quantity, and analogous to a "spatial dimension". It turns out that in specific cases, this is analogy seems to hold in fair detail. For example, the Ryu-Takayanagi formula relates the entropy of entanglement at the boundary of space to an area in space.

https://www.scientificamerican.com/article/tangled-up-in-spacetime/

https://www.quantamagazine.org/tensor-networks-and-entanglement-20150428/

junjunjun233
haushofer
It's not clear to me in these two papers what exactly is entangled and causes spacetime to emerge. Its content (matter and energy) or some yet to be discovered "atoms of space(time)"?

giovannifois
Demystifier
Gold Member
I thought only particles could be entangled.
No, all quantum objects can be entangled. Even the vacuum is entangled, which is the origin of Reeh-Schlieder theorem.

Haelfix
IMO, as the concept of entanglement is observer dependent in an wide sense, and entanglements between widely separated systems correlate "instantaneously" it almost throws in our faces that locality in ordinary 4D-spacetime and locality the more general "information space" so to speak can mix, and thus we have an observer dependent way of "mixing" internal and external degrees of freedom. While hard to grasp it hits the core of the foundational issues still not resolved, right?

Ie. what are external and what are internal degrees of freedom is ultimately observer dependent. We need to accept that, and find a way from there to emergence of the effectively objective spacetime symmetries.

/Fredrik

No, all quantum objects can be entangled. Even the vacuum is entangled, which is the origin of Reeh-Schlieder theorem.
I have a sense of how particles can be entangled. But I still don't understand how a field can be entangled. Is this a state in which every point in the field is entangled with every other point in the field? Or is it that one point in a field may be entangled with maybe one other point in that field? Or is it something else entirely?

Demystifier
Gold Member
But I still don't understand how a field can be entangled. Is this a state in which every point in the field is entangled with every other point in the field?
Yes. But in the case of vacuum, the degree of entanglement decreases with distance.

Or is it that one point in a field may be entangled with maybe one other point in that field?
That would also be entanglement, but I don't know any explicit case of that.

Or is it that one point in a field may be entangled with maybe one other point in that field? Or is it something else entirely?

Note sure if got the question, but what susskind said is that two quantum entangled black holes is like a wormhole, connecting two separated points.

I think it helps a little to think of entanglement is simply a dependence between outcomes of different measurements, for a given observer. So its kind of the measurements that are entangled. I principle this can be a measurement of ANYTHING. And this is a observer dependent constructon. This is why i think its confusing to say that "fields are entangled". If by fields we mean an observer defined quantum field that i may be more sound, but if its some classical or otherwise vague field whose "measurement" is not clear, it prefer to refrain from the terminology.

But how to recover some observer invariant description out of this, seems to me like a very hard task, and stil open question. I consider susskinds speak to have the purpose to make us think of this.

Did he expect us "understand" this?? I suspect not. Getting confused and embrace the confusion is probably a first good step. And i feel very confused.

/Fredrik

Is this a state in which every point in the field is entangled with every other point in the field?
Yes. But in the case of vacuum, the degree of entanglement decreases with distance.
I think I can understand this in terms of a field. For if I know everything about one point in a field, where it is, its velocity, its acceleration, then I think I can say something about the waves of the whole field, right? But that would be the case classically as well. So I'm not sure where the quantum entanglement comes in. It would seem that the uncertainty principle would blur any information I would suppose about the whole field based on what I know at a single point. Is this uncertainty principle why I would lose entanglement with distance?

Demystifier
Gold Member
Is this uncertainty principle why I would lose entanglement with distance?
No. Entanglement between different degrees of freedom is caused by interaction between those degrees of freedom. It diminishes with distance (in the case of vacuum) essentially because the effect of interaction diminishes with distance.

No. Entanglement between different degrees of freedom is caused by interaction between those degrees of freedom. It diminishes with distance (in the case of vacuum) essentially because the effect of interaction diminishes with distance.
What is "interacting"? I though only particles interacted with other particles. How can one point of a field interact with another point of a field, if it is not a particle? Thanks.

phinds
Gold Member
What is "interacting"? I though only particles interacted with other particles. How can one point of a field interact with another point of a field, if it is not a particle? Thanks.
Yes, I am puzzled by this as well. I'm glad you asked.

Demystifier
Gold Member
What is "interacting"? I though only particles interacted with other particles. How can one point of a field interact with another point of a field, if it is not a particle? Thanks.
Yes, I am puzzled by this as well. I'm glad you asked.
Guys, have you ever been reading a book on field theory? Even classical field theory (like classical electrodynamics) counts. According to field theory, it is fields that interact. Particles can be thought of as special quantum states of fields.

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craigi and Urs Schreiber
Urs Schreiber
Gold Member
By the way, some references that discuss in a bit more technical detail the entanglement entropy of fields that is being referred to in these kind of discussions are listed here

haushofer
It's not clear to me in these two papers what exactly is entangled and causes spacetime to emerge. Its content (matter and energy) or some yet to be discovered "atoms of space(time)"?
Got it: It is the entanglement of the field; even in the CFT vacuum one has AdS spacetime in the bulk.

Incidently this thread started in the qm section that imo more belongs in here.

A recent pondering from susskind takes EPR~ER to the next level and suggestd GR ~ QM

I just saw it and havent read it yet but - give or take the details how susskind envisions the implications in the string world - i definitely share the vision that space is emergent from the information picture. In its extreme i think it may even hold a possible solution to the landscspe problem but that is yet another huge step

/Fredrik

Demystifier
Gold Member
A recent pondering from susskind takes EPR~ER to the next level and suggestd GR ~ QM
Am I the only one who has a feeling that Susskind starts to sound like a crackpot? What will be the next step? classical physics = quantum physics? And after that, physics = consciousness?

Am I the only one who has a feeling that Susskind starts to sound like a crackpot? What will be the next step? classical physics = quantum physics? And after that, physics = consciousness?

Well, the paper is clearly not a hard/excplicit paper, i see it more as informal waving argument that suggests a direction of thinking. So i tend to judge it for what i think it is tended?

And given how little progress that has been made om the topic you learn to appreciate even the smallest glimpses.

I agree that qm = gr isnt the best headline, neither do i see any new thinking in his examples. My own approach that i admittedly still has a long wat togo would rather involve a reconstuction of a measurement theory (QM) in a way that spacetime emerges causated by data compression in the observer system.

( Btw, i partially enjoyed your 2013 solipsist HV paper... for an analogous reason. I think is along the right path. I plannned to start a thread on that as well but didkt get time yet.)

So my own perspective is open minded and "understanding" - this is hard stuff and i see only constructivity in whete researchers post soft papers as they can give ideas.

For a mathematician i suspect susskinds paper is all baloney but he isnt a crsckpot in eyes. But he has the ballls to publish a soft paper? Rather a soft ball in the right direction than hard balls in the wrong direction. Unless you are just into mathemqtics. Then the way of doing things rank higher than doinh the right thing.

/Fredrik

smodak
MathematicalPhysicist
Gold Member
Am I the only one who has a feeling that Susskind starts to sound like a crackpot? What will be the next step? classical physics = quantum physics? And after that, physics = consciousness?
Well by the criterion here in physicsforums where moderators judge physical claims without maths as crackpot, then yes he is a crackpot.

But perhaps in hypography forums he won't be judged so harshly... :-D LOL

haushofer
Am I the only one who has a feeling that Susskind starts to sound like a crackpot? What will be the next step? classical physics = quantum physics? And after that, physics = consciousness?
No. I've had the same feeling with some of his students. I can even remember collegues of mine walking away during talks, because it was one hour of handwaving speculation.

Sometimes that can lead to nice observations. But let's not overdo it :P

Demystifier
king vitamin
Gold Member
No. Entanglement between different degrees of freedom is caused by interaction between those degrees of freedom. It diminishes with distance (in the case of vacuum) essentially because the effect of interaction diminishes with distance.

You probably know this, but it's worth clarifying that you do not need interactions for entanglement. Even a free quantum field theory has an entangled vacuum state.

Demystifier
Gold Member
You probably know this, but it's worth clarifying that you do not need interactions for entanglement. Even a free quantum field theory has an entangled vacuum state.
Yes, but I actually wanted to say that what we call "free" field is actually an interacting field. Namely, the term ##(\nabla\phi)^2## in the "free" field Lagrangian density is actually an interaction in the same sense in which harmonic oscillator potential proportional to ##x^2## is an interaction. Indeed, you probably know that "free" field can be thought of as a series of an infinite number of coupled harmonic oscillators.

Could you please explain what you mean by "observer dependent"? Thank you.

Could you please explain what you mean by "observer dependent"? Thank you.

A concept or procedure to produce a number during a measurement is observer dependent if different observers follow the same "prescriptions" from their perspective and later compare their numbers they disagree.

A typical constructing principle for physical law is that laws of physics - to the extent that they are objective - must be seen the same to all observers.

When apparent disagreements appear, objectivity are often restored once we find the transformations that relate observers views and the laws can be formulated in the objective way. That was the case with sr and gr as well. But the observer dependence ive talked about relate observers that cant be generated just by simple diffeomorphisms. There is no known symmetry for this.

/Fredrik